Analyses of Ne-diffraction data from transition-metal surfaces based on charge-density calculations

Surface Science 167 (1986) L203-L209 North-Holland, Amsterdam

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S U R F A C E S C I E N C E LETTERS ANALYSES OF N e - D I F F R A C T I O N DATA F R O M T R A N S I T I O N - M E T A L S U R F A C E S BASED O N C H A R G E - D E N S I T Y C A L C U L A T I O N S M. B A U M B E R G E R , K.H. R I E D E R and W. S T O C K E R I B M Zurich Research Laboratoo', CH-8803 R~schlikon, Switzerland

Received 8 July 1985: accepted for publication 21 November 1985

We evaluate the proportionality constant ,8 for neon in the Esbjerg-Norskov potential Vk(r) = rio(r) from experimental data on Ni(ll0), Ni(ll3), C u ( l l 0 ) and Pd(ll0). Our calculations using overlapping atomic charge densities require that ,8 be material and surface-dependent. Although Ne diffraction is more sensitive to details of corrugation shapes than He. we found it to be insensitive to normal relaxations of the topmost layers.

In recent years, He diffraction has been used successfully to investigate surface structures of clean and adsorbate-covered systems. The surface lattice constants can be determined from the angular location of the scattering peaks. Analyses of diffraction intensities yield the corrugation function which, in many cases, reveals the surface geometry directly [1,2]. However, quantitative results for the bonding lengths of adsorbates are not straightforward to derive and in certain involved cases (like in adsorbate-induced surface reconstructions) even no information on the bonding sites can be obtained from the corrugation function without additional knowledge. As according to theoretical investigations [3], atomic beams scan the electronic charge distribution outside the surface, and the locus of the classical turning points lies on a surface of equal charge density, in principle, one should be able to obtain this structural information by relating the experimental corrugation to calculations of surface charge-density profiles. Esbjerg and Norskov propose the relation V~ = ,80(r) between the repulsive potential (Va) and the charge-density contour o(r) [3]. The equipotential surface Va = E,, is determined by the normal kinetic energy E,, of the particles. According to predictions obtained within the framework of this theory, Ne should scan smaller surface charge densities than He: the/~ value predicted by Manninen and coworkers [4] should be (/?....... = 666 eV au ~ while fl~,~,..... = 275 eV au3). Recent Ne-diffraction measurements on low-index metal surfaces [5-7], however, show the reverse. As at the moment, the theory fails to describe the real /? value, we evaluate it from the experiment by the following procedure: we search for that charge density whose surface contour fits the 0039-6028/86/$03.50 ~~ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

M. Baurnherger el al. / Ne diffraction from lransitton melals

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experimental diffraction intensities. Our results show that /8 depends both on the surface indices and on the material. As a consequence, unless ,8 (and hence the charge density) cannot be fixed by some independent means, no quantitative information on surface relaxation can be made on the basis of atom diffraction. The charge-density profiles were calculated by overlapping atomic charge densities. Comparison of self-consistent, all-electron calculations using the LAPW approach [8] with simple atomic charge superposition shows that in the low-density regime relevant for He and Ne scattering, the corrugation amplitudes for N i ( l l 0 ) vary less than 10%. The use of atomic charge density allows much simpler and faster computations which enable us to compare different surface-structure models with the experiment. This approach works as long as bonding effects can be neglected, which is most likely for clean metals. The atomic wave functions were computed using a Herman Skillman-like atomicstructure program [9]. Our program includes a change from local to nonlocal exchange at a distance r, where the two potentials cross. As Haneman and Haydock pointed out, the nonlocal exchange should describe better the real behavior in the low-density regime [10]: it takes account of the fact that far from the atom the electron sees a 1/r Coulomb potential, and produces wave functions which fall off slightly slower. For the local exchange, we use the potential proposed by Kohn and Sham [11] which is two-thirds of the Slater potential [12] used in the original Herman Skillman calculations. In our experiments, we used monochromatic beams of Ne with energies between 45-70 meV, These energies are appreciably higher than the attractive potential well which the particles first feel when they approach the surface ( < 10 meV). Therefore, we neglect this attraction. The repulsive part of the particle surface potential is steep enough to justify application of the hard-wall picture [5,6]. This approximation for the interaction potential was used successfully to solve structures from diffraction data [1,2]. We first checked whether it is possible to extract the degree of normal relaxation between the first and second layers at the surface from the experimental data. As a measure for the agreement between experiment and calculation, we used a reliability factor defined by

