摘要:

Faraday Discuss. Chem. SOC., 1990, 89, 137-141 EXAFS Study of the Influence of Hydrogen Desorption and Oxygen Adsorption on the Structural Properties of Small Iridium Particles Supported on A1,0, F. W. H. Kampers and D. C. Koningsberger Laboratory of Inorganic Chemistry and Catalysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Desorption of hydrogen at high temperature leads to a contraction of the Ir-Ir coordination distance of highly dispfrsed iridium metal particles. The long metal-support oxygen distance (2.55 A) observed if the metal crystallites are covered with chemisorbed hydrogen disappears after treatment in vacuum at 623 K. Instead, a metal-oxygen coordination in the metal-support inter- face is now detected with a distance of 2.19 A.It is concluded that the long metal-oxygen distances found for oxide-supported metal catalysts after reduction in H, originate from an M"-(OH)- interaction or from the presence of chemisorbed hydrogen in the metal-support interface. Admission of O2 at 77 K does not lead to a corrosive oxidation of the metal particles. The adsorption of O2 resulted in the same type of Ir-0 bonds as present in the metal-support after evacuation. Structural properties of small metal particles supported on non-interacting substrates (Mylar, rare-gas solids) have been studied extensively with EXAFS.'-3 The experiments were performed under vacuum showing contractions of the nearest-neighbour distance and a decrease of the Debye temperature of the metal particle due to the softening of the phonon s p e ~ t u r m .~ . ~ EXAFS experiments on dispersed metal catalysts supported on interacting substrates, e.g. y-A120, , have been carried out after the reduction treatment with the metallic particles covered with chemisorbed hydrogen.'-'" Under these condi- tions, contraction of the metal-metal coordination distance has not been observed. Tentative EXAFS results have been reported for Pt/NaY zeolite" and Rh/AIIOI1' catalysts under moderate vacuum conditions showing a contraction of the first-neighbour coordination distance. Chemisorbed hydrogen influences the electronic properties of the metal, which in turn may change the interaction of the metal particles with the support. The metal- support interaction has been studied with EXAFS for Rh/A1,03 ,6*7 Rh/Ti02 , Pt/AII03 ,9 and Ir/A1203'0 catalysts with the metal particles covered with chemisorbed hydrogen.Long metal-support oxygen bonds (2.55-2.75 A ) with the interfacial metal atoms coor- dinated by 3 oxygen ions of the support have been observed in all cases. However, in the literature'3-'5 EXAFS studies have been reported on metal catalysts which were treated with helium at high temperature after the reduction procedure, resulting in much shorter metal-support bonds 2.1 A and lower coordination numbers. Here the results are presented of an EXAFS study of a highly dispersed Ir/AlI03 catalyst, which was evacuated at high temperature after the reduction process. The influence of the desorption of hydrogen on the structural properties of the small metal particles has been studied.Furthermore, the effect of the evacuation process (removal of chemisorbed hydrogen and hydroxyl groups from the surface of the support) on the structure of the metal-support interface was investigated. Oxygen adsorption at 77 K 137138 Hydrogen Desorption and Oxygen Adsorption on Ir/ A120, was carried out in order to compare the metal-oxygen bonds formed by this adsorption process with the metal-oxygen bonds present at the metal-support interface. Ex per i men t a 1 A 0.8 wt % Ir/ y-A120, catalyst was prepared by incipient wetting of the support ( y-Al,O,, Ketjen type 000-1.5 E, surface are 200 m2 g pore volume 0.6 cm' g- ' ) with an aqueous solution of IrCl, - xH,O. Hydrogen chemisorption measurements resulted in H/M = 2.6, indicating highly dispersed metal particles.Further characterization of this catalyst with different physical methods has been described in ref. (16). The treatments of the catalyst prior to the EXAFS experiments were performed in a transmission EXAFS in sifu ~ e 1 1 . l ~ The following treatments were carried out: ( i ) reduction in flowing H2 at 673 K for 1 h; (ii) evacuation at 623 K for 2 h (vacuum: 10 -' Pa); (iii) O2 adsorption (10' Pa) at 77 K. EXAFS data were collected after treatments ( i i ) and ( i i i ) at 77 K. The EXAFS spectra were recorded at the EXAFS station of beamline X-1lA of the NSLS at Brookhaven (ring energy 2.5 GeV, ring currents 50-100 mA). The EXAFS data were analysed using phase shifts and backscattering amplitudes obtained from reference compounds.Data Analysis and Results EXAFS oscillations in k space were obtained from the X-ray absorption spectra by a cubic spline background subtraction and normalization by means of division by the height of the edge. The raw EXAFS data of the samples with their corresponding Fourier transforms are shown in fig. 1. Pt foil was used as reference for the Ir-Ir and Na,PtOH, for the Ir-0 contribution in the EXAFS spectrum. It has been shown theoretically'' and experimentally19-'o that platinum references can be used to analyse iridium EXAFS contributions. The main peak of the k ' Fourier transforms of the data of both samples [fig. l ( a ) and 1( b ) ] shows a complicated structure, arising both from the interference of the Ir-Ir EXAFS with oscillations caused by the presence of metal-oxygen bonds and from the k-dependent behaviour of the backscattering amplitude and the non-linearities in the phase shift function of the Ir-Ir absorber-backscatterer pair.The effect of the non- linearity of the phase shift and the k-dependent behaviour of the backscattering ampli- tude can be eliminated by using a Fourier transform, which is corrected for the Ir-Ir phase shift and backscattering amplitude. The data of the sample after evacuation and after oxygen admission at 77 K have therefore been analysed using phase- and amplitude- corrected Fourier transforms. Final coordination parameters have been obtained by optimizing k ' and k' fits in both k - and r-space in order to guarantee a unique set of parameters for the low and high-Z neighbouring s c a t t e r ~ .' ~ The results for the evacuated sample are listed in table 1. Fig. 2 ( a ) shows the comparison between the experimental data and the model calculated with the parameters listed in table 1. Admission of 0, at 77 K changes the EXAFS spectrum at the low k values [fig. l ( a ) and l(b)]. The low R side (representing the metal oxygen bonds) of the imaginary parts of both Fourier transforms shows nodes at the same R values but the amplitude after 0, adsorption is much higher, implying an increase in the number of metal-oxygen bonds. The high-k part of the EXAFS spectrum (Ir-Ir bonds) does not show any decrease in amplitude, implying a non-corrosive adsorption of oxygen at 77 K. The results of the EXAFS data analysis of the sample after 0, adsorption at 77 K are presented in table 1 and fig.2 ( b ) . Discussion The EXAFS results obtained for the same Ir/A1203 catalyst after reduction in H2 at high temperature with the metal particles covered with chemisorbed hydrogen haveF. W. H. Kampers and D. C. Koningsberger 139 2 1 2 0 .. * -2 0 5 10 k / A - ' k l k ' 5 -5 0 5 R I A Fig. 1. EXAFS spectra of the sample after re-reduction and evacuation ( a ) and after admission of oxygen at 77 K ( c ) with their k'-weighted Fourier transforms ( b ) ( k range 2.81-10.22 k') and ( d ) ( k range 2.80-10.24 & I ) , respectively ( - - - 9 . , magnitude and -, imaginary part). Table 1. Coordination parameters treatment reduction (427 K) 4.9 2.7 1 2.0 1.8 2.55 5 .O O2 at 77 K 5.5 2.64 5.5 1.1 2.21 9.0 evacuation (650 K) 4.0 2.64 2.8 0.7 2.19 3.5 been reported by van Zon'" and are included in table 1.It was concluded that the particle morphology is hemispherical with a diameter of 9 A consisting of about 12 atoms. By comparing the results of van Zen'* with the results presented here it can be seen that the coordination number of the Ir-Ir shell was decreased by the evacuation. It must therefore be concluded that the particle morphology changed during evacuation from hemispherical to (almost) flat. The Ir- Ir coordination distance was decreased by 0.07 A by removal of chemisorbed hydrogen. A decrease of te metal-metal coordination distance can normally be expected when going from bulk metal to very small metal particles, owing to a softening of the phonon spectrum caused by the dehybridisation140 Hydrogen Desorption and Oxygen Adsorption on Ir/ A1203 Fig.2. Fourier transforms of the experimental data: ( a ) of the evacuated sample (- - -, absolute part; -, imaginary part) and the calculated data using the parameters of table 1 ( . . . . , absolute part; --, imaginary part) k1 weighted ( k range 3.32-10.22 k'); ( b ) of the sample after O2 admission at 77 K (- - -, absolute part, -, imaginary part) and the calculated data using the parameters of table 1 (. * + * * , absolute part, --, imaginary part) k' weighted ( k range 2.80-10.24 k'. of the spd metal EXAFS results obtained on very small metal particles supported on high-surface-area oxides show bulk-like coordination distances, if the surface of the metal particles is covered with chemisorbed This is even the case for extremely small metal particles having an average diameter of ca.5 8,.' From the results obtained in this work (decrease of the metal-metal coordination distance in very small metal particles after removal of the chemisorbed hydrogen) it may be concluded that the chemisorption of hydrogen tends to cancel the effect of the dehybridi- sation of the spd orbitals when going to smaller particle sizes. The results of the analysis of the sample after oxygen admission at 77 K show no corrosive oxidation of the metal particles and an increase in the coordination number of the Ir-Ir shell. This can indicate formation of large particles but it is more likely that adsorption of oxygen at 77 K has resulted in a change in the particle shape from flat to spherical.The fact that the Ir-Ir coordination distance is exactly the same as in the evacuated sample suggests that the effect of oxygen adsorption on the of the orbitals is different from the effect of hydroEen chemisorption. An Ir-0 coordination with a distance of 2.19 A is observed after evacuation. This distance is significantly larger than the distance of 1.95 8, found for the Ir-0 bond in samples that were totally oxidized. It must therefore be concluded that in the evacuated sample this bond originates from the interaction of the particle with the support. The detection of metal-support oxygen bonds has been reported by seyeral inves- Metal-support bonds with distances in the range 2.5-2.7 A have been found for supported rhodium and platinum catalysts measured after reduction with lo5 Pa H2 present in the in situ EXAFS The metal-support-oxygen bond with a distance of 2.55 8, found for the same Ir/A1,03 catalyst after reduction'" is completely absent after evacuation at high temperature.Instead, a considerably shorter metal- support bond is detected. The evacuation procedure not only removes the chemisorbed hydrogen, but also leads to a dehydroxylation of the y-AI2O3 support. The Ir-0 coordination has a distance of 2.19 A, with a coordination number much lower than that found with the supporting surface covered with OH groups. This may lead to the conclusion that the long metal-oxygen distances found for oxide-supported metal catalysts after reduction originate from an M"-(OH) interaction or from the presence of chemisorbed hydrogen in the metal-support interface. Admission of O2 at 77 K onto tigators.h- 10.13- 16F.W. H. Kampers and D. C. Koningsberger 141 the Ir/A1203 catalyst did not lead to a corrosive oxidation of the metal particles. The adsorption of O2 resulted in the same type of Ir-0 bond as present in the metal-support interface after evacuation. It is not clear what kind of oxygen adsorption created this type of Ir-0 bond: molecular or atomic physisorption or possibly chemisorption. The nature of this bond has to be further investigated and a better understanding of this type of metal-oxygen interaction will also lead to an elucidation of the metal-support interaction. We are grateful to Professor Sayers for the provision of beamtime on the X-l1A EXAFS station of the NSLS at Brookhaven.References 1 G . Apai, J. F. Hamilton, J. Stohr and A. Thompson, Phys. Rev. Lett., 1979, 43, 165. 2 P. A. Montano, G. K. Shenoy, T. I . Morrison and W. Schulze, EXAFS and Near Edge Sfructure Ill, ed. K. 0. Hodgson, B. Hedman and J. E. Penner-Hahn (Springer-Verlag, Berlin, 1984), p. 231. 3 A. Balerna, E. Bernieri, P. Picozzi, A. Reale, S . Santucci, E. Burattini and S . Mobilio, P h j x Rev. B, 1985, 31, 5058. 4 A. Balerna and S . Mobilio, P h j x Rec. B, 1986, 34, 2293. 5 B. Delley, D. E. Ellis, A. J. Freeman, E. J . Baerends and D. Post, Phys. Rev. B, 1983, 27, 2132. 6 J . B. A. D. van Zon, D. C. Koningsberger, H. F. J. van’t Blik and D. E. Sayers, J. Chem. Phys., 1985, 7 D. C. Koningsberger, J.B. A. D. van Zon, H. F. J. van’t Blik, G . J. Visser, R. Prins, A. N. Mansour, 8 J. H. A. Martens, R. Prins, H. Zandbergen and D. C. Koningsberger, J. Phys. Chem., 1988, 92, 1903. 9 D. C . Koningsberger and D. E. Sayers, Solid State lonics, 1985, 16, 23. 10 F. B. M. van Zon, Thesis (Eindhoven University of Technology, 1988). 11 B. Moraweck and A. J. Renouprez, Surf Sci., 1981, 106, 35. 12 H. F. J. van’t Blik, J. B. A. D. van Zon, D. C. Koningsberger and R. Prins, J. Mol. Caral., 1984, 25, 379. 13 F. W. Lytle, R. B. Greegor, E. C. Marques, D. R. Sandstrom, G . H. Via and J. H. Sinfelt, J. Caral., 14 G . H. Via, J. H. Sinfelt and F. W. Lytle, J. Chem. Phys., 1979, 71, 690. 15 P. Lagarde, T. Murata, G. Vlaic, E. Freud, H. Dexpert and J. P. Bournonville, J. Catal., 1983, 84, 333. 16 B. J. Kip, J. van Grondelle, J. H. A. Martens and R. Prins, Appl. Catal., 1986, 26, 353. 17 F. W. H. Kampers, Thesis (Eindhoven University of Technology, 1988). 18 B. K. Teo and P. A. Lee, J. Am. Chem. Soc., 1979, 101, 2815. 19 B. Lengeler, in EXAFS and Near Edge Structure IV, ed. P. Lagarde, D. Raoux and J. Petiau (Les Editions d e Physique, 1986), p. C8-75. 20 F. B. M. Duivenvoorden, D. C . Koningsberger, Y. S . Uh and B. C. Gates, J. Am. Chem. Soc., 1986, 108, 6254. 82, 5742. D. E. Sayers, D. R. Short and J. R. Katzer, J. Phvs. Chem., 1985, 89, 4075. 1985, 95, 546. Paper 9/05383B; Received 14th December, 1989

ISSN:0301-7249    

DOI:10.1039/DC9908900137

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1990, 89, 143-158 GENERAL DISCUSSION Prof. A. M. Bradshaw (Fritz-Haber-Institut der MPG, Berlin) said: I have three questions to Dr Thornton. (i) Is there not a discrepancy between the X-ray absorption (NEXAFS) data of fig. 5 and the photoemission spectra of fig. lo? In the former, the conversion of the adsorbed SO2, including the re-adsorbed SOz, to the sulphate species is not complete at 150 K. (ii) Surely the degeneracy of the S 1s - tf resonance in the X-ray absorption spectrum of the adsorbed sulphate species would be lifted by the lower symmetry configuration of the surface regardless of the nature of the bonding (ionic or covalent)? Whether the splitting is actually observed will depend on the intrinsic linewidth and the instrumental resolution.(iii) Is it not somewhat dangerous to base the identification of the sulphate species on the existence of a peak at 2482eV in the X-ray absorption spectrum, particularly when the two peaks at higher energy in the model compound data are not reproduced? Dr G. Thornton (University of Manchester) replied: The apparent discrepancies in temperature-dependent behaviour observed in the NEXAFS and photoemission data arise from the different experimental procedures used. In the NEXAFS work we annealed the sample and then re-cooled to 100 K before recording spectra. This gave rise to re-adsorption of SO2. Hence, the NEXAFS data cannot be reliably used to judge the temperature of reaction. In contrast, photoemission measurements employed a temperature ramp such that data were collected at the anneal temperature.The degeneracy of the SO:- S 1s -+ tf resonance should be lifted by interaction with the surface. The lack of an observed splitting, or of a polarisation dependence of the white line suggests that the ‘tf’ charge density at the two types of oxygen site is sufficiently similar to prevent us resolving the effect. The assignment of the S K-edge NEXAFS in terms of SO:- is based on the energy position and structure of the white line, and its polarisation dependence. The higher- energy structure in the NEXAFS seen in the spectrum of Na,SO, is not observed in spectra of other sulphates, including CuSO,. Along with the consistent structure observed in the photoemission spectra, the evidence for SO:- seems rather compelling.However, surface vibrational data would provide valuable complementary information. Dr J. Robinson ( University of Warwick) communicated: We have recorded S K-edge spectra for alumina films that have been grown electrolytically from aqueous electrolytes containing sulphate ions. Films grown in this way are known to incorporate sulphur and from an analysis of the EXAFS data we have shown that it is an SO:- species that is incorporated (sulphur-oxygen bond length 1.44 A). The near edge spectra for these films are essentially the same as those observed for TiOz( 1 10)-S02 after heat treatment (fig. 5 ) , i.e. a very much stronger ‘white line’, relative to the post-edge amplitude, than is observed for Na,SO, and a broad, weak feature at 2498eV. These observations therefore support the hypothesis that it is indeed SOf that is present on the TiO? surface.The enhanced ‘white line’ is presumably due to the low conductivity environment whereas our studies of the near-edge structure for a range of inorganic crystalline sulphates show that the fine features in this region vary from material to material, presumably reflecting variations in the local structure and symmetry. Prof. D. P. Woodruff (Universitjj of Warwick) said: Dr Thornton has presented evidence for two surface reconstructions [on NiO( 100) and Ni( 11 l ) ] in which a pseudo- square mesh of the metal forms on the surface. Although this seems rather surprising, particularly on a substrate of different point-group symmetry, we have recently identified 143144 General Discussion Fig.1. Schematic diagram of the proposed Cu( 110)(2 x 3)-N structure shown as a plan view of the surface with small circles representing N atoms, large hatched circles representing top (reconstructed) layer Cu atoms, and large open circles representing second-layer (unreconstructed) Cu atoms. another example of this phenomenon; the Cu(100) (2x3)-N structure appears to be described by a slightly distorted square-mesh overlayer structure essentially identical to that seen in Cu(lOO)c(2 x 2)-N (fig. 1 ) . The evidence for this conclusion comes from low-energy ion scattering' and photoelectron diffraction.' 1 M. J. Ashwin and D. P. Woodruff, Surf: Sci., in press. 2 A. W. Robinson, D. P. Woodruff, J . S. Somers, A. L. D. Kilcoyne, D. E. Ricken and A.M. Bradshaw, SUCK Sci., in press. Prof. D. C. Koningsberger (Eindhoven Universify of Technology) began the discussion of Prof. Joyner's paper, and made the following points: Theoretical phase shifts obtained with MUFPOT or EXCURVE (Daresbury EXAFS data-analysis programs) for heavy scat- terers (like Rh and Pt) are good, but not good enough for low k (3 < k < 5 ) . The theoretically calculated EXAFS spectrum as shown in your fig. 1 does not agree with the experimental data for 7 < k < 9. Also, by using a k' weighting instead of k3 the deviations at low k will be much more pronounced. Why did you use such a short data range for your analysis of the reference compound? A larger data range would give a better judgement of the reliability of the data-analysis.The data are obtained for a bulk compound, so it must be possible to collect reliable data up to high k values ( k = 15). Why did you not include multiple scattering in the analysis of the Rh-C-0" entity? This led to the wrong coordination number for Rh-O*o and more importandly also to a completely wrong coordination distance: RcrY,, = 2.99 A us. Rt.XAFS = 2.84 A. We know from the EXAFS analysis of the Rh,(CO),CI, reference compound that the difference in phase between the 'normal' Rh-0 and the multiple scattering Rh-0" coordination is almost i-r rad. The analysis presented in fig. 2 is a first-order approximation and is certainly a long way from being a fit. Within this type of approximation it is possible to find all kinds of different solutions. Our data-analysis procedure' is based upon the use of: reference compounds, multiple shell fits in k and r space using both kl and k 3 weighting and identification of the different scatterers by applying phase- and amplitude-corrected Fourier transforms.General Discussion 145 s L m C L CI L a, L - 0 iL .- a - 20 10 0 -1 0 -20 .+, 0 1 2 3 4 5 - 15 2 X E 10 .- k 5 2 2 (3 c) L a 0 LL 0 0 1 2 3 4 5 Fig.2. ( a ) Magnitude (-) and imaginary part (- - -) of the Fourier transform (Rh-0 phase corrected) of the difference file (raw data minus Rh-0-C" contribution). ( b ) Magnitude of Fourier transform (Rh-0 phase corrected) of the difference file (-) and calculated Rh-0 (support) contribution (- - -). Our sample with a loading of 1 wt Oh' showed only a partial disruption of the metal particles after CO adsorption at room temperature just like your sample with 1 wt O h loading.Our ultra-dispersed 0.5 wt 9/0 sample was completely disrupted after CO adsorp- tion as published in ref. ( l ) , so Rh-Rh oscillations were absent in the data, leading to a less complicated analysis. Our analysis (including the multiple scattering of the Rh-0" coordination) showed clearly that the Rh-C coordination of the Rh-C-0" entity beats with an additional scatterer present in the sample. This leads to an Rh-C peak amplitude in the Fourier transform of the experimental data that is much too low [see fig. 7 ( c ) of ref. (l)]. After subtraction of the calculated Rh-C-0" contribution from the experimental EXAFS data a difference file is obtained, which gives, after Fourier-transformoation with an Rh-0 phase correction, an imaginary part peaking positively at 2.12 A (fig.2). This clearly demonstrates the presence of an oxygen scatterer instead of a chlorine scatterer as suggested in your paper. The phase of chlorine is almost T rad different from oxygen, which should have led to a negatively peaking imaginary part of an Rh-0 phase-corrected FT. For these reasons we believe that your analysis is not reliable and the conclusions derived in your paper are questionable. 1 D. C . Koningsberger e / al., J. Am. Chem. Soc., 1985, 107, 3139. 2 D. C. Koningsberger e / al., J. Mol. Catal.. 1984, 25, 379. Prof. R. W. Joyner (University ojLiuerpoo1) replied: Taking the points in the o5der raised: I do not accept that the theoretical phase shifts are inaccurate below k = 5 A '.Our published fit for rhodium metal [ref (4), fig. 1 of our paper] shoys an acceptable fit down to 4 A I . For the catalyst samples, in any case, the region 3.5-5 A - ' is dominated by metal-oxygen scattering, where there is no problem with the phase shifts and excellent agreement is achieved with model compounds. The data range analysed for the model compound was chosen to maximise the contribution of the weak scatterers, carbon, oxygen and chlorine, and hence produce optimised phase-shift corrections for these important scatterers. Above 10 A - I the spectrum of the crystalline compound is dominated by Rh-Rh scattering, which is of less interest. The question of multiple scattering is important and I will deal with it at some length.I t is widely recognised that multiple scattering of the photoelectron is significant when another atom is located directly between the emitter and the backscatter. In studies of146 General Discussion noble-metal catalysts this arises most commonly for the twice-nearest-neighbour distance in the face-centred cubic structure and for oxygen in linearly bonded carbonyls. It is also known as the focusing or searchlight effect. The consequences of the multiple scattering, as indicated in our paper, are to increase the amplitude of the EXAFS from the scattering atom, resulting in an anomalously large apparent coordination number. Also the error in the fitted interatomic distance is larger than normal. Thus multiple scattering must be included if one wishes to make statements about the environment of the carbonyl oxygen. We do not attempt to do this in our paper.It is also necessary to consider the influence of multiple scattering in one shell of neighbours on the rest of the spectrum. Here the experience of the face-centred cubic metals is instructive. Spectra, such as that shown in ref. (4), fig. 1 of our paper for rhodium metal, typically contain contributions from 4-6 shells of neighbours. Of these only the 2a shell, ( a = nearest-neighbour distance), is influenced by multiple scattering, with the con- sequences already indicated. This does not prevent accurate fitting of the other shells in the spectrum. Those at a, 2'"a and 3'"a are accurately fitted using the correct interatomic distances and coordination numbers, demonstrating that the influence of the multiple scattering is confined to the shell where it occurs.We therefore believe that our conclusions on other contributions to the spectra are unaffected by ignoring multiple scattering, which is accepted to occur in the rhodium-oxygen coordination. I t is also important to note that there is no involvement of multiple scattering in the spectra from the reduced catalysts or the catalysts examined after treatment in synthesis gas. Here the particles are small, so that the contribution from the 2a shell is insignificant, neither is there any significant contribution from carbonyls, as discussed in the text. It is also necessary to reiterate the account given in the paper of how we differentiate between chlorine and oxygen nearest neighbours in the spectra.We use a statistical approach which follows well established methods and which has been described in detail [ref. ( 1 2 ) of our paper]. These are similar to the R-factor analysis used in other structural methods and show clearly and quantitatively that the spectrum taken in carbon monoxide is much better described by chlorine neighbours, than by oxjgen. I am familiar with Prof. Koningsberger's methods of analysis and consider that Fourier-transform techniques are less reliable in applicidtion than he suggests. His methods claim to identify a range of very long, ca. 2.7 A, metal-oxygen distances in supported catalysts [see ref. ( I ) of our paper] which no other group has been able to identify.' Another major limitation of Fourier-transform methods is that they provide no objectively quantifiable assessment of goodness of fit, of experimental error or of correlation between parameters. Resulting conclusions may thus contain a significant subjective element. 1 F.W. Lytle, Plendry Lecture 'it the 9th lnterndtiondl C ongre\s on C d t d l y \ i \ , C"tlg.irq, 19x8 Prof. Koningsberger then continued: Your remarks concerning the use of a statistical test is in my opinion not relevant in this case for the following reasons. ( a ) Statistical tests can differentiate between different structural models if two data sets each of high quality both extending to high k values give seemingly good fits in k space. Your data set is not of high quality, it does not extend to high k values and the agreement between your fits and experimental data is marginal [see fig.2 ( a ) of your paper]. ( h ) The inclusion of multiple scattering in order to describe the Rh-0" coordination is of crucial importance for a reliable analysis. Describing the Rh-0" coordination with a normal Rh-0 phase shift leads to faulty identification of the other scatterers present in the spectrum. This means that a systematic error dominates your statistical test, making its outcome worthless. We did include in our analysis multiple scattering since we used the Rh-C-0" entity of the Rh,(CO),CI, compound as reference. This extensively described in ref. ( 1 ) of my last comment.Genera 1 Discussion 147 I also would like to make a remark concerning your results of the Rh(l)/AI2O3 catalysts after reduction at 473 K.Our Rh(0.5)/A1203 was reduced at 593 K. We have also seen chlorine neighbours after reduction at 473 K of an Rh(l)/TiO, catalyst.' Reduction at higher temperatures certainly leads to a decrease of chlorine neighbours from the support and this may explain in this case the observed differences. 1 D. C . Koningsberger er al., Proc. 8th Inr. Congr. Caral. (Verlag Chemie. Basel, 1984), Vol. 5, p. 123. Prof. Joyner replied: Prof. Koningsberger's comments on the application of statistical tests would be more convincing if he ever used them in his own work. His comments are wrong on several technical grounds. We are interested in identifying a neighbour, either chlorine or oxygen, which is of relatively low atomic number.For low-2 scatterers the backscattering factor decays much more rapidly than for rhodium, which does indeed scatter to high k. The contribution of the low-2 scatterers is most marked in the range we have deliberately chosen for data analysis, i.e. below lo&'. This maximises our chances of differentiating reliably between chlorine and oxygen, which we do with high statistical probability, as indicated in the text. I do not accept his comments on quality of data or of fits, which are in any case irrelevant to the point he makes about statistical analysis. The advantage of the statistical approach is that it explicitly takes account of the magnitude of noise in the experimental data and of the number of data points. Prof. D. A. King (University of Cambridge) said: Concerning fig.1 of your paper, I would like to ask whether you have made checks on the possibility that the standard compound, Rh2(C0)4C12, is decomposed by the intense X-ray beam on the wiggler line. This might explain the rather poor agreement between experiment and theory in this case. Checks could be made by, for example, checking the sample for weight loss after the EXAFS data have been collected. We have found that some organometallic com- pounds are particularly sensitive to X-ray beam damage. Prof. Joyner replied: Other than visual inspection, no check was made for beam damage. Dr J. F. W. Mosselmans (Uniuersity of Southampton) said: We have in the past (1985/6) studied Rh2(CO),CI, ' and fitted it using theoretical phase shifts and multiple scattering out to 17 k (table 1 and fig.3). If you record your spectra past 10 k, why do you not show your fits past that point? Multiple scattering in EXCURVE has been available for five years; does not using it in fitting carbonyl ligands make the whole fitting processoinadequate? Why is the first 1 A of the Fourier transform not shown? This prevents an assessment of the quality of the background subtraction which can affect the results obtained by curve fitting?' 1 R. J. Price, PhD Thesis (University of Southampton, 1987). 2 I. R. Beattie, N. Binsted, W. Levason, J. S . Ogden, M. D. Spicer and N. A. Young, High Temp. Sci., in press. Table 1. Rh,(C0)4C12 EXAFS parameters ~~~~~ coordination shell radius Debye-Waller atom no. /A factor/ A ' C 2 CI 2 0 L 3 Rh 1 1.87 0.002 2.39 0.005 2.03 0.004 3.20 0.0 18148 General Discussion 1 I I I 4 6 8 10 12 14 16 Fig.3. Rh K-edge EXAFS data of Rh2(CO),CI, with multiple scattering included for the Rh-C-0 unit. Refined bond angle 174(4)". ( a ) k3-weighted EXAFS and ( b ) Fourier-transform phase-corrected for carbon; (-) experimental data, (- - -) calculated fit ( R = 17.6%). Prof. Joyner replied: The spectrum which you present is very similar to that given in fig. l ( a ) , (our paper), in the range up to 10.5 A-', as is the quality of fit obtained. Note that our fit uses crystallographically correct distances (Rh-C, 1.77 and 1.85 A), whereas your single Rh-C distance is longer than either. The difference in the Fourier transform relates solely to the greater data range in your figure.We have been concerned to optimise phase shifts in the range where light backscat- terers (0, C, Cl) contribute most strongly, i.e. below ca. 10 k'. As indicated in my reply to Prof. Koningsberger, we do not attempt to make detailed statements about carbonyl bonding, and therefore consider the use of single scattering to be justified. The region of the Fourier transform below 1 8 , contains nothing of structural significance and is therefore not presented. Prof. Koningsberger continued: Neglecting multiple scattering leads not only to fault coordination numbers, but also to wrong coordination distances. A deviation of 0.15 K from the crystallographic Rh-0" distance is too large to be described as a second-order effect. Again I would like to emphasize that it is very likely that you obtain from your analysis an Rh-CI coordination instead of an Rh-0 coordination as we found for our Rh(0.5)/A1203 sample after CO adsorption at room temperature.In your analysis you have to compensate the incorrectly chosen Rh-0" phase shift by including aGeneral Discussion 149 scatterer which has a phase shift ca. n rad different from oxygen; this is just the case for chlorine. Inspection of fig. 7( c ) of our paper in ref. (1) will make this clear. 1 D. C. Koningsberger ef al., J. Am. Chem. Soc., 1985, 107, 3139. Prof. Joyner replied: I have already accepted that a multiple scattering treatment is needed to describe the oxygen moiety of the carbonyls accurately. I have also indicated why ignoring multiple scattering has no significance for the identification of the chlorine neighbour.Prof. G. N. Greaves (Daresbury Laboratory, Warrington) said: It cannot be stressed enough that multiple scattering corrections are essential in achieving accurate parameters for metal carbonyl structures using EXAFS spectroscopy. Work by the Southampton- Daresbury group demonstrates how crystallographic coordination numbers and inter- atomic distances along with credible Debye-Waller factors can be obtained from model systems with precision. Moreover the effect can be exploited to obtain M-C-0 bond angles where these linkages are distorted when a cluster becomes attached to a substrate. The point made earlier about the inherent instability of carbonyl clusters has been beautifully demonstrated using EXAFS in the case of the interaction of R U ~ ( C O ) , ~ with SiO., where exposure to air results in dissociation to a single metal unit.Multiple scattering analysis is a prerequisite in unravelling from EXAFS the changing architecture of adsorbed metal carbonyl clusters reliably. Prof. Joyner replied: I have nothing to add to my earlier comments on multiple scattering. I accept that carbonyl clusters can be decomposed by interaction with a support such as silica. We have not attempted to support carbonyls in our work. As with Prof. Koningsberger [ref. ( l ) , our paper], we have observed synthesis of carbonyls in situ, when metal particles have been exposed to carbon monoxide. These appear to be indefinitely stable in the X-ray beam and to decompose on exposure to synthesis gas under the conditions indicated, with the reformation of metallic particles.This is the result of catalytic significance. Dr J. T. Gauntlett (ICI, Runcorn) said: In your statistical analysis, can you be certain of your significances with such a small number of data points per k in the high region and a short data range? With such high apparent signal-to-noise at the end of the data sets, why did you not extend the data range? A cynic may say that, while the data do not appear to be filtered they do appear to be ‘smoothed’ by removing data points. Prof. Joyner replied: The statistical analysis of EXAFS data is discussed exhaustively in ref. ( 1 ) . The number of data points is represented in this analysis by the number of ‘degrees of freedom’, and the improvement in fitting index required for significance increases as the number of degrees of freedom decreases. High levels of significance may equally be achieved by a large number of points with a relatively low signal-to-noise ratio or by a smaller number of points with better signal-to-noise.At high k we have collected data at ca. 0.01 A ’ intervals with suitably long collection times to achieve good signal-to-noise, as the question recognises. Choice of data range is dictated by two main f!ctors. ( i ) Accuracy required: We estimate Rh-Rh distances toobe accurate to k0.02 A, using methods discussed in ref. ( 1 ). To improve this to 0.01 A would approximately double data collection time and not modify our conclusions at all. ( i i ) Balance between low-Z and high-Z scatterers: Because we are interested in low-Z scatterers (0, C, C1) as well as strong scatterers,150 General Discussion such as rhodium, we choose a suitable data range (3.5-10&’) where both are likely to be significantly represented.It is important to note that, in comparison to some data at this meeting, none of the data presented in our paper have been filtered or smoothed in any way. 1 R. W. Joyner, K. J. Martin and P. Meehan, J . Phy.~. C’, 1 8 7 , 20, 4005. Dr R. J. Oldman (ICZ, Runcorn) said: I have three comments to make following the discussion which has just taken place. First, multiple scattering is not a second-order effect in these systems. In table 1 for Rh,(CO),CI,, the apparent coordination number for oxygen is the largest and the apparent Debye-Waller term is the smallest, showing that this shell makes a large contribution to the spectrum.If this is not modelled correctly then the level of confidence in the rest of the model is reduced. As a second point, why do we use model compounds for EXAFS? Model compounds are to help develop and test theory as a prelude to solving an unknown structure. In the first instance we are concerned with testing the accuracy of phase shifts. If the agreement between experiment and theory for the model compound is not perfect we cannot hope to probe the more subtle aspects of our unknown. For example in the case to hand we are trying to decide between oxygen or chlorine bonding to rhodium. Finally, I would like to comment on the use of fitting statistics in EXAFS.These serve two purposes. First, they help to define a best fit between experiment and theory. However, this is only applicable to selecting options for structures if the fit is already quite good and there are no systematic residuals of the kind indicated in fig. 2. Secondly, having obtained a sensible solution, fitting statistics allow an estimate of the uncertainties in the derived structural parameters, especially where they are highly correlated, e.g. coordination number and Debye-Waller factors [ref. ( 1 2 ) l . Prof. Joyner replied: I agree that the carbonyl oxygen makes a large contribution to the spectrum measured in carbon monoxide. However, both Prof. Koningsberger and I conclude that the oxygen environment is not markedly changed between the model compound and the catalyst in carbon monoxide.In both cases it should be modelled by a similar single scattering treatment. I am in broad agreement with your comments about statistical analysis, but reject your assumption that we could achieve fits of as good or similar quality to fig. 2 with an oxygen neighbour instead of chlorine, for the catalyst in carbon monoxide. We weze unable to obtain convincing fits with an oxygen shell in the distance range 2.1-2.4A, and this was what led us to consider a chlorine neighbour. The improvement in fit was very marked, and the statistical result is a quantitative confirmation of this. I am not sure why you are unwilling to see statistical criteria used for choosing between structures. These are routinely used, as R-factor analyses, in other structural techniques.An R-factor analysis i s currently being implemented by Daresbury staff as part of the new E X C - U K V O ~ analysis package. The R factor which will be generated will merely be a normalised version of the fitting index which is the input data for our statistical analysis. The criteria propoged in ref. ( 1 2 ) of our paper still apply.’ 1 S . J. Gurman, personal communication The discussion then moved on to Prof. Thomas‘s paper, and Prof. Joynerosaid: For your dehydrated sample you observe by EXAFS, an N i - 0 distance of 2.02 A. This is very simiLar to that reported by Morrison era/.’ for trigonally coordinated Co” in zeolite A, (1.9 A ) using EXAFS and by Gallezot et al.’ for Cu” in the S I 1 site in zeolit? Y , using X-ray diffraction.You suggest that the distance deduced from XRD, 2.25 A, is an average of this value and longer, non-bonding Ni--0 distances. Is it possible toGeneral Discussion 151 allow for this mixture of environments in the Rietveld profile analysis, and thus bring XRD and EXAFS results into clear agreement? 1 T. I. Morrison, L. E. Iton, G. K. Sheno)., G. D. Stucky, S. L. Suib and A. H . Reis, J. Chem. Phys., (1980), 73, 4705. 2 P. Gallezot, Y. Ben Taarit and B. Imelik, J. Catal., 1972, 26, 295. Prof. J. M. Thomas ( The Royal Institution, London) replied: Diffraction is intrinsically an averaging technique. We could put different types of oxygen into the refinement, but the results would have no more significance than the average Ni-0 bond length that we outlined.Prof. J. V. Smith (University of’ Chicago) said: For the sites I and I’ the distortion of each six-ring of oxygen atoms in response to Ni bonding produces three short and three long Ni-0 distances. Do you see the long as well as the short distances in the fit of the Ni EXAFS spectra? A second part of the discussion concerns the short Ni-0 distance of 1.87 A. This might represent an Ni atom bonded to three oxygen atoms of a six-ring and an additional oxygen species projecting away from the six-ring down the three-fold axis. Prof. Greaves replied: Yes we do see the three long as well as the three short Ni-0 distances in our analysis of Ni K-edge EXAFS. As far as your second point is concerned, relating to the short 1.87 A distance, we have in fact explored the possibility of shifting the Ni along the three-fold axis away from the centre of the regular hexagonal site.However, the Rietveld figure of merit worsens by a factor of two. All the indications from XRD are that these Ni atoms occupy near-perfect S, octahedral sites. The 1.87 8, distance we interpret as being part and parcel of the SIC site. Prof. Koningsberger said: EXAFS seems to be more sensitive in detecting the different Ni-0 distances in the dehydrated Ni-Y than high-resolution powder diffraction. I agree with your explanation of the apparent discrepancy between the results of XRD and EXAFS concerning the XRD peak at 2.25 A. However, how do you explain that EXAFS is also seeing peaks around 2.49 and 2.68 8, with relatively high coordination numbers whereas these peaks are not detected with XRD? Prof.Greaves replied: The justification for including split oxygen shells in addition to the single Ni-0 distance of 2.02 8, in our EXAFS analysis comes from the XRD refinement. Here, in dehydrated Zeolite-Y, we detect not only Ni in S1 sites but also in S,, and S , , sites together with extra oxygens (which we call 0,) located just outside the framework. These split oxygen Ni environments are modelled in fig. 7 but the precise distances, as you know, can only come from Ni EXAFS. Dr I. K. Robinson (AT&T Bell Labs, Murray Hill, N J ) said: The cause of the discrepancy between the EXAFS and XRD determinations of the SI Ni-0 bond length is attributed to disorder of this site: the Ni occupied site has one bond length and the empty site another one.If the oxygen occupancy ( N ) were constrained to be the same as that of Ni, and two oxygen sites were refined, it might be possible to confirm this hypothesis. Prof. Greaves replied: I agree, this would be an interesting test of the hypothesis in principle. In practice it may not be significant, adding as it will to the queue of Rietveld fitting parameters.152 General Discussion Prof. Smith said: What is the accuracy of the AI-0 bond lengths given in your table 3? The bond lengths and errors can be compared with values obtained by Bragg diffraction of Al-0 (tetrahedral) near 1.74 A and Al-0 (octahedral) near 1.9 A, both of which vary somewhat depending on the stereochemistry of individual structures and on whether 0 occurs as 0’-, OH or H.0. Prof.Greaves replied: The shorter energy range obtainable from A1 K-edge EXAFS of ca. 280 eV, due to the proximity of the Si K-edge, clearly reduces the precision of the analysed Al-0 distance. However, oxygen backscattering is limited, usually being spent by 350-400 eV. The equivalent wavevector range of around 10 &’ can result in a precision of ca. 0.02 A or better. With the smaller bandpass of our Al EXAFS this precisio? will reduce to 0.04 A at worst, which is clearly sufficient to distinguish the 0.1-0.2 A difference in the Al-0 distance between octahedral and tetrahedral sites, but is unlikely t o differentiate particular types of oxygen. Dr J. Robinson (University of Warwick) communicated: We have been using Al K- edge X-ray absorption spectroscopy to study the structure of anodically formed oxide films on aluminium and have studied films prepared in many different ways, as well as a range of model compounds. Whilst it is true that the proximity of the Si K-edge limits the available data range for A1 EXAFS (the monochromator crystal used is quartz and hence it is impossible t o record data beyond the Si edge) additional structural information is available from the XANES region.If one takes the position of the half-edge height for a-Al’O, as a reference point (zero energy) then for all materials containing four- coordinate A1 there is a strong peak in the spectrum at -2 eV effectively shifting the edge energy by 3 eV. Similarly for five-coordinate A1 (in andalusite) there is a peak at ca.-1.5 eV. There are also other edge features that appear to provide a ‘fingerprint’ of the coordination. These observations have been confirmed for a wide range of materials. When investigating the anodic aluminas (where four-, five- and six-fold coordination can be observed depending on the method of formation) it was found that conclusions drawn from the mean Al-0 bond length obtained from the EXAFS were always consistent with those drawn from the near-edge features. Unfortunately Dooryhee et al. d o not provide a spectrum of a reference material and their data appear to have rather variable backgrounds, and therefore it is difficult to draw any conclusions from their XANES data. Prof. Thomas replied: We, of course, accept that XANES data provide a fingerprint for the coordination of Al in aluminosilicates. Our own data, obtained in several systems with Al in different coordinations, fully support this contention.Our data on the zeolites were refined using data from model compounds (including a-Al,O,). The change in bond length on dealumination, which is the most important feature of o’lr results is, we are confident, a reliable result, fully justified by the data. Dr Oldman began the discussion of Prof. Koningsberger’s paper: Are there any changes observable at the Ir L, white line which would help confirm changes in electronic state as a function of particle size or support interaction? Prof. Koningsberger replied: We have not yet systematically investigated the white-line intensities before and after desorption of hydrogen.However, we d o see a change in intensity of the L l l l white line after desorption of hydrogen. Dr Gauntlett said: Given earlier experimental’ and theoretical data which indicate that the packing in small metal particles is energetically favouring decahedral’.’ orGeneral Discussion 153 icosohedral* geometries, is it possible that your bond-length contractions on H2 desorp- tion are due to a morphology change from close-packed, stabilised by hydrogen, to a lower coordinate particle, such as icosohedral, when hydrogen is desorbed? 1 D. G. Duff, A. C . Curtis, P. P. Edwards, D. A. Jefferson, B. F. G. Johnson, A. I. Kirkland and 2 M. R. Hoare and P. Pal, Ado. Phys., 1972, 9, 209. D. E. Logan, Angew Chem., Int. Ed, Engl., 1987, 26, 676. Prof. Koningsberger replied: We have not detected any icosahedral structures after desorption of chemisorbed hydrogen.However, we do see a lower coordination number after evacuation. Careful inspection of the Fourier transform of higher quality data obtained on the same catalyst after evacuation shows the decrease in the second Ir-Ir shell. This points to morphological change after evacuation from a three- dimensional to flat monolayer-type metal particles. Contraction of the metal-metal distance after desorption of chemisorbed hydrogen has been observed for more catalytic systems (see our paper). Dr K. Prabhakaran ( University of Manchester) communicated: You concluded that using EXAFS you can establish the physisorption of 02. Do you not expect the beam to knock off the weakly physisorbed species instantly? Prof.Koningsberger replied: The a$orption of oxygen at 77 K creates a metal-oxygen coordination with a distance of 2.19 A. It is not clear whether the adsorption of oxygen is purely physisorption or chemisorption. The bond length of 2.19 A points to a donation of electrons from the metal atoms to oxygen, implying some kind of oxidation, leading to the formation of a chemical bond. This may explain why the X-ray beam will not knock off the adsorbed oxygen. On the other hand I am not so sure that the X-ray beam will knock off physisorbed species from a metal surface. This brings us to the difficult problem of radiation damage by X-rays in biological materials, which is still not satisfactorily solved. The Chairman of the session, Prof.A. J. Leadbetter (Daresbury Laboratory, Warrington) said: In trying to focus a general discussion of the morning's papers I suggest we consider separately ( a ) any scientific problems concerning the results in the papers and ( 6 ) the various questions which have arisen about EXAFS itself. With respect to the latter I remember much the same arguments about interpretation of EXAFS data back in the early 70s when I first met the subject. I am a little disappointed to find apparently the same arguments continuing still. On the other hand it is clear that EXAFS is a most valuable tool when used in the right way without extravagant claims about the possibilities; and indeed in many cases of physically ill-defined systems it is the only means of addressing crucial problems of local structure.May we therefore consider and clarify where differences and problems lie, where there is consensus and what key developments or experiments are needed for future progress. Prof. Thomas commented: Mr Chairman, you mentioned that some of the scientific questions to which we seek answers are accessible only via EXAFS. For the study of very small metal particles (supported on zeolites for example) nowadays, thanks to the work of Treacy and Rice ( J . Microsc., 1989) it has proved possible by using scanning transmission electron microscopy (STEM) with Rutherford scattering to count the number of atoms in a small cluster. Small aggregates of no more than three to five atoms can now be identified. This constitutes a separate, independent technique against which EXAFS can be tested.154 General Discussion I wonder whether Prof.Koningsberger has looked at a system like Pt in zeolite-L with both EXAFS, STEM or any other technique? Prof. Koningsberger replied: Indeed, we have looked with EXAFS at the Pt/L zeolite system. We have found a Pt-Pt coordination number ( N ) of 3.9, implying particles consisting of 5-6 atoms. Moreover, we d o detect Pt-Ba and R-Si interactions. The hydrogen chemisorption measurements confirm the EXAFS results; we found H/ M = 1.55. These values agree with an earlier published H/M us. N curve ( J . Catal., 1987). EXAFS spectroscopy can be extremely powerful for structural investigations of uni- formly highly dispersed catalytic systems. Prof. D. A. King (University ofCamhridge) said: In the EXAFS analyses referred to here the assumption is made, in writing the familiar expression: I [where ~ ( k ) is the normalised oscillatory part of the X-ray absorption coefficient, A is a constant for a given number of scatterers at a given temperature, k is the photoelectron wavevector, R, is the distance of atoms in shell i from the absorber atom, and 4 , ( k ) is a phase-shift term], that the pair distribution function between absorber and scatterer atoms has a Gaussian form.This is a harmonic potential approximation. If the potential is appreciably anharmonic, the pair distribution function is asymmetric, and an addi- tional phase term C , ( k ) appears’ in the sine function of eqn (1): c i J As we have shown for C1 on Ag surfaces, and for bulk AgCI,’ omitting this term can lead to a very significant error in bond-length determinations by EXAFS..4t room temperature for C1 on Ag the error is in the region of ca. 0.06 A. Typically, if the correct phase shift + ; ( k ) is used, the use of eqn (1) leads to an interatomic spacing that is too small. In practice, phase shifts are obtained a priori, by a routine based on a muffin-tin potential approximation, and these are then tweaked by fitting experimental data from a standard compound with known spacings R,, to obtain an apparent function 4 ( k ) . If eqn ( 1 ) is used in the fitting procedure, this tweaking will then incorporate both the true phase-shift term and the anharmonicity term contained in eqn (2). The problem is that the latter term is strongly temperature dependent, and the use of phase shifts obtained in this way will inevitably lead to erroneous bond lengths at any other temperature.Furthermore, the procedure assumes that X I ( k ) is the same in the model compound and in the test material, an assumption of doubtful validity. Of course, use of eqn (2) incorporates a new set of undetermined parameters into the analysis of a system where R, is not known. I very strongly urge that EXAFS data should be collected at low temperatures, where 1 ( k ) can safely be ignored, since the bottom of the pair potential function is essentially harmonic, and the Gaussian-based expression (1) can then safely be used. Our low-temperature studies of C1 on Ag{ 11 l} and Ag(ll0) have been guided by this principle.” 1 P.Eisenberger and G. S. Brown, Solid Stare Commun., 1979, 29, 481. 2 G. M. Larnble and D. A. King, Philos. Truns. R. Soc. London, Sect. A, 1986, 318, 203. 3 G. M. Larnble, R. S. Brooks, S . Ferrer, D. A. King and D. Norman, Ph>~.c. Rev. B, 1986, 34, 3975; D. J . Holrnes, N. Panagiotide.;, C. J. Barnes, R. Dus, D. Norman, G. M. Lamble, F. Della Valle and I>. A. King, J. Vuc. Sci. Technol., 1987, A5, 703. Dr J. C. Earnshaw (Queen’s Uniuersity of’ Belfasr) said to Prof. Koningsberger: In several of these papers the theoretical EXAFS spectra show deviations from the observedGeneral Discussion 155 data which do not appear to be randomly distributed about zero. Several of the fits would probably not be acceptable to a statistical test such as the runs test.If the sequence of residuals were similar for different observations with a given instrument this would presumably indicate systematic errors. However, if this is not the case do such non- random residuals indicate shortcomings of the model used? Prof. Koningsberger replied: I fully agree with you that systematic deviations point to shortcomings of the structural models used in the data analysis. Another more important problem is the use of inadequate phase shifts in the data analysis. Assuming that the phase shifts used are adequate, systematic deviations have to be minimized by a better choice of the structural model; i.e. the inclusion of additional neighbouring atoms in the analysis. Dr A. Fontaine (LURE, Orsay) said: The residual which is always found between the fit based on a model and experimental data does not always mean that experiments are not accurate enough, or conversely that the model is useless because it is unable to reproduce data exactly-physics is not mathematics, there are always approximations in models.Some approximations need to be relaxed to get a better description of the real one-some other ones may be important in issues other than the actual one we are concerned with. As soon as one wants an analytical formulation of a phenomenon there is a need to classify effects according to their importance. Dr Fontaine continued: The discussion on the capability of EXAFS to yield reliable information starts on the controversy for a very ill conditioned system. Poorly organised matter with many components is certainly not the perfect case.There are many other topics where difficulties are not concentrated. A clear example was given yesterday by Prof. Bradshaw’s talk, explaining how EXAFS can determine adsorbate position on a reconstructed surface. It is true also for bulky systems. Therefore, the general comment should emphasize the capability of EXAFS to extract the local order and the large benefit given by the polarised X-ray beams. In addition one has to recall that EXAFS is one part of core-level spectroscopy which has been proved to be efficient in addressing the electronic structure issue. Prof. D. A. King said: I wish to raise a general point about the validity of EXAFS analyses of essentially heterodisperse systems. In EXAFS analyses of perfectly crystal- line systems, the most accessible case arises where all absorber atoms occupy identical lattice sites.Then we can legitimately write down a single summation, applicable at low temperatures, of the form: ~ ( k ) =C A, sin { 2 k R , + 4 , ( k ) } . I (The notation is the same as in my previous comment.) Each interatomic spacing R derived from the analysis can then be assigned to a shell around the absorber atom, and, by triangulation, a structure may be derived. If, however, just two different lattice sites are occupied by the absorber atoms, there will be two sets of shells, i a n d j , deriving from each absorber atom and contributing to the data. Apart from the added complexity in the data due to the doubling of contributing shells, there is no means available for unscrambling the data into the two shell sets i and j.A structural assignment becomes virtually impossible. Of course, if we extrapolate this further, it is readily seen that a multishell EXAFS analysis becomes meaningless for a system where a significant number of different lattice sites are occupied. A typical heterogeneous catalyst consists of a distribution of particle sizes, and each particle can be expected to contribute a range of adsorbate sites. Apart from some average nearest- neighbour distance, it is difficult to see that any further information can be reliably obtained.156 General Discussion Even in the ideal case where adsorption has been studied on single-crystal surfaces, analyses of EXAFS data can be problematic. We have conducted a detailed study of the reliability of bond lengths and coordination numbers obtained from an exhaustive SEXAFS analysis of CI on Ag{llO}.' We find that, while reproducible bond lengths could be obtained from four atomic shells, and that two shells separated by as little as 0.3 8, could be distinguished, large correlations between Debye- Waller factors, coordina- tion numbers and inelastic terms in the EXAFS amplitude introduced a high degree of inaccuracy, up to *3, on the values obtained for the coordination numbers of all shells beyond the first.We concluded that coordination numbers could not be used to infer system geometry. I wish to make a plea for a systematic EXAFS study of a well defined model catalyst system, preferably a homodisperse system, to evaluate critically the potential of EXAFS as a tool for the study of catalysts generally.1 D. J. Homes, D. R. Batchelor and D. A. King, Sur- Sci., 1988, 199, 476. Prof. Joyner then said: The problem of characterising heterodisperse supported catalysts which Prof. King poses is rather more intractable and also slightly different from that he suggests. EXAFS is at its most useful for relatively small particle sizes, e.g. with diameters <15 A. There seems to be no sure way to prepare or characterise a monodisperse sample in this size range. In practice EXAFS appears to be the most reliable method currently available for determining average particle coordination num- ber, from which an average particle size may be inferred. The unique advantage of EXAFS is that it yields a true average of the environment.This is not true of X-ray diffraction, which accentuates the contribution of long-range order, or of electron microscopy, where the smallest particles, (typically d < 6-8 A), are not imaged. It is important to have use of an additional technique which can examine the range of structures present, and electron microscopy is clearly the best method to do this. Thus electron microscopy confirms that our Rh/ A1203 sample is reasonably monodisperse, (most particles <10 A diameter, no detectable particles > 15 A diameter), while the Rh/V203 catalyst contains some very large particles, ( d > 100 A), as already inferred from EXAFS. Prof. Thomas added: Prof. King raises an important issue when he makes a plea for an analysis of model (small) metal catalysts.The desire is for a definitive study involving small, well defined particles of metal of colloidal (or sub-colloidal) dimension. Specifically one should compare EXAFS data (of the kind that lead to metal-metal distances) with high-resolution electron microscopy (that leads to information concern- ing the morphology. When the size range of small metal particles is very narrow, one feels happier about statements (based on EXAFS) relating metal-metal distance to size. There is much to be said for taking, as Gallezot has done in his elegant radial- distribution curves, a zeolite of well defined cage size loaded with Pt or Pd. Combined EXAFS, RDF and HREM studies of these would be very helpful. Prof. Greaves said: The discussion so far has centred on the difficulties and uncertaint- ies inherent in EXAFS analysis and has not stressed the advantages and strategy for exploiting the technique.In the first place, of course, appropriate model systems must be incorporated in EXAFS measurements; most good experiments are comparative and seek to minimize fitting parameters by the use of well characterised crystalline models. Secondly, incorporating multiple scattering and also asymmetry in the central atom potential have been considered as added complications to analysis and the benefits they offer have been understressed. The multiple-scattering phenomenon enables bond angles in the 150-180" range (e.g. bridging units) to be analysed very precisely. This has been used to great effect in studying adsarbed metal cluster carbonyls.Non-Gaussian atomicGeneral Discussion 157 distributions can reflect important anharmonicity effects in atomic vibrations relative to the excited atom that are averaged out in XRD. These can be revealed by measuring EXAFS at a variety of temperatures, not just at low temperature. Thirdly, and this can’t be over emphasised, X-ray absorption spectroscopy is an underdetermined structural technique. As such, curve fitting is inevitable and people will argue until Doomsday about how equivocal or otherwise a particular model structure is. Nevertheless the most sensible strategy is to shore up against the uncertainties of a given EXAFS spectrum by making other independent measurements. For example, obtaining spectra from other elements in the same material, for single crystals (non-centrosymmetric) comparing polarised spectra for different orientations and for crystalline powders combining EXAFS with XRD as in the last paper.Use can be made of indirect structural probes like spin resonance, ionic transport, optical spectroscopy etc. Combined experiments like these are mutually beneficial because most structural techniques, perhaps with the exception of single-crystal diffraction, all share a measure of indeterminacy. Dr K. M. Robinson (US Naval Research Laboratory) said: What effect, if any, does the variable coherence length of the X-rays have on the minimum particle size observable with EXAFS? Prof. Koningsberger rFplied: No effect at all. The mean free path of the photoelectron is of the order of 8-10 A.In bulk compounds like metal foils up to 7-8 coordination shells are observable in the Fourier transform of good quality EXAFS data. On the other hand, EXAFS have been observed on diatomic molecules like Br2 which also show that the coherence length of the photoelectron does not determine the minimum particle size observable with EXAFS, The minimum particle size observable with X-ray diffraction is of the order of 20-30 A. Dr Fontaine said: The small particle investigation has to be carried out using the two usual routes: ( 1 ) The study of real systems which are appealing issues, the response of which cannot be delayed until all new modern tools are developed; ( 2 ) we need to develop fundamental studies where the metallic clusters are formed in flight, selected by a mass spectrometer, and later eventually condensed and isolated within a rare-gas matrix. This is a new class of experiments which is just starting and can provide answers to questions such as when metallisation begins. Dr Gauntlett said: Prof. Thomas mentioned an electron microscopic/ EXAFS study of colloidal sols. We too were involved in such a study with the microscopists coming to us at Southampton to confirm that their electron microscopy was relevant to the structures of the sols. I think, also that if we are to study small particles and perturb the theory to account for anharmonicity and particle size distributions, as suggested by Prof. King, the working part, on EXAFS standards must define a minimum data length and point frequency in order that we have good data from around 5 A to fit. Dr Fontaine said: At the very beginning of surface EXAFS J. Sthor was not able to produce data of good quality within a range larger than 3/4 of the oscillation. Nowadays this field is very active and unique results have been produced, as demonstrated by Prof. Bradshaw yesterday. Therefore if new domains appear and do not convince immediately because of their sin of infancy, let us wait a couple of years to see what the developments are. Prof. Koningsberger said: It is of extreme importance for the credibility of the outcome of EXAFS studies that the international community of X-ray absorption spectroscopists158 General Discussion reaches consensus about data-analysis procedures and minimum requirements for EXAFS papers. The coming workshop in Brookhaven (May 1990) organized by Prof. Stern on standards and criteria in X-ray absorption spectroscopy will discuss a com- parison of existing programs for calculating ab initio phase shifts used for analysis of EXAFS data. Also a list with minimum requirements for EXAFS papers will be discussed and this list will be widely spread amongst researchers in the field and editorial boards of important scientific journals.

