摘要:

OFFICERS AND COUNCIL OF THE FARADAY DIVISION 1993-94 President Prof. J. P. Simons (Oxford) Vice- Presidents who have held office as President Prof. A. D. Buckingham (Cambridge) Prof. R. Parsons (Southampton) Prof. P. Gray (Cambridge) Prof. N. Sheppard (Norwich) Prof. R. H. OttewiII (Bristol) Vice -Presidents Prof. A. Carrington (Southampton) Prof. I. W. M. Smith (Birmingham) Prof. M. A. Chesters (Nottingham) Prof. F. S. Stone (Bath) Prof. R. N. Dixon (Bristol) Prof. Sir John Meurig Thomas (London) Prof. M. J. Pilling (Leeds) Ordinary Members Prof. M. N. R. Ashfold (Bristol) Prof. J. Lyklema (Wageningen) Prof. R. J. Donovan (Edinburgh) Dr. W. Mackrodt (Runcorn) Dr. P. W. Fowler (Exeter) Prof. D. A. Parkes (Chester) Prof. H.M. Frey (Reading) Dr. S. L. Price (London) Prof. A. Hamnett (Newcastle) Dr. S. K. Scott (Leeds) Honorary Secretary Prof. M. J. Pilling (Leeds) Honorary Treasurer Prof. F. S. Stone (Bath) Secretary Mrs. Y. A. Fish Farada y Editorial Board Prof. I. W. M. Smith (Birmingham) Dr. B. E. Hayden (Southampton) (Chairman) Prof. A. R. Hillman (Leicester) Prof. M. N. R. Ashfold (Bristol) Prof. J. Holzwarth (Berlin) Dr. D. C. Clary (Cambridge) Dr. P. J. Sarre (Nottingham) Dr. L. R. Fisher (Bristol) Dr. R. K. Thomas (Oxford) Prof. H. M. Frey (Reading) Scientific Editor, Faraday Publications Dr. P. J. Sarre Editorial Manager, Faraday Dr. R. J. Parker Senior Assistant Editors Mrs. S. Shah Dr. R. A. Whitelock Assistant Editor Mrs. C. J.Seeley The Faraday Division of the Royal Society of Chemistry,previously The Faraday Society, founded in 1903 to promote the study of Sciences lying between Chemistry, Physics and Biology Faraday Discussions (ISSN 0301-7249) is published biannually by the Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4WF, England. 1994 Annual subscription rate EC €138.00, Rest of World €148.00, USA $259.00, including air-speeded delivery, Canada €155 + GST. Change of address and orders with payment in advance to: The Royal Society of Chemistry, Turpin Distribu- tion Services Ltd., Blackhorse Road, Letchworth, Herts SG6 lHN, UK. NB Turpin Distribution Services Ltd., is wholly owned by the Royal Society of Chemistry. Customers should make payments by cheque in sterling payable on a UK clearing bank or in US dollars payable on a US clearing bank. Air freight and mailing in the USA by Publications Expediting Inc., 200 Meacham Avenue, Elmont, NY 1103. Second class postage paid at Jamaica, NY 11431. USA Postmaster: send address changes to Faraday Discussions,Publications Expediting Inc., 200 Meacham Avenue, Elmont, NY 11003. All other despatches outside the UK by Bulk Airmail within Europe, Accelerated Surface Post outside Europe. PRINTED IN THE UK. 0The Royal Society of Chemistry 1994. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means, electronic, mechanical, photographic, recording, or otherwise, without prior permission of the publishers.

ISSN:1359-6640    

DOI:10.1039/FD99396FX001

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96, 17-31 From Quantum-state-specific Dynamics to Reaction Rates : The Dominant Role of Translational Energy in Promoting the Dissociation of D2 on Cu(ll1) under Equilibrium Conditions Charles T. Rettner", Hope A. Michelsent and Daniel J. Auerbach IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120-6099, USA We have calculated the rate of adsorption of isotropic D, gas on a Cu( 11 1) surface, using recently determined differential adsorption probabilities, as a function of translational energy, angle of incidence, and surface temperature for molecules in each vibrational-rotational state. If the D, gas is at the same temperature, T, as the surface, the mean probability of dissociation per collision, (So), is calculated to increase rapidly with temperature.Arrhenius plots of (So) us. 1/T are in good qualitative agreement with measurements for hydrogen dissociation on Cu, but display a distinct curvature over the range 300-1000 K. A detailed analysis of this temperature dependence 'reveals that the increase in (So) with T is due almost entirely to the increase in translational energy of the incident molecules. Increases in the populations of vibrationally or rotationally excited molecules are relatively unimportant, as are the changes in the adsorption with surface temperature. 'The dissociative chemisorption of hydrogen on copper surfaces has been the subject of considerable interest and study for at least 150 years.' Since the work of Taylor in 1931,2 it has been generally agreed that this process is highly activated. Measurements of the rate of dissociation of hydrogen and deuterium on copper films,7-'' f0ilS,9*12--14 and single crystal surfaces' '-' have typically yielded activation energies in the range 0.6 & 0.4 eV.Selected values of the activation energies are given in Table 1 and Fig. 1, beginning with the result of Melville and Rideal who made the first measure- ments yielding an activation energy for adsorption in this ~ystem.~ More recently, the hydrogen/copper system has been the subject of many dynamical studies that have sought to provide an understanding of the dissociation mechanism in terms of specific molecular motion^.''*'^ Molecular beam studies have shown that dissociation can be promoted with both translational and vibrational consistent with calcu- la ti on^.^^-^^ Recent desorption experiments have determined the effects of surface and rotational rn~tion~~'~~ on this process.Since one goal of dynamical measurements is to provide a detailed understanding of reaction rates, it is appropriate to reconsider the kinetic measurements on the hydrogen/ Cu system in terms of these new quantum-state-specific results. The question we address is this: How does thermal excitation lead to an increase in reaction rate? We find that by far the most important factor is the increase in the population of the high-energy tail of the Maxwell-Boltzmann distribution of molecular velocities. This same basic question t Present address : Harvard University, Department of Chemistry, 12 Oxford Street, Cambridge MA 132138, USA.17 18 year 1936 1948 1948 1949 1954 1956 1956 1968 1971 1972 1974 1987 1990 1992 Translation Energy Eflects on Dissociation of D, Table 1 Activation energies measured for hydrogen adsorption on copper authors and method Melville and Ridea13 pressure change Rienacker and Sarry7 p-H, conversion Kwan and Izu8 pressure change Kwan49' pressure change Mikovsky et a!.' isotope exchange Rienacker and Vorm~m'~ p-H, conversion Eley and Rossingtong p-H, conversion Volter et al." p-H, conversion Cadenhead and Wagner' surface oxide reduction and isotope exchange Alexander and Pritchard' ' surface potential change Kiyomiya et aL6 isotope exchange Gabis et uE.'~ permeation rates Campbell et surface oxide reduction Rasmussen et al.' temperature-programmed desorption ~~ ~ E,/ev" 0.85 0.54& 0.02' 0.86 0.86 1.oo 0.48 f0.03 0.42 f0.05 0.45 & 0.01 0.73 +_ 0.09 0.39 0.58 0.37 f0.06 0.53 f0.06 0.61 f0.004 0.62 k0.06 0.50 f0.013 surface T/K powder 345-443 film 623-893 film 573-673 powder 573-673 foil 583-623 foil 623-893 film 373-573 foil 353-453 (111)face 763-853 (100) face film 521-543 film 242-337 powder 3 13-363 foil 790-1020 (110) face 473-723 (100) face 21 8-258 a 1 eV = 23.1 kcal mol-'.'Where a range of values was given, error bars indicate range.25 1.c 20 0.f c I 15 5>, 0.E -E---. IULu" 10 30.4 0.2 5 0.c 0 1930 1950 1970 1990 year Fig. 1 Summary of selected activation energies reported for the dissociation of hydrogen on Cu. See Table 1 for references. C. T. Rettner, H. A. Michelsen and D. J. Auerbach 19 has recently been addressed by Campbell et a1.'6,34who reached a qualitatively similar conclusion. These workers measured the rate of the dissociation of H, and D2 on Cu(ll0) in a 'bulb' experiment using a buffer gas to control which degrees of freedom became equilibrated to the hot surface temperature prior to collision. From the manner in which the dissociation rate increased with buffer-gas pressure, they concluded that translational energy is the most effective in overcoming the activation barrier.2. Methodology 2.1 Arrhenius Expressions We are concerned here with the dissociative chemisorption reaction D,(g) + Cu( 11 1) +2D(ads)/Cu( 11 1) (1) in the limit of low surface coverage. The rate of adsorption is given by where kad,(T) is the rate constant for adsorption, and the square brackets indicate number density. It is generally assumed in kinetic studies that the temperature depen- dence of this parameter can be described by the Arrhenius relationship kads(T) = A exp(-Ea/kE3 (2) where E, is the activation energy for reaction, A is the pre-expcnential factor, and kB is the Boltzmann constant. Dynamical studies, in contrast, are concerned with the determination of adsorption probabilities as a function of the collision conditions.We have recently shown3, how the dissociation of D, on Cu( 111) depends on kinetic energy, Ei, incidence angle, Oi, rota-tional state, J, vibrational state, u, and surface temperature, T,. Using this information, it is possible to calculate the mean adsorption probability per collision with the surface, (So), averaged over all of the distributions relevant to the incidence conditions, Here So refers to the dissociation probability in the low coverage limit. The rate constant for adsorption is then related to (So) by kads( = kcod T)(SO( (3) The collision rate of the gas with the surface at temperature T,kc,,,, is given by k,,,(T)= ill = (kB 7'/2nm)1/2 (4) where rn is the molecular mass. Recent studies of the temperature dependence of hydrogen dissociation on Cu surface^'^*'^ employed a variation on eqn.(2) based on (So) rather than kads. These workers assumed (So( T))= A' exp( -E'&, 7') (5) The activation energy for adsorption based on this equation is slightly different from that based on eqn. (2). In one case the activation energy is obtained from the slope of a plot of ln(kads) us. 1/T; in the other it is obtained from the slope of a plot of ln((S,)) us. 1/T. Clearly both plots cannot be linear. The expressions for kads based on eqn. (2) and (5)cannot both hold since they differ by a factor of The activation energy deduced from the slope of a plot of ln((So)) us.1/T will differ specifically from that from a plot of ln((kads))us. 1/T according to E, = EL + k, T/2 20 Translation Energy Eflects on Dissociation of D, In this paper, we chose to work with eqn. (5), for which EL and A' can have a simpler physical interpretation. In the following, we will drop the primes in referring to these quantities. Note, however, that for experiments with T in the range 300-1000 K, the factor of k, T/2 is relatively insignificant, amounting to only ca. 5% of E, for this system. 2.2 Evaluation of So The mean adsorption probability per collision with the surface can be evaluated from detailed knowledge of the variation of the adsorption probability with the collision con- ditions. Knowing the dependence of So on a given variable, one can calculate the average adsorption probability for molecules with the distribution of that variable appropriate to the gas/surface system.The overall mean adsorption probability is obtained by suitable averaging over all relevant variables. Only recently has sufficiently detailed information become available to perform such an analysis for the D,/Cu( 1 11) system, which is the only system for which such information is available at present. 2.2.1 Form ofS,(E,, Oi, u, J, T,)forD&u( 111) We have recently shown32 that the dissociation probability of D, on Cu(ll1) depends on Ei, Oi, J, u, and T,, in a manner that is well described by the function 0.75 0.60 0.45 > -?. h0 0.30 0.15 \ \ \ \ \ '\ \ 0.00 0 2 4 6 810 1 2 14 J Fig.2 Values of the translational threshold, E,, for the dissociation of D, on Cu(ll1) plotted against rotational quantum number, J, for vibrational states o = (a)0, (b) 1 and (c) 2. The lines represent quadratic fits to the points performed for each vibrational state. The dashed portions of the lines are extrapolated beyond the range of the data. The form of these fitted lines is given in eqn. (8). The data points are from ref. 32. C. T. Rettner, H. A. Michelsen and D.J. Auerbach where the effective translational energy E, = Ei COS" Oi (74 E, is the kinetic energy required for the adsorption probability to reach half its maximum value, and W is a width parameter that controls the steepness of the function.We have found that molecular beam adsorption results are best described by n = 1.8,35 but are also consistent with perfect 'normal energy' scaling, i.e. E, = En= Ei cos2 Oi. It has been found that E, varies considerably with both u and J but that W is essentially independent of J, with values of about 0.16 eV for u = 0 and u = 1, and 0.14 eV for u = 2 for T, = 925 K. Fig. 2 displays the Eq parameters determined in a recent The lines are quadratic fits to the points, with the form E,(u = 0) = 0.607 + 0.0235 J -0.00264 J2 eV (84 E,(u = 1) = 0.396 + 0.0167 J -0.00183 J2 eV (8b) E,(v = 2) = 0.218 + 0.0132 J -0.00171 J2 eV (W Fig. 3 displays the dependence of the dissociation probability on kinetic energy for molecules in different vibrational and rotational states for normal incidence.These curves are based on eqn. (7),plotted for = 925 K. The upper panel is for molecules in A 1.2 > .g 1.0-.-a -$ 0.8 ti -0.6.-+--E 0.4 -0.2 0.0 -1.4 -I l'{'l'l't B translational energy/eV Fig. 3 A, Translational-energy dependence of the dissociation of D,(J = 2) on Cu(11 1) for mol-ecules with v = (a) 2, (b) l and (c) 0. B, Translational-energy dependence of the dissociation of D,(v = 0) on Cu(ll1) for molecules with J = (a)14, (b)12, (c) 0 and (d)4. Translation Energy EJgrects on Dissociation of D2 J = 2 with u = 0, 1, and 2. The lower panel is for molecules in u = 0 with J = 0, 4, 12, and 14. The curves in Fig. 3 have been normalized to unity for clarity of presentation.In fact the level at which the functions saturate at high kinetic energy is given by the parameter AO(v,J) in eqn. (7). For a given u, these parameters are found to be essentially indepen- dent of J, but vary with vibrational state. The values for u = 0, 1, and 2 are found to be in the ratio 0.54: 1.00 :0.77.32 Considering results of molecular-beam adsorption mea- surements, where absolute adsorption probabilities are obtained, we estimate that these numbers are about a factor of two too large. For the purposes of this paper, therefore we assume Ao(O, J) = 0.27 (94 Ao(1, J) = 0.50 (9b) A0(2, J) = 0.38 (94 We have recently shown that changing surface temperature is associated primarily with changes in the width parameters.We believe, therefore, that these values of E, can be considered independent of K. It has been shown3, that the dependence of the width parameters on T, can be described by W(U,J, K) = W(U,J, T, = 925K) + C,(T,-To) (10) where C, is equal to 5.6 x eV K-l, and To = 925 K. 2.2.2 Averaging over Incidence Conditions From the above expressions, we are able to obtain the dependence of the dissociation probability of D, on Cu(ll1) for all quantum states and kinetic energies relevant to a system at temperatures between about 100 and 1000 K. Given this information, it is a simple matter to evaluate adsorption probabilities for D, gas on a Cu(ll1) sample for conditions appropriate to a typical ‘bulb’ experiment.In such experiments, the crystal is exposed to gas that impinges randomly with a Maxwell-Boltzmann kinetic energy dis- tribution and a Boltzmann distribution of internal states. The effective translational, vibrational, and rotational temperatures will generally be the same as the surface tem- perature because of energy transfer from the surface to the gas phase. If the pressure above the surface is too low, however, this may not be the case. In the low-pressure limit, where the mean free path of the molecules is greater than the chamber dimensions, the effective temperature of the incident molecules may be that of the chamber walls or other objects in the chamber such as filaments. With increasing pressure of D, or of additional inert ‘buffer’ gases, translational energy will be the first degree of freedom to come to equilibrium with the surface temperature, followed by rotational and then vibrational energy.’ 6334 This order reflects the fact that translational-energy transfer is more efficient than rotational-energy transfer, which in turn is more efficient than vibrational-energy transfer.We assume that the probability distributions for the trans- lational, vibrational, and rotational degrees of freedom can be characterized by tem- peratures ‘T;, Ti,,,and Tot,respectively. Specifically, the adsorption rate per collision is given for each u-J state by the ratio of the probabilities for adsorption and for collision with a Cu( 11 1) surface placed in isotropic D, gas. Thus r2LaSo(Ei,4, V, J, 7JE exp(-E/k, ?;) dE cos 6i sin Oi doi GO(U, J, T,)>= (11)$’[E exp(-E/kB7J dE cos 6i sin Oi dei C.T.Rettner, H. A. Michelsen and D. J. Auerbach The overall mean adsorption probability per collision (So(TJ) is then (So(v, J, T,)) averaged over u and J, so that The statistical weight of the v-J state, N(u,J), is given by N(u,4 = ~XP(EJkB T,id2J + l)~,~XP(--E,/kB ‘Tot) (13) where E, and E, are the vibrational and rotational energies, respectively, and the term gnis the relative nuclear spin degeneracy, which for D, is equal to 2 for even J and 1 for odd J. For the special case of true ‘normal energy’ scaling (n = 2), which is a good approx- imation for the D,/Cu(lll) system,35 it is possible to obtain an analytical result for {So(Eo, W, T)),the mean adsorption probability per collision for a species with an adsorption function of the form of eqn.(7). Multiplying this adsorption function by the flux-weighted probability distribution function for En, P(E,, T)dE, cc exp(-E,/kB T) dE, (14) integrating over all positive En,and normalizing to the collision probability, we obtain -2 2k~TA,{1 + erf($) + exp(s)e~p[(~)~][1 -erf(& 5>1> (1%) For Eo 24W, this expression approximates to 2 2k~T 2k,T W This equation gives identical results to the full numerical integrations over Oi and Ei using n = 2 for the work presented here. Numerical integration has the advantage of being applicable to an arbitrary dependence on Oi, but requires considerably more com- putation time.In order to use eqn. (15) to evaluate {So), it is still necessary to average over quantum states. 3. Results and Discussion Adsorption probabilities have been calculated for D, on Cu(ll1) by substituting the expressions for the quantum-state-specific dissociation probabilities given in eqn (7)-( 10) into eqn. (11)-(13). Fig. 4 displays the predicted variation of the mean adsorption prob- ability per collision with temperature. Results are plotted as ln((S,)) us. 1/T. They were obtained assuming full equilibration of the gas at a temperature equal to the surface temperature. The approximate linear form of Fig. 4 indicates that the adsorption rate approximately follows Arrhenius behaviour, eqn. (5),so that a linear fit to these results yields an activation energy, E,, of 0.44 eV and a pre-exponential, A, of 6 x lop2.This fit is shown as a dashed line on the figure. Since the plot is not strictly linear, these param- eters depend on the temperature range. Between T = 500 and 1000 K we obtain E, FZ 0.51 eV and A FZ 0.2, whereas between 300 and 400 K we obtain E, = 0.36 eV and A M 4 x lop3.Clearly the values of E, are consistent with the range of values reported previously for the H,/Cu system, as summarized in Fig. 1 and Table 1. (A discussion of the isotope effect is given in Section 3.5.) Calculations performed using the measured E, Translation Energy Efects on Dissociation of D, TIK 1000 600 400 300 I I I I -8 -1 0 -1 2 h A0 !? -14 --1 6 -1 8 -20 \ I I I I I I 1.0 1.5 2.0 2.5 3.0 3.5 103 KIT Fig.4 Plot of ln((So)) us. 1/T for D&u( 111).The (So) values were calculated as described in the text. The dashed line is a linear fit, which gives an effective activation barrier of 0.44 eV and a pre-exponential of ca. 0.06. and W parameters, rather than using eqn. (8) and assuming fixed W for each 0, gave very similar results. 3.1 Activation Energies We now address the question of what determines the slope of such a figure. How should we interpret the phenomenological activation energy? Upon raising the system tem- perature, there are several different important effects that serve to change (So). (1) Raising the system temperature increases the number of molecules with high translational energies.(2) The width parameters, W(u),increase with increasing T, according to eqn. (lo), thereby increasing the probability for dissociation for molecules with En < Eo . (3) The rotational-state distributions also change with increasing temperature, again following eqn. (13). Fig. 5 displays rotational distributions for D,(u = 0) for tem-peratures of 300, 600, and 1000 K. (4) The populations of vibrationally excited species increases exponentially with tem- perature [eqn. (13)]. Fig. 6 displays the populations of D,(v = 1) and (v = 2) as a func- tion of temperature (solid lines) together with the (So) values (dashed line). 3.1.1 Role of Translational Energy While all these factors contribute to the overall temperature dependence to some degree, we have determined that the effect of temperature on the distribution of translational energies is by far the most important.One way to ascertain the relative importance on the (So) of the different factors is to calculate the overall temperature dependence of C. T. Rettner, H. A. Michelsen and D. J. Auerbach 0.4 t 0.4 1 . 0 2 4 6 8 10 J Fig. 5 Equilibrium rotational distribution of D, molecules at temperatures of (a) 1000,(b)600 and (c)300 K. These distributions are normalized to a sum of unity in each case. this probability with each of the separate variations with temperature suppressed in turn. We find that the calculated values of (So) are very sensitive to the translational temperature. For example, the lower dashed line in Fig.7 shows the result of holding ?; at 300 K. Comparing this with the result of the full calculation in which is equal to T at all temperatures (solid line), it is seen that holding ?; at 300 K gives (So) values that are up to a hundred times lower. We find that fixing ?; at yet lower temperatures further reduces (So) compared with the full calculation. 3.1.2 Eflect of the T, Dependence of the Width Parameter In contrast to the dramatic effect of holding constant, we find that suppressing the effect of increasing temperature on the other temperature-dependent terms is relatively weak. Fig. 7 indicates the effect of holding the width parameter, W,at the value that we estimate for T, = 0 K. Using eqn.(lo), we obtain W(T,= 0 K) = 0,109 eV, which leads to a reduction in (So) over the whole range of temperatures compared with the case where W increases with T. Using this width causes the slope for the range T = 500 and 1000 K to increase to 0.55 eV, compared to 0.51 eV for the full calculation. We conclude that changing surface temperature has a significant effect on the form of the ln((So)) us. 1/T curves. The origin of this effect is that the spread in velocities of the surface atoms, which increases with increasing T,, causes a ‘softening’ of the sharp adsorption us. energy function. Surface atoms moving away from the surface increase the effective translational energy of the gas-surface collision, thereby allowing adsorption to occur for translational energies below E, .The low probability of such surface motions is more than offset by the increase in So with translational en erg^.^'.^^ Translation Energy Eflects on Dissociation of D2 TIK 2000 1000 600 400 300 3.1.3 Role of Rotational Energy We have performed calculations with Totset to zero. In this case, all molecules are confined to the J = 0 state. Comparison of the resulting calculated variation of (So) with temperature with the dependence obtained with T,,, = T allows the effect of increasing rotational energy on (So) to be assessed. The result of this investigation is shown in Fig. 7. The solid line is the result of the full calculation presented in Fig. 4, while the upper dashed curve gives the result for Tot= 0 K.It is seen that the effect of ‘freezing’ rotation at 0 K is to increase the (So) values. Further study of this behaviour reveals, however, that the primary effect of increasing Totoccurs for rotational tem- peratures up to 300 K. Further increasing T,,, has little effect on (So). The initial decrease with increasing Totfrom 0 K results from the fact that the E, values (Fig. 3) increase with increasing J at low J, reaching a maximum at about J = 5. The mean value of E, for Tot= 300 K is considerably higher than the value for J = 0. Considering Fig. 3 and 6 together, it may be apparent that raising Totfrom 300 to 1000 K has little effect on the mean E, value. This observation is consistent with the fact that (So) values calculated for Tot= 300 K are almost indistinguishable from the full calculation.Raising the rotational temperature of D, from 300 to 1000 K has essentially no effect on the mean adsorption probability per collision. 3.1.4 Role of Vibrational Energy This same type of analysis has been applied to assess the relative importance of vibra-tional excitation. Specifically, we have calculated (So) values with all molecules con- C. T. Rettner, H. A. Michelsen and D. J. Auerbach TI 1000 600 400 I I I -6 -a 2-10 02 --1 2 -1 4 -1 6 \ \ \ I I I I\ I 0.0 0.5 1.0 1.5 2.0 2.5 103 KIT Fig. 7 Comparison of a number of different calculations of the temperature dependence of (So) for the DJCu(111) system. (b) is the result of the full calculation given in Fig.4.This is to be compared to (a) which was calculated while confining all molecules to J = 0; (c) which was calcu- lated while confining all molecuIes to u = 0; (d)which was calculated using a W parameter appro- priate to 0 K; and (e) which was calculated while fixing the translational energy distribution to that for 300 K. fined to u = 0. The resulting temperature dependence of (So) is given by the dotted line on Fig. 7. For temperatures below ca. 500 K, the result are indistinguishable from the full calculation. Even at the highest temperature, the results are within ca. 30% of the full calculation. In order to gain a better understanding of this result, we have calculated the contribution to (So) of molecules in each vibrational state.The results are given in the upper panel of Fig. 8. It is seen that the contribution from u = 0 molecules domi- nates for all temperatures. This result can be understood as follows. The Eo values for u = 0 molecules are higher than those values for u = 1 and u = 2, but by an amount that is only ca. 60% of their respective vibrational energies. Thus the increase in the mean dissociation probabilities per collision for vibrationally excited species does not make up for their low populations. The lower panel in Fig. 8 shows (So(u)) values calculated for each u. The values for u = 2 are much higher than for u = 1, which are in turn larger than for v = 0. At 500 K, for example, (S0(2)) and (So(l)) are ca. 7 x lo3 and 3 x lo2 times greater than (So(0)), respectively, but the populations of u = 2 and u = 1 mol-ecules are ca.2 x lo7and 5 x lo3 times lower than for u = 0. The conclusion that adsorption occurs predominantly through vibrational-ground- state species under equilibrium conditions is an important one. There has been consider- able debate recently about the relative importance of vibrational and translational energy in promoting dissociation in molecular beam experiments. 9-29 In this case it is now generally accepted that adsorption at low beam energies is dominated by vibra- tionally excited molecules. Indeed, measurements for En up to ca. 0.5 eV can be inter- preted entirely in terms of the adsorption of vibrationally excited species.' The key difference in the beam case is that the spread of translation energies is reduced in the Translation Energy Eflects on Dissociation of D, TIK 1000 600 400 300 I I I I -4- A- 2-6 % -8 v 0 -10C- C -16 -18 -20 -2 -4 AL v O-8 = -10 -1 2 -1 4 0 1 2 3 103 KIT Fig.8 A, Contributions to the overall mean adsorption probability per collision, (So), due to D, molecules in different vibrational states, (a)all vibrational states, (b)u = 0, (c)v = 1 and (d) u = 2. B, Values of the mean adsorption probability per collision for molecules in each vibrational state, (a)v = 2, (b)u = 1 and (c)u = 0. expansion process, but the vibrational distribution remains close to a Boltzmann dis- tribution at the nozzle temperature, Tnoz.Even though the molecules attain translational energies of over (5/2)kB KO=,the very high energy tails are not populated.3.2 Relationship between E,, E, and W The dependence of the form of the ln((S,)) us. 1/T curves on T, discussed above pro- vides an important clue to understanding the magnitude of the activation energy deter- mined for D,/Cu(lll) or a similar system. We have established that the primary contribution to the increase in (So) with increasing temperature is from the population of the high-energy tail of the translational-energy distribution. For a step function form for So(&,),we would then expect to obtain activation energies close to the E, values for the low rotational states of D,(u = 0). Setting the width parameter to 0 eV, we find that this is indeed the case.For this condition, we obtain an activation barrier of 0.65 eV, which is essentially identical to the mean value of E, averaged over population at 700 K. This result is consistent with eqn. (15b), which reduces to eqn. (5) when W = 0 eV, with A = A, and E, = E,. (In obtaining the mean value of E,, including vibrationally C. T. Rettner, H. A. Michelsen and D. J. Auerbach 29 excited states in the averaging lowers the mean by less than 1% compared to only averaging over the J states of u = 0. Moreover, the average E, value is relatively insensi- tive to the rotational temperature, falling by ca. 5 meV as this temperature is lowered from 1000to 300 K.) We conclude that the observed activation barrier is lower than the mean E, values because S,(E,) rises considerably before E, = E, .Considering the temperature range 500-1000 K, the activation barrier is reduced from 0.65 to 0.51 eV by using a width parameter of ca. 0.15 eV rather than 0 eV. Increasing this width to 0.2 eV causes the calculated activation energy to fall to 0.31 eV. The measured activation energy is thus quite sensitive to the magnitude of the width parameter. The specific dependence of the activation energy of the width parameter derives from the particular form of eqn. (7), which expresses the dependence of So in translational energy. Fig. 9 expands on this point. This figure shows plots of ln((S,)) us. 1/T for different values of W.Here we set T,,, = Ti,,= 0 K so that the temperature dependence reflects only changes in the translational-energy distribution of the incident molecules.The width parameter was set to be a fraction of the single E, parameter, that for D,(v = 0, J = 0). The curves are for E,/W = 2, 3, 4, 5, 10, and 100, labelled (a)-(f), respectively. The true results for the D,/Cu(lll) system are very close to curve (d), for W = E,/5, with a mean slope of 0.72 E,. Only when W is small compared with E, does the slope closely approach E,, such as for curve (f),which is for W = E,/100.For this case the slope is 99.8% of Eo . 3.3 Pre-exponential Factors Since plots of ln((S,)) us. 1/T are only approximately linear, the calculated pre- exponential factors vary with the temperature range under consideration, even more so TIK 1000 600 400 300 -6 -8 2 -10 0 v c \\\ <c--1 2 -1 4 -1 6 1.0 1.5 2.0 2.5 3.0 3.5 103KIT Fig.9 Effect of changing the width parameter relative to the E, parameter on calculated plots of ln((S,)) us. 1/T.The curves show results for E,/W = (a)2, (b)3, (c)4, (d) 5, (e) 10 and (f) 100. In all cases E, = 0.607 eV. Only when E, % W are the plots linear. 30 Translation Energy Eflects on Dissociation of D, than the activation energies. Examination of Fig. 7 and 8, however, indicates that the various plots converge as 1/T tends to zero on an intercept of ln((S,)) z -1 1. Again, we can understand this behaviour by examining the results of selected calcu- lations. In particular, we find that setting rot= Kib= 0 K and W = 0 eV, we obtain the expected result of a linear plot with slope of 0.607 eV [=E,(u = 0, J = O)] and intercept 0.27 [=A,(v = 0, J = O)].The ln[A,(u = O)] value therefore approximately gives the ln((S,)) intercept, which for a linear plot is equal to the pre-exponential. The curvature in the plots of ln((S,)) us. 1/T derives largely from the fact that W is not equal to zero (see Fig. 9). 3.4 Effect of Surface Roughness It has been stated that the dissociation of D, on Cu( 11 1) scales quite accurately with En, i.e. with Ei cos2 Oi. This scaling law is a good approximation only for flat surfaces, however. For a microscopically rough surface, results would be expected to scale simply with Ei. In addition to changes in the adsorption rate due to the fact that such samples would most likely be polycrystalline, we believe that the adsorption rates would be increased by the change in scaling law. Changing eqn.(7) from a dependence on En to one on Ei causes an increase in rate of about an order of magnitude for the parameters relevant to the D,/Cu(lll) system. Moreover, the activation energy is reduced by ca. 10% by this change. This effect should be considered in comparing results on single crystals with those on powder samples, for example. 3.5 Differences between D,/Cu(lll) and H,/Cu(lll) From what we have learned about the dependence of (So) on the collision conditions for D,/Cu( 11 l), we can estimate how we expect the H,/Cu(l 11) system to behave.Con- sidering the four temperature-dependent effects listed in Section 3.1, we can dismiss the rotational and vibrational effects at once. Rotational effects have been seen to be weak, and should be very similar for H, and D,. The vibrational excitation energy of H, is even higher than for D,, so there will be very little contribution to (So) from vibra- tionally excited species. Molecular-beam adsorption measurements indicate that the E, values are slightly lower for the H, case,' which would lead to correspondingly lower activation energies. The W parameters may also be smaller, however, particularly for low T,. Lower widths would result in an increase in activation energy. In conclusion, we do not expect the activation energy of the H2/Cu( 11 1) system to be substantially differ- ent from that for D2/Cu( 11 1).4. Summary and Conclusions We have calculated the temperature dependence of the mean probability of adsorption of isotropic D, gas on a Cu( 1 11) surface using quantum-state-specific adsorption prob- abilities. We have concluded that: The primary reason for the rapid increase in the adsorption rate with temperature is that increasing temperature causes an increase in the number of molecules with high translational energy. Plots of ln((S,)) us. 1/T are not necessarily linear, but may be nearly so over a limited range of temperatures. This curvature is expected, based on the smooth form of the dependence of So on En in the region of the threshold energy, E, . Linear plots with E, z E, are only obtained in the limit of E, $-W.The slopes of such plots give activation energies of ca. 0.5 eV, in agreement with measurements on the H,/Cu system. C. T. Rettner, H. A. Michelsen and D. J. Auerbach The effects of vibrational and rotational energy are relatively unimportant. We believe that similar results will hold for the H2/Cu( 111) system. We thank C. T. Campbell and R. N. Zare for useful discussions. We would also like to thank the ONR for partial support of H. A. M. under grant #NOOO14-91-J-1023. References 1 H. A. Michelsen, C. T. Rettner and D. J. Auerbach, in Surface Reactions, ed. R. J. Madix, Springer- Verlag, Berlin, 1993. 2 H. S. Taylor, J. Am. Chem. Soc., 1931,53, 578. 3 H. W. Melville and E.K. Rideal, Proc. R. SOC. A, 1936, 153,77. 4 T. Kwan, J. Res. Inst. Catal., 1949, 1, 95. 5 T. Kwan, Bull. Chem. SOC.Jpn., 1950, 23, 73. 6 M. Kiyomiya, N. Momma and I. Yasumori, Bull. Chem. SOC. Jpn., 1974,47, 1852. 7 G. Rienacker and B. Sarry, 2. Anorg. Chem., 1948,257,41. 8 T. Kwan and T. Izu, Catalyst, 1948, 4, 28. 9 D. D. Eley and D. R. Rossington, in Chemisorption, ed. W. E. Garner, Butterworths, London, 1956, p. 137. 10 D. A. Cadenhead and N. J. Wagner, J. Catal., 1971,21,312. 11 C. S. Alexander and J. Pritchard, J. Chem. Soc., Faraday Trans. I, 1972,68,202. 12 R. J. Mikovsky, M. Boudart and H. S. Taylor, J. Am. Chem. SOC.,1954,76,3814. 13 G. Rienacker and G. Vormum, 2.Anorg. Chem., 1956,283,287. 14 I. E. Gabis, A. A. Kurdyumov and S.N. Mazaev, Poverkhnost, 1987,12,26. 15 J. Volter, 11. Jungnickel and G. Rienacker, Z. Anorg. Chem., 1968,360,300. 16 J. M. Campbell, M. E. Domagala and C. T. Campbell, J. Vac. Sci. Technol. A, 1991,9, 1693. 17 P. B. Rasmussen, P. M. Holmblad, H. Christoffersen, P. A. Taylor and I. Chorkendorff, Surf: Sci., 1992, in the press. 18 H. A. Michelsen and D. J. Auerbach, J. Chem. Phys., 1991,94,7502. 19 B. E. Hayden, in Dynamics of Gas-Surface Interactions, ed. C. T. Rettner and M. N. R. Ashfold, Royal Society of Chemistry, Cambridge, 1991, pp. 137-170. 20 B. E. Hayden and C. L. Lamont, Phys. Rev. Lett., 1989,63, 1823. 21 G. Anger, A. Winkler and K. D. Rendulic, Surf: Sci., 1989, 220, 1. 22 C. T. Rettner, D. J. Auerbach and H. A. Michelsen, Phys. Rev.Lett., 1992,458, 1164. 23 J. Harris, S. Holloway, T. S. Rahman and K. Yang, J. Chem. Phys., 1988,89,4427. 24 J. Harris, Surf: Sci., 1989, 221, 335. 25 M. R. Hand and S. Holloway, J. Chem. Phys., 1989,91,7209. 26 J. K. Nsrskov, J. Chem. Phys., 1989,90,7461. 27 S. Holloway, J. Phys. Condens. Matter, 1991, 3, S43-S54. 28 D. Halstead and S. Holloway, J. Chem. Phys., 1990,93, 2859. 29 S. Kuchenhoff, W. Brenig and Y. Chiba, Surf: Sci., 1991,245,389. 30 C. T. Rettner, H. A. Michelsen, D. J. Auerbach and C. B. Mullins, J. Chem. Phys., 1991,94,7499. 31 H. A. Michelsen, C. T. Rettner and D. J. Auerbach, Surf: Sci., 1992,272,65. 32 H. A. Michelsen, C. T. Rettner, D. J. Auerbach and R. N. Zare, J. Chem. Phys., 1993,98,8294. 33 H. A. Michelsen, C. T. Rettner and D. J. Auerbach, Phys. Rev. Lett., 1992,69, 2678. 34 J. M. Campbell and C. T. Campbell, Surf: Sci., 1991, 259, 1. 35 C. T. Rettner, D. J. Auerbach, and H. A. Michelsen, Phys. Rev. Lett., 1992,68, 1164. 36 M. R. Hand and J. Harris, J. Chem. Phys., 1990,92, 7610. Paper 31032065; Received 3rd June, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600017

