J . Chem. SOC., Faraday Trans. I, 1984, 80, 61-71 Reaction of Modulated-molecular-beam Chlorine with Polycrystalline Iron BY MEHDI BALOOCH AND DONALD R. OLANDER* Materials and Molecular Research Division of the Lawrence Berkeley Laboratory and the Department of Nuclear Engineering, University of California, Berkeley, California 94720, U.S.A. AND WIGBERT J. SIEKHAUS Chemistry Division of the Lawrence Livermore National Laboratory, University of California, P.O. Box 808, Livermore, California 94550, U.S.A. Received 7th March, 1983 The volatilization of polycrystalline iron by chlorine gas has been studied by modulated- molecular-beam-mass-spectrometric methods. The reaction was investigated in the temperature range 300-1250 K at equivalent chlorine pressures from 2 x Torr. FeC1, was the only detectable volatile reaction product; its production rate increased rapidly with surface temperature and levelled off at ca.1100 K. Studies of the composition of the reacting surface by laser-stimulated desorption and by ESCA indicated the presence of a thin scale of a sub-stoichiometric iron chloride at the spot struck by the molecular beam. A reaction model based on diffusion of chlorine in the scale and production of gaseous FeC1, from parallel Eley-Rideal and Langmuir-Hinshelwood processes was developed from the molecular-beam data. to 3 x The chemical aspects of metal-halogen reactions have many technological impli- cations. The high volatility of metal halides has long been utilized in halogen lamp design and in the production and purification of metals' and may play an important role in the water-splitting cycle for hydrogen production.2 The reaction of chlorine with an iron surface has been studied by Frueharn, in a conventional reaction tube in the temperature range 530-920 K and at a chlorine partial pressure of several Torr.The dimer (FeCl,), was reported to be the dominant reaction product. Below 620 K the rate was controlled by diffusion through a surface scale (presumed to be FeCl,). Above 620 K the reaction depended on the properties and the flow rate of the inert carrier gas, indicating rate control by gas-phase mass transfer. Kishi and Ikeda4 studied the reaction of evaporated films of iron exposed to 10 Torr pressure of C1, for 10 s by X-ray photoelectron spectroscopy. From the chemical shift of the 2p3I2 state of iron, they concluded that an FeC1, scale was formed on the surface of iron.RHEED and Auger studies by Dagoury et aL5 of chlorine reactions on various low-index faces of iron confirmed the existence of FeCl, islands and chemisorbed chlorine on the surface for a gas pressure of ca. 1.3 x lo-, Torr and temperature ranging from 400 to 600 K. In the present work, the kinetics of the iron-chlorine reaction are investigated by modulated-molecular-beam techniques utilizing phase-sensitive detection of reaction products with an in situ mass spectrometer. All gas flows are collision-free, so that mass-transfer limitations are avoided and only surface reactions are detected. The data obtained by this method consist of signals of scattered and desorbed volatile reaction products which, in conjunction with surface analysis, provided the principal means of deducing a surface reaction model.6162 M. BALOOCH, D. R. OLANDER AND W. J. SIEKHAUS SOURCE bT b’. : . .. .. . TA R TO PUMP + DIFFUSION TO PUMP SCATTERED R EACTAN AND DESO RBED PRODUCT DIFFUSION+ t TO ION PUMP \ Fig. 1. Schematic representation of the modulated-beam reactive scattering apparatus. EXPERIMENTAL A detailed description of the molecular-beam apparatus used for the kinetic studies is given elsewheres but the principles of operation are shown in fig. 1. The apparatus consists of three differentially pumped chambers separated by collimating orifices. A beam of chlorine is formed by effusion and mechanically modulated in the source chamber.The incident chlorine beam is not heated and the temperature of the gas in the source is CQ. 300 K. A collimator shapes the beam to a thin pencil prior to striking the iron target in the second chamber. The intensity of the molecular beam of chlorine at the solid surface can be calculated for the fixed source-to-target distance from the gas pressure and the conductance of the hole in the source tube. The incident beam intensity can, if desired, be converted to an equivalent reactant gas pressure by standard gas kinetic theory form~lae.