ISSN:0301-7249    

DOI:10.1039/DC9908900143

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Furuday Discuss. Chem. SOC., 1990, 89, 159-168 Structure and Roughening of the Pt( 110) Surface Ian K. Robinson* and Elias Vlieg AT&T Bell Laboratories, Murray Hill, NJ 07974, USA Klaus Kern IG V- K FA Jiilich, D-5170 Jiilich, Federal Republic of Germany X-Ray diffraction using synchrotron radiation from the National Syn- chrotron Light Source at Brookhaven has been used to study the clean Pt( 1 10) surface prepared in ultrahigh vacuum. Three-dimensional cTystallo- graphic data show the structure to be 'missing row' with rilternate [ O l I] rows of atoms vacant in the top layer. Significant lateral relaxations are seen down to the fourth layer. Above 1080 K the surface undergoes a phase transition somewhat like that of Au(ll0). However, a distinct shifting of the half-order peak reveals the transition to involve the appearance of surface steps, and so it must be classified as a roughening transition instead of a simple 2D Ising model.With the advent of second-generation synchrotron sources that are operated in a dedicated manner for the production of hard X-rays, there has been a rapid growth of interest in advanced diffraction experiments. The older machines, optimised for high- energy physics experiments, and often running on an infrequent schedule, made it hard to justify leaving complex and expensive equipment permanently stationed at a beamline. Portable experiments were designed instead so that the progress of whole research groups would not be held to ransom by operating schedules. We will describe a set of recent experiments carried out at the second-generation National Synchrotron Light Source (NSLS) in an end-station on beamline X16A that is customised for a single purpose: X-ray diffraction in ultrahigh vacuum (UHV).The white beam is focussed by a toroidal mirror at 12.5 m onto the sample at 25 m. The resulting spot size is 1 mm x 1.5 mm. A double-crystal monochromator using Si( 1 1 1 ) is 2 m before the sample and selects an energy in the range 5-13 kV. Normally the energy is changed only to avoid fluorescence from the sample or analyser crystal. The sample sits on the intersection of axes of a five-circle diffractometer inside the Be window section of a UHV chamber.' A pressure of 10-"' Torrf at the sample is maintained by turbo-, ion-, getter- and sublimation-pumps.Clean metal surfaces are prepared by ion bombardment and annealing, then characterised by Auger spectroscopy and low-energy electron diffraction (LEED). The Pt crystal was cut and polished at Julich to within 0.1" of the ( 1 10) crystallographic plane. Careful preparation was necessary to achieve a highly ordered surface. First it was heated extensively to 1200 K in 10 Torr O2 to remove C impurities and sputtered with Art ions. Then it was annealed by gradually raising the temperature to 1000 K over an 8 h period; this resulted in the best ordered surface. The diffraction measurements were made using the computer-controlled diff rac- tometer. The diffraction geometry depended on the kind of measurement to be made. For high-temperature studies where the thermal diffuse background would be large, the grazing incidence geometry was used to minimise the penetration of the beam into the sample.' F o r three-dimensional crystallographic measurements, the five-circle mode3 .; 1 Torr = 101 325/760 Pa.159160 Structure and Roughening of the P t ( l l 0 ) Surface was employed to gain out-of-plane momentum transfer. In both cases the exact angular direction of the surface normal was determined by optical reflection of laser light; this information was combined with the crystallographic orientation of two reference bulk Bragg reflections to determine the precise setting for each measurement.2.3 In this way, no assumptions were needed about the exact cut direction of the surface. All diffraction settings referred to the reciprocal lattice of the crystal. Resolution was determined by the mirror aperture on the input and by 2 mm slits at 500 mm on the detector 28 arm.Structure Determination The technique of surface X-ray crystallography has been reviewed recently.435 Its basic distinction from bulk crystallography is due to the 2D nature of the diffraction itself. Instead of a lattice of sharp spots (3D S-functions) we have an array of diffuse Bragg rods (2D S-functions) in reciprocal space. The crystallographic information is contained in the intensity profiles of these rods. A truly 2D structure would yield flat, featureless rod profiles. Most real surfaces contain structural modifications in more than one layer. This gives rise to modulations of the rods, which can be analysed by fitting to learn about the multilayer structure.This applies equally well to interfaces between two crystals or between a crystal and an amorphous or liquid region.6 It is important to isolate the diffraction from the surface or interface from that of the remainder of the sample, which has considerably more total scattering power. While grazing incidence helps t o some extent here, this is best done by means of symmetry alone, particularly when accurate intensity data are needed. The bulk contribution is either three-dimensional or zero-dimensional (diffuse in all directions). We measure in places that are far away from the former, and subtract away the latter as background. This is particularly easy for a surface like P t ( l l 0 ) that is reconstructed: its surface has lower translational symmetry than the bulk and gives rise to fractional-order superlattice reflections that are unambiguously distinguishable.The work reported here uses data only from such reflections. Previous experimental work on the structure of Pt( 110) has not been quite as extensive as work on Au( 1 lo), but clearly indicates a 'missing-row' structure for both surfaces. For most experimental groups, the symmetry is 1 x 2, implying that the reconstructed unit cell is doubled in the long direction of the rectangle parallel to [loo]; one study' found in addition a way to make a stable 1 x 3 state (trebled unit cell) of the surface, but considered it might be stabilised by impurities. This uncertainty over the exact translational symmetry of P t ( l l 0 ) is discussed further in the next section but here we will concentrate on the most studied 1 x 2 surface.The two LEED studies of Pt( 1 lO)'?' agree well with each other as well. The proposed model, shown in fig. 1, has the following features. Of the two atoms in the top layer of the unit cell, one is missing. The atom that remains is relaxed towards the bulk. The atoms in the second layer move out of the way by means of lateral displacements. Consequently, the third layer is buckled and the fourth has lateral displacements too. As fig. 1 shows, these are the displacements permitted by symmetry. The inward relaxation and the missing-row features are also confirmed by medium-energy ion scattering (MEIS).' Theoretical work has also confirmed the missing-row structure for Pt( 110) and Au(llO).'".'' An interesting aspect of this work is that the trends in the periodic table can be understood to some extent.Pt, Au and Ir( 110) have stable missing-row structures. Unreconstructed Ag( 110) is marginally stable but can adopt the missing-row structure when the Fermi ievel is perturbed by the deposition of a small amount of alkali metal." Cu and Ni( 110) are stable as unreconstructed surfaces. X-Ray data were taken as scans of the diffractometer 8 axis (rocking curves). This correctly accounts for both sample mosaic and disorder effects to give a true integration of the intensity, provided the peak is not broader than the 28 resolution.' IntegratedI. K . Robinson, E. Vlieg and K. Kern 161 t" [ l o o ] Fig. 1. Atomic model of the 1 x 2 missing-row structure.Arrows indicate symmetry-allowed displacements. Labels correspond to parameter values in table 1. ( a ) Top view, ( b ) side view. intensity values were obtained as the area under the histogram minus background4 then corrected for Lorentz factor (sin 28) and for the variation of active sample area4 (sin 20). Structure factors (square root of intensity) were measured for eight half-order rods sampled at several values of perpendicular momentum transfer L to resolve the modula- tion of the continuous function F,,k( L ) . We use the same indexing system as LEED, defining two in-plane reciprocal lattice vectors as a1 = ( 100),,b,c, a2 = ~ ( O l ~ ) c u , , i c and the perpendicular reciprocal lattice vector a3 = i(O1 l)cub,c. Examples of the rod data are given in fig.2. It is immediately clear from the rapid modulation of the rods that a multilayer structure is called for. The number of layer spacings involved can be estimated at ca. 3 which is the inverse period of modulation. These curves are extremely similar to those measured for Au( 110)" and show a strong similarity between the structures, as expected. Moreover the corresponding parts of the (1.5,0, L ) and (2.5,0, L ) curves agree well with the much earlier rotating anode data for Au( 1 lO)I4; these were interpreted in terms of a two-layer model with an enlarged spacing that is inconsistent with the new data. We find it necessary to include four layers with significant modification to obtain a good fit. The refined parameters,I3 quoted in table 1, are in good agreement with the most recent LEED papers'.' (see below) and consistent with the MEIS result, when it is considered that what is measured is effectively the alignment angle between the first and second layer atoms, thereby coupling in-plane and out-of-plane displacements.Comparison with theory, table 1, is not quite so impressive. Both model calculations predict correctly that there is a contraction of the top-layer spacing, ad,, < 0, but only the embedded-atom calculation' I attains the correct magnitude. The tight-binding calcu- lation'" grossly underestimates all the displacements, while the other has the second-layer pairing in the wrong direction. What is needed is a first-principles calculation with relaxation of four layers of coordinates.162 Structure and Roughening of the Pt( 110) Surface 0 0.2 0.G 0.6 0.8 1.0 perp.momentum transfer, L Fig. 2. Measurements of the structure factor F,,,(L) along several reciprocal lattice rods for Pt(ll0). The line is the best fit to a missing-row structural model with parameters given in table 1. ( a ) (i, 0, L ) rod, ( b ) ($, 0, t), ( c ) (g, 0, L ) , ( d ) (i, 0, L ) . Table 1. A summary of the structural results and the most relevant related work on Pt( 110) - ( 1 x 2) X-rays" LEED' LEED' MEIS" experimental - -0.27 (10) -0.11 (8) 0.05 ( 1 ) 0.04 ( 1 ) -0.26 (3) -0.18 (3) 0.07 (3) 0.12 (6) 0.32 -0.28 (2) -0.01 (2) 0.04 0.05 (4) 0.17 -0.22 (4) 0.06 (4) <0.04 - 0.10 theoretical - - tight - bi nd i ng t' -0.1 1 0.02 0.02 embedded atom' -0.25 -0.07 -0.03 0.04 0.1 1 "This work.' Ref. (8). ' Ref. (7). ' I Ref. (9). " Ref. (10). ' Ref. ( 1 1 ) . All displacements are given in 8, and the error in the last digit is indicated in parentheses. The definition of the parameters Sd and p is explained in fig. 1 . b, represents buckling in the third layer, with a positive value meaning an upward displacement of the third-layer atom without a first-layer atom above it. We would like to reflect a little on the relative accuracy of determination of the various parameters with the aid of fig. 3. Pt(ll0) has suddenly become a well studied surface with state-of-the-art LEED and X-ray results to compare. It is also a relatively simple reconstructed surface with an agreed-upon structure and important structural parameters both parallel and perpendicular to the plane.It also displays simultaneously three contrasting modes of reconstruction: density modification (top layer), pairing (second and fourth layers) and buckling (third layer). Fig. 3 shows a side view ofI. K . Robinson, E. Vlieg and K . Kern 163 q1 / - I / / / / \ \ \ \ \ Fig. 3. Schematic reciprocal space diagrams showing the limited range of diffraction data available to different techniques. The rods represent data. The hemispherical diffraction limit is an arbitrary total resolution cut-off. ( a ) LEED: The cone angle is set by the angular size of the screen (120" here). LEED system designs might vary slightly but will not affect this picture dramatically. ( h ) Four-circle X-ray diffraction': Here the cone angle is given by the maximum tilt angle accessible to the sample, limited by feedthroughs etc.( 1 1" here'). The same tilting limitations and diagram apply to transmission electron diffraction (TED). ( c ) Five-circle X-ray diffraction' or X-ray diffraction with out-of-plane detector arms-": The limiting perpendicuiar limit is given by the wavevector times the maximum inclination angle (ca. 20"). reciprocal space with rods representing the desired data in an ideal diffraction experiment (LEED or X-ray). A cut-off hemisphere is drawn to indicate some desired resolution limit: a complete, accurate set of measurements inside the sphere of radius qma, would allow the structure to be determined to an error of order 5% of 27r/qmau due to series termination effects" and depending somewhat on the accuracy of the data.This error would be isotropic. However, neither technique can measure the full hemis here; a typical range of data is shown in the figure for LEED, four-circle' and five-circle surface X-ray diffractometers. LEED is primarily a back-scattering technique, probing mainly perpendicular momentum transfer. It is particularly sensitive t o vertical displacements. It was able to detect third-layer buckling in Pt(llO), that was beyond the level of significance of the X-ray data. Perpendicular distances are accurate in table 1; parallel ones are not. In the drawn-out history of the structure of the analogous Au( 1 lo), it was the discovery of the buckling, as well as the ability to handle such a large calculation, that led to the first really satisfactory agreement between LEED observation and calculation.'" P164 Structure and Roughening of the Pt(ll0) Surface Conversely, X-ray diffraction as most commonly practised is a grazing-angle tech- nique, with a correspondingly different subset [fig.3(6)] of the data sampled. The four-circle (sample-tilting) geometry is particularly restrictive. So little was the range of data for the old Au( 1 study that it was unable to distinguish a top-layer expansion (albeit with an enormous error bar) in a two-layer model from a contraction in a four-layer model. The parallel displacement was also exaggerated by a factor of two, well outside the quoted error, for the same reason: two smaller displacements (second and fourth layers) were apparently indistinguishable from a single large one (second layer).The extension to the five-circle mode has improved the situation significantly, as fig. 3 ( c ) shows. The incident beam can be inclined to a large angle relative to the surface, improving the range of perpendicular momentum transfer. This is analogous to moving the detector out of plane’.”; the ability to do both is an anticipated further improvement. This was the geometry used in the present study. Parameters for Pt( 110) in table 1 are still better determined in-plane than out of plane, but we have sufficient vertical informa- tion to avoid ambiguity in this and most other cases. More perpendicular resolution is needed to determine reliably the small (1-5%) layer spacing relaxations seen in many otherwise unreconstructed surfaces.LEED is still the best technique for this because of its great vertical sensitivity. Thermal Roughening We will use a slightly different definition of roughening from the conventional one that is discussed in theories of roughening: the divergence of the height-height correlation function. Instead we will refer directly to the distribution of surface steps. A surface with a high density of steps is deemed rough, therefore roughness can be measured in a very direct way as step density. Rough surfaces can be made by sputtering and partial annealing, or may exist as the equilibrium state above the ‘roughening temperature’, TR. Above TR, the configurational entropy component of the free energy outweighs the energy cost of the steps.Steps affect the diffraction from a missing-row reconstructed surface in a particularly dramatic way, provided the reconstruction extends right up to the steps on both sides. Because of the face-centring of the Pt lattice, each step acts as a domain wall with quadrature phase difference, which leads to shifted diffraction peaks. This was first seen on Au(110).I8 Since then it has been predicted that the shift should oscillate with perpendicular momentum transfer. l 9 Now that we can make the required measurements, this is just what we find for Pt(llO), as fig. 4 shows. We can make a simple one-dimensional model to describe the shifted lineshape at the in-plane diffraction position, L = 0. We generalise the previous derivationl’to include both the presence of quadrature steps (with total probability a ) and conventional antiphase domain walls (with total probability p ) .Examples of some common surface defects as imaged by tunnelling microscopy”) and their effective phase shifts are shown in fig. 5. These are also predicted to be the most stable line defect configurations theoretically.” As can be seen, both up and down single-height steps have the same phase shift of 1 (modulo 4) half-cell, while both kinds of antiphase defects have 2 (modulo 4). Step defects with a phase shift of three half-cells have also been postulated” but are rarely observed’” and are energetically unfavourable.” The asymmetry with respect to defects of phase shift 1 (included) and 3 (omitted) half-cells is the essential aspect of the model that gives rise to shifted diffraction peaks.The new derivation’3 predicts a Lorentzian shape for the (1.5,0,0) peak with a half-width of p/2+ a / 4 and a shift to higher momentum transfer of a / 4 . The temperature dependence of the lineshape was measured and found to behave reversibly. The data were fitted to adjustable Lorentzian lineshapes convoluted with the measured low-temperature lineshape; this latter function represents the known0.8 0.7 - 0.6 2 er: Y $ 0.5 2 0.4 m E c) 5 CI C 0.3 @ i% 0.2 0.1 0 I. K . Robinson, E. Vlieg and K . Kern 165 1.45 1.50 1.55 2.45 2.50 2.55 parallel momentum transfer [ RLU] Fig. 4. Locus of the peak position in reciprocal space for a missing-row structure containing random steps, adapted from Fenter and L u . ’ ~ Superimposed on this are our data for R( 110) on a normalised vertical scale, showing good agreement with the prior predictions.instrumental resolution function as well as the residual finite size effects of the domain structure in the annealed sample. The dependence of the fitting parameters is,shown in fig. 6. The height, I ( T ) , is explained by the theoretical curve, I ( T ) = lolt(*’ where t = T / Tc- 1 and p’= 0.1 1 k0.01, and serves to identify the value of Tc = 1080* 1 K (precision)+50 K (accuracy). The deviation from the ideal curve close to T, is due to the appearance of critical scattering which was not modelled. Above T, the half-width diverges linearly with t. Both of these aspects are exactly in accord with the 2D Ising which has p‘= 1/8 and v = 1 (correlation length exponent).Furthermore, they agree well with LEED data for the closely analogous phase transition for Au(110).’5 Strong symmetry arguments have been used to predict that missing-row structures should fall in the Ising universality class,*‘ and Monte Carlo simulations have shown this to be in good agreement with the Au(ll0) result^.^' Notwithstanding this apparent agreement between Pt( 1 lo), Au( 110) and the 2D Ising model, we now turn to the last curve of fig. 6 showing peak shift versus temperature. This result is completely contrary to the Ising classification because it implies that steps form spontaneously above the phase transition. This immediately implicates some roughening character. Villain and Vilfan” had proposed that there might be separate roughening and Ising transitions close to the same temperature, but had not considered the possibility of a single transition with characteristics of both.If there are two transitions, they fall within 5 K of the same T,, as fig. 6 shows. A six-vertex model has been used28 more recently to describe the Au(ll0) surface theoretically; no Ising transition was found, but only a roughening transition instead. The lineshape model proposed in fig. 5 implies the missing-row ground state is now fourfold degenerate when steps are allowed, and so the correct universality classification could be a chiral four-state model.166 Structure and Roughening of the Pt( 110) Surface I E - 4 4 \ I n A ! I n nn A n Fig. 5. Atomic models of Pt( 110) surfaces containing a perfect ( 1 x 2) reconstruction (top), the same interrupted by a single height step (middle), and the same interrupted by antiphase defects (bottom).The lateral phase shift across the defect is indicated in units of half a unit cell spacing. a, p and I - CY - p refer to the assumed probabilities per site of the various configurations. The slopes of half-width versus T and peak shift versus T in fig. 6 allow us to quantify the relative probabilities of steps and antiphase defects using the expressions quoted above:” a = 6.6t and p = 2.81. This means that thermally induced steps are 2-3 times more common than antiphase defects. The corresponding values for Au( 110)’” are (Y = 0 and p = 5.2t, since no shift was seen. However, the spatial non-uniformities associated with LEED measurements in general make the technique rather insensitive to peak shifts.The published results‘”’’ were made at an energy corresponding to L=O.5 in fig. 4 where the shift should vanish: half the steps would be invisible and half would appear as antiphase domain walls. The quantity measured in the LEED experiment is therefore a / 2 + P , which has a value 6.lt for Pt(ll0) and 5.21 for Au(ll0). The two surfaces are indeed similar, but the experimental question of whether steps are involved with the Au( 110) 1 x 2 phase transition remains open. The fact that steps appear spontaneously in Pt( 110) as a function of temperature is a clear indication that the 1 x 2 reconstruction is only marginally stable. Theoretical studies showed that the free-energy difference between a 1 x 2 unit cell and step configur- ation is extremely small.” A 1 x 3 reconstruction comprising alternating up and down steps in a regular array is also a relatively favourable state, seen experimentally7 and expected from theoretical work.21*‘‘) One way of understanding the shift of the diffraction peak is to consider that Pt( 110) is tending, at elevated temperature, from a 1 x 2 state (peak at 1.5) to 1 x 3 (peak at 1.6667) by the random appearance of partial 1 x 3 unit cells, as in fig.5. A recent X-ray diffraction study3’ of Au( 110) actually found the 1 x 3 state to be more stable than the 1 x 2 state and that its phase transition shifted the peak in the opposite direction, from the 1 x 3 towards the 1 x 2. This suggests that theI. K .Robinson, E. Vlieg and K . Kern 20 10 - - 167 0.08 0.06 n 2 a! u 5 z 3 0.04 C-: 5 5 0.02 z m c \ Y ?J 0 Fig. 6. Temperature dependence of the Lorentzian fitting parameters of the Pt( 110) radial lineshape measured at (1.5,0,0.06). 0, peak height fit with T, = 1080 K, p, = 0.1 1 . V, Half-width; A, shift. high-temperature state of this Au(ll0) crystal may be the same mixture of two- and three-atom wide facets as that seen on Pt(ll0) even though their low temperature structures have different translational symmetry. We have enjoyed discussions of surface phase transitions with P. Bak, D. Huse, R. J. Birgeneau, T. L. Einstein and L. D. Roelofs. The crystal was expertly cut and polished by U. Linke at Julich. NSLS is supported by the United States Department of Energy under contract DE-AC02-76CH00016.References 1 P. H. Fuoss and 1. K. Robinson, Nucl. Inst. Merh., 1984, 222, 171. 2 I. K. Robinson, Rev. Sci. Instrum., 1989, 60, 1541. 3 E. Vlieg, J. F. van der Veen, J. E. Macdonald and M. Miller, J. Appl. Crvsrallogr., 1987, 20, 330. 4 I. K. Robinson, in Handbook on Synchrotron Radiarion, ed. D. E. Moncton and G. S. Brown (North- Holland, Amsterdam, 1990), vol. 111, chap. 5. 5 R. Feidenhans'l, S u r - Sci. Rep., 1989, 10, 105. 6 I . K. Robinson, W. K. Waskiewicz, R. T. Tung and J. Bohr, Phys. Rev. Lett., 1986, 57, 2714. 7 P. Fery, W. Moritz and D. Wolf, Phys. Rev. B, 1988, 38, 7275. 8 E. C. Sowa, ivl. A. van Hove and D. L. Adams, Surf: Sci., 1988, 199, 174. 9 P. Fenter and T. Gustafsson, Phys. Rev. B, 1988, 38, 10197. 10 H .J . Brocksch and K. H. Bennemann, Suet Sci., 1985, 161, 321. 1 1 S. M. Foiles, Surf: Sci., 1987, 191, L779. 12 J . W. M. Frenken, R. L. Krans, J. F. van der Veen, E. Holub-Krappe and K. Horn, Phys. Reu. Lett., 1987, 59, 2307. 13 E. Vlieg, I . K. Robinson and K. Kern, Surj. Sci., submitted. 14 1. K. Robinson, Phjps. Rev. Leu., 1983, 50, 1145. 15 H. Lipson and W. Cochran, The Determination 01' Crjvctal Structurec (Cornell University Press, 3rd edn, 1966), chap. 12, pp. 317-357. 16 W. Moritz and D. Wolf, Sutf Sci., 1985, 163, L655.168 Structure and Roughening of the pt( 110) Surface 17 M. Nielsen, Z. Phys. B, 1985, 61, 415. 18 1. K. Robinson, Y. Kuk and L. C. Feldman, Phvs. Rev. B, 1984, 29, 4762. 19 P. Fenter and T. M. Lu, Surf: Sci., 1985, 154, 15. 20 G. Binnig, H. Rohrer, C. Gerber and E. Weibel, Sur-: Sci., 1983, 131, L379; T. Gritsch, D. Coulman, R. J. Behm and G. Ertl, Phvs. Rev. Lett., 1989, 63, 1086. 21 L. D. Roelofs, S. M. Foiles, M. S. Daw and M. Baskes, Phys. Rev. Lett. 1989, 63, 2578. 22 J. Villain and I. Vilfan, Surt Sci., 1988, 199, 165. 23 I . K. Robinson, E. Vlieg and K. Kern, to be published. 24 L. Onsager, Phys. Rev., 1944, 65, 117. 25 J. C. Campuzano, M. S. Foster, G. Jennings, R. F. Willis and W. Unertl, Phjx Rev. Lett., 1985, 54, 2684. 26 P. Bak, Solid State Commun., 1979, 32, 581. 21 M. S. Daw and S. M. Foiles, Phjx Rev. Lett., 1987, 59, 2756. 28 A. C. Levi and M. Touzani, Surf Sci., 1989, 218, 223. 29 J. C. Campuzano, G. Jennings and R. F. Willis, Surf: Sci., 1985, 162, 484. 30 M. Garofalo, E. Tosatti and F. Ercolessi, S u ~ t Sci., 1987, 188, 321. 31 G. A. Held, J. L. Jordan-Sweet, P. M. Horn, A. Mak and R. J. Birgeneau, Solid State C'ommun., 1989, 72. 37. Paper 9105299B; Received 6th December, 1989

