From an analysis of diffraction data for Au(lll), we deduce that the observed 23-fold periodicity in the (110) direction can be described by a regular superstructure of one-dimensional extended stacking faults. We propose that this surface is a realization of the Frenkel-Kontorova model of competing interactions and that the periodic changes in^ stacking from ^^Cto ABA may thus take the form of solitons. The solitons, of half-width 11.8 A, lead to an average compression of 4% in the (110) direction.PACS numbers: 68.20. + t, 79.20.Rf Gold has the highest ductility and malleability of any element and therefore it is not surprising that it is the only metal for which the closed-packed (111) surface of an fee crystal has been observed to reconstruct. The Au(lll) reconstruction has been studied by LEED,^"^ reflection high-energy electron diffraction,"^ and TED^"^ (transmission electron diffraction). For all these experiments the observed splitting of the surface layer diffraction peaks has been interpreted in terms of a (/?xl) superstructure with /? = 22-23 along the {110) direction corresponding to an overall contraction of 4.4%. Recent highly resolved TED experiments by Takayanagi and Yagi'^ suggest that the compression is not uniform, but localized in two narrow transition regions where the stacking changes abruptly from ABC to ABA. In contrast to these observations Marks, Heine, and Smith^ report on electron microscopy studies with single-atom resolution which reveal an expansion of about 5% both normal to and within the surface plane in agreement with a postulated strong repulsion between the d shells of the atoms resulting from depletion of sp electrons in the surface layer. To resolve this issue we have studied Au(lll) single-crystal surfaces with high-resolution helium-atom diffraction. Compared to TED experiments He-atom diffraction probes only the very first layer and is completely insensitive to the bulk.Our diffraction results reveal up to five satellites of the specular beam along the (110) direction with a particularly strong second-order peak [ Fig. 1(a)]. We also observe a shift and a splitting of the (112) diffraction spots and threefold symmetry of the full diffraction pattern in place of the sixfold symmetry seen in all previous experiments [ Fig. Kb)].The He diffraction apparatus is the same as that used in high-resolution time-of-flight studies of surface phonons.^ The angle between incident and detected beams was fixed at 90° and the diffraction peaks are mapped out by rotation of the cyrstal in the scattering plane and about its surface normal. The He nozzle beam source is cooled by a closed-cycle He re-frigerator down to 40 K corresponding^ to a minimujn beam energy of about 8 meV (A:,-"^4 A~\ X = 1.6 A) with a resolution of 0.16 meV full width at half maximum (FWHM). The absolute value of /cy could be established to within better than 0.5% from a time-of-2.5 2.0 h 1.5h

Differential cross sections have been measured for the scattering of helium atoms from isolated CO molecules on a Pt(111) surface. The cross sections reveal an oscillatory structure as a function of scattering angle extending to large momentum transfer on both sides of the specular peak. Using a hard hemisphere model to approximate the interaction potential, the data can be well reproduced by a hard core of radius about 2.5 Å. This result is compared to the charge density profile of the adsorbed molecule and also to the gas phase interaction potential, and in both cases good agreement with the experimentally predicted classical turning points is found.

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Large-angle-diffraction oscillations in the intensity of helium atoms elastically scattered from randomly stepped Pt(lll) are reported. A formalism based on the concept of reflection-symmetry interference explains the observed features and the data analysis yields a value of 4.4-4.6 A for the hard-core repulsive cross section of a single step. The observed oscillations are sensitive to the presence of adsorbates at step sites.PACS numbers: 79.20. Rf, 61.16.Fk, 6L70.Ey, 68.35.Dv There is now considerable evidence that surface defects (steps, kinks, and point defects) provide the active sites for chemical reactions on single-crystal surfaces. 1 LEED provides the present standard technique for determining defect geometries and densities, 2 but to date its sensitivity has only been sufficient to study the statistical distribution of defects and not their individual details. The angle or energy dependence of the specular scattering of He atoms has been shown to provide quantitative information on step heights and average densities, 3 and more recently the attenuation of the specular beam in He atom scattering by steps has been demonstrated. 4 Since the integral total cross sections derived in the latter type of measurement are dominated by long-range attractive forces, they are rather large (= 12 A) (Ref. 4) and consequently do not provide direct details on the physical size or orientation of the steps, nor on changes in the immediate environment of the single steps as may occur during gas adsorption. In this Letter, we report on the first observation of large-angle hard-core diffraction from single randomly spaced monatomic steps on a single crystal surface, in this case Pt(lll). Since the observed diffraction patterns are determined by the interference of atom trajectories probing the repulsive potential of the step and the adjacent undisturbed smooth mirrorlike regions, the actual size and orientation of the single steps could be determined. We also see striking changes in the step diffraction as CO is adsorbed at the steps, demonstrating that valuable chemical information on active sites in heterogeneous catalysis can be obtained by this new technique.The observation of diffraction from single steps has been made possible by the introduction of highresolution He nozzle beams and sensitive time-offlight detection techniques used to study surface phonons. 5 The apparatus is essentially identical to that used in the phonon studies; however, in the present experiment only the elastic peak is of interest. The helium beam energy can be varied between 8 and 80 MeV (/c/ = 4-12.7 A"" 1 ) with a velocity resolution Av/v of 1%. The polished Pt (111) crystal was cleaned in vacuum (base pressure 10"" 10 Torr) by cycles of sputtering, annealing at 1000 K, and heating in oxygen until no impurities were detected in the Auger trace. In most of the experiments the sum of incident 0, and final angles B f is 90°. The parallel momentum transfer, AJ£= B fc/(sin0/--sin0/), is varied by rotation of the crystal in the scattering plane ...

Phys. Rev. Lett. 54, 1940 (1985].In our recent Letter we introduced an ab initio model for spherically symmetric charge relaxation of ions in a crystal, called potential-induced breathing (PIB), and demonstrated its importance in the calculation of elastic constants. We also investigated the splitting of the longitudinal optic (LO) and transverse optic (TO) mode frequencies, which results from the macroscopic field associated with longitudinal modes. In the discussion immediately before and after Eq. (5) we argued, incorrectly, that the only contributions to the LO-TO splitting from PIB were from terms involving S*, the derivative of the self-energy of the fcth ion with respect to the electrostatic potential at the fcth-ion site. In fact, other terms within the PIB model contribute as well. Further study has shown that the treatment of macroscopic field effects in the PIB model is not straightforward. This will be discussed in a future paper (R. E. Cohen, L. L. Boyer, and M. J. Mehl, to be published).