~ Beam-formation and vacuum-pump limitations result in a maximum achievable equivalent pressure at the target surface of ca. 3 x lo-* Torr. The high-purity polycrystalline target, previously polished and washed with alcohol, is heated to temperatures up to 1250 K by radiation and by electron bombardment from a hot filament.Portions of the scattered chorine and desorbed reaction products are detected by a quadrupole mass spectrometer mounted in a third chamber, which communicates with the target chamber via a 1 mm diameter orifice. The mass-spectrometer ionizer has a direct line-of-sight view of the beam spot on the target. The modulated signals from the mass spectrometer are processed by a lock-in amplifier to yield the apparent reaction probability, E (the ratio of the amplitudes of the product and reactant signals, corrected for ionization efficiencies of the mass spectrometer) and the phase lag, 4, which is the difference between the product and the reactant phase angle^.^ Phase-sensitive detection responds only to the fundamental mode of the periodic input signals at the frequency of modulation provided by the beam chopper.Thus the modulation frequency becomes the third controllable experimental variable, for which a range of l&103 Hz is achievable. RESULTS MOLECULAR-BEAM DATA The iron-containing ions observed in the mass spectrometer using 70 V ionizing electrons were FeCQ (20%), FeCl+ (50%) and Fe+ (30%). All had the same phase angle and the same dependence on surface temperature. Therefore it was concluded that FeC1, was the sole volatile product of reaction under low-pressure/high- temperature experimental conditions.J . Chem. SOC., Faraday Trans. 1, Vol. 80, part 1 Plate 1 Plate 1. Scanning electron micrograph of an iron surface after reaction with a chlorine beam.M. BALOOCH, D. R. OLANDER AND W. J. SIEKHAUS (Facing p . 63)REACTION OF MOLECULAR-BEAM CHLORINE WITH IRON 63 0 7 I I 15 lo4 KIT Fig. 2. Apparent reaction probability and phase lag of FeCl, as a function of target temperature; I, = 4.8 x l0ls molecule cm-, s-l,f= 20 Hz. Fig. 2 shows the measured reaction probabilities and the conjugate phase lags for this product as functions of surface temperature. The apparent reaction probability increases rapidly with temperature up to ca. 1100 K and then levels off. Below ca. 850 K the phase lag approaches a limiting value of approximately 45O. The beam-intensity dependence of the molecular-beam data is shown in fig. 3 and 4 for three different surface temperatures. At the highest temperature (1 150 K) the reaction appears to be linear, while at low temperature (817 and 585 K) higher-order reaction behaviour with respect to the incident chlorine molecule beam is observed.The frequency dependence of the apparent reaction probability and phase lag is shown in fig. 5 and 6, again for three different temperatures. At 1233 K, the surface chemical process is fast with respect to the time scale of primary-beam modulation so that the apparent reaction probability does not change appreciably with frequency and the phase lag is nearly zero. At 952 K, the phase lag is substantial and goes through a maximum at ca. 250 Hz. At 622 K, the phase remains constant at ca. 45O up to 250 Hz and decreases at higher chopping frequencies. SURFACE CHARACTERIZATION Information on the chemical state of the surface at the beam spot is essential for understanding the mechanism of the chlorine-iron reaction.To the unaided eye, the post-reaction surface at the beam spot appeared bluish-black in colour. Plate 1 shows a scanning electron micrograph of this surface. When analysed by AES in a different64 M. BALOOCH, D. R. OLANDER AND W. J . SIEKHAUS A " 1 A 6 585 K 1 Fig. 3. Effect of chlorine beam intensity on the apparent reaction probability of FeC1, for three different target temperatures at a fixed modulation frequency; f = 20 Hz. vacuum system, however, no chlorine was detected on the reacted spot. This element may have been lost by hydrolysis due to moisture in the air to which the specimen was exposed during transfer.To detect a non-volatile chloride coating on the reacted surface, a specimen was heated to 700 K and exposed to a chlorine pressure of Torr in a system equipped with ESCA. The spectrum was recorded after one hour exposure to C1, under the above conditions. The width and position of the chlorine peak corresponded to a mixture of FeCl,, FeCl and adsorbed C1, confirming the observations of Kishi and Ikeda.4 Finally, laser-stimulated desorption was applied to characterize the surface during exposure to chlorine. An iron target, held at 900 K in an environment of Torr of chlorine, was rapidly heated to a high temperature by a Nd glass laser pulse. Species desorbed from the surface were detected by an in situ quadrupole mass spectrometer. Both FeCl+ and FeCl; ions were detected, with the integrated signal from the former about twice that of the latter.In separate tests, it was determined that ca. 20% of FeCl, fragmented to FeCl+ at the ionizer electron energy of 15 eV used in these experiments. Thus, the