ISSN:0301-7249    

DOI:10.1039/DC9908900159

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1990, 89, 169-180 Structure of the Ge( 11 1)-c(2 x 8) Surface as determined from Scattered X-Ray Intensities along Crystal Truncation Rods Roelof G. van Silfhout and J. F. van der Veen FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands C . Norris Leicester University, Leicester LEI 7RH J. E. Macdonald University of Wales, Cardif CFl 3TH In an X-ray diffraction study of the c(2 x 8) reconstructed Ge( 11 1) surface we have measured intensity profiles along integer-order rods of Bragg scatter- ing perpendicular to the surface plane. The diffracted intensity profiles are explained in terms of a simple adatom model for the reconstruction. The adatoms are found to occupy T4 sites on a distorted bulk-like substrate.We rule out any model for c(2 x 8) reconstruction that is based on stacking faults in the substrate. For the adatom model we give best-fit values for the positions of the atoms at the surface and compare them with those obtained from total-energy and Keating-energy minimisation calculations. 1. Introduction X-ray diffraction has become an important tool for the structure analysis of reconstructed single-crystal surfaces.' By measuring the intensities of in-plane fractional-order reflec- tions under grazing scattering conditions, one obtains a projection of the positions of the atoms in the surface unit cell onto the plane of the surface. A determination of the atomic coordinates in the direction normal to the surface requires a measurement of the scattered intensity along the fractional-order or integer-order rods of Bragg scattering perpendicular to the surface plane.The integer-order rods are called crystal truncation rods (CTRs) because they originate from the abrupt truncation of the crystal lattice at the surface.' The total structure factor at a given point along a truncation rod is the sum of the surface and bulk structure factors whose relative phase difference depends on the positions of the atoms in the surface unit cell relative to those in the bulk lattice. It is the interference between surface and bulk scattering that makes CTR profiles sensitive to the detailed atomic structure of the surface, provided the surface superlattice is well ordered and in coincidence with the bulk crystal lattice.However, the intensity distribu- tion is also strongly dependent on atomic-scale roughness. Therefore, in any surface structure analysis by this method one must allow for truncations of the crystal at different heights, caused by steps, (adatom) vacancies or other structural defects. We note that the analysis of X-ray rod profiles is analogous to understanding LEED I - V curves but with the important advantage that the measured intensities can be analysed with the use of kinematical scattering theory. In this work, we present a structure determination of the ~ ( 2 x 8 ) reconstructed Ge(ll1) surface which is entirely based on the analysis of CTRs. To our knowledge, this is the first time that this method is used for a structure determination of a clean 169170 Structure of the Ge( 11 1)-c(2 x 8) Surface Fig.1. Ball-and-stick model of the reconstructed G e ( l l 1 ) surface. ( a ) Shows a top view of the ( 2 x 2 ) surface unit cell used t o model the reconstruction. The two possible adatom adsorption sites T4 and H3 are indicated. The arrows represent the in-plane displacements of the atoms to which the adatom is bonded (enlarged by a factor of 3). Dashed lines represent mirror planes of the 3m bulk symmetry. ( b ) shows, in side view, the best-fit model for the reconstruction with the relaxations drawn to scale and the adatom at the T4 site. The atoms whose positions were allowed to vary are numbered 1-17 (see also table 1). reconstructed surface. Previously, it has been used to investigate surface roughness,' the structure of interfaces [Si( 11 l)/a-Si, Si( 11 1)/Si02 and Si( 11 1)/NiSi2 3.4] and the & x & - R30" reconstructions on Si( 11 1) induced by Bi and Ag a d ~ o r p t i o n . ~ , ~ The c(2 x 8) reconstruction of the clean Ge( 11 1) surface has been investigated previously by a wide range of surface-sensitive techniques including low-energy electron diffraction (LEED),' scanning tunnelling microscopy (STM),* medium-energy ion scat- tering (MEIS)' and grazing incidence X-ray diffraction."' The c(2 x 8) indexing of the reconstructed unit cell for the Ce( 11 1) surface was proposed by Chadi and Chiang" and supported by the theoretical analysis of missing LEED spots by Yang and Jona.'?R.G. van Silfhout et al. 171 For the c(2 x 8) unit cell three different rotational domains can be distinguished. Apart from rotational domains, STM work by Becker et al.s shows translational domains of c(2 x 8) interspersed by smaller c(2 x 4) and (2 x 2) surface unit cells.The protrusions seen in the STM images were interpreted as adatoms or clusters of adatoms. In an M EIS investigation, Mar6e et al.” compared the surface-blocking pattern of backscattered ions from Ge( 11 1)-c(2 x 8) with those obtained for the same scattering conditions on Si( 11 1 j-(7 x 7). They concluded that the Ge( 11 1)-c(2 x 8) reconstruction is structurally different from Si( 11 1)-( 7 x 7): no evidence was found for the presence of stacking faults on Ge( 11 1). The results of Mar6e et al. disprove the dimer-chain model proposed by Takayanagi and Tanishiro13 and are instead consistent with a simple adatom mode114 where the adatoms are located at positions with threefold symmetry either above a second-layer atom (T4 or filled site) or above a fourth-layer atom (H, or hollow site); see fig.l ( a ) . The adatom model was confirmed in a grazing-incidence X-ray diffraction study by Feidenhans’l et a/.’’ From a total of 64 integrated in-plane intensities the lateral positions of the atoms in the reconstructed unit cell projected onto the surface plane were determined. From the lateral displacement pattern the T, site for the adatom was favoured. In a recent STM study, Becker et a1.15 compared the S i ( 1 1 1 ) - ( 7 ~ 7 ) and Ge( 11 1)-c(2 x 8) reconstructions using dual polarity scans. Again no stacking faults were observed for the ~ ( 2 x 8 ) reconstruction, confirming the findings of Marie et al.9 Their observations are in agreement with the simple adatom model.In none of the above investigations could one unambiguously distinguish the T, site from the H3 site for the adatom. According to pseudopotential calculations by Northrup and Cohen,I6 both sites are energetically favourable. A detailed self-consistent energy- minimisation scheme by Meade and Vanderbilt” predicted T4 to be the lowest-energy site. In the latter calculation, a 2 x 2 unit cell containing a single adatom was taken as the basic building block of the reconstruction and the atoms surrounding the adatom were allowed to relax. In this paper we present measurements of CTRs for the Ge( 11 1)-c(2 x 8) reconstruc- ted surface at room temperature.The results are consistent with the simple adatom model and a kinematical analysis of diffracted intensities gives the height and occupancy of the adatoms. The adatom site is unambiguously determined to be T4. We observe lattice distortions in the layers below the adatom and give atomic coordinates for the first four atomic layers. Finally, we compare our coordinates with those predicted by available theoretical models. 2. Experimental The X-ray diffraction measurements were performed at the wiggler station 9.4 at SRS, Daresbury (U.K.). A wavelength of 0.80 A was selected using a channel-cut Si( 11 1) monochromator. The setup consists of an ultra-high vacuum system (base pressure 5 x lo-” Pa) coupled to a five-circle diffractometer.” Our observations were made on a Ge( 1 1 1 ) crystal (8 x 8 x 1.5 mm3, miscut < 0.05O) cleaned by repeated cycles of sputtering (800eVi AT+, 1 pAcm-.’ for 15 min) and annealing (700°C for 20min).After this treatment a sharp ~ ( 2 x 8 ) electron diffraction pattern was observed with the in situ reflection high-energy electron diffraction (RH EED) facility. The procedure for align- ment of the vertically mounted sample with respect to the diffractometer has been described by Vlieg er a1.l9 The use of a five-circle diffractometer rather than an ordinary four-circle setup enlarges the accessible range of momentum transfers and allows for the constraint that the surface normal lies in the horizontal plane during scans.172 Structure of the Ge( 11 1)-c(2 x 8) Surface Scans of perpendicular momentum transfer along the rods were done in a symmetric mode keeping the angle of exit af equal to the angle of incidence ai.The incoming X-ray beam was defined by slits in both horizontal (86 p m ) and vertical (3 mm) directions. This results in a footprint on the sample which just fits its horizontal dimension at an incidence angle of 0.88", which is well above the critical angle for total reflection (0.163" for 0.8 A wavelength). The diffracted intensities were measured with a solid-state Ge detector. Slits in front of the detector limited the angular acceptance to 0.4" in the out-of-plane direction and to 0.3" in the in-plane direction. All intensities were normalised to the total intensity of the incoming X-ray beam as measured by a monitor placed between the monochromator and sample.A hexagonal unit cell spanned by primitive lattice vectors { ai} was adopted according to the usual choice made in LEED experiments where a , and a? are parallel to the surface plane and u3 is perpendicular to it (fig. 1). The vectors {ai} are in the conventional cubic coordinate system given by with where a. is the bulk Ge lattice constant (5.658 A). Henceforth, we specify the position of an atom r, in the unit cell as r, = cial + cja,+ c ~ u , . The corresponding reciprocal space is described by the reciprocal lattice vectors {bl}: with lbll = Ib21 = (477/3a0)& and Ib,( = ( 2 r / 3 a O ) f i . The momentum transfer vector 4 is represented by Miller indices (hkl) in reciprocal space with 4 = hb, + kb, + lb,.With this choice of vectors {bl}, CTRs are labelled by the in-plane Miller-index pairs ( h k ) , with h and k integers. Momentum transfer in the perpendicular direction is given by the index 1 which may assume any real value. A part of the reciprocal space thus defined is shown in fig. 2 with the hatched regions indicating the CTRs and the ranges that were scanned. The analysis of the measured intensity distribution along the (00) rod, for which there is no momentum transfer in the surface plane, cannot give any information on the lateral positions of the atoms. Therefore, we also measured the (10) and (10) rods for positive values of the perpendicular momentum transfer. In this experiment the integrated Bragg intensity for a given reflection ( h k l ) is measured by rotating the crystal around the surface normal ( 4 axis") using a detector with a wide in-plane angular acceptance.The background-subtracted total sum of detected photons is taken as a measure of the integrated intensity. The structure-factor intensity is obtained by multiplying the integrated intensity by the inverse Lorentz factor sin 28 cos a, [see ref. ( l ) ] and normalising the result to the size of the illuminated area, which is proportional to (sin a,) I . Finally, a correction is made for the horizontal polarisation of the radiation by multiplication with (cos2 28 cos' 2 a , ) - ' . Here, 2 8 is the in-plane scattering angle, which is constant for ( h k l ) along a given CTR, and a l ( = a , ) is the angle of incidence with respect to the surface plane.For 1 values increasing along the (10) and (TO) rods over the range 0.1 < 1 < 4 (fig. 2) the angles a , and a , increase symmetrically from 1" to 11". Within this 1 range we measured a total of 274-scans across the rods. The window in 1 accepted by our detector equals A1 = 0.08. The specularly reflected intensity distribution along the (00) rod was measured in a different way. Instead of taking a series of transverse momentum scans at different 1 values we directly measured the intensity along the rod by counting the scattered photons within the angular acceptance of the detector while symmetrically increasing a , and ar (keeping a , = a , ) . The structure factor intensity lF(,,l,l' is then obtained by multiplying the measured intensity with sin' a , .The latter factor takes into account the change inR. G. van Silfhout et al. 173 3 I 0 Fig. 2. Reciprocal-space diagram for a diamond-type crystal terminated with a ( 1 11 ) plane. Only integer-order rods are shown. ( a ) Shows the in-plane projection with bulk Bragg points indicated as solid circles. ( h ) Shows a cut normal to the surface through the (TO) and (10) rods, with the decaying intensity distributions around the bulk Bragg points schematically indicated. The ranges scanned are indicated by the shading. both the illuminated surface area (sin a i ) and in the cross-sectional area of the rod intersected by the Ewald sphere (sin ai). An additional cos? 2 a i correction is made to account for the polarisation. 3. Results The integrated intensities measured along the (00), (10) and (TO) rods are shown in fig.3 and 4. In the latter figure we have inverted the intensity distribution along the (TO) rod through the origin of reciprocal space in order to obtain the lower half of the (10)174 Structure of the Ge( 11 1)-c(2 x 8) Surface rod at negative I values. This procedure is just an application of Friedel's inversion The experimental data set shown was collected from a surface that had been subjected to at least eight sputtering/annealing cycles. This pretreatment was found necessary for obtaining a well ordered flat surface. All transverse momentum scans were repeated at least once and the intensity distributions were highly reproducible. The error bars given reflect the uncertainty in the background subtraction or the difference between symmetry- equivalent transverse momentum scans, whichever was largest.rule IFhh-ll = IFT;(rl. 3.1. Surface Roughness We investigate the morphology of the surface by comparing the measured intensities along the (00) rod with the structure-factor intensities IFo0,12 calculated for crystal models with varying surface roughness. First consider the case of an abruptly terminated crystal having an ideally flat bulk-like surface (unreconstructed and unrelaxed). The unit cell as defined by {ai} encloses three bilayers with the familar ABC stacking of a diamond-type crystal. In order to study the roughness related to individual bilayers we treat our crystal as a stack of bilayers. Each bilayer is shifted over a vector Ad" = $a, + ;az + +a3 relative to the neighbouring one below.This results in a phase factor for the nth bilayer of exp (in$hkl), with $hk/ = 27r(Arbi q ) = 27r($h + i k + i I ) . (3) The total structure factor Fk;fk is obtained by summing over all the bilayers which make up the crystal:' where Ghk, is the structure factor of a single bilayer, f is the atomic scattering factor for Ge and v-' is an absorption length in units of bilayer spacing. The (hkl) values corresponding to bulk Bragg points are obtained for = 2.rrm or 2h + k + I = 3m ( m integer). Thermal vibrations of the atoms are taken into account by multiplying the right-hand side of eqn (4) by a Debye-Waller factor exp [-Bq2/(4.rr)']. For bulk germanium, Batterman and Chipman" determined the parameter B to be 0.58 A2 at room tem- perature.We use this value throughout our analysis although the Debye-Waller factor represents only a small correction for the range of momentum transfers scanned in our experiment. Numerical evaluation of IFkLf'II' using eqn (3)-(5) in the limit of negligible absorption ( L.' - 0) yields the dashed curve in fig. 3. The measured intensities follow this curve closely except for the minimum where there is a slight deviation. We now show that surface roughness associated with terraces of bilayer height cannot be the cause of this deviation. Let us model roughness in the manner described by Robinson.' One adds onto the flat surface first a bilayer with fractional occupancy p (with 0 < p < I), then a second layer with occupancy P', and so on.By modifying the summation over bilayers as given by eqn (4) one obtains for the structure-factor intensity of the rough surface One readily sees that IFiIGSh12 s lFk:jklZ, which contradicts our observation of intensities higher than those calculated for a flat bulk-like surface. Fig. 3 shows for illustration a curve calculated for P = 0.05. Clearly, the minimum of this curve between the (000)R. G. van Silfhout et al. 175 Fig. 3. Intensity distribution along the (00) rod of the reconstructed Ge( 11 1 ) surface. Measured intensities are indicated by solid circles. The different curves represent the structure factor intensities calculated for a flat bulk-like surface (---), a rough bulk-like surface with bilayer occupancy p = 0.05 (-.-) and a surface reconstructed according to our best-fit model (-).and (003) bulk Bragg peaks is too deep. Other realistic (multilevel) models of roughness exhibit qualitatively the same behaviour. We conclude that our sputtered and annealed Ge( 11 1)-c(2 x 8) surfaces are essentially flat ( p < 0.01). 3.2. Structure Determination The measured intensities near the minimum of the (00) rod are slightly higher than those calculated for a flat bulk-like surface. The model structure factor intensities \Fool12 along this rod can be made to fit the data better by the introduction of a higher average density of atoms at the surface. We do this by placing a layer of adatoms just above the surface plane. The total structure factor for the model system on which the fit is based is given by (7) F;;d" = Fb,,"Jk + OF;;,?, where is the structure of the atomic layer added, rad = (@a, + c;'ua.+ c;"u3) is the position of the adatom and 8 is the monolayer fraction of adatoms in this layer. [ O = 1 corresponds to an adatom coverage of 7.2 x l O I 4 atoms cm-', being the areal density of atoms in a single atomic plane]. Constraining the substrate atoms to be on bulk lattice sites we obtain the best, but not yet acceptable, fit for a quarter monolayer of adatoms ( 8 = 0.26 f 0.02) at height above the second-layer substrate atoms of zad = 0.20 Iujl = 2.0 A. Position- ing the adatoms on a T4 or an H3 site (fig. 1) makes no difference to the intensity profile of the (00) rod provided the height is the same, but has a large effect on the (10) rod. This is not surprising, since the change from T4 to H3 over the displacement vector Arad = { a , -+a2 [fig.l ( a ) ] alters the phase of FYi/ relative to Fy$;k. Fig. 4 shows the structure-factor intensity calculated for the two different positions of the ad-atom on a176 1 oe 1 o5 1 o3 1 o2 Structure of the Ge( 1 1 1)-c(2 x 8) Surface Fig. 4. Intensity distributions along the (10) rod of the reconstructed Ge( 11 1 ) surface. Measured intensities are indicated by solid circles. The different curves represent the structure factor intensities calculated for a flat bulk-like surface (---), for a bulk-like surface with a quarter of a monolayer of adatoms placed on a T, site (-. -), for the same surface but with the adatoms on a H, site (-..-) and for our best-fit model with adatoms on a T, site and substrate atoms relaxed to the positions listed in table 1 (-).bulk-like lattice using 8 = 0.25 and zad = 0.20 Iu31 as obtained from the fit to the (00) rod. The structure-factor intensity lF:,$k/2 for the bulklike surface without adatoms lies between the curves calculated for the two adatom positions. The data matches none of the three curves except for perpendicular momentum transfer values in the range -2 < 1 < 2 where the measured intensities follow the calculated intensities for the T4 model quite closely. From this we conclude that the adatoms occupy T4 sites. In order to account for the large oscillatory excursions in the measured intensities at larger 111 values we must introduce vertical relaxations in the substrate.In doing so, we must allow for lateral displacements as well. From the oscillation period we estimate that the adatom-induced distortions extend over the two outermost bilayers. We now search fgr the structure model giving the best fit to the measured intensities along both the (00) and the (10) rods. Our starting point is a ( 2 x 2 ) surface unit cell three bilayers deep on top of a semi-infinite bulk crystal with a single adatom positioned at a T4 site (fig. 1 ) . The structure factor for this model is given by with where the summation extends over all atoms in the 2 x 2 reconstructed unit cell. The factor 4 takes the larger size of the 2 x 2 surface unit cell with respect to the 1 x 1 bulk unit cell into account. As the surface may not be reconstructed over its entire area, we allow for a certain fraction ( 1 - y ) of the surface area to be bulklike.This fraction we simply model with the structure factor F ~ ~ ~ k . ' 2 x 2 ' describing a 2 x 2 surface unit cell with the adatom (atom number 1 ) removed and all other atoms at bulk positions. In the fitsTable 1. List of structural parameters for the reconstructed Ge( 11 1) surface with error bars in parentheses" total energy Keating fit y = 0.93 (1); x 2 = 1.3 y = 0.96 (2); xz = 7.7 y = 0.73 (4); x1 = 121 bulk atom number c', C? c3 c1 c, c7 CI c2 c3 c 3 1 2 3 6 7 10 11 14 15 18 19 1 1.667 1.667 1 0 1 0 0.333 1.333 0.333 1.333 1 0.333 1.333 1 1 1 1 1.667 1.667 1.667 1.667 1.25* 1.083 1.083 1 1 0.75 0.75 0.667 0.667 0.417 0.417 - - 1.203 (3) - - 1.136 (4) 1.63 (3) 1.31 (2) 1.071 (2) 0.952 (2) - - 0.707 ( 1 ) 0.680 (1 ) - - 0.663 ( 1 ) - - -0.02 (2) 0.96 ( 1 ) 1.021 (2) -0.01 ( 1 ) 0.99 ( 1 ) 0.763 (1) - - - - 1.206 - 1.117 1.634 1.317 1.072 - 0.95 1 -0.022 0.956 1.016 - - 0.710 - 0.679 1.357 1.680 0.663 - - 0.430 1.346 1.674 0.412 - - -0.002 0.999 0.763 - 1.201 (1) 1.088 ( 5 ) 1.079 (2) 0.962 1.01 1 0.72 1 0.758 0.672 0.663 0.422 0.415 C $2 3 * The adatom.(' Atoms are numbered as in fig. 1. Their positions are given by r, = c i a , + c i a, + c i a 3 , with { a , } the fundamental translation vectors as defined in fig. 1 and the text. Positions are given for a bulk-terminated crystal (2nd column), for our best-fit structure model (3rd column) and for models based on the total-energy calculation of Meade and Vanderbilt'' (4th column) and the Keating-type calculation by Pedersen?? (5th column).Open dashed entries in the table indicate that the corresponding coordinate is fixed to its bulk value. The fraction of reconstructed surface area y is a free parameter in all fits. Reduced x2 values are given for the different models. L 4 4178 Structure of the Ge( 11 1)-c(2 x 8) Surface we treat y as a free parameter and allow the positions of atoms 1-17 to vary in accordance with the 3m symmetry of the bulk, keeping all other atoms in the cell at bulk positions. The mirror planes in the surface unit cell are indicated as dashed lines in fig. l ( a ) . This symmetry constraint reduces the total number of structural parameters to 13. We impose the additional constrapt that the magnitudc of the atom displacements decreases with increasing depth.A XL-minimisation procedure?' yields a good simultaneous fit to the measured intensities along the (00) and (10) rods (solid curves in fig. 3 and 4). We note that only a single scaling factor is used in the fits to the measured intensity distributions along the (00) and (10) rods. We find a best-fit y value of 0.93*0.01, i.e. 93% of the surface area is reconstructed, equivalent to an adatom coverage of 8 = 0.23 f 0.01 monolayer. The best-fit atomic positions within the 2 x 2 surface cell are given in table 1. The reduced x2 value of our best fit is 1.3, which we consider satisfactory. The coordinates of the atoms not listed (e.g. numbers 4 and 5 ) are readily derived from the tabulated ones (e.g. number 3) by performing rotations over 120" around the surface normal or a reflection across a mirror plane, see fig.l(a). The quoted uncertainties in the structural parameters were derived from a least-squares analysis?' and correspond to the chapge of a given parameter, with the other parameters relaxed, such that the reduced x- value increases by one. The best-fit relaxed adatom model is shown to scale in fig. l ( b ) . Atoms 3-5, to which the adatom is bonded, are radially displaced over 0.1 A toward the adatom and displaced downward by 0.12 A relative to their bulk positions. As a result, atoms 6 and 10 are displaced downward by 0.47 and 0.42 A, respectively. The pushing-down of atom 10 in turn gives rise tosmall distortions in the second bilayer. Atom number 2, which is not bonded to an adatom, is pushed up above its bulk position over a distance of 0.52 A.4. Discussion and Conclusion The atomic coordinates at the reconstructed Ge( 11 1) surface have been determined for a ( 2 x 2 ) rather than a ~ ( 2 x 8 ) surface cell. From the work of Feidenhans'l ef al." we know that the symmetry of the surface is lower than the 3rn symmetry that we have imposed in order to reduce the number of free structural parameters. Asymmetric lateral displacements of the substrate atoms around the adatom over a distance of typically ca. 0.06 A were observed by Feidenhans'l et al. Such displacements are small compared to our accuracy for the in-plane coordinates (ca. :.l A). I f the in-plane coordinates of atoms 1-17 are fixed to their bulk values, the X--value increases from 1.3 to 2.4.Our in-plane resolution could be improved by performing more integer-order rod scans for higher ( h k ) indices. The accuracy for the coordinates along the direction perpendicular to the surface was 0.03 A. Besides c(2 x 8) reconstructed domains, (2 x 2) and c(2 x 4) domains have been observed in STM images.x3" All observed surface unit cell sizes and their inequivalent rotational domains can be obtained by translations of the ( 2 x 2 ) surface unit cell over in-plane bulk translational vectors and/ or rotations over 120" around the surface normal. It is readily shown that the structure-factor intensity for integer-order reflections is the same for the different translational and rotational (2 x 2) domains. We now compare our results with available theoretical models.Table 1 gives the atomic coordinates resulting from a total-energy I' and a Keating-energy" minimisation. The Keating model is based on a ~ ( 2 x 8 ) surface unit cell with asymmetric lateral displacements as determined by Feidenhans'l et a1.l') Its in-plane atomic coordinates are left out from table 1 . The perpendicular coordinates are avFraged over the c(2 x 8) cell and the spread therein is indicated in parentheses. The X--values listed for both models were obtained in a fit where only the fraction y of the reconstructed surface area was allowed to vary. In fig. 5 we have plotted the calculated structure factor intensity along the (10) rod for the models with y fixed to 1.00, together with the resultR. G.van Silfhout et al. 179 L, 0 Y perpendicular momentum transfer, I (r.1.u.) Fig. 5. Structure-factor intensities along the (10) rod calculated for different models of the reconstructed Ge( 11 1 ) surface. (- - -) and (-. -) curves represent the structure models based on a total-energy calculation by Meade and Vanderbilt” and a Keating-type calculation,23 respectively. In both model calculations the whole surface was assumed to be reconstructed, i.e. y = 1.00. The (-..-) dotted curve represents a model for a bulklike surface with 20% of the first bilayer faulted. Our best-fit model (table 1) is given by the solid curve (see fig. 4). of our minimisation procedure. The total-energy calculation shows a remarkable agree- ment with our results; the model curve for y at its optimum value of 0.96 (not shown in fig.5 for clarity) comes close to the curve for our best-fit model. The main difference is the relaxation of the atom within the first layer (number 2) that is not bonded to the adatom: the so-called rest atom. In our model the rest atom moves further outward by 0.19 A with respect to the total-energy model while the Keating model has the rest atom almost unrelaxed. The failure of the Keating model to predict the outward displacement of the rest atom can be understood if the displacement is due to a charge transfer within the surface unit cell. In the Keating approach23 one only deals with elastic properties of the model such as bond-length deformation and bond-angle distortion but electronic effects are neglected. A transfer of an electron from the adatom to the rest atom would completely fill the rest-atom surface states consistent with a completely filled surface band arising from the rest-atom dangling bond^.^,'^.'^ The associated rehybridisation of the rest atom gives rise to the s2p3 character typical for a graup V element.The rest atom is then pushed up because of a repulsive electrostatic interaction with the bonds to its neighbours. Localized on the adatom is an empty surface state of sp’ character. From the values given in table 1 we calculate the bond len th between the adatoms the adatom and the atom in the second layer just below the adatom is 2.46*0.02 A. These distances are to be compared with a bulk bond len th of 2.45 A. The rest atom Stacking faults form an essential ingredient in the dimer-chain model proposed by Takayanagi and Tanishiro.13 A remarkable effect on the rod profile is noted for the stacking-fault model, because the 3 m bulk symmetry is converted locally into a 6 m (higher) symmetry.Already for a fraction of stacking faults in the outermost bilayer as small as 20%, two pronounced peaks develop around the (107) and (103) points in and the atoms in the first layer (number 3-5) to be 2.54*0.03 1 . The distance between has bond angles of 98.5” and bond lengths of 2.51 *0.03 R with its neighbours.180 Structure of the Ge( 11 1)-c(2 x 8) Surface reciprocal space and the (10) rod becomes symmetrical around I = 0, which is in contradiction with our observations. We conclude that stacking faults are absent in the Ge( 11 1)-c(2 x 8) reconstructed surface.In summary, we have demonstrated the use of integer-order rod scans in surface X-ray diffraction for the structure determination of a clean reconstructed surface. The applicability of kinematical scattering theory greatly facilitates the analysis of the measured intensity profiles along the rods. For the Ge( 11 1)-c(2 x 8) reconstruction we confirm the simple adatom model. We find the adatom to occupy the T, site and the surrounding atoms to be relaxed over large distances. The structure is in good agreement with the theoretical model by Meade and Vanderbilt,” except for the position of the rest atom which is slightly higher than predicted. We would like to thank the Daresbury staff, in particular Dr G. Clarck, for able assistance during the measurements. One of us (R.v.S.) would like to thank Alan Parsons for his support. J.Skov Pedersen (Ris@) is gratefully acknowledged for access to his unpublished results on the Keating model. This work is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and is made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References 1 R. Feidenhans’l, Surf Sci. Rep., 1989, 10 (3), and references therein. 2 S. R. Andrews and R. A. Cowley, J. Phys. C, 1985,8,6247; I . K. Robinson, f h y s . Rev. B, 1986,33,3830. 3 I . K. Robinson, f h y s . Rev. Lett., 1986, 57, 2714. 4 I. K. Robinson, R. T. Tung and R. Feidenhans’l, Phys. Rev. B, 1988, 38, 3632. 5 T. Takahashi, S. Nakatani, T. Ishikawa and S. Kikuta, Surf Sci., 1987, 191, L825. 6 T. Takahashi, S. Nakatani, N. Okamoto, T. lshikawa and S. Kikuta, Jap. J. Appl. fhys., 1988, 27, L753. 7 R. J. Phaneuf and M. B. Webb, Surf: Sci., 1985, 164, 167. 8 R. S. Becker, J. A. Golovchenko, B. S. Swartzentruber, fhys. Reu. Leu, 1985, 54, 2678. 9 P. M. J. MarCe, K. Nakagawa, J. F. van der Veen and R. M. Tromp, Phys. Rev. B, 1988, 38, 1585. 10 R. Feidenhans’l, J. S. Pedersen, J. Bohr, M. Nielsen, F. Grey and R. L. Johnson, Phys. Rev. B, 1988, 38, 9715. 1 1 D. J. Chadi and C. Chiang, Phys. Rev. B, 1981, 23, 1843. 12 W. S. Yang and F. Jona, Phys. Rev. B, 1984, 29, 899. 13 K. Takayanagi and Y. Tanishiro, f h y s . Rev. B, 1986, 34, 1034. 14 W. A. Harrison, Surf Sci., 1976, 55, 1 . 15 R. S. Becker, B. S. Swartzentruber, J. S. Vickers and T. Klitsner, Phys. Rev. B, 1989, 39, 1633. 16 J. E. Northrup and M. L. Cohen, Phys. Rev. B, 1984, 29, 1966. 17 Robert D. Meade and David Vanderbilt, Phys. Rev. B, 1989, 40, 3905. 18 E. Vlieg, A. van’t Ent, A. P. de Jong, H . Neerings and J. F. van der Veen, Nucl. Instr. Meth. A, 1987, 19 E. Vlieg, J. F. van der Veen, J. E. Macdonald and M. Miller, J. Appl. Cryst., 1987, 20, 330. 20 €3. W. Batterman and D. R. Chipman, Phj1.s. Rev., 1962, 127, 690. 21 F. James, Proceedings of the C E R N Computing and Data Processing School, Austria, 1972, and references therein. 22 J. S. Pedersen, unpublished work, 1988. 23 P. N. Keating, fhys. Rev., 1966, 145, 637. 24 F. J. Hirnpsel, D. E. Eastman, P. Heimann, B. Reihl, C . W. White and D. M. Zehner, fhys. Rev. B, 1981, 24, 1120. 262, 522. Paper 0/00957A; Received 2nd March, 1990