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss.,1993,96,33-41 Semi-classical Multi-dimensional Study of the Inelastic and Reactive Interaction of D&, j)with a Non-rigid Cu(ll1) Surface Gert D. Billing Department of Chemistry, H. C. $9rsted Institute, DK 2100 (j9, Copenhagen, Denmark Mario Cacciatore Centro Chimica dei Plasmi, Dipartimento di Chimica, Universita di Bari, 70126 Bari, Italy Classical trajectory and semi-classical wavepacket calculations on the dynamics of deuterium colliding with a Cu(ll1) surface have been per- formed. It is shown that both electron-hole pair and phonon excitation may be important dynamical aspects to include in the treatment. The calcu- lations were carried out using an analytical potential surface fit to ab initio potential data. The lowest barrier height to dissociation on this surface is ca.0.9 eV. This results in very small dissociation probabilities at energies below 1 eV. It is shown that a potential-energy surface with a barrier of ca. 0.5 eV is more reasonable if agreement with recent experimental data is to be obtained. Although the reactive interaction of H, and D, with a Cu surface has been the subject of several experimental and theoretical investigations (for a recent review see ref. 1) there are still some persistent difficulties with several fundamental aspects of the interaction dynamics, namely the position and height of the reaction barriers and the importance of the energy partitioning between the translational and the internal motions of hydrogen impinging on the surface.In the present paper we present semi-classical studies on the inelastic and reactive interaction of state-selected D,(v) molecules colliding with a Cu(111) surface. We also investigate the importance of dynamical features such as phonon-excitation, electron-hole pair excitation, tunnelling and discuss the results in the light of recent experimental data. The semi-classical model for molecule-surface interaction has been discussed in a number of papers.2 We shall here only summarize the important aspects: The dynamics of the incoming molecule is treated by classical mechanics or within a mixed quantum classical description where two (of the six) coordinates are quantized, the bond distance r and the distance from the ‘centre of mass’ of the diatom to the surface 2.In this latter description a wavepacket is propagated in time. The motion of classical and quantum variables is coupled to excitation processes in the metal through an effective potential. The effective potential is obtained- by solving the time-dependent Schrodinger -equation for the phonons and the electrons in the metal. The phonons and electrons are excited by time-dependent forces arising from the molecule-surface interaction. Thus in the case of a classical description of the motion of the deuterium molecule we use the following 33 Dynamics of MoEecule-Surface Interaction effective Hamiltonian : + 2 Cjo(2JAf’) 1 J$(t) dt’qj(t’)sin[wij(t’-t)] i=l j=F+1 where the first term denotes the kinetic energy of the atoms in the gas phase, VH2is a Morse interaction potential, Vo the potential for the molecule-lattice interaction with the lattice atoms in their equilibrium positions.The next term is the effective potential arising from the molecule-phonon interaction. It is dependent upon time and the surface temperature T,. The last term is a similar interaction term due to the interaction between the molecule and the electrons in the metal. These effective potentials are obtained as expectation values of the total interaction potential with the wavefunctions describing phonon as well as electron-hole pair excitation in the solid. The phonons are excited through the molecule-surface interaction potential, which is taken as a sum of atom-atom potentials, using 89 Cu atoms arranged in three layers, i.e.ca. 300 phonon modes are included in the calculations. When the molecule approaches the surface some charge is transferred from the metal to the molecule. This excess charge has also been determined uia ab initio calculation^.^ In ref. 4 an analytical expression has been fitted to these data. The interaction between the molecule and an electron in the metal is then taken as a screened Coulomb interaction between this excess charge and the electron. Thus the time-dependent coupling elements are : where +Xx) is a one-particle electron wavefunction, Z(t) the distance to the surface and k, a screening factor often set equal to ik, where k, is the Fermi wavenumber. The single-particle electronic wavefunctions were obtained using the one-dimensional Bloch potential model.Using this approach we have found that the energy-loss mechanism at chemical energies (i.e. below 5-10 eV) is mainly due to phonon excitation. For light atoms and molecules, such as hydrogen and deuterium, typical energy losses to the surface phonons are 5-10% of the kinetic energy. The electron-hole pair excitation has however an indirect effect upon the phonon excitation because the electonic friction increases slightly the ‘residence’ time at the surface and thereby the phonon interaction is increased. The net energy transfer to the phonons can therefore (especially in the Table 1 Energy transfer Eads(in kJ mol-’) to a Cu(ll1) surface for reflected (non-dissociative) trajectories as a function of incident angle (Bi) and screening parameter (see text) Bi k, = k, k, = 03, only phonon excitation ~~ 0 7.3 6.5 15 7.0 6.2 30 7.6 5.2 4.3 45 4.0 2.7 2.5 The initial kinetic energy of the hydrogen molecule is 150 kJ mol-’.G. D. Billing and M. Cacciatore no-screening case) be significantly enhanced compared with the situation where electron-hole pair interaction is neglected4 (see ref. 4 and Table 1). Semi-classical Calculations In the wavepacket calculations two of the six degrees of freedom for the molecule motion are quantized. The remaining, i.e. the polar angles 8 and q5 defining the orienta- tion of the diatomic molecule and the (X, Y) coordinates specifying the position on the surface are still treated classically.The dissociative coordinate r and the tunnelling coor- dinate 2 are quantized. Thus the mixed Hamiltonian is: ti2 a2 ti2 a2Hmixed= ------+ -1 (Pi + P;)2mi?r2 2M i?Z2 2M where rn and M are the reduced and total masses of the diatomic molecule. The wave- function is assumed to be a product SCF-type wavefunction @(r, z,t)yphonon({Qk))yelectron (4) where @(r,2,t) initially is a product of a vibrational Morse function for the diatom and a Gaussian wavepacket for the 2 translational coordinate. The classical equations of motion for the rotational motion of the molecule and the translational motion along the surface (the X, Y motion) are solved using an effective potential obtained by averaging over the quantum coordinates.Thus we have Kff = VO((Z>,09,x,y, 8, 4) + c vk(l, K)vil)((z),(r), x,y, 0, #) + V$f (5)k where () denotes the expectation value and Vh') the first derivative of the interaction potential with respect to the phonon mode k. The wavepacket is propagated by solving the time-dependent Schrodinger equation : where Rin denote the first two terms of eqn. (3). Further details concerning this approach can be found in ref. 2 and 5. Potential-energy Surface (PES) In molecular dynamics calculations the first step is the search for a sufficiently accurate PES where the dynamics takes place. Unfortunately, there do not generally exist accu- rate a6 initio electronic structure calculations for chemisorbed molecules.Experimental information on the nature of the interaction potentials is also sparse if not controversial. Therefore one often has to rely on approximate model surfaces. The PES assumed in the present study is the one obtained by us as an analytical fit to the ab initio points report- ed by Madhavan and Whitten3 for H, interacting in different H-H bond distances and different geometries with a sufficiently large Cu cluster. The interaction potential is written as: Dynamics of M oEecule-Surface Interaction where r is the H-H distance and R,, the distance from the H atom number n and the surface atom number a. The potential V(R,r) is given by: V(Rr) = Vl(R)fl(r) + V2Wf2(W -f1(r)I + V3@)[1 -f2(r)l (8) where Vl(R) = 375 exp(-2.27R) -16860f(R)exp(-5.07R) (9) V2(R)= Vl(R)[l -1.33 exp g(R)] (10) Vj(R) = 4.82 exp[ -1.52(R -1.85)]{exp[ -1.52(R -l.85)] -2) (1 1) g(R)= 5.86(R2 -3.86R + 3.73); R < 1.93 (12) g(R)= 22.7(R -1.93)2; R > 1.93 (13) f(R)= 1.0; R > 1.5 (14) f(R)= exp[-5(R -1.5)2]; R -= 1.5 (15) fl(r) = 1; r c 0.794 fl(r) = exp[ -19.2(r-0.794)2]; r > 0.794 (16) f2,(r)= 1; r c 1.24 f2(r)= exp[ -1.43(r-1.24)*]; r > 1.24 (17) r/A Fig.1 Potential contour map for hydrogen interacting with a Cu(111) surface shown as a function of the distance from the atom closest to the surface, z, and the internuclear H-H distance, r. The hydrogen molecule approaches the surface parallel to an on-top site. The energies on the contour map are given in .f = 100 kJ mol-'.The contour interval is 0.25 i. G. D. Billing and M. Cacciatore All distances are in A and the energies in units of 100 kJ mol-'. The functional fit4 to the ab initio points3 has a standard deviation of ca, 30% to the ab initio points, i.e. if the ab initio data are reliable it can be considered to be a fairly good representation of the potential interaction. Fig. 1 shows a 2D plot of the total potential: where VD2(r)is a Morse potential. The activation barrier is strongly dependent upon the site and the orientation of the molecule. For an on-top site perpendicular configuration we have a barrier of 90 kJ mol-', whereas in the parallel orientation at the top and bridge sites we have barriers of 170 and 210 kJ mol-', respectively. This strong depen- dence with surface site and orientation suggests a rotational quantum number depen- dence of the sticking coefficient.Also it means that experimental observations cannot be interpreted in terms of a single activation barrier. The surface also shows the appearance of a chemisorption barrier for hydrogen in a slightly stretched-bond configuration (rz 0.75-0.85 A). Results In Table 2 we report the semi-classical dissociation probabilities obtained on the Madhavan-Whitten surface. The deuterium molecule is initially in different vibrational states. On this surface the tunnelling probability is very sensitive to the vibrational content of the molecule. Thus the energy threshold is lowered with the vibrational quantum n~mber,~ i.e.the barrier to dissociation is lowered when the molecule interacts Table 2 Dissociation probability, Pdiss., energy transfer to phonons (Eads), average values of final vibrational (v) and rota- tional (j) actions for the reflected (non-reactive) trajectories as a function of the initial vibrational-rotational state (v, j) and kinetic energy Ei of the deuterium molecule (1, 0) (1, 0) (1, 0) (1, 0) (1, 0) 1.55 1.70 1.80 2.00 2.50 0.00 0.05 0.14 0.33 0.61 0.73 0.83 0.66 0.45 0.90 3.0 3.4 3.7 6.7 7.0 0.139 0.149 0.168 0.200 0.238 100 100 120 120 135 (2, 0) (2, 0) (2, 0) (2, 0) (2, 0) 0.50 1.00 1.30 1.55 2.00 0.00 0.00 0.03 0.18 0.32 2.0 1.9 1.6 1.4 1.3 0.5 2.1 3.7 5.7 8.8 0.035 0.079 0.109 0.135 0.182 25 00 20 00 39 (5, 0) (5, 0) (5, 0) (5, 0) (5, 5) 0.50 1.00 1.55 2.00 1.00 0.00 0.00 0.55 0.92 0.00 5.0 4.3 3.1 4.6 0.5 5.9 9.2 9.4 0.035 0.076 0.145 0.075 40 00 59 116 100 (7, 0) (8, 0) 0.50 0.50 0.00 0.00 7.0 8.0 0.5 0.7 0.035 0.035 24 24 N,is the number of trajectories and the probability for reflection is 1 -Pdiss.Dynamics of Molecule-Su face Interaction Table 3 Isotope effect on sticking probability, Pdjss, final vibrational and rotational excitation of the scat- tered molecules and energy transfer to the surface phonons (Eads) as a function of initial kinetic energy E,; the initial vibrational-rotational state of hydrogen and deuterium (v,j) is (1,O) H2 1.55 0.11 0.70 3.4 0.070 100 1.70 0.25 0.68 3.3 0.079 100 1.80 0.29 0.40 4.4 0.090 120 2.00 0.50 0.37 5.3 0.098 120 2.50 0.81 135 D2 1.55 0.00 0.73 3.0 0.14 100 1.70 0.05 0.83 3.4 0.15 100 1.80 0.14 0.66 3.7 0.17 120 2.00 0.33 0.45 6.7 0.20 120 2.50 0.61 0.90 7.0 0.24 135 Nt indicates the number of trajectories.0.60 1.20 3.90 3.60 3.30 3.00 2.70 2.40 ,’,,,,-2.25 2.40 / 0% 2.10 h( 1.80 1.50 1.20 0.90 0.60 0.30 0.00 0.60 1.20 1.80 2.40 3.00 r/A Fig. 2 As Fig. 1 but for the modified potential surface [I/,(R)= 200 exp(-2.50R) -16860 exp(-5.07R)I.The barrier for sticking is the parallel on-top configuration ca. 0.4-0.5 eV. G. D. Billing and M. Cacciatore 0.10 0.84 1.59 2.33 3.08 0.10 0.84 1.59 2.33 3.08 ---3.91 ----3.g1kl 3.13 3.13 ---OS.Q< 1.56 1 -2.34 h( 2.342.34 ------1.56 ----.-f-0.78 0.78 0.78 --0.00 J I1 I1 I1 I I I I I I I I I I IT 0.00 0.00 0.00 0.10 0.84 0.10 0.84 1.59 2.33 3.08 rlA 0.10 0.84 1.59 2.33 3.08 0.10 0.84 1.59 2.33 3.08 3.91 3.91 3.13 3.13 -5 2.34 2.34 1.56 1.56 0.78 0.78 ._ 0.000.00 0.10 0.84 1.59 2.33 3.08 r/A r/A Fig.3 A wavepacket initialized as a product of a Morse wavefunction in r and a translational wavefunction in 2 approaches the Cu(ll1) surface with incident angle (Oi, 4J = (0, 0), initial vibrational state u = 0 and kinetic energy 0.48 eV. The part of the wavepacket scattered to large r values is absorbed by an imaginary potential placed near the grid edge at rmax= 3.5 A.The wavepacket is initially centred at 2 = 3.5 A with a width A2 = 0.2 A. (a) t = 5, (b) t = 7.5, (c) t = 10 and (d) t = 12.5 z (lz = s). with the surface in a stretched-bond c~nfiguration.~ However if the molecule has an initial kinetic energy which is below the barrier the probability for dissociation is very small and the molecule will be scattered back from the surface with only little vibra- tional quenching and rotational excitation. In this case the average energy loss to the surface phonons Eadsis typically 743% of the impact energy. Although this value is small owing to the large mass difference between the deuterium molecule and the surface atoms, the term can play an important role for the isotopic effect.Thus the trajectory calculations show that, for the molecules in a given translational and internal state, the dissociation probability for deuterium is smaller than that for hydrogen (see TabIe 3). Dynamics of Molecule-Surface Interaction Since the zero-point energy and the vibrational energy spacing of deuterium is smaller than that of hydrogen, one would expect a T-V energy transfer mechanism to be more effective for D, than for H,. Therefore the smaller D, dissociation probability can be assigned to the smaller total energy available and the higher energy loss (for D,) to the dumping of translational and internal energy to the surface phonons. Recent experimen- tal data are not consistent with a barrier for dissociative sticking of 0.9 eV, i.e.the barrier of the Madhavan-Whitten ab initio surface. Thus Rettner et aL6 find a stick- ing probability of ca. 0.05-0.1 at Ei = 0.5 eV increasing to ca. 0.3 at 0.8 eV. Since the tunnelling contribution cannot be estimated using the quasi-classical trajectory ap- proach for the incoming molecule we have estimated the tunnelling probability using both a simple model4 and the wavepacket approach mentioned above. Both calculations show negligible tunnelling at kinetic energies around 0.5 eV. We must therefore question the ab initio data used when obtaining the analytical surface for the molecule-Cu inter- action. However, it is possible by adjusting two parameters in the analytical fit to the Madhavan-Whitten data to obtain a surface with an energy barrier around 0.4-0.5 eV (see Fig. 2).This modified surface has, contrary to the original one, a barrier for adsorp- tion in the entrance and a barrier for dissociation in the exit channel. This surface was also used for propagating the wavepacket on the (2,r) grid with 256 grid points in the 2 coordinate and 64 in the r coordinate. Fig. 3 shows a time-resolved picture of the wave- packet propagation. The initial kinetic energy is 50 kJ mol-’ (ca. 0.5 eV). We notice a considerable increase in the tunnelling probability, measured by the flux of the wave- packet being adsorbed by an imaginary potential placed near the r = rmaxgrid edge. Although these calculations are extremely lengthy we have been able to estimate the probability for dissociative sticking to be around 0.15 to 0.2 in the kinetic energy range 0.48-0.75 eV for collisions with incident angles (&, $i) = (0, 0) and randomly chosen aiming points, These data are certainly in much better agreement with experimental data and our best estimate of the barrier height is therefore around 0.4-0.5 eV.Our calculations on the hydrogen/deuterium Cu interaction dynamics can be summarised as follows: (1) It is necessary to include the full corrugation of the surface. (2) For high accuracy work phonon coupling should also be included in the dynami- cal description. I I I I 0.30 > 0.20 .-c .--P n & 0.10 8 9 10 11 12 TIT Fig. 4 The ‘dissociation’ probability is given by the adsorbed flux over the grid edge as a function of time for the wavepacket from Fig.3. The probability of having a bond distance larger than twice the equilibrium bond distance in D, is also shown. G. D. Billing and M. Cacciatore (3) Electron-hole pair excitation can play an important indirect role in the energy transfer, even at low collision energies. (4) In the tunnelling region it is necessary to treat at least two of the six degrees of freedom for the molecular motion by quantum mechanics. This makes the dynamical calculations extensive but possible. The main problem is, however, that reliable potential-energy surfaces for molecule-surface interactions are essentially unavailable at present. References 1 G. P. Brivio and T. B. Grimley, Surf Sci.Rep., 1993, 17, 1. 2 G. D. Billing, Chem. Phys., 1982,70,223;Comput. Phys. Rep., 1990,12,383. 3 P. Madhavan and J. L. Whitten, J. Chem. Phys., 1982,77, 2673. 4 M. Cacciatore and G. D. Billing, Surf Sci., 1990,232, 35. 5 G. D. Billing, A. Guldberg, N. E. Henriksen and F. Y. Hansen, Chem. Phys., 1990,147, 1. 6 C. T. Rettner, D. J. Auerbach and H. A. Michelsen, Phys. Rev. Lett., 1992,68,1164. Paper 3/02974C; Received 21st May, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600033

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96,43-54 Rotational Effects in the Dissociative Adsorption of H2on Cu(ll1) George R. Darling and Stephen Holloway"? Surface Science Research Centre, University of Liverpool, PO Box 147, Liverpool, UK L69 3BX Experimental studies show that the dissociation probability of H, molecules impinging on a Cu(111) surface is strongly affected by the initial rotational state. Increasing the angular momentum slightly suppresses the dissociation at low J, but strongly enhances it at high J. We show that this is due to two competing effects; one is essentially orientational, and results in the decrease in dissociation probability, while the increased dissociation is due to the transfer of energy from the rotational coordinates into the reaction coordi- nate (R-T transfer).Quantum-mechanical wavepacket calculations are used to illustrate these effects, focussing in particular on the close connection between R-T and vibrational-translational (V-T) coupling. Vibrational excitation is now well known to promote the dissociation of H, on Cu surfaces.' This is due to the occurrence of a strong curvature in the interaction potential as the bonding switches from intramolecular to H-surface bonding before the disso- ciation barrier, and a sharp decrease in the energies of the effective vibrational levels, or, in the jargon of the field, the barrier is late., The vibrations and translations are strongly coupled in this curved interaction region resulting in enhanced dissociation, and also, if there is sufficient curvature before the barrier, in vibrational excitation of the scattered fraction3 such as observed in the H2/Cu( 11 1)system4.' More recent desorption experiments by Rettner et al.have examined the role of initial rotation on the dissociation of D, and H,.6*7 Molecules that recombine and desorb from Cu( 11 1) are state-selectively detected and, by appealing to microscopic re~ersibility,~.'dissociation probabilities are determined as a function of initial rotation- al state, J. Fitting these with a functional form which is roughly sigmoidal, they observe a slight upwards shift of the midpoint of the rise with increasing J until J z 5 or 6, when there is a monotonic decrease with increasing J. This is shown in Fig. 1.In this paper, we shall present theoretical models of these phenomena. Proper simu- lations of the rotational effects in dissociative adsorption require four dimensions; the H, centre of mass-surface distance, 2, the molecular bond length, x, and the two rota- tional degrees of freedom, 8 and @. This major project is underway and completed results will be presented elsewhere. Following from the theoretical studies of vibra- tionally enhanced dissociation, however, we can illustrate the effect of placing energy into the various coordinates by performing lower-dimensional calculations on appropri- ate model potential-energy surfaces (PESs). The results obtained supply us with an intu- itive picture which can then be used to unravel the more complicated results of higher-dimensional simulations.The models used here are two-dimensional, illustrating the competing effects of rotational-energy transfer and orientational hindering on the -f And Department of Chemistry. 43 44 Rotational Eflects in H, Dissociation 0.6 (a) h C 0.- c. n ///,o "." 0.0 0.2 0.4 0.6 0.8 1.o I I Ill I Fig. 1 (a) Experimental J-dependent adsorption probabilities (arbitrarily scaled) for D, in the vibrational ground state. Numbers on the curves indicate the value of J; 0,points of inflection. (b) Plot of the point of inflection, E,, us. J for three initial vibrational states n indicated by the numbers on the curves. From the experimental results of Michelsen et aL7 dissociation reaction.The next two sections contain model calculations for helicopter and cartwheel dynamics. The effect of translational, vibrational and rotational energy on dissociative adsorption is discussed. Finally a summary with some conclusions are pre- sented at the end of the paper. Releasing the Rotational energy For a diatomic molecule, the involvement of vibrational energy in dissociation has a clear origin in the geometry of the PES, the coordinate initially corresponding to vibra- tion evolves into the reaction coordinate as the molecule dissociates. The location of the barrier on the, now familiar, elbow potential (x and Z) then determines whether the vibrational energy is available for promotion of the reaction. The contribution from rotations is, however, less clear. In the free molecule there is some coupling between rotation and vibration, due simply to the centrifugal stretching of the bond.The size of G. R. Darling and S. Holloway Table 1 Internal energy and expectation value of the bond length as a function of rotational state for a free Morse rotor corresponding to H, in the vibrational ground state J e,/eV xla, 0 0.269 1.453 4 0.413 1.474 8 0.768 1.529 12 1.293 1.611 16 1.935 1.720 20 2.645 1.855 this is simple to estimate from the moment of inertia and the bond force constant. For the vibrational ground state the bond length, x, as a function of J, is given in Table 1. In order to place this in context, theoretical estimates hitherto have placed dissociation barriers at extensions of Ax z 1 a, (x > 2.4 a,) and therefore R-V coupling at this level certainly could not be responsible for shifting the dissociation probabilities by the amount shown in experiment.Rather, in this section, we shall show that the vibrational and rotational couplings are intimately connected via the surface, i.e. it is the strong change in the bond length before the activation barrier which is responsible for the release of both vibrational and rotational energy into the reaction coordinate. The model that we employ derives from a close-coupling wavepacket (CCWP) treat-ment of the problem." If we write the wavefunction as an expansion in time-independent basis functions in the rotational coordinate, with time-dependent wavepackets for the molecular centre of mass-surface distance and the molecular bond length i.e. where, for simplicity, we consider only one rotational dimension, then substitution into the Schrodinger equation gives .av a$j(x, 2,t)I -= i 1yj(e)at at where KxJK0)are the kinetic energy operators in the x,Z(0)coordinates. The equation of motion for a particular channel wavepacket can now be obtained by projecting into the functions yit The first term on the right-hand side represents a 'rotationally adiabatic' contribution to the dynamics, while the second term represents the coupling between different rota- tional states. If we set these off-diagonal matrix elements of the potential to zero, then Rotational Eflects in H, Dissociation 4.0 03 3.0 .-+ !! 8 g 2.0 Q) m 't Tm 1.0 r 0.0 I I 0.0 1.o 2.0 ,3.0 H- H separationla, Fig.2 The late-barrier PES used in the calculations. This is based on the results of ab initio calculations by Muller," however, the barrier has been altered to remove the many sharp reson- ances, and a realistic physisorption well has been added. The zero in the x coordinate is the equilibrium bond length of H, in the gas-phase (ca. 1.4 ao). we obtain a new two-dimensional model of the sticking in which the rotational state appears in the J,2/2px2 term, which we can simply add to the potential, (V)yi.This model represents the dissociation of 'helicopter' rotors from a structureless surface and will be the subject of our first study.? Our PES is based on the ab initio calculations of Miiller,ll although we have moved the barrier to make it somewhat less late to avoid the complication of strong vibrational resonances.2*13 In addition, we have included a realistic physisorption well. This changes the shape of the barrier in the entrance channel in such a way as to fix the relative positions of the dissociation thresholds for the different vibrational states. l4 The PES is shown in Fig. 2, and the detailed form is given in the Appendix. Quantum- dynamical simulations have been performed with the split-operator method' ' using a projection grid-cutting technique to extract final, state-resolved probabilities.I6 The eigenfunctions of the initial state are those of the rotating Morse oscillator correspond- ing to the free molecule plus the centrifugal term.They (and the eigenvalues) were deter- mined using the relaxation method of Kosloff and Ta1-E~er.l~ The dynamics on the two-dimensional PES shown in Fig. 2 can be usefully (but qualitatively) described in terms of the vibrationally adiabatic potentials.12 These are the energy eigenvalues of the one-dimensional potentials obtained by taking slices of the PES orthogonal to the reaction path. By analogy, adding in the centrifugal term we obtain a set of J-dependent potentials for each vibrational state. These are shown in Fig. 3. The barrier for both n = 0 and TI = 1 clearly decreases with increasing J. This is due simply to the barrier occurring at an extension in excess of the gas-phase equilibrium bond length, xeq.Thus the barrier decreases relative to the energy of the vibrational ground state of the free molecule, because the contribution there from the centrifugal term is correspondingly smaller than at xeq.t Rotational motions with the angular momentum, J, perpendicular to the surface plane are commonlyreferred to as helicopters, while those with J parallel are cartwheels. G. R. Darling and S. Holloway 0.6 (a)t 0.4 1 0.2 } fl '-u.z \' -0.4 . \ -0.6 0 1 2 3 4 I' -0.4 1 0 1 2 3 4 reaction path/a, Fig. 3 Vibrationally adiabatic potentials for the PES shown in Fig. 2, with the centrifugal term added, thus supplying a J-dependence. The reaction path is taken to be the line of steepest descent from the barrier maximum, with the zero occurring in the physisorption well, which has been set to 0 eV for convenience.(a) Vibrational ground state, (b)first excited state. Numbers on the curves indicate the J values. We can express this in terms of energy exchange. In the gas phase, the molecule has vibrational energy Erot= J2/21 (for a plane rotor, moment of inertia, I, and angular momentum, J). If the angular momentum remains fixed throughout the dissociation (i.e. the potential is independent of 4),then due to the increase in I = p2as the bond length stretches, Erotmust decrease. At least part of the excess energy is then available to assist in the dissociation, further stretching the bond, and further reducing the rotational energy.This analysis is borne out in the full dynamical results for this model, shown in Fig. 4. The oscillations in the dissociation probabilities for energies above the dissociation threshold are due to the onset of vibrational excitation in the refle~tivities,~ and to vibrational resonances remaining at high energies. l2 Note that, as in previous studies, ,the dissociation reaches 50% of the saturation value at an energy, E~ approximately equal to the adiabatic barrier height. Rotational Efects in H, Dissociation 1.o >. 0.8 c..- D a9 0.6 P C .-0 c. $ 0.40 .--0 0.2 0.0 0.2 0.4 0.6 0.8 1.o 1.2 translational energy/eV Fig. 4 Dissociation probabilities for perfect helicopters in the vibrational ground state on a struc-tureless surface as a function of initial translational energy, and for a range of initial rotational states.The PES is that in Fig. 2. Numbers on the curves indicate the J values. We can quantify the influence of rotational energy by plotting E~(J)~~(0)-as a function of the internal energy of the initial state (note that this is less than the sum of vibrational energy and rotational energy of a rigid rotor because of the centrifugal coup-ling in the gas phase) and this is shown in Fig. 5. Included in this figure are the results obtained by assuming vibrational adiabaticity for this PES, that is, the adiabatic barrier heights relative to the J = 0 molecule shown in Fig.3. As noted above, this is a good description for the vibrational ground state in Fig. 4, but it is a poor description for n = 1. Although the approximation appears worse for high J, it is actually at low J b(J)-%(O) 0.0 0.2 0.4 0.6 I I I I 0.0 h1-0.1 W I h3 w -0.2 -0.3 Fig. 5 Midpoint, cH, of the rise in dissociation probability us. internal energy of ro-vibrational state, for two different initial vibrational states, n,and two choices of PES topology: (---) early and (-) late barrier. The late barrier PESs shown in Fig. 2, and the parameters for the other case are given in the appendix. 0,Indicate the results obtained by assuming vibrational adia-baticity for n= 0 on the late barrier PES, i.e.the difference between the adiabatic barrier heights calculated from Fig. 3, while +,show the same for n = 1. G. R. Darling and S. Holloway where the sticking has substantial non-adiabatic effects due to the strong T-V coupling before the barrier (plotted in the figure are the differences between J and J = 0). This becomes less apparent for increasing J because the centrifugal term begins to dominate the potential, causing the barrier to move from late to early, as can be seen in Fig. 3. This movement of the barrier also alters the vibrational efficacy to dissociation. The energetic separation of the dissociation curves for n = 1 and n = 0 decreases from 0.3 eV at J = 0 to 0.19 eV at J = 10, a far greater amount than the decrease in the 0 -,1 vibrational quantum, which is only ca.30 meV. To demonstrate the strong interplay between vibrational and rotational motion and their effects on dissociation, we have also computed the dissociation probabilities for a middle and an early barrier, We have chosen the parameters to give the same barrier height in all cases, although we would not expect an early barrier to be so high.18-19 This allows us to observe effects due only to the barrier position. The middle barrier shows a reduced vibrational effect compared to a late barrier, while the early one shows no vibrational effect,' in agreement with the Polanyi rules2* for gas-phase scattering. It ,can be seen that this is also mirrored in the variation of E~ with J, i.e. it is weaker for the middle barrier (not shown for clarity) and essentially zero for the early barrier (there are slight variations in this case, due primarily to a combination of interpolation errors and the existence of threshold oscillations), as shown in Fig.5. In other words, when the vibrational enhancement of the sticking disappears, so also does the rotational enhance- ment. This clearly illustrates that it is the large extension of the bond before the disso- ciation barrier which is responsible for the observed rotational enhancement. Orientational Hindering The previous section dealt with molecules confined to remain in the broadside orienta- tion with respect to the surface which is believed to be the most favourable geometry for dissociation, In a realsitic beam, however, there will be molecules striking the surface with all orientations, and rotating molecules will sample the potential for a range of these during the collision.This is the origin of the decrease in dissociation with increas- ing J at low J. We can illustrate this by using an approximate PES based on the vibrationally adia- batic potential obtained for the ground-state molecule shown in Fig. 3. From the enlargement in Fig. 6 it can be seen that this is approximately Gaussian along the reaction path for the broadside geometry. For other orientations, there is very little information from which to construct a potential, however, it is clear that it must increase to a very high value for a molecule approaching end-on, i.e.at the energies of interest molecules striking end-on will simply reflect. To treat this, we add another Gaussian, with a much greater magnitude than the first. Thus, our second model involves the coordinates s, the position on the reaction path, and the polar angle, 8, coupled by the potential v(s, 8) = vb exp[ -Pb(s -sb)2] + c(e)K exp[ -Pe(s -sel2] (4) where C(8) is a corrugation function in the polar angle whose form is sinusoidal. The parameters are vb = 0.58 eV, sb = 2.9 a,, fib = 1.3 ai2, = 2.58 eV, s, = 3.7 a,, Pe = 0.9 ao2. In this example, we are simulating the scattering of perfect cartwheel rotors. If the bond length (ie. moment of inertia, which is equivalent to the 'mass' in the 8 coordinate) does not change, then the model represents an early barrier system.2' Fig.7 shows the sticking for a number of J states as a function of translational energy (the initial state is a plane wave in the 8 coordinate and a Gaussian wavepacket in the s coordinate). Clearly, the rotational motion strongly suppresses the sticking. The reason for this has been noted bef~re.~~,~~ As molecules rotate ever faster, they have a greater chance of Rotational Efects in H, Dissociation 5.0 0.5 4.0 0* 0.4 a (D 3.0 5>,1-5.% 0.3 m 4--aa c a 2.0 g0.2 II I I I 1.o 0.1 0.o 0.0 0.0 1.o 2.0 3.0 4.0 reaction path/a, Fig. 6 Vibrationally adiabatic potential for n = 0, J = 0 taken from Fig. 3 and the change in the molecular bond length along the reaction path 0.4 0.6 0.8 1.o 1.2 1.4 translational energy/eV Fig.7 Dissociation probability of cartwheel rotors on an early barrier PES with strong corruga- tion in the rotational coordinate as a function of initial translational energy and for various initial rotational states (J-values indicated on the curves.) Only one rotational dimension is included, so the states correspond to plane rotors. The step-like behaviour in the lower J states is caused by the onset of strong reflectivity into higher rotational states. G. R. Darling and S. Holloway 0.8 0.6 0.2 0.0 translational energy/eV Fig. 8 Dissociation probability as a function of initial translational energy, for several initial J states (values indicated on curves), for a model simulating planar cartwheels incident on a PES with a late barrier. The change in bond length has been approximated by varying the moment of inertia using the results of Fig.7. The result for J = 4 has been omitted for clarity, since it overlays those for J = 0 and J = 2. rotating out of the broadside configuration before reaching the transition state to disso- ciation, and they then scatter back from the higher barriers at less-favourable orienta- tions. In other words, they are moving so quickly in the rotational coordinate that they fly by the opening which leads to dissociation at 8 = 42. Following the quantum study of and the classical one of Beauregard and Mayne,2s we can extend this model to include a late barrier potential by making the moment of inertia vary along the reaction path.? Fig.6 shows the molecular bond length as a function of s for the PES in Fig. 2. To a good approximation, this can be represented by a linear function with a gradient of 2 switching on at s = 2.2 a, (the gradient is 2 rather than 1 because the reaction path must properly be calculated on a mass-scaled potential, i.e. with the x coordinate shrunk by a factor of 212). With this modification, it is no longer possible to use the split-operator method for propagation, because the kinetic-energy operator in the &coordinate depends on s, and so we must instead use the Chebychev method.26 With an initial wavepacket incident from the left in Fig. 6 and C(Q)= $(l + cos 20), we obtain the results shown in Fig.8. Clearly, the change in moment of inertia has reduced the orientational hindering at low J, and completely overwhelmed it at high J. This is exactly the trend required for agreement with experiment, cJ: Fig. 1. However, it is instructive to consider the extent to which the parameters for this PES must be changed for the agreement with experiment to be lost. If we make the surface more open, i.0. allow molecules with less favourable bond orientations to stick, by changing C(Q)to C(0) = $(1 + cos 28)3, then we find that orientational hindering is no longer in evidence. In other words, the corrugation must also be felt by molecules only slightly out of the broadside configuration for the suppression of sticking at low J to occur.t A similar model is also being investigated by Thomas Brunner. Rotational Eflects in H, Dissociation Alternatively, we can have C(0) = $(l + cos 20), but alter the strength of the corrugation by changing s, to 3.2 a,. In this case, we find that it is the R-T coupling which is lost, although the surface may now be too strongly corrugated to produce the smooth physi- sorption well seen in e~periment.’~ Conclusions We have demonstrated that coupling of the rotational coordinate with the reaction coordinate is intimately bound with the observation of vibration-translation coupling. Both arise from the large change in the molecular bond length induced by the PES. This causes an increase in the moment of inertia of the molecule with a corresponding decrease in the rotational eigenvalues, and, hence, the R-T coupling.For an early barrier, there is no bond extension at the transition state, and so also no vibrational and no rotational enhancement of dissociation. Rapid rotation can also inhibit sticking, however, owing to the strong anisotropy in the potential as a function of the orientational coordinates. This effect would be expected to occur for all early barrier systems. For a late barrier, we have demonstrated that it can be overcome at high J by the R-T coupling, giving rise to the initial slight drop followed by a strong rise in the dissociation probability as a function of J observed in the experiment. Slight variations to the two-dimensional PES employed indicate that observation of both could be a sensitive indicator to the precise details in and near the interaction region of the potential.We are grateful to Charlie Rettner and Dan Auerbach for helpful discussions on this subject. G.R.D. would like to thank IBM Almaden Research Laboratory for their hospi- tality during the course of this work. Appendix We have constructed our PES by defining equipotentials for a basic ‘elbow’, onto which we can add barriers and physisorption wells. The equipotentials are based on the function For each (x, 2)we evaluate f(x,z)= i/d[(i+ 1/x4)(1+ 1/z4)-11 the bond length at 2 = on curve y. This is clearly singular for x, 2 = 0, so we must offset the curves by some amount, p. To change the angle between the exit and entrance channels, this is further twisted with a step function z+2, = z-Z,,,s(x -rn, , wl) (A3) where s(a, b) = i(1 + tanh ab) Using these elements , we then obtain an equivalent bond length, x,(x, 2)=f(x’, 2’)+f[x’ -f(x’, Z‘),2’ -f(x’, Z’)]-p (A5) where x’ = x + p, 2’ = 2, + p, and the second term on the right-hand side forces the equipotentials to be almost identical in shape rather than softening at large x and 2.G. R. Darling and S. Holloway With x, we calculate the bare elbow potential K(x, Z) = D(1 + exp[ -ax,(x, 2)]}2 The dissociation barrier and physisorption well are treated as separate components, with another step function to switch between them. The former is a Gaussian in both x and 2, &(x, 2)= VO exp(-Px(x -xb)2 -pZ(zf -zb)2)s(x -2, -m2 7 w2) (A7) (note that 2, replaces 2 on the right-hand side).The latter is composed of an exponen- tial repulsion term and a Van der Waals attraction wheref, is the usual cut-off function defined by fc(x)= 1 -[2x(1 + x) + l]exp( -2x) (A101 which are combined to give where 2, is again used in place of 2 on the right-hand side. The second step is included to force the replusion to die off at small 2 where it is replaced by the repulsive part of V, going around the elbow. The parameters have been chosen to give a well of depth ca. 30 meV outside of the reaction zone, in agreement with experimental results.28 The full potential is V(x,z, = I/e(x, z,+ Vb(x, z,+ Khys(X, 2) (A12) with the parameter values for the late barrier shown in Table Al.Although this form may seem impossibly cumbersome, the step functions actually make it possible to manipulate one region of the PES with relatively little disturbance to other regions. Thus to change to a middle barrier, we make the following parameter adjustments; Zoff= 0.18 a,, Vo = 0.72 eV, Px = 0.07 ai2, xb = 0.5 a,, P, = 1.0 ai2, yb = 0.5 a,, m2 = -0.7 a,, and to get an early barrier; Zoff= 0.18 a,, V, = 0.77 eV, xb = 0.01 a,,Liz = 1.0 ai2,yb = 1.2 a,, m2 = 1.6 a,. Table 1A The parameters for the model PES shown in Fig. 2. Ener- gies (D, V,, V, and Cvw)are given in eV, while units for other param- eters are given in the text elbow potential dissociation barrier physisorption potential D = 4.76 Vo = 0.7 Vl = 0.85 O! = 1.028 p, = 0.05 p, = 1.8 p = 2.0 Xb = 1.0 Z, = 0.25 Zoff= 0.3 p, = 0.0 C,, = 5.306 m, = 1.3 y, = 0.0 k, = 0.5 w1 = 1.5 m2 = 0.0 z,,= -1.9 w2 = 1.5 m3 = -0.1 w3 = 2.0 Rotational Eflects in H, Dissociation References 1 B.E. Hayden, in Dynamics of Gas-Surface Interactions, ed. C. T. Rettner and M. N. R. Ashfold, Royal Society of Chemistry, London, 1991, p. 137. 2 S. Holloway, in Dynamics of Gas-Surface Interactions, ed. C. T. Rettner and M. N. R. Ashfold, Royal Society of Chemistry, London, 1991, p. 88. 3 G. R. Darling and S. Holloway, J. Chem. Phys., 1992,97, 734. 4 A. Hodgson, J. Moryl, P. Traversaro and H. Zhao, Nature (London), 1992,356,501. 5 C. T. Rettner, D. J. Auerbach and H. Michelsen, Phys.Rev. Lett., 1992,68,2547. 6 H. A. Michelsen, C. T. Rettner and D. J. Auerbach, Phys. Rev. Lett., 1992,69, 2678. 7 H. A. Michelsen, C. T. Rettner, D. J. Auerbach and R. N. Zare, J. Chem. Phys., 1993,98,8294. 8 T. B. Grimley and S. Holloway, Chem. Phys. Lett., 1989,161, 163. 9 H. A. Michelsen and D. J. Auerbach, J. Chem. Phys., 1991,94,7502. 10 R. C. Mowrey and D. J. Kouri, J. Chem. Phys., 1986,84,6466. 11 J. E. Muller, Surf: Sci., 1992, 272,45. 12 D. Halstead and S. Holloway, J. Chem. Phys., 1990, 93, 2859. 13 S. Holloway and G. R. Darling, Comments At. Mol. Phys., 1992,27, 335. 14 G. R. Darling and S. Holloway, Surf: Sci., in the press. 15 M. D. Feit, J. J. A. Fleck and A. Steiger, J. Comput. Phys., 1982,47,412. 16 G. A. Gates, G. R. Darling and S.Holloway, unpublished work. 17 R. Kosloff and H. Tal-Ezer, Chem. Phys. Lett., 1986,127,223. 18 J. Harris, Appl. Phys. A, 1988,47,63. 19 G. R. Darling and S. Holloway, J. Chem. Phys., 1992,97, 5182. 20 J. C. Polanyi, Science, 1987, 236, 680. 21 S. Holloway and X. Y. Chang, Faraday Discuss. Chem. Soc., 1991,91,425. 22 S. Holloway, J. Phys.: Condens. Matter, 1991, 3, S43. 23 A. Cruz and B. Jackson, J. Chem. Phys., 1991,94, 5715. 24 B. Jackson, J. Phys. Chem., 1989,93,7699. 25 J. N. Beauregard and H. R. Mayne, Chem. Phys. Lett., 1993,205,515. 26 H. Tal-Ezer and R. Kosloff, J. Chem. Phys., 1984,81,3967. 27 S. Andersson, L. Wilzen, M. Persson and J. Harris, Phys. Rev. B, 1989,40, 8146. 28 S. Andersson, L. Wilzen and M. Persson, Phys. Rev. B, 1988,38,2967. Paper 3/03507G; Received 16th June, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600043