surface composition probably has a chlorine-to-iron ratio of less than two. However, thermal dissociation of FeCl, by the laser pulse could have contributed the FeCP signal detected by the mass spectrometer. The visual and instrumental evidence described above, although qualitative, strongly suggests that the surface exposed to the reactant molecular beam was covered by an iron chlorine scale of undetermined stoichiometry. The coating must have contained more than a monolayer of chlorine for so small a quantity could not have provided the strong ESCA and mass-spectrometer signals in the laser pulsing tests.REACTION OF MOLECULAR-BEAM CHLORINE WITH IRON 8om 60 65 - 585 K I 2 5 0 0.5 Clz beam intensity, Io/1016 molecule cm-2 s-1 Fig.4. FeCl, phase-lag dependence on chlorine beam intensity for three different target temperatures at a fixed modulation frequency; f = 20 Hz. The scale could not have been pure FeCl, because the vapour pressure of this compound at 700 and 900 K (0.01 and 4 Torr, respectively) is far greater than the lo-' Torr pressure of C1, which supplied this element to the surface. Even if all of the incident chlorine molecules reacted to form FeCl,, the high volatility of this substance at the test temperatures precludes the presence of a scale of pure FeCl,.The Cl/Fe ratio of the scale must be sufficiently larger than zero to contain significant quantities of chlorine but sufficiently smaller than two to prevent it from vaporizing into the vacuum. DISCUSSION KCAL 1 IUN MUUEL The evidence cited above indicates that the reaction mechanism should include the sub-stoichiometric chloride scale on the iron surface during corrosion. Incident molecular chlorine from the beam chemisorbs dissociatively on the exposed surface of this scale and reacts to produce the volatile FeCl, species which is ultimately detected by the mass spectrometer. Inclusion in the model of a scale on the reacting surface is consistent with many previous metal + halogen studies. McKinley6 reported a NiF, scale produced in the Ni+F, reaction. Machiels and Olanders assumed a fluoride scale on tantalum to explain their molecular beam results on the Ta+F, system.This inference was subsequently confirmed by N ~ r d i n e . ~ Paullo showed that during the reaction between iron and chlorine at low pressure (ca. Torr), a solid reaction product was present at the surface, growing as a thin continuous layer. The molecular-beam data in fig. 2-6 exhibit characteristic signatures which indicate the presence of certain elementary processes in the mechanism of the surface reaction. The relationship of distinctive features of the apparent reaction probability and the66 M. BALOOCH, D. R. OLANDER AND W. J. SIEKHAUS I I I I I I I I I I modulation frequency, f/Hz 50 100 200 500 1041 10 2 0 K) Fig. 5. Modulation-frequency dependence of the apparent reaction probability for three target temperatures and fixed chlorine-beam intensity; I, = 4.8 x 1Ols molecule cm-2 s-l.chopping frequency, f/Hz Fig. 6. Modulation-frequency dependence of the FeCl, phase lag for three target temperatures and fixed chlorine-beam intensity; I, = 4.8 x 10l6 molecule cm-2 s-l.REACTION OF MOLECULAR-BEAM CHLORINE WITH IRON 67 phase lag of the product to particular steps in the mechanism have been catalogued previ~usly.~? l1 One such feature is the near 4 5 O phase lag which is observed at low temperatures and low frequencies (fig. 2 and 6). This behaviour is strongly indicative of a diffusion-controlled step in the mechanism. When coupled with the previously discussed likelihood of an FeCl, layer (0 < x < 2) on the reacting surface, the most probable diffusional process is migration of chlorine in this scale.Another aspect of the data which serves as a guide to modelling the reaction is the behaviour of the apparent reaction probability and the phase lag as the incident-beam intensity is varied. Except at very high temperatures, the reaction is non-linear with respect to chlorine-beam intensity (fig. 3 and 4). The most likely source of this non-linearity is reaction of adsorbed chlorine with the top of the FeCl, scale to produce adsorbed FeC1,. This is a Langmuir-Hinshelwood type of surface reaction, which was also observed in the Ta+ F, system.6 The third salient point of the data which suggests a particular surface step is the variation of the phase lag with modulation frequency.As seen in fig. 6, the phase lag decreases with increasing frequency at 622 K and exhibits a maximum at 952 K. This phenomenon can only occur if two parallel reaction paths are available for the production of the same species.’ Basically, the phase lag is a measure of the time between the arrival of a chlorine molecule at the surface and the emission of an FeCl, product molecule. In a simple adsorption-desorption mechanism, the phase lag directly measures the mean lifetime of the adsorbed species and 4 increases with increasing modulation frequency. In a branched process, the interaction of the two reaction-product vectors can result in a maximum of the type observed in fig. 6 if the branching ratio favours the channel with the longer residence time.In a steady-state experiment, the fast but low-probability channel contributes little to the total product rate. The dominance of the high-probability but slow channel occurs at low frequencies in a modulated-beam experiment as well. As the modulation frequency is increased, the slow branch becomes demodulated, so that its contribution to the apparent reaction probability decreases and its contribution to the phase lag increases. At high frequencies, the slow channel is immeasurable by phase-sensitive detection and only the fast, low-probability branch provides a signal. If this branch is very fast, the phase lag can decrease with increasing frequency for a significant range of modulation frequencies. Assuming that the slow branch is the Langmuir-Hinshelwood step discussed above, the most likely candidate for the fast branch is a reaction of the Eley-Rideal type, which occurs with zero delay and hence induces no phase lag in the product signal. A final direct hint of the reaction mechanism is obtained from the behaviour of the apparent reaction probability at high temperature.Fig. 2 indicates that for T > 1100 K the reaction phase lag is almost zero and the apparent reaction probability is insensitive to temperature. This behaviour suggests that the production of FeC1, is limited solely by the rate of supply of reactant C1, to the surface; all other steps in the mechanism are rapid compared with the millisecond time scale of beam modulation. Therefore, the apparent reaction probability in this limit is identical to the sticking probability of C1, on the coated surface.Large, temperature-independent sticking probabilities have been found in other halogen-metal 8 v l2 SURFACE STEPS The overall reaction is driven by dissociative chemisorption of molecular chlorine on the surface of the FeCl, scale exposed to the impinging reactant beam. This process is characterized by a sticking probability, q, which, from the high-temperature limit68 M. BALOOCH, D. R. OLANDER AND W. J. SIEKHAUS of the apparent reaction probability shown in fig. 2, is approximately 0.03. The rate of adsorption is expressed by (1) where I is the intensity of the CI, molecular beam striking the surface. Modulation of the incident beam is represented by Rads = 2q1( 1 - 6) where I, is the amplitude of the beam and g ( t ) is the gating function of the modulator, which is a square wave of frequencyf Hz.The quantity 8 in eqn (1) is the fraction of the FeCl, surface occupied by adsorbed FeCl,. This portion of the surface is inactive for chlorine chemisorption. Some sort of coverage-dependence of chlorine sticking on the surface is needed in order to match the rapid drop of the apparent reaction probability with decreasing temperature (fig. 2). The Langmuir model in which sticking varies linearly with surface coverage has been assumed since this type of behaviour is frequently exhibited by heterogeneous reacting systems. Following the qualitative discussion of the reaction mechanism given earlier, FeCl, is formed by two parallel channels. The dominant path is the reaction of surface- adsorbed chlorine with the scale. This Langmuir-Hinshelwood step is characterized by a rate constant kLH, and to reflect the observed non-linearity of the reaction discussed previously the kinetics are assumed to be mth order with respect to the chlorine adatom concentration, n.The rate of this step is given by R,, = kI,Hrzm. (3) In the Eley-Rideal process, an incident C1, molecule strikes the FeCl, surface where it directly produces FeCl, and a chlorine adatom. The rate of this step is described where qER is the probability that an incident C1, molecule undergoes reactive adsorption when it strikes the portion of the surface not covered with adsorbed FeCl,. Adsorbed FeCl, produced at the rate given by the sum of eqn (3) and (4) is assumed to leave the surface by simple desorption Rdes = kdes ( 5 ) where kdes is the first-order rate constant for FeC1, desorption.The analogous process of desorption of adsorbed chlorine is not considered in the model because no experimental evidence was found for atomic chlorine leaving the surface. The ab- sence of halogen adatom desorption is consistent with previous halogen-metal studies.s* l2 DIFFUSION IN THE SCALE A scale of approximately constant thickness is maintained by the balance of two