J. Phys. Chem. 1993,97, 42884292
Alloying Effects on X-ray Absorption Edges in Ptl-,Ni, Single Crystals B. Moraweck' and A. J. Renouprez Institut de Recherches sur la Catalyse, 2 Avenue Albert Einstein, F 69626 Villeurbanne Cgdex, France
E. K. Htil and R. Baudoing-Savois Laboratoire de Spectromttrie Physique, UniversitL Joseph Fourier, BP 87, F 38402 Saint Martin &Heres Cgdex, France Received: August 3, 1992; I n Final Form: January 28, I993
Electronic structure modifications of platinum and nickel produced by alloying these two metals were studied on a series of single crystals of different composition by X-ray absorption spectroscopy, using synchrotron radiation. Both Pt and N i absorption edges show simultaneous structure changes. These modifications are located mainly several electronvolts above the Fermi level. The variation in hole number in the Pt 5d band was estimated by several analysis methods which all conclude to an electron transfer from nickel to platinum. Conversely, the modifications observed on the Ni K edge are situated at the neighborhood of Efand are interpreted as a population rearrangement between 3d, 4s, and 4p levels. These observations are finally discussed by comparison with photoemission results and published calculations of density of states.
I. Introduction Platinum is still the major constituent of the active phase of catalysts used for crude oil reforming or for the reduction of pollution by carbon monoxide or nitrogen oxide. To improve the reactivity or reduce the cost of the catalyst, platinum is frequently associated with other metals such as Rh, Pd, Sn,or Pb. For other typical reactions, transition metals alloyed to nickel appear also to exhibit interesting properties. For example, bimetallic Pt-Ni catalysts have been shown to enhance by a factor 100-1000 the activity of pure metals for neopentane isomerization and hydrogenolysis. This effect is maximum for some peculiar concentrations of both elements. It has been attributed to an electroniceffect originating in the alloying of platinum and nickel as shown by a rather rough analysis of the Pt Llll X-ray absorption edge.' Besides, alloy single crystals actually constitute good models for real bimetallic catalysts since they exhibit measurable reactivitiesand have the advantage that their surface composition and structure can be determined by surface science methods, as reported in previous ~ o r k s for ~ -Pt ~ alloyed with Fe, Co, and Ni. The main reason invoked for the observed modified chemisorptive properties is changes in the electronic structure of both elements. These changes arise from modifications of local environments of surface atoms due to segregation and/or reconstruction effects. Indeed, in the case of bimetallic Pt-Fe particles: important modifications in the 5d band of platinum were observed as a function of the alloy composition, and a correlation with their reactivity and selectivity was established. This was achieved by studying the Pt LIIand L11l X-ray absorption edges which are known to probe the vacant states in the 5d-6s As a final important comment, we emphasize that very little work has been devoted to the simultaneous analysis of the Pt edges and of the other element in the compound; in the present paper we shall systematicallydescribe and analyze the correlations observed both on the Pt LIIJIIedges and on the Ni K edge, in a manner similar to the work published by two of us6 for Pt-Fe bimetallic catalysts. 11. Theoretical Considerations
Historically, but also in a logical order, the first attempts were to understand the pure Pt metal absorption edge spectra. One of the first questions raised by the experimental results was the presence of the so-called "white line" at the Llll edge and the
quasi-absence of an equivalent feature at the LIIedge. Following the arguments of Mott,l3 Brown et a1.8 gave a first theoretical explanation based on a band structure analysis with only the 5d levels. They obtained a good qualitative agreement in which the Llll edge is found to be dominated by the unoccupied d5/2 final state contribution with a ratio of h5/2 to h3J2 of about 14. h 5 ~ 2 and h3~2represent the hole number in the 5d5~2and 5d3~zbands according to the notation of Mattheiss and D i e t ~ .However, ~ this theoretical ratio was by far too large compared to the experimental values (about 2-3). Mattheiss and Diet29 resolved this discrepancy by introducing relativistic effects due to the large atomic number of Pt and hybridization effects of the 6s,6p states with the 5d states of Pt. The net effect is that the ratio hslz/h3~2is then reduced by the hybridization effects to a value of about 3, in excellent agreement with experiment. Although this points to a need of using a good band structuremodel, they noticed, however, that integrated areas of the absorption edge were not seriously sensitive to the details of the model parameters. At this point we are left with a good model for pure Pt LIIand L I Iabsorption ~ edges, where the final states available for the Lll1 transition are dominated by the 512 character. The problem of Pt-based alloys is actually more formidable, on both the theoretical and experimental sides. On the theoretical side very few calculations are available with, at the same time, the necessary ingredients (relativistic effects and more than only Pt 5d levels) in the model and calculated results for energies well above the Fermi level. We shall discuss the theoretical investigations relevant for Pt-Ni alloys in the discussion of section IV. On the experimental side two complementary procedures were proposed to analyze the final states involved in the transition: (a) LII and Llll spectra in Pt-based alloys are respectively compared to the corresponding spectra from pure Pt; a variant of this method makes use of the Au spectra with the idea that Au has virtually a full 5d band (no white line), so that it could represent an experimental reference close in nature to the continuum arctg shape. Another variant amounts to fit the edge shape by a combination of an arctg continuum contribution and of a Lorentzian shape to account for the final state distribution. This procedure has been fully exploited by Qi et a1.I0for Pt metal and Pt-(Al, Si, or Ge) alloys. (b) In a similar context, taking advantage of the theoretical
0022-365419312097-4288SO4.0010 , 0 1993 American Chemical Society I
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Alloying Effects in Ptl-,Ni, 900 800
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Figure 2. Ni K absorption edges of Ptl_,Ni, alloys and pure nickel.