ISSN:0301-7249    

DOI:10.1039/DC9908900169

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Furaduy Discuss. Chem. Soc., 1990, 89, 181-190 X-Ray Scattering from Surfaces and Interfaces Roger A. Cowley Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU Chris A. Lucas Department of Physics, Universiry of Edinburgh, MayJield Road, Edinburgh The theory of X-ray scattering from surfaces is reviewed. A simple kinemati- cal derivation is given of the surface truncation rods occurring near Bragg reflections and of the specular reflectivity. The dynamical theory is then discussed and it is shown that the 1/ O2 tails in the theory arise from kinematic surface scattering, and, furthermore, also have the same origin as the specular reflection for 8 > 8,. The effect of surface roughness is then described. The techniques are then used to analyse X-ray measurements of the photodisso- lution of silver into A S ~ ~ S , ~ .X-ray measurements are performed of the powder scattering from the thin silver layer, of the reflectivity and of the off-specular scattering at small angles. By combining all of these a detailed picture of the dissolution process is constructed. The process is then used to construct a diffraction grating and this is studied by X-ray reflectivity to study in detail the lithographic process. The extent of the biurring of the steps is determined and a model of the strucure constructed. 1. Introduction X-ray scattering techniques are proving to be very effective in studying the properties of surfaces and interfaces. This is because with many other probes, such as low-energy electrons, there is a very strong interaction with the surface and the results are difficult to interpret. In contrast, the interaction between X-rays and surfaces is weak and the results can frequently be interpreted in terms of the kinematical theory of X-ray diffrac- tion.Since, however, the scattering is weak, the experiments are relatively difficult and have been performed in detail only comparatively recently. Many of these experiments have been performed using synchrotron sources because of the high brightness, but nevertheless it is possible to study surfaces and interfaces with conventional X-ray sources and for the last 5 years there has been such a programme based in Edinburgh University. The first studies’ demonstrated the existence of scattering from the surface in the neighbourhood of the Bragg reflections, the crystal truncation rods, and these were rapidly followed by a study’ of the structure of the interfaces between the ferroelectric domain walls in KDP.The techniques were then used to study the structure of oxide layers on silicon,334 and of a number of semiconducting heterostructures.5-9 These results have shown that for many problems conventional X-ray techniques can be used for surface problems, and the undoubted fact that they are cheaper to set up close to other facilities, plus the difficulty of obtaining adequate synchrotron beam times means that conventional X-ray techniques will continue to be an important too! despite the advan- tages of the brightness and tunability of synchrotron sources. This paper reports on two aspects of X-ray scattering from surfaces.In the next section we show that the kinematical theory of the surface scattering around the Bragg reflections and for the reflectivity can be derived simply. The results of the corresponding dynamical theory are then outlined. Finally, the effects produced by surface roughness are discussed. 181182 X-Ray Scattering from Surfaces and Interfaces The second part of the paper describes a recent experiment in which X-ray techniques have been used to study the photodissolution of silver in chalcogenide glasses. 2. Theoretical Considerations 2.1. Kinematical Theory The kinematical theory of X-ray diffraction shows that the cross-section for an unpolarised beam scattered by an angle 28 is given by 1 + COS 28 -- ““(5) ( ) S(Q> dR where the second factor is the polarisation factor and S ( Q) = ((P ( Q ) P ( - Q>> (2) where Q is the wavector transfer in the experiment and p ( Q ) is the Fourier transform of the electron density in the crystal.We shall evaluate p ( Q ) for a particularly simple case to illustrate how the scattering arises from surfaces and interfaces. In the usual elementary derivation of the scattering, p ( Q ) is calculated by summing it over all the electrons in the crystal. We modify the conventional argument by considering that the surface of the crystal is perpendicular to the z axis and z = 0, so that the summation over the z direction is from 1 = 0 to 1 = CO. The scattering amplitude from each plane of a cubic monatonic crystal is then X p ( Q ) = b 1 exp (iQ& -p1) I = 0 (3) where p is the attenuation of the beam from one plane to the next, and is given for a symmetrical Bragg reflection by p = 2apu,,/sin II, (4) where po is the linear absorption cofficient, and II, is the angle between the surface and the incident beam.When the summation in eqn (2) is performed p ( Q ) = b / [ l -exp (iQA - d l and if Q2 is close to a Bragg reflection ( Q = G + q ) then S ( Q > = Ihl2/[(qZ4’+p21. ( 5 ) The scattering amplitude of each plane if there are N , atoms in the x direction and N,, in the y direction becomes, in the usual way, for large N , and N,. where S ( q , ) is the usual delta function. Eqn (5) shows that each Bragg reflection is associated with lines of scattering in reciprocal space directed along the z direction, and varying in intensity as N,N,./q: for large q-, showing that the intensity is indeed proportional to the area of the surface.The peak of the intensity is proportional to N , N , , / p 2 , and more usefully the integral of S ( Q) over a Bragg reflection is I = 4.rr’(f’(Q)I~N,N,/(pa3). (7) Since l/p is the penetration depth of the X-ray beam in the crystal, the integrated intensity is proportional to the illuminated volume of the crystal, as expected.R. A. Cowley and C. A. Lucas 183 These results also provide a kinematical theory of the reflectivity by applying these results to the case when G=O. The results then show that there will be a specular reflection, perpendicular to the surface and decreasing in intensity as qr'. For small angles and an incident wavevector k, q= = 2 k sin 4, and so this gives the result that the reflectivity is proportional to $-* instead of the result familiar from electromagnetism that the reflectivity at large angles is proportional to $-".This difference arises, however, from the different ways in which the reflectivity has been defined. In our case we have assumed that the surface area illuminated is N,N,,U* and fixed. In the usual derivation for electromagnetism the surface is much larger than the incident beam, when the surface area illuminated 'the footprint' is the beam area A divided by sin $. Consequently, for small $ this introduces an additional factor of $ - I . The other factor arises because our final result is expressed as a delta function of q\- and q,,, whereas the electromagnetic theory is the intensity observed in an angular interval.The integration over q.\- to give the intensity within a constant angular interval leads to another factor of $ - I . Con- sequently, when these two essentially geometric factors are included the above theory gives expressions not only for the scattering around the Bragg reflections but also for the specular reflectivity. These expressions are valid provided that the kinematical theory is appropriate, that is, when the intensity has fallen to 1% of the peak intensity in the Bragg reflection or reflectivity curve. Although these results have been derived for the simplest possible form of interface, they are readily extended to more complex interfaces and to layered structures.The advantage of working in this kinematical region is that the theory is transparent and readily derived, and the models can be refined on the basis of experimental results. 2.2. Dynamical Theory The kinematical theory developed in the previous section is dependent upon the assump- tion that the scattering is weak, and does not appreciably deplete the incident beam. The dynamical theory removes these restrictions by taking account of multiple scattering processes. In detail the theory is complex, and the results are dependent on the boundary conditions between the waves in free space and those in the crystal. It is not appropriate in a discussion meeting to give a full development of the theory, but merely to illustrate the points relevant to our considerations. The dynamical theory has been solved'' for a semi-infinite crystal with a flat surface at z = 0.The well known result is that the ratio of the reflected to incident intensity is given by where y is proportional to qz and inversely proportional tof( Q), while q., and q!, are zero. This result for large y gives (4y2)-', which has the familiar qL* tails with an intensity proportional to If( Q)12, the kinematical result. A detailed analysis shows indeed that for large qz, where the intensity is weak, the result is identical to that obtained in the previous section. This shows that the 9;' tails in the dynamic theory are not an intrinsically dynamical effect, but arise because the surface is explicitly included in the calculation. This analysis also enables us to understand the difference between the dynamical theory of Ewald and that of Darwin.The theory of Darwin, whose result is quoted above, treated the case of an attenuating slab of thickness t. He then first took the limit pt >>O, and then the limit as p + 0. In this analysis the X-rays interact with only one surface. In contrast Ewald considered p -+ 0 and then t -+ co and obtained the result for y z 1 I/&,= 1 - J ( y 2 - l)/lyl.184 X-Ray Scattering from Surfaces and Interfaces In the limit for large y this yields 1 / ( 2 y 2 ) , twice as large as the Darwin result, because the X-rays now interact with both surfaces, and since they are far apart the intensities add. The analysis can also be used to describe the reflectivity by considering the case of Bragg scattering by the (000) reflection.By considering that the angle of incidence is small, it can be shown that the angle when y = 1, is the critical angle and that the reflectivity curve is given by eqn (8) with the appropriate allowance for the angular factors as discussed in the previous section. 2.3. Surface Roughness Nearly Smooth Surface In the previous two sections we have assumed that the surface or interface was flat at z = 0. We now extend the argument to a surface whose position in the z direction is given by z = 8(x, y ) . The kinematical scattering is then S ( Q) =? (exp iq,( 8' - 8,)) exp (iqll - r ) d r ii.. (9) where q1 = (q;, q,.) and r = (xl - x2, y , - y 2 ) . The problem of calculating the intensity then depends on the correlation function in the position of the height of the interface at two different positions 8, and 8'. One of the simplest interesting nearly smooth surfaces is the homogeneous Gaussian rough surface,'." described by a mean statistical height S = (@)"?, and a Gaussian correlation length, 1 which describes the extent of the fluctuations in the (x, y ) plane.The intensity of this model is then given by where and Q'I bl' Q ) =- D exp [-l2q:,D/(4S'qf>] with D = 1 -exp ( - S ' q : ) . The first term I,( Q) is the 'Bragg-like' surface term, perpendicular to the average surface but now modified by the Debye-Waller factor for the roughness. The form of the term is independent of the in-plane correlation, 1. The second term is the diffuse scattering associated with the roughness.When Sq, << 1 , the measuring scale, q l ' , is larger than the roughness and the width of the diffuse scattering in q I 1 is independent of q, A%' = 211 while if Sq, >> 1, then and the width increases with 4,. Other correlation functions lead in detail to different expressions, but a nearly smooth surface, which on average has a flat surface, always gives rise to a surface 'Bragg-like" component to the scattering.R. A. Cowley and C. A. Lucas .- Y 140- B c) m f - - cd 70- 185 A c C Y .- II: c) i I I illumination time/s Fig. 1. The peak intensity obtained from a silver (1 11) powder peak as a function of the illumination time. Rough Surfaces Rough surfaces are ones in which the average position of the surface gets further and further away as r gets larger.Such surfaces occur above the surface roughening transition. In this case there is no Bragg-like component but only diffuse scattering and in practice this is probably difficult to study in detail. Dynamical Sea ttering Eflects In the preceding part of this section we discussed the scattering from rough surfaces using only kinematical theory. The analysis of the scattering from rough surfaces using the full dynamical theory is much more complex and the results more difficult to interpret. Nevertheless the r e s u l t ~ ~ * * ~ ~ are qualitatively understood. Basically, whenever either the incident or scattered beam is incident or emitted at close to the critical angle, the effect of the surface scattering is enhanced and the full dynamical theory must be used.This makes the interpretation of the experimental results more difficult than when the kinematical theory is appropriate. 3. Experimental Study of the Photodissolution of Silver in Chalcogenide Glasses 3.1. The Photodissolution process When silver is deposited on chalcogenide glasses and illuminated, the silver diffuses into the g1a~s.I~ This diffusion changes the chemical properties, and in particular the rate of etching, so that these systems may have potential in lithography. They have therefore been ~ t u d i e d ' ~ by X-ray techniques to determine the way in which the disso- lution process occurs. Most of the measurements were made on a sample consisting of 3200 8, of A S ~ ~ S , ~ , on a glass slide onto which 200A of silver was evaporated. The first experiment was to measure the powder using a beam incident at 2" to the layer.Before illumination well defined silver powder peaks were observed which on illumination with a 200 W Hg lamp steadily decreased in intensity as shown in fig. 1. At large times no sharp powder peaks were observable showing that the reaction product has an amorphous structure.186 X - Ray Scattering from Surfaces and Interfaces 0 . 0 0.5 1 . o 1.5 incident angle/" Fig. 2. The reflectivity curve of the sample before illumination plotted against the incidence angle I). The calculation is displaced for clarity. ( x ) Data; (-) simulation (x0.5). 0.00 0.75 1.50 incident angle/" ' I I I I I I I I 1 0.00 0.75 1.50 incident angle/ " 0.00 0 75 1.50 incident angle/" incident angle/" Fig.3. The reflectivity curve as for fig. 2 but after illumination for ( a ) 100, ( 6 ) 160, ( c ) 320 and ( d ) 600 s.R. A. Cowlqv and C. A. Lucas 187 The X-ray reflectivity was measured as a function of the illumination time and the results are shown in fig. 2 and 3. The results before illumination (fig. 2) show oscillations and the good fit can be accounted for by a layer of 23 A of oxide, 184 8, of silver and 3200 8, of As,,)S,,. After 100s of illumination (fig. 3) the oscillations in the reflectivity are weaker but occur at very similar angles. This suggests that the silver layer thickness is much the same as for zero illumination but that the average Ag electron density has decreased. There is no sign of a well defined product layer. With increasing illumination times, the fringes moved to smaller angles and then disappeared (fig.3). At 320s the spacing of the fringes suggests a layer about 3-4 times thicker than the original silver layer, which is presumably the reaction product layer, which then diffused further into the chalcogenide on more illumination. In addition to the reflectivity measurements, studies were also made of the scattering at a fixed angle of scattering, and by varying the angle of the sample, as shown in fig. 4. In all of the measurements there is considerable scattering in addition to the specular reflectivity peak. This shows that the surfaces and interfaces are not flat. The peaks for Ic, = 0.4 and 0.6" at 80 s arise from a dynamical enhancement of the diffuse scattering as discussed in the previous section.These peaks steadily move out to 0.25 and 0.75" as the critical angle decreases because the electron density of the surface decreases when the silver is exhausted. There is, however, clearly additional scattering centred around the specular reflection which begins to increase in intensity for t = 100 s and appears to saturate for times longer than 300 s. This scattering can be interpreted at least qualita- tively in terms of the theory given in the previ2us section and suggests that the roughness occurs on a length scale of the order of 10'A. On the basis of these experimental results, we suggest the following model for the photodissolution process. Initially the reaction occurs at grain boundaries or voids keeping the average thickness of the silver layer nearly the same but reducing its average electron density, but giving a very inhomogeneous reaction product layer.As the reaction proceeds from 100 to 300 s, silver islands are formed, while the product layer develops into a reasonably homogeneous layer, with, even at the end, silver or silver-oxide islands causing the strong diffuse scattering. Upon further illumination the reaction product layer moves into the chalcogenide region destroying any sharp interface between these layers. Experiments were also performed with other thicknesses of materials and the results were essentially the same although the times lengthened for the thicker layers. 3.2. Scattering from a Lithographic Structure Potentially the photodissolution process is ideal for lithography, and hence X-ray scattering has been used to study a structure produced by the photodissolution process.A film of 700 A silver with 2200 A of A S ~ ~ S , ~ ) was exposed to light through a mask which illuminated strips of the surface 2 p m wide and separated from one another 4 pm. If the silver penetrates the chalcogenide only in the regions where the film is illuminated, etching away the pure chalcogenide then leaves a nominal structure of rectangular blocks of product material 2 p m wide and 2200 A thick. The structure was studied by X-ray scattering techniques and the result of varying q , (perpendicular to the lines of the grating) is shown in fig. 5 . The peaks show that a regular pattern was produced and the calculation shows the result expected using the kinematical theory and the nominal structure discussed above.Clearly the lithographic process is successful. In more detail, measurements were made of the intensity of the central 1st and 2nd diffraction harmonics of fig. 5 as a function of qz as shown in fig. 6. Surprisingly the 9- dependence is quite different for each of the different peaks. The oscillations observed188 X-Ray Scattering from Surfaces and InterfacesR. A. Cowley and C. A. Lucas 189 t. lOOOOj ' ' ' ' I ' ' ' ' ' 0.775 0.925 1.075 1.22s incident angle/" Fig. 5. The intensity observed in a I) or q.,. scan from the diffraction grating for a scattering angle of 2.0". The lower part shows the calculation for the nominal structure. 1 0.05 0.08 0.11 0.14 0.17 0.20 0.23 Q,/A-' 0.05 0.08 0.11 0.11, 0.17 0.20 0.23 Q , / k ' Fig.6. The qz dependence of the intensities of the ( a ) zeroth ( b ) , first- and ( c ) second-order peaks of fig. 5. The upper part shows the observed results and the lower the calculated behaviour using the model described in the text.190 X-Ray Scattering from Surfaces and Interfaces in the zeroth layer correspond to those associated with the 700 A silver layer, whereas the longer period associated with the first-order satellites corresponds to a period of ca. 150 A, which is absent in the nominal structure. In fact the nominal structure gives the same qz dependence for all the satellites. Because of these deficiencies a new model was developed in which the nominal structure was modified in two ways. It was assumed first that the raised blocks were not vertical but had a base width of 2.4 p m and a top width of 1.8 pm, and secondly that there was silver on the top of the blocks with a thickness of 120 A and width 0.5 pm.The existence of silver on the blocks was first suggested by electron microscopy. The result of calculating the qz dependence of the peaks is shown in fig. 6 for this model and the results clearly show many of the observed features. We conclude that X-ray scattering is able to provide information about the effectiveness of lithography. 4. Conclusions We have discussed the theory of surface scattering and have shown that many of the results can be obtained using the kinematical theory of X-ray diffraction. This result is important because it is relatively easy to interpret kinematical scattering data.Close to Bragg reflections and to the critical angle for total reflection, the kinematical theory is inadequate and the full dynamical scattering theory must be used. We have then illustrated the power of X-ray scattering for determining the properties of thin layers by studying the photodissolution process. This involved a combination of powder diffraction from thin layers, specular reflection and diffuse scattering measure- ments, and the combination of these has enabled us to build up quite detailed models of the processes. We are grateful to A. P. Firth for growing the silver/chalcogenide films and for numerous discussions on their properties, and to H. Vass for technical assistance. The work was supported financially by the S.E.R.C. and by GEC to whom C.A.L. is grateful for a CASE studentship. References 1 S. R. Andrews and R. A. Cowley, J. Phys. C, 1985, 18, 6427. 2 S. R. Andrews and R. A. Cowley, J. Phys. C, 1986, 19, 615. 3 R. A. Cowley and T. W. Ryan, J. Phys. 0, 1987, 20, 61. 4 R. A. Cowley and C . A. Lucas, J. Phvs. (Paris), 1989, in press. 5 T. W. Ryan, P. D. Hatton, S. Bates, M. Watt, C . Sotomayor-Torres, P. A. Claxton and J . S. Roberts, 6 C. A. Lucas, P. D. Hatton, T. W. Ryan, S. Miles and B. K. Tanner, J. Appl. Phys., 1988, 36, 1936. 7 C . A. Lucas, D. F. McMorrow and S . Bates, in Hereroepitaxial Approaches in Semiconductors: Lattice 8 T. W. Ryan, C . A. Lucas, P. D. Hatton and S. Bates, J . Phys. (Paris) Colloq., 1987, C5, 109. 9 S. Bates, P. D. Hatton, C . A. Lucas, T. W. Ryan, S. J. Miles and B. K. Tanner, Advances in X-rav Semicond. Sci. Tech., 1987, 2, 241. Mismatch and its Consequences ( Electrochem. SOC., 1989). Anal-vsis, 1987, 31, 155. 10 W. H. Zachariasen, Theor?. of X-ray diflraction in Crystals (Wiley, New York, 1945). I 1 M. V. Berry, Philos. Trans. A , 1973, ,4213, 611. 12 A. V. Andreev, Sou. Phys. Upsk, 1985, 28, 70. 13 S. K. Sinha, E. B. Sirota, S. Garoff and H. B. Stanley, Phj1.s. Rev. B, 1988, 38, 2297. I4 K. Tanaka, in Fundamental Ph?uics uf Amorphous Semiconductors, ed. F. Yonezawa (Springer Verlag, 15 C . A. Lucas, Thesis (Edinburgh University, 1989), t o be published. Berlin, 1981). Paper 9/05493F; Received 28th December, 1989