processes. Removal occurs at the top by desorption of FeCl, and regeneration takes place at the interface with the substrate metal at a rate governed by chlorine diffusion through the scale. Upon arriving at the metal interface, chlorine converts Fe to FeCl, and thus scale growth occurs.Except for the volatilization process occurring at the top, the mechanism is equivalent to the classical Wagner model of scaling. The modification involving simultaneous removal by volatilization and growth by diffusion- controlled scaling was first analysed by Rosner and A1lend0rf.l~ The model has been applied to molybdenum oxidation wherein MOO, is volatile14 and most recently to the Ta + F, reaction.6 While the time-averaged properties of the reacting system determine the thicknessREACTION OF MOLECULAR-BEAM CHLORINE WITH IRON 69 of the scale, the modulated portions of the surface reactions (to which the detection system responds) are influenced by the periodic change in dissolution and diffusion of chlorine into the scale.As the chlorine concentration on the surface increases during the beam-on portion of a modulation cycle, not only do surface reactions proceed faster but more chlorine is lost to the solid beneath the surface. Conversely, when reactant supply ceases abruptly during the beam-off part of the cycle, the scale can continue to act as a source of chlorine to the surface adatom population. When this flywheel effect of bulk diffusion dominates the purely surface steps, the response of the chemical system is identical to the thermal response of the earth’s surface to diurnal heating by the sun,15 in which the surface temperature lags the driving heat flux by 45O. The discussion at the beginning of this section pointed out regions of the experimental variables which elicited a phase-lag response near 45O.Thus, the action of the bulk as a source or sink of chlorine atoms must be considered in assessing the response of the surface reactions to the incident modulated beam. The diffusion process is described by Fick’s law where C and D are, respectively, the concentration and diffusion coefficient of chlorine in the scale and z is the depth beneath the surface. The connection between the surface concentration of chlorine adatoms, n, and the bulk concentration of chlorine in the scale at the surface, C(z = 0), is assumed to be linear C(z = 0) = Hn (7) where H is the surface-to-bulk solubility coefficient. This formalism for including the effect ofbulk diffusion on surface kinetics hasin the past been applied to molecular-beam studies of other gas+ solid reaction^.^^ 11$ l6 QUANTITATIVE MODELING The net effect of the elementary processes acting in concert is determined by mass balances on the surface species contained in the model.For chlorine adatoms, the balance is and for FeC1, on the scale surface the analogous balance n = &ds - RLH + - Rdiff NS8= R,,+R,,-Rdes where N , is the number of surface sites per unit area (ca. (8) (9) is 1015 crn-,). The mathematical treatment of this type of molecular-beam analysis has been elaborated 16, l7 Basically, the component rates on the right-hand sides of eqn (8) and (9) are expressed by eqn (1) and (3)-(6). The driving force for the reaction is the periodic supply of chlorine represented by eqn (2). These equations are solved by Fourier expansion7 or other16 techniques.Part of the solution involves treatment of Fick’s second law describing chlorine diffusion in the scale, for which eqn (7) is a boundary condition. The end result of the analysis is the reaction-product vector, which is the ratio of the rate of FeCl, desorption to the rate of C1, supply to the surface (i.e. Rdes/Z). This vector exhibits a phase lag 4 in addition to an amplitude factor, which is the apparent reaction probability E. The quantities are directly comparable to the experimental measurements. The detailed treatment of the analytical model of the Fe + C1, reaction outlined here is presented in ref. (1 8). The model contains 10 adjustable parameters. The sticking probability is directly70 M. BALOOCH, D. R. OLANDER AND W. J.SIEKHAUS determinable from the high-temperature limit of the apparent reaction probability shown in fig. 2. The reaction order of the Langmuir-Hinshelwood step [the exponent m in eqn (3)] must be greater than unity to reflect the increase in E with I,, shown in fig. 3; the choice m = 2 adequately fits the data, although this number cannot be fixed with high precision. The remaining eight parameters, representing the pre-exponential factors and activation energies of the Langmuir-Hinshelwood rate constant kLH, the direct reaction probability qER, the mean lifetime of FeCl, on the scale surface, N,/k,,,, and the combined solution-diffusion parameter