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Figure 1. Theoretical equilibrium phase diagram of Ptl-,Ni, (from ref 14).
result of Mattheiss and Dietz? Mansour et al.’ tried to evaluate relative rather than absolute variations of the unoccupied final states by comparing the samples of interest with respect to a reference of bulk well-defined pure Pt metal. They applied this procedure to pure Pt supported on various carriers or particles of different sizes. We shall investigate how far this method can be extended to Pt-Ni alloys of different compositions. In the present paper we shall follow procedures similar to those used by Qi et a1.I0or Mansour et al.’ but using pure Pt instead of Au spectra as references. In addition, we also give the results from the fit using the Lorentzian and arctg continuum function.llJ2 In all three cases we limit the energy range to about 10-15 eV close to the edge, for the sake of comparison between the analyses and to emphasize band structure contributions. (c) Conversely, LIIand LlIl Pt spectra for the same sample can be compared by means of the difference (LIII- kL11)~after appropriate normalization and shift of the respectiveenergy scales. The difference procedure may be justified as follows: (i) There is experimental evidence that the difference becomes essentially zero for energies larger than about 30-40 eV above the edge, simply because the EXAFS type parts of the LIIand Llll spectra are identical for Pt in the same crystallographic environment. (ii) If the d5/2 final states dominantly contribute to the LIIIedge spectra, one can expect a significant correlation between the number of 5/2 holes in the Pt band and the integrated areas of the difference curve. This hope is particularly relevant owing to the theoretical result of Mattheiss and Dietz9 on the relatively weak sensitivity of integrated areas to the details of the theoretical parameters. The present work provides a full analysis of the Pt-Ni edge spectra in terms of this difference procedure.
III. Experimental Section 1. Samples. The Pt and Pt-Ni samples were cut along a (1 11) orientation from a single crystal rod. Pt-Ni alloys had bulk concentrations of 78, 50, and 10 at.% Pt as confirmed by fluorescence measurements in a scanning electron microscope. The Pt-Ni phase diagram is relatively simple as reported by Dahmani et al.:I4 at high temperature, the alloy is fcc and substitutionally disordered (phase A l), stable in the whole range of concentration. At lower temperature, the diagram exhibits ordered phases for compositions around Pt75Niz5 (L12), Pt50Ni50 (Llo), and Pt25Ni75 (1512) (Figure 1). Grazing incidence x-ray diffraction above and below total reflection confirmed that our samples were in the substitutionally disordered phase down from the bulk up to the surface region. The same samples were also studied by LEED, which confirmed the substitutional disorder in the very top surface region and allowed a very detailed description of surface segregation effects.2-5 2. Experimental Setup. The spectra were recorded by using the synchrotron radiation emitted by the storage ring DC1 at LURE on the experimental station XAS4. The Pt LII,Pt LIII,
and Ni K absorption edges were recorded using a Si(311) twocrystal spectrometer with a typical resolution of AE/E = 2 X l t 5 . In the Ni K absorption region harmonic contamination was removed by a two glass mirror device under total reflection conditions at the incidence of about 4 mrad. The energy steps were 0.3 and 0.5 eV, respectively, for the K and for the Llll and LII absorption regions. The experiments were run in two detection modes: transmission mode (photon detection) was used for the Pt and Ni foils, whereas the reflection mode (electron detection) is required for the thick monocrystalline samples. The transmission mode was used for energy calibration with the following samples: two Pt foils, 4 and 12 pm thick for the Pt 41and LIIIedges, respectively, and a 5-pm Ni foil at the Ni K edge. The absorption coefficient is defined as log(Z/Zo): IOand I are, respectively, the incident and the transmitted X-ray fluxes detected by two separated ion chambers connected to voltage-frequency converters. In the electron yield mode, the absorption coefficient, is definedI5 as (Z/Io): IO is the incident X-ray flux measured, as previously, by a ionization detector, whereas I is the signal corresponding to the electrons ejected from the sample. Indeed, when X-ray photons strike a sample, photoelectrons are ejected from a core level to unoccupied states leaving a core hole. The relaxation of the system can proceed via radiative (X-ray fluorescence) and/or nonradiative (Auger effect) processes. These very energetic Auger electrons can escape directly from the sample or, on their travel to the sample surface, suffer many inelastic collisions and induce a cascade of secondary electrons. Both contributions are collected by the detector which contains the He ambient pressure to enhance the efficiency to low-energy secondary electrons.15-18