ISSN:0301-7249    

DOI:10.1039/DC9908900181

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Furuday Discuss. Chem. SOC., 1990, 89, 191-200 X-Ray Scattering from Semiconductor Interfaces J. E. Macdonald Physics Department, University of Wales College of Cardifl P.O. Box 913, CardifCFl 3TH, UK X-ray diffraction has been used to determine the structure of surfaces over the past decade or so. The concepts involved in surface structure determina- tion may be extended to the study of buried interfaces. A formalism for the determination of the structure of epitaxial interfaces is outlined, together with its application to the NiSiJSi(111) interface. The use of a grazing incidence diffraction geometry to investigate strain relaxation in lattice- mismatched epilayers on the monolayer scale is discussed. The technique has been employed to monitor strain relaxation in thin Ge overlayers on Si(OO1) substrates with greater sensitivity than is attainable using other techniques.The results indicate that strain relaxation in this system relates primarily to islanding on the surface rather than the formation of misfit dislocations. For several decades, X-ray diffraction has been a powerful tool for determining the structure of bulk materials. The advent of intense synchrotron sources has led to the application of X-ray diffraction (XRD) to determine the detailed atomic structure of reconstructed surfaces. The comparatively low count rates obtained with X-rays are compensated by the applicability of the kinematic approximation, which assumes single- scattering processes in contrast to electron diffraction techniques. The surface scientist indeed possesses a range of experimental techniques giving structural information, both as direct images and in a more indirect manner, such as diffraction. These include electron diffraction and microscopy, atomic diffraction and inelastic scattering, X-ray diffraction, ion scattering, scanning tunnelling microscopy and surface-extended X-ray absorption fine structure spectroscopy (SEXAFS). Techniques based on diffraction are primarily suited to the study of the ordered regions of the surface, since disordered regions give rise to much weaker diffuse scattering between Bragg peaks.Tunnelling microscopy provides a localised, direct image of ordered and disordered regions thus providing a very powerful tool. However, the precision of the resulting atomic coordin- ates is low and the technique is insensitive to sub-surface relaxations.Ion scattering primarily probes ordered regions of the surface, but is more sensitive than diffraction to the presence of disorder, and gives information in direct space without resort to the use of reciprocal space. SEXAFS gives the coordination number and bond lengths of neighbouring atoms for specific atomic species. Electron spectroscopy can also be used to indicate the bonding between atoms and thus gives more indirect information on their structure. Thus a range of complementary techniques may be brought to bear on a particular problem. Despite the intense study of the structure of surfaces over recent years, there remains a paucity of information on the structural properties of interfaces.This is largely due to the fact that buried interfaces are inaccessible to many of the above surface-science techniques which have limited penetration. XRD would appear to be a suitable candidate for such studies owing to the variable penetration of the incident beam with angle of incidence and its sensitivity to scattering from a single monolayer. Most of the principles which have formed the basis of the use of XRD for the study of reconstructed surfaces 191192 X - Ray Scattering from Semiconductor interfaces may be applied directly to the study of buried interfaces, particularly where the overlayer is amorphous. Here we recap briefly the concepts involved in XRD studies of surfaces and of interfaces under amorphous overlayers. We then extend these ideas to the study of crystalline epitaxial interfaces and to the investigation of strain in lattice-mismatched systems, illustrating their use with suitable examples.Structure of Surface and Crystalline-Amorphous Interfaces Following the initial work of Marra and Eisenberger on the Ge(001) 2 x 1 surface,' XRD has been used to determine the detailed atomic structure of many reconstructed surfaces, particularly for semiconducting materiak2 The fractional-order peaks, which arise from the surface periodicity being a multiple of that for the underlying crystal, are uncontaminated by bulk scattering and thus may be used to determine the structure of the reconstructed unit cell. By measuring the variation of the fractional order peak intensity with wavevector normal to the surface the relaxation induced in deeper atoms by the surface reconstruction may also be probed.' In systems where the lateral registry of the reconstructed structure onto the bulk structure is unclear, the coherent interference between scattering from the surface and the bulk may be exploited.For instance, the structure of the GaSb( 11 1) 2 x 2 reconstruction was determined from the fractional-order peaks, as described above. Since the bulk structure is known the structure factors, and hence amplitudes, of the scattering from bulk and surface could be calculated. By considering the scattering in regions of reciprocal space where both components con- tribute, the resulting interference pattern could be compared with the calculated scatter- ing for different models of the r e g i ~ t r y .~ These ideas are extended to the investigation of epitaxial interfaces below. Similar measurements have been used to investigate the Si( 11 1)/a-Si interface. The stacking fault and dimers of the 7 x 7 reconstruction of the clean Si surface5 were found to be preserved under the amorphous layer.' Similarly, measurements of crystal truncation rods, used for determining surface roughness, may also be applied to the roughness of buried interfaces.' Structure of Epitaxial Interfaces A detailed knowledge of the atomic structure of interfaces is crucial to the understanding of interfacial electronic states. In the case of a fully coherent, epitaxial, crystalline overlayer deposited on a substrate, the diffracted amplitudes for both the substrate and the film may be calculated separately provided their unit cell structures are known.The observed diffracted-intensity distribution will then be the square of the magnitude of the total scattered amplitude. This total amplitude is given by summing coherently the diffracted amplitudes for the substrate and film, taking into account the phase shift due to the displacement of the origin of the unit cell of the epilayer relative to that of the substrate. This displacement is governed by the bonding at the interface. The same principle has been used to deduce the registry of a reconstructed unit cell onto the underlying bulk crystal, as noted above. A simple optical analogy of this situation is that of the diffraction pattern for a pair of overlapping diffraction gratings of known spacing.If one grating is moved with respect to the other, the diffraction pattern changes. Thus the observed diffraction pattern may be used to determine the relative displacements of the gratings. Consider a substrate having direct unit-cell parameters a l s , a2s and a3s, with corre- sponding reciprocal lattice vectors 6, , 6, and 6?, and an epitaxial film having unit-cell parameters a , , , a,, and a3,. For the case of a coherent epitaxial film we can take a , , = a , , = a , and = a,, = a,. We can also take a? = a?, and all to be normal to the surface, with = ~ a , . Let the displacement vector between the unit cells of the substrate and film at the interface be A = Ala, +A,a,+A,a, (fig. 1). The finite penetration of theJ.E. Macdonald 193 Fig. 1. A schematic diagram of the unit cells of the substrate and film. The displacement vector, A, describing the bond distance and lateral registry at a coherent epitaxial interface is shown. X-ray beam may be represented by a l / e penetration depth, A. Then the scattered amplitude for the substrate is A, = F, C exp (iQ - n ~ ) C exp (iQ * n2a2) 1 exp (iQ - n3a3) exp ( - n 3 a 3 / A ) " I " 2 "3 ( 1 ) 1 1 - exp (- iQl - a3) exp (- a3/A)' = (27-r)'N1 N2FsS( QII - H ) Here the scattering vector Q = QII + QI where QiI = Q , b , + Q2b2 and Q1 = Q3b3 are the components parallel and perpendicular to the interface respectively and H is an in-plane reciprocal lattice vector. The summation over n3 extends in the negative direction since we sum over unit cells extending into the bulk whereas u3 is directed towards the surface.N1 N2 is the number of illuminated unit cells on the surface. The structure factor, F,, is given by the usual summation over atoms j in the unit cell having position rJ and Debye- Waller factor, WJ F, =Cf; ~ X P (iQ * r,) exp(- W,>- (2) J Eqn (1) describes the scattered amplitude for a sharply terminated surface of a crystal. The scattering is sharp in Qil around a reciprocal lattice point but falls off approximately as QI' normal to the surface from the Bragg peak. This amplitude profile is usually referred to as a crystal truncation rod.8*9 We can write the corresponding equation for the film as where the film is of thickness Nf unit cells. The scattered intensity is then given by I = /A, + exp( iQ*A)Al-12.(4) Thus, since A, and A,- may be calculated for a given structure, the displacement vector, A, may be determined. In principle, additional contributions from modifications to the structure at the interface and at the uppermost reconstructed surface may be included. These would be A, = F, and A, = F, for the interface and reconstructed surface, respec- tively, the structure factors given by corresponding expressions to (2), together with appropriate displacement vectors A, and A,. Eqn (4) is then replaced by ( 5 ) I = IA,+ exp( iQ - A)A,.+ exp( iQ - A,)A, + exp( iQ - Ar)Arl'.194 X-Ray Scattering from Semiconductor interfaces 1- ' 0.8 0.9 1.0 1.1 1.2 1.3 Q3 (r.1.u.) Fig. 2. ( a ) The calculated intensity for differing values of the interfacial separation, d, for NiS&/Si(lll).d/a,= 1.0(- - - ) 1.05 (- -), 1.1(-). ( b ) The integrated intensity ofthe (O,O, Q3) rod, corresponding to the ( 1 1 1 ) bulk cubic direction. The result of the four-parameter fit, involving a scale factor and the parameters Nr, d and r,~, is shown as a solid line. However, such an expression contains too many parameters to be of general use and simplified expressions containing two or three of these terms would be used in practice. In all such expressions care must be taken in the choice of consistent unit-cell parameters. The above formalism is a generalised form of that presented by Robinson et al. in a study of the interface structure of Nisi,/%( 1 1 l).'" This is an ideal test system in that the two materials are well lattice-matched, enabling the growth of high-quality layers, and the interface structure has also been well characterised using X-ray standing-wave fluorescence yield measurements,' ' ion scattering" and high-resolution electron micro- scopy." Samples were prepared by evaporating 20A of Ni onto the cold substrate, followed by an anneal at 550 "C.The film was capped with amorphous Si, allowing the experiment to be performed in air using a standard 4-circle diffractometer at Stanford Synchrotron Radiation Laboratory. Measurements of the (0, 0, Q3) truncation rod, corresponding to the ( 1 1 1 ) direction in the usual cubic notation, were used to determine the height of the Ni atomic planes relative to the substrate Si atoms, d, and the ratio of the epilayer lattice parameter to that of the substrate, 77.Scans were performed by varying QI. across the rod to obtain the integrated intensity at each point along the rod, thus accounting for thermal diffuse contributions to the background. The resulting data are shown in fig. 2 together with model calculations for various values of the interfacialJ. E. Macdonald 195 separation. The data were fitted with a four-parameter model which gave values of d = (1.10 f 0.02)a, and 77 = 0.996 f 0.003, where a , is the spacing between (1 11) planes in Si. These values are in reasonable, though not exact, agreement with those obtained from the other techniques. The ideal interface, with bulk bonds throughout and no relaxation, has d/a, = 9/8 and hence the resulting value corresponds to a contraction at the interface.The above study demonstrated the usefulness of this interference technique for determining interface structures. Similar measurements using several truncation rods, having different values of QII, would enable the determination of the lateral registry of the film onto the substrate. This would be useful, for instance, to resolve the current disagreement concerning the structure of the CaF,/Si( 11 1) i n t e r f a ~ e . ’ ~ ” ~ By increasing the measured range in QI the layer structure may also be characterised. However, the sensitivity of the technique does entail the need for high-structural-quality interfaces and epilayers. Care must be taken in dealing with surface and interface morphology and it may well be that the number of systems studied using this interference technique will be limited by the structural quality of samples.Relaxation of Strained Interfaces There has been extensive interest in recent years in the growth of heavily strained layers, involving materials having a large lattice mismatch, in order to exploit the in-built strain to modify the electronic or optical properties of the material.16 As the thickness of the overlayer is increased the strain energy increases until it is relieved by the formation of misfit dislocations. Most studies of strain relief have concentrated on thick films having comparatively low lattice-mismatch values. For monolayer-scale films, the surface energy becomes relatively more important and the role of islanding in strain relief must also be considered.Here an XRD study of thin Ge films on Si(OO1) substrates is described to illustrate the use of a grazing incidence geometry for investigation of strain relief near an interface.”.” For a strained, unrelaxed layer, the lattice parameter of the epilayer and the substrate are identical in the plane of the interface thus causing a tetragonal distortion of the epilayer unit cell. As the layer relaxes, its in-plane lattice parameter increases towards its bulk value and the tetragonal distortion is reduced thus changing a3f, as illustrated in fig. 3. Conventional XRD studies of strained layers involve scans along QL with QII being small or zero. Consequently strain relaxation is detected as a shift in the epilayer peak as the tetragonal distortion is relieved.In the grazing-incidence geometry both incident and diffracted beams are close to the plane of the interface and thus QI == 0. The strain distribution is probed by scanning radially outwards in reciprocal space (the so-called S/2S scan) through the region around a substrate Bragg peak. The peak from an unrelaxed epilayer coincides with that of the substrate as a result of their identical in-plane lattice spacings. Any relaxed material having an in-plane spacing different from the substrate value gives rise to a separate peak and thus relaxation in small localised regions of the epilayer may be detected, even when the rest of the layer is fully strained. The grazing-incidence geometry also benefits from a much narrower intrinsic peak width for the epilayer owing to the much larger extent of the film parallel to rather than normal to the interface.The scattering from the substrate crystal truncation rod, which can obscure the epilayer peak in the conventional geometry, may also be resolved entirely and consequently does not obscure the epilayer scattering. The limited beam penetration of the grazing-incidence geometry also suppresses the background owing to thermal diffuse scattering from the bulk. The experiments were performed at the Synchrotron Radiation Source in Daresbury ( U K ) using unfocused radiation from the superconducting Wiggler beamline. The equipment consists of a large 5-circle diff ractometer, coupled to an ultrahigh-vacuum196 X-Ray Scattering from Semiconductor interfaces 0 0 0 0 0 0 0 0 0 0 0 0 ( a ) 0 0 0 0 0 0 e o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( b ) 0 0 0 0 0 0 0 0 8 2 xo x o x x x x x x x x 0 0 0 0 x x x x 8 9 9 9 8 P .o x o %-+ 8 --@- @ QL rn - x o a// relaxed layer Q// strained layer Fig. 3. A schematic side-view of ( a ) direct space ( b ) reciprocal space for a fully strained and partially relaxed layer. In ( a ) the open and filled circles denote substrate and. epilayer atoms, respectively. In ( b ) the open circles and crosses denote substrate reciprocal lattice points and the peak position for the substrate and a fully relaxed epilayer, respectively. A radia! scan at grazing incidence is denoted as an arrow.chamber having in situ MBE growth facilities as well as standard surface-science analytical techniques.'' A monochromatic beam of wavelength 0.8 8, was incident at an angle of 0.09" onto the physical surface, just below the critical angle of 0.12", corresponding to a penetration depth of 100 8, in a flat Si crystal. The detector subtended an angle at the sample of 0.10" normal to the surface at a mean take-off angle of 0.13". The real unit-cell vectors were related to the conventional bulk cubic real cell vectors by a, = (1, 1, O)cubic, a2 = (1, -1, O)cubic and aj = (0, 0, 1/4)cubic. The Si(OO1) substrates were cleaned by light sputtering with 800eV'r Ar' ions for 60s followed by an anneal for 3 min at 1060 "C. Deposition of Ge was performed using a Knudsen effusion cell which gave a deposition rate of 1 monolayer (ML) per 18 min f lo%, calibrated by Rutherford backscattering.For Ge/Si(001), 1 ML corresponds to a thickness of 1.41 A. The substrate was held at 550°C during deposition and immediately cooled to room temperature before measurement. This procedure was repeated after deposition of each monolayer. Radial scans (along Q , ) through the (2,0,0) Bragg peak were performed at grazing incidence at each coverage in order to give the distribution of lattice spacings parallel to the interface (fig. 4). The resolution along Q , was 0.02 reciprocal lattice units (r.1.u.) as determined by the detector aperture slits and the illuminated surface area. The peak profile remains unchanged for a coverage 8 s 3 ML owing to the coherent epitaxial nature of the Ge layer.The wings of the peak are not substantially broadened indicating the high crystalline quality of the overlayer. At 4 ML, a weak shoulder appears on the i.1 e V = 1.602 18x 10 "'J.J. E. Macdonald 197 1.85 1.90 1.95 2-00 2.05 2.10 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) Q, (r.1.u.) 5000 .- Y 4 0 0 0 C f 4 3000 a v .- 3 2000 v) C 0 * c 1000 .C 0 3000 40001 ( g ) 0 0 0 i 0 0 1 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) 0 0 1.85 1.90 1.95 2.00 2.05 2.10 Q, (r.1.u.) Fig. 4. Radial scans as a function of coverage for sample I. The intensity is plotted on an arbitrary scale. On this scale the Bragg peak intensity is CQ. lo5. For 0 = 11 ML, circles denote data for angles of incidence and exit p = 0.09", p' = 0.13", respectively, and triangles represent the same scan with p = 0.07", p' = 0.05", leading to a reduced effective penetration depth.A (a) Clean Si, ( b ) 1.6 ML Ge, ( c ) 3.2 ML Ge, ( d ) 3.9 MLGe. (e) 4.7 ML Ge, (f) 5.5 ML Ge, (8) 7.1 ML Ge, ( h ) 11.0 ML Ge.198 X-Ray Scattering from Semiconductor interfaces Bragg peak owing to the onset of strain relaxation. Upon further deposition the shoulder develops as the layer relaxes further. At a coverage of 11 ML the peak from the overlayer occurs at Q, = 1.925 r.1.u. which is close to that expected for bulk Ge (Q, = 1.920 r.1.u.). This gradual shift shows that the strain is relaxed gradually after exceeding the critical thickness, which is 3-4 ML in this case. Strain relief is incomplete even after deposition of 11 ML of Ge.A further striking feature of the radial scan for sample I is the ‘plateau’ of scattering between the bulk values of Ge and Si. This indicates that the strain is not constant in the epilayer, but rather that there is a distribution of intermediate values of strain. The question arises whether the strain is distributed laterally across the layer or as a function of height above the interface. Consequently, the scan was repeated with the angle of both incident and scattered beams being below the critical angle. The effective penetration depth was thus reduced from 100 to 40 8, and led to the scan profile denoted by triangles in fig. 4. Here the scattering from the plateau in the region Q1 = 1.95-2.00 r.1.u. suffers more severe attenuation than the peak at Q1 = 1.925 r.1.u.This indicates that the atomic layers closest to the interface are still strained while the uppermost layers are almost fully relaxed. Note that the values of the penetration depth quoted above are difficult to interpret in view of the islanding that occurs at this coverage, as discussed later. A significant fraction of the beam may be totally externally reflected from the tops of islands thus shadowing parts of the surface. Several studies have shown that growth and annealing conditions affect strain relaxation in thick layers and that relaxation is a kinetically driven Con- sequently, the above measurements were repeated on a similar sample which was maintained at 520 “C during deposition and measurements. The onset of strain relaxation was found to occur at 3 ML and subsequent relaxation was more rapid.Samples prepared by MBE at a much faster growth rate of 0.5 8, s-I onto substrates at 400* 50 “C and capped with amorphous silicon (supplied by C. Gibbings, British Telecom Research Laboratories) again showed the onset of strain relief at 4 ML. In general, the coverage at which strain relief sets in has been found consistently to be 3 or 4 ML but the details of the strain distribution as a function of coverage are dependent on the growth procedure. We thus conclude that the critical thickness for the onset of strain relief in Ge/Si(001) is 3-4 ML. In contrast, the values of critical thickness for strain relief reported using reflection high-ener y electron diffraction (RH EED).?’, low-energy electron diffractionz3 and ion scattering2’is 6 ML.As seen from fig. 4 the amount of relaxed Ge increases rapidly at ca. 5-6 ML indicating that the epilayer is only partially relaxed for 6 =: 3-5 ML. Raman scattering and ion scattering are less sensitive to partial relaxation of the epilayer and thus yield the higher value for the critical thickness. Thus the high resolution and dynamic range of XRD yields considerable sensitivity to strain relaxation in thin epilayers. Electron microscopy studies of Ge layers, using similar growth conditions, show that islands form on the Ge surface at a coverage of 3-4 ML, and that these islands cluster with annealing time25 in good qualitative correspondence with the above results for strain relaxation. Ge layers deposited at room temperature form islands upon heating above 250°C for coverages greater than 3 ML.’6 Thus the critical thickness at which islands form and the critical thickness for the onset of strain relaxation coincide.There are no current data for the critical thickness for dislocation formation or migration, but calculations using equilibrium model^''^^^) and using energy minimisation for empirical potentials”T3’ yield values in the range 7-15 ML. These comparisons indicate that the initial relaxation of strain is closely related to islanding of the surface rather than to the formation of dislocations, as is the case for thicker films. This would appear to be a reasonable conclusion in view of the larger relative effect of the surface in monolayer- thick films than in thicker films which are not so heavily strained.The grazing-incidence geometry has also been used for a similar study of the initial stages of growth of GaAs on Si(O01).33 In contrast to Ge/Si(001), a mismatch of 1.55%J. E. Macdonald 199 was observed for the lowest measured coverage of 1.5 ML (1 ML=2.8 8, for GaAs/ Si( 001)) and the amount of relaxed material increases approximately linearly with the deposited amount, indicating that the interface is not fully coherent. The average lattice parameter for the overlayer increased gradually with layer thickness up to 20 ML. By varying the angle of incidence, a lattice parameter gradient could be detected, corresponding to a mismatch of 3.8% for the surface region and an average value for the complete overlayer of 3.3570, for a layer thickness of 15 ML. Thus the growth of GaAs on Si(OO1) is confirmed to be of a Volmer-Weber growth mode, in which the epilayer forms islands immediately on deposition.This islanding process is again accompanied by strain relaxation. Conclusions The concepts involved in the use of X-ray diffraction to the determination of reconstruc- ted surface structures may also be applied to the study of interfaces. In contrast with reconstructed surfaces, there is no region in reciprocal space where scattering from the interface is totally uncontaminated by bulk scattering. However, the coherent interfer- ence between scattering from the epilayer and the bulk may be exploited to probe the interfacial structure. Rod scans of the scattered intensity between Bragg peaks normal to the surface may, in principle, be used to study the structure of the interface and epilayer together with the strain normal to the interface.This technique has been applied to the Nisi,/%( f l l ) interface to determine the interfacial separation and the epilayer lattice parameter normal to the interface. Further work is required to determine the practical limitations, such as sample quality. The grazing incidence geometry, for which the momentum transfer is almost entirely in the plane of the interface, is most suited to studies of strain parallel to the interface. It benefits from several advantages over the conventional geometry for strain relaxation studies of ultra-thin films. The lateral strain distribution is measured directly and the measurements are very sensitive to small amounts of relaxed material.Depth information about the strain distribution may be obtained by varying the angle of incidence around the critical angle for total reflection. The results for Ge/Si(001) show that strain relaxation sets in at a coverage of 3-4 ML and proceeds gradually with increasing coverage. At a coverage of 11 ML the strain distribution displays two components, corresponding to almost fully relaxed Ge and a region having intermediate strain values. The results indicate that strain relaxation accompanies the onset of islanding on the surface. C. Norris, J. F. van der Veen and several workers from Leicester University and the FOM Institute, Amsterdam are thanked for a pleasant collaboration. Helpful discussions with I .K. Robinson and R. Feidenhans’l are also gratefully acknowledged. This work is supported by the S.E.R.C. and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References 1 P. Eisenberger and W. C. Marra, Phys. Rev. Lett., 1981, 46, 1081. 2 R. Feidenhans’l, S u r - Sci. Rep. 1989, 10, 105. 3 J. S. Pedersen, R. Feidenhans’l, M. Nielsen, K. Kjaer, F. Grey and R. L. Johnson, Surj Sci., 1987, 189/190, 1047. 4 R. Feidenhans’l, M. Nielsen, F. Grey, R. L. Johnson and I. K. Robinson, Surj Sci., 1987, 186, 498. 5 K. Takayanagi, Y. Tanishiro, S. Takahashi and M. Takahashi, S u r - Sci., 1985, 164, 367. 6 1. K. Robinson, W. K. Waskiewicz, R. T. Tung and J. Bohr, Phys. Rev. Lett. 1986, 57, 2714. 7 R. A. Cowley and C. Lucas, Coll. Phys.1989, 50, C7-145. 8 I . K. Robinson, Phys. Rev. €3, 1986, 33, 3830. 9 S. R. Andrews and R. A. Cowley, 3. Phys. C 1985, 18, 6247.200 X-Ray Scattering from Semiconductor interfaces 10 I. K. Robinson, R. T. Tung and R. Feidenhans’l, Phys. Rev. B, 1988, 38, 3632. 1 1 E. Vlieg, A. E. M. J. Fischer, J. F. van der Veen and G. Materlik, Sur- Sci., 1986, 178, 36. 12 E. J. van Loenen, J. W. M. Frenken, J. F. van der Veen and S. Valeri, Phys. Rev. Lett. 1985, 54, 827. 13 R. T. Tung, J. M. Gibson and J. M. Poate, Phys. Rev. Lett., 1983, 50, 429. 14 J. L. Batstone, J. M. Philips and E. C. Hunke, Phys. Rev. Lett. 1988, 60, 1394. 15 R. M. Tromp and M. C. Reuter, Phys. Reu. Lett. 1988, 61, 1756. 16 E. P. O’Reilly, Semicond. Sci. Technof., 1989, 4, 121. 17 A. A. Williams, J. E.Macdonald, R. G. van Silfhout, J. F. van der Veen, A. D. Johnson and C. Norris, J. Phys. Condens. Matt., 1989, 1, SB273. 18 J. E. Macdonald, A. A. Williams, R. van Silfhout, J. F. van der Veen, M. S. Finney, A. D. Johnson and C. Norris, in Proceedings of NATO ARW, Kinetics of Ordering at Surfaces, (Plenum Press, New York, 1990) in press. 19 E. Vlieg, A. van’t Ent, A. P. de Jong, H. Neerings and J. F. van der Veen, Nucf. Instrum. Meths. 1987, A262, 522. 20 R. H. Miles, T. C. Gill, P. P. Chow, D. C. Johnson, R. J. Hauenstein, C. W. Nieh and M. D. Strathman, Appl. Phys. Lett., 1988, 52, 916. 21 D. J. Lockwood, J-M. Baribeau and P. Y. Timbrell, J. Appf. Phys., 1989, 65, 3049. 22 T. Sakamoto, K. Sakamoto, K. Miki, H. Okumura, S. Yoshida and H. Tokumoto, in Proceedings of NATO ARW, Kinetics of Ordering at Surfaces, (Plenum Press, New York, 1990), in press. 23 K. Eberl, E. Freiss, W. Wegscheider, U. Menczicar and G. Abstreiter, Thin Solid Films, 1989, 183, 95. 24 J. Bevk, J. P. Mannaerts, L. C. Feldman, B. A. Davidson and A. Ourmazd, Appl. Phys. Lett., 1986,49, 286. 25 M. Zinke-Allmang, L. C. Feldman, S . Nakara and B. A. Davidson, Phys. Rev. B, 1989, 39, 7848. 26 H-J. Gossmann and G. J. Fisanick, J. Vac. Sci. Technof. A, 1988, 6, 2037. 27 J. H. van der Merwe, J. Appf. Phys., 1962, 34, 123. 28 J. W. Matthews and A. E. Blakeslee, J. Vac. Sci. Technof., 1975, 12, 126. 29 R. People and J. C. Bean, Appf. Phys. Lett., 1985,47, 322; 1986, 49, 229. 30 P. M. J. Maree, J. C. Barbour, J. F. van der Veen, K. L. Kavanagh, C. W. T. Bulle-Lieuwma and M. P. A. Wiegers, J. Appf. Phys., 1987, 62, 4413. 31 M. H. Grabow and G. H. Gilmer, Semiconductor-based Heterostructures, 1986, 3; and private communi- cation. 32 C . C . Matthai and P. Ashu, Coffoq. Phys., 1990, 51, C1. 33 N. Jedrecy, M. Sauvage-Simkin, R. Pinchaux, J. Massies, N. Greiser and V. H. Etgens, J. Cryst. Growth, 1990, accepted. Paper 0/00500B; Received 1 st February, 1990

ISSN:0301-7249    

DOI:10.1039/DC9908900191

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Furuduy Discuss. Chem. SOC., 1990, 89, 201-210 GENERAL DISCUSSION Dr I. K. Robinson (AT&TBell Labs, Murray Hill, N J ) said: Since we submitted our paper there have been some theoretical developments from Jaques Villain and Igor Vilfan of CENG, Grenoble. These are very relevant to the discussion of the differences between surface roughening transitions and Ising transitions. In our original paper' we showed that steps appear spontaneously on Pt( 110) above its transition temperature of 1080 K. This was a direct conclusion from the systematic shifting of the half-order diffraction peaks. We inferred that the presence of steps implies a rough surface and therefore that the transition had the characteristics of a roughening transition. We did not observe the power-law lineshapes or the logarithmic divergence of the height fluctuations that are supposed to accompany such a transition,2 however.Instead we observed critical exponents p = 0.1 1 * 0.01 and v = 0.95 f 0.09, consistent with the theoretical values p = 1/8 and v = 1 for the 2D Ising model. Villain and Vilfan3 have now proposed an escape from this apparent paradox. They suggest that the steps appearing above the transition can be bound together. The transition can then be classified truly as 2D Ising if the structure of the domain wall were such a bound pair of steps. This situation is drawn schematically in fig. 1. The phase of the domains between the walls is marked '+' or '-' to denote the fact that they make an antiphase pattern. There are now only two degenerate ground states, which is appropriate for the Ising classification.The construction forbids any height divergence, so the surface is never rough. The critical behaviour is 2D Ising. The diffraction from such a structure is also derived by Villain and Vilfan.' It is clear that this should not be critically dependent on whether the steps are bound or not, so it is not surprising that they calculate a similar lineshape to ours, with the same shifting of the half-order peaks as we do.' Instead of describing the shift and half-width independently in terms of step and wall densities, /3 and a, they use two lengths: the correlation length & (separation of walls) and wall thickness L. In the statistical- mechanical model the lengths would fluctuate about these average values.In this way all of the observed behaviour of Pt(ll0) at high temperature can be explained with only step-type defects, provided they are constrained to be bound. In our model, we needed to admit the presence of ca. 20% of antiphase defects as well, even though these are energetically less f a v o ~ r e d . ~ The difference is somewhat semantic, since these antiphase defects (our paper, fig. 5, marked ' p ' ) are actually double-step domain walls of the type now proposed, but with a wall thickness, L=O. At the quantitative level, the new model has some problems. In principle L and & could have different temperature dependences above the transition. For example, L might stay roughly constant, while & becomes critical. Experimentally, the peak shift is seen to be linear' in t = T / T,- 1 , which implies' L ( t ) = & ( I ) = 1 / t .That the walls become thinner with increasing T3 is a little counter-intuitive. According to the new model,' as T, is approached from above, L( t ) diverges; as the steps effectively unbind, more steps could form inside the walls and roughen the surface as T decreases. Conversely, the walls become more tightly bound at higher T, apparently making it unlikely that the surface would roughen at high temperature. Roughening is assumed to take place by an unbinding of the step pairs. What is needed now is another experiment to test these predictions. It should be reasonably straightforward to measure the integer-orders (crystal truncation rods) as a function of temperature. This would immediately answer the question of what happens to the roughness.If the new model3 is right, no change should be seen; the old model' 20 1202 General Discussion lsing domain wall m I Y Fig. 1. Sketch of the model proposed recently by Villain and Vilfan to explain the phase transition of Pt(ll0). Ising antiphase domains are labelled '+' and '-'. The domain walls are made up of a pair of monatomic steps having a characteristic separation L. assumes no interactions between the steps and so predicts an increase of roughness above T,. Roughening might anyway be seen at higher temperatures still. 1 I . K. Robinson et al., this volume. 2 J. Villain, D. R. Grempel and J. Lapujoulade, J. Phys. F, 1985, 15, 809. 3 J. Villain and I. Vilfan, to be published. 4 L.D. Roelofs, S. M. Foiles, M. S. Daw and M. Baskes, to be published Dr J. Villain and Dr I. Vilfan (CEA-CENG, Grenoble) communicated: We will try to give an answer to Dr I. K. Robinson's criticism of our model of the Pt or Au(ll0) deconstruction transition.' According to our model, an Ising wall is composed of two steps (one up, one down) at the distance L;' see fig. 1 of ref. (1). The experimental data then suggest that L decreases with increasing temperature above the transition, and this is hard to understand, as criticized by Robinson. Also, a roughening transition is expected to occur at higher temperature and was not observed. On the other hand, the measured critical exponents are Ising-like.' We will not solve this puzzle, but propose some directions which have a chance to lead to the solution.The first possibility is that the deconstruction transition is really Ising-like and the roughening transition was not observed. The decrease of the wall thickness with increasing temperature might be due to the following effect: with increasing temperature, the number of steps or walls tends to increase, therefore the number of wall crossings increases. Wall crossings might favour narrow wall configurations. The second possibility is that suggested by Robinson et aL3 The transition is a roughening transition but has the exponents of the Ising model. There is no theoretical hint that this can happen, but it is possible to exhibit a simple model of a roughening transition which, in contrast with the S.O.S. model, is not in the Kosterlitz-Thouless universality class.According to Robinson et al.,3 the elementary excitation on the reconstructed 1 x 2 surface is a 1 x 3 step [see fig. 1 of ref. ( l ) ] which shifts the periodic structure of the reconstructed surface by a / 2 ( a is the lattice constant) in the directionGeneral Discussion 203 I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I I I Fig. 2. Top view on a reconstructed s I p 1 I ‘ I I I I I I I I I I I I 1 I I I I I I I I I I I I irface. Four roughening v I I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I ills are needed to create a domain. - Full and dashed lines represent top and bottom rows, respectively. perpendicular to the rows. As the critical region is approached from either side, domains nucleate and grow until eventually their size diverges at the critical point.However, the simple roughening domain, surrounded by one roughening wall, cannot nucleate because it can not match the periodicity of the surrounding reconstructed surface on both sides of the domain at the same time. Four steps are needed instead, see fig. 2. One can imagine models where 2p steps, instead of 4, would be necessary. The most important parameters are p and the interaction U between steps. In the case of Au( 1 lo), U is negative.5 For large enough p (and presumably for 2p = 4) the situation is the following. For U larger than some value U2 (which turns out to be negative) the surface becomes rough at the deconstruction transition. For U smaller than some value U , , the deconstruction transition is of the Ising type and there is a roughening transition at a higher temperature.The transition for large U is of the Pokrovskii-Talapov-Gruber- Mullins type, with a = v = 1/2. The existence of an intermediate region between U , and U, is a pure speculation. The critical exponents in that region are not known but it is not excluded that they have the Ising value. Similarly, if U , = U-,, it is not excluded that the exponents at that particular point have the Ising value. Thus, recent experiments on Au( 1 10) should stimulate further theoretical work. Experimentally, it would be of interest to measure carefully the surface roughness (the exponent x), as already suggested by Robinson in the previous comment. 1 1. K. Robinson, previous comment.2 I . Vilfan and J. Villain, Phys. Reu. Left., submitted. 3 I . K. Robinson, E. Vlieg and K. Kern, Phys. Ret.. Lett., 1989, 63, 2578 4 J . Villain and I . Vilfan, Europhys. Lett., 1990, 12, 523 5 J . Villain and I . Vilfan, to be published. Prof. D. P. Woodruff (University of Warwick) said: I would like to raise a general question concerning the precision and reliability of surface X-ray diffraction methods in determining spacings perpendicular to the surface. My question arises because of a clear discrepancy between a recent determination of the structure of Cu( 110) (2 x 1 ) - 0 by this method’ when compared with several other determinations. In particular, the 0-2nd layer Cu spacing deduced from X-ray diffraction implies an 0-Cu bond length204 General Discussion to this layer of 1.81 A, whilst SEXAFS,’ photoelectron diffraction”‘ and LEEDs all show that this parameter is close to 1.98 A.These techniques are all rather sensitive to this parameter so it is difficult not to conclude that the X-ray diffraction result is incorrect. This discrepancy is disturbing because one of the virtues of X-ray diffraction is that there is an objective (x’) test of the quality of a structural assignment, and this apparently strongly favours the 0-Cu distance which we dispute. 1 R. Feidenhans’l, F. Grey, R. L. Johnson, S. G. J. Mochrie, J. Bohr and M. Nielsen, Phys. Rev. B, 1990, 2 M. Bader, A. Puschmann, C . Ocal and J. Hease, Phys. Rev. Lett. 1986, 57, 3273. 3 A. W. Robinson, J. S. Somers, D. E. Ricken, A. M. Bradshaw, A. L.D. Kilcoyne and D. P. Woodruff, 4 A. L. D. Kilcoyne, D. P. Woodruff, A. Robinson, Th. Lindner, J. Somers, D. Ricken and A. M. Bradshaw, 5 S. R. Parkin, H. C. Zeng, M. Y . Zhou and K. A. R. Mitchell, Phys. Rev. B, 1990, 41, 5432. 41, 5420. Surf: Sci., 1990, 227, 237. this volume. Dr I. K. Robinson replied: The paper by Feidenhans’l et al.’ indeed claims a great sensitivity to the height of the oxygen atoms in Cu( 110)/0, with a xz of 2.6 for 0.34 8, below the surfaceoand a x2 of 10.7 for 0.34 8, above. The quoted error bar in the vertical position of 0.17 A is consistent with the statistical significance of the result. While I cannot judge why there is such a large discrepancy with photoelectron diffraction, I can point out some possible additional sources of error with the X-ray technique in general, that may not have been considered in the study of Cu(llO)/O here.’ 1.As I discussed in fig. 3 of our paper,’ the limited range of perpendicular momentum transfer means that coordinates are better determined parallel than perpendicular to the surface. For the same range of perpendicular momentum transfer as Feidenhans’l et al.,‘ we claim vertical error bars of 0.10 8, for Pt( 110). This seems to correspond roughly. 2. Oxygen is a very light atom compared with Cu or Pt, however. Not only is its contribution to the diffraction intensity already weak, but it is swamped by the much larger signal from the induced missing-row reconstruction from the Cu( 110). In very recent work3 on Cu(OOl)/O we found large uncertainties even in the parallel positions of the oxygens for this reason.3 . Structural parameters can be strongly coupled. In the situation of poorly deter- mined vertical coordinates the effect can be aggravated to the extent that a small error parallel can couple to a large vertical error. I suspect that the x2 value quoted above for the oxygens above did not allow the relaxation of other parameters in the problem. The distinction between the two oxygen sites might then be less clear. 4. In the case of Au(ll0) the earlier X-ray study4 did not consider fourth-layer relaxations and the best fit was to an expansion of the top-layer spacing. With a better range of perpendicular data and inclusion of the relaxations the top layer became contracted.5 The change was twice the size of the original error bar because the mistake was a systematic omission from the model and not just statistical uncertainty.5. Roughness has a big effect on the crystal truncation rods (CTRs) and relatively little effect on the fractional order data.‘ The Cu( 110)/0 analysis’ makes use of CTRs in determining the structure. This is a relatively new addition to the technique, and the correct way to handle roughness is still rather experimental. 1 R. Feidenhans’l, F. Grey, R. L. Johnson, S. G. J. Mochrie, J. Bohr and M. Nielsen, Phys. Rev. B, 1990, 41, 5432. 2 I . K. Robinson et a/., this volume. 3 I . K. Robinson, E. Vlieg and S . Ferrer, Phys. Rev. B, submitted. 4 I . K. Robinson, Phys. Reu. Lett., 1983, 50, 1145. 5 E. Vlieg, I . K. Robinson, K. Kern, Surt Sci., in press.6 I. K. Robinson, Phjrs. Rev. B, 1986, 33, 3830. Dr R. G. van Silfhout (FOM-Institute for Atomic and Molecular Physics, Amsterdam) also responded to Prof. Woodruff: The virtue of an X-ray scattering experiment asGeneral Discussion 205 opposed to electron scattering (LEED, RHEED) is the fact that, away from the bulk Bragg peaks, kinematical scattering applies, i.e. multiple scattering events do not occur. Therefore the x’ objective’ represents a strict measure of the goodness of a structural model proposed. A clear demonstration of the sensitivity that can be achieved is given in our paper’ on the Ge( 11 1)-c(2 x 8) reconstruction. With regard to the X-ray scattering experiment of Feidenhans’l on the oxygen induced 2 x 1 reconstruction on the (110) face of a copper crystal I would like to note that the range of perpendicular momentum transfer probed is relatively small and the scattering from a low-2 adsorbate like oxygen is very weak. These two facts result in a relatively large error bar of 0.2 8, and the LEED, SEXAFS and photoelectron diffraction results agree with the X-ray scattering study just within the error bar.1 R. Feidenhans’l, Surj Sci. Rep., 1989, 10, 3 and references therein. 2 R. G. van Silfhout, J. F. van der Veen, C. Norris and J. E. Macdonald. Prof. Woodruff continued: I should stress that I do not wish to question the quality of the data presented here by van Silfhout er al. or to suggest that the X-ray diffraction method is intrinsically flawed. However, I am concerned that the objective criterion of the fit (x’) appears to give the method an impression of superiority over other methods which may not be justified.In the case of the Feidenhans’l study of Cu( 110)(2 x 1)-0’ the authors show theoretical curves for two different O-layer spacings (differing by 0.68 A) which to an untrained eye are not really distinguishable when compared with the experimental data (for which there is a slight ambiguity in the absolute scaling). In the same paper, however, these authors claim that the x 2 values for these two spacings are 2.6 and 10.7 and that the two spacings are therefore very clearly distinguishable on this criterion. Incidentally, if we assume that all the appropriate authors are quoting errors as standard deviations then the X-ray diffraction result for the 0 to second Cu layer spacing in this system does differ by more than one standard deviation from the LEED2 and photoelectron diffraction3 results; the differences are 0.22 * 0.18 and 0.20 f 0.19 A, respectively.Using the same criteria the LEED and X-ray diffraction values for the top to second Cu layer spacings differ by 0.16 * 0.06 A, a very substantial discrepancy. 1 R. Feidenhans’l, F. Grey, R. L. Johnson, S. G . J . Mochrie, J. Bohr and M. Nielsen, Phw. Rev. B, 1990, 41, 5420. 2 S. R. Parkin, H . C. Zeng, M. Y. Zhou and K. A. R. Mitchell, Phys. Rev. B, 1990, 41, 5432. 3 A. W. Robinson, J . S. Somers, D. E. Ricken, A. M. Bradshaw, A. L. D. Kilcoyne and D. P. Woodruff, Surj: Sci., 1990, 227, 237. Prof. A. M. Bradshaw (Fritz-Haber-Insrirut der MPG, Berlin) said: Bearing in mind that the Pt(ll0) surface can also be prepared with a (1 x 3) re-construction’ and that recent RHEED results‘ show evidence for ( 1 x n ) reconstructions ( n = 2 , 3 , 4 , .. . ), one wonders whether the stabilising factor for a particular reconstruction is the amount of some surface impurity in very low concentration. On Pt silicon and calcium belong to the commonest surface contaminants. Since small quantities of alkali metals (<0.1 monolayer) are known to induce the (1 x 2) reconstructions of Ag(l10) and Cu(1 it is possible that calcium as an alkaline-earth metal is fulfilling a similar role in the present case. I am certainly not suggesting that Dr Robinson and his co-workers have been any less careful than others in preparing this particular surface: on the contrary, the (1 x 2) reconstruction is currently accepted as the most stable configuration for clean Pt{ 110).It is, however, necessary to point out that the concentration of impurity required to give rise to such an effect may not be easily detectable with standard surface analysis techniques. 1 P. Fery, W. Moritz and D. Wolf, Phys. Rev. B, 1988, 38, 7275. 2 H. Meyer-Ehmsen el a/., to be published. 3 B. E. Hayden, K. C. Prince, P. J. Davies, G . Paolucci and A. M. Bradshaw, Solid State Comrnun., 1983, 48. 1325.206 General Discussion Dr I. K. Robinson replied: The concentration of alkali metal needed to reconstruct Ag( 110) is of the order of 0.2 monolayer. 0.05 monolayer is needed to form the 1 x 3 instead of 1 x 2 on Au( 1 lo).In spite of the difficulty of seeing K and Ca in a crowded region of the Pt Auger spectrum, these are nevertheless detectable levels, and we are sure our sample was at least this clean. In the course of the experiments reported here, we followed the recipe of Fery et al. to make a Pt( 11O)l x 3. This failed completely and we succeeded only in facetting our crystal, which now must be repolished. Theory confirms the experimental fact that Au(ll0) and Pt(ll0) 1 x 2 surfaces are marginally stable with respect to formation of 1 x 3s.' The energy difference between 1 x 3 and 1 x 2 is of order 20 meV. The excitation energy of a step is even smaller still,' and we have shown that the phase transition is primarily mediated by steps. The question remains valid therefore whether the transition is in any way affected by impurities.I believe this can be answered experimentally by deliberately introducing alkali metal. Since the statistical mechanics of phase transitions is fairly well understood, this is a reasonable way to determine step formation energies. Such experiments are hard but worth trying. 1 L. D. Roelofs, S. M. Foiles, M. S. Daw and M. Baskes, to be published. Prof. D. A. King (University qfCam6ridge) said: We have found experimentally that the reconstruction of Pd{ 1 lo}, Ag{ 110) and Cu,,Pd,,{ 110) surfaces to a missing-row structure, as obtained from complete LEED I-V analyses, requires fairly significant alkali-metal coverages, amounting to 0.08 to 0.14 monolayer, to reconstruct the surface fully.'T2 This does suggest that very small amounts of impurities are not likely to be the cause of the Pt{ 1 lo} ( 1 x 2) missing-row structure.3 1 C.J. Barnes, M. Lindroos and D. A. King, SUTJ Sci., 1988, 201, 108. 2 C. J. Barnes, M. Lindroos, D. J . Holmes and D. A. King, Surf Sci., 1989, 219, 143. 3 in Physics and Chemistry of Alkali Metal Adsorption, ed. H. P. Bonzel, A. M. Bradshaw and G. Ertl (Elsevier, Amsterdam, 1989), p. 129. Prof. Bradshaw replied: A recent first-principle total-energy calculation by Fu and Ho' has indicated that a ( 1 x 2) reconstruction of the Ag{ 1 lo} surface is induced when an excess charge as low as ca. 0.05e per surface atom is added to the surface. Assuming that a fully ionised calcium adatom could be the source of this excess charge, the concentration required to induce the reconstruction would be ca.0.025 monolayer. This figure already implies that impurities of the order of a per cent or so could have a significant effect. 1 C. L. Fu and K. M. Ho, PI?!..\. Rev. Lc)rr., 1989. 63, 1617. Prof. J. F. van der Veen ( FOM-Institutefor Atomic and Molecular Physics, Amsterdam) said: In the thermal roughening study of P t ( l l 0 ) you find a critical exponent p' of 0.1 1 * 0.01. The critical temperature T, has been determined with an accuracy of *50 K. To what extent does an error in T, affect the value of p'? Dr I. K. Robinson replied: In the paper I am distinguishing an absolute accuracy of *50 K, limited by the thermocouple calibration, from the precision of the fitted value of T,., which is *l K.Prof. P. Pershan (Harvard Universiry)asked Dr Macdonald: Can you comment on whether or not the miscut, between the surface and the lattice, affects the onset of strain relaxation? Dr J. E. Macdonald (University of Wales College of'Card(fl) replied: Our work was performed on samples where the surface was aligned to within 0.05" of the crystallo- graphic planes. As yet, we have not studied miscut samples.General Discussion 207 Prof. King said: As a matter of information: Professor Cowley raises the matter of dynamical contributions in X-ray diffraction from surfaces at grazing angles close to the critical angle. Under what conditions can we safely ignore dynamical contributions in these experiments? Prof. R. A. Cowley (University of Oxford) replied: The conditions under which dynamical effects can be ignored depends on the accuracy required.They are important whenever either the incident beam and/or scattered beam has an angle to the surface close to the critical angle. Experience suggests that if 8/ 8, > 2, the dynamical corrections can usually be ignored. Prof. G. N. Greaves (SERC Daresbury Laboratory, Warrington) said: I would like to add some structural chemistry with regard to the photodissolution of silver in chalcogenide glasses. In collaboration with groups from Cambridge and Edinburgh we have measured Ag K-edge EXAFS in chalcogenide glasses at normal and grating incidence. We find the coordination number of silver is low (around three chalocogens) and generally much better ordered than in crystalline chalcogenides.Moreover silver enters chalcogenide glasses without requiring extra chalcogens. This suggests that silver bonds to sulphur or selenium, utilizing their lone-pair electrons, cross linking the molecular or layer-like units present. The existence of such intermediate-r$nge order has been inferred from the strong pre-peak in the structure factor (ca. 1 A-I). This feature is sensitive to thermal history and also to illumination with band-gap light. Such reconfiguration aids the dissolution of silver from the surface into bulk glass. Prof. Cowley said to Dr I. K. Robinson: Scattering from surfaces is normally given in reciprocal space by rods perpendicular to the surfaces. I do not understand how you can obtain curved or wavy lines as shown in your results.Are they the result of two close lines where intensities vary with L to give an apparent wavy structure? Dr I. K. Robinson replied: I also have some trouble in seeing why the position of the surface diffraction peak should oscillate in reciprocal space. This was predicted by Fentner and Lu' and seems to agree well with the experiment presented in our paper. I think this complicated behaviour is linked to the face-centering of the crystal lattice. The crystallographic phase shift between adjacent regions of the surface caused by a step is a function of both gll and g , . It may help visualisation of the result to consider various special positions along the rod, with reference to fig. 5 showing the atomic models of steps in Pt( 110): q1 = 0: Steps up and down both give a phase shift of ~ 1 2 .The peak at (1.5,0,0) is maximally shifted to smaller q , l . q , = 1: Steps up and down both give a phase shift of - ~ / 2 . The peak at (1.5,0, 1 ) is maximally shifted to larger q . 4 =0.5: Steps up give no phase shift and are iherefore inirihible. Steps down give a phase shift of T. The domains are thus antiphase. The peak at (1.5, 0, 0.5) is broadened but not shifted in q l l . Near this reciprocal space position, the surface appears miscut because one kind of step is invisible; the diffraction rod passing through (1.5, 0, 0.5) is therefore inclined to the perpendicular. The net result is the sinusoidal variation of position that was predicted by Fentner and Lu. 1 P. Fentner and T. M. Lu, Surf. S t r , 1985, 154, 15 Prof. Pershan commented: One simple way to look at the importance of dynamical effects on the (0, 0,O) rod is that for Q, = (47r/A ) sin 8,, the refracted wavevector Q' inside the material is Q'=J(Q'- Q:) == Q- Q:/2Q+* - * .208 Genera 1 Discussion When one can neglect Qf/2Q << Q, dynamic effects are not important.In our experiments we find that dynamical effects are negligible when ( Qc/ Q) 6 to i. Dr I. K. Robinson said: I wish to point out a basic difference between the formalism of the crystal truncation rod (CTR) presented by Prof. Cowley'.' and that derived by myself.' The discussion relates directly to the results on Ge( 1 1 1 ) presented by Dr van Silfhout4 and the analysis of the NiSi,/Si( 11 1) interface presented by Dr Ma~donald'.~ where the structural analyses made use of CTRs.The Andrews and Cowley' derivation examines the effect on a Bragg-peak lineshape of a sharp boundary in the integration volume of the Fourier transform. They show this to consist of a rod, perfectly sharp in section, with an intensity variation of as a function of momentum transfer q away from the Bragg peak along the direction perpendicular to the surface, and presumes 1q1<< 1 . Eqn (1) agrees also with the asymptotic behaviour of the exact dynamical calculation for the shape of the peak.' My own derivation' considers the kinematic sum over the layers of a crystal in which the incident and exit beams cross well defined outer surface layers (usually the same). In the limit of an infinite crystal with vanishing absorption per layer, the intensity is found to vary as (2) where q is in suitably dimensionless units that the Bragg peaks occur at q = n, 2 7 ~ .. . . The CTR is thus seen to originate as a special kind of finite-size effect. The calculation implicit in eqn (2) was used in the two papers presenting CTR The first point I wish to make is that these two results are not merely the same for 1q1<< 1, as can be seen by inspection, but identical, by virtue of the exact equality' I, = 1/lqI2 (1) I? = I / sin' q The reciprocal space sum of the intensities of the rods emerging from all the Bragg peaks along the specular direction is identical to the periodic form of eqn (2). The second point is that this equivalence of the two derivations breaks down when the crystal structure is sufficiently complicated.The generalisation of eqn (3) works for the case of a primitive lattice of layers with equal weight, AAAA . . . . It also works for an ABABAB.. . structure, but not for one with a non-uniform layer spacing, such as Ge( 11 1)" or Si( 11 l).' This is illustrated in fig. 3, which shows the specular CTR intensity calculated by the layerwise summation method'*x for a Ge( 1 1 1 ) surface with two possible terminations: between the 'double layers' of atoms, and splitting the double layer. The atomic models are shown in ( a ) and their corresponding intensities as the two kinds of dashed curve in ( b ) . Both curves reproduce the correct intensity ratio 2 : 1 : 0: 1 : 2 for the (000) : ( 1 11) : (222) : (333) : (444) Bragg peaks of the diamond lattice. However, in one case there are nodes of zero intensity along the rod profile, but not in the other, and there is almost a factor of 10 difference over most of the region near (222).Very clearly, the profile is sensitive to the choice of termination. Indeed the success of the work presented by Dr van Silfhout' depends precisely on this sensitivity. The construction of the CTR intensity by reciprocal space summation of a line of l/Iql' functions weighted by the square of the structure factor gives the solid curve roughly midway between the two dashed curves of fig. 3(6). Since the details of the termination are nowhere considered in this construction, the result is independent of the surface model. All curves superimpose close to and at the Bragg points, where the theories become equivalent.The equivalence will generally hold in the limit / q ( << 1, the region of validity of the approximations used by Andrews and Cowley.General Discussion 209 1 o4 1 o3 A vl c aJ C W Y .- Y .- 2 lo2 - a - a 10 1 Fig. 3. ( a ) Side view of an atomic model of a Ge(ll1) surface. The two kinds of dashed lines are possible terminations of the lattice. ( b ) Intensity profiles of the specular (along the line perpendicular to the surface) crystal truncation rod from Ge( 11 1). Various bulk Bragg peak locations are marked. The solid line is calculated as the sum of l/lql’ tails of all the Bragg peaks along the line, as in eqn (3), but weighted by the square of the structure factor. The two dashed curves are calculated by the layer-wise summation method for the two surface terminations of ( a ) .It has been argued’ that the success of the layer-wise summation method requires the surface to be mathematically flat, containing no miscut: there would in reality always be some slight miscut, which would cause the &function rods emerging from one Bragg peak to not quite overlap those of the next peak; the amplitudes would not be able to interfere, so only a sum of intensities would be observed. There are several faults with this argument: (i) The ‘real’ surface also has an energetic distinction between the possible terminations. For example, one termination of G e ( l l 1 ) in fig. 3 ( a ) has three times as many broken bonds as the other. Whichever chemical state is preferred will fill most of the surface area and will bias the step distribution accordingly.(ii) The argument applies to miscut surfaces considered to be ideal regular staircase arrangements. ‘Real’ surfaces have a distribution of steps that broadens the rods so that they can in fact210 General Discussion overlap. (iii) The surface free energy changes with crystallographic orientation because of the extra energy in the steps. The equilibrium morphology, as determined by the WuIff construction,”’ can lead to facets of exact low-index orientation, for which the CTRs would indeed align perfectly. ‘Real’ surfaces are known to behave this way.“ Experimentally, there are several examples of amplitude interference effects along CTRs4,”6.g that demonstrate the validity of the layer-wise summation technique.There is also one reported case9 where this is found not to work, and where the sum over Bragg peaks is preferred. I have enjoyed many lengthy conversations of these points with Jakob Bohr, Larry Sorensen, Elias Vlieg and Hoydoo You. 1 R. A. Cowley et al., this volume. 2 S. R. Andrews and R. A. Cowley, 1. Phys. C, 1985, 18, 6427. 3 I. K. Robinson, Phys. Rev. B, 1986, 33, 3830. 4 Paper 2, this volume. 5 Paper 4, this volume. 6 I . K. Robinson, R. T. Tung, R. Feidenhans’l, Phys. Rev. B, 1988, 38, 3632. 7 1. S. Gradshteyn and I . M. Ryzhik Tables oflntegrals, Series and Products (Academic Press, New York, 8 I . K. Robinson, W. K. Waskiewicz, R. Tung and J. Bohr, Phps. Rev. Lett., 1986, 57, 2714. 9 H. You, personal communication and H. You et al. to be published. 1965). 10 A. Zangwill, Physics at Surfaces (Cambridge University Press, Cambridge, 1988). 11 J . C. Heyraud and J . J . Mktois, Surf Sci., 1983, 128, 334. Prof. Cowley said: The truncation rod form l/q’ is, of course, valid for q much smaller than l / a and for q large enough that dynamical effects are not important. A well defined rod probably occurs only if it is associated with a particular crystal plane when the interference effects from different reciprocal lattice points will be important. The dynamical theory is needed if the intensity scattered is a large proportion of the incident beam or if either the incident or scattered beam is close to glancing incidence or very close to a Bragg reflection. Prof. Pershan said: It seems to me as though the appearance of interference effects on truncated rod intensity depends on the resolution of the spectrometer, in the same way that two-slit interference patterns in optics depend on the collimation of the light. There is a sum rule fixing the integrated intensity but the visibility of the interference depends on surface features relative to the spectrometer. Dr Macdonald said: For sufficiently thin films, the fringe separation is large compared to the resolution width. The experimental data may then be simulated by a convolution of the scattering function with the instrumental resolution function.