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96, 55-65 State-selective Studies of the Associative Desorption of Hydrogen from Pd(100) and Cu(100) L. Schroter, Chr. Trame, J. Gauer and H. Zacharias Fachbereich Physik, Universitat Essen, 0-4300 Essen I, Germany R. David IG V,Forschungszentrum Jiilich, D-5170Jiilich, Germany W. Brenig Physik Department, T U Miinchen, 0-8046 Garching, Germany Vibrational-state populations and velocity distributions of H, , HD, and D, desorbing from Pd( 100) are measured with rotational state selectivity over a wide temperature range from T, = 325 to 825 K. At all surface temperatures the vibrational populations, increasing exponentially with T,, are found to be significantly higher than those expected for thermally equilibrated mol- ecules. The slopes of Boltzmann plots are considerably lower than expected for a thermal excitation mechanism of the vibrational states at the corre- sponding gas-phase energies.They also show a non-trivial isotope effect. The velocity distributions from clean Pd(100) are found to be Maxwell- Boltzmann-like. The translational energies of H, molecules are accommo- dated at the surface temperatures, whereas those of D, are higher than kT, by ca. 10-30 meV. Both the vibrational excitation and the isotope effect in translation can be understood with a quantum-mechanical model calcu- lation on a two-dimensional potential-energy surface. The vibrational-state selective angular distributions for desorption from Cu( 100) display a differ- ent behaviour for ground and excited states.The distributions for the vibra- tionally excited states are broader than that of ground-state molecules. They also show an isotope effect. The reaction dynamics of hydrogen on various metal surfaces has been the subject of many theoretical and experimental investigations. Detailed information has been gath- ered, particularly for two systems, hydrogen on copper and on palladium surfaces.'.' While copper shows a high thermodynamic barrier to dissociative adsorption and associative de~orption,~.~ Thethe adsorption on palladium is mainly n~n-activated.~.~ internal state-specific measurements of the flux of associatively desorbing molecules from Cu(ll1) and Cu(ll0) by Kubiak et aL7 revealed, for the vibrational degree of freedom, a 50-100 times higher population than expected thermally.A corresponding study for desorption from poly-Pd also showed an overpopulation of the vibration by an order of magnitude.' A basic difference between the two systems arises from the electronic structure of the metals. In particular, for the s metal, theoretical calculations show for dissociative adsorption of hydrogen a high barrier late in the adsorption channel.' Classical trajectory and quantum-mechanical calculations on two-dimensional reaction potentials confirmed the enhanced vibrational population observed in desorp- tion, and hence predicted a greatly enhanced sticking for vibrationally excited hydrogen 55 Associative Desorption of Hydrogen on copper.’ 0-14 In subsequent adsorption studies several groups investigated the influ- ence of the incident kinetic energy and angle and the contribution of vibrational excita- tion to the sticking probability in copper.15-18 Vibrational energy of molecules incident on the copper surface strongly enhances the dissociative sticking probability. The coup- ling of translational and vibrational degrees of freedom deduced from the adsorption measurements has been confirmed in desorption. The translational energy decreases by ca. 0.2 eV for each increase of the vibrational quantum in the desorbing D,. The rotational-state resolved kinetic energy varies also for each vibration in a non-monotonic fashion, becoming significant for J” > 8.” This shows that the rotation of a molecule might also enhance the sticking in dissociative hydrogen adsorption.The adsorption of hydrogen on clean palladium shows mainly non-activated behav- iour without a significant thermodynamic barrier.6 Earlier state-integral measurements of the desorption flux from palladium’ yielded Maxwellian velocity distributions with TkinT,, in accord with the recent adsorption data. In this paper we report results of x internal state-specific measurements for the vibrational and translational degrees of freedom for the associative desorption of hydrogen and its isotopes from Pd( 100). The angular distribution of the flux of molecules being adsorbed or desorbed is commonly related to the dynamics of the interaction between the molecule and the surface.The existence of energetic barriers on the pathway from the adsorption state to the gas phase can be related to an angular distribution peaked in the direction of the surface normal.20 For the recombination reaction of hydrogen atoms on metal surfaces angular distributions strongly peaked in the normal direction have been observed for copper surfaces in de~orption~.~~ as well as in adsorption.6 For clean palladium surfaces, on the other hand, mainly cosine distributions were obtainede6 Berger and Rendulic recently found that the angular distribution of the sticking coefficient of H, on Cu(ll0) broadens with increasing temperature of the nozzle of the molecular beam source.22 This observation is interpreted to be due to the contribution of vibrationally excited molecules to the sticking.The number of vibrationally excited molecules increases with the temperature of the beam nozzle. Theoretical calculations of Kuchenhoff and Bre~~ig,~also predict, at a given kinetic energy, a considerably broader angular distribu- tion for the sticking of (u” = 1) molecules compared to ground-state molecules. In this paper we report first results on vibrational-state selectively measured angular distribu- tions for H, and D, desorption from Cu(100). Experimental A detailed description of the experimental method has been given previou~ly.~~ Briefly, the experiments are carried out in an ultra-high-vacuum (UHV) chamber with a base pressure of 3 x lo-’’ mbar (see Fig. 1). Order and cleanliness of the surface are deter- mined by low-energy electron diffraction (LEED) and Auger spectroscopy.Adsorbates are removed when necessary by soft Ar+ ion sputtering at low energy and current density. After sputtering the surface is annealed before an experimental run. Hydrogen atoms are supplied to the surface of the Pd(100) and Cu(100) crystals by permeation through the bulk of the radiatively heated sample. The thicknesses of the samples are 1 mm and 0.5 mm for Pd(100) and Cu(lOO), respectively. The experiments are performed at constant temperatures which range from 325 to 825 K for palladium, and at 885 K for copper. During desorption from palladium the pressure in the chamber is kept in the (6-30) x lo-* mbar range by adjusting the stagnation pressure at each temperature accordingly. Because of the much lower permeation rate of hydrogen through copper the corresponding chamber pressure rises only up to 3 x mbar at 500 mbar stag- nation pressure.This average hydrogen pressure in the chamber gives rise to a back- ground signal which has to be taken into account. L. Schriiter et al. 57 SHG Nd YAG laser 3I vuv detect ion generation nm 106-108 np Cu(100) Fig. 1 Schematic diagram of the experimental set-up For state-selective detection of desorbing hydrogen molecules resonantly enhanced two-photon ionization [(l + 1’) REMPI] is empl~yed.~’ The first excitation step from the electronic ground state XICS+(u”,J”) to the intermediate B’C:(u’, J’) provides the vibrational- and rotational-state selectivity.This Lyman band transition is excited by vacuum ultraviolet (VUV) laser radiation tunable in the 106-108 nm spectral range. The VUV radiation is generated by frequency tripling, in xenon gas, the frequency doubled output of a tunable dye laser. In the interaction region with the desorption flux about 5 x lo9 photons per pulse are available with a spectral bandwidth of 0.8 cm-’. Ioniza- tion of the electronically excited molecules is carried out with a second UV laser beam, either at a wavelength around 320 nm, the fundamental of the VUV radiation, or at 266 nm, the fourth harmonic of the primary Nd :YAG pumping laser. In either case a laser pulse energy of ca. 5 mJ in a 5 ns pulse is provided for the ionization step.The laser beams interact with the desorption flux at a distance of 20 mm in front of and in a plane parallel to the surface. For the measurement of the state-selected angular distributions the laser beams and the detector are located in a differentially pumped section of the apparatus (see Fig. 1). At a distance of 9 mm in front of the crystal a 2 mm diameter hole in the separating wall selects a 5O-wide section of the desorption flux. Angular distribu- tions are obtained by rotating the sample around a vertical axis. In this part of the chamber the base pressure is ca. 6 x lo-’’ mbar, which rises to ca. 5 x lo-’’ mbar during desorption. The generated hydrogen photoions are detected by a time-of-flight spectrometer using two-stage microchannel plate (MCP) amplification and a 50 R impedance-matched anode.The output of the MCP detector is processed by a counting electronic or a digital oscilloscope (LeCroy 9400) and transferred to a microcomputer (DEC, LSI 11/23). Results Vibrational Population In the desorption flux of hydrogen isotopes from the palladium surface single rovibra- tional states can be clearly resolved by (1 + 1’) REMPI spectroscopy.26 The relative heights of lines originating in X ‘c: (0’’= 1) being proportional to the population in Associative Desorption of Hydrogen (v” = l), to those from X ‘Xl (0’’= 0), representing the ground-state population, increases nearly exponentially with the surface temperature, T,. A Boltzmann plot of the logarithm of these intensity ratios for the three hydrogen isotopes H,, HD, and D, is shown in Fig.2 as a function of T,’. In this plot a nearly linear dependence on TSp1 over more than two decades of the population is observed. The behaviour of the vibrational degree of freedom during desorption can be described by the motion of the two atoms involved on a two-dimensional potential- energy surface (PES).’-I4 One coordinate of this PES is the reaction path, s, the other being the vibrational motion orthogonal to s. The dynamics of the recombination is determined by the curvature K(S) of the PES along the reaction coordinate s, and the diagonal potential V(s) along the reaction path. The vibrational frequency o(s) is assumed to vary along the reaction path.For the model calculation (see also ref. 13) we assume a smooth variation of the diagonal potential V(S)= E,/cosh2(h) (1) The maximum of this symmetrical potential at s = 0 is the nominal barrier height E,. II is a scaling parameter which describes the halfwidth of the curvature K(S) ~(s)= l/ro(s) = {ro cosh2[L(s -so)])-’ (2) where ro denotes the radius of curvature of the PES and so the position of the maximum curvature. The variation of the vibrational frequency along the reaction path is taken as W(S) = coo -A/cosh2(h) (3) where A is a parameter. Although different for all three isotopes, this parameter A shows the same relationship between isotopes as their vibrational frequencies in the gas phase = [IJ(pD2/PH2)lAD2 (4) where p denotes the reduced mass of the molecule: A,, = J2 AD, and similarly AH, = J(l.5) AD,Note that the parameters K and V of the PES are independent of the mass of the isotopes, while the vibrational frequency cu depends on the mass.Adsorbed deuterium atoms with a thermal distribution of energies at T,, i.e. a Maxwellian kinetic energy 1.0 2.0 3.0 1.0 2.0 3.0 1.0 2.0 3.0 103KIT, Fig. 2 Boltzmann plot of the relative vibrational excitation in hydrogen desorption from Pd(100) us. Ts-for (a)H, ,(b) HD and (c) D, L. Schruter et al. distribution and a Boltzmann population of the D-Pd bond, are allowed to recombine on this PES. The results of this model calculation are compared with the experimental data for D,. The parameters which fit the data best are shown in Table 1, yielding a height of the activation barrier of E, = 0.2 eV, and, for deuterium, A,, = 0.14 eV.The corresponding theoretical results for the other isotopes H, and HD are then calculated on the same PES, just changing the isotope specific values for the vibrational energy, (~(s),and the parameter A according to eqn. (4). A comparison of the vibrational popu- lation obtained from this model calculation, shown as lines in Fig. 2, with the experi- mental data reveals a very good agreement. Table 1 Parameters of the PES for the reaction of deuterium on Pd(100) ro/A A,,/eV EJeV E,,,/eV 2.75 0.5 0.25 0.14 0.2 0.13 The difference in zero-point energies of two adsorbed atoms and a desorbing mol- ecule leads to the interesting fact that part of this zero-point energy can be made avail- able for overcoming the barrier against recombination.Since these zero-point energies differ considerably for the different hydrogen isotopes, the effective barrier heights, Eeff, show also a significant variation. This effective barrier height can be calculated from Eeff= E, -$h[w(s= CO) -U(S = O)] (5) Eqn. (5) yields Eeff= 0.13 eV for D2,Eeff= 0.11 eV for HD, and Eeff= 0.10 eV for H, , The effective height of the barrier is now in the range of the thermal energy of the surface. The model calculation also predicts the vibrational population at a given T,. At T, = 677 K a value of 1.3% population in U” = 1 is obtained for D,, which can be compared with the experimental value2 determined by VUV laser-induced fluorescence to be (1.5 & 0.3)%.Velocity Distributions State-selective velocity distributions can be determined with REMPI by measuring the time-of-flight (TOF) from the ionization volume to a fast ion detector.28 Because of the short ionizing laser pulse duration of only 5 ns short flight distances of only a few cm are sufficient for an adequate velocity resolution for thermal molecules. In general, with pulsed REMPI, the measured TOF spectra, nl(t),are density-like, because in a short time interval a stationary volume-distributed part of the flux is probed.’ The distribution n,(t) has thus to be transformed from the density-time domain into the flux-velocity domain, Fflux(v). This can be done by the transformation where I dt/du I represents the Jacobi determinant.The average kinetic energy of a desorb- ing particle with mass rn is then obtained from The summation is carried out over all velocities ui. For Maxwellian velocity distribu- tions the experimental TOF data are more easily fitted directly in the time domain by a Associative Desorption of Hydrogen reverse-transformed Maxwell velocity distribution n,(t) =constant x t-4 exp[ -mL?/2kT,j, t2] (8) Gindenotes the temperature parameter of the distribtion, L is the length of the flight path, and k the Boltzmann constant. The mean kinetic energy of the desorbing mol- ecules is then related to the temperature parameter Kinby (Ekin)=2kT,,, . In order to check the measurement set-up Fig.3 shows a typical TOF spectrum of H, where the chamber is backfilled with hydrogen at a pressure of 9 x mbar. In this case a density-like Maxwell velocity distribution has to be fitted to the data. As can be seen the H, (u” =0, J” = 1) ion signal is well fitted with a velocity distribution with Tkin=300 K as temperature parameter. The additional ion signal at a flight time of ca. 9.5 ps can be assigned to H+ ions. These atomic hydrogen ions are produced from hydrogen molecules by multiphoton dissociation and ionization according to the follow- I I I I 1 I I I I (a) 0 2 4 6 8 10 12 14 16 18 20 TOF/ps Fig. 3 (a) Velocity distribution of a bulk sample of H, (d’=0,J” = 1) at room temperature; (b) enlarged portion of the TOF spectrum around the H+ atom peak.The solid line gives the expected TOF distribution for H atoms that dissociate from thermal H, molecules with Ekin= 0.433 eV. The data are fitted only when the velocity distribution of the H, molecules is also taken into account. T =300 K. L. Schrb;ter et al. 61 ing excitation pathway :29 H, X ‘Zgf(u”,J”)+ hv,,, -P H2 B ‘Z:(v’, J’) (14 H, B ‘Z;(v’, J’) + hvuv-+ HlX ’Z+ + e-(Ekin) (Ib) -+ H, Rydberg(v, J) (Ib’) H, Rydberg(v, J) + H,fX ’Z+ + e-(Ekin) (14 +HC(ls), ’s112)I+ HC(2s), 2S1/29 (2P), 2P1,2.3p)I (14 HC(2s), ’Slj2 (2P)2P1/~,7 3/2)I hvuv +H+ + e-(Ekin) (14 After the first state-selecting excitation step (Iu) the absorption of a UV photon (A < 320 nm) may lead to the production of H; ions via direct ionization (Ib) or autoionization from an excited Rydberg state (Ic).For hydrogen, this last process has a significant pr~bability.~~,~’The highly excited Rydberg state may also dissociate into two neutral hydrogen atoms, one in the (Is), ,S1,, ground state, the other in the n = 2 excited state (Ic’). Absorption of a second UV photon from the laser beam now leads to ionization of only the n = 2 hydrogen atoms (Id). The processes (Ia, b’, c’, d) thus produce atomic hydrogen ions via (VUV + 2UV) REMPI. The dissociation of the hydrogen molecule from the Rydberg state (Id) is accompained by a transformation of electronic energy in excess of the dissociation threshold into kinetic energy of the two neutral atoms. From the spectroscopy of hydrogen this excess energy is well known for a given UV photon energy.In the present case for H, XIX,f(u”= 0, J” = 1) excited via the P-branch into €3 ‘E:(v’ = 3, J’ = 0) and a UV photon energy of 3.9 eV (R = 319.35 nm) this excess energy amounts to 0.866 eV, distributed equally over the two hydrogen atoms. The H+ ion TOF signal is thus a convolution of a sharp 0.433 eV kinetic energy from the disso- ciation and the velocity distribution of the parent H, ground-state molecules, which in this case is a Maxwellian velocity distribution with Tkjn = 300 K. It is evident from Fig. 3(b) that the fast ion signal can be fitted well by taking both the thermal energy of the parent H, molecules and the energy in excess of the dissociation threshold into account.The fast H+ ion signal can thus always serve as a cross-check to the fit of the velocity distribution of the slower H; ion signal. The relative intensity of the H+ and the HZ signals depends on (i) the probability of exciting a Rydberg state [process (Ib’) versus (Ib)], and (ii) the dissociation probability of this Rydberg state compared to its autoioni- zation probability [process (Ic’) versus (Ic)]. The relative height thus varies strongly with the intermediate B-state level excited and the wavelength of the UV laser beam. Fig. 4 shows a typical velocity distribution measured for D2 (u” = 1, J” = 2) mol-ecules desorbing from Pd(100) at T, = 683 K. It is evident that this distribution cannot be described by a Maxwellian distribution at T,, shown as a dashed line, but has to be fitted with a considerably higher temperature parameter Tkin.A best fit is obtained for Gin= 775 K. Such velocity distributions have been measured for many surface tem- peratures between T, = 440 K and 825 K. H, molecules desorbing from Pd(100) in the vibrational ground state with J” = 0 to 5, thereby spanning an internal energy range E,,, = 0-1740.2 cm-’ (0,216 eV), always show velocity distributions with Gin= T, within the experimental uncertainty. D, molecules also show a linear increase of (Ekin)/2kwith T,, however, with energy offsets which vary slightly for different internal states. Linear least-squares fits to the data assuming a constant slope of one and having as free parameter the intercept of the fits with the kinetic energy scale at T, = 0 K support this conclusion. The intercepts obtained from the least-squares fits are shown versus the internal energy E(v”,J”) in Fig.5 for each internal state. The dashed line at an intercept value I = 0 meV represents the case of thermal equilibrium at the surface temperature T,. The velocity distributions of €3, molecules (filled symbols) can well be Associative Desorption of Hydrogen (7111111111 20 40 60 80 100 120 140 160 180 TO F/ps Fig. 4 TOF distribution for D, (u” = 1, J” = 2) desorbing at T, = 683 K from Pd(100) I I I I I I I I 40 -””= 0 V’‘ = 1 30 -0 -20 -00 10-062-0. om---e----A ---------E B-10--.--20 --30 -I I I I I I I I I described as equilibrium distributions at T,? independent of the internal rotational state. For D,, however, intercepts of ca.10 f7 meV for D, (d’= 0, J” = 2 and 3) and 28 & 5 meV for D, (v” = 0, J” = 4 and 5) and the vibrationally excited D2 (v” = 1, J = 2) are obtained. The correlations of the fits with linear regressions of slope one are rather good (r = 0.85 to 0.99). Angular Distributions Fig. 6 shows in polar coordinates rovibrationally state-resolved angular distributions of the hydrogen and deuterium desorption flux from a Cu(100) surface. In all cases the Cu(100) surface was kept at a constant temperature of T, = 885 K. In Fig. 6(a) are plotted results for H, desorption in the vibrational ground state (v” = 0, J” = 5) (filled symbols) and for desorption in the vibrationally excited state (0’’ = 1, J” = 1) (open symbols).In Fig 6b the corresponding results for D2 desorption in (v” = 0, J” = 5) (filled symbols) and for D, (u” = 1, J” = 0 and 2) (open symbols) are shown. Least-squares fits L. Schriiter et al. 20 10 0 10 20 I‘ 111’ 20 I0 0 10 20 20 10 0 10 20 Fig. 6 Angular distributions of H, and D, desorbing in the vibrational ground and excited state from Cu(100) at T, = 885 K. (a) .,H, (u” = 0, J” = 5); n = 6.2; 0,H, (u” = 1, J” = 1); n = 5.0. (b)., D, (u” = 1, J” = 0) and 0,D, (0’’ = 0, J” = 5); n = 7.5; 0, D, (u” = 1, J” = 2); n = 5.7. of the data points to cos” 0 functions are shown as lines in the figures. For the ground- state molecules we obtain exponents for the cosine function of n = 6.2 for H, (J” = 5) and n = 7.5 for D, (J” = 5).These exponents are in agreement with those obtained earlier in state-integral measurement^.^-^' The corresponding exponents for the vibra- tionally excited states are n = 5.0 for H2 (u” = 1, J” = 1) and n = 5.7 for D, (u” = 1, J”’ = 0 and 2). It is evident that the angular distributions for molecules desorbing in the vibrationally excited state are considerably broader than for those in the ground state. As may be noticed in Fig. 6(b),the angular distributions for the different rotational states (v” = 1, J” = 0) and (u” = 1, J” = 2) of D, are fairly similar within the experimen- tal uncertainties. Under the assumption that the angular distributions do not change significantly with J” in both the ground and the vibrationally excited state, which might not be justified for weakly populated high-l” states, a correction factor for the total state population can be derived by integrating the angular distributions over 8.For H, (0’’ = 1) this integral is ca. a factor of 1.14 larger than for H, (d‘ = 0). The same numeri- cal value of 1.14 for this ratio D, (u” = 1)/D2 (u” = 0) is derived for deuterium. These factors should be applied as a correction when vibrational-state populations are deter- mined from measurements at @ = 0’. It should be noticed that a rotationally symmetric dependence of the desorption flux around the azimuth angle was assumed. Discussion For a molecule which shows a cosine angular distribution in desorption from palladium and a nearly Maxwellian translational energy distribution5 it might be expected that the internal degrees of freedom would also be in equilibrium with the surface.However, static thermal models were not able to explain the main observations: the temperature Associative Desorption of Hydrogen dependence of the vibrational population, the non-trivial isotope effect of the slopes of the Arrhenius plots, and the absolute magnitude of the vibrational p~pulation.~~.~~ Thus, a dynamical treatment of the H atom recombination is required. Without a realis- tic ab initio PES the calculations described above are performed on a model PES with a curved reaction path. Along this reaction path an energetic barrier against the recombi- nation of the hydrogen atoms with a Gaussian shape [eqn.(l)] is assumed. The width and the height of this barrier are fitted to the experimental data for D, desorption. The velocity distribution of the adsorbed atoms is taken to be thermal at T,, thus modelling the thermal character of the reaction. The other important ingredient in the calculation is the variation of the hydrogen vibrational frequency along the reaction path, account- ing for the fact that the atoms experience attractive forces after surmounting the maximum of the barrier. With these assumptions and an adjustment to the D, data the temperature dependence of the vibrational population in H, and HD can be predicted quite well, including the non-trivial isotope effect.From this model calculation it can be concluded that excess zero-point energy can be made available to overcome the energetic barrier. This leads to different effective barrier heights with Eeff= 100 meV for H, and 130 meV for D,, i.e. lower for hydrogen than for deuterium. It is then expected that deuterium molecules desorb with a higher kinetic energy than hydrogen moleules. The translational energy measurements confirm this expectation. For H, complete accommodation of the kinetic energy to T, is observed, whereas for D, an additional energy offset of 10 to 30 meV compared to Ekin= E, is found. This supports the existence of a small barrier against recombination also on a palladium substrate, although the absolute value of the kinetic energy is over- estimated by this model PES even when a van der Waals attraction of the hydrogen molecules by the surface is included in a discussion of kinetic energies.Recent results for desorption from Cu( 1 1 1) show also that D, molecules have systematically higher kinetic energies than H, molecules in the corresponding internal state^.^ For desorption from Pd(100) neither molecule shows a significant dependence of the translational energy on the rotational or vibrational state. This is in constrast to recent measurements for the desorption from Cu(l1 1),19931 where a strong decrease in &in with increasing vibra- tional state, and in addition with increasing J” for J” > 8, especially in the ground vibrational state, has been observed.For the palladium substrate the coupling between the internal degrees of freedom and the translation seems thus to be much weaker than for copper, which, in view of the small barrier, is not unexpected. Measurements of the state selective-angular distributions from Cu(100) support this strong coupling between internal and translational degree of freedom. The angular dis- tributions for (u” = 1) states are significantly broader than those for ground-state mol- ecules. Berger and Rendulic22 measured recently the sticking coefficient of H, on Cu(ll0) for cold seeded hydrogen beams. At an incident kinetic energy of 0.2 eV the angular dependence of the initial sticking coefficient was found to be proportional to cos” 8, with n = 6.6 for a nozzle temperature of TN= 1200 K and n = 4.3 for TN= 1700 K.At the higher nozzle temperature the amount of vibrationally excited H, (u” = 1) in the beam is considerably larger (population ca. 2.9%) than at the lower TN(less than 0.7%), when a cooling of the vibrational degree of freedom during the beam expansion is neglected. From these experimental data it is qualitatively evident that vibrationally excited molecules show a broader angular distribution in sticking than ground-state molecules. Theoretical calculations by Kuchenhoff and Brenig23 show that at TN= 1700 K and &in = 0.15 eV the sticking of H, on copper is dominated by (u” = 1) molecules. A cosine distribution with n = 4.5 is obtained. A similar result is found for D, with an exponent of n = 6.5 for (d’= 1) and &in = 0.1 eV.Both the experimental and the theo- retical sticking coefficients show distributions in qualitative agreement with the observa- tions presented here for desorption. Also, the same isotopic behaviour is found in that the D2 distributions remain narrower than those of H, in the respective vibrational L. Schrater et al. state. Differences between the sticking measurements and calculations and the desorp- tion data arise from the distribution of kinetic energies present in the desorption flux. In this latter case the mean energies range from 0.31 eV (v” = 1) to 0.55 eV (0‘’ = 0) for H, and from 0.46 eV (v” = 1) to 0.62 eV (0’’ = 0) for D, ,31 These energies are thus consider- ably larger than the energies where tunnelling of H atoms through the barrier becomes important (below 0.1 eV), which, according to the theoretical calculations, generates a narrow H, angular distribution.We are grateful for financial support by the Deutsche Forschungsgemeinschaft (Za 110/2). References 1 G. Comsa and R. David, Surf: Sci.Rep., 1985,5, 145. 2 K. Christmann, Surf: Sci. Rep., 1988,9, 1. 3 G. Comsa and R. David, Surf: Sci., 1982,117,77. 4 G. Anger, R. Winkler and K. D. Rendulic, Surf Sci., 1988,220, 1. 5 G. Comsa, R. David and B. J. Schumacher, Surf: Sci., 1980,95,210. 6 K. D. Rendulic, G. Anger and A. Winkler, Surf Sci., 1989,208,404. 7 G. D. Kubiak, G. 0.Sitz and R. N. Zare, J. Chem. Phys., 1985,83, 2538. 8 H. Zacharias and R.David, Chem. Phys. Lett., 1985, 115, 205; L. Schroter, R. David and H. Zacharias, Appl. Phys. A, 1986,41,95. 9 J. Harris, T. S. Rahman and K. Yang, Surf: Sci., 1988, 198, 312. 10 J. Harris, S. Holloway, T. S. Rahman and K. Yang, J. Chem. Phys., 1988,89,4427. 11 J. Harris, Surf: Sci., 1989, 221, 335. 12 M. R. Hand and S. Holloway, J. Chem. Phys., 1989,91,7209; Surf: Sci., 1989,211/212,940. 13 W. Brenig, S. Kuchenhoff and H. Kasai, Appl. Phys. A, 1990,51, 115. 14 S. Kuchenhoff, W. Brenig and Y.Chiba, Surf: Sci., 1991,245, 389. 15 B. E. Hayden and C. L. A. Lamont, Phys. Rev. Lett., 1989,63, 1823. 16 B. E. Hayden and C. L. A. Lamont, Surf: Sci., 1991,243,31. 17 C. T. Rettner, D. J. Auerbach and H. A. Michelsen, Phys. Rev. Lett., 1992,68, 1164. 18 H.F. Berger, M. Leisch, A. Winkler and K. D. Rendulic, Chem. Phys. Lett., 1990,175,425. 19 H. A. Michelsen, C. T. Rettner and D. J. Auerbach, Phys. Rev. Lett., 1992,69,2678. 20 W. van Willigen, Phys. Lett. A, 1968,28, 80. 21 C. T. Rettner, H. A. Michelsen, D. J. Auerbach and C. B. Mullins, J. Chem. Phys., 1991,94,7499. 22 H. F. Berger and K. D. Rendulic, Surf: Sci., 1991,253,325; H. F. Berger, Ph.D. Thesis, Graz, 1992. 23 S. Kuchenhoff and W. Brenig, Surf. Sci., 1991,258, 302. 24 L. Schroter, R. David and H. Zacharias, Surf: Sci., 1991,258,259. 25 W. Meier, H. Rottke, H. Zacharias and K. H. Welge, J. Chem. Phys., 1985, 83, 4360; W. Meier, H. Rottke and H. Zacharias, Znst. Phys. Con$ Ser., 1988,94,93. 26 L. Schroter, S. Kuchenhoff, R. David, W. Brenig and H. Zacharias, Surf: Sci., 1992, 261,243. 27 L. Schroter, H. Zacharias and R. David, Phys. Rev. Lett., 1989,62, 571. 28 L. Schroter, G. Ahlers, H. Zacharias, R. David, J. Electron Spectrosc. Retat. Phenom., 1987,45,403. 29 H. Zacharias, Appl. Phys. A, 1988,47,37. 30 G. Herzberg and Ch. Jungen, J. Mol. Spectrosc., 1972, 41, 425; Ch. Jungen and 0. Atabek, J. Chem. Phys., 1977,66,5584. 31 C. T. Rettner, H. A. Michelsen and D. J. Auerbach, J. Vac.Sci. Technol.,in the press. Paper 3J031425; Received 28th May, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600055