IV. Absorption Edge Analysis To analyze our edge spectra, we used a classical procedure. The baselinedue toabsorption fromother edges was approximated by a linear regression,extrapolated above the edge, and subtracted from the experimental data. The spectra were then normalized by adjusting the step across the absorption edge to unity, by the mean value of EXAFS taken over about 40 eV. 1. Nickel Edge. The nickel Kedge spectra for Ptl,Ni, alloys (x = 0.22,0.50,0.90) and pure nickel are shown on Figure 2. The edgestructure is found to bestrongly sensitiveto the nickel content. Indeed, when the Ni concentration increases, the features C and D exhibit an energy shift, which is attributed to changes within EXAFS oscillations as a function of unit cell parameter. Conversely,the peaks A and B are more sensitiveto a modification in the alloy density of states.I9 The edge structure corresponds to transitions from 1s level to unoccupied 4s,4p states and to hybridized 4s,4p-3d states. Their contributions correspond respectively to the main feature (peak B in Figure 3) and to the smaller feature (peak A in Figure 3) separated from each other by only a few electronvolts. The contribution corresponding to peak A reflects the electronic density with mainly 3d character. To emphasize the variations, at the onset we generated difference spectra obtained by subtracting the pure nickel spectrum from the alloyed nickel one. An example of this procedure is given in Figure 3, where we observe two contributions
Moraweck et al.
4290 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 NI K edge
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Figure3. Nickel Kedgefor purenickeland Ptl-,Ni,alloysandvariations with the nickel content of the difference area corresponding to peaks A and B. P t Ll
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Llll and L I Iabsorption edges of pure Pt and two alloys and the area difference variation with the nickel content.
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Figure 4. Pt Llll and LIIabsorption edge of Ptl-,Ni, alloys.
of opposite sign for the features A and B. These areas are expressed in electronvolts because the abscissa scale is in electronvolts and the absorption coefficients is dimensionless. Interestingly, the variation of the difference areas (up to 1 eV) with nickel content is not linear, ruling out a trivial dependency with composition. Moreover, A and B contributions vary in a compensating way. These two results confirm a band structure modification by alloying nickel to platinum. I The platinum LIIIand 41 2. Platinum LIIand L I ~Edges. edges in pure platinum and alloys may be analyzed independently in a similar way as for the Ni Kedge, but they can also be compared to each other as presented below. The normalized spectra are reported on Figure 4. Clearly, region B, extending from about 20 eV above the edge, is concerned by EXAFS-type oscillations which are shifted toward higher energies according to an increase of nickel content associated with a unit cell parameter decrease. From earlier theoretical and experimental works, we know that region A, which extends from a few electronvolts before the main inflection point to about 20 eV above the onset, contains information about the electronic structure of the probed element. More precisely, the Ll11 near edge structure corresponds to 2~312