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(N denotes the number of measured intensities 1~; ). We plot the R-factor as a function of the normal interlayer spacing and surface density for N i ( l l 0 ) in fig. la and for Cu(ll0) in fig. lb (for Ni(ll3), see ref. [16]). In none of these cases does the R-factor show a clear minimum. Instead, a continuous minimum valley is observed. This proves that Ne scattering alone is not sensitive enough to allow determination of surface relaxation. The proper charge density can only be fixed with the aid of additional information from other surface-sensi-

M. Baumberger et al. / Ne diffraction from transition metals

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tive methods. Ion-beam-scatterlng [13] and LEED [14] results give a contraction between 5% and 9% for Ni(ll0)."Thus, the proper Esbjerg-Norskov parameter/3~e(Ni(ll0)) lies around 175 eV au 3. Figs. 2.:and 3 show that the

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M. Baumberger et al. / Ne diffraction from transition metals

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diffraction intensities from the charge-density contour calculated by superposition of atomic Ni charge densities (Ni configuration 3d94s ]) fits the experimental data well. Note, however, that the corrugation along the close-packed rows is slightly smaller (dcajc = 0.024 ,~, dexp - 0.033 ]~); therefore the experimental out-of-plane scattering is enhanced with respect to the intensities calculated. For Cu(110), experimentally no out-of-plane scattering cold be detected. This means that the corrugation along the rows is practically zero. In contrast to this, the charge-density profile calculated for Cu(110) gives appreciable out-of-plane scattering (see fig. 4). The best fit was achieved for a charge density of 3.45 × 10 -4 e / a u 3. An inward relaxation of the topmost layer of 10% as derived from LEED data and theoretical calculations was assumed [15]. The resulting Esbjerg-Norskov parameter /9 is 130 eV au 3. The corrugation ( d ~ c = 0.04/k) along the rows causes a diminution of the in-plane scattering;

M. Baumberger et aL / Ne diffraction from transition metals

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the beam sequence, however, is well reproduced (dashed line in fig. 4). Simulating the smear-out of the charge along the rows by averaging the corrugation in this direction, we obtain a good fit of the measured intensities (see dotted lone in fig. 4). O n Pd(ll0), the situation is even worse. It was impossible to fit the diffraction intensities by superposition of atomic charge densities. The Cu results had already shown a non-negligible corrugation along the close-packed rows. But on Pd(ll0), this corrugation is more than two times larger than experimentally derived (dex p = 0 . 0 4 ,~, dcalc = 0.096 ,~). The total intensities diffracted into the first out-of-plane series of beams is approximately proportional to the square of the corrugation amplitude along the rows. This leads to an out-of-plane scattering much too strong as compared to experiment which prevents fitting to the real scattering. Since at a charge density 1.74 x 10 -3 e / a u 3, the average corrugation amplitude perpendicular to the rows matches the one found in the experiment (0.425 A), we are able to estimate the fl value for this material to be fl = 220 eV au 3.

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Fig. 4. Top: in-plane spectrum for N e / C u ( l l 0 ) . Full line: experiment. Dashed and dotted lines: results obtained by superposition of atomic charge densities. A contraction of 10% for the interlayer spacing is assumed in accordance with LEED calculations. Dotted lines: diffraction intensities after averaging the density along the rows simulating the smear-out of the charge. Dashed lines: the in-plane intensities (~v = 0 °) are too small because intensity is lost in the out-of-plane scattering (q~ = 5.7 °) owing to the corrugation along the close-packed rows, not observed experimentally.