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96,67-93 GENERAL DISCUSSION Dr. A. Hopkinson (IBM Research Center, Sun Jose, USA) opened the discussion: Regarding the comparison between an adsorption event, in which phonons propagate into the bulk from the impact site characterised by the adsorbate located in a ‘dent’ on the surface, and desorption; I do not agree that the reverse process of desorption, in which the solid lattice first deforms so that the adsorbate sits in a dent on the surface before one or more phonons converge at the adsorption site resulting in desorption, is in anyway unphysical or is in anyway not the exact time-reverse of the adsorption process. Dr. J. Harris (IFF der KFA Jiilich, Germany) replied: If I understand the thrust of your objection here it would seem the point you have missed perhaps is that, in the sticking event, which believers in detailed balance via microscopic reversibility regard as reciprocal to a desorption event, the initial dent in the lattice and the subsequent healing of the lattice can often, but not always, occur on quite different timescales.Prof. J. C. Polanyi (University of Toronto, Ontario, Canada) asked: In your calcu- lations on the effect of methane translational energy on the cross-section for the reaction CH; surface, did you also explore the effect of vibrational excitation in the CH4? I mention this since you have made the nice point that inclusion of surface recoil on impact has the effect of shifting the location of the crest of the energy barrier on the potential-energy surface (PES).You went on to say that in a case where this shift was to a Eater position along the reaction coordinate the inclusion of recoil led to a smaller probability for reaction. If, however, you rely on reagent vibration to provide a major fraction of the energy required for barrier crossing then this same shift in barrier crest due to surface recoil should enhance the reaction probability. Is it known whether this is the case? Dr. J. Harris responded: There is the usual vibrational enhancement you get in entrance-channel activated desorption that devolves from the kinds of energy diagrams that govern these processes. The enhancement has been demonstrated experimentally for CH4 dissociation on several metal substrates, and its magnitude is given roughly cor- rectly by the theory.The dependence of the effect on incident energy did not come out quite right so there are some details missing, but there is no reason to believe that we are missing anything of central importance. As a general comment in this context, I should say that the very nice clear-cut picture you have set out for gas-phase reactions, with early and late barriers accessed preferentially by translational and vibrational energy, does not quite translate through to the kinds of surface reactions we are discussing here. This is because of the broaden- ing of the levels at a metal surface. In the gas phase you can think in terms of decoupled coordinates in entrance and exit channels with a coupling region about the ‘seam’ that may have an extent that is less than 0.1 eV.On the surface however, this region will usually be of extent ca. 1.0 eV or more. This means that the behaviour of the system cannot be deduced from the PES near the seam but depends on couplings that occur as much as 1.0 eV away, basically spanning the entire energy diagram. In such a case the kind of seam you have and the exact placement of the saddle point on it does not give a unique guide as to how the system behaves because the coordinate couplings do not switch off fast on either side. A particularly cute illustration, easy to demonstrate on a suitable low-dimensionality diagram, is the manner in which a molecule with lots of vibrational energy but very little translational energy can nevertheless ‘climb’ a hill which appears to be predominantly 67 General Discussion ‘in’ the translational coordinate.As the system traverses the PES in the vibrational direction, sufficient vibrational -+ translational energy transfer occurs per pass to carry the system one stage further up the hill. You then get ‘positive feedback’, or what I have tried to dub ‘bootstrapping’, so that once the process has started it keeps on going until the seam is crossed. The hallmark of this kind of behaviour is a rather sharp threshold in incident translational energy below which an incident molecule is backscattered, having apparently interacted with the surface only very weakly, and above which the molecule dissociates.What you see in the gas phase is then at first sight quite puzzling. As the energy increases the molecules first scatter as from a mirror, then suddenly they disappear as though the mirror has become a perfect sink. Even in such cases, however, as seems to be generally observed in dissociation at metal surfaces, vibrational energy is less effective than translational energy in promoting dissociation; that is, if you have E of energy available then it is better to put all of this in translations than to divide it between translations and vibrations. Drs. D. J. Auerbach, C. T. Rettner and H. A. Michelsen (IBM Research Center, Sun Jose, USA) said : Your lecture addresses many interesting and controversial issues and will surely provoke much lively discussion.Let us begin by taking up one such issue, the question of the applicability of the principle of detailed balance. The paper stresses that there are severe limitations of the applicability of the principle of detailed balance to dynamics at the gas/solid interface. We agree that this principle should not be applied to all non-equilibrium systems. However, we believe that it can be usefully, and accurately, applied to relate a wide variety of adsorption and desorption data. In fact, the particular case discussed, that of the trapping and desorption of atoms is the very area where detailed balance has found its broadest application and longest list of There are two ways of reading your objections: 1. Detailed balance should not be applied to treat scattering experiments since it is not correct.2. Since, if detailed balance is not rigorously correct for gas-solid interactions under the conditions of molecular beam experiments, ‘tests’ of detailed balance are not partic- ularly interesting. If it works, it works; if it does not work it does not work. There are no interesting theoretical issues. We disagree with both of these statements. Indeed, it is well known that what is generally understood by the principle of detailed balance is noi rigorously applicable to dynamics at the gas/solid interface. There are quite fundamental objections. Wenaas’ for example, has pointed out that detailed balance requires both time-reversal invariance and invariance under reflection of spatial coordinates.The later symmetry is broken in particle-surface collisions. This is, however, a ‘straw man’, since this principle would, in any case, only be valid under equilibrium conditions. A closely related relationship, the principle of reciprocity, can be applied to derive the relationships relevant to gas-surface collisions, but this principle is again only valid at equilibrium. Even this principle, then, tells us little about what to expect for a non-equilibrium system. Instead, we must turn to considerations of time- reversal symmetry and the principle of microscopic reversibility, which are more gener- ally relevant to gas-surface studies under non-equilibrium conditions. The debate is not, then, about whether the principle of detailed balance applies to non-equilibrium surface science experiments. We agree that it does not.Rather, we are concerned with whether the recipe generally used to compare adsorption and desorption phenomena is valid. When ‘the principle of detailed balance’ is applied to gas-surface interactions, we are assuming that the energy distribution of a species leaving the surface with energy E in quantum state n is given by: f(n, E) dE = S(n, E)P(n, E) dE General Discussion where S(n, E) is the energy dependence of the adsorption probability of the species in state n, and P(n, E) is the relative population of this state with energy E. Eqn. (1) is identical to what would be predicted by the principle of detailed balance (were it valid for gas-surface interactions) and to what would be predicted using the principle of reciprocity for a system at equilibrium.The issue at hand, however, is to understand under what conditions eqn. (1) is valid for a non-equilibrium system. Grimley and Hoiloway4 have shown that trapping and desorption can be rigorously related to each other under non-equilibrium conditions; as a consequence of the time- reversal symmetry of the relevant wavefunctions. This prescription is also supported by detailed experiments concerning trapping4e~orption.~.~ In our paper, we have related recombinative desorption to activated dissociative chemisorption. Specifically, we have measured quantum-state-specific kinetic energy distributions of D, desorbing from Cu, which we have analysed uia eqn.(1) to obtain the corresponding quantum-state-specific adsorption probabilities. We have found that these inferred adsorption probabilities are fully consistent with detailed (non-equilibrium) adsorption measurements. So detailed balance holds for this system as well. We can certainly imagine circumstances under which eqn. (1) would not be expected to hold, whereupon detailed balance would not work. One key point is that the system under study must be fully reversible at the temperature of the experiments. Irreversible chemisorption e.g. of 0, on tungsten, could not be addressed using eqn. (1); nor could systems involving sputtering or damage to the surface. We also believe that the states of the surface species must follow a canonical distribution of energy characteristic of T,.If this distribution were perturbed, (yielding a distribution of states that differ significantly from equilibrium) then again detailed balance would not apply perfectly. We fully agree with Dr. Harris that such deviation would hardly be earth shaking. However, the issue of the precise circumstances and magnitude of deviations from detailed balance, seems to us to be a very fertile ground indeed for further investigation. In the example of the D, interactions with Cu discussed in our paper, eqn. (1) enables us to obtain details of the rotational state dependence of adsorption that we could not otherwise obtain. To allow the application of detailed balance to a wide variety of other systems, we need a better knowledge of the accuracy of this method under a wide variety of conditions. We believe that further theoretical studies and simulations can potentially shed much light on this important issue.1 E. P. Wenaas, J.Chem. Phys., 1971,54376. 2 E. W. Kuipers, M.G. Tenner, M. E. M. Spruit and A. W. Kleyn, Surf. Sci., 1988,205,241. 3 C.T.Rettner, E. K., Schweizer and C. B. Mullins, J. Chem. Phys., 1989,90, 3800. 4 T.B.Grimley and S. Holloway, Chem. Phys. Lett., 1989, 161, 163. Dr. J. Harris replied: I think my position on detailed balance is more clearly set out in my paper than it is in either of the two ‘ways of reading’ you do not agree with. To be concrete, my objection to the use of detailed balance in your own work refers to the notion that you can by these means ‘obtain’ quantities which ‘otherwise you could not obtain’. In my view, this involves a slight self-deception, at least it does if the word obtain is interpreted to mean measure.Since eqn. (1) is not a rigorous law in a non- equilibrium situation, we can refer only to whether deviations from it are large or small. If you establish that these deviations are small, in some restrictive, illustrative or aver- aged sense, with respect to a given system (which you have indeed done for the D,/Cu data), it is still a hypothesis that they remain small when applied to other situations. The results you obtain, on the basis of eqn. (1) holding in situations where you have not shown that it holds, may seem to you to have the force of ‘data’, but some aspects of them seem rather suspect from the theoretical point of view. I am not wishing the fol- lowing scenario on you, or predicting it, but it would not surprise me unduly if the last word with regard to some of your conclusions has yet to be spoken.If this does turn out General Discussion to be the case, then will we all get subjected to a fresh batch of papers reporting on the ‘surprising failure of detailed balance in H,/Cu scattering’? Yet another paper tiger slain ! In my opinion, the raw scattering data on the H,(D,)/Cu system that you present in your papers are quite outstanding and it is unnecessary and even retrograde to attempt to interpret them in terms of a vague quasi-thermal ‘theory’ that you yourself agree is not rigorous under the conditions that prevail in the experiment.Dr. S. Holloway (Uniuersity of Liverpool) communicated: You observe that on Ni(110) the sticking probability is unity, within experimental error, yet an elastic fraction is observed that suggests scattering from a weakly corrugated potential, typical of a physisorption interaction.’ You then pose the question of how a single adiabatic PES can account for these data. The possibility you suggest is that the dissociated fraction moves on the adiabatic ground-state PES while the elastic fraction remains on the non- adiabatic H,/Ni PES. You maintain that this seems quite likely because the reduction in the dissociation barrier (which facilitates the dissociation) is a consequence of s + d electron transfer at the surface and that this is a ‘slowish’ process.Exactly how slow, I wonder? How could one estimate the order of magnitude for remaining on such a non- adiabatic state after the adiabatic barrier has been crossed? An alternative explanation has been previously suggested and dynamical calculations have been performed, albeit for limited dimensionality, in order to quantify the effect., Suppose that the barrier to dissociation is constrained in some coordinate. Detailed calculations on simple metal surfaces have shown that molecules generally have lower barriers in the broadside orientation and also that certain parts of the unit cell have lower dissociation pathways than Restricting the argument to the former (and stronger) of these constraints, let us interpret the data by assuming that 95% represents the fraction of the solid angle (about 8 = 0’) which contains molecules that are in unfa- vourable orientations for dissociation.This implies that all molecules with polar angles in the ranges 0 -= B/degrees < 18 and 72 < B/degrees < 180 could scatter elastically. The consequences of this would be that the scattered fraction would have a massive align- ment.6-8 If, on the other hand, this 5% were to scatter from the non-adiabatic H,/Ni repulsive wall as you suggest, then from measurements of the angular anisotropy on Cu,’ one might expect virtually no alignment in the scattered fraction. Therefore, the experiment that suggests itself is to measure the alignment moments of the scattered flux or perform a post-permeation experiment, measure the alignment and invoke detailed balance.1 H. J. Robota, W. Vielhaber, M. C. Lin, J. Segner and G. Ertl, Surf Sci., 1985, 155, 101. 2 G. R. Darling and S. Holloway, J. Chem. Phys., 1990,93,9145. 3 P. K. Johansson, Surf Sci., 1981, 104, 510. 4 P. J. Feibelman, Phys. Rev. Lett., 1991, 67,461. 5 D. M. Bird, L. J. Clarke, M. C. Payne and I. Stich, Chem. Phys. Lett., 1993,212,518. 6 S. Holloway and B. Jackson, Chem. Phys. Len., 1990,172,40. 7 X. Y. Chang and S. Holloway, Surf: Sci., 1991,251/252,935. 8 S. Holloway and X. Y. Chang, Faraday Discuss. Chem. SOC.,1991,91,425. 9 L. Wilzen, F. Althoff, S. Anderson and M. Persson, Phys. Reu.B, 1991,43, 7003. Dr. J. Harris communicated in reply: There are really two issues here. Possibly, I erred by failing to make this sufficiently clear. The main point I wanted to stress relates to the question of the likely importance of non-adiabatic effects in surface processes. I suggested that if one is really serious about establishing this then there is a simple way of doing it, via the H,/Ni(llO) experiment (or an equivalent). I have not made an esti- mate of the ‘survival probability’ of the initial state in such a case (why is this dramat- ically more difficult than estimating an ion survival probability?) but it is certainly different from zero. Since the s + d transfer process is certainly a slowish process, while General Discussion an H2 round trip is rather fast, this might be thought of as, in some sense, an upper bound for ‘typical’ strengths of non-adiabatic fractions in surface processes.Now, whether or not the coherent fraction observed for Ni(ll0) is due to non-adiabaticity, it does appear to be in the per cent range, which is then ‘an upper bound for an upper bound’, if you will, So I guess I was trying to say, as an additional counterweight to Ronnie KoslofYs position, that, if the data we have available so far are correct, then the issue as to whether the non-adiabatic fraction is large or small may in fact already have been decided (if you believe all the bits and pieces in the argument, and with the restriction to processes with no sharp levels). The other issue is whether or not the coherent fractions that have been observed (for Ni and Pt only, as far as I know) are due to the non-adiabatic effect or to something else like bits of the adiabatic PES that bounce the H, rather than dissociate.I rather favour the non-adiabatic explanation for the case of Ni because it explains very neatly why the elastic fraction looks just as one would expect for a physisorption system. I would not expect ‘smooth surface’ behaviour in the other case (though this may be what low- dimensionality model calculations show). If a careful experimental study shows the strengths of the Bragg beams, as a function of surface temperature and incident energy, continuing to display ‘physisorption-like’ behaviour, then the interpretation would be strengthened.It should also be possible to distinguish between the adiabatic versus non-adiabatic explanation via the sensitivity to surface temperature, as well as via the isotope effect. So I do not think you need to go to the lengths you suggest. What is required in the first instance is measurement of the Bragg peak strengths as a function of T, and Ei, Oi just as in a standard He-diffraction experiment (though some way would have to be found to get rid of the H2 that dissociates). Prof. A. D. Buckingham (University of Cambridge) communicated : You emphasised the importance of polarization forces in the interaction of molecules with a metal surface. You indicated that these arise from a contribution to the electronic wavefunc- tion that can be represented by the transfer of an electron from the highest occupied orbital of the adsorbate to an unoccupied orbital of the metal or from the metal to the lowest unoccupied orbital of the adsorbate.In conventional intermolecular force theory such a contribution would be called a charge-transfer interaction. Polarization is due to distortion of the electronic structure of one molecule by the (non-uniform) electric field of the other; it can be described by a mixing of the occupied and unoccupied orbitals of one molecule due to the presence of the other. In the case of CO interacting with a metal, there will be a polarization of the metal by the electric field of the CO and this gives rise to an ‘image’ force of attraction.How important are such image forces? Is there experimental evidence for charge transfer between an adsorbate and the substrate? Dr. J. Harris communicated in reply: The term charge transfer is usually restricted to cases where the HOMO of one bonding fragment lies higher in energy than the LUMO of the other. Here, the opposite is the case and the partial occupation of the LUMO is governed by potential matrix elements that drive the ‘inelastic hop’. There is, of course, more than one matrix element involved and I can agree that it would be desirable to distinguish between e.g. intra-fragment and inter-fragment polarization. Sometimes the latter is referred to as ‘donation’ cf. the Blyholder picture of CO adsorp-tion with ‘donation’ of metal electrons CO 2n*-orbitals and ‘back-donation’ of CO lone-pair electrons to the metal.However, there does not seem to be any unanimity of nomenclature with regard to polarisation effects in general. As regards the second and third parts of your comment, there are charge displace- ments when molecules like CO are adsorbed on surfaces but these cannot ordinarily be General Discussion interpreted in terms of a charge transfer. The experimental monitor is the change in work function which depends linearly on the change in surface dipole that occurs on adsorption. It is possible to measure this, therefore, but not to convert it to a charge transfer because the extent of the region over which charge displacements occur is typi- cally as large as the bond distance. This kind of situation occurs also in molecules, a classic example being BF, whose dipole moment ‘points the wrong way’ and so, if inter-preted in terms of charge transfer, would imply that the boron atom is more electro- negative than fluorine ! Prof.R. A. Marcus (California Institute of Technology, USA) opened the discussion of Dr. Holloway’s paper: Ideas and results in papers here on the H, + Cu surface reac- tion have much in common as Halstead and Holloway have pointed out,’ with those introduced in the mid-sixties to treat the H + H, +H2 + H gas-phase reaction, with terms such as vibrational adiabaticity,’ local reaction path curvature, K(S) and (transverse) vibration frequency w(s),~ as seen in various papers in this Discussion.Some other ideas introduced for gas-phase reactions3 might also be extended to the H, + Cu reaction. For example, action-angle variables can be defined not only for vibrations, J, , but also for the 8 and the cp rotations, e.g. the actions J, and J,. Using the relevant canonical transformation one can then calculate these quantities from the coordinates and momenta along a classical trajectory. In this way adiabaticity and deviations from it could be explored. In particular, some rotational motions evolve into vibrations or into hindered rotations. A rather approximate formula connecting them has been suggested earlier,3 and its applicability to the present system could be studied. Rotationally non- adiabatic effects would be reflected in deviations from the formula. One trend noted in some of the present papers and seen earlier in classical trajectory studies of the H + H, reaction is the decrease, at low H, rotational angular momentum J, in the collision effectiveness with increase in J. This behaviour was interpreted earlier in terms of a statistical factor: closely spaced rotational energy states of H, evolve into more widely spaced bending vibrational states of the transition state H-H-H.This effect, well known in transition state theory, is described there in terms of ratios of partition functions and is a statistical way of describing steric hindrance effects (orientation requirements) : restricted orientation in the transition state corresponds to more widely spaced energy levels for that motion and to a smaller transition-state parti- tion function.A similar effect appears to occur in the H, + Cu reaction. A key question regarding further information on rotational effects concerns the rela- tive role of the J, (cartwheel) and J, (helicopter) motions in explaining the trends observed on the dependence of sticking and desorption coefficients on the rotational state. An experimental answer to this question would be obtained when one is able to measure the polarization of the rotating H, and D, molecules in the desorption experi- ments or the dependence of sticking on the polarization. 1 D. Halstead and S. Holloway, J. Chem. Phys., 1990,93, 2859. 2 R. A. Marcus, J. Chem. Phys., 1965,43, 1598. 3 R.A. Marcus, J. Chem. Phys., 1966,45,4500; 1967,46,959; 1968,49,2618. Dr. Holloway replied: It would indeed be possible to employ action-angle variables to good use in surface reactions. I intend to explore such avenues in the near future in a series of classical dissociation studies. I am, however, pessimistic when it comes to H, and D, dissociation: I believe that the quantum nature of the dynamics will prevail. Prof. Marcus communicated: This point on quantum effects is an interesting and important one : Certain quantum effects, namely nuclear tunnelling and quantum mechanical interference, are not captured by classical trajectories, though the former is General Discussion sometimes estimated approximately by extension to the complex plane, such as that in the so-called ‘Marcus-Coltrin’ path and in its descendants due to Truhlar, Garrett and co-workers.A different quantum effect is that in an adiabatic process, in which a change in vibrational energy, (n, + $)h(vi-vr), can be used to overcome (or, if adverse, increase) the energy barrier to reaction. In a vibrationally adiabatic process this energy difference is reproduced by a classical trajectory, namely by Ji(vi-vf), where J, is the action variable of the ith vibration, vi is the frequency of that vibration in the reactants, and v’ is its value in the transition state. [J, = (n,+ f)h]. Prof. Polanyi addressed Dr. Auerbach and Dr. Holloway: Dr. Holloway has present- ed some interesting new results on a quantum calculation of the effect of reagent rota- tion on reaction probability using a ‘late’ energy-barrier PES.He anticipates a convergence of these findings with the classical theory of the same phenomenon. On his PES there is a significant effect of reagent rotation on the probability that H, reacts with Cu( 11 1). The effect is twofold, and qualitatively mirrors that observed experimentally in gas- phase exchange reactions some years ago by means of infrared ‘chemiluminescence depletion’. Similar behaviour has also been found in crossed-beam experiments.394 The characteristic dependence of reaction probability and rotational quantum number, J, of the molecule whose bond is being severed is an initial decline followed by an increase. Ref. 2 suggests possible contributing factors.In the initial region of declining reaction probability the effect of increased J appears likely to be a decrease in the time that the molecule under attack spends in a favourable alignment for reaction with respect to the attacking gas atom or, in the present case, surface atom. This ceases to be important at high J when the molecule enters and leaves the preferred orientation many times in the course of a reactive encounter, becoming a ‘blur’ as seen by the attacking gas atom or surface atom. This would be expected to happen at lower values of J for longer approach times (lower collision energy). At high J, rotational energy will, for the first time, become significant in terms of the energy barrier to reaction. On a late-barrier (endoergic) PES the vibrational-rotational interaction will cause the bond under attack to stretch.This stretching (vibration) will be helpful in crossing a late barrier. This is not to say that this second effect, which causes reaction probability to increase with J, can only be conceived of as occurring on surfaces having a late barrier. If the relative timing of approach [e.g. BC(J) approaching a surface, S, to give disso- ciative adsorption] to rotation is correct, then the rotational motion should contribute to the compression of the B-S or C-S bond with resultant enhanced barrier crossing on an ‘early’ barrier surface. It is evident that the ratio of the approach time (B-S or C-S decreasing) to the rotational period (B-C executing a rotation in state J)is likely to play a crucial role in determining the contribution of rotation to reaction, in the gas or at the surface.These various points were discussed for a gas-phase reaction in ref. 2. 1 A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi and J. L. Schreiber, Faraday Discuss. Chem. SOC., 1973,55,252. 2 B. A. Blackwell, J. C. Polanyi and J. J. Sloan, Chem. Phys., 1978,30,299. 3 H. H. Dispert, M. W. Geis and P. R. Brooks, J. Chem. Phys., 1979,70,5317. 4 M. Hoffmeister, L. Potthast and H. J. Loesch, Book of Abstracts, XIZ, International Conference on the Physics of Electronic and Atomic Collisions, Gatlinburg, 1981. Drs. Rettner, Michelsen and Auerbach replied: We agree that there are strong simi- larities between our observations of the effect of reagent rotation on the reaction prob- ability of H, and D, at a Cu(ll1) surface and your earlier observations on gas-phase reactions. The analogies with gas-phase reactions are very instructive and have helped to Genera1 Discussion guide our approach to surface reaction dynamics. The explanations that we, and others, have offered to account for the role of rotation in dissociation dynamics are very close to your qualitative description of the role of rotational motion in A + BC reactions.One minor difference is worth noting, however. We do not believe that the incident molecule becomes a ‘blur’ until very high J. A D, molecule in J = 6 rotates only 40” during the time it would take to move forward 0.5 A at 0.6 eV, even in the absence of steric hindrances to rotation.The study of gas-phase reactions is generally more advanced than that of gas/surface reactions because of the added experimental difficulties of dealing with the surface case. The hydrogen/Cu system is the gas/surface system for which we have the most detailed knowledge. Let us take this opportunity to brag about the progress in surface chemical dynamics. Note that we have obtained not only the dependence of reactivity on reagent rotation, but also the dependence on reagent vibration and on reagent kinetic energy. This knowledge of the role of all three forms of energy is in fact the basis of the present study and allows us to ‘understand’ the thermal chemistry in microscopic terms.Drs. G. R. Darling and S. Holloway (Unitlersity of Liverpool) communicated in reply to Prof. Polanyi: We would like to thank Professor Polanyi for drawing our attention to useful references to a similar phenomenon in the gas phase. It is true that if the molecule rotates many times in an encounter with the surface it will appear to be a ‘blur’. For light diatomics, however, this would be equivalent to a very high J-state indeed. For instance, an H, molecule in the J = 10 state with 0.5 eV translational energy rotates only once in the time taken to travel 3 au, clearly not enough to become ‘a blur’. The rotational energy can be of assistance in overcoming an early barrier as out- lined, however, this effect occurs only for very particular initial conditions, which in all likelihood have very small measure in phase space.Prof. P. Tetenyi (Institute of Isotopes, Budapest, Hungary) addressed Dr. Auerbach : I would like to ask about the possible interpretation of the numerical values of the pre- exponential factor. It seems we are faced, presumably, with a compensation between the pre-exponentials and the activation energies: comparison of data from Fig. 4 and 9 of your paper indicates values of E of 0.44 and 0.607 eV while the respective In A values are -2.813 and 0.27. A compensation between the energy and entropy factors of the activation, a widely discussed, but not quite understood phenomenon, can take place. Would you please comment on this? Drs. Rettner, Michelsen and Auerbach responded : Compensation effects are said to occur when the pre-exponential factor and activation energy of a given reaction change in such a way as to have opposite effects on the reaction rate. Thus a reduction in the pre-exponential factor can partially offset, or compensate, the effect of decreasing activa- tion energy.In surface science, such effects are often seen in studies of reaction rates as a function of surface coverage, for example. In the context of our calculations for the D,/Cu( 11 1) system, one must first ask what it is that is to be changed, in order to look for compensation effects. The results that you mention do indeed show a compensation effect of sorts. The activation energy and pre-exponential factor obtained from the slope of the Arrhenius plot of Fig.4 are both smaller than those obtained from curve of Fig. 9(f). However, we would not consider this behaviour a true compensation effect. Rather, it is a manifestation of the fact that the plots are curved. The effect that you refer to can be understood by studying Fig. 9 in detail. The different lines have very different curva- tures. For molecules in a single v-J state, when E, + W,we obtain a straight line with slope equal to E, and intercept equal to In (A).When E, and W are comparable, the plots are curved. Over a limited range of temperatures, these curved plots would give General Discussion smaller activation energies and pre-exponential factors. The intercept (at 1/T = 0) would, however, be the same.Prof. K. Kunimori (University of Tsukuba, Ibaraki, Japan) said: Some people believe that hydrogen chemisorption on metals is a structure-sensitive process; i.e. the sticking probability depends strongly on the surface structure of metal crystals. It seems to me that, in your calculation, you consider such effects only by using the width parameter [W in eqn. (7a)l. What about the active sites on the metal surface? (1) What do you think about the effect of stepped sites? Even if you use the flat Cu( 11 1) surface, some defects, including steps, may be present on the surface. (2) What about the more open Cu surfaces or the stepped surfaces? (3) In your study using the flat Cu( 11 1) surface, your conclusion is that the translational energy is important, while vibrational and rotational energies are relatively unimportant.However, if you think about the effect of active sites in more detail (as a chemist), you would expect that the rotational and/or vibrational motions of the molecule are also important for the disso- ciative adsorption on some active sites. In conclusion, I do not think it would be sufficient to elucidate the mechanism and dynamics of the dissociative chemisorption in detail using only the parameter W in your calculation. Drs. Rettner, Michelsen and Auerbach replied: We do not believe that defects on our Cu(ll1) sample play an important role in our measurements. The reason is simple. We observe sticking probabilities below lop6.As you correctly point out, the surface must have a substantial number of step sites and other defects. If the sticking probability were strongly enhanced at these sites, we would not observe such small sticking probabilities.The following observations support this view. As part of a closely related study of H, dissociation on the Cu(ll1) surface, we accidentally measured the sticking on a surface that had been sputtered at 100 K, but not annealed. For Ei = 0.3 eV, the sticking prob- ability was found to be ca. 0.002, which is indistinguishable from the measurement on the annealed surface. The surface damaged in the former case was evident from the fact that the shape of the TPD spectrum for H, desorption looked quite different from that for the annealed surface. More generally, we must certainly agree that the reaction probability may depend on the site or impact point.Further, the reaction may have different behaviour on different faces of Cu. We have so far only made measurements on Cu(l11). Our measurements are simply an average over the impact sites within the unit cell. This average will affect the width of the adsorption function, W,as you suggest. This, however, is not the only effect of averaging over sites. Different sites probably have different effective barriers, which would be represented via the E, parameter of the adsorption functions. If some sites have much higher barriers, the saturation value of the sticking probability will be reduced. This effect would be represented via the A parameter in the adsorption func- tion.Thus all of the parameters in the adsorption function are likely to be influenced by the effect of different sites on the surface. Your speculations that the role of vibration or rotation might be increased at certain active sites are interesting. Perhaps experiments on other, more open faces of Cu will reveal such effects. Prof. 6. D. Billing (University of Copenhagen, Denmark) said: The point I wish to raise is that the sticking probability is strongly site dependent. We find in our D,/Cu calculations variations in the dissociative sticking probability of ca. 15 orders of magni- tude as a function of where the molecule hits the surface within the unit cell. Thus, in principle, we have an infinite number of activation barriers.Is there any hope that from General Discussion experimental data one can obtain information on the site dependence of the activation barrier ? Drs. Rettner, Michelsen and Auerbach replied: The results of our experiments are simply the sum over the contributions from different sites or impact points on the surface. We have no way of controlling the impact site experimentally. Thus the simple answer to your question is no, there is no direct experimental way of obtaining the site dependence. We may hope to gain some insight into this question from comparison with theoretical studies, such as your own, and by studies on different surface orientations. Dr. K. W. Kolasinski (Fritz-Haber-Institut, Berlin, Germany) said: I would like to return to the discussion of detailed balance.As we have seen in the work of Auerbach et al., the H,/Cu system is an example where this principle works beautifully, even under non-equilibrium conditions. The adsorption and desorption results are perfectly consis- tent and detailed balance can be used to synthesize the desorption results from the adsorption data and vice versa. However, I would like to present some recent results which apparently contradict detailed balance or, more accurately stated, contradict the common perception of detailed balance. As Prof. Harris stated, adsorption and desorption correspond to two regions of con- figuration space which need not necessarily have perfect overlap. At equilibrium this overlap is perfect.Indeed, it must be, as the principle of detailed balance is one of the foundations of chemistry and it must hold at equilibrium. But what if the initial condi- tions of the desorption experiment are not related to the initial conditions of the adsorp- tion experiment by a simple equilibrium in the molecular coordinates? In this case we cannot predict the properties of the desorption distribution based on the results of adsorption experiments. This is not a contradiction of detailed balance. It is, however, a case in which it is invalid to apply detailed balance as is commonly done. For the H,/Si system, we have results which appear to contradict detailed balance. Specifically, my co-workers and I at Stanford have measuredlP3 the internal state dis- tributions of H, , HD, and D, thermally desorbed from Si(lO0) and Si(ll1).In Berlin we have measured4 the translational energy of D, desorbed from Si( 100) and Si( 11 1). This enables us to sum the internal and translational energies of desorbed D, in order to determine the height of the saddle-point in the desorption transition state. This value should be closely related to the activation energy for adsorption if detailed balance holds. We obtain a value of 40 & 60 meV. This value stands in contradiction to the activation barrier height obtained by the heated nozzle experiments of Ho et aL5 and various calculation^^^^ which estimate a value of 1-2 eV. The low value that we measure is also extremely difficult to reconcile with the estimated sticking coefficient of -c That is, it is difficult to reconcile these diverse data if only the molecular degrees of freedom are considered.For the H,/Cu system, all of the gross characteristics can be explained simply be considering the molec- ular degrees of freedom. We believe that a consistent interpretation of the adsorption-desorption results can be proposed for the H,/Si system without invoking a contradiction of detailed balance, if the surface degrees of freedom are assumed to play an essential role in the dynamics. Because of the highly localized, covalent bonding in the HJSi system, the surface degrees of freedom play a much more active role in the adsorption-desorption dynamics than in the case of H,/Cu. When H atoms are chemisorbed on a Si surface, the surface relaxes and the vibra- tional properties of the surface also change substantially.In a desorption experiment, this allows the system to explore regions of configuration space which are effectively closed channels for adsorption on the clean surface. Some of the channels available in the desorption experiment correspond to low activation barrier events in the molecular General Discussion coordinates. In desorption, the adsorbates can effectively wait until they find favourable conditions for recombination and it is these low-barrier pathways that we observe. In adsorption, it is highly improbable that the low-barrier configurations present them- selves to an incident molecule because they are not within the range of normal thermal excitations of the clean surface.Furthermore, during the impulsive collision between an incident hydrogen molecule and the surface, the molecule can neither force the surface into the proper configuration (due to the mass mismatch) nor can it wait around for the surface to readjust and attain a favourable configuration. Therefore, only the high- barrier pathways are probed in the adsorption experiments. In summary, since the initial conditions of adsorption and desorption experiments are so different, in particular, because the surface configuration is so different in the two experiments, it is not valid to apply the principle of detailed balance to the observation of activated adsorption and to conclude that the desorbed molecules must have a highly energetic, non-equilibrium distribution.That is, detailed balance cannot be used carte blanche to relate adsorption and desorption distributions if the degrees of freedom of the surface play an integral role in the adsorption/desorption dynamics. There may be a substantial activation barrier for this system. However, if such exists, it is in the coordi- nates of the surface atoms and, therefore, it is impossible to probe its energetic nature directly on the basis of desorption product distributions. 1 K. W. Kolasinski, S. F. Shane, and R. N. Zare, J. Chem. Phys., 1992,96,3995. 2 S. F. Shane, K. W. Kolasinski, and R. N. Zare, J. Chem. Phys., 1992,97, 1520. 3 S. F. Shane, K. W. Kolasinski, and R. N. Zare, J.Chem. Phys., 1992,97, 3704. 4 K. W. Kolasinski, W. Nessler, A. de Meijere and E. Hasselbrink, Phys. Rev. Lett., submitted. 5 W. Ho, personal communication. 6 C. J. Wu, I. V. Ionova, and E. A. Carter, Surf. Sci., 1993, 295, 64. 7 2. Jing and J. L. Whitten, J. Chem. Phys., 1993, 98, 7466. Drs. Rettner, Michelsen and Auerbach replied: You have raised a number of inter- esting points. First, let us consider your new results for the HJSi system. We do not accept that you have shown that detailed balance does not work for this system. In order to compare adsorption and desorption experiments, the two processes must be related quite precisely. The velocity distribution in desorption at a given angle can be obtained from detailed balance if the curve for the adsorption probability, as a function of kinetic energy, is known for that angle.What appears to be known for this system is that the adsorption probability is small for all energies up to ca. 1 eV. What curve should be used to predict the velocity distribution for desorption? One that is rigorously zero until 1 eV? We need to know the numbers. Since the form of the velocity distribu- tion in desorption predicted from detailed balance is insentitive to absolute adsorption probabilities, it is only the shape of the adsorption curve that matters. For example, regardless of how small the adsorption probability is, if the probability is roughly constant at all kinetic energies up to 1 eV, we would expect a roughly Boltzmann distribution for desorption. In order to comment further, one needs the actual form of the adsorption curves.In addition to using the actual form of the adsorption curve, one should use the curve appropriate to the actual desorption conditions, including surface temperature. You state that: ‘In adsorption, it is highly improbable that the low-barrier configu- rations present themselves to an incident molecule because they are not within the range of normal thermal excitations’. Since the range of normal thermal excitations depends critically on the actual surface temperature, we need to know absolutely the dependence of the adsorption probability on kinetic energy for the surface temperature employed. Curves for lower surface temperatures (even guessed ones) should only be used very cautiously.These arguments notwithstanding, we agree that detailed balance cannot be used to relate adsorption and desorption in a totally general manner (see our comments on Dr. General Discussion Harris’s paper). In particular, detailed balance should not be applied to systems that would not exist under equilibrium conditions. But we are not aware of any reason why the H,/Si system should not follow this principle. In our opinion, careful application of the principle of detailed balance will be shown to hold for this system. The comparison must await measurements of the adsorption probability us. kinetic and internal energy under the conditions used in your desorption measurements. Prof. M. Rocca (University of Genova, Italy) commented: I should like to mention in this discussion on detailed balance that the surface can be strongly modified by adsorp- tion.In particular, I suggest that much can be learned from the 0, interaction with Ag, Pd and Pt where dissociation is observed only above a critical temperature, K,of the order of 150 K. It has been demonstrated experimentally that increasing translational energy does not help in overcoming the barrier of dissociation [in Genova for O,/Ag(llO) and in San Jose by A. Luntz for O,/Pt(lll)]. We have evidence for OJAg(l10) that the effect is connected to the onset of a local roughening of the surface which is closely related to the dissociation process and which is inhibited for tem- peratures less than T,.In the theoretical description of the chemisorption process one should therefore consider the possibility of a temperature-dependent PES. Dr. Holloway responded: I think that it is possible to conceive of trajectories in scattering that will never give rise to dissociation no matter how high the initial kinetic energy is raised. The timescale for a trapped particle to dissociate via a thermal mecha- nism is so long (approximately lo1, times as long as a scattering event) that in this time it will explore a sufficiently large region of phase-space to find the requisite ‘hole’ through which to pass and dissociate. Dr. J. Harris communicated in response to Prof. Rocca: You are quite right to say that large scale changes akin to surface phase transitions can have a strong influence on the kinds of trajectories that contribute to, in particular, desorption phenomena.Any cooperative motion of the surface will influence the desorption of adsorbed particles in a way that would not be mirrored in the concomitant sticking process. This is especially clear cut in the case where the cooperative motion is in some sense ‘adatom induced’. Here you have quite obviously a situation where the desorption and sticking processes access quite different regions of phase space. Prof. S. Stolte (Vrije University, Amsterdam, The Netherlands) addressed Dr. Auer- bach: Your paper, in which you extract from experimental data on quantum-state-spe- cific dynamics the thermal rate of adsorption for the D2/Cu( 11 1) system for T = 300 to 1000 K triggers also for me the dzbated view-point of detailed balance and micro- reversibility. Are we really ready to wave the flag for the H, ,D2/Cu( 11 1) system, i.e.are there currently experimental data available confirming on thermal systems your results as shown in Fig. 4 and 5? Drs. Rettner, Michelsen, and Auerbach replied: It is not possible to make a detailed comparison with thermal data on the rates of dissociative adsorption for two reasons: 1. The results discussed here are on D, interactions with Cu(ll1) while the thermal data is for H,. We have made measurements for H, but have not yet completed the kind of analysis reported here. 2. There is a lack of modern high-quality thermal adsorption measurements on well characterized single crystal surfaces. Prof.Marcus asked Dr. Kolasinski: In your description of a lack, or possible lack, of microscopic reversibility in the Si + H, system, was the desorbed H, typically formed in a vibrationally excited state? If so, in the reverse process, was the sticking of the incom- General Discussion 79 jng H, also studied as a function of vibrational state of the H,? If not, it would appear that the experiments do not yet test microscopic reversibility. Dr. Kolasinski replied: In our experiments at Stanford, we did indeed find an enhanced population of v = 1, ca. 20 times greater than the thermal expectation at the surface temperature. This amounts to ca. 8% of the total population being desorbed in v = 1 for D, and 1% for H,.The adsorption of H, on Si(100) has been investigated by Ho's group at Cornell. They used molecular beams produced with the aid of a heated nozzle. Such a source produces a beam which is translationally as well as vibrationally hot. The amount of vibrational excitation which they could achieve was comparable in magnitude to that which we observed in desorption. They observed no sticking which could be attributed to the interaction of molecular hydrogen with the surface. An experiment in which a vibrationally excited state has been prepared spectroscopically and scattered from the surface, such as that for the H,/Cu system performed by Hodgson et al.', has yet to be carried out for the H2/Si system. 