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5d312and 5d5/2 allowed transitions, whereas the LII edge is only concerned by the 2p1p 5djp transitions. We observe that the "white line" decreases in intensity when the nickel content increases. In the case of the LIIedge of the Ptlo-Niso alloy, this feature has almost disappeared. This suggests that we are faced with an electron excess (versus pure platinum) at the platinum site in Pt-Ni alloys. According to the theoretical arguments developed in section I1 on platinum edges, the following procedures have been applied to estimate the variation of the 5d hole numbers with nickel content. (i) In a manner similar to our analysis of the Ni K edge, we have evaluated the difference area between spectra from pure Pt and Pt alloys. We have only considered here the first peak in the differencecurvevery close to the edge (Figure 5). Upon alloying, this difference area (expressed in electronvolts) varies in a similar way for both edges: up to 1.3 eV for the Llrl edge and only 0.3 eV for the LIIedge. This gives, thus, evidence of a simultaneous change for the Ni K edge (Figure 3) and for the Pt L11 and LIII edges. However, Figures 3 and 5 are characterized by large error bars, the origin of which must be discussed. In our experimental setup the resolution and repeatability of the encoder corresponded to about 0.3 eV a t 11 keV. This directlycontributes to the uncertainty on the energy scale of our edge spectra. To estimate carefully the resulting errors in Figures 3 and 5, we have shifted the respective edge spectra for the pure and alloyed element by k0.3 eV and determined the corresponding variations in the difference area. Obviously, the uncertainty on the area resulting from the errors in the energy scale is of the same order of magnitude as the estimated variations. In our opinion this method does not seem a good way to evaluate with suitable precision small charge transfers. (ii) An absolute determination of the electron vacancies at the Llrl and LIIedges may be also performed by fitting the edge with the sum of a Lorentzian and an arctangent functions.llJZ In the
Alloying Effects in PtI,Ni,
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Figure 7. Charge fractional change in Pt 5d band as a function of nickel content. PtL
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Figure 6. Pt Llll edge resonance: example of experimental data and calculated profile and variations of the Lorentzian area with the nickel content.
interactive least-squares process the height, width, and energy position of the two functions were adjustable parameters. We present the results of the fitting process of the LIIIedge resonance (Figure 6) using a Lorentzian shape to reflect the unoccupied density of states. We notice a decrease in the density of states for Llll as expected from the previously observed results. (iii) The method developed by Mansour et al.’ aims at determining&, the charge fractional change of the number of d-band vacancies relative to a reference material. The first relevant quantity is the normalized difference area, A , between Llll and LIIedges of pure platinum. According to the number of holes in the 5d3/2 (h3,2) and 5ds/2 (hS/2)levels of platinum, the following areas are then defined:
= A(h5/2 + h3/2)/h5/2 and = Ah3/2/h5/2 Mansour et al.7 then used difference areas between the experimental spectra from the samples under study and pure platinum. In our cases these quantities are AAi = ( t i area),l,oy - (Li area),”,,
pt
These areas are evaluated up to the cross-pointbetween the spectra above the edge. Thus, the charge fractional change is expressed as fd
= (AA,
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A j and A2are, respectively, the area of LIIIand LIIedges and L 4 3 and AA2 are the edge area variations between the sample and the reference material. This method does not attempt to determine the total number of unoccupied d states and is claimed to be not very dependent on an accurate determination of the absolute areas. From Figure 7,we point out that & regularly increases with the increase of nickel content. (iv) The normalized difference area (LIII- I c L ~presented ~)~ and justified in section I1 is a procedure which should provide a measurement of the variation of the electron vacancies in the 5d5/2band. However, the absolute number of these holes can only be derived from a comparison with similar results obtained from pure platinum on one hand with, at the same time, theoretical calculations of the partial densities of 5d,,2 and 5d3p states on the other hand. This discussioon is left to the following section. We only present here on Figure 8 the results on both pure platinum and Pt-Ni samples. The normalized difference area decreases
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Figure 8. PtsoNiso alloy: L edges and their normalized difference area and normalized difference area variations for Ptl-,Ni, alloys with the nickel content.
quasi-linearly, by about 20% under alloying in the whole concentration range, indicating a progressive filling of the 5d band.
