General formulas are given for the exact calculation of the nonequilibrium properties of the one-dimensional system of equal-mass hard rods both for a finite but large system and in the limit of infinite size. Only properties which depend upon labeling one or more of the particles are nontrivial in this system. Various results are obtained on Poincaré cycles, delocalization of a particle with time and electrical conductivity when one particle is charged.

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Elastic low-energy-electron-diffraction intensity-energy spectra are calculated for Ni (001), (110), and (111) surfaces between 10 and 220 eV by the layer -K.o«inga-lt"ohn-Rostoker method and compared with recent room-temperature experimental results. The calculation uses the Wakoh self-consistent muffin-tin potential, retains eight phase shifts, and includes finite temperature effects (assuming a Debye spectrum). An effective Debye temperature of 335'K is found from the temperature dependence of spectral intensities, an energy-dependent imaginary potential roughly of the form P = 0.85K "3 for electron energy E (in eV) is determined by matching features of the calculated spectra to experiment, and the best values of the first interlayer spacing are found to be 1.76 A (the bulk spacing) + 0.02 + 0.02 A on the (001) surface, 1.24 -(0.06~0.02) A on the (110) surface, and 2.03 -(0.025 + 0.025) A on the (111) surface, With these parameters, excellent agreement with observed spectra is obtained in positions and shapes of peaks for several beams and a large number of incident angles. For all faces a small systematic deviation in peak positions is found with a ccnstant 11-eV inner potential, suggesting an inner potential varying from the expected static value of 13.5 at low energies to about 9 eV near 220 eV. Comparison of relative intensities between calculation with the above P(E) and experiment suggests that excitation of 3p electrons from Ni significantly enhances electron absorption above 65 eV.

The degree to which the surface atomic arrangement influences the bonding geometry of sulfur atoms on (001), (110), and (111) Ni surfaces is investigated by an analysis of experimental low-energy electron diffraction data. For all surfaces, the sulfur atoms reside in high-coordination sites-the atomic hollows of the surface; all nearest-neighbor Ni-S bond lengths are less than those of stable bulk compounds.In several previous studies 1 " 6 the applicability of low-energy electron-diffraction (LEED) intensity-energy calculations to determine the structure of clean nickel surfaces and chemisorbed atoms on the (001) nickel surface has been demonstrated. Knowledge of the bond lengths and bond sites for crystallographically different surfaces is basic to an understanding of surface chemical bonding. Ion-neutralization spectroscopy 7 and LEED/radiotracer 8 studies have attempted to determine the geometric structure of chemisorbed sulfur overlayers on Ni(001), Ni(110), and Ni(lll), but have obtained only qualitative information.We report here a structural analysis for chemisorbed sulfur overlayers on (110) and (111) nickel surfaces which, together with our previous analysis on the (001) surface, 5 " 6 allows for the first time the crystallographic dependence of chemisorption bond sites and bond lengths to be examined. We also demonstrate that the LEED analysis which was successful for c(2x 2) chalcogen structures on the (001) surface of nickel 4 is also applicable to e(2x 2) and/>(2x 2) sulfur overlayers on the (110) and (111) surfaces of nickel, respectively. A general conclusion is that the Ni-S bond lengths found on all surfaces are smaller than those occurring in stable Ni-S bulk compounds, but are comparable to the bond length which occurs in the metastable y phase of NiS (millerite).The application of the layer-KKR (Korringa-Kohn-Rostoker) method to the calculation of LEED intensity-energy spectra is identical to that previously discussed. 2t4,5t9 Using the symmetries observed from the LEED pattern to fix the translational periodicity of the overlayer atoms, we then model the particular overlayer mesh on the surface for different registries with the substrate (bonding sites) and for a large number of vertical displacements d L from the sub-strate. As previously described, 4 ' 5 when the calculations are carried out over a sufficiently large energy range, the model geometry is the dominating factor in the theoretical spectra and the fit to experiment-in contrast to the effects of small variations in the atomic scattering potentials, in the degree of damping of the electrons, or in the Debye temperature of surface atoms. Hence, it is possible to make a clearcut discrimination between bonding geometries despite the uncertainties in the scattering potential and the surface boundary conditions, and despite the approximations in the theory (e.g., use of muffin-tin potentials and isotropic thermal motion).In the model calculations, the self-consistent Hartree-Fock-Slater potential for Ni constructed by Wakoh 10 and a su...

General methods are developed for evaluating Mayer cluster diagrams for systems of molecules with orientation-dependent forces. These methods are particularly useful for obtaining chain and ring contributions. Simplification occurs for ordinary two-body forces in the absence of external fields because of invariance under rotation of the two-body complex as a whole. Using these methods we adapt Mayer's rearrangement procedure to calculate the cluster expansion of the potential of the average force between two ionic or dipolar solute molecules that are immersed and fixed in a gas of dipolar molecules. The comparison of this potential with the corresponding macroscopic quantity leads to a cluster expansion for the dielectric constant of the dipolar gas.

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