1 A. Hodgson, J.Moryl, P.Traversaro and H. Zhao, J. Phys.: Condens. Matter, 1991,3,5217. Dr. Holloway asked Dr. Auerbach: How can I begin to reconcile the fact that I believe that (J, m,) states will have dissociation functions S (Ei, J, m,) that depend critically upon m, and yet the shape of the experimentally determined S(E,, J) appears to be independent of J? Drs. Rettner, Michelsen and Auerbach replied: You raise a very interesting and important question. We do not fully understand why our observed adsorption functions seem to have the same width, W, and saturation value, A, independent of J. One might speculate that this behaviour is related to a strong anisotropy which mixes different M states, but this is only a loose speculation. Further work is needed to resolve this ques- tion.Prof. D. A. King (University of Cambridge) addressed Dr. Auerbach and Dr. Hol- loway: My comment relates to the problem of detailed balance in relation to adsorption and desorption processes. I wish to give three very different examples, each illustrating the care with which the principle must be applied. 1. Some years ago, we' reported angle-resolved thermal desorption data for N, from W{110}, which was shown to exhibit a lobular distribution which was attributed to a barrier for the dissociative adsorption process of 17.4 kJ mol -Subsequently, Auerbach and coworkers2 studied the adsorption process using a supersonic beam source, and reported a variable adsorption barrier, averaging 41 kJ mol- ', apparently contradicting our work.However, in the desorption process molecules adsorbed on the surface select the lowest available activation barrier, whereas in the adsorption process both the molecular orientation and the point of impact at the surface are random, and many unfavourable collisions are sampled. Indeed, the data of Auerbach and co-workers2 clearly show a threshold for the adsorption process at ca. 17 kJ mol-l, in very good agreement with the desorption data.3 2. Recently we have attempted to adsorb N2 dissociatively on Pt{ 1001 [(hex-R) and (1 x l)] using a supersonic beam source, and we had no success at all, even up to beam energies of 3 eV obtained using a hot nozzle and helium ~eeding.~ However, when Pt is heated in ammonia, decomposition to gaseous N, is observed, implying that there should be a dissociative adsorption path.Detailed balance is, however, maintained. Thus, Foner and Hudson' measured the vibrational state distribution of N, formed during NH, decomposition over Pt at 1000°C, and report that N, is desorbed with v 3 5, leading to a zero sticking probability regardless of translational energy for vibra- tionally cold N, . General Discussion 3. Adsorbate-induced surface restructuring raises the question of the proper sticking probability to be used in applying detailed balance to a desorption process, where the surface restructures during or after desorption. This can be a very large effect. For example, the Pt(100) clean surface is stable with a hex-R 0.7" reconstruction; the 0, sticking probability on this surface at thermal beam energies is ca.3 x 10-l4; but on the metastable (1 x 1) surface it is ca. 0.2.6 Since the (1 x 1)-+ hex-R 0.7" transition is rather slow, in this case desorption would (temporarily) leave a (1 x 1) surface, and the proper value for s is therefore likely to be 0.2, and not 3 x I believe that this example is relevant to the problem raised by Dr. Kolasinski. There are no situations where detailed balance is flouted, but the details may some- times be obscure. 1 R. C. Cosser, S. R. Bare, S. M. Francis and D. A. King, Vacuum, 1981,31,503. 2 J. Lee, R. J. Madix, J. E. Schlaegel and D. J. Auerbach, Surf Sci., 1984,143,626. 3 R. Raval, M. A. Harrison and D. A. King, in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, ed.D. A. King and D. P. Woodruff, Elsevier, Amsterdam, 1990, vol. 3A, p. 39. 4 X.-C. Guo, J. Bradley and D. A. King, unpublished results. 5 S. N. Foner and R. L. Hudson, J. Chem. Phys., 1984,80,518. 6 X.-C. Guo, J. M. Bradley, A. Hopkinson and D. A. King, Surf Sci., 1993,292, L786. Drs. Rettner, Michelsen and Auerbach replied: Your examples are all very good illus- trations of the care that must be used in the application of detailed balance in relating adsorption and desorption processes. Indeed, unless care is taken, apparent violations of detailed balance arise. Your first example illustrates this point rather well. In addition to your comments, we note that the N,/W(1 10) desorption data are relevant to the covered surface.These results cannot be related to adsorption measurements on the bare surface. In fact, the adsorption results were found to be almost independent of incidence angle. Applying the principle of detailed balance, we would conclude that the desorbing mol- ecules should follow a cosine distribution, in clear contradiction to the measured desorp- tion angular distributions. We suspect that the lobular distributions result from strong lateral interactions present on the covered surface. Another case that illustrates the care that is needed in applying the principle of detailed balance is that of adsorption and desorption measurements for the H,/Cu system. Adsorption is found to scale quite accurately with the energy associated with motion normal to the surface.This scaling means that the energy required to activate the adsorption process varies strongly with the angle of incidence. Yet, Comsa and David have reported1 that the mean energy of molecules desorbed after recombination is almost independent of the angle of desorption. This behaviour is an apparent contra- diction of detailed balance. A careful examination, however, shows that these desorption results are fully consistent with normal energy scaling for the adsorption and detailed balance., The apparent discrepancy arises essentially because the adsorption does not increase as a step function of the energy of incidence. 1 G. Comsa and R. David, Surf Sci., 1982,117,77. 2 H. A. Michelsen and D.J. Auerbach, J. Chem. Phys., 1991,94,7502. Prof. King communicated in response to Drs. Rettner, Michelsen and Auerbach: I was very interested in your comment on the N2/W{ 1101 system. Certainly, if the adsorp- tion path were the reverse of the desorption path, a sticking probability for dissociative N, adsorption which is invariant with incident angle is only consistent with cosine law desorption. However, I cannot agree with the suggestion that our observation of a lobular (ca. COS~.~0) desorption distribution is due to lateral interactions between adatoms. Firstly, we found a cos 8 distribution for N, recombinative desorption from W/{ 3101, independent of coverage,' despite the clear existence of lateral interactions in the adlayer; the essential difference between (110) and (310) surfaces is that N, disso- General Discussion ciative adsorption is activated on the former but not on the latter.There are many other examples of quasi-cos 8 desorption distributions for systems where the adsorption process is non-activated, even where strong lateral interactions exist, and also of lobular distributions for activated systems. Secondly, since recombinative desorption necessarily involves adatoms moving into neighbouring sites during the process of desorption, it is difficult to see how lateral interactions with the rest of the adlayer would be anything more than a second-order effect on the desorption distribution. Of course, I am not suggesting that detailed balance is violated in this case.Rather, I think that your observation, coupled with ours, remains unexplained. The temperatures at which the two experiments, adsorption and desorption, were conducted are very dif- ferent, and this may be the underlying reason. For instance, a well ordered p(2 x 2) structure, attributed to underlayer adsorption, is only formed after annealing:2 the adatoms may be adsorbed into a less stable overlayer state at lower substrate tem- peratures, whereas desorption occurs from the more stable underlayer state. But clearly, more experiments are needed to resolve this. 1 R. C. Cosser, S. R. Bare, S. M. Francis and D. A. King, Vacuum, 1981,31, 503. 2 C. Somerton and D. A. King, Surf. Sci., 1979,89,391. Dr. E. Hasselbrink (Fritz-Haber-Institut, Berlin, Germany) communicated to Prof.King: Do you mean that, loosely speaking, detailed balance is a nice principle, and that if it does not produce the right results, one only has to think harder to lift the apparent contradiction? This would indicate that the principle is not useful to predict desorption characteristics from adsorption data or vice versa, but rather only allows a check, by comparison of both sets of data, whether all changes of the system occurring upon desorption or adsorption have been considered appropriately. Prof. King communicated in reply: No, that is not what I mean at all. Detailed balance is an excellent tool, but it must be used with care and understanding; and it can be very useful in making predictions.Let me illustrate this by expanding on my N,/Pt{100) example to make a clear prediction. We know from the work of Stoner and Hudson that the associative desorption of N, from Pt produces vibrationally excited N, (v 2 5) only. From detailed balance we therefore predict a finite sticking probability only for gaseous vibrationally excited N, . We have found experimentally in accordance with this, that s = 0 for ground state N, . Now we can confidently predict significant sticking for 2, 2 5. Of course, this is a consequence of time reversal of trajectories. The N,/Pt{lOO} results can be interpreted using the simple PES sketched in Fig. 1, with a so-called late barrier. Because of the height and position of the barrier, any trajectory taken by a desorbing molecule will involve significant molecular vibrational excitations (e.g.trajec-tory A, shown as a full line). An unsuccessful adsorption trajectory, B, is shown as a dashed line. By time reversal we readily see that only trajectories like A can lead to dissociation. Prof. Marcus communicated : In respect of the discussion on microscopic reversi- bility, I would like to add a few remarks which supplement those already present' in the literature. Suppose we consider for the sticking experiment an incident beam of molecules with known velocity, known angle of incidence to the surface, and in a known internal state (rotational-vibrational-electronic) or in a known distribution of internal states. We con- sider a desorption experiment for a solid sparsely populated with the absorbate, and consider the case of an (assumed) equilibrium distribution of the adsorbate on the various surface sites, a surface with a known temperature.This local equilibrium General Discussion dN-N Fig. 1 Schematic potential-energy surface representing dissociative adsorption of a molecule such as N, restriction will exclude certain systems from the present comment. State-to-state reversi- bility (microscopic reversibility) is a consequence, of course, of the laws of dynamics, be they quantum or classical. When these state-to-state quantities are averaged over an equilibrium ensemble, one obtains a microscopic reversibility for an equilibrium system (more precisely, detailed balance, since were are now dealing with an ensemble).It is only for constrained ensembles that possible departures from detailed balance may occur. However, detailed balance should follow for the ensemble assumed above, upon averaging the state- to-state quantities over that ensemble. 1 T. B. Grimley and S. Holloway, Chem. Phys. Lett., 1989, 161, 163, and references therein. Dr. J. Harris communicated in reply: Your argument is subject to the formal objec- tion that the ‘assumed thermal distribution’, insofar as this refers to adsorbates of finite binding energy, must correspond to zero coverage. Certainly, this may be a purely formal objection of the ‘nit-picking’ variety, However, the point is not that such things as ‘quasi-equilibrium’ or approximate reciprocal relationships, as they follow from assumed conditions of detailed balance, do not occur.The statement is only that they may or may not occur, In order for the concept of detailed balance in non-equilibrium ensembles to be useful it would be necessary to establish which systems, or classes of systems, can be relied upon to exhibit ‘quasi-equilibrium’ distributions (or within which bounds of accuracy it would be legitimate to assume such distributions). Prof. A. Gonzalez Ureiia (Universidad Complutense de Madrid, Spain) said: This is a question for Dr. Auerbach related to Dr. Holloway’s comment about the fact that no resonances are shown in your data on the energy dependence of the dissociation prob- ability. I would like to know the translational energy resolution that you have in your experiments.As you know in both crossed-beam and beam-surface scattering experi- ments resonances have only been noticed when collision energy resolutions of a few meV or even lower were achieved. Drs. Rettner, Michelsen and Auerbach replied: We do not believe the lack of SUE-cient energy resolution is the explanation for the fact that we do not observe the reson- ance which appear so prominently in the calculations of Dr. Holloway and co-workers. The calculated resonances are indeed much broader than the width of the adsorption functions we report. The calculations are for restricted dimensionality. Thus one possible General Discussion explanation for the difference between our observations and the calculations is that averaging over the full dimensionality of the problem reduces the resonance effects.This explanation, however, has some problems. One might expect such averaging to yield adsorption functions much broader than those we observe. Further work is required to understand the differences between our observations and the calculations. Dr. Holloway added: Probably the width of the resonances and thresholds are sufi-cient to be observable at low surface temperatures using existing technology. Prof. H. Zacharias (University of Essen, Germany) communicated : The inhibition of hydrogen sticking at low J with increasing rotational motion that you report in your paper, may reflect a more general behaviour. Earlier we have observed experimentally a strong rotational cooling in the desorption of H, and D, from Pd(100)' in the tem- perature range 325-740 K.At a surface temperature of ca. 725 K, for example, a rota- tional temperature of ca. 340 K was observed for D,. This reflects, for J = 5, a population of only 28% compared with the equilibrium population at T,. Applying detailed balance arguments the sticking of J = 5 is reduced to ca. 0.14 compared with unity for J = 0, when an exponential decrease of the sticking probability with J is assumed. Since we could measure the rotational population due to experiment con- straints only up to J = 5 we cannot assess, whether the sticking probability increases again with J at higher angular momenta as was observed by Rettner et al.1 L. Schroter, R. David and H. Zacharias, Surf Sci., 1991,258,259. Drs. Darling and Holloway communicated in reply: We agree that the inhibition of hydrogen sticking at low J is a general effect (it should be observed for all systems where there is a much larger dissociation barrier in one orientation than another) and are particularly happy to see that it has already been observed in desorption experiments from Pd(100). However, as regards looking for the decrease in sticking at high J, this only occurs when there is a late barrier to dissociation, i.e. when the barrier occurs at extended bond length. This is not generally expected for low barriers,' but we note that the results, in Prof. Zacharias' paper in this Discussion, on the same system seem to require a late barrier (on at least part of the PES) in order to be reproduced.Observa- tion of the rotational enhancement of sticking at high J and its accompanying vibra- tional enhancement of sticking, would be a good piece of evidence in support of this. 1 G. R. Darling and S. Holloway, J. Chem. Phys., 1992,97, 5182. Dr. A. P. J. Jansen (Eindhouen University of Technology, The Netherlands) communi-cated: I wonder if the classical explanation for the results of the cartwheel rotation with an early barrier is correct. Using a CCWP formalism one can write Y(s,8, t) = 1 t+kJ(s,t) exp iJ0 J(even) The equations of motion for the $J~ are J2 $Jri = [K + -+ -d0V(s, 0) t,hJ + d0V(s, 0) exp i(J'-l)Oa$ 21 2ndt 2n j ] J' Neglecting the last term results in equations of motion that differ only in the rotational energy.For the early barrier, i.e. fixed H-H distance, this is a constant. The rotational velocity may be J dependent, but as the orientational distribution is J independent, the dynamics will be the same for all J. Consequently, in order to give the molecule an orientation in which it can dissociate, the coupling between Js must be included. For an oriented H, molecule there must be 84 General Discussion many terms in the first equation above. The results of the simulations show that it is easier for low I JI to couple to other Js than it is for high I J I. The last term in the equations of motion that couples the Js depends only on the difference J' -J, which would not explain the J dependence. However, as the rotational energy depends quadra- tically on J, so that (Ko)lJl+2-(Ko)IJIcc I J 1, the coupling will be less effective for high I J 1 than for low IJ I.The fact that +2 -increases with I J I seems essential. If J2/21 in the equations of motion would be replaced by an expression with (Ko)lJl+2> (Ko)lJl (meaning high I JI states rotate faster), but (Ko)lJl+2-(Ko)\jl < -(Ko)lJl-2(meaning the increase in rotational energy is less than linear), then high I J I states would more easily become oriented so that they would dissociate more readily. Drs. Darling and Holloway communicated in reply: It is certainly true that in order to dissociate, the coupling between different J states must be included, in the limit of infinite H-H separation, the 8 dependence will be a 6 function, i.e.a constant over all J. This can be seen quite clearly in CCWP calculations of the dissociation of H, 'cartwheels'. However, to estimate relative coupling strengths based on the energetic separation of the rotational states would seem, to us, to imply that perturbation theory is valid which, owing to the large corrugation, is not true here. Also, the orientational hindering effect described in our paper is observed quite clearly in classical calculations of H2 dissociation,2 where the picture outlined by Dr. Jansen is not valid, since the rotational energy is not quantized. Unfortunately, isotope effects would tend to reduce the orientational hindering in both models, since it results in lower rotational energies and also smaller velocities, and so this cannot be used to distinguish between the two.We are not aware of any other effect which may be used. 1 G. R. Darling and S. Holloway, to be published. 2 J. N. Beauregard and H. R. Mayne, Chern. Phys. Lett., 1993,205,515. Drs. Michelsen, Rettner and Auerbach opened the discussion of Prof. Zacharias' paper: The origin of peaked angular distributions, such as those reported in your paper, is easily understood in terms of the kinetic energy and incidence angle dependence of the adsorption probability. If the adsorption increases strongly with the kinetic energy associated with motion normal to the surface, a straightforward application of detailed balance will yield an angular distribution peaked strongly around the normal direction.This is illustrated in Fig. 2, where we show a hypothetical adsorption probability func- tion together with the Maxwell-Boltzmann distributions of energy of normal motion, En,for angles of incidences Oi = O", 30" and 45". The desorbed flux at a given angle is just the product of the corresponding energy distribution and the adsorption function. The variation of the degree of overlap of the tails of the adsorption functions and energy distributions clearly has the consequence of a rapid decrease in desorption flux with angle. To illustrate this idea, and to compare qualitatively with the results presented in your paper, we have taken our determination of the quantum-state-specific adsorption probabilities for the D2/Cu( 111) system and applied detailed balance to calculate quantum-state-specific desorption angular distributions.The results are illustrated in Fig. 3(a)-(c) for desorption of molecules with rotational state J = 0 and vibrational state ZJ = 0, 1 and 2, respectively. Also shown (dashed line) are angular distributions of the form cos" (&), where n was adjusted to give approximate agreement with the numerically predicted results. For u = 0, 1 and 2, we find that the angular distributions are well represented by this form with n z 12, 8 and 4, respectively. These angular distributions were obtained assuming a surface temperature of 885 K and that the adsorption follows normal energy scaling.Our results are seen to be in good qualitative and even semi- 85General Discussion 1 EfVIeV Fig. 2 Illustration of the origin of peaked desorption angular distributions in terms of activated adsorption and detailed balance. (a)-(c) are Maxwell-Boltzmann distributions for the probability of a given normal energy for angles of incidence of 45", 30" and O", respectively. (d) is a model adsorption probability function, So. The amount adsorbed or desorbed at a given angle is calcu- lated as the product of So by the Maxwell-Boltzmann distribution appropriate for that angle. quantitative accord with the results presented in your paper. Considering the scatter in the data and the fact that the two experiments concern different faces of Cu, the agree- ment is as good as might be expected.A major uncertainty in the application of our results is our lack of knowledge of the angular dependence of the adsorption functions. At low surface temperature, we have determined that molecular beam adsorption measurements for Cu( 111) are consistent with normal energy scaling. At high surface temperature, results might scale with Ei cosmOi with rn < 2. Likewise a value of rn < 2 might be appropriate for Cu(100). We find, however, that decreasing rn to 1.5, say, broadens the angular distributions only slightly. The u = 0, J = 0 results broaden from a cos', 8, dependence to a cosl0 8, dependence, for example. Prof. Zacharias responded : The agreement between the predicted angular distribu- tions and those measured by us is indeed fairly satisfying, The remaining uncertainty from a possible angular dependence of the sticking function could, in principle, be solved by measuring, with internal state selectivity, the velocity distribution of molecules desorbed at defined angles.However, this task is currently beyond the sensitivity of our apparatus. Prof. Stoke said: In your paper you report that your beautiful measurements of the state-dependent angular distributions for the associative desorption of hydrogen from Cu( 11 1) exhibit a strong coupling between the internal and translational degrees of freedom. Would one expect the presence of such a coupling also to the orientation/ alignment properties of the H, molecules desorbed from the surface.The polarization dependence of the REMPI detection method applied could possibly inform us about the presence of such a coupling. General Discussion Fig. 3 Polar plot of the angular distributions for D, being desorbed from Cu(lll), calculated using the adsorption functions from our paper. The points are values of the calculated angular distributions and the solid lines cos” distributions, shown for comparison. Results are shown for three vibrational states, u = (a) 0, (b) 1 and (c) 2. The corresponding values of n are 12, 8 and 4. The results are all for rotational state J = 0 and a surface temperature of 885 K. Prof. Zacharias replied: A few years ago we carried out a (1 + 1’) KEMPI experi- ment to measure the rnj population in rotational states of hydrogen desorbed from Pd(lOO).l The ion signal from desorbing H, (u” = 0, J” = 1) showed a significant depen- dence on the direction of the polarization of the laser light, E, relative to the surface normal, 2.The ratio of the signal with E perpendicular to 2, I,, and E parallel to 6, Z II , observed was Z,/Zll = 0.57. The ionization signal from isotropic hydrogen did not show any dependence on the orientation of the laser polarization. However, the interpretation of this experimental finding is not straightforward. The signal detected is due to Hi ions generated in the (1 + 1’)REMPI process: X ‘Z;(U” = 0, J” = 1) + hv,,, + B ‘Z.U+(U’= 3, J‘ = 0) -PB ‘Z;(U’ = 3, J’ = 0)+ hv,, H;(u*, J* = 0, 1) HZ -P Hl ,Zt(v, J) The H; state which is reached by UV laser excitation from the B ‘Z: state is a super- position of a continuum state and a high molecular Rydberg state.The high-lying General Discussion 87 Rydberg state, which is dominantly excited in this process, subsequently autoionizes. It is known experimentally that the relative contributions of the continuum and the stable states to the mixed state change drastically with the wavelength of the exciting UV radiation. 9 In order to interpret the polarization dependence of the signal in terms of a J vector alignment one has to know the directions of the transition dipole moments relative to the molecular axis for both, the state selecting B tX exciting transition and the ionizing Hl + B transition.The first step is a parallel transition. The second step includes a contribution from a parallel transition, ,Ef + e-tB ‘X; , and one from an unknown sum of one or more unidentified Rydberg states. This last contribution makes any inter- pretation of the polarization dependence of the signal highly speculative, if not imposs- ible. This problem can be avoided only either by calibrating the polarization dependence on a sample with known mjanisotropy, or by using only VUV laser-induced fluores- cence via the BIZ: state to measure the mjdistribution. Although this last method is much less sensitive than the REMPI scheme, it provides reliable results. Such measure- ments are currently in progress in our laboratory.1 L. Schroter and H. Zacharias, J. Chem. SOC.,Faraday Trans. 2,1989,85, 1361. 2 W. Meier, H. Rottke, H. Zacharias and K. H. Welge, J. Chem. Phys., 1985,83,4360. 3 W. Meier, H. Rottke and H. Zacharias, Inst. Phys. Con$ Ser., 1989,94, 93. Dr. Darling said: The purpose of this comment is to point out the danger of inter- preting complicated desorption data solely in terms of a two-dimensional model calcu- lation. The authors observe a population of the v” = 1 state of desorbing D, which is in excess of a Boltzmann population, and additionally that the TOF for D, is best matched by assuming a translational temperature in excess of the surface temperature, T,, by ca. 90 K (although T, is a good fit for H,). In the standard language of two-dimensional ‘elbow’ potentials, this implies a non-zero barrier to desorption which occurs at finite bond extension.Invoking microscopic reversibility, this gives a late barrier to disso- ciation. In other words, the dissociation is activated and is greater for vibrationally excited molecules than for vibrationally cold, i.e. there is a vibrational enhaiicement of the sticking. The model PES used exhibits such features, however, previous experiments have shown that the dissociation barrier is approximately This being the case, one would expect it also to be early,3 so there would be no vibrational enhancement of the diss~ciation.~ This contradiction can be resolved if we simply note that the PES is not the same at all surface sites or molecular orientations.The experimental results of Rendulic et al., show a slow, steady increase of the sticking with translational energy indicative of such a distribution of barrier heights, and recent calculations of the PES for H,/Mg(0001) show very different PES topologies at different sites.’ To restate, then, it is not that one two- dimensional PES is better than another, but that the total effects are produced by inter- action with many sites corresponding to different two-dimensional PES. Obviously, this will have an influence on the shapes and energetic locations of the dissociation/ desorption probabilities, which in turn determine the Eoltzmann plots shown in Fig. 2 of your paper. It has been shown previously that inversion of such plots to obtain the dissociation probabilities is a non-unique pro~ess.~.~ Bearing this in mind, it is still an important observation to note that the vibrational state-resolved aspects of the desorption require, for explanation, a late, non-zero barrier to dissociation.This should, in principle, be observable in molecular beam experiments by comparing the sticking of seeded and unseeded molecular beams at the same ‘normal energy ’. 1 G. Comsa, R. David and B-J. Schumacher,Surf. Sci., 1980,95, L210. General Discussion 2 K. D. Rendulic, G. Anger and A. Winkler, Surf: Sci., 1989, 208,404. 3 see, for example, J. Harris in this Discussion. 4 D. Halstead and S. Holloway, J. Chem. Phys., 1990,93,2859. 5 D. M. Bird, L. J. Clarke, M. C. Payne and I.Stich, Chem. Phys. Lett., in the press. 6 G. R. Darling and S. Holloway, Surf Sci., 1992, 286, L305. 7 H. A. Michelsen and D. J. Auerbach. J. Chem. Phys., 1991,94,7502. Dr. A. Gross (Technische Universitat Miinchen, Germany) commented : Neglecting the lateral corrugation of the surface in a simulation of an associative desorption process is certainly justified if there is one preferred reaction path to desorption which is energeti- cally much more favourable than all others. Recent two-dimensional calculations by Russ and Brenig’ with a more realistic PES than that presented in your paper show an even better agreement with experiment with regard to the vibrational heating of the desorbing molecules. However, a small barrier is needed in order to reproduce the vibra- tional heating.This barrier leads to translational heating of the desorbing molecules which in the case of H, is at variance with experiment. The inclusion of a physisorption well in front of the barrier reduces translational heating, but also vibrational heating. One possible explanation for the absence of translational heating may be energy transfer to the phonons which is neglected in two-dimensional calculations. 1 W. Brenig and R.Russ, to be published. Dr. Darling opened the discussion of Dr. Billing’s paper: You state that ‘since the zero-point energy and the vibrational energy spacing of deuterium is smaller than that of hydrogen, one would expect a T-V energy transfer mechanism to be more effective for D, than for H, .Therefore the smaller D, dissociation probability can be assigned to . . . the higher energy loss . . . to the surface phonons’. This is, however, incorrect. It is not the absolute vibrational energies which are important, but the change in these as the molecule travels ‘round the elbow’, through the interaction region. This change is greater for H, than for D, and so, for a late barrier PES, one would expect the disso- ciation of D, to be less than that of H2 in the absence of inelastic effects, as shown in the calculations of Hand and Holloway ’and Halstead and Holloway.2 1 M.Hand and S. Holloway, Surf Sci., 1989, 211/212, 940. 2 D. Halstead and S. Holloway, J. Chem. Phys., 1990,93, 2859. Dr. A. Harris (A T & T Bell Laboratories, New Jersey, USA) added: I would like to follow up on the previous question regarding the nature of the reactivity difference of D, and H,.In your paper you attribute the reactivity difference to more efficient energy transfer from D2 to the lattice before the transition state is reached. Do you have any feeling for the relative importance of these two effects, at least using the potential-energy surface that you have discussed? More generally, how much would the reactive sticking probability increase for either H, or D, if no energy transfer occurred? How much of this effect can be attributed to the electronically non-adiabatic effects? Prof. Billing replied: We have not investigated this particular point. On one of our surfaces the barrier for chemisorption is early so here I would not expect a large zero- point vibrational effect.Since we are speaking about a tunnelling process the main dif- ference in the two cases will simply be due to a mass effect in the tunnelling probability. However, on top of this comes the phonon energy loss, which, since the sticking prob- ability varies rapidly with energy, can give a substantial change in the energy available for the tunnelling process. A rough estimate can be given by decreasing the kinetic energy with the phonon energy loss, which is 5 to 10%. We expect that the difference is mainly due to the phonon coupling and less to the inelastic electronic effects since they typically, when included, only change the energy transfer by ca. 20-30%.(See e.g. ref. 1.) General Discussion 1 G. D. Billing and M. Cacciatore, Surf. Sci., 1990, 232,35; G. D.Billing, Chem. Phys., 1987, 116, 269; M. Rakovshik and G. D. Billing, Chem. Phys. Lett., 1991,185, 1. Dr. Auerbach asked: In the summary of your paper, you state that electron-hole pair excitation is important in the energy transfer, even at low collision energy. Can you elaborate on this point. What is the indication in your calculations that this is the case? How big is the effect? It would be fascinating to try to observe this eEect. Is there a distinct experimental signature predicted by your results? Prof. Billing replied: We have seen the effect of electron-hole pair excitation in the energy accommodation and in the scattering angle, i.e.in the energy loss loops (ref. 1). We would expect to see the effect of this process more at low impact angles and higher energies. However, it is probably difficult to design an experiment which distinguishes between phonon and electronic friction, since both are present. However, our investiga- tions seem to indicate that the latter will take over at increasing energies and low approach angles. 1 G. D. Billing, Chem. Phys., 1987, 116, 269; M. Cacciatore and G. D. Billing, Surf. Sci., 1990, 232,35. Dr. Holloway asked: Can you explain why your PESs appear very smooth at the seams and yet you obtain large inelasticity due to electron-hole pair excitation? In a true theory, of course, these would be coupled and not introduced separately.Prof. Billing replied: In the contours of the PES one process is, so to speak, hidden. This is the ‘adiabatic’ charge-transfer process, i.e. the effect of this process is taken into account by running trajectories or wavepackets on the lower adiabatic potential surface. On top of this we include inelastic electron-hole pair excitation processes. These pro- cesses do couple to the dynamics through an effective potential. However, it is not this effective potential which is shown in the figures, it is the adiabatic potential. Dr. T. F. Heinz (IBM T. J. Watson Research Center, New York, USA) said; In your paper you state that electron-hole pair excitation, while not in itself significant for energy transfer, may have an important indirect effect on the efficiency of coupling between an incident molecule and substrate phonons.This situation would appear to imply that the motion of the molecule is appreciably altered by electron-hole pair cre- ation, but in such a way that the net interaction involves little energy transfer. First, could you give some more details describing this process? Secondly, could you indicate any experimental signatures of non-adiabatic effects of this type? Prof. Billing replied: As I mentioned in my answer to Professor Auerbach we expect to see an increase in the importance of electron-hole pair excitation compared with phonon excitation at higher energies and smaller approach angle. But I doubt whether the experimental signature comes as an abrupt change. Rather, one would see a gradual transition from a region where one mechanism dominates to one where the other domi- nates.Dr. Holloway said: I think that the depth of the resonance in the modified PES (Fig. 2) must severely perturb the dynamics. There is no experimental evidence for this (i.e. a dissociation probability that initially drops before taking of€). Prof. Billing communicated in reply: The PES (Fig. 2) is the adjusted ab initio surface. It is adjusted to have a barrier at about 0.5 eV. It should be mentioned that we did not have any ab initio points for distances less than 0.9 8, from the metal-surface and that values at small z values are less accurate. Hence the indication of a chemisorbed General Discussion molecular state which the surface exhibits for this particular geometry may not be real.Its presence increases the residence lifetime at the surface and would therefore affect the dissociative sticking probability at energies below the barrier. This is also seen in the calculated sticking probabilities which do not drop as rapidly with decreasing energy as the experimental values. So I agree that it may be an artefact due to the extrapolation into a region where there are no ah initio points. Prof. R. Kosloff (Hebrew Uniuersity, Jerusalem, Israel) said : The mixed classical quantum calculations just described are based on a time-dependent self-consistent field (TDSCF) approximation. The dissociation of molecules at a surface split the wavefunc- tion to a reactive and non-reactive part.This in turn causes a correlation between the reactive degree of freedom and both classical degrees of freedom. What theoretical means are used in your work to overcome this problem, if it is important? An even more severe case of correlations exists for reactions which take place on more than one adiabatic surface. See for example ref. 1. 1 R. Kosloff and A. D. Hammerich, Faraday Discuss. Chem. Soc., 1991,91,239. Prof. Billing replied: It is true that the TDSCF method can only deal approximately with this problem and a multi-configuration method should be used instead. The way we try to deal with this splitting is simply that the part from the wavepacket which leaves the surface is used for determining the dynamics of the remaining classical degrees of freedom for the molecule being scattered away from the surface. If one wishes to follow the dynamics of the adsorbed atoms one should use the other part of the wave- packet for this purpose.In our case the latter wavepacket is being absorbed by an optical potential at the grid edge and we have therefore not considered this possibility. Furthermore, we only use the wavepackets at low energies, where the non-adiabatic transition probability to the upper adiabatic surface is small. Thus the classical dynamics is assumed to follow the lower surface irrespective of the non-adiabatic process. Prof. A. W. Kleyn (FOM Institute, Amsterdam, Netherlands) asked: 1. At these dis- cussions and also elsewhere many theoretical studies have been presented concerning H, and D, interacting with Cu(ll1).Do all these studies converge to the same physical picture of the interaction or do discrepancies remain? 2. Is the PES you use similar to the others used in the trade? 3. How sensitive is the importance of the electron-hole pair channel to the choice of the PES and relevant parameters? Prof. Billing replied: Our original potential surface was similar to others in the sense that the barrier was ca. 0.9 eV, which, however, when compared to experimental data, is too high. On the other hand LDA calculations apparently underestimate the potential surface (see e.g. ref. 1). As far as the qualitative behaviour is concerned there are also some differences. We have a barrier for chemisorption of molecular hydrogen in the entrance and a barrier for dissociation in the exit channel.This could easily be due to insufficient ah initio information or to the representation of the data. This representation was taken in a pair-wise additive form in order to be able to include the phonon forcing in a straightforward manner. The electron-hole pair excitation is sensitive to the potential surface in the sense that the molecule may come closer to the surface if the potential parameters are changed and hence the interaction with the electrons will increase and thereby the electronic ‘friction’. 1 J. A. White and D. M. Bird, Chem. Phys. Lett., 1993, 213,422. Genera2 Discussion Prof. Kleyn said: You seem to show in your Table that the sticking probability has a lateral dependence.This is well known to occur. Holloway et aE. have invoked this for interactions at thermal energies.' Horn et al. have seen this for alkali-Ag( 11 1) inter-actions at hyperthermal energies2 Is this surprising to you in view of the specific system you consider? 1 D. Holstead and S. Holloway, J. Chem. Phys., 1988,88, 7197. 2 T. C. M. Horn, Pan Haochang, P. J. van den Hoek and A. W. Kleyn, Surf: Sci.,1988,201,573. Prof. Billing replied: We find that the sticking probability is determined from many different factors all of which may be important. These are: site dependence of the reac- tion barrier, the amount of energy transfer to the surface, non-adiabatic curve-crossing effects, the initial quantum state of the molecule and the position, width and magnitude of the barrier.The importance of some of these aspects can be predicted without actual calculations. For instance, will the energy transfer play a smaller role for light mass molecules, i.e. is this effect less important for hydrogen than for deuterium? Also the strong site dependence appears to be a universal feature but unless the details of the multidimensional PES are known only quantitative predictions can be made. Prof. T. Uzer (Georgia Institute of Technology, Atlanta, USA) communicated: When using the calculationally advantageous classical or semi-classical methods to model reactive processes, the results could differ substantially from quantal calculations if the process takes place near the energy theshold.In this region, often quantization con-straints as well as the zero-point energy of the vibrations involved restrict the energy available for the quantum-mechanical process quite drastically. One case in point is our recent modelling' of the predesorption proce~s~?~ substrate -CO (v = 1) +substrate + CO (v = 0) Here, one quantum of CO-stretching excitation is used to break the weak substrate- surface bond. When treated classically, the energy reservoir (the CO stretch) can release arbitrary amounts of its energy (including all of it) to the reactive desorption coordinate, whereas in the quantal calculation only one quantum can be released. As a result, we find that, depending on excitation, the classical rate can be several orders of magnitude faster than the quantal rate.4 1 Y.Guan, J. T. Muckerman and T. Uzer, J. Chem. Phys., 1990,93,4383,4400. 2 J. Heidberg, H. Stein and H. Weiss, Surf: Sci.,1987, 184, L431. 3 H-C. Chang and G. E. Ewing, Chem. Phys., 1989,139,55. 4 Y.Guan, J. T. Muckerman and T. Uzer, J. Chem. Phys., in the press. Prof. Billing replied: In the low-energy range we of course have to use a quantum- mechanical description of the tunnelling and dissociative degrees of freedom : However it turned out that our quantum and classical mechanical calculations are consistent at energies above the barrier (see ref. 1). Thus we believe that this mixed quantum4assical description is adequate for studying dissociative sticking processes.1 G. D. Billing, A. Guldberg, N. E. Henriksen and F. Y. Hansen, Chem. Phys., 1990,147, 1. Dr. J. Harris said : Advances in electronic structure calculations, specifically in density-functional methods, are such that it cannot, in general, be considered adequate to use parameterized potentials, or PES constructed on an ad hoc basis. It is now quite possible to obtain reliable information with useful accuracy for most surface processes and adsorption systems. General Discussion Prof. Billing communicated in reply: Our PES is not ad hoc. It was obtained as a fit to ab initio points. Unfortunately, neither standard SCF/CI methods nor local density methods are yet always reliable as far as the potential barriers are concerned.Therefore some empirical adjustment has to be made. But the situation here just resembles the one known from gas-phase reactive scattering, where similar adjustments of ab initio data are made. Dr. D. Bird (University of Bath) commented: I would like to point out that one can do much better now than use an essentially empirical PES for the H,/metal interaction, like Fig. 2 in Prof. Billing’s paper. We have recently performed first principles density functional theory calculations (using a plane-wave pseudopotential method) for H,/ Cu (001)’ to explore a number of sections through the six-dimensional PES. We find no sign of the molecularly chemisorbed precursor state which is very marked in Prof. Billing’s work, but we do find a considerable surface corrugation, both in the hindered rotation/translation of the transition state and in the variation of the barrier height across the surface. 1 J.A. White and D. M. Bird, Chem. Phys. Lett., 1993,213,422. Prof. Billing communicated : As mentioned before, the surface was not empirical but fitted to the available ab initio data. However, these data did not include any informa- tion on the dependence on the surface phonon coordinates, i.e. the calculations were done for the equilibrium positions of the lattice atoms. In order to ‘extract’ this informa- tion we had to introduce an atom-atom representation of the potential. This informa- tion is necessary for including the phonon forcing, which we know is important. But we also know that non-adiabatic electronic transitions can strongly affect the sticking prob- ability (see ref.1).If this is so I think that one has to rely on empirical or semi-empirical PESs for some time yet. The reason being that methods based on the Kohn-Sham equation only operate with the lower electronic surface. 1 N. E. Henriksen, G. D. Billing and F. Y. Hansen, Surf. Sci., 1990,227,224; G. D. Billing, A. Guldberg, N. E. Henriksen and F. Y. Hansen, Chem. Phys., 1990,147, 1. Prof. Zacharias said : The very promising developments in electronic structure calcu- lations are highly welcome. Calculations of reaction dynamics should be performed on such potentials, once they are available for the HJPd system. It may be interesting to note that internal state resolved experimental data are currently also being determined for the H,/Ni system.’ These d metals certainly have a different electronic structure than the theoretically often featured s metals.The variation of the interaction over various geometrical configurations across the unit cell found theoretically for H,/Cu(100) is certainly interesting. For our group it is especially interesting that orientational effects are calculated, which in principle can be probed experimentally by the polarization dependence of VUV laser-induced fluores- cence. However, in an experiment where the desorption products are probed, it might be justifiable to assume that the reaction occurs along the lowest energy path. Depending on the amount of variation in the barrier heights at different locations the recombi- nation process may then be modelled using just a single two-dimensional potential to provide an understanding of the basic processes.Our measurements indicate that the coupling of the rotation and the translation in the HJPd system is weak, which is different from the H,/Cu system. Moreover, the energy separation between vibrational and rotational states in hydrogen is large. A full six-dimensional calculation thus appears not to be necessary to describe the behaviour of H, vibration and translation in desorption. General Discussion The nearly perfectly accommodated translational energy of H, to the surface tem- perature, but yet the significant vibrational heating is still not understood, as Dr. Darling correctly mentioned. The vibrational heating implies that there is a barrier between the adsorbed hydrogen atoms. This barrier leads then to additional trans- lational energy as the newly formed molecule departs from the barrier. The incorpor- ation of an attractive precursor state after the barrier, as was recently done by Brenig and RUSS,~ slows the desorbing molecules down to some extent, while retaining the vibrational heating. However, an excess translational energy still results from the calcu- lation. Thus, it may be necessary to include the interaction of the departing molecules with surface phonons in the calculation to obtain a satisfactory theoretical description of the experimental results. This reasoning finds additional support from adsorption experiments when one con- siders the behaviour of the initial sticking coefficient so as the hydrogen beam energy is ~aried.~Sticking increases strongly from ca. 0.24 to 0.65 as the beam energy is decreased from 1200 to 125 K. It also increases slightly from so = 0.24 to so = 0.34 as the beam energy is increased from 1200 to 2400 K. For high beam energies the angular distribu- tion of the sticking coefficient is also slightly forward peaked (COS" 9, n = 1.6). This may be taken as a hint that a distribution of barrier heights across the unit cell may be sensed by adsorption experiments. 1 G. Pozgainer, K. D. Rendulic and A. Winkler, Surf: Sci., in the press. 2 W. Brenig and R. Russ, personal communication. 3 K. D. Rendulic, G. Anger and A. Winkler, Sutf Sci., 1989,208,404.