V. Discussion Before a comparison of our results with theoretical calculations of empty states and with photoemission experiments, we first need to discuss the relative merits and drawbacks of the four methods used above. The first method (difference spectrum between sample and reference) is, unfortunately, the only one which can be used for the Ni Kedge. It allowed, however, evidence of a rearrangement between unoccupied nickel states. Further, interpretation should rely on calculationsof partial densities of nickel states in platinumnickel alloys, over an energy range extending up to 20 eV above the Fermi level. A drawback of this method is the choice of the limits in energy to evaluate the area of the peaks A and B (Figure 3): they are taken as the cross-points of both spectra which are dependent on the alloy composition. This is also true for the Pt L edges. Looking carefully at the third method (evaluationof thecharge fractional change), we pointed out that the PAi quantities are also defined in the same way. Therefore, Mansour’s method suffers from the same drawback. However, it is able to evidence a charge transfer from nickel to platinum. At this point we are left with two methods which do not depend significantly on the energy range used above the onset: the decomposition method (arctg + Lorentzian functions) which probes the 5d band and the (L11- kL11)method which should be more selectiveof the 5d5p states. These last two methods appear to be better suited to extract quantitative and reliable estimations
4292 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
of alloying effects in the 5d Pt band. One further advantage of the (Lllr- kL1,) methodis that it minimizes theuncertainty arising from the calibration by the adjustment performed using one oscillation of the EXAFS curve a t about 30 eV above the onset. Interestingly, the present results on Pt-Ni monocrystalline alloys agree well with the results reported by Moraweck et a1.6 concerning Ptl,Fe, particles supported on charcoal. The comparison of these two sets of results is given in Figure 8. Qualitatively the four methods described and discussed above agree well together. The variations of the platinum d filling are rather small, and a continuous decrease of empty states as a function of nickel enrichment is observed. In the meantime the nickel valence band undergoes a rearrangement upon alloying. This is in good agreement with the results of calculations of DOS with the RKKRCPA method performed by Staunton et al.20 Unfortunately, these calculations are limited to a very few electronvolts above the Fermi level, and it would be necessary to extend such calculations over an energy range comparable to the experimental one. Indeed, it has been shown by Matheiss and Dietz9 that the 5d hole number varies from 0.3 over an energy range of 0.5 eV to 1 if the 5d band is entirely considered. In the absence of results from other techniques sensitive to the unoccupied states such as BIS and X-ray emission experiments, it is interesting to discuss available photoemission results, since photoemission and X-ray absorption are complementary techniques. In their experimental photoemission study of platinumnickel alloys Schevchik and Bloch2I reported a shift in opposite directions of the Ni 2p3p and of the Pt 4f core levels as a function of the nickel composition. From this opposite shift they deduced a charge transfer from platinum to nickel: this is in complete disagreement on one hand with our results obtained from X-ray absorption experiments at the Pt Ledges, and, on the other hand, with the DOS curves computed by Staunton et al.20for Pt70Ni30 and PtSONiS0 compositions, in which we observe that an increase of nickel content decreases the density of unoccupied.states in both the 5d,,2 and the 5d3p bands. It is, however, known from several experimental examples that, in alloys, a direct correlation between core-level shifts and charge transfers is not straightforward. Indeed, in the case of Pd-Ni a shift of the Pd core level to higher binding energy is observed upon alloying. But Pd is more electronegative than Ni and a net negative charge is expected on Pd, which should result in a shift of its core level to smaller energy. Similarly, in the case of A u S n alloys reported by Friedman et a1.,23the core level of Sn is found to be shifted by 0.4 eV upward, suggesting a charge transfer from Sn to Au. The Au 4f levels are thus expected to be shifted to lower energy, which is not the case. In his review paper on this subject, EgelhofP4 has considered the various reasons for this apparent discrepancy. The first point is that Er, the Fermi level, can shift along with the core level upon alloying. Also, a change in atomic volume upon alloying can make an initial state contribution to the observed shift, without any charge transfer. The squeezing of valence electrons into a smaller volume, the core-valence repulsion, will shift the core eigenvalues to smaller binding energy. Another argument considered by many authors is the fact that the observed shifts can be also attributed to final state effects, Le., screening of the core hole. A final possibility is more in line with our experimental results concluding to complex configuration changes in both valence bands of platinum and nickel. Indeed, Friedman et al.23 show that in the example of the A u S n alloys a small 5d 6s transfer, identified by MBssbauer spectroscopy, is the cause of the observed shift of Au 4f level to higher energy. This transfer offsets the Au core level to smaller binding energy, as was indeed expected from the electronegativity difference.