So far, we have shown that Ne scattering is insensitive to normal relaxation of the top layer. Even for the simple surfaces considered, atomic superposition cannot describe the real corrugation along the rows: for Ni(ll0), the calculated out-of-plane scattering is smaller than measured; and for Cu(ll0), where one finds experimentally only in-plane scattering, there is an appreciable out-ofplane scattering. This means that the charge is differently distributed along the close-packed rows in different metals, which points to different bonding characteristics. The Esbjerg-Nerskov parameter/3 is at least in this approach material-dependent. In the last example, we demonstrate that /3 has also to be surface-dependent. Recent investigation of Ni(ll3) [16] allows us to compare this surface with the (110) of the same material. We constructed the N i ( l l 3) charge-density contour by superposition of atomic charge densities assuming a relaxation of 15.9%; this contraction of the first interlayer spacing was found by LEED [17]. The best fit was achieved at a charge density of.3..9X10 -4 e / a u 3. The corresponding parameter/3 with 125 eV au ~ is substantially smaller than for

M. Baumberger et al. / Ne diffraction from transition metals

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Ni (110) (175 eV au~). Thus, we are faced with the fact that 13 c a n n o t be transferred from one surface to another. From our work, we can draw the following conclusions: atomic beam diffraction is an excellent a n d very sensitive tool for studying the surface charge distribution. By c o m p a r i s o n with experimental corrugations, the quick a n d simple method of overlapping atomic charge densities can give hints on surface b o n d formation a n d charge redistribution. Q u a n t i t a t i v e d e t e r m i n a t i o n of geometrical relaxation effects is impossible without i n d e p e n d e n t knowledge of the E s b j e r g - N o r s k o v parameters. Previous claims [18] for such a sensitivity of atomic b e a m diffraction have to be treated with caution, especially since He is even less sensitive t o corrugation details than Ne. We also believe that the u n c e r t a i n t y of the proper E s b j e r g - N o r s k o v parameters a n d the oversimplified picture of superposition of atomic charge densities does not allow evaluation of b i n d i n g parameters for adsorbate-covered systems [19]. The authors wish to express their thanks to Professor H.C. S i e g m a n n for his interest in this work, to Dr. E. Stoll for stimulating discussions, a n d to the Schweizerische K o m i s s i o n zur F~3rderung der Wissenschaftlichen F o r s c h u n g for financial support.

References [1] T. Engel and K.H. Rieder, in: Structural Studies of Surfaces, Springer Tracts in Modern Physics, Vol. 91 (Springer, New York, 1982). [2] K.H. Rieder, Phys. Rev. B27 (1983) 7799. [3] N. Esbjerg and J. Norskov, Phys. Rev. Letters 45 (1980) 807. [4] M.J. Puska, R.M. Nieminen and M, Manninen, Phys. Rev. B24 (1981) 3037; M. Manninen, JK. Norskov and C. Umrigar, to be published. [5] K.H. Rieder and W. Stocker, Phys. Rev. Letters 52 (1984) 352. [6] B. Salanon, J. Phys. (Paris) 45 (1984) 1373. [7] K.H. Rieder and W. Stocker, Phys. Rev. B31 (1985) 3392. [8] D.R. Hamann, Phys. Rev. Letters 46 (1981) 1227. [9] F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, EnglewoodsCliffs, NJ, t963). [10] D. Haneman and R. Haydock, J. Vacuum Sci. Technol. 21 (1982) 330. [11] W. Kohn and L.J. Sham, Phys. Rev. 140 (1965) Al133. [12] J.C. Slater, Phys. Rev. 81 (1951) 385. [13] R. Feidenhans'l, J.E. Sorensen and 1. Stensgard, Surface Sci. 134 (1983) 329. 114] Y. Gauthier, R. Baudoing, Y. Joly, C. Gaubert and J. Rundgren, J. Phys. C17 (1984) 4547; W.Reimer, W. Moritz, R.J. Behm, G. Ertl and V. Penka, to be published. [15] J.R: Noonan and H.L. Davis, Surface Sci. 99 (1980) L424. [16] K.H. Rieder, M. Baumberger and W. Stocker, to be published. [17] D.L. Adams, W.T. Moore and K.A.R. Mitchell, Surface Sci. 149 (!985) 407. [18] N. Garcia, J.A. Barker and I.P. Batra, Solid State Commun. 47 (1983) 485. : [19] I.P. Batra and J.A. Barker, Phys. Rev. B29 (1984) 5286. . . . . . . .