ISSN:1359-6640    

DOI:10.1039/FD9939600067

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96,95-104 Photochemistry of C2H2on NaCl(100) S. Keith Dunn and George E. Ewing Indiana University, Bloomington, IN 47405, USA Recent experiments show that the photochemistry of C,H, on NaC1( 100) is remarkably simple, producing only hydrogen/deuterium exchange: C,H, + C,D, e2C,HD. A new mechanism of this surface bound reaction is proposed. We suggest that it is the substrate, NaCl, that absorbs the exciting 184.9 nm photons to produce self-trapped excitons (STE). The triplet STE then transfers its energy to adsorbed acetylene which then diffuses along the surface and reacts with its neighbours to achieve the hydrogen/deuterium exchange. In this paper we continue our exploration of the photochemistry of acetylene on NaCl( 10O).'q2 We have chosen this particular substrate because so many properties of this alkali-metal halide are well explored.We have chosen acetylene as the adsorbate because its gas-phase properties, including its photochemistry, studied over the '9'decades3-'continue to intrigue both experimentalist^^-^ and theoreticians.' ' More-over, we have determined the adlayer structure of acetylene physisorbed to NaCl(100) by polarized infrared spectroscopy. ' Salt Spontaneously formed NaCl crystals are simple cubes. The size scale of these cubes (with occasional rectangular shapes) ranges from 10 to 100 nm for salt crystals sublimed in uacuo, as observed by transmission electron microscopy (TEM).I3 Evaporation of ocean brine produces pm sized cubic ~rystal1ites.l~ Salt for seasoning, that appears on our dining-room table, consists of nearly perfect cubes, with dimensions somewhat less than 1 mm, as examination with a simple lens will show.Boules of NaCl drawn from a melt, are easily air-cleaved along their (100)planes with a small hammer and chisel to produce cubes or any rectangular shapes whose dimensions can be tens of centimetres.' Microscopic examination of the faces of the larger NaCl crystals has been provided by a variety of techniques. One of the early demonstrations of the wave properties of matter was by helium scattering from a slab of air-cleaved salt by Estermann and Stern in 1930.16 They showed that the diffraction pattern from the NaCl(100) face was consis- tent with the ion spacings of the bulk crystal.Both TEM17i'8 and atomic force micros- copy (AFM)" measurements on the surfaces of single crystals reveal flat terraces extending for 100 nm or so which are then interrupted by steps of atomic dimensions. Infrared spectroscopy of probe molecules physisorbed to single crystal NaCl( 100) is also consistent with the regularity of these surfaces.20.21 These techniques continue to be #applied to explore the surface of salt samples with dimensions of the order of 1 cm. Surface diagnostics for pm and sub-pm sized cubic crystallites, while being less direct, are nevertheless consistent with exposed (100) faces. Isotherms of CO physisorbed to both single ~rystal~~,~~ and crystallite samples24 at similar temperatures yield compa- rable heats of absorption.Moreover, these heats of absorption are consistent with calcu- lated values of CO bonded to Na' sites at the (100) s~rface.~'~~~ The position of the main fundamental infrared absorption band of CO on the crystallites is within 0.1% of 95 Photochemistry of C2H2on NaCl( 100) its value on single crystal NaC1(100).27 Yet there are differences in the infrared spectros- copy on the two substrates. Satellite absorption features and an increased bandwidth for CO on crystallites is consistent with the expected heterogeneity of their surfaces. This heterogeneity arises because the fraction of sites at corners or edges of 100 nm cubes approaches 1% of those on face and vacancies or other defects can become trapped at the surface.28 In general, however, thermodynamic, theoretical, and spectro- scopic evidence shows that the crystallites, like the large single crystals, primarily expose their (100) faces.High-purity single crystals of NaCl have a wide transparent range, only becoming opaque in the ultraviolet below 170 nm and in the infrared beyond 15 pm.15329 Some of the energy states of the pure crystal that we will refer to later are given in Fig. 1. In particular, absorption near 145 nm (69 000 cm-') signals transition from the valence band to the conduction band.30 Transitions to longer wavelengths (to 170 nm) correlate to excited Rydberg states of an isolated C1- that in the crystal becomes delocalized into free exciton~.~'~~~ The free excitons, in turn, distort the crystal lattice such that pairs of halide ions become drawn together to produce the excited molecular ion, [Clie-1, where the brackets indicate the presence of the surrounding lattice.The first excited states of this STE are bound and are of character 'XT and 'Xi. They can relax radi- atively to a repulsive 'El,ground These states and their transitions are shown in Fig. 1. Defects induced by doping or radiation can give rise to colour centres in single crystals. The corresponding absorptions in the visible and ultraviolet have been widely e~plored.~~~~~~~~*~~ Optical properties for salt crystallites are similar to those of single crystals in the infrared. This has made them useful substrates for a variety of spectroscopic experi- NaCl [Cl, e-] HCCH (SW80 60 40 20 0 Fig.1 Energy level diagram for the NaCl ~ubstrate,~' the STE33,38([Clye-I), acetylene5' and ~inylidene.~The C and A notation for acetylene refers to linear geometries, while the A and B notation in parenthesis corresponds to the trans-and cis-bent isomers, respectively. The large and small arrows correspond to radiative and non-radiative transitions. S. K. Dunn and G. E. Ewing nient~.~~?~',2 However, defects incorporated into the crystallites during preparation increase their absorption throughout the ultraviolet and into the visible to give them a blue ~ast.~~?~' The optical properties we have been reviewing are associated with transitions in the interior of crystals or crystallites.STEs and colour centres at the surface of NaCl have also been the subject of a number of investigation^.^'-^' Acetylene A manifold of some of the electronic states of acetylene together with those of salt are reproduced in Fig. 1. All these excited states correlate to nz +-nu transitions from the ground state.49 The singlet state~,~' 'A, and 'B,, are accessible by the 184.9 nm mercury transition shown by the vertical arrow to the left of Fig. 1. The singlet of vinylidene isomer C=CH2, 'A,, is above that of HCECH ground-state' singlet, 'A,. Among the triplet excited states5' are the HC=CH isomers, trans-bent 3B, and cis-bent 3B2 which correlate to 'C: for the linear molecule and trans-bent 3A, and cis-bent 3A2 which correlate to 'C, and vinylidene'*'' 3A2 and 3B2.Some of these isomers may well be participants in the photochemistry we will describe.The dissociation energy' for C2H-H is at DO, = 45 800 cm-', below that of one of our excitation lines, 184.9 nm (54069 cm-'), but inaccessible to another, 253.7 nm (39 412 cm-'). In the 184.9 nm photochemistry of gas-phase acetylene Zelikoff and Aschenbrand found that two distinct mechanisms are imp~rtant.~ One involves excited-state acetylene molecules, while the other involves radical formation. The polymer is formed by excited metastable molecules colliding with those in the gound state according to the following reactions : C2HT + C2H2-+ C4H4* (1) C4H4*+ C2H2-+ C,H,*, etc. (2) where * represents electronic excitation.Other photolysis products, such as diacetylene and molecular hydrogen, are formed by radical production C2H2+ hv + C2H + H (3) with quantum yield,4 @ = 0.06, followed by the recombinations, C2H + C2H -+ C4H2 (4) H+H-+H2 (5) They found no evidence for radicals promoting polymerization, C2H + C2H2 -+ C4H2 + H. (6) However, H atoms do react with C2D2in the gas phase as follow^:^^-'^ H + C2D2F? C2H,Dt (74 C2H,Dt 4D + C2HD (7b) where t represents vibrational excitation. When thermal (300-400 K) H atoms are used, the C2H2Dt intermediate has a lifetime of the order of 1 ns, so that collisional vibra- tional relaxation competes with unimolecular dissociation. However, when high- energy (1 eV) H atoms are used, there is no intermediate complex; the isotope exchange occurs through a direct displacement reaction :52 H + C2D2-+ C2HD + D.(8) Since there is no long-lived intermediate, little internal equilibration of the collision energy takes place, so the D atom produced in eqn. (8) is translationally hot. Photochemistry of C,H2 on NaCl(100) While gas-phase acetylene photolysis is ineffective with 253.7 nm radiation, it is readily achieved on the addition of mercury vapour. The excited Hg (3P1)formed reacts with C2H2to produce triplet acetylene5 and hydrogen, vinylacetylene and benzene.56 Acetylene and NaCl(100) Acetylene is physisorbed to the (100) faces of both crystallites and single crystal NaCl.'i29' Our experimental preparation of these substrates and methods for determin- ing isotherms are described elsewhere.'~2~12~27 The results are shown in Fig.2. At 152 K we have adsorption on crystallite NaCl. The substrate has been produced by in vucuo sublimation of a salt sliver weighing ca. 50 mg and yields a surface area of ca. 10 m2 corresponding to a film of cubic crystallites with dimensions ca. 100 nm. The crystallites are calibrated to determine the number of Na' (or Cl-) adsorption and then acetylene is admitted to the system. The fraction of sites covered, 0,and the equilibrium gas pressure are measured. The curve through the data is a Langmuir isotherm with 0 increasing gradually with pressure from to 10 mbar. At 84 K the isotherm was measured on single crystal NaCl with a total surface area of only ca. 10 cm2.Here the extent of coverage, measured photometrically,'2 appears as a step function at an equi- librium pressure of 2 x mbar. While these isotherms are qualitatively different, a single model of the adsorption process is consistent with physisorption to NaCl( 100) faces. Application of the quasi- chemical adsorption approximation finds a bond between acetylene and the surface of 30 kJ mol-' and a much weaker near-neighbour acetylene attraction of 4 kJ mol-'. At higher temperature, e.g. 152 K, the near-neighbour interactions are relatively unimportant and molecules are adsorbed to surface sites with near disregard as to whether near-neighbour sites are occupied or not. This adsorption process follows Lang- muir behaviour as observed.At low temperatures neighbouring attractions are now important. Adsorption occurs with island formation and full coverage is achieved pre- cipitously, again as observed. I, 84 K 152 K 1.0 -QFA O 0.5 -0.0 --A 4 I //// I I I I S. K. Dunn and G. E. Ewing high-temperature phase low-temperature phase +*++.++++++*++*+ + + + + ++ + + + + + + +++++ + + + + t + ++++++++++ ++++A + + + Fig. 3 Two phases of acetylene on NaCl. The structure of the low-temperature phase is from ref. 12 The characteristic temperature, r, across which islands do or do not occur, is obtained from the near-neighbour interaction energy.57 For acetylene T, = 90 K. Above K, acetylene forms in a high-temperature or lattice gas phase as suggested in Fig.3 from the model of Uebing and G~mer.~~ Here these molecules, which at sub-monolayer coverage are confined to two dimensions, can scoot along the surface and collide with one another. Below the molecules, even at low coverage, are found mostly in islands in a low-temperature ordered phase as shown in Fig. 3. The adsorbed molecules in both the high- and low-temperature phases must, of course, make appropriate excursions away from the surfaces to establish their gas-phase equilibrium pressures. The infrared spectroscopy in the C-D stretching region of C2D2 on NaCl(100) crys- tallites and single crystal is shown in Fig. 4. (The protonated, C,H, ,spectrum shows the same behaviour and will be discussed later.) The crystallite spectrum at a coverage of 0 = 1.5 at 150 K is for the high-temperature phase.The main feature at 2405 cm-’ is within 1% of the gas-phase band origin,59 2427 cm-’. A satellite feature appearing at I .o I\ h v)w.-C 3 .I__(0.0 1500 2450 2300 2350 2300 C/cm-’ Fig. 4 FTIR spectra of C2D2 on NaCl. (a)C2D2 on crystallites at 150 K. The asterisk corre- sponds to molecules adsorbed onto defect sites. (b)C2D, on single crystal NaCl(100) at 80 K. The coverage for both spectra is 0= 1.5. Photochemistry of C2H2on NaCl( 100) 2340 cm-', and marked with an asterisk, is assigned to absorption by C2D2 adsorbed to edges of the cubic crystallites. The absorbance of this satellite feature is ca. 1% of the main band.This percentage is consistent with the fraction of edge sites for cubes, 100 nm on a side, that make up this crystallite substrate.24 The acetylene spectrum at 84 K in Fig. 4, also at a coverage of 0= 1.5, is on the NaCl(100) face of the single crystal. The absorption profile of C2D2, broadened by the heterogeneity of NaCl crystallites, encompasses the sharp triplet on the more homoge- neous NaCl single crystal surface. The analysis of the triplet is given elsewhere.12 Use of polarized infrared spectroscopy and comparison of absorption by C2H, and mixtures of isotopes reveals a bilayer structure. The bottom layer has the molecules, in a T-arrangement, lying nearly flat against the surface as shown in the low-temperature phase structure of Fig.3. An upper layer of acetylene molecules, has half the surface density of the bottom layer. Photochemistry of acetylene on NaCl(100) has so far only been possible with crys- tallite substrates. Here we have used crystallites with dimensions ca. 100 nm, that were substrates for the 150 K infrared spectrum of C2D2 in Fig. 4 and the isotherm of Fig. 2. The spectrum in Fig. 5(a) results from a 50 : 50 vol.% mixture of C2H2 and C2D2 at 150 K at a coverage of 0= 0.05. The region near 2400 cm-' resembles that of C2D2 in Fig. 4, except that the lower-frequency satellite feature, again marked with an asterisk and associated with absorption by defect-bound molecules, has an absorbance comparable to that of the main feature. Since crystallite edge (or other defect) sites bind molecules more tightly than the (100) face at low coverage, (e.g.0z0.05),these sites are the first to trap molecule^.^^,^' As total coverage increases, to say 0z0.1, adsorption by mol- ecules on defect sites is saturated and only the main absorption feature grows with increasing coverage. Absorption in the 3200 cm-' region is from the asymmetric C-H 0.2 - C2H2 :a1 Before Irradiation C2Dz h .-v)c C 3 4 v Q) ctc) L5 8 (6) C2H2 1 After Irradiation C2 HD * 0-I I I 3200 2800 2400 t/cm -' Fig. 5 FTIR spectra of acetylene isotopomers on crystallites NaCl at 150 K and 0= 0.05. Peaks marked with an asterisk correspond to molecules adsorbed onto defect sites. (a) Before radiation with 184.9 nm and (b) after 90 min photolysis.S. K. Dunn and G.E. Ewing vibration of C,H2. Its band profile mimics that of C2D,. Absorption by molecules on the (100) face is at higher frequency and the satellite feature, marked with an asterisk, is due to absorption by C,H2 molecules on edge sites. The sample was then irradiated with light from a 1.6 W low-pressure mercury dis- charge lamp.27 Fig. 5(b)shows the spectrum obtained after the initial mixture of C,H, and C2D2 was exposed to unfiltered UV radiation for 90 min. The peaks from C2H2 and C,D, have decreased in intensity, while new peaks appear in the 3300 cm-' and 2500 cm- ' regions from the hydrogen- and deuterium-stretching modes of C2HD. Con- tinued UV exposure (up to 8 h) produces no further spectral changes.With the use of a filter which blocks 184.9 nm radiation but passes 253.7 nm and other longer wavelength Hg lines no photolysis is observed. Thus the effective radiation for the acetylene pho- tolysis is the 184.9 nm line. Integrated absorbance measurements of the infrared bonds show that the total number of acetylene molecules is conserved, and the final mixture of isotopomers is 50% C,HD, 25% C,H2 and 25% C,D,. After 90 min of exposure to 184.9 nm light at 150 K, the reaction, has reached equlibrium where k, and k, are the rates of the forward and reverse reac- tion. It is important to emphasize that the characteristic CH vibrations of ethylenic or other hydrocarbons that are products of gas-phase acetylene photoly~is~.~ that would appear in the region 3200-2400 cm-' are absent in Fig.5. We have monitored the reaction rates for a variety of temperatures and coverages. Photometry measurements have allowed quantum yields to be obtained. For the condi- tions of the experiment shown in Fig. 5, 0 = 0.05 and 152 K, the quantum yield is = 30. (This means 30 hydrogen/deuterium exchanges for each photon absorbed by acetylene.) The reaction rate increases exponentially with temperature. An Arrhenius plot of ln[k,(T)/k1(150 K)] us. 1/T is consistent with an activation energy, E, = 7.3 kJ mol-' and a pre-exponential factor of 2.6 x lo1, s-'. These Arrhenius parameters suggest that the reaction rate might be diffusion limited. Adamson offers an empirical guide that the barrier for surface diffusion is generally about one quarter that for desorption.60 The isosteric heat of adsorption for acetylene', on NaC1( 100) (closely related to the physi- sorbed bond strength) is AH,,,(@ = 0.5) = -30 kJ mol-', so the activation energy observed for the hydrogen exchange is comparable to that expected for surface diffusion.Furthermore, the pre-exponential factor is approximately what we expect for the fre- quency of the frustrated translational surface mode.', So, it is reasonable that the acti- vation energy for the reaction corresponds to the barrier for surface diffusion, and the pre-exponential factor represents the frequency of attempted site-to-site jumps. If this interpretation is correct then the adsorbed molecules must be mobile in order to react.All our data is qualitatively explained if the rate of the hydrogen exchange is diffu- sion limited. Referring again to the model of Uebing and GomerS8 they find for T < T, that the adsorbates are predominantly in the ordered phase (see Fig. 3), and diffusion is minimal, even at low coverage. Above T, the diffusion rate is shown to exhibit an Arrhenius-type temperature dependence. They also note that diffusion is slower at high coverage due to clustering. We observe no reaction below T, (20-77 K) and an exponen- tially temperature-dependent reaction rate above T,. Additionally, we observe a signifi- cant decrease in the rate at high coverage (0z 1). The reaction rate thus follows the trends Uebing and Gomer predict for surface diffusion.This further supports the sugges- tion that the reaction is diffusion limited and, therefore, confined to the mobile lattice- gas phase. We have proposed that the hydrogen exchange occurs by direct dissociation of acetylene from S, [eqn. (3)] followed by a radical chain reaction with propagating steps Photochemistry of C2H2on NaCl( 100) like reactions (7) and (8).l We suggested that the restricted environment in the low- temperature phase inhibited the dissociation, so that only the high-temperature phase was photoreactive. The high quantum yield was explained by the chain-reaction mecha- nism. However we can also account for the large quantum yield for photoinduced hydrogen/deuterium exchange, its temperature and coverage dependence by another simple model.We begin with interpreting the rate of surface diffusion by60 z-' = v exp(-D,/RT) (10) where v = 2.6 x 10l2 s-' and Do = 7.3 kJ mol-' are the previously determined Arrhe- nius parameters. The frequency at which C2H2 can jump to a neighbouring site is then T-' = 7 x lo9 s-'. The time, t, to reach a site occupied by another C2H2 separated by a mean distance F is given by the random-walk relationship6' t = r2z/a2 (1 1) where a is the distance between nearest sites (the surface lattice constant). The fractional surface coverage of occupied sites (C2H2 molecules), in the limit of low coverage of the lattice gas can be roughly related through 0 = a2/F2 (12) So eqn. (1 1) becomes t = z/0 (13) For our experiment at 0=0.05 the time for an excited C2H, to find a partner is thus cu.3 x lop9s. With a quantum yield Q = 30, the excited state must have a lifetime of at least 9 x lo-* s. When steric factors are included, this lifetime could be an order of magnitude longer, or 3 1 ps. This model explains the reduced quantum yield at low temperature since as T is reduced the time between surface collisions is increased and the reactive metastable acetylene can relax before it reacts. In the region of low coverage the model requires that the exchange rate should increase with coverage. However, this experiment has not been attempted. At 0z 1 the adlayer molecules will all be locked into a single island and their T orientations and restricted migrations will prohibit hydrogen/deuterium exchange, as we observe.With a metastable lifetime requirement of 2 1 ps what sort of excited states are possible for exchange reaction? The singlets decay too rapidly. The 'A, state of acety- lene has a lifetime of 250 ns62 and those of 'B, and vinylidene 'A, are even shorter.' However, triplet-state acetylene lifetimes can exceed 1 ps.' ' If a triplet is the reactive intermediate how is it formed? Our 184.9 nm excitation accesses the 'A, and 'B, states of acetylene as we see in Fig. 1. Intersystem crossing to the triplet manifold has been inferred from lifetime measurements of the C2H2 ('A,) * Ar van der Waals complex.62 It has been suggested that Ar acts as the 'heavy atom' to accelerate the crossing process.The C1- surface ions on NaCl( 100) being isoelectronic with Ar could play the same role. An alternative possibility is that NaCl, and not C2H2, is the important antenna for photon capture. The STE is generated after the defect-containing NaCl has absorbed 184.9 nm photons. The triplet STE state of the salt, 'E:, has the same symmetry as the lowest triplet in acetylene (in the limit of the linear molecule) and is in near resonance as we can see in Fig. 1. This is a direct analogy to the transfer that occurs when Hg 'Po collides with ground state acetylene5' to excite 'B2. Further evidence of this mechanism is supplied by our recent result that adsorbed acetylene quenches triplet radiation from the STE.63Finally photon capture by NaCl and its transfer to surface adsorbed C2H2 S.K. Dunn and G. E. Ewing (or C2D2) does not require such a large quantum yield for hydrogen/deuterium exchange. This mechanism for adsorbed molecule excitation is also consistent with the .~~study by Leggett et ~ 1 of OCS on an LiF(100) single crystal. They found the OCS dissociation by 222 nm light to be lo3 to lo4 times faster when it was adsorbed on LiF(100) than in the gas phase. They proposed that photon excitation of one of the many colour centres in the interior of LiF transfers its energy to an adsorbed molecule which then dissociates. It remains to suggest a mechanism for reactions of triplet acetylene with ground state molecules to achieve the hydrogen/deuterium scrambling.There appears no precedent in the gas phase. Reactions like eqn. (1) and (2) produce a variety of hydrocarbons leading on to a polymer. However, as we see in Fig. 5 the only CH(CD) absorption features are acetylenic. Radical reactions such as eqn. (7) and (8) can achieve hydrogen/deuterium scrambling, but they require direct excitation of acetylene to produce dissociation. Moreover the adsorbed-phase quantum yield by this excitation mechanism (without transfer from the substrate) of = 30 is 500 times that of the gas-phase pro~ess.~ Perhaps an intermediate triplet vinylidene is produced. It is accessible to many of the energy states we have been discussing. We have proposed several scenarios of triplet-singlet reactions elsewhere.' We explore here another mechanism.Excited-state triplet (and singlet) acetylene is more basic than in the ground state because the lone (non-bonded) electrons are exposed in the cis or trans isomers. The basic nature of the excited state is consistent with proto- nation reaction rates which are orders of magnitude faster than in the ground state.65 Ah initio calculations show that triplet C2H; is considerably more stable than C,H2 in its triplet state.66 Thus we propose an acid (ground state) and base (excited state) reac- tion facilitated by the underlying substrate ions. The reaction might be represented sche- matically as C2H; + C2D2+ [C2H2D+* C2D-]* C2HD* + C2HD (14) where the transition state, represented by the brackets, is stabilized by the ionic surface.Clearly we are left with many questions on the photochemistry of C2H2 on NaCl(100). We hope to resolve these questions in the near future. This work has been supported by the National Science Foundation under grant CHE9 1-5444. References 1 S. K. Dunn and G. E. Ewing, J. Chem. Phj's., 1993,97,7993. 2 S. K. Dunn and G. E. Ewing, J. Vac.Sci. Technol. A, 1993,11,2078. 3 M. Zelikoff and L. M. Aschenbrand, J. Chem. 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H. de Boer, Electron Emission and Adsorption Phenomena, Cambridge University Press, Cambridge, 1935. 32 C. Kittel, Introduction to Solid State Physics, Wiley, New York, 6th edn., 1986 33 M. N. Kabler, Phys. Rev., A, 1964,136, 1296. 34 V. N. Kadchenko and M. Elango, Phys. Status Solidi A, 1978,46,315. 35 J. Ramamurti and K. Teegarden, Phys. Rev., 1966,145,698. 36 R. F. Wood, Phys. Rev., 1966,151,629. 37 M. N. Kabler and D. A. Paterson, Phys. Rev. Lett., 1967, 19, 652. 38 M. Ikeya and J. H. Crawford Jr., Phys. Lett. A., 1973,45,213. 39 A. Smakula, Opt. Acta, 1962,9,205. 40 T.Miyata and T. Tomiki, J. Phys. Soc. Jpn., 1967,22,209. 41 R. St. C. Smart and P. J. Jennings, Trans. Faraday Soc., 1971,67, 1193. 42 P. A. Cox and A. A. Williams, Surf: Sci. Lett., 1986, 175, L782. 43 U. Barjenbruch, S. Folsch and M. Henzler, Surf: Sci., 1989,211/212, 749. 44 S. Dieckhoff, H. Muller, W. Maus-Friedrichs, H. Brenten and V. Kempter, Surf: Sci., 1992,279,233. 45 M. A. Elango, A. P. Zhurakovskii, V. N. Kadchenko and Kh. R-V. Iygi, Sou. Phys. Solid State, 1977,19, 2158. 46 A. P. Zhurakovskii, Sou. Phys. Solid State, 1981,23, 167. 47 S. G. Zavt and T. Y. Saks, Sou. Phys. Solid State, 1973,14, 2502. 48 T. Y. Saks and S. G. Zavt, Sou. Phys. Solid State, 1977, 19, 1085. 49 G. Herzberg, Electronic Spectra of Polyatomic Molecules, Van Nostrand Reinhold, New York, 1966.50 H. Lischka and A. Karpfen, Chem. Phys., 1986,102,77. 51 V. K. Hoyermann, H. G. Wagner, J. Wolfrum and R. Zellner, Ber Bunsenges, Phys. Chem., 1971,75,22. 52 G. W. Johnston, S. Satyapal, R. Bersohn and B. Katz, J. Chem. Phys., 1990,92,206. 53 S. Nagase and C. W. Kern, J. Am. Chem. Soc., 1979,101,2544. 54 W. A. Payne and L. J. Stief, J. Chem. Phys., 1976,64, 1150. 55 H. R. Wendt, H. Hippler and H. F. Hunzcher, J. Chem. Phys., 1979,70,4044. 56 S. Shida and M. Tsukada, Bull. Chem. Soc. Jpn., 1970,43,2740. 57 T. Hill, An Introduction to Statistical Thermodynamics, Addison-Wesley, Reading, MA, 1960. 58 C. Uebing and R. Gomer, J. 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ISSN:1359-6640    

DOI:10.1039/FD9939600095

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Ultraviolet-laser-induced Desorption of CO and NO from Pt Surfaces K. Fukutani, M-B. Song and Y. Murata Institute for Solid State Physics, University of Tokyo, 7-22-1Roppongi, Minato-ku, Tokyo 106, Japan Desorption of CO and NO molecules chemisorbed on Pt(001) and Pt( 11 1) surfaces at 80 K induced by ultraviolet nanosecond-pulsed laser irradiation has been studied by a resonance-enhanced multiphoton ionization tech- nique. Desorption is not thermally driven, but induced by electronic excita- tion. CO desorption from Pt(ll1) and NO desorption from both Pt surfaces are found to be single-photon processes, while CO desorption from Pt(001) is a three-photon process. The translational, rotational, and vibrational tem- peratures of desorbed NO from Pt(OO1) are independent of pump-laser wavelength in the energy range 3.5-6.4 eV.For NO from Pt(l1 l), on the other hand, the internal-energy distribution is strongly dependent on pump- laser wavelength. On the basis of these results, the desorption mechanism induced by valence-electron excitation for molecules chemisorbed on metals has been discussed in connection with the unoccupied electronic structures of the adsorbate and the metal. U1 t raviole t (UV)-laser -induced processes accompanied by valence-elect ron excitation on solid surfaces, such as desorption, dissociation and reaction, have recently attracted the attention of surface physicists and chemists. Dominant static problems in fundamental surface science have been solved and the interest of researchers in this field is shifting to the investigation of dynamical phenomena. Desorption of molecules chemisorbed on metal induced by UV-laser irradiation via a non-thermal process is a typical dynamical phenomenon and is revealing a new understanding of the gas/surface interaction.This is also the simplest surface reaction. These quantum-mechanical studies are finally expected to give us essential information on catalytic activities on metal catalysts. The desorption of molecules chemisorbed on metal is scarcely induced by valence- electron excitation, since the electronically excited intermediates are rapidly de-excited to the ground state owing to a strong interaction between the adsorbate and the sub- strate. Recently, UV-laser-induced desorption in a few systems has been observed using a nanosecond-pulsed laser as a pump laser : NO desorption from Pt(OOl), '-' Pt( 1 1 1),4*5 Cu(11 1)6 and Ag(l1 1),6 and CO desorption from Pt(OOl).7*8 The state-selective detection of desorbed molecules is very important for discussing the desorption mechanism. We have previously studied desorption induced by an excimer laser of NO from Pt(OOl)293 and Pt(111),9 and CO from Pt(OOl)778 at 80 K using the resonance-enhanced multiphoton ionization (REMPI) technique, from which the internal-energy distribution of the desorbed neutral molecules is obtained.In the present study, we have measured CO desorption from Pt(ll1) at A = 193 nm. Prominent different features were observed between these experiments.NO desorption from both Pt(OO1) and Pt(ll1) is a single- photon process, while CO is desorbed from Pt(001) and Pt( 11 1) via three- and single- photon processes, respectively. Moreover, in the case of NO from Pt(OOl), the internal- and translational-energy distributions, and the desorption cross-section are independent of pump-laser wavelength. On the other hand, the internal-energy distribution in NO 105 Ultraviolet-laser-induced Desorption desorption from Ptjll 1) is strongly dependent on the pump-laser wavelength. These results are closely related to the high adsorption state selectivity observed in NO desorption from Pt(OO1).lO*ll The desorption mechanism has been discussed in com- bination with the unoccupied electronic structures of the adsorbed species and the substrate Pt.Experimental A block diagram of an experimental set-up is shown in Fig. 1. The UV light generated from an excimer laser of ArF, KrF, and XeF (1= 193, 248, and 352 nm, hv = 6.4, 5.0, and 3.5 eV, respectively) was used as a pump laser, which was linearly polarized using a polarizer. The pulse duration was 11 11sand the repetition rate was 10 Hz. This light was introduced into an ultra-high vaccum (UHV) chamber equipped with a low-energy elec- tron diffraction (LEED) and Auger electron spectroscopy (AES) system through a synthesized-quartz window. The temperature increase of the sample is expected to be less than 10 K in NO desorption, since a low laser fluence of lower than 2 mJ cm-2 was used in the experiments.Thus, thermal effects can be ignored. Higher fluence was used in the case of CO desorption (maximum fluence: 20 mJ cm-2), but the REMPI spectra and the translational-energy distributions have been found to be independent of laser fluence. A YAG-pumped Coumarin 450 or 460 dye laser (pulse duration: 6 ns, tunable wave- length range: 2 = 446-460 nm) was frequency-doubled by a P-barium borate (BBO) crystal to ionize the desorbed neutral NO and CO molecules. The ions generated by personal transient cornputer * recorder b 1 I delay pulse excimer generator laser i Nd:YAG laser t coumarin dye laser I I meter J =223-230nm Fig. 1 Schematic diagram of the experimental arrangement for the state-selective study of laser-induced desorption. KDP, potassium dideuteriumphosphate crystal ; BBO, /3-barium borate crystal; MCP, microchannel plate.K. Fukutani, M-B. Song and Y. Murata laser irradiation were accelerated to the inlet of a flight tube biased at a negative voltage, and were detected by a microchannel plate after travelling down the flight tube, which is used for separating two kinds of ion signals, For example, NO+ ions are generated just above the surface by the three-photon process, which is a combination of neutral desorption by the single-photon process and the non-resonant two-ionization process by ArF excimer laser irradiation,' and also by REMPI of desorbed neutral NO molecules. Only the latter ions were detected separately in the present study.In CO desorption from both Pt(001) and Pt( 11 1), neutral CO and CO+ ions are desorbed by laser irradia- tion via the different processes. This problem and detailed experimental conditions for desorption of CO from Pt( 1 1 1) will be described elsewhere.12 Detection of desorbed NO molecules was accomplished by (1 + 1) REMPI via the A 2C+ t X 'll transition. Rotational lines were clearly separated. In the case of CO, on the other hand, (2 + 1) REMPI via the B 'X+ t X 'C+ transition was used for detection of desorbed neutral CO, where all the intensity lies in the Q head, and rotational lines cannot be resolved. The effective spectral resolution is determined by lifetime broaden- ing due to predissociation and ionization.The time-of-flight (TOF) spectrum giving the translational-energy distribution of desorbed neutral NO or CO molecules was measured by varying the delay time from pulsed-pump laser irradiation to the pulsed-probe laser firing with a fixed distance between the surface and the probe laser beam. Pt(OO1) and Pt( 11 1) samples were initially bombarded by Ar ions and cleaned by + repeated cycles of annealing in ambient oxygen gas at 1100 K for ca. 30 min and flash- ing at 1400 K. The surface cleanliness and ordering were checked by AES and LEED. The sample was cooled to 80 K and exposed to NO or CO gas. Results Laser Fluence Dependences The desorption yield of NO from Pt(OOl)2>3 and Pt(lll)9 shows a linear dependence on pump-laser fluence at A = 193, 248, and 352 nm.Fig. 2(a) shows the desorption yield of NO molecules (v = 0, J = 1/2-9/2, R = 1/2) from Pt(ll1) with A = 193 nm, where v is the vibrational quantum number, J is the rotational quantum number, and R is the spin-orbit state. The SZ = 1/2 state corresponds to the 2111,2spin-orbit state of an NO molecule. CO desorption from Pt( 11 1) at A = 193 nm also shows a linear dependence of the desorption yield on laser fluence, as shown in Fig. 2(b). The probe laser was tuned at the top for the (v = 0) Q head. These results show that NO desorption from Pt(OO1) and Pt(111) and CO desorption from Pt(11 1) occur via a single-photon process. On the other hand, CO desorption from Pt(OO1) shows a supralinear dependence of the desorption yield (Y)on laser fluence (I;) at 2 = 193 nm; Y c;c FW3,as shown in Fig.2(~).~ That is, CO desorption from Pt(OO1) occurs via a three-photon process in spite of the non- thermal process. At A = 248 and 352 nm, CO desorption from Pt(OO1) cannot be observed. It is emphasized that only CO from Pt(OO1) is desorbed by a multiphoton process induced with a nanosecond pulsed laser via the non-thermal process. Internal-energy Distributions Fig. 3 shows the internal-energy distribution of the desorbed NO molecules from Pt(11 1) at A = 193 nm in the R = 1/2 and 3/2 states and in the u = 0 and 1 states. These data were obtained from the intensity distributions of each REMPI spectrum. The linear relation of ln[N(J)/(2J + l)] and rotational energy describes a Boltzmann distribution.The rota- tional temperature (T,) was obtained from the linear relation. All of the rotational- energy distributions of NO desorption from Pt surfaces at 80 K exhibit a nearly Boltzmann form and no distinct difference for the populations of the two spin-orbit states was observed. However, the rotational temperature in NO desorption from 108 Ultraviolet-laser-inducedDesorption 1 I(6)L 4-0 0 a 2-0 a. I I I laser fluence/mJ cm-2 I I I I*.a1 I,, 0 5 10 laser fluence/mJ cm-2 Fig. 2 Desorption yield of (a) NO from Pt(11l), (b)CO from Pt(ll1) and (c)CO from Pt(OO1)as a function of pump laser fluence at 193 nm Pt(001) is independent of pump-laser wavelength and is ca. 300 and 350 K in the v =0 and 1 states, respectively, while this value in NO from Pt(ll1) is strongly dependent on pump-laser wavelength; 490 K at A =193 nm and 290 K at A =352 nm in the v =0 state and 500 K at 1%=193 nm in the t: =1 state.n 7+2 252.2 -C K. Fukutani, M-B. Song and Y. Murata 109 In order to get the degree of vibrational excitation, the populations in the v = 0 and 1 states were obtained by summing over the rotational states. The vibrational-state population of u = l/v = 0 is also independent of pump-laser wavelength in NO from Pt(OO1) and is 0.1. On the other hand, this value in NO from Pt(ll1) is strongly depen- dent on pump-laser wavelength; ca. 0.4 at il = 193 nm and ca. 0.06 at 3, = 352 nm. Taking account of the Franck-Condon factors and assuming a Boltzmann distribution for vibrational excitation, the vibrational temperature (T,) was obtained: ca.1100 K at A = 193-352 nm for NO from Pt(OOl), ca. 2900 K at il = 193 nm and ca. 1000 K at 1= 352 nm for NO from Pt( 11 1). Fig. 4(a) and (b) show REMPI spectra of the neutral CO molecules desorbed from Pt(l11) corresponding to ZI = 0 and 1 states. These spectra are similar to those obtained for CO from Pt(OOl).7 The rotational-energy distributions are compared with simula- tions of REMPI spectra computed assuming a thermal distribution in the rotational- energy partitioning. The simulated REMPI spectra have been computed following the scheme proposed by Tjossem and Smyth.' The rotational temperatures estimated from .. . .* .* *; . 230.06 230.08 230.1 probe-laser wavelength/nm 0.dh..c.as*-,1-. --I Yl I -I_0 230.24 230.26 230.28 probe- laser wavelength/nm Fig. 4 (2 + 1)-REMPI spectrum of CO desorbed from Pt(ll1) at 80 K in the B 'Cf +X 'Cf transition. (a)v = 0 and (b)v = 1. Ultraviolet-laser-induced Desorption the simulation are 150 and 200 K in the v = 0 and 1 states, respectively, for CO from Pt(OOl), and 150 and 70 K in the v = 0 and 1 states for CO from Pt(ll1). The population in the v = 0 and 1 states was obtained from the relative intensity of the REMPI spectra shown in Fig. 4 for CO from Pt(lll), in which the translational temperature is independent of the vibrational state as described in the next subsection.The population of v = l/v = 0 is ca.0.3, which corresponds to a vibrational temperature of ca. 2700 K.On the other hand, the population of v = l/v = 0 for CO from Pt(OO1) could not be obtained from the REMPI spectra, since the translational temperature is strongly dependent on the vibrational state. The population in this system was obtained from the TOF spectrum. TOF Spectra The translational-energy distribution can be obtained from the TOF spectrum. Fig. 5 shows a TOF spectrum of NO desorbed from Pt(11 1) corresponding to v = 0, J = 1/2-9/2, i2 = 1/2 states at 1 = 193 nm. The solid curves are the fits to a sum of two non- Maxwellian distributions I(s)= s3 exp(-as2 -bs -c), where s is the velocity of the molecule and a, b, and c are fit parameters.Mean translational energies ((E,)) are obtained from numerical calculation and the mean translational temperature is defined by = (Et)/2k,. Since the slow component is at the sample temperature of 80 K, this component is considered to be a thermal desorption channel temporarily trapped in a precursor state. In the present study, only the fast component was probed when measur- ing the internal-energy distribution. The mean translational temperatures at low J states are ca.650 K for NO from Pt(OO1) and 1020 and 760 K at 3, = 193 and 352 nm, respec- tively, for NO from Pt(ll1) in the v = 0 state. On the other hand, IT; = 2200 K for NO (v = 1) from Pt(ll1). A strong dependence of on the vibrational state for Pt(ll1) contrasts with the low dependence observed for Pt(OO1). A strong dependence of the TOF spectrum on the rotational quantum number was found.The spectrum shifts to a shorter TOF as J is increased. The mean translational temperatures increase with increasing J number; 760, 960, and 2000 K for J = 15.5, 22.5, and 30.5. This tendency was also observed in NO from Pt(ll1); 1970, 2290, and 3920 K for J = 15.5, 22.5, and 30.5. *l 10 20 TO F/ps Fig. 5 TOF spectrum of desorbing NO (J = 1/2-9/2, i2 = 1/2) from Pt(l11)at i= 193 nm in the t! = 0 state. The solid curves are the fits to a sum of two non-Maxwellian distributions. K. Fukutani, M-B. Song and Y. Murata c0 10 L 3 TOF/ps Fig. 6 TOF spectrum of desorbing CO (Q head) from Pt(ll1) at A =193 nm in the u =0 state.The solid curve is the fit to a non-Maxwellian distribution. Fig. 6 shows a TOF spectrum of CO desorbed in the u =0 state from Pt(ll1) at J.=193 nm. The mean translational temperature is as high as ca. 2900 K for both u =0 and 1 states. On the other hand, the mean translational temperature of CO from Pt(001) is strongly dependent on the vibrational state, 150 K in the u =0 state and 1300-2000 K in the u =1 state, in which the mean translational temperature shows J-state depen- dence and increases with increasing J value. The population of u =l/u =0 is 0.025 obtained from the relative integral intensity of the TOF spectrum, and corresponds to a vibrational temperature of 860 K. The above results are summarized in Table 1. They show clearly that the UV-laser- induced desorption in these systems is a non-thermal process.Discussions NO Desorption from Pt(001) The translational, rotational and vibrational temperatures of NO desorbed from Pt(OO1) are independent of photon energy in the range 3.5-6.4 eV, suggesting that the desorp- tion of NO follows the same mechanism at these excitation energies. The initial step of the electronic excitation should be the same in this energy range, although there is still a slight possibility that the same intermediate state of the NO desorption originates from different electronic excitations. It is instructive to describe the electronic structure of the Pt bulk and adsorbate NO. By photoelectron spectroscopy (PES), the Pt d bands were Table 1 7;, T,and T,for NO and CO desorbed from Pt(001) and Pt(ll1) at 80 K and photon energy (hv) of the pump laser ~___ system hv/eV TJK T,/K T,/K NO/Pt(OOl) 6.4-3.5 650 300 1200 NO/Pt( 11 1) 6.4 1020 490 2900 3.5 760 290 1000 CO/Pt(001) 6.4 150 150 860 CO/Pt( 11 1) 6.4 2900 150 2700 17; and T,are for the u =0 state. Ultraviolet-laser-induced Desorption found to have a ca.8 eV width below the Fermi level (Ef),14while occupied electonic levels of NO adsorbed on Pt were located at 2.7 eV (275,) and 9.6 eV (50 and 171) below E,.15 Additionally, the unoccupied 2x, level was found by an inverse photoemission study on NO/Pt(lll), to lie at 1.5 eV above Ef.16 Fig. 7 shows a schematic energy diagram for NO adsorbed on Pt.An energy diagram for CO on Pt is also shown. The unoccupied 50, and 271, states for the CO monolayer on Pt( 110)were observed at ca. 1.5 and 3.0-5.0 eV, respectively, by inverse photoemi~sion.'~ The 274, state cannot be observed by PES owing to the overlap with the metal d bands." Photon energies of 4.2 and 11.1 eV for NO on Pt are thought to be required for the 2nn,+ 2711, and 271, + (50, 171) transitions, see Fig. 7. Therefore, the direct excitation of adsorbates can be excluded, because no substantial difference in the desorption cross- section was observed at photon energies in the range 3.5-6.4 eV and enhancement of the desorption cross-section is expected to occur at 3.5 and/or 5.0 eV. The energy levels probed by photoemission studies are different from those of the 271, + 271b transition, while the final states in the normal and inverse photoemission processes are positively and negatively charged states, respectively.Apart from the intra-adsorbate excitation, three possible electronic excitations are considered: a Pt valence electron to the Pt conduction band (substrate excitation), an NO 2nb electron to the Pt conduction band, and a Pt valence electron to the NO 27t, state. Further information about the electronic excitation might be obtained by measur- ing the incidence angle dependence of the desorption yield using a polarized pump laser. As described by Richter et al.,19 however, adsorbate and substrate excitations are not discriminated by this measurement, because the mean-square electric field parallel to the surface has a similar angle dependence to the absorption coeficient, after taking account of the increase in the irradiated area.Pt NO co 4 Ef > 1> g -4 Cal -8 -1 2 Fig. 7 Electronic structure of the Pt bulk bands and NO and CO molecules adsorbed on a Pt surface K. Fukutani, M-B. Song and Y, Murata 113 The relative yields were measured at angles of 25" and 81" from the surface normal in p and s polarizations at 3, = 193 nm. These values are in good agreement with the absorption coefficient of a Pt substrate, calculated following the Fresnel equations using the refractive index of Pt. Moreover, the internal-energy distribution was found to be independent of the pump-laser polarization.' These results are consistent with the initial step of photodesorption being the Pt valence-electron excitation to the conduc- tion band.Thus, the most probable mechanism is as follows: a hot electron excited to the conduction band is transferred to the unoccupied state of the adsorbates. Subse- quently, a negative ionic state is formed and desorption occurs via this intermediate state following the mechanism described by Antoniewicz.20 When the lifetime of the intermediate state is long, the de-excitation to the ground state of the adsorbate leads to clesorption, while a short lifetime of the intermediate state results in recapture. NO desorption from Pt(001) at 80 K was found to show a remarkable adsorption- state selectivity."*' ' LEED, reflection absorption infrared spectroscopy, and ultraviolet photoelectron spectroscopy (UPS) show that the adsorption species active to UV-laser- induced desorption are NO molecules adsorbed at defect sites located in the boundary between the hex and 1 x 1 areas, which appear after the partial (hex)+(l x 1) restructuring induced by NO adsorption on Pt(OOl)-hex R0.7" at 80 K.Electronic states of NO at defect sites are considered to be localized because of a disordered structure, in contrast to an ordered structure in the NO-adsorbed layer on the hex and 1 x 1 areas. Consequently, a relatively longer lifetime in the negatively charged state of the interme- diate is expected for this adsorption species. Similar problems might occur for CO desorption from Pt(001).On the other hand, there is no adsorption-induced restructuring on Pt( 11 1). A long lifetime of the intermediate state results in large energy transfer into the molecular motion owing to the electron-phonon interaction, and is considered to yield high excitation in the translational, rotational, and vibrational degrees of freedom. This effect is demonstrated by the result that the rotational temperature increases with increasing J number. The vibrational-energy excitation is also observed, as listed in Table 1. CO and NO Desorption from Pt Surfaces Various experimental results were obtained for NO and CO desorption from Pt(001) and Pt(ll1). These results can be consistently interpreted by the model of substrate excitation and negative-ion formation, and by considering the unoccupied electronic structures of the Pt and the adsorbate, although the substrate excitation model is derived from NO desorption from Pt(OO1) at 80 K.The 27ra state of NO and CO on Pt shown in Fig. 7 plays an important role in a single-photon desorption process. We speculate a desorption mechanism for a single-photon process. Fig. 8 shows a schematic energy diagram of the unoccupied states, in which the Pt bands correspond to the projected bulk bands at the r point. The Pt bulk bands13 are projected along the corresponding symmetry axis [the T-A-X and T-A-L directions for the (001) and (1 11) surfaces, respectively]. Unoccupied levels of adsorbates NO and CO are also shown.The 27ca states of NO and CO on Pt are located at positions of a low local density of state or a local band gap of the Pt bulk bands at r. Another unoccupied state of 50, for CO on Pt(ll0) can be observed by inverse photoemission at ca. 1.5 eV above E, .I7 This state is induced by the hybridization of the (30 50orbital with the Pt d bands. Since the Pt d bands are wide in the range down to 8 eV below E,, a strong resonant 50-d interaction results in the increase of the bonding- antibonding splitting and the 50, manifold is shifted, in part, above E,. We assume that the defect level appearing at the boundary between the hex and 1 x 1 areas of Pt(OO1) forms an extrinsic surface state located in a low density-of-state Ultraviolet-laser-induced Desorption E/eV 15t EfeV Ef +'"Ef I I Fig.8 Schematic energy diagram for the photodesorption mechanism. (a)NO on Pt(001), (b)NO on Pt(l1l), (c) CO on Pt(OOl), and (d) CO on Pt( 11 1). Left-hand side shows the empty Pt bands and right-hand side shows the unoccupied states of adsorbates. The Pt bands show the projected local density of state at the r point. These are projected along the T-A-X direction for Pt(OO1) and the T-A-L direction for Pt(ll1) from the bulk band structure.14 The thick solid line shown on the left-hand side of (a) and (c)is the defect level appearing at the boundary between the hex and 1 x 1 areas. The energy of this level is assumed. position, as shown by a thick line in Fig. 8(a) and (c).Thus, the 271, state of NO adsorbed at the defect sites on Pt(001) is coupled with the defect level, as seen in Fig. 8(a).The 27ca state of CO on Pt(001) is decoupled with the Pt defect level and the 5a, state is coupled with the bulk Pt bands, as seen in Fig. 8(c). The 2na and 50, states of NO and CO on Pt( 111) are isolated in the local band gap, as seen in Fig. 8(c) and (4. The strong resonant 50-d interaction causes the attenuation of the 27c-d inter-action.17 Therefore, it is considered that only the 271, state plays a significant role in the intermediate state in the photodesorption process, while excitation to the intermediate state of the 50, state is thought to be quickly quenched and does not contribute to the desorption process.Although the 50, state on NO cannot be observed, the strong reson- ant 5a-d interaction is also expected and the 271-d interaction is considered to be attenuated. The 271, states of NO and CO on Pt surfaces are located at the local band gap and a longer lifetime is expected in the intermediate state of the 271, state. Therefore, laser-induced desorption with the single-photon process can be observed for CO from Pt(l11) and NO on Pt(001) and Pt( 11 1). On the other hand, CO desorption from Pt(OO1) K. Fukutani, M-B. Song and Y. Murata via a single-photon process may be strongly suppressed, since the 50, state of CO on Pt(001) is strongly coupled with the defect level. The dominant process in NO desorp-tion from Pt(001) corresponds to the rapid de-excitation channel in CO desorption from Pt(001). Moreover, this system has a complicated electronic structure.Thus, it is con- sidered that a multiphoton process appears in de~orption.~ UV-laser-induced desorption of NO from Ni and Pd surfaces cannot be observed.21*22The d bands of these metals are narrower than those of Pt. Therefore, the 5a orbital on NO scarcely interacts with the d bands of these metals and the 2n-d interaction is strongly resonant. In this case, the de-excitation process is rapid via a chemical bond formed by the 2na-d interaction and desorption does not occur. Next, we discuss the pump-laser wavelength dependence. In the case of NO and CO adsorbed on Pt( 11 l), the large dispersion of the Pt d bands is reflected in photoexcita- tion, that is, the final energy position in photoexcitation depends on the excitation photon energy due to the energy and the momentum conservation derived from Fermi’s golden rule.Thus, the energy position of the intermediate state after tunnelling of a hot electron generated by photoexcitation depends on pump-laser wavelength. The electron tunnelling occurs very rapidly and can be regarded as a Franck-Condon transition. Therefore, the adsorbate position at the time of electron tunnelling is restricted in the range of adsorbate-substrate vibrational amplitude in the initial ground state and depends on the photoexcitation energy. As the NO or CO position is further from the surface, the lifetime of the intermediate state must be longer because of the relatively weak interaction with the substrate. On the other hand, the N-0 or C-0 distance at the time of electron tunnelling holds the same distribution as that in the ground state, i.e.the interatomic distribution is independent of pump-laser wavelength. The equi- librium distance of NO-or CO- in the intermediate state is longer than that in the ground state of each adsorbate molecule. Thus, a longer lifetime should yield higher e:xcitation in the vibrational population. The translational temperature is also higher with increasing lifetime of the intermediate state. On the other hand, NO desorption from Pt(OO1) is independent of pump-laser wave- length in the internal- and translational-energy distributions. This may be an exception- al case.The final state in photoexcitation in NO on Pt(OO1) is a flat band corresponding to the defect level, since only NO molecules coupled with the defect level of Pt are active to photodesorption. Therefore, a hot-electron energy does not depend on pump-laser energy, and the intermediate state at the time of electron tunnelling is in the same photon energy range, 3.5-6.4 eV. This work was supported by a Grant-in-Aid on Priority Area Research on Photo-excited Process supported by the Ministry of Education, Science, and Culture, Japan. We are grateful to Prof. K. Terakura for valuable discussions and advice. M-B.S. acknowledges a Fellowship from the Owi-Su Fund for Korea-Japan Cultural Exchange. References 1 K. Max, S. Mizuno, M.Yamada, I. Doi, T. Katsumi, S. Watanabe, Y. Achiba and Y. Murate, J. Chem. Phys., 1989,91, 690. 2 K. Fukutani, A. Peremans, K. Mase and Y. Murata, Phys. Rev. B, 1993,47,4007. 3 K. Fukutani, A. Peremans, K. Mase and Y. Murata, Surf: Sci., 1993,283, 158. 4 S. A. Buntin, L. J. Richter, D. S. King and R. R. Cavanagh, J. Chem. Phys., 1989,91,6429. 5 R. Schwarzwald, A. Mod1 and T. J. Chuang, Surf. Sci., 1991,242,437. 6 S. K. So, R. Franchy and W. Ho, J. Chem. Phys., 1991,95, 1385. 7 A. Peremans, K. Fukutani, K. Mase and Y. Murata, Phys. Rev. B, 1993,47,4135. 8 A. Peremans, K. Fukutani, K. Mase and Y. Murata, Su$ Sci.,1993,283, 189. 9 K. Fukutani, Y. Murata, R. Schwarzwald and T. J. Chuang, Surf: Sci., in the press. 10 K. Mase, K. Fukutani and Y.Murata, J. Chem. Phys., 1992,96, 5523. 11 M-B. Song, S. Mizuno, K. Fukutani and Y. Murata, Chem. Rev. Lett., 1992, 196,559. Ultraviolet-laser-induced Desorption 12 K. Fukutani, M-B. Song and Y. Murata, to be published. 13 P. J. H. Tjossem and K. C. Smyth, J. Chem. Phys., 1989,91,2041. 14 N. V. Smith, Phys. Rev. B, 1974, 15, 1365. 15 H. P. Bonze1 and G. Pirug, Surf: Sci., 1997,62,45. 16 V. Dose, Surf: Sci. Rep., 1985,5, 337. 17 G. Rangelov, N. Memmel, E. Bertel and V. Dose, Surf: Sci., 1991, 251/252,965. 18 S. Ferrer, K. H. Frank and B. Reihl, Surf. Sci., 1985, 162, 264. 19 L. J. Richter, S. A. Buntin, D. S. King and R. R. Cavanagh, Chem. Phys. Lett., 1991,186,423. 20 P. R. Antoniewicz, Phys. Rev. B, 1980,21, 3811. 21 P. M. Fern, F. Budde, A. V. Hamza, S. Jakubith, G. Ertl, D. Weide, P. Andresen and H-J. Freund, Surf: Sci., 1989,218,467. 22 J. A. Prybyla, T. F. Heinz, J. A. Misewich and M. M. T. Loy, Surf: Sci. Lett., 1990, 230, L173. Paper 3103144F; Received 27th May, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600105