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VI. Conclusion We have used X-ray absorption spectroscopy to study the alloying effect on the electronic structure (partial state density) in Pt,-,Ni, by analyzing the Pt Llll and LIIand Ni K edges. We have also estimated the number of holes in the Pt 5d band, which provides information about the charge transfer between the two constituents of the alloy. It is concluded that the Pt Llll and LII edge structures are sensitive to the compositionand show a change in a rather large energy range above the edge (30-40 eV), while this range is more reduced around the Ni K edge and rather localized around the Fermi level. The decrease of the number of 5d holes in platinum points out a charge transfer from Ni to Pt with a simultaneouspopulation rearrangement around Er. This needs to be confirmed by a careful theoretical analysis taking into account the spin-orbit coupling for platinum. In our study, X-ray absorption spectroscopyturns out to be an efficient probing tool to study the alloying effect. From comparison with valence band photoemission spectroscopy, it appears that one advantage of X-ray absorption is due to its selectivity; both state densities, indeed, located respectively on Pt and Ni are separately probed. It may be noted that minor changes in total DOS are hardly detected by UPS since they only correspond to very small relative variations. From the different methods of analysis applied in this work, our conclusions are in agreement with trends indicated by the available band structurecalculations using different models to estimate, respectively, the empty and the full band.
Acknowledgment. We are greatly indebted to the scientific and technical support of the Laboratoire pour I'Utilisation du Rayonnement Electromagnetique (LURE) for dedicated runs. This work is part of the scientific program run by the Groupement Surface Rh6ne-Alpes and by the Surface Alloy program within the Surface Crystallography Network supported by the European Science Foundation. References and Notes (1) Renouprez, A. J.; Moraweck, B.; Imelik, B.;Perrichon,V.;DominguezEsquivel, J. M.; Jablonski, J. Proceedings of rhe 7rh Congress on Catalysis; Kcdansha: Tokyo, 1981; p 173. (2) Beccat,-P.; Gauthier, Y.; Baudoing, R.; Bertolini, J. C. Surf. Sci. 1990, 238, 105. (3) Baudoing-Savois, R.; Gauthier, Y.; Moritz, W. Phys. Rev. 1990, 8 4 4 , 12977. (4) Gauthier, Y.; Baudoing, R.; Jupille, J. Phys. Rev. 1989, B40, 1500. (5) Gauthier, Y.; Baudoing, R.; Joly, Y.; Rundgren, J.; Bertolini, J. C.; Massardier, J. Surf. Sci. 1985, 162, 342. (6) Moraweck, B.; Bondot, P.; Goupil, D.; Fouilloux, P.; Renouprez, A. J. J . Phys. (Paris) 1986, 47 (C8), 279. (7) Mansour, A. N.; Cook, J. W., Jr.; Sayers, D. E. J . Phys. Chem. 1984, 88, 2330. ( 8 ) Brown, M.; Peierls, R.E.; Stern, E. A. Phys. Rev. 1977, B15, 738. (9) Mattheiss, L. F.; Dietz, R. E. Phys. Rev. 1980, B22, 1663. (10) Qi, B.; Perez, I.; Ansari, P. H.; Lu, F.; Croft, M. Phys. Rev. 1987, 837, 2972. (11) Lytle, F. W. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 1251. (12) Horsley, J. A. J. Chem. Phys. 1982, 76, 1451. (13) Mott, N. F. Proc. Phys. SOC.London 1949,62A, 416. (14) Dahmani, C. E.; Cadeville, M. C.; Sanchez, J. M.; Moran-Lopez, J. L. Phys. Reo. Lett. 1985, 55, 1208. (15) Kordesch, M. E.; Hoffman, R. W. Phys. Rev.1984, 829, 491. (16) Guo, T.; den Boer, M. L. Phys. Rev. 1977, 831, 6233. (17) Pandya, K. I.; Yang, K.; Hoffman, W. R.; OGrady, W. E.; Sayers, D.E. J . Phys. (Paris) 1986, 47, (C8), 159. (18) Tourillon, G.; Dartyge, E.; Fontaine, A.; Lemonnier, M.; Bartol, F. Phys. Rev. Lett. 1987, AI21, 251. (19) Azaroff, L. V. J. Appl. Phys. 1967, 34, 2809. (20) Staunton, J.; Weinberger, P.; Gyorffy, B. L. J. Phys. F Mer. Phys. 1983, 13, 779. (21) Schevchik, N. J.; Bloch, D. J . Phys. F Met. Phys. 1977, 7 , 345. (22) Steiner, P.; Hufner, S.Acta Met. 1982, 29, 1885. (23) Friedman, R. M.; Hudis, J.; Periman, M. L.; Watson, R. E. Phys. Rev. 1973, B8, 2433. (24) Egelhoff, W. F., Jr. Sur5 Sci. Rep. 1987, 6, 253.