ISSN:0301-7249    

DOI:10.1039/DC9908900201

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1990, 89, 211-229 Langmuir Monolayers: Structures and Phase Transitions Zhong-hou Cai and Stuart A. Rice Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, IL 60637, U.S.A. This paper briefly reviews information recently obtained from grazing incidence X-ray diffraction studies of the structures of the several phases in the high-surface-density region of an amphiphile monolayer on water. We also present a new theory, based on a density functional formalism, for the transition between untilted (hexagonal) and tilted (distorted hexagonal) phases in these monolayers. We find that in the region from 0 to ca. 0.5 rad tilt angle the tilted states are thermodynamically more stable (ca. 0.2-2.0 kB T per segment lower in free energy) than the untilted state, so that the monolayer, when expanded, always adopts the value of tilt angle determined by the area per molecule. Eventually, for large tilt, say e.g.>0.6 rad, the chemical potential of the monolayer increases as the tilt increases. There is, then, a minimum of the free energy uersus tilt angle for which the constraint derived from the area per molecule is effectively relieved. We find that an incompressible monolayer has a small change in average density and a large change in area per molecule across the transition. Conversely, a monolayer with large compressibility has a large density change and a small change in area per molecule across the transition. Our analysis coi,rectly reproduces the principal features of the observed phase transitions.We speculate on the nature of 'island phases' and the relation of these to the close-packed phases of the monolayer. 1. Introduction The macroscopic properties of monolayers of various long-chain amphiphile molecules supported on water have been studied for most of this century. The results of the many studies of the equation of state, i.e. the functional relationship between the surface pressure (the excess surface tension due to addition of the amphiphile) and the area per molecule, establish that such monolayers can support several different phases,' but yield no information about the microscopic structures of the phases. There have been of course, many speculations concerning the structures of the various surface phases of the monolayer, each speculation usually based on the characteristics of a simple model.' Until very recently, tests of these speculations were not possible with the existing experimental techniques.The experimental situation has now been dramatically changed by the increase in the availability of intense X-rays from synchrotron sources, and by the development of the grazing incidence X-ray diffraction technique.'." Indeed, it is now possible to study directly the microscopic structure of a Langmuir monolayer. This paper briefly reviews a subset of the information available from such studies of the structures of the several phases supported in the high-density region of an amphiphile monolayer on water, and describes a new theoretical analysis of the transition between phases with tilted and untilted molecules.The theory correctly reproduces the principal features of the observed phase transitions. Although no attempt has been made to describe the characteristics of a particular system, there is enough similarity in the behaviour of the several systems studied5-9 that it is legitimate to say that the theory is in sensible agreement with experiment. 21 1212 20 0 Langmuir Monolayers 40; ( d ) 20 - ( b ) 15 20 25 30 15 20 25 30 15 30 A/A2 Fig. 1. Surface pressure versus the surface area per molecule for several monolayers supported on water. ( a ) CZ1H430H (1 1 "C); ( b ) C20H4,C02H (3.0 "C); (c) C,9H39COZH (ca. 20 "C);' ( d ) (S)-CF3(CF2)9(CH2)20COCH2CH( NHl)CO, (20 0C).8 2. Background Information Surface structure determination by X-ray diffraction has been recently r e ~ i e w e d , ~ so there is no need to describe the experimental methodology in this paper.For our present purposes it suffices to note that the X-ray scattering from an amphiphile monolayer is so weak so that even with the new synchrotron X-ray sources diffraction studies are very difficult. One consequence of the weak scattering is that it is very difficult to observe diffraction peaks other than those of first order, so that the majority of the inferred structures are based on some combination of first-order diffraction data, X-ray reflectivity data and ancillary information; in a few cases the structural inferences are strengthened by the data obtained from second-order diffraction peaks or out of plane diffraction intensity measurements. To date, structures inferred in this fashion have been reported for four Langmuir monolayer systems, each consisting of a single-chain amphiphile molecule supported on water; all of the data are representative of the region of the phase diagram where the surface density is high.The four water-supported monolayer systems referred to aret built from, respectiveiy, the molecules (I) CZ,H430H,5 (11) C20H4,C02H,6 (111) C,9H39C02H,7 and the fluorinated chiral molecule (IV) (S)- CF3(CF2)9(CH2)20COCH2CH( NH3+)C02 .' This small data set provides hints concern- ing both the similarities and the differences between the structures and properties of the different monolayer systems, and partially illustrate the richness of the spectrum of monolayer structures.The similarities in the properties of these systems begin with the equation of state in the high-surface-density region. Each of the systems mentioned has isotherms in the high-density region of the surface-pressure-surface-area plane which are sensibly linear (but with different slopes) above and below a 'kink' that is taken to signal a phase transition (fig. 1 ) . The 'kink' is, typically, at a surface pressure of ca. 20 mN m-' and at a surface area per molecule, depending on head-group size and effective chain diameter, of ca. 0.20 nm' (hydrocarbon tail)-0.285 nm2 (fluorocarbon tail). Some of the isotherms for C 2 , H,,OH have rounded or nearly flat (isobaric) portions immediately below the 'kink', and the isotherms for C,,,H,,CO,H have both an isobaric region and a third sensibly linear portion for areas per molecule larger than ca.0.23 nm' (see fig. 1 ) . As to the similarities between these systems at the molecular packing level, the following observations are pertinent. ( 1 ) Three of the systems mentioned (11, I 1 1 and IV) undergo a hexagonal-to-distorted hexagonal (face-centred orthorhombic) structuralZ-h. Cai and S. A. Rice 213 model I tilt (a,+a2) nn model I1 tilt (a1 - a21 Fig. 2. Top view of molecular chains in a monolayer. Both the untilted and tilted structures are shown. In model I the tilt is toward a nearest neighbour in the hexagonal unit cell and in model I1 it is between nearest neighbours in the hexagonal unit cell. phase transition as the surface pressure is lowered along an isotherm across the 'kink', and it appears likely that the fourth ( I ) does alsc.In each case it is believed that in this 'low-pressure (below the 'kink')-high-temperature' distorted hexagonal structure the molecules are tilted with respect to the normal to the surface, that the density of the monolayer is independent of the area per molecule, and that the projection of the molecular tilt on the surface accounts for the increase in area per molecule as the isotherm is traversed in the direction of decreasing surface pressure. (2) In system 111 the data, taken at 20 "C, definitely establish that the tilting increases continuously from 0" to ca. 35" as the area per molecule is increased from 0.197 (at the 'kink') to 0.24 nm2;' similar behaviour is inferred for system 11.' (3) Although in both systems 111 and IV the tilt direction is towards a near neighbour (fig.2), at least one property of the distorted hexagonal phase of system IV differs from those of systems I1 and 111; in system IV the tilt angle in the distorted hexagonal phase is independent of the area per molecule, with a fixed value of ca. 21".8 See note added in proof. Consider, now, the region of the phase diagram where the pressure is above the 'kinks' in the isotherms. The following are found. (4) In system I there is a hexagonal-to- distorted hexagonal structural transition as the temperature is lowered along a high- pressure isobar (30 mN m-'); the transition temperature is ca. 16 "C.' ( 5 ) The same distorted hexagonal structure is found in system I 1 at high pressure (35 mN m - ' ) and low temperature (0.2-7.5 "C);* we refer to it as the 'high-pressure-low-temperature' distorted hexagonal structure mentioned above.The available isobaric diffraction data for system I 1 d o not cover as large a temperature range as do those for system I , and the transition to the hexagonal phase has not yet been seen. The data for monolayer systems I and I I are consistent if the hexagonal-to-distorted hexagonal phase transition in system I1 at 35 mN m ' is at about the same temperature as in system I at 30 mN m I , which is a reasonable assumption by virtue of the great similarity of the two amphiphile tail structures. The variation of structure along a high-pressure isobar has not yet been studied in systems 111 and IV.(6) In systems I and I 1 the suggested 'high-pressure-low- temperature' distorted hexagonal structures have the molecules tilted with respect to the normal to the surface by order of 2-5";9 at low temperature, below ca. 5 "C, the tilt214 La ngmuir Monola yers direction is along the line between near-neighbour molecules, whereas above 5 "C the tilt direction is between near-neighbour molecules. (7) In the 'low-pressure-high- temperature' distorted hexagonal phases of systems I and I1 it is suggested that the direction of the tilt is towards a neighbour molecule when the temperature is below ca. 4 "C and between neighbour molecules above that temperature.' (8) In system 11, in the region of the phase diagram with the third nearly linear portion of the isotherm mentioned above, there is an expanded hexagonal phase with spacing between the molecules large enough to permit free rotation around the long axis of the amphiphile; for example, when the system temperature is 1.5 "C this structure is stable over the range 0-8 mN m-' and 0.24-0.255 nm2 per molecule.' It is not known if the molecules in this phase are tilted with respect to the normal to the surface.It has also been found that rapid uniaxial compression of system I generates the distorted hexagonal structure in the region of the equation of state where the hexagonal structure is expected." When the compression is stopped and the surface pressure becomes isotropic the distorted hexagonal structure relaxes into the expected hexagonal structure. Preliminary experiments suggest that a similar phenomenon occurs in system 11." Finally, there is a relevant observation for a system similar to systems I1 and 111: electron microscopy and electron diffraction studies of room-temperature monolayers of C,,H3&OZH transferred from the supporting water to a carbon film show that when the area per molecule is 0.38 nm2 the system is heterogeneous, consisting of a mixture of empty space and hexagonally close-packed molecules in nearly circular islands with diameters of 10-20 nm." It should be noted that no mention has yet been made of the influence of amphiphile tail flexibility on the character and location of phase transitions.It is known, from studies of the vibration spectra of the lamellar paraffin hydrocarbon crystals with carbon chain lengths like those of the smphiphiles I, I1 and 111, that the concentration of gauche conformations in the molecules in the solid is quite high near the melting points of the crystals.13 For example, Maroncelli'" estimates that near the melting point of C,,H,,, between 6 and 12% of the molecules have end gauche defects of the form (gtt .. .) and between 12 and 24% of the molecules have internal kink defects of the form ( . . . gtg' . . . ). Kawai et aZ.15 have used measurements of the linewidth of the symmetric CD, stretching band in a monolayer of stearic acid-d,, supported on water to argue, without making quantitative estimates, that gauche conformations are introduced progressively in the amphiphile chain as the area per molecule is increased from 0.195 to 0.25nm' (the 'kink' in the isotherm is at 26 mN m and 0.195 nm' per molecule at 20 "C; the surface pressure decreases nearly linearly along the isotherm from the value 26 mN m-' at the 'kink' to essentially zero at 0.25 nm' per molecule).Although the molecular packing in the stearic acid monolayer in this surface-density range has not yet been determined, it is reasonable to assume that at corresponding points along the isotherm it is like that for the other monolayers discussed above. I f that assumption is made we expect that, as the surface pressure is lowered along the isotherm across the 'kink', there is a transition from a hexagonal to a distorted hexagonal structure, and that below the 'kink' the tilt of the molecules increases continuously. It is not at all clear at present how the gauche conformation concentration influences the structures of the phases supported by an amphiphile monolayer, or the transitions between those phases. 3.Theory of the Hexagonal-to-distorted Hexagonal Structural Transition in Amphiphile Monolayers 3.1. General Remarks Density functional theory provides a systematic representation of the properties of an inhomogeneous system.'" The formulation of the general theory invokes a variationalZ-h. Cai and S. A. Rice 215 principle to define the inhomogeneous equilibrium state for a system in the external potential U ( r , , r2, . . . , rN). Of course, the probability density in the grand canonical ensemble for a given system configuration is a functional of U ( { r } ) . It can be shown that for a given interaction potential, V ( { r } ) , the role of U ( { r } ) and the density distribution can be inverted, i.e.U ( { r } ) is uniquely determined by the equilibrium density distribution p o ( r ) . Then the variation of the grand potential, SZ, = -pV, which is a functional of the density distribution, with respect to the class of all density distributions consistent with the potential U ( { r } ) , satisfies Alternatively, one can say that varying equilibrium density distribution via the relation is a generating function which defines the spatially with u ( r ) = p - U ( r ) ( 3 ) where p is the chemical potential of the system. The equilibrium density distribution can also be represented in the form P o ( r ) = z exp { - W ( r ) + d P o ; rl} (4) where c [ p o ; { r } ] is the effective one-body potential energy o f the system and z = ( 2 ~ r n k , T / h ’ ) ~ / ~ exp ( p / k k B T ) is the fugacity of the system ( p = l/kBT). The effective one-body potential energy can also be thought of as the contribution to the chemical potential due to the interactions.If we define where then and we are led to the relation W P l = 3.2. Perturbation Expansion Our description of the phase transitions in the monolayer is based on the behaviour of the one-molecule distribution functions of the ordered structures a and b, both of which are periodic in fixed, oriented crystals. Since the contributions to the free energy associated with fixing the positions and orientation of a macroscopic crystal are negligible with respect to the other contributions to its free energy, we can arbitrarily choose the position and orientation of the reference structure a.For most of the calculations reported we assume that the molecules in structure a have their molecular axes normal216 Langmuir Monolayers to the surface. Structure b, which is assumed to have tilted molecules, is described using the same origin of coordinates as used for structure a. The spirit of our analysis is that the chemical potential of structure b, for a given tilt of the molecular axes, can be calculated from the chemical potential of structure a via a perturbation expansion. In order to evaluate the difference in grand potential between the two phases we make a functional expansion of the one-body effective potential c [ p ; { r } ] about its value in structure a.The result of this expansion is, to second order where c2 is the two-particle direct correlation function. Higher-order terms in the expansion involve successively higher-order direct correlation functions, about which there is so little information that the series is truncated at second order as shown above. The one-body density distributions in the two fixed and oriented structures can be represented by the Fourier series expansions where {"k,} and {'k,,} are the reciprocal lattice vector sets of structures a and b and " k , ) and &,( 'k,,,) are the corresponding expansion coefficients. The zero-wave-vector Fourier expansion coefficients &(O) and 4 b ( O ) are the mean densities of structures a and b, which we denote pa and p b .After some straightforward algebraic manipulations and changes of variable of integration we find that the difference in grand potential per unit cell is where (16) J 1 a3 =- C 4b(bkm)4b(bkm,)C'2(bkkm.) d r exp {i(bk, + bkmr) - r } 2N m,m'+0 1 as=- 2 N n,m#O c 4 a ( " k n ) 4 b ( " k m ) { ~ ' 2 ( b k ~ ) - ~ 2 ( a k n ) } J dr exp {i(ak, + b k m ) . r } (18) and C'?(k) is the Fourier transform of the two-body direct correlation function. Clearly, the free-energy difference between structures a and b depends on the density difference between the structures and the order parameters of the two structures [the coefficients +&,("kr,) and +h(hk,,,)]. For a structural transition in which there is no densityZ-h. Cai and S.A. Rice 217 change, such as in the vicinity of the 'kink' in the monolayer isotherm, the formalism described simplifies. We find, in the limit that the density distribution change is small 19) I PbW = P h ) exp dr2 c*[p'i; r, r,",(r2) - P ' h ) I ii x exp { c 4h(bkm)mL) exp (ihk,,, * 4 which, with the Fourier series expansions of the density distributions, takes the form C + b ( ' k m ) exp {ibk * r ) = c 4 , ( " k f l ) exp {idkfl - r> m = O I? : 0 m -0 - 1 ~,("k,,)C"2(dk,,) exp (i"k, - (20) t l - 0 Cai and Rice" have developed suitable approximations and a systematic method to solve eqn (20) for the order parameters in the kinds of monolayers described in section 2; the details of their analysis, along with a discussion of the approximations involved, are reported elsewhere.3.3. Monolayer Model We now consider a model of the dense monolayer, that is the monolayer in the region of the surface-pressure-surface-area diagram where the area per molecule ranges from, say, 0.20 t o 0.25 nm2. We represent the (assumed) all-trans chain of the amphiphile by a linear array of spherical pseudoatoms, each pseudoatom replacing a CH, group. We then assume that in the high-surface-pressure-high-temperature regime these molecules are packed in a hexagonal array with zero tilt relative to the normal to the surface. The unit cell in the surface can then be characterized with the two unit vectors a , and a2 (fig. l ) , while the vertical component of the C-C bond length is along the unit vector a 3 . Of course, the monolayer we consider differs from an infinite crystal by not having extension in the direction normal to the surface or, put another way, it is discontinuously truncated at the monolayer/water and the monolayer/vacuum surfaces.In the theory of finite crystal structure such a situation can be described by the use of a suitable external potential. We assume that this external potential varies sufficiently little with the changing tilt of the molecules that it need not be explicitly represented in the analysis, which is equivalent to the approximation The models of the monolayer we consider allow tilting of the molecules along the symmetry directions of the in-plane unit cell, but not in other directions; these are shown in fig. 2. In model I the molecules tilt along a , + a, , which is towards a nearest neighbour in the hexagonal unit cell, or along a , - a , , which is between nearest neighbours in the hexagonal unit cell.Note that in these models the components of a , + a , and a , - a , normal to the tilt direction are independent of the tilt, whereas the components parallel to the tilt increase as the tilt increases. If the hexagonal surface unit cell has inter- molecular separation a and the C-C bond length in the amphiphile chain is r C c , the reciprocal lattice vectors of the untilted structure are Zbexp { - p u ( r ) + c [ p a ; r l } z p ~ ( r ) * (21) b , =3(-j-&+j) a218 Langmuir Monolayers where 6 = rcc sin ( Occ/2) is the z component of rcc and Occ is the C-C-C angle. We shall later verify that the change in monolayer density with tilt is very small for a range of conditions.For the present we assume that the density is a constant so that the reciprocal lattice vectors can then be represented in the form 6 , = ?( $+ cos ( y)$ - sin ( y ) z 9 2 T i b3=- b cos y for model I, while for model 11 b, =--(- 27r cos ( y ) i 2 Ti b3=- b cos y where y is the tilt angle. To solve eqn (20) we need to know the functional forms of the two-body direct correlation function and the order parameters. We can calculate the two-body direct correlation function by using our knowledge of, say, the structure of the hexagonal unit cell in the surface. We proceed by constructing a pair correlation function for the structure and then use the Ornstein-Zernike equation. Starting with the form where K is determined from the normalization condition rr we find i( k ) = d r { g 2 ( r ) - l} exp {ik r ) I i = 2 Eqn ( 3 2 ) is very useful as a description of the structure, and it has been obtained without making explicit use of the form of the intermolecular potential energy.However, eqn ( 3 2 ) has a flaw which must be corrected; it implies that &(O) + -a. Although this result is correct for the incompressible lattice constructed, it must be replaced for the formalism to be useful for the description of a compressible monolayer. Indeed, the correct value for Q O ) isZ-h. Cai and S. A. Rice 219 Table 1. Reciprocal lattice vector (RLV) sets for untilted crystalline phase ~ M ma M RLV C exp ( i k . r ) 1 1 0 1 2 6 b, b2 , - b2, b, , - b , 6 - , bz -b2 4 cos (5) cos (T) + 2 cos (5) which we use in our analysis.As to the order parameters, we assume that each segment of a molecule has a Gaussian distribution of positions centred on the lattice position, and write I d r exp [ -Ir J - r017j ~ ~ exp {-i"k, - r } (34) where the integrations are over the Wigner-Seitz cell of the lattice and the width parameter (T was chosen to be one tenth of a C-C bond length. In eqn (34) 2.1, is the unit cell volume of structure a. 4. Results We have used the analysis described in the preceding section to calculate the free energy of a monolayer as a function of the tilt of the amphiphile molecules. The calculations are carried out to second order in the expansion in reciprocal lattice vectors. The symmetry of the first Brillouin zone of the hexagonal unit cell, corresponding to vertical amphiphile molecules, is Cbh, and of the distorted hexagonal unit cell, corresponding to tilting of the amphiphile molecules along either a, + a2 or a , - a,, is CZv.Therefore, as the molecules of the monolayer tilt, the six reciprocal lattice vectors of the hexagonal cell which belong to the same symmetry class split into subsets. We display, in tables 1-3, the components of each reciprocal lattice vector set for the monolayers with hexagonal and distorted hexagonal structures, along with the degeneracies and the expansion of Cj exp {ikj - r } where j runs over all members of the reciprocal lattice vector subsets. In our numerical calculations we have chosen for the hexagonal lattice constant in real space an average value derived from the high surface- pressure diffraction data for monolayers I, I1 and 111.Fig. 3 shows the fractional change in average density of the monolayer as the amphiphile molecules tilt, calculated in the one-order parameter and two-order para- meter approximations. Note that the maximum density change is only of the order of 0.2%, validating the approximation of constant density made in one stage of our analysis. In the small tilt region, y (0.2 rad, there is no significant difference between the predictions for models I and 11, and only small differences for larger values of y. Fig. 4 and 5 show the calculated change in grand potential as a function of tilt angle and of area per molecule, respectively. The grand potential of the monolayer at first decreases with increasing tilt angle, reaches a minimum value, and thereafter increases as the tilt angle increases.We find that model I1 has a minimum grand potential when220 Langmuir Monolayers Table 2. Reciprocal lattice vector (RLV) sets for tilted distorted hexagonal, crystalline phase; modsel I mbL RLV C exp (ik - r ) 1 1 2 2 3 2 4 2 5 1 6 1 7 2 8 2 9 1 10 1 0 b l , b2 -b, 9 -b2 bl + b2 -b, - b, b3 - b3 1 2 cos (z) exp ( i 27r cos a yy ) exp (-1 .27r 7) sin yz 2 cos (””> exp (-i 27rc0syy) exp ( i- 2 y y z ) 2 cos (5) exp ( -i 47r cos YY) exp ( 47r YZ) a& a exp(i 47r cos a yy ) e x p ( - i Y ) 47r sin yz a 7r cos y y 27r sinyz 2 cos (5) exp ( i a ) exp (-i 7) 2 cos (z) exp ( - i 27r cos 7’) exp ( i +) exp i- exp (-i ”) b cos y ( b f ,“f y ) y =tilt angle.the tilt is 0.47 rad, at which its value is ca. 2.0 kBT per segment larger than the corresponding minimum for model I at 0.57 rad. Our calculation picks out the observed tilt direction,’ with an estimated difference in free energies of the two tilted structures large enough on a per molecule basis to be consistent with the observed structure, yet also small enough to also be consistent with the apparent switching of tilt direction inferred from the experimental data.’ That is, our model of the monolayer does not account for myriad small details of the molecular interactions which, when the chemical potential differences between three structures are small, lead to the transformation of one into one or the other of the second and third structures.Of course, it must be remembered that the tilt angle is not a controllable variable in the monolayer system; it is constrained by the controllable area per molecule, and what is observed is the tilt as a function of area per molecule. The implication of this observation is that, when the area per molecule is fixed by the external conditions, the system adopts the tilt angle corresponding to that value of the area per molecule and is not free to increase the area per molecule until the unconstrained minimum of the free energy versus tilt is reached. A comparison of the predicted tilt with area per molecule and that inferred for a monolayer of arichidic acid at 20°C is displayed in fig. 6. There is an interesting characteristic of the phase transition described above, namely a sensitivity to the magnitude of the monolayer compressibility. We show in fig.7 the 3.0”C isotherm for a monolayer of C,,,H,,CO,H on water.” The area per molecule, lattice constant (for a hexagonal lattice), compressibility and value of F2(0) for the statesZ-h. Cai and S. A. Rice 22 1 Table 3. Reciprocal lattice vector (RLV) sets for tilted distorted hexagonal crystalline phase; model I1 L %L RLV 1 exp (ik * r ) 1 2 3 4 5 6 7 8 9 10 1 2 2 1 1 2 2 2 1 1 1 27r cos 6x 27r sin 6z 2 cos (T) exp (i ) exp (-i -) a& exp (-i 47r cos Sx 4 7 sin Sz 2 cos (T) .67r cos Sx) exp ( i- 67ras; SZ) 7T cos sx a& 2 cos (F) exp (-1 2 cos (?) exp (i ti exp i- ( b’,rrS) exp (-i *) b cos 6 .67r sin 6z ) exp (-1 7) 6 =tilt angle. Table 4. area chainjA* lattice constant/8i (d7r/dA),/ 10’’ dyn cm3 C2(0)/8i3 a b d e f g h C I j k I 18.6 18.8 19.0 19.1 19.3 19.4 19.5 19.8 20.2 20.7 21.1 21.6 4.63 4.66 4.68 4.70 4.72 4.73 4.75 4.78 4.83 4.89 4.94 4.99 -2.83 -2.83 -2.83 -2.83 -2.83 -1.76 - 1.46 -0.625 -0.290 -0.136 -0.0363 -0.0363 -578 -595 -613 -629 -648 -399 -335 -135 -53.6 -13.7 15.0 15.2 indicated along the isotherm in fig.7 are listed in table 4. As one passes along the isotherm from the state labelled ( a ) to the state labelled (k) there is a marked variation in the density change accompanying the tilting transition.- Consider the portion of the isotherm labelled (a)-( e). In this region the surface-pressure-surface-area relationship is very nearly linear and the compressibility, which is small, is very nearly constant; the222 0.005 0.000 5 - 0.005 -0.010 Langmuir Monolayers I I , I I l l 1 ( b ) 1 1 1 1 I l l 1 - I 1 1 f 1 1 1 1 1 I I I I I 1 ' I 1 ' 0.005 I I I l l 1 I l l 1 I I I I corresponding calculated values of QO) vary from -5.78 to -6.48 nm2.As long as the compressibility is small we find that the density change in the tilting transition is small (fig. 8) and the change in grand potential as a function of tilt angle rather insensitive to the small range of &(O) cited (fig. 9). However, when the compressibility of the monolayer becomes large, as in the portion ( h ) - ( k ) of the isotherm, the density change in the tilting transition also becomes large (fig. 10). Of course, as the tilt angle in the distorted hexagonal structure increases, the effective area occupied by a molecule increases; we show in (fig.11) the change in monolayer grand potential with the change in effective area per molecule for the values corresponding to the minima in the grand potential as a function of tilt angle. Note that as QO) increases from -6.00 to -0.15 nm2 the change in the area per molecule at the minimum of the grand potential as a function of tilt angle decreases from 0.034 to 0.028 nm2. It is possible, then, that at point 1 on the isotherm shown in fig. 7 the distorted hexagonal structure has the most favourable tilt angle, that is the constraint of fixed area per molecule has been effectively relieved.Z-h. Cai and S. A. Rice 223 L Q) n Fig. 4. Change in grand potential of the monolayer (Z2(0) = -800 A’) as a function of tilt angle in the two-order parameter approximation, when the tilt is along a, + a2 (-) and along a, - a2 (---).L n 10 5 0 -5 - 10 16 18 20 22 24 26 AIA’ Fig. 5. Change in grand potential of the monolayer (2*(0) = -800 A’) as a function of area per molecule in the two-order parameter approximation when the molecules tilt along a , + a2 (-) and along a , - a2 (- --). We close this paper with a remark and a conjecture. First, the observation that rapid uniaxial compression of a monolayer of I generates a distorted hexagonal structure which, after the surface pressure becomes isotropic, relaxes to a hexagonal structure’* is consistent with the existence of a small tilt angle in the hexagonal structure as suggested by Bohanon et aL9 This follows once it is recognized that if the amphiphile molecules have any non-zero tilt there are non-zero projections of the molecular axes on the surface, which in effect, define a director which can be oriented by the uniaxial compress-224 Langmuir Monolayers 19 2 0 21 22 23 24 A / A z Fig.6. Comparisons between the predicted tilt as a function of area per molecule for a constant density monolayer (---) and that for monolayers calculated with F2(0) = -6-00 A-' (-), -140 A' (. * - -), -50 A' (- -), and -15 A' (---). ( a ) model I . ( b ) model 11. ( c ) observed tilt as a function of area per molecule for system I l l . From ref. 7.2-h. Cai and S. A. Rice 40 - I 5 E 20- h '0 P \ 225 I 1 1 1 1 1 1 1 1 1 1 1 - - - 0 - - 1 1 1 1 1 1 1 1 1 1 1 1 0.005 0.000 r -0.005 -0.010 0.0 0.2 0.4 0.6 0.8 Y/rad 0.0 0.2 0.4 0.6 0.8 ylrad Fig.8. Fractional density change as a function of molecular tilt angle for monolayers with c2(0) = -800 A, (-), -600 A, (. . . - .), and -400 (---). ( a ) model I , ( b ) model 11.226 - c ; M % L- 0 . i%. 5 Q -5 Langmuir Monolayers I I I I I I I I 1 1 1 1 I l l I I - 5 - ( b ) - - I I I I I I I I I l l 1 I l l I l l 1 I I I I I l l 1 I I I I 5 - E I l l 1 I I I I I I I I I I I I 0.0 0.2 0.4 0.6 0.8 ylrad Fig. 9. Changes in grand potential of monolayers with Fz(0)= -600 A' (-), -50 A' (- - -), -15A3 (---),andOA3 ( - - . . . ) a s t h e y t i l t (a)alonga,+a,and(b)alonga,-a,. ion that lifts the symmetry of the system. As to the conjecture, referring to observation (8) listed in section 2, we hypothesize that in the lowest-pressure linear portion of the monolayer isotherm, system I1 consists of islands of molecules ordered in the distorted hexagonal structure with tilt angle corresponding to the value when the area per molecule is unconstrained.Perhaps this conjecture also applies to observation (3) of section 2. The electron microscopic evidence for the existence of islands in the transferred monolayers of C,,H35COzH'2 is compatible with this conjecture. However, it must beZ-h. Cai and S. A. Rice 227 0.0 5 -0.2 \\ -0.2 0.0 0.2 0.4 0.6 0.8 y l r a d Fig. 10. Fractional change in density of monolayers with z2(0) = -600 A’ (-), -140 A’ ( * - * -), -50 A’ (- - -), -15 A’ (---), and 0 A’ (---) when the molecules tilt ( a ) along a, + u2 and ( b ) along u, - u2.emphasized that it is not known if the ‘island phase’ with ordered islands is an equilibrium state of the monolayer. Even if it is an equilibrium phase the analysis described in this paper can only hint at its existence and is inadequate to predict its occurrence, because the ‘island phase’ is discontinuous in space, whereas the density functional formalism applies to inhomogeneous but continuous systems. This research was supported by a grant from the National Science Foundation.228 Langm u ir Monolayers L u Q 0 2 4 6 8 AA/A2 0 2 4 6 8 AA/A2 Fig. 11. Change in grand potential of moonolayers with ?,(O) = -600 A' (-), -350 A' (. - * - .), -140 A3 (- * -), -50 A3 (- - -) and -15 A3 (---) versus the change in effective area occupied by molecules tilting as in ( a ) model I and ( b ) model 11.References 1 G. L. Gaines, Insoluble Monolayerrs at Liquid-Gas Interfaces (Interscience, New York, 1966); W. D. 2 G. M. Bell, L. L. Combs a n d L. J. Dunne, Cbem. Rev., 1981, 81, 15; A. Caille, D. Pink, F. d e Verteuil 3 W. C. Marra, P. Eisenberger and A. Y. Cho, J. Appl. Phjx, 1979, 50, 9J7. 4 R. Friedenhans'l, S U T - Sci. Rep. 1989, 10, 105. 5 S. Barton, B. Thomas, E. Flom, S. A. Rice, B. Lin, J. B. Peng, J . B. Ketterson a n d P. Dutta, J. Chem. 6 B. Lin, T. M. Bohanon, M. C . Shih a n d P. Dutta, submitted to Pbys. Rev. Lett. 7 K. Kjaer, J. Als-Nielsen, C . A. Helm, P. Tippman-Krayer a n d H. Mohwald, J. Pbys. Cbem., 1989, 93, 8 S. G. Wolf, M. Deutsch, E. M. Landau, M. Lahav, L. Leiserowitz, K, Kjaer and J. Als-Nielsen, Science, 9 T. M. Bohanon, B. Lin, M. C . Shih, G. E. Ice a n d P. Dutta, in press. Harkins, The Physical Chemistry of Surface Films (Rheinhold, New York, 1952). a n d M. J. Zuckermann, Can. J. Phys., 1980, 58, 581 Phys., 1988, 89, 2257. 3200. 1988, 242, 1286.Z-h. Cai and S. A. Rice 229 10 B. Lin, J. B. Peng, J. B. Ketterson, P. Dutta, B. N. Thomas, J. Buontempo and S. A. Rice, J. Chem. Phys., 1989, 90, 2393. 1 1 B. N. Thomas, B. Lin, S. A. Rice and P. Dutta, work in progress. 12 N. Uyeda, T. Takenaka, K. Aoyama, M. Matsumoto and Y. Fujiyoshi, Nature (London), 1987,327,3 19. 13 M. Maroncelli, H. L. Strauss and R. G. Snyder, J. Phys. Chem., 1985, 89, 4390; J. Chem. Phys., 1985, 14 M. Maroncelli, Ph.D. Thesis (University of California, Berkeley, 1983). 15 T. Kawai, J. Umemura and T. Takenaka, Chem. Phys. Lett., 1989, 162, 243. 16 J. L. Lebowitz and J. K. Percus, J. Math. Phys., 1963, 4, 116, 248; F. H. Stillinger and F. P. Buff, J. Chem. Phys., 1962, 37, 1 ; D. Chandler, J. D. McCoy and S. J. Singer, J. Chem. Phys., 1986, 85, 5977. 17 Z. Cai and S. A. Rice, manuscript in preparation. 18 S. Shin and S. A. Rice, J. Chem. Phys., 1990, 92, 1495. 82, 2811. Paper 9/05195C; Received 6th December, 1989 Note added in prooj Professor M. Deutsch of Bar-Ilan University has informed us of new measurements of the properties of System IV, which is inferred that the tilting of the molecules increases as the area per molecule increases, just as in the other systems cited.