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96, 117-127 Electron-driven Dynamics at the Gas/Solid Interface: Dissociation, Desorption and Reaction of Adsorbed Molecules Richard J. Guest, Ian M. Goldby and Richard E. Palmer* Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, UK CB3 OHE Darren N. Bly, David M. Hartley and Philip J. Rous Department of Physics, University of Maryland Baltimore County, Baltimore, MD 21228-5398, USA This paper considers dynamical processes which can be initiated by low- energy (1-50 eV) electrons in adsorbed molecular layers. We have investi- gated the production of negative ions by electron-stimulated desorption from well ordered monolayer and multilayer films of 0, on graphite. Reson- ances are observed in the yield of both 0-and 0; ions, and are attributed to the process of dissociative electron attachment.In the monolayer regime, the 8 eV resonance which dominates the 0-yield at higher coverages is found to be suppressed, and dipolar dissociation dominates. This suppress- ion is attributed to the image potential, which attracts low-energy ions back to the surface. The angular distribution of 0-ions desorbed from the monolayer 6 and ( phases we found to be almost independent of the initial molecular orientation on the surface. Classical trajectory calculations indi- cate that the molecule becomes rotationally excited prior to dissociation, causing the initial orientational order to be lost. This marks a difference between the dissociation and desorption dynamics of physisorbed and chemi- sorbed molecules, where the angular distribution of desorbed fragments is generally taken to reflect the molecular orientation on the surface.1. Introduction Electron-capture mechanisms have been invoked to explain a number of dynamical phe- nomena occurring at the gas/solid interface. Low-energy electrons are important not only in direct processes such as electron-stimulated desorption2 (ESD) and similar elec- tron impact interactions, but also in a number of indirect effects, such as molecular beam scattering3 and dissociative ad~orption,~ where the electron originates in the sub- strate itself. It has been shown recently by several that low-energy electrons originating from the substrate play a crucial role in photon-stimulated desorption of an adsorbate from a substrate.The observation of all these electron-driven processes indi- cates the need for a good understanding of electron-molecule dynamics at surfaces. In this paper, we present the results of a study of the dissociation and subsequent dynamics of weakly bound (condensed or physisorbed) oxygen molecules on a highly oriented pyrolytic graphite8 (HOPG) surface. The use of the O,/graphite adsorbate system allows us to orient the molecules on the surface in two different geometries.' By varying the coverage we can select either the 6 phase (with the molecular axis approx- imately parallel to the surface) or the ( phase (with the molecular axis approximately perpendicular to the surface).This enables us to study the effects of molecular orienta- tion in electron stimulated desorption. Sanche," in his study of molecular films of 0, 117 Electron-driven Dynamics on polycrystalline Pt (where the orientation of the 0, molecular axes is not known), found that two molecular dissociation processes seen in the gas phase'' are preserved when the oxygen molecules are condensed onto a surface. These were dissociative attachment (DA) e-+ O,+O; -+O + 0-(1) and dipolar dissociation (DD) e-+O,-+OT-)O+ +O-(2) Sanche and co-workers12 have also demonstrated that negative ions produced by DA can react with co-adsorbed molecules, thereby illustrating the possibility of inducing chemical reactions on surfaces with low-energy electrons.In this paper we explore the reaction of 0-ions produced by DA and DD processes with neighbouring 0, mol-ecules in the O,/graphite system, and we investigate reaction cross-sections as a fuiiction of incident electron kinetic energy (Ekin). 2. Experimental Methods The ESD experiments were performed in an ultra-high vacuum (UHV) chamber fitted with a pulse-counting mass spectrometer (Hiden Analytical) to detect the desorbed ions. The electron beam was produced by a custom-built computer-controlled low-energy electron gun; this was mounted on a turntable. In addition the system was equipped with an electron energy loss spectrometer (EELS) for structural characterisation of the 0, films.13 The HOPG sample was cleaved in air before mounting on a liquid-helium cold-finger with a base temperature of 20 K.The sample was regularly cleaned by heating to 900 K in UHV with surface cleanliness being monitored by EELS. Measurements of the angular distribution of desorbed ions were performed by rotat- ing the electron gun and sample in concert, with the mass spectrometer fixed in space. Owing to the limited angular range of the electron gun on the turntable (40"), scans were taken with the electron beam incident at three different angles to the surface to cover the whole angular range of interest. This produced three overlapping ion angular distribu- tions which were scaled in the overlap region (due to the angular dependence of the electron impact cross-section) to give the complete angular profile.3. Experimental Results and Discussion Fig. 1 shows the 0-yield as a function of incident electron energy for three different coverages of O,/graphite and two coverages of O,/Ar/graphite; these coverages corre- spond to the 6 and phases (i.e. 'lying down' and 'standing up' molecules, respectively) , three monolayers (ML) of 0, on the surface, and 1 ML of 0, adsorbed on 1 Langmuirt (L) and 5 L argon films on graphite. For the 3 ML case, the 0-yield has also been recorded with a 2 eV retarding potential applied to the mass spectrometer; this is shown as the open circles in Fig. l(c). For comparison, Fig. 2 shows the yield of O+ ions produced by electron impact on 3 ML O,/graphite as a function of incident electron energy. It can be seen that dipolar dissociation is the only dissociation mechanism operating here, as no signal is seen below ca.20 eV. Furthermore, it can be seen that the signal level for O+ is between one and two orders of magnitude less than for 0-.It is conceivable that this is some func- tion of the channeltron in the mass spectrometer, but there is no obvious physical reason why this should be the case. This implies that the 0' ion is more prone to re-neutralisation than the 0-ion; hence fewer escape the surface and are detected. -f 1 Langmuir (L) = Torr s. R. J. Guest et al. N 200025001 * C 0 Is, 5 -t400v) 1000L 0 500c,,-0 5 10 15 20 electron energy/eV 600000 400000 200000 0 5 10 15 20 electron e nerg y/eV Fig.1 Energy dependence of the 0-yield produced by electron impact on (a) 1 ML 6 phase, (b)1 ML < phase, (c)3 ML of 0, on graphite, (d) 1 ML of 0, on 1 L of Ar on graphite and (e) 1 ML of 0, on 5 L of Ar on graphite. Also shown in (c) are the results obtained when a retarding potential (V,) of -2 eV is applied to the desorbed ions at the mass spectrometer (0).Electron angle of incidence = 60"and of emission = 30". 60 50 N 40 10 0 0 5 10 15 20 25 30 35 40 electron energy/eV Fig. 2 Energy dependence of the O+ yield produced by electron impact on 3 ML of 0, on graphite. Angles of incidence and emission as in Fig. 1. Electron-drivenDynamics It can be seen from Fig. l(c) that three DA resonances are observed in the electron energy range studied, at 8, 10 and 13.5 eV. These positions agree well with the reson- ances observed in 0, on polycrystalline Pt.I4 At higher incident-electron energies, dipolar dissociation is seen to occur.Although the resonances are very pronounced at 3 ML 0, coverage, they are seen much less strongly in the monolayer c phase, and are not detectable in the 6 phase. However, when an argon spacer layer is inserted between the oxygen layer and the graphite surface, the resonances appear again, with their inten- sity increasing with the spacer thickness. There are a number of possible explanations for this apparent quenching of the DA resonances in the monolayer regime on graphite. First, it could be due to a reduction in the resonance lifetime; such quenching has been proposed in resonance scattering experiments on other physisorption systems.15 However, resonance scattering studies from 0, on graphite16 have provided no evidence of such quenching. An alternative explanation of the apparent quenching of the DA resonances arises if we consider the effect of the image potential on the dynamics of the desorbing ion at the surface.For an ion to be detected, it must have sufficient velocity normal to the surface so that it can overcome the image potential and reach the mass spectrometer. Photoemission' and electron scattering13 studies have shown that the image potential in monolayer O,/graphite (6 or 5 phase) is ca. 1.5 eV; in the multilayer regime, on the other hand, the polarisation potential drops to ca.0.6 eV. If the 0-ions are emitted with an Ekinof the order of 1.5 eV, many more will be seen emerging from the multilayer on graphite than the monolayer. From Fig. l(c), we know that ions produced from the 8 eV DA resonance have less than 2 eV kinetic energy since applying a 2 V retarding potential to the mass spectrometer causes the resonance to disappear. Thus a far smaller proportion of the ions emitted from the monolayer will have suficient Ekinto escape the surface, compared with the multilayer regime. (The intensity differences between the 6 and c phases are a result of the different orientation of the molecular axis on the surface and will be discussed later.) Inserting the argon spacer layer has the effect of increasing the distance of the oxygen molecules from the surface, thereby reducing the image potential, and allowing more ions to escape the surface and be detected.We now turn to measurements of the angular distribution of emitted 0-ions. Fig. 3 shows the distribution of 0-ions emitted from the c phase of O,/graphite via DA and DD processes and from the 6 phase via DD. The angular distributions have been fitted with Gaussian distributions and the best-fit half-width half maxima (HWHM) are as follows: 5 phase DA, 21"; c phase DD, 28" and 6 phase DD, 35". Electron-stimulated desorption ion angular distribution (ESDIAD) measurements represent an established method of determining molecular orientation on a surface,18 and it is usually assumed that the molecule dissociates such that the fragments fly off along the direction of the bond axis.The results shown in Fig. 3 clearly show that this assumption is not valid for the O,/graphite physisorption system as for both 'lying down' and 'standing up' mol- ecules, the ion angular distribution peaks along the surface normal direction. To explain these angular distributions, it is necessary to consider the dynamics of the desorbing oxygen fragments. In principle, the measured angular distribution will depend on a number of factors: (i) the initial molecular orientation on the surface, (ii) the dynamics of the dissociation process and (iii) image potential effects as the 0-ion recedes from the surface. The effect of the image potential on the trajectory of the desorbing ion has been considered in some detail by Clinton" and Miscovic et aL2' The component of ion velocity normal to the surface is reduced, whereas the velocity parallel to the surface is unaffected.This has the effect of increasing the polar angle of desorption of the 0-ion away from the surface normal. The magnitude of the broadening depends on the ion Ekin,its initial direction and the strength of the image potential. If the normal component of velocity of the ion is suficiently small, the ion will be recaptured by the image potential and presumably re-neutralised. Image potential effects can account for R. J. Guest et al. t 0 10 20 30 40 50 60 70 80 90 emission angle, @/degrees Fig. 3 Experimental angular distributions of 0-ions produced by electron impact on 0, physi-sorbed on graphite.(a) 1 ML c phase, 8 eV electrons, (b) 1 ML c phase, 20 eV electrons and (c)1 ML 6 phase, 20 eV electrons. The results were obtained using three different electron incidence angles with respect to the surface normal (see text): 65" (a),35" (+) and 5" (m). In each case, the (-data have been fitted with a Gaussian distribution peaked along the surface normal best-fit HWHM of 21 & lo(5 phase, 8 eV), 28 & 3 ([ phase, 20 eV) and 35 f3" (6 phase, 20 eV). ) with the width of the 5-phase angular distribution as they increase the polar angle of desorp-tion, but they cannot explain the &phase distribution peaking along the surface normal direction; to understand this, it is necessary to consider the dynamics of the molecular dissociation process itself. Electron-driven Dynamics 4.Theoretical Methods In order to understand the experimental ion angular dis ributions, we have implemented a semi-classical trajectory calculation to explore further \he dissociation dynamics of the O,/graphite system. The electronic excitation produced by electron impact is modelled as a vertical, Franck-Condon transition, placing the molecule on an excited-state molecule-surface potential-energy surface (PES) and on a repulsive branch of the 0; intra-molecular PES. As the system propagates over this multi-dimensional PES the electronically excited molecule may de-excite or desorb and/or fragment. The classical Hamiltonian of the molecule-surface system is derived from the clas- sical three-body problem.Hasselbrink2' employed a similar model to study state dis- tributions in photon-stimulated desorption of chemisorbed diatomic molecules in which the surface is represented by a point mass.? The system of coordinates appropriate to the (diatomic) molecule-surface system is : r, the internuclear separation of the adsorb- ate; z, the normal surface-adsorbate centre-of-mass separation; and 6, the orientation of the molecular axis with respect to the surface normal. The conjugate momenta are P,, P, and J, respectively. The Hamiltonian of the system is,22 where p is the reduced mass of the molecule, m is the reduced mass of the molecule- substrate system, V,, is the intramolecular potential and Vms is the molecule-surface potential.For O;, the intramolecular PES for dipolar dissociation was fitted to calcu-lation~.~~*~~We took the A2H, state to be the predissociating state of O;, crossing adiabatically to the 'Zi state which is asymptotic to the ion pair. The intramolecular PES for dissociative attachment via the A 'nuI compound state was fitted to the calcu- lations of Michels and Harri~.~~,'~ The ground-state O,/graphite interaction potential was modelled as the sum of a (repulsive) overlap term and an (attractive) dispersion term, 3V;;urf-mol = A exp(-Kz) -Cz-(4) The free parameters were fitted to the surface-molecule interaction potential derived from a sum of Lennard-Jones 0-C pair potentials.These pair potentials were obtained from Bethanabotla and Steele,27 and reproduce the temperature-dependent orientation- a1 order of the O,/graphite system. Using this approach the well-depth for the fitted 0, on graphite physisorption potential was found to be 80 meV, comparable with the value of 90-100 meV cited by Vidali et a1.28 The form of the model excited-state O,/graphite potential depends upon the disso- ciation channel. For the 0; state leading to dipolar dissociation, the molecule-surface interaction potential of the predissociating state was taken to be of dipole-image dipole form. After curve-crossing onto the ion-pair state, this term was replaced by the inter- action potential of the pair of ions and their individual images in the substrate.For dissociative attachment, the dominant interaction is that of the molecular ion with its image. Upon molecular fragmentation the additional electron was localised on one or other at om. The ground-state configuration of the system prior to excitation of the molecule was described by a joint probability distribution of the coordinates in a six-dimensional phase space. The ground-state molecule-surface and intramolecular vibrational wave- ? This assumption places the molecule-surface system in a rotating frame, resulting in spurious centrifugal forces. Consequently, in deriving the Hamiltonian we represent the surface as a semi-infinite object to ensure that the molecular dynamics is calculated in an inertial frame.R. J. Guest et al. functions were determined from the ground-state PESs described above. The distribu- tion of molecular orientations of the ground state for both the [ and 6 phases was obtained from the molecular dynamics simulations of Bethanabotla and Steele.28 The conjugate momenta were obtained by Fourier transformation. The de-excitation of 0: and electron detachment from 0; were modelled by a product of relaxation probabilities, P(z, r) = C exp(-az)exp(-br) (5) 'The parameters C, a and b were adjusted to give a mean relaxation time of 5 fs. Computational implementation involved numerical integration of Hamilton's equa- tions, starting from a random set of initial coordinates derived from the ground-state distributions. The time interval for each integration step was 0.1 fs.Between each step of the integrator, relaxation of the excited state was allowed with the appropriate probabil- ity. The trajectory of each excited molecule was followed for 12 ps. After this time inter- val the average ion surface separation was greater than 296 A and the average ion-ion distance was beyond 773 A.This process of coordinate selection, integration, test and trajectory calculation was repeated in order to assemble a representative sample of desorbed atomic ions. Typically, the trajectories of 105-107 molecules were followed, resulting in a final yield of several thousand ion fragments. 5. Theoretical Resufts First we consider dipolar dissociation, occurring for incident electron energies above a threshold of ca.17 eV. The calculated ion angular distributions of desorbed 0-ions from both the 5 and 6 phases are shown in Fig. 4. The calculated ion fluence was convolved with the angular resolution function of the mass spectrometer which has a half-width of ca. 7.5". The calculated ratio of 0-yields, 5 : 6, was ca. 50 : 1, in reason- able agreement with the experimental ratio of ca. 100: 1. Both distributions peak normal to the surface. The calculated ion angular distribution from the 5phase is signifi- cantly narrower than that of the 6 phase. When fitted to Gaussians, the HWHM of the calculated ion angular distributions are 32" & 3" and 24" & 4" for the 6 and 5 phases, respectively. These calculated widths are in good agreement with the experimental dis- tributions, which have HWHM of 35" k 3" for the 6 phase and 28" k 3" for the c phase.In the c phase, the ground-state 0, molecules are, on average, oriented normal to the surface. Thus, the observed and calculated distributions of 0-ions from the 5phase appear to be in accord with the conventional ESDIAD mechanism, in which the momentum transfer to the dissociation fragments occurs predominantly along the bond axis.,' This interpretation assumes that, on the timescale of dissociation, the orientation of the bond axis remains fixed with respect to the surface. This interpretation fails when applied to the ion angular distributions obtained from the 6 phase because, prior to dissociation, the 0, molecules are oriented, on average, parallel to the surface.Both the calculated and experimental angular distributions of ions have greatest fluence in the direction normal to the surface. The similarity between the [ and 6 phase angular dis- tributions suggests that the initial orientational order of the 0, molecules is lost during the dissociation process. The trajectory of a typical desorbing molecule is shown in Fig. 5. Upon excitation the predominant motion is the rapid expansion of the intramolecular bond. The kinetic energy associated with this motion (given by the difference between the potential energy of the molecule in its initial excited-state configuration and the dissociation limit of the excited-state intramolecular potential well) is of the order of 4 eV; almost two orders of magnitude larger than the molecule-surface binding energy of 80 meV.Consequently, the expansion of the intramolecular bond forces the end of the molecule nearer the surface against the hard repulsive wall of the molecule-surface potential. This collision Electron-driven Dynamics 0 10 20 30 40 50 60 70 60 90 emission angle to normalidegrees emission angle to normalidegrees Fig. 4 Calculated angular distributions of 0-ions from 0, physisorbed on graphite. (a) 1 ML 6 phase DD, (b) 1 ML [ phase DD, (c) 1 ML 5 phase DA, with the electron localised on the atom closest to the surface, (d) 1 ML ( phase DA, with the electron localised on the atom farthest from the surface and.(e) 1 ML [ phase DA, with the electron randomly localised on either 0 atom.In each case the data have been fitted with a Gaussian distribution about the surface normal (+--) with best-fit HWHM of 18 & 2" (5 phase DA), 24 f4" ([ phase DD) and 32 f3" (6 phase DD). results in energy transfer into rotational and translational modes; as the molecule is thrown away from the surface its orientation is randomised. This molecule-surface collision, and the subsequent rotational excitation, is the dynamical origin of the similarity between the angular distributions of the 6 and [phases. This mechanism explains the similarity of the ion distributions from both phases but does not explain the existence of the peak normal to the surface. En route to the mass- spectrometer the desorbing ions must escape the image potential well.As indicated above, the height of this barrier, for both the 6 and [ phases, is ca. 1.5 eV.r3i17 The mean Ekinof the desorbing 0-ions was found to be ca. 2 eV. The similarity of the ion Ekin and the barrier height implies that the image potential acts as a filter, selecting for desorption only those ions with the largest components of velocity normal to the surface. Ions desorbing at larger angles relative to the surface normal arc back into the surface. We now consider dissociative attachment. Since DA produces an ion and a neutral atom, an additional degree of freedom enters the problem: the location of the trapped electron upon dissociation of the molecule. Fig. 4(c) and (d) show the calculated 0-ion R.J. Guest et al. 10 0-2-0-6-4-2 0 2 4 60-8-8-6-4-2 0 2 4 6 8 distance in the plane of the surface/A Fig. 5 Trajectory evolution of a desorbing molecule. The time between frames is 1 fs; (a)0.0 fs-(h)7.0 fs. angular distributions when the electron is localised, on the 0 atom, respectively, closer to and farther from the surface. Fig. 4(e) shows the resulting distribution if the electron is randomly localised on either 0 atom. Again, the model distribution, like the experimen- tal distribution, Fig. 3, is peaked on normal. The HWHM of the calculated and experi- mental distributions are 18" f2" and 21" & lo,respectively. 6. Reactions on Surfaces In addition to studying the dissociation dynamics of 0, ,we have explored the chemical reactions which can occur between the 0-ions produced by DA and neighbouring oxygen molecules. We found that in addition to 0-ions, it was possible to detect with the mass spectrometer 0; ions emitted from the surface.0, is formed by the collision of an 0-ion produced by DA (or DD) with another 0, molecule 0-+o,+o, (6) Fig. 6 shows the yield of 0; ions from a 4 ML film of OJgraphite as a function of incident electron energy; the figure shows a broad peak at ca. 13.5 eV with a shoulder at ca. 8 eV. Comparing the 0; spectrum (Fig. 6) with the 0-yield (Fig. l), we see that the 8 eV feature is almost completely suppressed in the 0; yield, such that the spectrum is domi- nated by the 13.5 eV DA resonance. This effect appears to be another manifestation of the polarisation potential effects; for 0; to escape the surface and be detected, it must have sufficient velocity normal to the surface to escape the surface polarisation potential EEectron-driven Dynamics 15 ll,llll,llrll,l,lll,llll ---e --em -N lo --5--c-.-m m-0" 5-e 0\fie*--? -eme 3 --(estimated to be 0.6 eV at this coverage17).It is possible to estimate the kinetic energy of the desorbing 0; species by considering a simple binary collision model for this reac- tion. In this model, the 0-ion coalesces with a stationary 0, molecule, and there is no significant exchange of momentum with neighbouring molecules. The reaction is exo- thermic, liberating 1.75 eV of energy3' (assuming reactants and products are in their ground states), but conservation of momentum requires that the kinetic energy of the 0, species is one third of the initial 0-kinetic energy.Sambe and Ramaker3' have assigned dissociation limits to the 0; DA resonances and this allows the kinetic energy of the fragments from an isolated 0, molecule to be determined. Thus for the 13.5 eV resonance the maximum 0-&in is ca. 3.75 eV, whereas for the 8 eV resonance, it is ca. 2.25 eV. This gives values of 1.25 and 0.75 eV for the 0; ion Ekin,respectively. It is readily apparent that the 0; ion &in at 8 eV incident-electron energy is close to the value of the polarisation potential whereas at 13.5 eV electron energy it is signifi- cantly greater.Thus, only a few 0-trajectories from the 8 eV resonance lead to desorp- tion (those close to the surface normal direction), while many more trajectories may lead to desorption at 13.5 eV, explaining the dominance of the higher energy DA resonance in the 0; yield spectrum. Conclusions We have studied the desorption of negative ions (0-and 0;) produced by low-energy electron impact on physisorbed films of oriented 0, molecules on graphite. The relative contributions to the 0-yield from DA and DD are dependent on the thickness of the adsorbate layer. This result is explicable in terms of the relative magnitudes of the ion Ekinand the image/polarisation potential, which also appears to determine the yield of 0; ions as a function of incident-electron energy.We have also measured the angular distribution of emitted 0-ions; these are found to be independent of the initial molecu- lar orientation on the surface, suggesting a loss of orientational order on the timescale of dissociation. Classical trajectory calculations show that this is due to rotational excita- tion of the molecule during the dissociation process and we anticipate that this could be a quite general feature of the dissociation dynamics in physisorption systems. We are grateful to the UK SERC and the Royal Society for financial support of this work. R.J.G. wishes to thank ICI for a CASE studentship. P.J.R. acknowledges support from the Donors of the Petroleum Research Fund, administered by the American R. J.Guest et al. 127 Chemical Society, and P.J.R. and D.N.B. acknowledge support from the UMBC Desig- nated Research Initiative Fund. We thank Dr. A. W. Moore of Union Carbide for providing the HOPG crystals. References 1 R. E. Palmer, Prog. Surf. Sci., 1992,41, 51. 2 R. D. Ramsier and J. T. Yates, Surf: Sci. Rep., 1991, 12, 243. 3 A. Danon and A. Amirav, Phys. Rev. Lett., 1988,61,2961. 4 C. T. Rettner and C. B. Mullins, J. Chem. Phys., 1991,94, 1626. 5 St-J. Dixon-Warren, E. T. Jensen and J. C. Polanyi, Phys. Rev. Lett., 1991,67,2395. 6 R. A. Bennett, R. G. Sharpe, R. J. Guest, J. C. Barnard, R. E. Palmer and M. A. MacDonald, Chem. Phys. Lett., 1992, 198, 241. 7 G. Dujardin, L. Hellner, L. Phillipe, R. Azria and M. J. Besnard-Ramage, Phys.Rev. Lett., 1991, 67, 1844. 8 M. S. Dresselhaus and G. Dresselhaus, Adv. Phys., 1981, 30, 139. 9 R. J. Guest, A. Nilsson, 0.Bjorneholm, B. Hernnas, A. Sandell, R. E. Palmer and N. Mirtensson, Surf: Sci., 1992, 2691270,432. 10 L. Sanche, Phys. Rev. Lett., 1984,53, 1638; J. Phys. B, 1990,23, 1597. 11 D. Rapp and D. D. Briglia, J. Chem. Phys., 1965,43, 1480. 12 L. Sanche and L. Parenteau, J. Chem. Phys., 1990,93,7476. 13 E. T. Jensen, R. E. Palmer and P. J. Row, Phys. Rev. Lett., 1990, 64, 1301; Chem. Phys. Lett., 1990, 16, 204; Surf: Sci., 1990,237, 153. 14 R. Azria, L. Parenteau and L. Sanche, Phys. Rev. Lett., 1987,59, 638. 15 K. Jacobi, M. Bertolo and W. Hansen, J. Electron Spectrosc. Relat. Phenom., 1990,54/55, 529. 16 R. E. Palmer and P.J. Rous, Rev. Mod. Phys., 1992,64,383. 17 A. Nilsson, R. E. Palmer, H. Tillborg, B. Hernnas, R. J. Guest and N. Mirtensson, Phys. Rev. Lett., 1992,69,2426. 18 T. E. Madey and J. T. Yates Jr., Surf: Sci., 1977,63,203. 19 W. L. Clinton, Surf: Sci., 1981,112, L791. 20 Z. Miscovic, J. Vukanic and T. E. Madey, Surf: Sci., 1984, 141, 285. 21 E. Hasselbrink, Chem. Phys. Lett., 1990, 170, 329. 22 E. Whittaker, Analytical Dynamics, Dover, New York, 4th edn., 1944. 23 F. R. Gilmore, J. Quant. Spectrosc. Radiat. Transfer, 1965,5, 369. 24 P. M. Dehmer and W. A. Chupka, J. Chem. Phys., 1975,62,4525. 25 H. H. Michels and F. E. Harris, in Seventh International Conference on the Physics of Electronic and Atomic Collisions: Abstracts of Papers, North-Holland, Amsterdam, 1971, vol. 11, p. 1170. 26 G. J. Schulz, Rev. Mod. Phys., 1973,45, 3. 27 V. Bathanabotla and W. Steele, Can. J. Chem., 1988,66,866. 28 G. Vidali, G. Ihm, H-Y. Kim and M. W. Cole, Surf. Sci. Rep., 1991,12, 133. 29 See, for example: T. E. Madey, S. A. Joyce and A. L. Johnson, in Interactions of Atoms and Molecules with Surfaces, ed. V. Bortolani, N. H. March and M. P. Tosi, Plenum, New York, 1st edn., 1990. 30 Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 72nd edn., 1991. 31 H. Sambe and D. E. Ramaker, Surf: Sci., 1992,2691270,444. Paper 3/03074A; Received 27th May, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600117

出版商:RSC    

年代:1993

数据来源: RSC

摘要:

Faraday Discuss., 1993,96, 129-149 Photochemistry of Adsorbed Molecules Part 13.-Localised Atomic Scattering in the Photolysis of HI/LiF(OOl) V. J. Barclay, W-H. Hung, J. C. Polanyi,* G. Zhang and Y. Zeiri? Department of Chemistry, University of Toronto, Toronto M5S lA1, Canada We have measured the translational energy distribution, P(E;), for atomic H coming from 248 nm and 193 nm photolysis of HI adsorbed on LiF(001) at a coverage of 0.7 ML (monolayers). At both wavelengths P(Ek) showed evi- dence of three contributions as follows: (a) The most energetic H was desig- nated H(1); the energetics indicated that in this channel HI(ad) photodissociated to give ground-state I(2P3,2). (b) Fast H with approx- imately 1 eV lower peak energy was designated H(I*); in this case the energy corresponded to HI(ad), giving H + I*(2P1,2).(c) The third component was slow H observed down to ~0.5eV; it was interpreted as being inelastically scattered and was designated H(Ine1).For photolysis at 248 nm the highest energy component, H(I), had a peak translational energy (Ek), = 2.0 eV, and the second component H(I*) had (Ek), = 1.1 eV. For photolysis at 193 nm H(1) had (E;), = 3.4 eV and H(I*) had (Ek)p= 2.5 eV. These energies for the scattered H at each wavelength are the same as those reported for H recoil- ing from photolysed gaseous HI; it appears therefore that HI(ad) gives the contributions H(1) and H(I*) by elastic scattering. The yield ratio H(I)/H(I*) from HI/LiF(001) was comparable with that for the gas phase for 248 nm photolysis of HI/LiF(001), but was greatly reduced from its gas-phase value at 193 nm.Taken together with the enhanced H(Ine1) at 193 nm, this sug-gested markedly increased inelastic energy loss in collisions of the 3.4 eV H-atoms with the substrate and/or co-adsorbate. Theory, also reported here for the first time, predicted at 0.7 ML that HI(ad) would be tilted with the H-end down ca. 15" more steeply than for HBr(ad), but pointing at F-on LiF(001) as reported previously for HBr/LiF(001) [E. B. D. Bourdon et al., J. Chem. Phys., 1991, 95, 1361). This resulted in localised atomic scattering (LAS) offF-. Energy loss from the 3.4 eV H photorecoiling from HI(ad) and then colliding with F-in the substrate can be due (i) to the more complex trajectories that theory predicts for the case that HX is tilted downwards more steeply, (ii) to increased 'chattering' due to the high impact energy, and (iii) to inelasticity due to strong encounters between the photorecoiling H and adjacent HI(ad).1. Introduction The photochemistry of adsorbates is being pursued in a number of lab~ratories.'-~ A particular attraction of this line of research is the possibility that it offers for the study of inelastic and reactive encounters in an ordered layer. In an earlier experimental paper' we showed that in the case of HBr adsorbed on LiF(001) the H-atom points downward by 21 5" from the plane of the crystal in a hydrogen-bonded Br-H.--F- alignment, t Present address: Dept. of Physics, N.R.C.N., P.O.Box 9001, Beer Sheva, Israel 84190. 129 LAS in the Photolysis of HI/LiF(001) hence one can study the scattering of photorecoiling H off F-sites on the surface in what we have termed 'localised atomic scattering' (LAS).6-9 Theoretical values of 23" and 26" were calculated by alternative approaches for this Br-H downward The photochemistry of HBr/LiF(OOl) was previously studied at 193 nm.l0 The H-atom energy distribution was measured, as also was the anisotropic scattering, P(O'),of the fast (elastic) component of the H-atoms which was found to peak at 55" to the normal with respect to the LiF(001) substrate. This observed scattering angle of 55" is 14" less than that expected for specular scattering (69"); this was attributed to the effect of LAS off F-.In the present paper we give first results for the H-atom energy distribution from photolysis of HI/LiF(001) at 248 and 193 nm, and discuss our findings in the light of a simple classical trajectory calculation. In a subsequent paper we shall compare the experimental energy distributions reported here and also the angular distributions with a full dynamical study employing an optimised interaction potential. Localised scattering as an outcome of surface-aligned photochemistry has been posited independently in a theoretical study by McCarthy and Gerber, who considered the system IC1/MgO(OO1).l' The concept is also paralleled in a different context in studies of resonances and cage effects in the scattering of photorecoiling H from Ar within the gaseous complexes Ar-HX (X = Cl, Br).12'13 The Ar in the complex has a somewhat similar role to the F-surface atom encountered by the photorecoiling H from HX in the present work, i.e.it is struck in a restricted range of impact parameters due to prior alignment of HX. The relevant electronic states for the bound-to-free transitions in HI are given in Fig. 1. The lowest asymptote corresponds to the formation of H + I(2P3/2)(ground-state halogen atom); the higher asymptote to H + I*(2Pljz)(excited-state halogen atom). The difference in energy is 0.9 eV for E(I*)-E(I).I4 Dissociation to the more stable (lower) 4 3 2 h'2-0 -1 -2 -3 1.5 2.0 2.5 3.0 3.5 4.0 r/A Fig. 1 Potential-energy curves for HI (adapted from ref.15 and 17). The nature of the transition from ground to excited state is shown in parentheses: I= perpendicular; 11 = parallel. The atomic asymptotes for I and I* are indicated. V. J. Barclay et al. asymptote gives rise to H-atoms with higher translational energy, and dissociation to the upper asymptote gives a lower H-atom energy. In our earlier experimental study" of HBr/LiF(001) we found that the translational energy of the scattered H-atoms peaked at two energies corresponding to those from the gas-phase photodissociation, and con- cluded that these H-atoms had been elastically scattered from the surface. The yields of the high- and low-energy components in the H-atom translational- energy distribution from the HBr/LiF(OOl) at 193 nm corresponded closely to the 6/1 yield obtained for Br/Br* in gas-phase photolysis." Note that the energy of the recoiling H from HBr is 2.6 and 2.1 eV, a lower range than for H recoiling from HI at the same wavelength, due to the strong bond in HBr.Two elastically scattered peaks were once again obtained in the translational energy distribution of H from HI/LiF(001) at 3, = 248 nm and at 193 nm. At 193 nm the relative yields of the high- and low-energy H-atoms differed markedly from the gas phase. This finding is discussed here in terms of classical trajectory calculations and is attributed to increased inelasticity at the high translational energy (3.4 eV) of fast H in the system HI/LiF(001) at 193 nrn.2. Experimental The experiments were performed in a UHV chamber (base pressure 1 x lo-'' Torr) shown schematically in Fig. 2. The apparatus has been described in detail elsewhere." A doubly differentially pumped mass spectrometer rotates around the crystal, permitting measurement of time-of-flight (TOF) spectra at specified angles to the surface, and angular distributions at specified product translational energies. The TOF path length from crystal to mass-spectrometer ioniser was 175 mm. The LiF(001) surface was cleaved in air and then annealed in UHV at a temperature of ca. 700 K by radiation heating for at least 12 h prior to an experiment. The LiF crystal was mounted on a manipulator with xyz translation and polar rotation. The crystal could be cooled to 85 K by means of a closed-cycle helium refrigerator. The HI MASS EXCIMER LASER Fig.2 Schematic of the UHV chamber. The photolytic laser beam comes from below. The differ- entially pumped mass spectrometer was rotated around the cooled crystal giving time-of-flight spectra as a function of 0'. See ref. 10. LAS in the Photolysis of HI/LiF(001) (Matheson; 99%) was purified by freeze-pumpthaw cycles before being introduced into the chamber by background dosing onto the LiF(001) surface. An excimer laser (Lumonics TE860-4) was used to irradiate the adsorbate-covered surface at 5" glancing incidence (i.e. 85" from the surface normal). The laser output was 80 mJ per pulse at 248 nm and 45 mJ per pulse at 193 nm. The corresponding intensities at the crystal surface lay in the range 1-2 mJ cm-2 per pulse, due to losses at mirrors and due to the large spot-size at the glancing angle.In the TOF measurement the LiF crystal was held at a temperature of 85 K. Follow-ing ca. 600 laser shots, co-added to produce one TOF spectrum, the LiF crystal was heated to room temperature to remove residual adsorbate prior to re-dosing. This single dosing procedure contrasts with that used in our earlier photochemical study of HBr/LiF(001). The crystal samples purchased at that data showed efficient photodesorption of intact HBr, hence a constant coverage (roughly ascertainable) was obtained by balancing continuous dosing against photodesorption. The crystals used in the present work showed negligible photodesorption, perhaps due to lower impurity levels, hence this procecedure was no longer feasible.Instead we formed a stable adsorb- ate layer prior to photolysis, and following ca. 600 shots (this would correspond to ca. 10% dissociation for HBr but only ca. 1% for HI) the residue was removed and the crystal re-dosed. This modified method of dosing could give rise to a different adsorbate structure (since the adsorbate layer has time to equilibrate) and also to a different average degree of contamination of adsorbate with photoproduct (e.g. if the halogen was inefficiently photodesorbed it would accumulate following a period of continuous dosing of the cold crystal with concurrent photolysis). We therefore repeated our earlier translational energy and angular distribution measurements on HBr/LiF(OO 1) using this single dosing method; we could detect no sigr,ificant changes. Coverages were estimated as follows.Following exposure of the cold crystal to a known dose in Langmuir (L), the desorption yield was measured by integrating the 2.5 h2 2.0 3 4 1.5 m w I! 1.0 .->. a 0.5L F 0.0 0 0 1 23 4 56 exposure/L Fig. 3 Integrated yield from TPD at various coverages. (a) HBr; (b) HI. The slope changes at around 2 L, indicative of 1 ML coverage. V.J. Barclay et al. 133 temperature-programmed desorption (TPD). The TPD was obtained by ramping the sample temperature at a linear rate of ca. 1 K s-', with the mass-spectrometer axis along the normal to the surface.A TPD for HBr/LiF(001) can be found in our earlier paper." The monolayer and multilayer components were found to be less well separat- ed in the TPD for HI than that for HBr. Both HBr and HI showed a peak desorption yield at ca. 110 K corresponding to a heat of adsorption A,, H FZ 0.27 eV assuming a pre-exponential factor of 1OI2 (ref. 16). The integrated TPD yields are shown for HBr and HI in Fig. 3(a) and (b) as a function of the dose in L. It is evident that in both cases the yield function shows a change in slope at ca. 2 L; we ascribe this to a change from a layer in contact with the crystal (<1 monolayer, ML) to an overlayer (>1 ML). The doses of HBr (used in the check mentioned above) and of HI, both 1.5 L, are therefore considered to correspond to ca.0.7 ML. 3. Results 3.1 Energy Distributions Fig. 4(a) shows a typical TOF spectrum of H-atoms from HI adsorbed on LiF(001) at ca. 0.7 ML coverage, The photolysis wavelength was i= 248 nm, and the mass-spectrometer detector was set roughly at the peak of the H-atom angular distribution 45" to the normal. The corresponding translational-energy spectrum is shown in Fig. 4(b). A conversion factor of t2 (t = time; t-' corrects for the changing efficiency of the ioniser with velocity, and a further t3 converts the corrected TOF to an energy distribution) has the effect of magnifying errors at the low-energy end of the TOF spec- trum. The TOF shown in the figure represents the sum of three individual single-dose spectra, each taken with ca.600 laser shots directed at a freshly prepared surface. Fig. 4(b) shows two distinct peaks centred at 1.1 and 2.0 eV, corresponding, within experimental error, to the excess energies from the two HI photodissociation pathways in the gas phase at A =248 nm.15917 Since these same energies are present in the scat- tered H, we conclude that [as for HBr/LiF(001) at ?, = 193 nm in our earlier work''] there is efficient elastic scattering of H at the crystal. The ratio of the yield of scattered H at 1.1 eV to that at 2.0 eV is ca. 2/1. Photolysis to form I* gives the slower photorecoiling H, and photolysis to form I gives the faster H. The ratio of yields of I/I* in gas-phase photolysis at 248 nm is 54/46.'5*'7 This is within a factor of two of the observed ratio of 'slow' to 'fast' H leaving the surface at 45" [Fig.4(b)]. There is a small amount of inelastic scattering yielding very low energy H, indicated in Fig. 4(b) as H(Ine1). This is a broad distribution, extending from r-ughly 0 to 1 eV. The-inelastic events could involve collisions between photorecoiling H and the surface, or H in collision with co-adsorbed HI(ad). A similar low-energy tail on the two hot- atom translational energy peaks in the scattered H was observed for HBr/LiF(OOl), 13. = 193 nm, icour previous work." It was ascribed in the earlier experimental study to the effect of H +HBr(ad) collisions, since the magnitude of the 'tail' was found to increase with coverage.The ratio of yields for the two peaks in the scattered H energy distribution that we ascribe to elastic scattering at 248 nm, H(1) at 2.0 eV, and H(I*) at 1.1 eV, varied with the angle 0' at which the scattered H was measured. The ratio H(I)/H(I*) was ca. 2 from 0 to 50°, decreasing to unity in the region 50-90". This appeared to be due to a some- what broader angular distribution for H(I*) than for H(1). Fig. 5(a) and (b)show the TOF and the corresponding translational energy distribu- tion for H-atoms scattered from HI/LiF(001) at a markedly shorter photolytic wave- length, il = 193 nm. The detection angle was 57.5", and the coverage was 0.7 ML. The LAS in the Photolysis of HI/LiF(001) 0 5 10 15 20 25 time of flight/ps 00 05 10 15 20 25 30 translational energy/eV Fig. 4 (a)Experimental TOF spectrum of H-atoms detected at 8' = 45" after 248 nm photolysis of HI/LiF(001).(b)Translational energy distribution derived from (a),showing peaks due to product formation of I and I*. The gas-phase ratios, I/I* (ref. 15, 17) are shown as vertical lines, normalised to the higher peak. spectrum shown is (as before) the sum of three spectra, from three separate dosings of the crystal. The qualitative appearance of this energy distribution was insensitive to the angle of observation. We expected in this case to observe an elastic peak, H(I), at 3.4 eV, and a second peak, H(I*), at 2.5 eV since these are the measured energies of H-atoms recoiling from HI(g) at A = 193 nm. These two elastic peaks are indeed evident in Fig.5(b). However, the ratio of the yields of these peaks (in contrast to the situation at R = 248 nm) differs markedly from the ratio of I/I* in the photolysis of HI(g) at the same wavelength, 193 nm. The H(1) peak in the gas pha~e'~?'~ is nine times the H(I*) peak, whereas the H(I) peak for H scattered from LiF(001) is 0.25 times the H(I*) peak, a discrepancy of 36 times. We discuss the origin of this discrepancy in Section 4.3 below. There is an additional change in the qualitative nature of the translational energy distribution of H from HI/LiF(001) at 0.7 ML as between Fig. 4(b)(A = 248 nm) and 5(b)(A = 193 nm). Inelastic scattering has altered from being a relatively minor pathway at V. J.Barclay et al. h2 15 Y I I I I I 0 5 10 15 20 25 30 time of flight/ps n I m v 06-Q > w.-v) 04-+-0) .-C 0 2-0 o--00 05 10 15 20 25 30 35 40 45 50 translational energy/eV Fig. 5 (a) Experimental TOF spectrum of H-atoms detected at 0' = 57.5" after 193 nm photolysis of HI/LiF(001). (b) Translational energy distribution derived from (a), showing peaks due to product formation of I and I*. Gas-phase ratios, I/I* (ref. 15, 17), are shown as vertical lines, normalised to the higher peak. 248 nm to being the major pathway at 193 nm [compare H(Ine1) in each figure with the elastically scattered H at the right in that figure]. These two new features at 2= 193 nm, loss of the rapidly moving H(1) and gain in +H(Inel), are likely to be related.For the calculated angle at which the photorecoiling H from HI(ad) impacts on the surface F-the energy loss may be greater at 3.4 eV collision energy than at 2.5eV, for reasons noted in Section 4.3. Inelastic collisions with co-adsorbed HI(ad) will also result in greater energy loss in the case that the colliding species is moving faster, espezially if the enhanced translation allows reaction or abortive reaction to occur in H + HI(ad) encounters as is the case here. Before presenting some model calculations illustrative of inelastic processes that could be responsible for energy loss from the 3.4 eV H, we consider other possible explanations for the observed marked diminution in H scattered from the surface at 3.4 eV.136 LAS in the PhotoZysis of HI/LiF(001) The first alternative explanation is a possible experimental artefact. Following electron-impact ionisation H+ is accelerated into a 115" deflector prior to entering the quadrupole field of the mass spectrometer. We have considered the possibility that low- energy ions may be deflected whereas high-energy ions are lost. The relative transmis- sion efficiency of the deflector has been measured (ref. 18, Fig. 2.5).If the ion acceleration voltage is set to 2 eV below the optimal value, the transmission is found to be virtually flat for incoming atoms of 0-4 eV. As a further check we have recorded an approximate TOF on a machine that has the mass spectrometer in line with the crystal (no deflector); we obtained a spectrum in qualitative accord with Fig.5(b). Another explanation for the anomalous ratio of the elastic-peak heights in Fig. 5(b) could, in principle, be a dramatic change in the relative yield of I/I* in the photolysis of HI(ad) as compared with HI(g). This could arise from a change in the nature of the crossings and avoided crossings between electronically excited states, so that disso- ciation takes place to a different asymptote. Since no marked change in I/I* was observed at A = 248 nm, nor in Br/Br* at A = 193 nm in our previous work, it appears improbable that the surface induces a change in branching ratio, due to the above effects, of well over an order-of-magnitude in I/I* at A = 193 nm. A third possible explanation for the dramatic change in branching ratio at 193 nm concerns the effect of the surface in polarising the incident photolysis radiation (initially unpolarised).Owing to surface reflectance, the p-polarisation of the laser field is enhanced by 37%, in comparison with s-polarisation. A 'horizontal' molecule, i.e. one lying with its principal axis parallel to the plane of the surface, would thus have its perpendicular transitions enhanced. Conversely, a 'vertical ' molecule, sitting perpen- dicular to the surface, would have its parallel transitions enhanced. In the most conser- vative estimate, if all adsorbate were parallel to the surface, the branching ratio for I/I* for HI(ad) photolysed at 193 nm would be 9 x 1.37/1 i.e. 12/1; whereas if all adsorbate molecules were vertical, the branching ratio would be 9/1.37, i.e. 6/1.A median tilt angle of 0 = 130"(FWHM = 30") is predicted for HI/LiF(001) as a result of theoretical calcu- lations reported in the next section. Since half of the adsorbate molecules would have 0 somewhat less than 130" and the other half would be tilted at 0 somewhat greater than the median, the small effect of UV polarisation should be undetectable on the average, whereas the modification in the yields from the two pathways (fast/slow H) is very large. We have, in addition, empirical evidence that laser polarisation is not the cause of the large anomaly in the fast/slow H-atom yield ratio at 193 nm, since we have obtained H-atom TOF at angles to the normal ranging from 10 to 80" (with fixed laser angle-of- incidence).Within a factor of ca. 2 the yield ratio is as depicted in Fig. 5(b). It follows that reflection enhancement of the p-polarisation of the incident light can be ruled out as the dominant source of the anomaly in the ratio of H(I)/H(I*) at 3.4 eV. 3.2 Angular Distributions We shall discuss the angular distributions for the high-energy elastically scattered H-atoms in detail in a subsequent paper (see Section 3.1, above). We summarise their major features here. For 248 nm irradiation of HI/LiF(001) the fastest H (2.0 eV) gave an angular dis- tribution that peaked at 8= 45 k 5". (The yield of H was integrated over k0.5 eV centred on 2.0 eV.) The form of P(0') was represented by a slow rise from 0 to 45" and a steep decline (to 50% by ca.55") in the range 45-90". The integrated yield at <45" was roughly double that at 245". For 193 nm irradiation the fastest H (3.4 eV) gave a markedly broader angular distribution. (The yield of H was, once again, integrated over f0.5 eV, but centred this time on 3.4 eV.) The signal-to-noise was poor due to the feeble signal at 3.4 eV, ascribed in the foregoing text to inelastic scattering. The P(0') exhibited no clearly defined peak; V. J. Barclay et al. 137 the maximum yield lay in the range 20-50". The breadth of the angular distribution was indicative of a significantly modified interaction with the LiF surface at 3.4 eV as com- pared with 2.0 eV. In the following sect@ we link the modified dynamics at 3.4 eV to more complex encounters, H + Surf and H + HI(ad), resulting in energy loss that dimin- ishes the yield of 3.4 eV H-atoms.A minority of such more complex encounters (H colliding with the heavy atoms, F or I) can deflect the H trajectory without the loss of >0.5 eV. In this case the scattered H will be included in the P(0') for 3.4 eV, but one would expect the angular distribution to be broadened, as indeed observed. 4. Theoretical In order to provide an acceptably realistic, yet simple, model of the high-energy hydro- gen scattering from the LiF(001) surface and from adsorbed molecules, we have per- formed a stochastic classical trajectory (SCT) calculation, using the generalised Langevin equation, which includes 'ghost particles' in the substrate, as described in ref.19. These ghost particles allowed the surface to exhibit motion and thereby to exert random damping forces on adsorbates, as in ref. 8 and 20, and in contrast to the 'frozen' surface used in ref. 9 (quantum scattering calculation). The equilibrium geometry for HBr/ LiF(001) has been studied extensively in ref. 7. Forms for the potential were recommend- ed, which, with some modifications, have been used in the present study. An earlier study* of HBr/LiF(001) using this general form of the potential gave a dynamical simulation of LAS, i.e. of the photolysis of a single HBr adsorbate molecule with the H-atom directed at a preferred location on the corrugated surface. This study predicted the form of non-reactive H-atom scattering patterns near the 'zero coverage' limit, in which the predominant scattering is from the crystal surface.The mass ratio was such that very little energy transfer between the hot H-atom and the surface occurred so that collisions were nearly elastic. In the present case the photon energy was 193 nm, i.e. 148 kcal mol-l. About 72 kcal mol-' of this energy was consumed in breaking an HI bond, leaving an excess energy Ex, = 76 kcal mol-l, as determined from Ex, = E(hv) -Do, where Do is the bond-dissociation energy. In photolysis, most of the excess energy becomes translational energy of the H-atom, E,, which is modified to Ek following collision with the surface and/or adsorbate. A fraction of the excess energy was used to overcome the energy of physisorption, AQad, w5kcal mol-'.In the calculation, further excess energy, ca. 10 kcal mol-', arose from the repulsion between atomic H in electronically excited HX and the surface. This repul- sion, was related to the fact that at the instant of photolysis, the H was changed from being molecular H within HX to atomic H. The energy available for translational excitation of the departing atomic H was therefore' In the present work we consider a coverage of one molecule and also 0.7 ML. The 0.7 ML coverage consisted of 14 molecules, with 1'-(6-represents a negative charge of less than unity) located over Li'. The 14 molecules were distributed on adjacent sites within an 18-site area of LiF consisting of a 7 ion x 7 ion slab with periodic boundary condi- tions.8 At 0.7 ML the hot H-atom will in many cases collide with HX(ad) before leaving the surface; provision is made for this in the calculation by including both inelastic and reactive encounters with H with adsorbate, as described below.4.1 Potential The interaction potential is described in three parts; the physisorption potential (adsorbate-surface and adsorbate-adsorbate), the reactive potential, and the switching LAS in the Photolysis of HI/LiF(001) function that switches between atomic and molecular environments as the photofrag- ment interacts with co-adsorbate. The physisorption potential-energy function used7-9g20 for HBr/LiF(OO 1) was applied once more to HI/LiF(001).It can be summarised as : The interaction of the adsorbate molecule with the LiF(001) surface (Vas) and with other adsorbates (Vaa) was described by potentials which consisted of electrostatic (T/el) and non-electrostatic (Vnel)contributions whose pairwise functional forms were described in ref. 7. The parameters used in that work for the potential functions were intended to describe HBr/LiF(001) with HBr in its ground electronic state. We have, in the present work, replaced these parameters by values appropriate to HI(ad); see Table 1. The fol- lowing is a brief description of the terms in the physisorption potential. The electrostatic interaction between the adsorbate and surface, V::, was the prin- cipal contributor to the overall stability.As estimated from Monte Carlo calculations of one monolayer coverage, the electrostatic adsorbate-surface interaction contributed ca. 75-85% of the total energy of HI/LiF(001) physisorption, as compared with ca. 80-95% of the total energy of HBr/LiF(001) physis~rption.~~~' It is thus important to model this term accurately. In the two point-dipole model chosen to model the adsorbate molecule the charge cloud on the molecule was approximated as two point-dipoles, pH and px, situated at the nuclei of an adsorbate molecule. The point-dipole was taken as pi = piu, where u is the unit vector pointing along the bond axis of the molecule to which the nucleus belongs. The adsorbate-surface electrostatic potential was described by the interaction of these point-dipoles fixed on the H and X sites with the permanent electric field at the (001) face of the LiF ionic crystal.Lennard-Jones and Dent have derived the form of this electrostatic potential.22 The values used for the HBr point-dipoles are as in ref. 8. The values used for the HI point-dipoles were apportioned to give the experimen- tally known molecular dipole23 and calculated quadr~pole;~~ they were pl= 1.3672 Dt at the hydrogen site and p2 = -0.9195 D at the iodine site. With no repulsive potential to counteract the electrostatic term, the adsorbate dipoles would fall into the surface ions. The force to balance the strong ion-dipole forces was provided by the non-electrostatic potential. In constructing the non-electrostatic adsorbate-surface potential, Vzl, we used the damped Tang-Toennies potential2 which was summed as a 2D Fourier series26 over (001) layer of the solid.7 The c6 and Table 1 Calculated Tang-Toennies gas atom plus surface-ion potential parameters [Lennard-Jones (6-12) parameters for the adsorbate HI] Tang-Toennies A/eV /J/%.-' c,/eV A6 c,/eV A' H(atom)-Li+ H(at om)-F -H(mo1)-Li + H(mo1)-F -I-Li + 174.6 174.5 189.0 177.1 1680.0 3.776 2.877 4.50 3.28 4.156 0.125 2.585 0.125 2.585 2.435 0.196 3.404 0.196 3.404 3.914 I-F - 630.0 3.092 57.90 122.0 Lennard-Jones (6- 12) &/kcal mol - 4 H-H 0.0266 2.735 1-1 0.561 3.89 H-I 0.122 3.310 t 1 D x 3.335 64 x C m. V.J. Barclay et al. c8, and Born-Mayer parameters needed for the H-Li+, H-F-, Br-Li+ and Br-F- interactions are as given in ref.8 (Table I). Values for the H-surface ion interaction parameters are given for both atomic and molecular environments. This is because the charge distribution around an atom depends on whether it is a free atom or is bound to another atom. Thus, a distinction should be made between atomic and molecular states of the H and X atoms when assigning parameters for their interactions with the LiF surface. In practice, however, the types of environment (and the switching between them; vide infra) were found to be significant only for the H-atom. The non-electrostatic parameters for the I-atom were obtained from the polarisabil- ities and the HI-HI dispersion coefficients.The derivation followed that for the Br-atom parameters7.* and is discussed in more detail elsewhere.21 The values used are given in Table 1. Where more than one adsorbate molecule was present, inclusion of the adsorbate- adsorbate interactions (electrostatic, nonelectrostatic, and reactive) was necessary. In previous work the Vgf term was modelled by three fractional point charges along the axis of HBr.7 The point charges were chosen so as to give the correct dipole and higher multipoles of HBr. One of these point charges, q3 (Fig. 1, ref. 7), was located 1.29 8, beyond the centre of the Br atom, away from the H. This was unphysical. In the present dynamical study we replaced the three point-charges by two point-dipoles located on the I-atom and H-atom, respectively, This was thought to be advantageous in order that the charges q3 on adjacent adsorbate molecules did not repel and obstruct reorganisation of the adsorbate during equilibration.In the previous work using Monte Carlo techniques27 this problem was less severe since molecules were free to flip through 90 or 180”during equilibration. The energy of interaction between two adsorbates modelled by two point-dipoles, described above, is based on the standard dipole-dipole interaction term, as in ref. 28 : The adsorbate-adsorbate point-dipole interactions were calculated between each nucleus of each pair of molecules a distance rij apart, with four interaction terms per adsorbate pair. Finally, the last term of the physisorption potential in eqn.(2), the non-electrostatic adsorbate-adsorbate term, V/antl, was modelled using a Lennard-Jones (6-12) function; the parameters are given in Table 1. We turn next to the reactive potential, H + H’X. Such a collision can have three outcomes: H + H’X +HX + H’ (exchange), +HH’ + X (abstraction), or -+H + H’X(v’, J’) (inelastic scattering). Although the branching ratios are not the subject of this paper, abortive exchange or abstraction, or full exchange reaction, was a significant source of H(Ine1). The interaction of the atomic photofragment H with its nearest molecular neighbour was modelled using a London-Eyring-Polanyi-Sat0 (LEPS) potential,29 as in ref. 30. The Morse parameters D,,p and re ,and Sat0 parameters S, for H + HI were for H-I D,= 73.78 kcal mol-’, p = 1.750 k’,re = 1.604 8,, and S(H1) = 0.0915, as given in Table I of ref.31. For H-H the corresponding parameters were 109.458 kcal mol-’, 1.9413 A-’, 0.742 8, and 0.353, as given in Table I of ref. 30. The closest HX molecule to a photorecoiling H situated in the forward hemisphere (i.e. along the direction of motion) is designated the ‘target molecule’. The interaction potential with this target molecule was changed from the adsorbate-adsorbate physi-sorption potential to the reactive potential following collision with the surface when a target molecule was identified. The need for a switching function is apparent from the following considerations. The interaction of H and H’ in an H + H’X(ad) reactive or inelastic encounter as already 140 LAS in the Photolysis of HI/LiF(001) noted is described by a LEPS function.The incoming H must gradually be reduced in size from its atomic to its molecular radius, and must at the same time have its point- dipole increased from zero at infinite separation to the value appropriate to HX at equilibrium re. This affects the interaction of H with surrounding atoms. Concurrently the departing H’ goes through reciprocal changes. In order to represent these changes in a smooth fashion we have scaled the atomic radius and the point-charge to the bond order (the ‘fraction’ of a bond, first introduced by Pauling3,). The gradual shift from ‘atomic’ to ‘molecular’ H interaction with the neighbouring environment was accom- plished by means of a ‘switching function’ based on that employed by Shustor~vich.~~ Details of the switching function used are to be found in another paper from this labor- atory.,’ The slow-moving photorecoiling X is assumed to be non-reactive.Once reaction occurred, for computational simplicity, the product H-atoms were not allowed to react with another adsorbate. 4.2 Trajectories The calculations reported here were of two kinds. In the first idealised case, a single adsorbate molecule was artificially fixed at a certain geometry above an Li’ ion site, and not allowed to thermalise. In the second more realistic case, several molecules rep- resenting ca. 0.7 ML coverage were distributed over a section of the crystal and allowed to thermalise.Thermalising the ensemble consisted of integrating the initial configu- rations of the adsorbate particles for tens of thosands of time-steps of 10 au (1 time au z 2.4 x s) until thermal equilibration to within 10 K of the surface tem- perature of 100 K was achieved. Ghost particles (see Section 4.1) permitted the exchange of energy with the substrate during equilibration.’ For both idealised and realistic cases, photolysis was initiated as described in ref. 8, and the trajectory was integrated with a time-step of 1 au for up to 20000 steps or until the product atom and/or molecule were desorbed. Both idealised and realistic trajec- tories included ghost particles, in order to allow exchange of energy between the adsorb- ate and the surface.For realistic calculations, the identity of the target molecule was checked every 100 time au along a trajectory, and reaction was considered to have occurred once the photofragment had been closest to a certain target atom for three vibrational periods of the newly formed molecule. Both HX and H, were observed as reaction products; a detailed description of the reactions occurring in sub-monolayer surface-aligned photochemistry forms the basis of a separate report from this group.20 Desorption for either reactive or non-reactive cases was considered to have occurred after the molecular product was 4.5 8, from the surface, or the H-atom was 10 8, from the surface. Over 1600 trajectories with 0.7 ML coverage were sampled. For this substantial coverage the pattern of adsorption is significant.Previous theoretical studies of HBr/ LiF(001) supported the hypothesis of a ‘checkerboard’ pattern (Fig. 6), where the ratio of adsorbate molecules per unit cell is 1 : 2, with alternate cells having no adsorbate molecule. The unit-cell size of LiF(001) is 4.03 A whereas the lattice constant of solid HBr (Phase I1 in this temperature range) is34 3.96 8,. We modelled the HI as being in a checkerboard adsorption pattern for which only alternate sites are occupied. This mini- mised the difference in AadH between HBr and HI (ca. 10% difference). Experimentally, it was found that AadH (HBr) z AadH (HI) to within 5-10% assuming the same pre- exponential factor. Although the lattice constant for solid HI at 80 K, 4.27-4.32 is larger than that of the LiF(001) unit cell, since only alternate sites are adsorbed there is sufficient room on the crystal surface to accommodate a checkerboard HI/LiF(001), albeit with a larger z-height variation than for HBr.Islanding was promoted in the initial distribution of the adsorbate by choosing adjoining adsorption sites. During V.J. Barclay et al. Fig. 6 Calculated equilibrium geometries of HX adsorbed on LiF(001) at 100 K. Top-down view. The lattice ion positions and the van der Waals radii of H and X are drawn to scale. (a) HBr/ LiF(001); (b)HI/LiF(001). equilibration the I moves very little; only the H moves substantially. For the given coverage and various energies, the following approximate numbers of trajectories were run: 800 at 3.4 eV, and 400 at each of 2.5,2.0 and 1.1 eV.4.3 Theoretical Results Fig. 6 shows, for comparison, top-down views of typical adsorption patterns for HBr and HI on LiF(OO1). The surface ions are represented only by ' + ' and ' -'. The aster- isks indicate the atomic centres. The van der Waals radius36 of each adsorbate atom has 142 LAS in the Photolysis of HI/LiF(001) been drawn in. Atoms which were obscured by another atom, when seen from this perspective, are drawn with a broken line. The geometries shown in Fig. 6 were calculated by the stochastic classical trajectory (SCT) approach described in the previous section. Comparison of the tilt angles with those obtained by the Monte Carlo method used in earlier work7 shows that the X-H bond was tilted down slightly more steeply in the SCT approximation (2-3").We attrib- ute this to the small extension that occurs in the non-rigid X-H bond, in the SCT calculation; the stretched bond hydrogen-bonds a little more strongly to the underlying F-. Although the adsorption patterns for HBr [Fig. 6(a)] and HI [Fig. 6(b)] bear great similarity, two differences are apparent. The HBr adsorbate molecules are in better regis- try with the underlying lattice (the Br-atoms sit more squarely atop the Lif ions) than their HI counterparts. Secondly, the tilt angle of HI adsorbed on LiF(001) is greater than that of HBr. This is evident from the fact that the H-atoms are more completely obscured in Fig.6(b).This difference in tilt angle, 8, is more clearly evident in the dis- tributions, P(8),shown in Fig. 7. The tilt angle is almost coverage-independent in the case of HBr but changes signifi- cantly for HI. Energy minimisation for the case of an isolated 0 K molecule showed tilt angles of 116" for HBr8 and 118" for HI. The lattice constant for HI (in contrast to HBr) is so close to the unit-cell size of LiF(OOl), that the adsorbate-adsorbate interaction is sensitive to coverage. The isolated HI adsorbate sits with its I-end ca. 2.65 A above the surface. As more HI molecules are added in a checkerboard pattern to the LiF(001) surface to increase the coverage to 0.7 ML, the I-end rises 0.35 A, whereas the H-end rises by only 0.2 A from the surface.Fig. 7 shows this leads to an increased HI tilt angle of 130" (12" steeper tilt) at 0.7 ML. By contrast, with increasing coverage to 1.0 ML the peak in the HBr tilt angle is constant to within 4". 4.3.1 Inelastic Collisions fi +Surf The significance of tilt angle to the scattering dynamics is demonstrated in Fig. 8, which shows two trajectories with Ex, = 3.4 eV and the I-atom set at a single selected position 15 1 70 90 110 130 150 Oldegrees I i; Fig. 7 Calculated polar angle 8 of thermalised ensembles of adsorbate molecules on LiF(001) at T = 100 K for HBr (-) and HI (----) V. J. Barclay et al. 0 2 4 6 8 x = y cut/A x = y cut/A Fig. 8 Calculated trajectory of an H-atom after photolysis of HI(ad) to show the effect of increas- ing tilt angle. The cut along the LiF surface is in the (111) plane.The I-atom is fixed to be at (1.282, 0.997, 3.440) with the coordinate system defined as in Fig. 6. The H-I bond length is fixed as its gas-phase value23 of 1.609 A. Dashed lines indicate van der Waals atomic36 and ionic3* radii, and the solid lines show the non-electrostatic corrugation contours for the surface at 20 kcal mol-intervals. Excess energy of photolysis = 3.4 eV. Numbers along the trajectories indicate 5 fs intervals. (a) Initial tilt angle 8 = 130" leads to a direct scattering event; (b) initial tilt angle 8 = 145" leads to an indirect scattering event. slightly displaced from a Li' site (see caption). These are representative calculations both in respect of the position of the I-atom and the I-H tilt; the actual value of the tilt angle depends sensitively on the (x, y) position of the I-atom over the unit cell.In Fig. 8(a) the H-atom is tilted down from the normal to the surface plane by 8 = 130". The subsequent H-atom trajectory corresponds to 'direct' reflection at the surface (DIR in LAS in the PhotoEysis of HI/LiF(001) the figure). In Fig. 8(b),where the tilt angle has been made greater, 0 = 145",the H-atom trajectory reflects back almost normal to the surface and hence is 'indirect' (IND), colliding with the surface and the parent I-atom. A systematic variation of the tilt angle of the idealised LAS event with I directly over Li+ and the I of HI 3.4 A above the centre of Li', is shown in Fig.9, where the scattering angle 8' is plotted as a function of the tilt angle 8 for a 20" range in 8. Four distinct regions are observed, I-IV, in this small range of angles; they differ in the sign of the slope, dsl/dO. The open circles on Fig. 9 denote eight tilt angles for which the corresponding trajec- tories are shown, according to region, in Fig. 10. Examination of Fig. 10 shows that each successive region of the scattering curve in Fig. 9 corresponds to one additional turning point in the trajectory of the scattering H. The turning points are due to collisions with the surface, 's', or with another adsorbate molecule, 'a'. Region I has s only; I1 has s followed by a; I11 s, a, s and IV s, a, s, a. Fig. ll(a) gives the energy of the scattered H-atom as a function of initial tilt angle.The scattering angle (taken from Fig. 9) is shown as a broken line for comparison. In region I the H-atom suffers a glancing collision with the surface with result that rela- tively little energy is transferred. As the tilt angle increases the energy transfer becomes markedly more efficient, to the point where an H-atom initially at 6 eV can lose up to half its energy. (This, of course, takes no account of restrictions on energy transfer that may arise from phonon quantisation.) Fig. ll(b) shows the amount of translational energy gained by the I-atom and by the surface. Most of the energy lost from H goes to the surface. Since the H and I masses are very different, kinetic energy transfer to the I is not great.Through conservation of momentum, the kinetic energy transferred to the I-atom in a single encounter is expected to be only ca. 0.05 eV. The substantially larger energies being transferred at large 0 are due to multiple encounters. The amount of energy lost can be seen in Fig. 12 to depend not only on the initial tilt angle 0, but also on Ex,, which increases in the figure from 1.1 to 6.0 eV. The degree to which the H-atom can penetrate the potential-energy contours depends on its initial energy, Exs.The inner-energy contours of the surface corrugation have a smaller radius 40 70 135 140 145 150 %/degrees Fig. 9 Dependence of scattering angle, 8', on the initial tilt angle, 8,for a selected: zI = 3.43 8, and Ex,= 6.0 eV.The Roman numerals, I-IV, indicate four different scattering regions corresponding to I-IV in Fig. 10. The numbers 1-8 indicate the corresponding trajectories in Fig. 10. V.J. Barclay et al. 2 4 6 8 113 2 4 6 8 10 r/A rlA 6 6 4 4 2 2 0 0 2 4 6 8 10 2 4 6 8 10 r/A r/A Fig. 10 Trajectories of 6 eV H-atoms from scattering events with I-H tilt angles given in Fig. 9 designated by number (1-8) and region (I-IV). The open circle denotes the initial H-atom position (the I-atom is not shown). Dashed lines indicate the ionic38 radii. Collision with the surface is denoted 's'; collision with the parent I-atom is denoted 'a'. (I) Direct scattering, with only one (glancing) collision with the surface; (11) steeper initial tilt leads to collision with the surface, followed by collision with the parent I-atom; (111)still steeper tilt angle leads to repeated collision with the surface; (IV) chattering (two surface collisions, s) is occurring.The effect of a small change (1") in the initial tilt angle is shown in each panel (the steeper tilt angle leads to the trajectory denoted by the lighter line). of curvature than the outer-energy contours. This affects the scattering angle at the first encounter with the surface. As a consequence, at high energy the H-atom is reflected more nearly normal to the surface and collides with the parent I-atom, leading to greater energy loss (see below). Thus, the shape of the Ek(8)curve in Fig. 12 depends on Ex,.The high-collision-energy case (6.0eV) exhibits the earliest onset of increased energy loss, i.e.indirect scattering begins at the smallest 8. Fig. 13 illustrates the effect of increasing Ex, on the scattering dynamics. With the same tilt angle, chosen as 8 = 154", for Ex,= 3.4 eV the reflected H has a single glancing collision with the parent I [Fig. 13(a)], whereas for Ex, =6.0eV [Fig. 13(b)] the H is scattered directly back toward I and chatters several times between I and the surface. The resultant final translational energy was E!,. =2.2 eV (energy loss 1.2 eV) in the former case and Ek =2.8 eV (energy loss 3.2 eV) in the latter. 4.3.2 Inelastic Collisions fi +HI(ad) The solid line in Fig. 14 shows preliminary calculated results for scattered H-atom energy distributions simulating 193 nm photolysis at 0.7 ML coverage.We have LAS in the Photolysis of HI/LiF(001) 6 20 . (a) I I 30 5- 40 v) 50 2 4 -.:.. 0 60 9 ?E 70 3- .. *..; E'(H) - 80 90 135 140 145 150 1 5 Oldegrees Fig. 11 (a)Energy of the scattered H-atom E& as a function of initial tilt angle (solid line; left-hand ordinate axis). The scattering angle is shown as a broken line (right-hand ordinate axis). (b) Energy of the scattered I-atom and the energy absorbed by the surface, as a function of initial tilt angle. The panels designated I-IV indicdte the same regions as in Fig. 9 and 10. l'00120 130 140 O 150 1 tl/deg reesk L4777-Fig. 12 Energy of the scattered H-atom, Ek, as a function of initial tilt angle, 8,for four different excess photolysis energies, Ex,, as noted V.J. Barclay et al. L 4 0 \ /\/+\ -/ \""!"~'!"''!"'~'"'0 included two channels for HI photolysis, combined according to the gas-phase branch- ing ratio15*17 of 9/1. The values of Ex, governing the energy of the collision with the surface were 3.4 eV for H(1) and 2.5 eV for H(I*). The simulation gave a ratio of fast scattered H-atoms [the H(1) channel] to slower H-atoms [the H(I*) channel] that was about one order of magnitude less than the gas-phase ratio. This high degree of inelas- ticity corresponds qualitatively to the observed loss of the high-energy peak in the scat- tered H energy distribution; see Fig.5(b). According to these model c_alculations the major pathway for inelastic energy loss from scattered H stems from H +HI(ad) collisions. We have divided the trajectories LAS in the Photolysis of HI/LiF(001) 1 2 3 4 E;/eV Fig. 14 Heavy solid line: calculated energy distributions for H-atoms after photolysis of HI/ LiF(001) at 0.7 ML with A = 193 nm, showing peaks due to the I, I* and inelastically scattered channels. For reference, the gas-phase ratios (ref. 15, 17) are_ indicated as vertical lines normalised to H(I*). The broken line indicates the contributicn from H + Surf collisions, and the light solid line gives the contribution from H + HI(ad) collisions (see text). that go to make up the computed P(ET)curve in Fig.14 into a component aFribable to H + Surf collisions (broken line) and a second (larger) component due to H + HI(ad) (thin solid line). The criterion for separation was the magnitude of the impact parameter with respect to a 'target' HI(ad). If, after collision with the surface a trajectory had an impact parameter in excess of 2.5 8, we considered that it would transfer a minor amount of energy to the target molecule. This impact parameter was selected as being slightly in excess of the maximum impact parameter that led to reaction. It has the effect of separating the encounters into two categories with markedly different attributes. For b > 2.5 (dashed curve, Fig. 14) a large fraction of the trajectories result in an energy loss of only ca.0.2 eV and a small fraction have an energy loss of 1-2 eV. By contrast for trajectories with b < 2.5 8, the most probable outcome is an energy loss in the region of 1-2 eV. It appears, therefore, that the major contribution to the energy loss from the 3.4 eV H-atoms at 0.7 ML, according to this model, comes from + HI(ad) inelastic encounters. This type of inelastic encounter is explored in a forthcoming paper.20 At lower coverages, particularly in the absence of islanding, the major energy loss can be expected to arise from collisions with the surface. In studying H-atom angular distributions by recording P(W) for only the highest-energy H-atoms, even at ca. 1 ML, one is selecting those H that were reflected from the surface but did not encounter a co-adsorbate molecule (see Fig.14). We have made use of this in our previous work" on HBr/LiF(001) in order to probe the potential in the neighbourhood of F-at the LiF surface. In a subsequent paper on H + Surf in HI/LiF(001) we shall discuss the form of P(@)for the fast elastically scattered component of H, as obtained from both experiment and theory.37 We thank Darrick Heyd and Erik Jensen for kindly verifying some TOF measurements on a differently configured apparatus. We thank David Jack for his assistance with the HI parameters and Colin Stanners for helpful discussions. We are also indebted to the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Ontario V. J. Barclay et al. 149 Laser and Lightwave Research Centre, and the National Networks of Centres of Excel-lence Program for their support of this work.References 1 W. Ho, in Desorption Induced by Electronic Transitions, DIET IV, ed. G. Betz and P. Varga, Springer- Verlag, Berlin, 1990, p. 48. 2 X-L. Zhou, X-Y. Zhu and J. M. White, Surf. 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Reeves and D. W. Robinson, Chem. Phys., 1965,42, 1465. 36 A. Bondi, J. Phys. Chem., 1964,68,441. 37 V. J. Barclay, W-H. Hung, J. C. Polanyi, Y. Zeiri and G. Zhang, unpublished. 38 R. D. Shannon, Acta Crystallogr., Sect. A, 1976,32, 751. Paper 3/04280D; Received 19th July, 1993

ISSN:1359-6640    

DOI:10.1039/FD9939600129

出版商:RSC    

年代:1993

数据来源: RSC