H2D, were determined by fitting the entirety of the data to the model. The best-fitting theoretical curves shown along with the data points in fig.2-6 correspond to the following surface rate constants kLH/cm2 s-l= 300 exp (-46/RT) qER = 2 x exp ( - l / R T ) (kdeS/Ns)/ss1 = 2 x 1013 exp (- 36/RT) where the activation energies are in kcal mol-1 and R is the gas constant. CONCLUSIONS Although the large number of parameters used in the data fitting precludes a claim to uniqueness of the model, several features lend credence to its general form. First, inclusion of a sub-stoichiometric FeC1, scale in the model is supported by qualitative surface analysis and is consistent with similar scale formation observed in other gas-solid reactions which produce a volatile product. Secondly, the conjugate pairs of data points ( E , 4) cover ranges of the three experimental variables (f, I, and T ) that are sufficiently broad to circumscribe closely the nature of the surface mechanism.These data exhibit features that strongly indicate certain elementary steps in the overall process; it would not be possible to remove from the model solution diffusion in a scale, a branch mechanism for FeCl, production, or non-linearity in one of the branches and still obtain reasonable agreement with the ensemble of the data. Thirdly, none of the pre-exponential factors or activation energies of the surface steps are outside the theoretically acceptable ranges for the processes they claim to represent. The type of surface reaction leading to the production of adsorbed FeCl, by the Langmuir-Hinshelwood branch of the mechanism has been analysed by Baetzold and Somorjai.l9 Using transition-state and hard-sphere reaction models to estimate pre-exponential factors, they find that low values such as that observed here for kLH are not uncommon for many bimolecular surface reactions. The pre-exponential factor of kdes is consistent with a simple desorption process; it approximates the frequency of adatom vibration normal to the surface. FeCl,.production by the Eley-Rideal branch is small with respect to that of the Langmuir-Hinshelwood step and is significant only at high frequencies. At 1100 K, the direct reaction probability, qER, is ca. 1.5 x los3, which is ca. 5% of the sticking probability. The low activation energy of the direct reaction step (ca. 1 kcal mol-l) is consistent with values reported for similar Eley-Rideal processes in other reaction systems.Bernasek and Somorjai20 found an activation energy of 0.6 kcal mol-l at high temperatures for the D,+H + DH+D surface reaction on stepped Pt surfaces, and McCarty et d 2 l estimated 2.5 kcal mol-l for the decomposition of acetic acid on nickel surfaces at elevated temperature.REACTION OF MOLECULAR-BEAM CHLORINE WITH IRON 71 This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under contract no. DE-AC03-76SF00098 and U.S. Department of Energy under contract no. W-7405-Eng-48, and by the U.S. Army Research Office, Research Triangle Park, North Carolina under contract no. 158 12-MS. Proc. Symp. High Temperature Metal Halide Chemistry, ed. D. L. Hildenbrand and D. Cubicciotti (The Electrochemical Society, Princeton, New Jersey, 1978). K. F. Kroche, H. Cremer, G. Steinborn and W. Schneider, Int. J. Hydrogen Energy, 1977, 2, 269. R. T. Frueham, Metal. Trans., 1972, 3, 2585. K. Kishi and S. Ikeda, J. Phys. Chem., 1974,78, 107. G. Dagoury, D. Vigner, M. C. Paul and J. Rousseau, Proc. 7th Znr. Vac. Congr. and 3rd Int. Conf. on Solid Surfaces, 1977, 1093. A. J. Machiels and D. R. Olander, Surf. Sci., 1977, 65, 325. R. H. Jones, D. R. Olander, W. J. Siekhaus and J. A. Schwarz, J. Vac. Sci. Technol., 1972, 9, 1429. J. D. McKinley, J. Chem. Phys., 1966, 45, 1966. @ P. C. Nordine, J. Electrochem. Soc., 1978, 125, 498. lo M.-C. Paul, Docteur Cycle (Universitb de Pans Sud, Centre D’Orsay, 1975). l1 J. A. Schwarz and R. J. Madix, Surf. Sci., 1974, 46, 317. l2 J. D. McKinley, J. Chem. Phys., 1964, 40, 120. l3 D. Rosner and H. D. Allendorf, J. Phys. Chem., 1970,74, 1829. l4 D. R. Olander and J. L. Schofill Jr, Metal. Trans., 1970, 1, 2775. l5 H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solidr (Oxford University Press, Oxford, 2nd l6 H. C. Chang and W. H. Weinberg, Surf. Sci., 1977, 65, 153. l7 H. C. Chang and W. H. Weinberg, Surf. Sci., 1978, 72, 617. edn, 1959), p. 65. M. Balooch, W. J. Siekhaus and D. R. Olander, Investigation of the Iron-Chlorine Reaction by Modulated Molecular Beam Mass Spectrometry, U.S.D.O.E. Report UCRL-88 163, 1982. R. C. Baetzold and G. A. Somorjai, J. Catal., 1976, 45, 94. 2o S. L. Bernasek and G. A. Somorjai, J. Chem. Phys., 1975,62, 3149. J. McCarty, J. Falconer and R. J. Madix, J. Catal., 1973, 30, 235. (PAPER 3/367)