ISSN:0301-7249    

DOI:10.1039/DC9908900211

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Faraday Discuss. Chern. Soc., 1990, 89, 231-245 Structure of Surfaces and Interfaces as studied using Synchrotron Radiation Liquid Surfaces P. S . Pershan Physics Department and Division of Applied Science, Harvard University, Cambridge, M A 02138, USA The use of specular reflection of X-rays to study the structure of the liquid/vapour interfaces along the direction normal to the surface is described. If RF(6) is the theoretical Fresnel reflection law for X-rays incident on an ideal flat surface at an angle 8, and R ( 8 ) is the measured reflectivity from the true surface, the ratio R(B)/R,(B) is a measure of the electron density along the surface normal; i e . where pCn is the electron density far from the surface, d ( p ( z ) ) / d z is the gradient of the average electron density along the surface normal and Qz = ( 4 7 r / A ) sin ( 6 ) .For simple liquids p&'d(p>/Jz == [1/J(2.rr(r2)] exp (-z2/2cr2), and R(6)/RF(6) =exp (-Q2cr2), where cr2 is dominated by the mean-square average of thermally excited fluctuations in the height of the surface. For liquid crystals and for lyotropic micellar systems temperature-dependent structure in R (6) is due to surface-induced layering in ( p ( z ) ) . Other experimental results from thin layers of liquid 4He and monolayers, of amphipathic molecules on the surface of H 2 0 will be described. The possibility of complementing specular reflectivity measure- ments of surface roughness by studying diffuse scattering at small angles off of the specular condition will also be illustrated with results from the H 2 0 surface.Although X-ray specular reflection from surfaces was observed over sixty years ago'-4 practical application to the characterization of surfaces has only been done r e ~ e n t l y . ~ The purpose of this manuscript is to review some of the fundamental principles of the technique and to report some of our recent results on liquid and solid surfaces. In addition we will also discuss related experiments in which diffuse scattering is observed at small angles from the specular condition. The latter can be used to study structure within the plane of the surface. The basic idea for specular reflectivity is the recognition that even at X-ray wavelengths one can introduce a macroscopic dielectric constant to describe the average properties of the electromagnetic waves in materials: where p is the electron density in the material, A is the X-ray wavelength ( i e .A0/27r = c ) , m and e are the electron mass and charge, respectively, and re is the classical radius of the electron.? Neglecting polarization effects, which are not significant at small angles, ~ = 1 - 4 ~ p e * / m w ' = 1--preA*/T ( 1 ) + This form neglects both absorption and dispersion. The effect of dispersion can be accounted for if the electron density p = ( I / V ) C, 2, is replaced by peq = (1/ V ) 1, f ; ( O ) , where Z, is the number of electrons on the jth atom, f , ( O ) is the real part of the atomic scattering factor of the jth atom in the forward direction, and the sum { j } includes all atoms in the volume V. For most cases p = p e q . The effect of absorption is included by setting E " = ( A / 2 7 r ) p , where p - ' is the X-ray decay length of the material for power.23 1232 Structure of Surfaces and Interfaces the classical result for the reflection coefficient of an electromagnetic wave incident at an angle 8 ( i e . 8 = 0 is parallel to the surface) from an ideal flat interface between vacuum ( E = 1 ) and material of relative permittivity E is: sin ( e ) - J [ E -COS* ( e ) ] sin ( 8 ) + J[ E - COS’ ( e ) ] RF(0) = * There is a critical angle 8, = cos-’ ( E ) = J( preA2/ T ) such that for 8 d 8,, RF( 0 ) = 1 and for O w ? , , RF(8)=(8,/28).4 For water, 8,=0.152” when A = 1.54w. The mechanism for characterization of the structure of non-ideal surfaces, along the normal direction, depends on analysis of deviations between the measured reflectivity R ( 8) and the ideal, or Fresnel, reflectivity RF( 8) over a range of angles 8 - A/(2AL), where AL is one measure of the spatial resolution.Since RF( 8) falls as the fourth power of the incident angle, meaningful chacterization of many surfaces require measurements over a very wide dynamic range of reflectivities, typically 10(9-10), and this is the primary reason why synchrotron radiation is required. Theory for Non-ideal Surfaces Specular Reflectivity When 8 >> 8, the reflection from a real surface is most easily obtained by summing over the scattering from infinitesimally thin layers Sz at some distance z from the average location of the interface, which is taken to be the x-y plane at z=O.For incident wavevector ko the amplitude of the scattered wave at a distance R from the sample, in a direction defined by k”, is approximately given by dx dyp(x, y, z) exp {i[k”-ko] - r } . R - r,Sz EO (3) where Q = k” - ko. Since the condition that Q.x = Q,. = 0 corresponds to the incident and reflected angles being equal and in the same plane; this term can be identified with the contribution of the thin layer to the specularly reflected signal. The term proportional to [ p ( x , y, z) -(p(z))] gives rise to diffuse scattering that will be discussed below. When 8 >> 8, a useful expression for the ratio of the specularly reflected signal to that from an ideal surface, is obtained by the following steps:‘,’ ( 1 ) Integrate eqn (4) from z = -a to +a by parts to express the answer in terms of d(p(z))/dz.(2) Square the result and use of the standard interpretation to substitute [47r*S( QY)S( Q,,)]’ = A,,.[47~’8( Q,-)S( Q,)], where A,, is the illuminated cross-sectional area of the interface. (3) Calculate the detected power by integrating clEs12/4~ over the area of the detector. Since the solid angle of the detector can be expressed as, dCl= ( A / 2 ~ ) ~ ( 1 / 8 ) dQx dQ,, this eliminates the 8- functions. (4) Normalize the scattered intensity to the incident power 8A,,.cl E01*/4r. Eqn ( 5 ) follows if one uses the asymptotic form RF( 8 ) == ( 8,/28)4 with Q_ = ( 4 ~ / A ) 8 . There are a large class of problems, some of which will be illustrated below, for which R ( 8 ) / R , ( 0 ) = 1 for small 8.In these cases eqn (5) can be used for all 8 so longP. S. Pershan 233 as Qz corresponds to the value inside the material; i.e. Qz == (47~/A)d( O2 - 8;). A different approach, that allows for solutions when R( 8)/RF( 8 ) # 1 for small 8 is to solve the one-dimensional wave-equation where Qc= (47~/A)8,, with suitable boundary conditions. For 8 >> 8, the results are identical to those of eqn (5) regardless of whether or not R ( 8 ) # RR( 8) for small 8. Diffuse Scattering Diffuse scattering is observed when the wavevector difference Q has a non-vanishing component q = ( Qx, Q),) parallel to the surface. For an incident angle 8, and detected radiation that makes angles 8’ with the surface and with the plane of incidence Qx = ( 2 ~ / h ) cos ( 8 ’ ) sin ($) Qy = ( 2 ~ / A)[ cos ( 8 ) - cos ( 8 ’ ) cos ($)I == ( 2 7 ~ / A )[ 1 - 02/2 - ( 1 - 8”/2) cos ($)I Qz = (27~/h)[sin (8’) +sin (O)] = ( 2 7 ~ / h ) [ 8’+ 81.(7) If the mean-square variation in the height of the surface inhomogeneities is small compared to 1/ Qz one can define a surface density ps(x, y) and make the approximation, [p(x, y, z ) - ( p ( z ) ) ] = p,(x, y ) 6 ( z ) . The differential cross-section for surface diffuse scat- tering can then be expressed as w here839 T( 8 ) = (26/ e c ) ’ J [ F( 8 ) 1. (9) The surface enhancement factor T ( 8) occurs because scattering from surface inhomogeneities is proportional to the square of the total surface field, not the square of the incident field. For 8 d 8, the amplitudes of the reflected and incident fields are equal and because the phase of the reflected wave varies from T, when 8 = 0, to 0 when 8 =: 8,, the total field at the surface varies from zero to twice the incident field for 8 = B C .The function T ( 8 ) , which is proportional to the square of the field, varies from 0 to 4, as 8 increases from 0 to 8,, and then falls to unity for 8 >> 8,. The factor T ( 8’) appears because of a similar effect in the coupling between the surface currents and the scattered fields, and the angular dependence of these two factors helps in distinguishing surface scattering from other diffuse scattering processes.I0 The cross-section for diffuse scatter- ing can be expressed in term of height fluctuations q(x, y) of the surface by the substitution (psps(x, y)) = p 2 ( q q ( x , y ) ) into eqn (8).Experimental The main features of the experimental geometry for studying the liquid/vapour interface are illustrated in fig. l.11712 The incident beam is deflected downward by an angle 8 and a detector, of height h and width w is located a distance L from the sample surface. In order to insure that the incident beam strikes the centre of the sample for all 8, it is on an elevator such that its vertical position can be continuously adjusted. The detector can be moved both vertically, to vary 8’, and along an arc to vary $. In all of our experiments the incident beam is highly collimated such that the spread in incident wavevector k” is negligible. The height of the incident beam hO, however, is not negligible234 Structure of Surfaces and Interfaces Fig.1. Schematic illustration of the geometry for X-ray scattering study the liquid/vapour interface. The detector slit, of height h and width w, is shown in the position for detection of the specularly reflected beam ( 0 = 8’ and II, = 0). and for small angles 8 the ‘footprint’ of the beam on the horizontal interface can be large. Verification of the alignment of beam and sample positions is achieved by measuring the specularly reflected intensity as a function of detector angle 8’, for different vertical displacements of the sample. Both the intensity and shape of the signal are constant for the range of sample positions where the beam is intercepted by a flat portion of the sample. The height h and the width w of the detector slit are set in order to intercept all of the specularly reflected signal fully.When the surface is sufficiently flat this is identical to the physical size of the incident beam ko at the detector position. For specular reflection studies the angular resolution of the spectrometer, A8, is determined by a convolution of the angular distribution of the incident beam and the surface normal. In contrast, for diffuse scattering measurements and practical slit dimensions, the appropriate resolution is determined by a convolution of the detector size with a suitable projection of the illuminated cross-sectional area of the sample. If the height h of the detector is larger than the height of the incident beam, and if the spectrometer is near to the specular condition (8’- 8 and + = 0 ) the projection of the resolution (for diffuse scattering) on the horizontal liquid surface has full widths.where L is the distance from sample to detector. The usual situation on scanning either 8’ or t,h is that the measured intensity I ( 8 ’ , t,h) has a sharp central peak at the specular condition and a broad flat background off of the specular. Specular reflection R ( 8 ) is then taken to be the difference between the signal in the specular position and the diffuse scattering background at small values of either 8’-8 or +. For some surfaces the background depends on the offset and it is necessary to develop an extrapolation procedure suitable to the particular surface. ’’ Results Water Specular Reflectivity / Roughness Specular reflectivity data from the free surface of H 2 0 , as shown in fig.2 ( a ) , is typical of the reflectivity from a number of surfaces.’ There is a small region for 8 < 8, where the reflectivity is essentially 100% followed by a rapid fall, shown here over eight ordersP. S. Pershan 23 5 1 o5 1 o3 10’ h 9 a: lo-’ 1 o - ~ 1 o - ~ 1 i a: s! \ 0.1 0.0 2.90 2.75 2.60 “b, 0 .15 .3 .45 Q</A-? 2.45 \ 0 .1 .2 .3 .4 .5 .6 .7 1 Q,/A-‘ s 1 it size/ mm Fig. 2. ( a ) Measured reflectivity from H 2 0 with a detector of height h = 2.0 mm at 600 mm from the sample.13 The solid line is the best fit of the theoretical form given by eqn ( 1 1) to the data. Error bars that are not shown are smaller than the size of the symbol. ( b ) The logarithm of the same data as in ( a ) plotted versus of.The slope of the solid line indicates a value of u2 = (2.70* 0.03 8, j2. ( c j Comparison between the slope of data like that shown in ( b ) for detector heights h = 0.8, 20.0 and 5.0 mm and the theoretical result for capillary wave roughness, eqn (15). of m a g n i t ~ d e . ~ ~ ’ ~ ” ~ As can be seen from fig. 2( b ) , in which the same data are normalized to RF( 0) and plotted as log, [ R ( 0)/ RF( O ) ] uersus (I:, the data are essentially of the form where cr2 = (2.70 f 0.03 A)2. This data were taken from the surface of H 2 0 on a Langmuir trough” in which the surface tension was monitored in situ to be 72.5 * 0.4 dyn cm-I, the detector height was 2.0 mm and the distance to the sample was ca. 600 mm.? It is straightforward to demonstrate that this form is consistent with the profile ( p ( z ) ) / p = [ 1 / d ( 2 n c r 2 ) ] exp ( - z 2 / 2 u 2 ) by substitution into eqn (5).Alternatively, one can numeri- cally integrate the data to obtain the Patterson function:I6 with Qz = (47r/h) sin ( O ) , and demonstrate directly that Z ( s ) =. [ 1 / d ( 4 n u 2 ) ] exp ( -s’/402). It is interesting to compare this measurement with the reflection predicted by assuming Taking y the water surface is made rough by thermal excitation of capillary + A previously reported larger value of a’=(3.3*O.l A ) was reported for a H,O surface in which the surfaced tension was not monitored;x however, an independent measurement on a clean surface essentially agrees with the present v a 1 ~ e . I ~236 Structure of Surfaces and Interfaces to be the surface tension and ~ ( x , y ) to be the height of the water surface at some point ( x , y ) the energy per unit area of a rough surface is given by: where g is the acceleration of gravity.From standard statistical physics the mean square value of the height fluctuations: where k i = pg/ y = (0.36 cm-’)’ and Qmax is an upper cut-off that is necessary in order to fix the number of thermal surface modes. In analogy with the Debye theory of heat capacity one might guess Qmax - v/molecule radius = ( T/ 1.93 A) for water. Taking y =: 73 dyn cm-’ this integrates to ( ~ ( x , y)’) = (3.98 A)’ or nearly twice the measured slope. The origin of this discrepancy is that for a finite-size detector slit the spectrometer is unable to distinguish between ‘true specular reflection’ and the sum of specular reflection and diffuse scattering at small angle to the specular reflection. Stated another way, for a rough surface R ( 8 ) is less than RF(8) because of destructive interference between signals reflected from different heights ~ ( x , y ) f ~ ( x ’ , y’).Since a spectrometer with finite resolution cannot detect interference between points that are too far apart, long-wavelength height variations do not affect the measured reflectivity. The measured slope should actually be compared to where A,, is a circular area in the Q.y-Q,. plane with outer radius Qmax and a rectangular inner cutout with dimensions determined by the spectrometer resolution, eqn (10). The minimum dimensions of AAQ are much larger than k, and if AQ, >> AQ,.the slope approximately given byR Fig. 2(c) shows the comparison of the best fit values of (T, calculated by numerical integration of eqn (15) over the measured resolution function for data taken with three different detector heights h.l3 The only adjustable parameter in the fitting procedure was the value of Qmax = ( v / 1.4 A) that was common to all three fits. This is slightly larger than the guess of ( 4 1 . 9 3 A); however, in view of the naive nature of the theory the difference is not serious. In particular X-ray measurements over the accessible range of angles cannot distinguish between one particular value of Qmax for an interface that is locally sharp, and a smaller value of Qmax for an interface that locally has a more gradual profile.Diffuse Scattering According to this model R ( 8 ) / RF( 8) < 1 because thermally excited capillary waves scatter radiation away from the specular condition. Fig. 3 illustrates diffuse scattering data from the surface of H 2 0 that was taken by fixing the incident angle and sample position and scanning the detector angle 8’ in the plane of incidence, i.e. $ = 0.” The peak at 8 = 8’ is the specular signal and the weaker peaks at 8’= Oc correspond to the structure of T ( 8 ’ ) discussed above. The solid lines through the data are calculated by averaging the cross-section [eqn (S)] over the angular distribution of the incident beam10' 1 oo L 0 E * .- 2 10-1 L 0 a E 0 UY * --. ,x .- v1 c C Y .- I o - ~ 1 o - ~ P. S. Pershan 1 I 1 I I I ~(=0.64" I I 1 0 0.2 0.4 0.6 3.8 1.0 PI" 237 Fig.3. Scattered intensity from the surface of HzO, in the plane of incidence and as a function of detector angle 8' for incident angles 8 = 0.64 and 0.96"." The peaks at 8' = 8, == 0.13" are due to the surface scattering enhancement factor, the peaks at 8'= 8 are the specular reflectivity signals. The solid line is the theoretical prediction calculated with no signijicant adjusrable parameters. and integrating over the detector resolution. The only adjustable parameter is a small constant background, of the order of 10% of the peak at 8'= 8,. Agreement between data and theory for both the diffuse scattering, and the resolution dependence of R ( 8)/ RF( 8) confirms the role of thermally excited capillary waves and demonstrates the quantitative reliability of the experimental technique.Insoluble Monolayer on Water These two previous results for H20 buttress the hope of being able to make quantitative interpretation of R( 8)/RF( 8 ) data on more complex surface structures. One example of this is illustrated by the data in fig. 4 ( a ) for the ratio R(8)/RF(8) of a monolayer of Lignoceric acid (CH3(CH2)22COZH) on water at pH 2, using HCI, at different surface pressures.15 This data, like the above data for H20 was taken on a specially constructed trough, to be described elsewhere, in which the surface tension could be continuously monitored. Fig. 4 ( 6 ) illustrates details of the profiles that gave the best fit to the data when substituted into eqn ( 5 ) . Particularly interesting is the fact that as the pressure increases the position of the local maximum moves away from the interface to the vapour, implying that the distance between the acid head group and the alkane/vapour interface has increased.Interpretation of these specular reflectivity results can be aided by recent surface scattering studies on the in-plane structure of monolayers. A number of different groups have been applying this technique, in which the incident angle 8 is adjusted to be slightly23 8 1.25 1.20 Structure of Surfaces and Interfaces - - -- - 1 oc 10 ' lo-* 1 o - ~ 1 o - ~ 1 o - ~ 1 o-6 L a: a: 1 I I I I 35 -\ 0.2 0.4 0.6 Q+-' ?r = 3.5 71 = 1.2 71 = 9.4 n = 9.8 12.5 0.95 I I I 10 15 20 25 30 35 40 ZI A Fig. 4. ( a ) The ratio R( B)/R,( 0 ) for different surface pressures (dyn cm-') of a Lignoceric acid (CH3(CH,),,C02H) monolayer on water.The solid lines correspond to the R ( O ) / R , ( 0 ) predicted by best fits of real space density models. ( h ) shows details of the electron density profiles corresponding to the best fits in ( a ) . The origin of the abscissa ( z = 0) is defined by the alkane/vapour interface. The data were recorded at room temperature and the subphase was at pH2.P. S. Pershan 239 1 o2 10' 1 oo lo-' tY --. 1 o - ~ 1 o - ~ 1 o-6 1 o - ~ bE---- 9CB 1 OCB I ~ I 1 I Z I I I 0.50 0.75 1.00 1.25 1.50 Q= I 00 Fig. 5. The ratio of R ( O)/ RF( 0) for four different liquid-crystal systems: ( a ) SOCB, ( b ) 9CB, ( c ) a mixture (9CB),_,(lOCB), with x=0.15 and ( d ) 10CB. !n all cases the temperatures are ca. 0.05 "C above the transition to the smectic-A phase.less than t?,, insuring that the incident beam penetrates only evanescently into the bulk, i.e. intensity- exp ( - K Z ) , where K = (27~/A)d( Of - t?2).15718-21 When the surface monolayer is crystalline, Bragg-like scattering from surface monolayers has been observed at angles I) == sin-' ( h / 2 a ) , where a 2 4.3 A is the lattice spacing of the two- dimensional surface crystal. By monitoring the scattered intensity as a function of the 8' it is possible to demonstrate the existence of surface phases in which the orientation of the alkane chains with respect to the surface normal changes. These results, clearly that most of the structural features of crystalline surface monolayers can profitably be studied using X-ray techniques.Liquid Crystals The two examples discussed thus far dealt with systems in which the surface structure is confined to distances no more than one or two molecular lengths from the interface. Liquid crystals represent a class of systems for which the surface can induce structure that penetrates hundreds of molecular lengths into the bulk. Fig. 5 displays data showing the ratio R ( t?)/R,( 8 ) as a function of Qz/Qo, where Qo = ( 2 n / D ) and D is the smectic-A layer spacing for the respective molecules, octyloxycyanobiphenyl 80CB, nonyl- cyanobiphenyl 9CB, a mixture (9CB), ,( lOCB), with x -0.15 and 10CB. In all cases the temperature is ca. 0.05 "C above the transition to the smectic-A phase. Both 80CB and 9CB have second-order phase transitions from the nematic to smectic-A phases, in which critical smectic fluctuations in the nematic phase have characteristic lengths along the layer normal (ti/) and parallel to the layers (tl) that diverge as the transition is approached; e.g.,$I/, - ( T - TNA/ TNA) - v / / , ~ where TNA is the nematic to smectic-A transition temperature. Analysis of the temperature dependence of the shapes of the peaks in R ( B ) / R , ( 0) at QZ =: Qo establish that surface induces smectic order in the nematic phase, and that this order penetrates into the bulk a distance that is equal to240 Structure of Surfaces and Interfaces 3.5 y ' " ' ' ' ' ' ' ' ' 1 0.08 v) Y .- G 1 . x 01 C 0) c c) .- c) .- 2.5 2.0 1.5 1 .o 0.5 0- h .z 0.06 1 -E 2 0.04 x &- vl C .- 0.02 .- 0 Fig. 6.Specular reflectivity as a function of temperature for Qz = (27r/D) for: ( a ) IOCB, ( b ) llCB, (c) 12CB, ( d ) 120CB, ( e ) 140CB and (f) 160CB. [l,.22-24 The physical significance of this is that although the symmetry of the surface forces local smectic order, the penetration into the bulk is determined by the bulk susceptibility. This type of behaviour, in which the thickness of the surface induced phase diverges in proportion to the critical divergence of the bulk correlation length is termed critical a b ~ o r p t i o n . ~ ~ . ~ ~ The situation is slightly different for the mixture of (9CB)o.ss(10CB)0,15 which has a first-order transition to the smectic-A phase. Analysis of this system indicates that the surface-induced order penetrates into the bulk from 2 to 4 times further than the bulk critical length depending on the temperature.12,27 Since the transition from the nematic to smectic-A phase is first-order the critical length does not diverge and the 'wetting' of the surface by the smectic-A phase is incomplete.25726 The wetting for x =0.15 is larger than the wetting for a mixture with x = 0.30 and we suspect that there is a true wetting transition as x approaches the tricritical point at x = 0 for (9CB),-,( lOCB), mixtures. The case of lOCB is different in that that system undergoes a first-order transition from the isotropic to smectic-A phases and there is no evidence for critical smectic fluctuations in the isotropic phase. The data clearly indicate that even in the isotropic phase the surface has induced smectic order.The extent of this order, and the manner in which it develops with temperature is illustrated by the data in fig. 6, which displays the reflected intensity at Q- = Qo as a function of t = ( T - TIA)/ TIA, where TIA is the isotropic to smectic-A transition temperature, for six different liquid crystals. 12,27,28 Acalysis of the angular dependence of R ( B)/R,( 0 ) confirms that each step corresponds to an increase in the number of smectic layers. On cooling 12CB there is a surface transition to one layer at a reduced temperature t = 0.04 or T - TIA = 13 "C followed by a successive transition up to ca. six layers, after which the growth appears continuous. The evolution for llCB has fewer discrete transitions, and the evolution for lOCB appears continuous.There are two important things to note regarding these data. First, mixtures in which the concentration 9CB is equal, or greater than that of 10CB, have a small temperature region of nematic phase between the isotropic and smectic-A that shrinks to zero for (9CB),--,(lOCB), with ~ ~ 0 . 4 5 . ~ ~ Thus lOCB is relatively near to a region of the phase diagram in which the nematic order is stable, while 11CB and 12CB are more distant. The differences in the temperature evolution of 10, 1 1 and 12CB, with relatively sharp layer transitions more prominent for the longer homologues, suggest that the width of the physical interface between the surface induced smectic region andP. S. Pershan 241 the bulk isotropic is broadened out, or made more diffuse by the proximity of the nematic phase.According to this interpretation the proximity of the nematic phase stabilizes a region, between the surface smectic and the bulk isotropic, that has well developed molecular orientational order but only partial smectic order.3o73' With increas- ing distance from the part of the phase diagram in which the nematic order is stable, as in going from lOCB to llCB and 12CB, this effect becomes weaker and the profile from smectic to isotropic becomes sharper. A similar effect is shown for three homologues in the nOCB series; 120CB ( d ) , 140CB ( e ) and 160CB ( f ) . A second interesting feature of these data is that although one might argue from the data in fig. 6(a)-(c) that in the nCB series the thickness of the surface smectic layer diverges with decreased reduced temperature, indicative of complete wetting of the isotropic surface by the smectic-A phase, it is absolutely clear that the wetting by 160CB is not complete.? The surfaces of these systems exhibit an interplay between the surface-induced nematic, or molecular orientational order, and the smectic- A, or positional order.In spite of considerable effort the critical properties of the second-order transition from the nematic to smectic-A phases in the bulk are not understood and one line of speculation attributes this to an incomplete understanding of the interplay between these two order Hopefully, the surface problem will present new insights that might guide theoretical development of theories for the bulk transition. Lyot ropic One other type of liquid/vapour interface that we have studied is that of a micellar mixture of caesium perfluoro-octanoate(CsPF0 and water.34 For a narrow range of temperatures these mixtures form lyotropic liquid crystals in which oblate micelles orient to produce a uniaxial nematic phase.As the temperature is lowered the system undergoes what appears to be a second-order transition to a smectic-A phase; however, the question of whether the smectic-A phase consists of layers of oblate micelles, or whether it consists of bilayers of amphiphillic molecules separated by layers of water is not yet Fig. 7( a ) shows data for R ( 8 ) / R , ( 8) for a mixture containing ca. 60 wt YO of water at temperatures 2 and 7 "C above TNA. The first of these is in the nematic phase and the second-is in the isotropic- however, they both have peaks at QZ == 0.1 17 A that correspond to 2 n / ( 5 4 A), where 54 8, is approximately equal to the layer spacing in the bulk smectic phase.Furthermore, in both cases the peaks have lineshapes with a pronounced minimum at the low-angle side. There is not sufficient space to present a full analysis of these lineshapes; however, the principal conclusion can be illustrated by the model density profile ( ~ ( z ) ) , shown in fig. 7 ( b ) , that was used to calculate the solid line running through. the 2 "C data in (a).36 First, the electron density oscillates between a maximum value that is ca. 85% of the electron density of bulk fluorocarbon (i.e. 1.81 x electron density of water) and th,e electron density of water.The full width of the surface layer is very close to the 12.5 A that corresponds to the length of the fully extended CsPFO molecule and the full width of the electron density maxima below the surface are about twice that width, or 25.0 A. Taken together these indicate that surface consists of a relatively dense monolayer of CsPFO, followed by CsPFO bilayers, all of which are separated by layers of water. Since the maximum density of the subsurface bilayers is the same as the maximum density of the surface monolayer we believe that they are most likely intact bilayers, and not layers of positionally correlated micelles. While this does not exclude the possibility that the bulk smectic consists of positionally correlated micelles, we think that is unlikely.? Ocko el argued that the wetting for 12CB was incomplete on the basis of more detailed lineshape analysis for T + T,, .242 10 1 - 0.1 Structure of Surfaces and Interfaces - - 100 I I I I I I I A 1.75 B i P) $ Q -.. t.1 h 1.50 1.25 1 .oo 0.75 Q 0.50 0.25 0 w 0.01 ' I I 1 I L 1 I 1 1 J 0 0.1 0.2 0.3 0.4 -50 0 50 100 150 200 Q,/A- ' z / A Fig. 7. R ( O ) / R , ( 0) from the surface of a mixture of CsPFO and H,O (ca. 60 wt % H20) in the nematic phase at T - TNA z 2 "C and in the isotropic phase at T - TNA = 7 "C. ( a ) T - TNA -- 2 "C, ( b ) T - T = 7 "C. The solid line through the nematic data is the ratio R ( O)/R,( 0) predicted from the electron density model illustrated in B. Secondly, the similarity between the shapes of the two peaks, at T- T N A z 2 "C in the nematic phase, and T - T N A =: 7 "C above T N A in the isotropic phase, together with further data not included here indicates that although the near surface region is relatively insensitive to the equilibrium bulk phase, even in the isotropic phase the surface induced order extends a number of layers below the surface. This penetration is temperature dependent, and as T N A is approached other data not shown here indicate penetration to distances at least 100 layers (i.e. 5000 A).The fact that the 2 "C peak is sharper, and more intense, is a consequence of this. The temperature dependence of these surface peaks provide a strong indication that the bulk nematic to smectic-A transition is truly second-order. Liquid 4He The last example of liquid surfaces to be described is illustrated by preliminary results of X-ray reflectivity from the surface of liquid 4He.37 Aside from the non-trivial cryogenic problems that must be solved in order to study this interface, the fundamental difficulty has to do with the fact that the electron density of 4He is low, i.e.ca. 11% of the electron density of H20. Since the reflectivity varies as the square of the electron density this means that the reflectivity from "He/vapour interface should be ca. 1% of that of the H,O/vapour interface. Even with the largest possible synchrotron intensities this weaker signal, and its accompanying small value for 8,, would made the experiment very difficult. To circumvent this problem we elected to study thin layers of 4He physisorbed onto the surface of a flat Si/SiO wafer. A general expression for the ratio of the reflectivity from an 4He layer of thickness D on a substrate to the reflectivity from an ideal substrate with the electron density of Si can be represented as where a ( Q = ) and P(Q=) correspond to the amplitudes of the signal reflected from the 4He/vapour interface and the 4He/Si interface.At small angles a ( 0 ) =: ( p H e l p s i ) and0.9 ii 5 0.8 & 0.7 0.6 P. S. Pershan I - - - - I I 3.5 - 0.0'30 0.075 0. 100 0. 125 0. 150 0. 175 0.200 Qz/A-' 243 Fig. 8. Preliminary measurements of R(O)/R,(O) for a 1908, layer of 4He adsorbed on a flat wafer of Si/SiO at 2.35 K. p(0) = 1 - a(O), such that with a ( 0 ) =: 0.05 the cross-term 2ap cos (Q,D) = 0.1. The predicted reflectivity oscillates with a period of AQz = 277/ D and a peak-to-peak ampli- tude that is ca.20% of the mean reflectivity. This is a relatively large effect and easy to observe. Fig. 8 shows preliminary data from a 190A thick layer at a temperature of 2.35 K that was measured using a 12 kW rotating anode X-ray source. Both the amplitude and the period of the oscillations are within a few percent of the theoretically expected values. The overall decay with increasing Qz reflects the roughness of the bare Si/SiO substrate. More specifically, since both the 4He/vapour and the 4He/Si interfaces have finite widths, both a ( Q z ) and p ( Qz) must decrease with increasing Qz. Using synchrotron radiation it should be able to follow the interference oscillations over at least four times as many periods as for this data set. From the variation of their amplitudes with angle we expect to determine the width of the 4He/vapour interface as a function of both temperature and film thickness. This is a problem that has received very much theoretical a t t e n t i ~ n .~ ' Summary The main goal of this paper has been to present the underlying concepts behind the use of X-ray specular reflectivity to study liquid surfaces. In fact, these same ideas carry over to the study of solid surfaces and, in some cases, such as for the study of buried solid-solid interfaces, X-ray reflectivity may facilitate measurements that are not practical by other techniques. '6*39,4" The microscopic structure of liquid surfaces, on the other hand, cannot be studied by very many techniques, and we have tried to illustrate by example some of the types of measurements that can, and have been done. In almost all cases neutron scattering can be used in much the same way as X-rays to carry out similar studies; however, there are two main differences4' First, X-rays have the advantage that synchrotron sources provide many orders of magnitude larger incident flux, per solid angle than any conceivable neutron source.As a consequence, specular reflectivity of X-rays can be carried out over dynamic ranges of the order of 10'" or244 Structure of Surfaces and Interfaces larger, while for neutrons it is difficult to achieve a dynamic range of lo6. Since the spatial resolution of the reflectivity technique is directly related to the attainable range of QZ and since the reflectivity falls rapidly with increasing QZ this is a severe limitation on use of neutrons for certain classes of problems.The main advantage of neutrons derive from the fact that by substitution of deuterium for hydrogen it is possible to vary the contrast between different parts of organic fluids. For example, it is very difficult to do precise small-angle reflectivity studies of polymer conformation at the liquid/vapour interface for the purpose of characterizing the power-law dependence of the polymer density at large distance^.^*-^^ The difficulty arises primarily because the critical angle 8,, typically of the order of 0.15", corresponds to a Qz = 0.02 A-' in the vapour. As 8 OC refraction effects result in smaller values of Qz inside the material; however, since these are delicately dependent on both the direction of the incident beam and the orientation of the surface normal it is difficult to make quantitatively accurate measurements at values of QZ inside the material that are significantly smaller than ( 4 7 r / h ) 8 , .For neutrons, on the other hand, with a suitable mixture of protons and deuterons the value of 8, can be reduced to zero, and it is relatively easy to measure the specular reflectivity at angles that are much less than 0.15". In general, specular reflection using both neutron and X-rays are promising tech- niques for the study of liquid surfaces. They each have specific advantages and in many cases they compliment each other. The structure of the interface between a polymer solution and its vapour is just one example of a problem for which full understanding will surely require both types of measurements. This work was supported by the National Science Foundation through grants to the Harvard Materials Research Laboratory, NSF-DMR-88-12855 and NSF-DMR-86-14003. Research carried out at the NSLS, Brookhaven National Laboratory, is supported by the Department of Energy, Material Sciences and Division of Chemical Sciences under contract D E- AC 02 - 76C HOOO 1 6.References 1 J. A. Prins, Z. Phys., 1928, 47, 479. 2 E. Nahrig, Phys. Z., 1930, 31, 401. 3 H. Kiessig, Ann. Phys., 1931, 10, 769. 4 A. H. Compton and S. K. Allison, X-Rays in Theory and Experimentation (Van Nostrand, New York, 5 See the following brief review and the references therein: S.A. Rice, Nature (London ), 1985,316, 108. 6 P. S. Pershan a n d J. Als-Nielsen, Phys. Rev. Lett., 1984, 52, 759. 7 J. Als-Nielsen, Solid and Liquid Surfaces Studied by Sjvtchrotron X-Ray Dlfraction in Structure and Dynamics oj' Surfaces 11: Topics in Current Physics, ed. W. Schommers and P. van Blanckenhagen (Springer-Verlag, Berlin, 1987), vol. 43, p. 181. 8 A. Braslau, P. S. Pershan, G. Swislow, B. M . Ocko and J . Als-Nielsen, Ph-vs. Rev. A , 1988, 38, 2457. 9 S. K. Sinha, E. B. Sirota, S . Garoff and H . B. Stanley, Phys. Rev. B, 1988, 38, 2297. 1935). 10 R. S. Becker, J . A. Golovchenko and J . R. Patel, Phys. Rev. Letr., 1986, 50, 153. 11 J. Als-Nielsen and P. S. Pershan, Nucl. Instrum. Methods, 1983, 208, 545. 12 P.S. Pershan, J. Phys. ( P a r i s ) , 1989, 50, C7-1. 13 D. K. Schwartz, M. L. Schlossman, E. H . Kawamoto, G. J . Kellogg, P. S. Pershan and B. M. Ocko, Phys. Rev. A , 1990, in the press. 14 J . Daillant, L. Bosio, J . J. Benattar and J . Meunier, Europhys. Lett., 1989, 8, 453. 15 M. L. Schlossman, D. K. Schwartz, E. Kawamoto, G. J . Kellogg and P. S . Pershan, X-ray Rejlectivity of' a Long Chain Fatty Acid Monolayer at the Water/ Vapor Interface, Materials Research Society Meeting, Boston, MA, Nov. 1989. 16 I . M. Tidswell, B. M. Ocko, P. S. Pershan, S. R. Wasserman, G. M. Whitesides and J . D. Axe, Phys. Rev. B, 1990, 41, 11 11. 17 A. Braslau, M. Deutsch, P. S. Pershan, A. H . Weiss, J. Als-Nielsen a n d J . Bohr, Ph>*s. Reo. Letr., 1985, 54, 114. 18 S. G.Wolf, E. M. Landau, M. Lahav, L. L-eiserowitz, M. Deutsch, K. Kjaer a n d J . Als-Nielsen. Thin Solid Films, 1988, 159, 29.P. S. Pershan 245 19 S. G. Wolf, L. Leiserowitz, M. Lahav, M. Deutsch, K. Kjaer and J. Als-Nielsen, Nature (London), 1987, 328, 63. 20 P. Dutta, J . B. Peng, B. Lin, J . B. Ketterson, M. Prakash, P. Georgopoulos and S. Ehrlich, Phys. Rev. Lett., 1987, 58, 2228. 21 P. Dutta, K. Halperin, J. B. Ketterson, J. B. Peng, G. Schaps and J. P. Baker, Thin Solid Films, 1985, 134,5. 22 J . Als-Nielsen, F. Christensen and P. S. Pershan, Plrys. Rev. Lett., 1982, 48, 1107. 23 P. S. Pershan and J. Als-Nielsen, Phys. Rev. Lett., 1984, 52, 759. 24 P. S. Pershan, A. Braslau, A. H. Weiss and J. Als-Nielsen, Phys. Rev., 1987, 35, 4800. 25 M. E. Fisher, J. Chem. Soc., Faraday Trans. I , 1986, 82, 1569. 26 P. G. de Gennes, Rev. of Mod. Phys., 1985, 57, 827. 27 A. Braslau, Thesis (Harvard University, Cambridge, MA., 1988). 28 B. M. Ocko, A. Braslau, P. S. Pershan, J. Als-Nielsen and M. Deutsch, Phys. Rev. Lett., 1986, 57, 94. 29 J. Thoen, H. Marynissen and W. Van Dael, Phys. Rev. Lett., 1984, 52, 204. 30 J. V. Selinger, Phys. Rev. A, 1988, 37, 1736. 31 A. A. Chernov and L. V. Mikheev, Phys. Rev. Lett., 1988, 60, 2488. 32 T. C. Lubensky, J. Chern. Phys., 1983, 80, 31. 33 C. Dasgupta, Phys. Rev. Lett., 1985, 55, 1771. 34 N. Boden and M. C. Holmes, Chem. Phys. Lett., 1984, 109, 76. 35 M. C. Holrnes and J. Charvolin, J. Phys. Chem., 1984, 88, 810. 36 G. Swislow, D. Schwartz, P. S. Pershan, B. Ocko, D. Litster and A. Braslau, to be published. 37 L. Lurio, T. Rabedeau, I . Silvera and P. S. Pershan, to be published. 38 D. 0. Edwards, Physica, 1982, 109 & IlOB, 1531. 39 S. M. Heald, H. Chen and J . M. Tranquada, Marer. Res. SOC. SjJmp. Proc., 1986, 54, 165. 40 R. A. Cowley and T. W. Ryan, J. Phys. 0, 1987, 20, 61. 41 See, for example, the several papers in the Proceedings of the International Conference on Surface and Thin Film studies using Glancing-Incidence X-ray and Neutron Scattering, Marseille (France, 1989), ed. M. Bienfait and J. M. Gay; J. Phys. (Paris), 1989, 50, Colloq. 7. 42 R. Vilanove and F. Rondelez, Phys. Rev. Lett., 1980, 45, 1502. 43 D. Ausserre, H. Hervet and F. Rondelez, Phys. Rev. Lett., 1985, 54, 1948. 44 J. M. Bloch, M. Sansone, F. Rondelez, D. G . Peiffer, P. Pincus, M. W. Kim and P. M. Eisenberger, Phys. Rev. Lett., 1985, 54, 1039. Paper 0/00419G; Received 26th January, 1990

ISSN:0301-7249    

DOI:10.1039/DC9908900231

出版商:RSC    

年代:1990

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1990, 89, 247-258 GENERAL DISCUSSION Prof. R. H. Ottewill (University of Bristol) said: First, I would like to compliment Prof. Rice on his interesting treatment of a two-dimensional analogue of ‘hard-sphere’ liquid freezing to a solid phase. In the classical literature on monolayers of fatty acids it was concluded that at an area per molecule of 25 A’ the head groups are planar close-packed and as the surface pressure increased and the area per molecule decreased the head groups assumed a staggered arrangement. There is support for this view from neutron reflectivity experi- ments. Do these changes affect the arguments given in the paper? The paper also considers fluorocarbon chains, and an interesting question is the arrangement of the molecules in a mixed film of hydrocarbon and fluorocarbon chains.Can the theory predict whether mixing or phase separation will occur in such films and how this will depend on chain length? Prof. S. A. Rice (University of Chicago) replied: There are (at least) two observations associated with the staggering and nestling of adjacent amphiphile molecules in a monolayer. First, in several cases it has been shown that an amphiphile monolayer transferred to a solid substrate has an ordered structure with the chains tilted by an amount that corresponds to the best nestled fit of the nearest-neighbour all-trans chains; that angle is uniquely defined by the geometry of the all-trans carbon chain, and is ca. 23”. Secondly, as you note, it has been suggested that compression of a mobile Langmuir monolayer can lead to staggering of the head groups, and of course also the rest of the chain molecule, since such staggering reduces the projected area per molecule.Such staggering is seen in the results of computer simulations as well as being supported by the results of neutron reflectivity measurements. The data sets briefly described in my paper, and other unpublished data of which I have been informed, are consistent in showing that below the ‘kink’ in an isotherm there is continuous tilting of the amphiphile molecules in a mobile liquid supported Langmuir monolayer. I believe that the arguments that restrict the molecular tilt to a specific angle defined by the best registry of the all-trans CC backbones of adjacent molecules have referred only to the properties of immobile monolayers on solid supports.If the head groups of the molecules are pinned to specific positions on the surface, they cannot move to form a distorted hexagonal array that accommodates the tilting, so perhaps the mechanism of tilting of molecules in immobile monolayers is different from that in mobile monolayers. In my model the molecules are smooth cylinders, so there is no possibility of registry of adjacent chain backbones, nor is there any possibility of staggering of the head groups. Note also that there is no explicit reference to an intermolecular potential in the model; all of the effects of the assumed cylindrically symmetric potential are subsumed into the direct correlation function. In its present form the model describes the generic features of the tilting transition in a mobile Langmuir monolayer, but cannot account for subtleties such as must be associated with the anisotropy of the potential field of the all-trans amphiphile molecules, which anisotropy generates in the monolayer the analogue of the rotator I-rotator I1 transitions seen in the lamellar crystalline alkanes when the surface pressure is high enough and the temperature low enough.As to mixing of perfluoro- and perhydro-carbon chains, as far as I know, given the behaviour of mixed crystals of perfluoro- and perhydro-alkanes, and the behaviour of mixed bilayers, in general one should expect phase separation. I expect that an analysis, along the lines presented in the paper, of a mixture of cylinders with different diameters, 247248 General Discussion will exhibit phase separation, just as does a mixture of hard spheres of different diameters.In each case the phase boundary will depend on the diameter ratio. Dr K. M. Robinson (US Naval Research Lab., Washington DC) said: I wanted to comment that in recent data of n-pentadecanoic monolayers on HCl/ H 2 0 substrate, that I have seen island formation at low pressure. However, the structure was the rectangular lattice seen in a single layer of the 3D crystallographic pentadecanoic crystal and not the proposed h.c.p. structure. This may be intrinsic to the C,, system with its shorter chain length than those discussed. Prof. Rice replied: The data relevant to the existence of island structure in a somewhat expanded monolayer that I have seen are from the work of Lin, Bohanon, Shih and Dutta (submitted to Phys.Rev. Lett.). These data show that the spacing of the molecules in the monolayer remains invariant even when the area per molecule increases and the surface pressure decreases along an isotherm. However, only one reflection is observed, so any inference concerning the packing structure, and the presence or absence of tilting of the molecules, is guesswork. The theory discussed in my paper does not predict the existence of an island phase, let alone the packing structure in that phase. What that theory does show is that the tilting of the molecules in the monolayer is associated with an increasing area per molecule up to a maximum tilt of ca. 0.5 rad, beyond which increasing the tilt as the area per molecule increases raises the chemical potential.An extrapolation of the results of the calculation suggests that the response of the monolayer to increases in area per molecule beyond that characteristic of the maximum tilt is to transform to a different phase. It would be consistent with the theory 'if that phase consisted of islands of tilted molecules; it would be equally consistent if the underlying lattice were not hexagonal, as your measurements show. I should also comment that the molecular dynamics simulations of Harris and Rice' show that island structures are stable in the somewhat expanded monolayer (0.64 nm2 per molecule) and that in very small islands (100 molecules) the average tilt, neglecting edge effects, is essentially zero.Recent calculations by M. Klein2 show that in larger islands the molecules are tilted as in the homogeneous region, corresponding to the higher density portion of the isotherm. 1 J. G. Harris and S. A. Rice, J. Chem. Phys., 1988, 89, 5898. 2 M. Klein, personal communication. Dr K. M. Robinson then said: In the case of CIS we saw two distinct peaks (10) and (01) which corresponded, within resolution, to the 3D layer data. However, with a polymerised 16, 8-diacetylene, higher-order peaks were also observed which agreed with e-diffraction data of ex-situ films, except with a unit cell relaxed perpendicular to the direction of polymerisation. Prof. P. S. Pershan (Harvard University) said to Dr Robinson: Within the past two weeks we have observed diffraction peaks from freely supported monolayers of lignoceric acid [CH3(CH2)22C02H] at the vapour/water (pH 2 using HCl) interface. The pre- liminary analysis of these data suggests an untilted orthorhombic phase within reciprocal lattice vectors of QI.= 1.54 and 1.65 k'.' Can you compare the position of the peaks for the orthorhombic phase that you observed to these? 1 M. L. Schlossman, D. K. Schwartz, S. Lee, G. Kellogg and P. S . Pershan, 1990. Dr K. M. Robinson replied: Within the resolution of our first diffractometer the diffracted peaks agree with your orthorhombic data at low 7 ~ . As to the in-plane/out-of- plane position, our resolution, at the time, could not distinguish this at these high 28.General Discussion 249 Prof. R. A. Cowley (University of Oxford) said: Would you please elaborate on the choice of Qmax in your calculation of the Debye-Waller factor? In liquid helium the specific heat is given correctly only if Qmax is larger than the roton Q and is ca. 3r/ a.Why therefore is it justified to have Qmax = r / a in water?. Prof. Pershan replied: We do not believe the upper cut-off, qmax, of the capillary wave theory has any physical significance for reflectivity measurements in which the in-plane resolution Aq << qmax. It is tempting to imagine height fluctuations of an interface in which the local density profile has some width go. Then if the root-mean-square height of capillary waves is g h one might argue that the root-mean-square average width of the interface would be d(c~i+u:). Although we argued just this in the first paper that we published on the roughness of water,’ since ui L- In( qmax), unless there is some way to measure independently either go of the short-wavelength portion of the capillary wave spectrum, it is not possible to distinguish experimentally one particular value of qmax from another.In princinle, there are ways in which this might conceivably be done; however, it certainly is not done in the experiments discussed here in which A q is of the order of hundreds of reciprocal angstroms. Independently of one another Daillant et al., and our group remeasured the roughness of the air-water interface for clean water and found that the data were consistent with a value of oo=0.273 In the data presented here, we take go = 0 and allow qmax to be the single adjustable parameter; however, the data would also be consistent with finite values of go and a smaller value of qmax * 1 A.Braslaw, M. Deutsch, P. S. Pershan, A. H. Weiss, J. Als-Nielsen and J. Bohr, Phys. Rev. Letr., 1985, 54, 114. 2 J. Daillant, L. Bosio, J. J. Benattar and J. Meunier, Europhys. Lett., 1989, 8, 453. 3 D. K. Schwartz, M. L. Schlossman, E. H. Kawamoto, G. Kellogg, P. S. Pershan and B. M. Ocko, Phys. Rev. A, 1990, in press. Dr J. C. Earnshaw (Queen’s University of Belfast) said: Meunier’ has apparently solved the problem of the cut-off of the capillary wave contribution to surface roughness by introducing coupling of the capillary modes at high q. This leads to a scale dependence of the tension of a clean liquid surface, so that in Pershan’s eqn (14) y becomes where ym is the macroscopic surface tension and a = 3/8r.The q2 dependence tames the high-q divergence of the integrated capillary wave amplitude. The arbitrary nature of Q,,, thus disappears. For a surface supporting a monolayer, the bending elastic modulus becomes scale- dependent also, although no analytic expressions are available. 1 J. Meunier, J. Phvs. (Paris), 1987, 48, 1819. Prof. Pershan replied: I understand that Meunier’s form for the dispersion of the surface tension is consistent with our observations; however, since I do not believe that there is an experimental basis for separating the effects of the intrinsic width uo from an arbitrary cut-off to the capillary wave spectrum at qmax I also do not believe that the X-ray reflectivity data can be used as a basis for choosing between Meunier’s form and any other method of truncating the short-wavelength fluctuations.Meunier may be absolutely correct, but we do not have a proof of that, and he may yet be wrong. Mr P. Lambooy (FOM Institute for Atomic and Molecular Physics, Amsterdam) said: An alternative way to prepare samples for studying the smectic (or lyotropic lamellar) liquid/air interface is to use freely suspended films. The thickness of these films can vary from two to thousands of layers. The shape of the surface of a film is determined250 General Discussion 1 o4 I n I Fig. 1. Reflectivity data for free standing films of 8CB of 160 ( a ) , 43 ( b ) , 16 (c) and 4 ( d ) layers. ( a ) , ( b ) and ( c ) are shifted for reasons of clarity.by its supporting frame. We have succeeded in making frames sufficiently large and flat to allow X-ray reflectivity for q 2 0.05 & I . As an example, reflectivity data for films of octylcyanobiphenyl (8CB) are shown in fig. 1. As can be seen most clearly for the thick films, two distinct features mark the curves. First, the smectic density modulation with period d = 2 7 ~ / q ~ , gives rise to a Bragg-like peak at qo, which is broadened due to the finite number of smectic layers. Secondly, far from the Bragg peak the signal is dominated by the so-called Kiessig fringes. These fringes are due to the interference of the signal reflected from the two interfaces. The total thickness, D, of the film is given by D = 4.rr/Aq, where Aq is the period of the fringes. The fact that these two thicknesses can be determined indepen- dently makes the method very sensitive to the out-of-plane structure of the surface layers. The films mentioned here appear to have an extended top layer at both sides, with a thickness 1.36 times the spacing of the interior layers.In fig. 2 a model is shown for the four layer film. Details are described elsewhere.' In summary, the simple way to detect relaxations of surface layers and the absence of any scattering from a bulk below make X-ray reflectivity of free-standing smectic films a very promising technique. 1 S. Gierlotka, P. Lambooy and W. H. de Jeu, Europhys. Lett., 1990, 12, 341. Prof. Pershan then said: Mr Lambooy has described a very beautiful experiment. A similar experiment was done by Sorensen and colleagues at the University of Washington, Seattle.' As Prof.Rice has pointed out, the structure within the plane is important and in these free films this is most easily probed in transmission.' By suitable shielding essentially all stray scattering between the incident beam and the detector can be eliminated and it is practical to observe diffraction peaks that are between 10-l2 to of the incident beam. Much of this work has been r e ~ i e w e d . ~ 1 D. B. Swanson, H. Stragier, D. J. Tweet and L. B. Sorenson, Bull. Am. Phys. Sac., 1988, 33, 311. 2 D. E. Moncton and R. Pindak, Phys. Rev. Lett., 1979, 43, 701. 3 P. S. Pershan, Title (World Scientific, Singapore, 1988). Prof. Rice said: Prof. Pershan has described how measurements of the X-ray reflec- tivity of a liquid/vapour interface can be used to obtain information about the densityGeneral Discussion 25 1 t I I 1 I I 1 J 1 04t7.0 0.1 0.2 0.3 q1A-I 1.21 I 1 I 1 1 I position/ A Fig.2. ( a ) Simulation of the reflectivity of curve ( d ) in fig. 1 . Dots are the data, the solid line is the simulation. ( b ) Model used for the simulation in 2 ( a ) . profile along the normal to that interface. It is also of interest to obtain information about the distribution of atoms or molecules in the plane of the liquid/vapour interface. We have carried out such measurements for the liquid/vapour interface of Hg. The results of these measurements are worth citing because they cast light on the adequacy of the most widely used approximation in the treatment of the properties of an inhomogeneous fluid, namely the local-density approximation.I will also describe some very recent incomplete and preliminary results for the structure function in the liquid/vapour interface of Ga, because these preliminary results, if they stand up to critical examination, are startling. It is pertinent to begin by noting that the distributions of atoms in the liquid/vapour interfaces of metals and dielectrics are different. The liquid/vapour interface of a dielectric is a diffuse region, ca. two molecular diameters in width, in which the density along the normal falls smoothly and uniformly from the bulk value to the vapour value. In contrast, in the liquid/vapour interface of a metal the density distribution along the normal shows oscillations with a spacing of an atomic diameter for ca.three atomic diameters into the bulk liquid. In the particular case of Hg the theoretically predicted density distribution along the normal to the interface' is in agreement with the observed X-ray reflectivity as a function of angle of incidence.' The structure factor in the liquid/vapour interface of Hg was measured, using the method of grazing-incidence in-plane X-ray diffraction, by Thomas et aL3 The results of that work are displayed in fig. 3, along with the structure factor for bulk liquid Hg as determined by Bosio et al.4 The local-density approximation to the description of an inhomogeneous liquid, in its simplest and most widely used form, asserts that the properties of an inhomogeneous252 General Discussion 2 I Fig.3. The transverse structure function in the liquid/vapour interface of Hg at 298 K. The solid line is intended to guide the eye. The dashed line is the structure function of bulk liquid Hg at 293 K. fluid at the point r are the same as those of a homogeneous fluid that has the same density as that at the point r. Since the amplitudes of the outermost two peaks in the density distribution in the liquid/vapour interface of Hg are 1.3- 1.5-fold greater than that corresponding to the bulk density, application of the point local-density approxima- tion suggests that the transverse (in-plane) structure function in the liquid/vapour interface should be considerably different from the bulk-liquid structure factor, which is clearly not the case.As shown by Harris and Rice,' the local-density approximation proposed by Fischer and Methfessel,6 which uses the point density averaged over a region the size of the ion, more accurately describes the behaviour of the transverse structure function in the liquid/vapour interface. The physical basis for this result is the following. The presence of a density gradient in an inhomogeneous liquid implies the existence of a non-zero average interatomic force which balances the thermodynamic force, derived from the density gradient, which tends to uniformize the system. That average intermolecular force acts on a distance scale of the order of an atomic diameter. The point local-density approximation, which represents the properties of the inhomogeneous liquid at r by those of the homogeneous fluid whose density is the same as that at r, sets the average intermolecular force equal to zero, an approximation which is inconsistent with the non-vanishing density gradient. To retain the average inter- molecular force which supports the density gradient in the liquid to lowest order it is reasonable to use the density averaged over a region the size of an atom, since the repulsive force between atoms, which dominates the determination of the local structure, acts on that length scale. The important point is that it is necessary to have at least rudimentary consistency in the force balance in order to describe an inhomogeneous fluid, such as the liquid/vapour interface.It is with some trepidation that I report the preliminary results of an experiment to measure the transverse structure factor in the liquid/vapour interface of Ga, carried out just last week by my students and postdoctoral associates Tony Acero, Zhong-hou Cai, Erik Flom, Binhua Lin and Britt Thomas.The data I show reached me only 48 h before I left for this meeting, and have not been reduced in any form. The possibility that theGeneral Discussion 253 0.06 0.05 0.04 x c) .- E" Y .- 0.03 0.02 0.01 0 8 6 a B 0 8 0 2 2.2 2.4 2 . 6 2.8 3 Ikl Fig. 4. Raw data (superposition of four data sets) from a study of the in-plane scattering of X-rays from the liquid/vapour interface of Ga at 290 K. In this set of experiments the angle of incidence is 2 mrad, which is less than the critical angle for total external reflection. Under these conditions only an evanescent wave penetrates the liquid and generates scattering from the liquid/vapour interface.particular features shown in the data set are artifacts cannot yet be ruled out. Briefly put, the experiment consists of introducing liquid Ga into a high-vacuum chamber by forcing it through a capillary so that the surface is grown in the vacuum. The transverse structure factor in the liquid/vapour interface is then measured by grazing-incidence X-ray diffraction. Only the in-plane diffraction was measured in these experiments. The apparatus was set up with the expectation that only in-plane scans of the scattered X-ray intensity would be needed; changing the slit system in the detector arm so as to have the flexibility to generate rod scans could not be carried out in the time available for this synchrotron run. Fig.4 shows the superposition of the raw data from four scans across the first peak of the transverse structure function of the liquid/vapour interface of supercooled Ga (17 "C) when the X-radiation is incident on the interface at 2 mrad. Fig. 5 shows the raw data from the same region of the transverse structure function, at the same temperature, when the radiation is incident at 10 mrad, which is greater than the critical angle for total external reflection, and thus corresponds to measuring the intensity of X-rays scattered from the bulk liquid. The striking difference between these raw data sets is the very sharp diffraction peak at 2.60 A-'. The width of this diffraction peak is resolution-limited, by the Soller slits employed, at 0.025 A-1.Indeed, this diffraction peak is so narrow that it can easily be missed if the steps in the angular scan are not very small. Experiments carried out in the supercooled liquid domain (at 5 and 17 "C) and in the ordinary liquid domain (at 40 and 75 "C), all show this very narrow diffraction peak, but the intensities at the different temperatures vary widely and not in any apparently consistent fashion. Data taken very near the melting point (at 29.5 "C) do not show the peak. Taken at face value, these data suggest that the outermost one or two layers of atoms in the liquid/vapour interface of Ga have real-space ordering with a considerable correlation length. If the diffraction is from Ga,O, on the surface254 General Discussion 1.75 1.5 1.25 I x 1 .I Y E .E 0.75 0.5 0.25 I I l4 I I arb 0 n o 0 0 U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1.5 2 2.5 3 3.5 4 Ikl Fig.5. Angle of incidence is lOmrad, which is greater than the critical angle for total external reflection. Under these conditions the X-rays penetrate deeply into the liquid and what is observed is scattering from the bulk phase. we have the interesting observation of the transverse structure factor of liquid Ga in contact with a stiff monolayer. The principal uncertninty as to the reality of the results cited is associated with the possible existence of surface impurities. None of the likely impurities in the 99.9999% Ga used is sufficiently surface active to yield high surface concentration, and it is unlikely that leaching of components from the stainless-steel container yields strongly surface- active elements.As noted above, the Ga is introduced into the vacuum chamber by growing droplets in the vacuum at the end of a stainless-steel capillary; the droplets fall off the end of the capillary and eventually fill a stainless-steel pan. The residual pressure in the continuously pumped chamber (which was designed for a different experiment requiring only modest vacuum quality) was much poorer than that in a classical ultrahigh vacuum experiment, namely ca. lo-' Torr. However, there is a kinetic barrier to the oxidation of bulk Ga, so the rate of oxidation of the surface of Ga is many orders of magnitude less than the rate of collisions of residual oxygen molecules with the surface.In fact, there was no apparent change in the observed diffraction pattern with time and the addition of new Ga, layered on the old liquid surface, also did not lead to any change in the diffraction pattern. Although it is not a good indicator of lack of surface contamination, the condition of the liquid Ga surface was observed through a window throughout the experiment, during which lengthy period it was mirror bright, apparently very clean, and obviously fluid ( e . g . the surface supported ripples when perturbed). None of the preceding 'hand-waving' is convincing. Indeed, it is possible to construct a slightly distorted packing of Ga,O, molecules with oxygens in the surface plane that would give a diffraction peak at 2.60A-*.It is clear that the experiments described must be repeated under ultrahigh vacuum conditions, rod scans as well as in plane scans of the scattered X-ray intensity must be carried out, etc. We hope to carry out all of these experiments in the near future. 1 M. P. D'Evelyn and S. A. Rice, J. Chem. Phys., 1983, 78, 5081.General Discussion 255 Fig. 6. Specular X-ray reflection from a surface covered by a thin quasi-liquid layer. The density variation across the surface is schematically indicated by the function p ( z ) in the right-hand part. From: B. Pluis et al., Surf. Sci., 1989, 222, 4845. 2 L. Bosio and M. Oumezine, J. Chem. Phys., 1984, 80, 959. 3 B. N. Thomas, S. W. Barton, F. Novak and S. A. Rice, J. Chem. Phys., 1987, 86, 1036. 4 L. Bosio, R. Cortes and C.Segaud, J. Chem. Phys., 1979, 71, 3595. 5 J. G. Harris and S. A. Rice, J. Chem. Phys., 1987, 86, 5731. 6 J. Fischer and M. Methfessel, Phys. Rev. A, 1980, 22, 2836. Prof. Pershan said: Of course I agree with Prof. Rice that an understanding of the liquid/vapour interface requires information on the structure parallel, as well as perpen- dicular to the interface. We have carried out experiments on freely supported monolayers of lignoceric acid [CH3(CH2)22C02H] at the vapour/water (pH 2 using HC1) interface, similar to those on other surfactants that were mentioned in his paper.' By moving the spectrometer described in fig. 1 out of the plane of incidence we have been able to explore both the structure in and out of the plane of the surface. For monolayers such as these the characteristic in-plane distances are of the order of the molecular dimensions of 4-5 A.We have also done experiments on micellar systems in which the in-plane distances are an order of magnitude larger.273 1 M. L. Schlossman, D. K. Schwartz, E. H. Kawamoto, G. J. Kellogg, P. S. Pershan, B. M. Ocko, M. W. Kim and T. C. Chung, in Materials Research Conference, Boston, 1990. 2 G. Swislow, D. Schwartz, P. S. Pershan, B. Ocko, D. Lister and A. Braslau, in preparation. 3 G. Swislow, D. Schwartz, P. S. Pershan, B. Ocko, D. Lister and A. Braslau, Buff. Am. Phys. Soc., 1987, 32, 902. Prof. J. F. van der Veen (FOM Institute for Atomic and Molecular Physics, Amsterdam) said: You have observed an ordering effect at the surface of a liquid metal just above the freezing transition.One can also look at the other side of the transition (melting instead of freezing). We have seen a disordering of a solid metal surface just below the melting point. Here I am referring to the phenomenon of 'surface melting'. We have performed X-ray reflectivity measurements of the density profile of an atomically clean Pb( 110) surface just below the bulk melting point T, .' The analysis method used is the same as that discussed by Prof. Pershan (fig. 6). At 0.2 K below T, we observed an oscillation in the reflectivity us. momentum-transfer curve (fig. 7). The oscillation indicates the presence of a thin layer on the surface having a density 3-4% lower than that of solid Pb. From ion-scattering measurements we know that this layer is disordered.2 All this we take as evidence for the presence of a disordered liquid-like skin on the surface just below the bulk melting point.1 B. Pluis et al., Surf: Sci., 1989, 222, 4845. 2 B. Pluis et al., Phys. Rev. B, 1989, 40, 1353.256 General Discussion 1 .o 0.5 1 .o 1 .o 1 .o 1 .o 0.5 0 0-7 Q / Q C 0.5 0.5 0.5 0.5 0 Fig. 7. Measured normalized reflectivities R ( Q)/RF( Q) from Pb( 1 lo), as a function of Q/ Q, for different temperatures: ( a ) 300 K, (b) 581.2 K, ( c ) 592.8 K, ( d ) 599.8 K, (e) 600.5 K. The bulk melting point is at T, = 600.7 K. The solid curves are the best fits to the data for density profile as shown in fig. 6, which models a surface covered by a thin liquid-like layer. The dashed curves are the optimal fits to the data for a model which assumes the surface to be dry and rough.From: B. Phis er al. Surf: Sci., 1989, 222, 4845. Prof. Cowley asked Prof. Rice: What was the experimental configuration for your X-ray experiments on gallium? Prof. Rice replied: A schematic diagram of the experimental arrangement is shown in fig. 8. The key elements of the apparatus are (a) the means of directing the X-rays from the synchrotron onto the horizontal liquid surface, (6) the sample chamber, (c) the detector characteristics and ( d ) the vibration isolation of the apparatus. 1 1 L I DEC PRO 350 ORTEC ORTEC 972 A 918 AMPLIFIER Fig. 8. Schematic diagram of the experimental apparatus. SM refers to a stepper motor and associated controller. A, Horizontal hutch slits; B, deflecting mirror; C , entrance half slit; D, sample; E, vertical Soller slits; F, horizontal exit slits; G, NaI detector.General Discussion 257 ( a ) The X-rays from the synchrotron are deflected downwards onto the liquid surface, at a controllable angle, by a long Pt-coated float glass mirror.With an angle of incidence of 1 mrad the footprint of the projected X-ray beam on the liquid surface is of the order of 15 cm long by 0.8 cm wide. The X-ray path between the deflecting mirror and the sample chamber is via a Kapton-windowed He-filled tube. (6) The sample chamber used in this experiment was designed for a different experiment, namely the study of the structure of a monolayer of long-chain molecules adsorbed on a liquid-metal surface. Consequently the chamber is rather large and has numerous openings, e.g.for two electrobalances, one to measure the deposition of material on the surface and the second for a Wilhelmy balance. Many of these openings have Viton O-ring seals since easy access to the internal monolayer compression mechan- ism is required. In particular, the cylindrical Be window spans 135" and mates with the chamber via two flanges, each with an O-ring seal. The total length of the O-ring seals in the chamber is considerable, and even with all extraneous apparatus removed the ultimate pressure that can be achieved with a turbomolecular pump is of the order of 10p7Torr. The Be window is tall enough to permit rod scans over the angular range appropriate to the typical tilt angle range of an adsorbed monolayer of long-chain amphiphile molecules.( c ) The detector arm swings in the horizontal plane and has a vertical slide that permits the 5 cm NaI detector to be moved out of the plane of the interface for rod scans. In the experiments reported the Soller slits and detector were almost in contact with the Be window. The Soller slits used had an in-plane resolution of 0.025 A-'; the intensity in the vertical direction was integrated over the full height of the slits. The discovery of the sharp diffraction features superimposed on the liquidlike in plane X-ray scattering from the liquid/vapour interface of Ga was a surprise, and we did not have enough synchrotron time to modify the detector arm with a supplementary slit to provide resolution in the vertical direction and thereby permit execution of rod scans.( d ) The mirror for deflecting the incident radiation onto the liquid surface and the sample chamber were mounted on a pneumatic vibration isolation table which was, in turn, mounted on a hydraulic lift table. The detector arm was mounted on a turntable that was on a bridge that spanned the vibration isolation table and was bolted to the hydraulic lift table. This scheme, which successfully removed all of the mechanical noise incident from the surroundings, was adopted to avoid tilting of the incident X-ray deflecting mirror and sample chamber relative to the radiation swath from the syn- chrotron, which would have resulted from the substantial change in position of the centre of mass of the apparatus as the rather heavy detector arm moved in the azimuthal direction.Prof. Rice then addressed Prof. van der Veen: It is now accepted that at the surface of a crystalline metal the separation of the two outermost planes is somewhat less than in the bulk, of the next pair of planes somewhat more than in the bulk, etc., which is equivalent to an oscillation in the density along the normal to the surface. This density oscillation will introduce structure in the reflectivity ratio R ( Q)/RF( Q). Have you ascertained that such structure is different from the form of R(Q)/R,(Q) you show and interpret as evidence for a liquid layer atop the crystal? Prof. van der Veen replied: The Pb( 110) surface indeed exhibits a strong oscillatory relaxation. The first interlayer distance is contracted by 16% of the bulk spacing, the second and third interlayer distances are expanded and contracted by 8 and 7%, respectively.' The structure in the reflectivity ratio R(Q)/R,(Q) as a result of this relaxation appears at much larger perpendicular momentum transfer values than the values probed in the reflectivity experiment discussed here.The relaxation effect is therefore of no concern. 1 F. W. M. Frenken ef al., SurJ: Sci., 1986, 172, 319.258 General Discussion Prof. J. M. Thomas (The Royal Institution) communicated: The fascinating remarks of Professor Rice concerning the observation that liquid gallium remained as such even though its temperature fell well below (some 40°C) that of the freezing point of the element, prompts me to recall a short report published in 1826 in a magazine that was produced at The Royal Institution.In the Q. J. Sci. Arts, vol. XXI, p. 392 Michael Faraday described the ‘Fluidity of Sulphur at Common Temperatures’ thus: Fluidit-y of Sulphur at common Temperatures.-Having placed a Florence flask contain- ing sulphur upon a hot sand-bath, it was left to itself. Next morning, the bath being cold, it was found that the flask had broken, and in consequence of the sulphur running out, nearly the whole of it had disappeared. The flask being broken open, was examined, and was found lined with a sulphur dew, consisting of large and small globules intermixed. The greater number of these, perhaps two-thirds, were in the usual opaque solid state; the remainder were fluid, although the temperature had been for some hours, that of the atmosphere. On touching one of these drops, it immediately became solid, crystalline, and opaque, assuming the ordinary state of sulphur, and perfectly resembling the others in appearance. This took place very rapidly, so that it was hardly possible to apply a wire or other body to the drops quick enough to derange the form before solidity had been acquired; by quick motion, however, it might be effected, and by passing the finger over them, a sort of smear could be produced. Whether touched by metal, glass, wood, or the skin, the change seemed equally rapid; but it appeared to require actual contact; no vibration of the glass on which the globules lay rendered them solid, and many of them were retained for a week in their fluid state. This state of the sulphur appears evidently to be analogous to that of water cooled in a quiescent state below its freezing point; and the same property is also exhibited by some other bodies, but I believe no instance is known where the difference between the usual point of fluidity and that which could thus be obtained is so great: it, in the present instance, amounts to 130°, and it might probably have been rendered greater if artificial cold had been applied.-M.F. Experiments of the kind described by Rice on supercooled gallium could, with profit, be carried out on surfaces of supercooled and freshly crystallized sulphur, especially since there would be much to be gained in ascertaining which of the very many polymorphic forms of sulphur-22 are known-of the solid is generated when the surface of the liquid crystallizes.

ISSN:0301-7249    

DOI:10.1039/DC9908900247

出版商:RSC    

年代:1990

数据来源: RSC