Atom Motion at Model Crystal Surfaces

Abstract

We have studied the motion of atoms in and near the surfaces of model crystals using an expectation value of the form < u_α($\overrightarrow{e}$) u_β($\left( \overrightarrow{{{e}'}} \right)$ >, where u_α($\overrightarrow{e}$) is the α^th Cartesian component of displacement of atom $\overrightarrow{e}$ from its equilibrium position. The method of continued fractions has been used to construct the spectral densities ρ_αβ($\overrightarrow{e}\overrightarrow{{{e}'}}$ ;ω). Analysis of these densities provides insights into which phonons contribute to atomic displacements, parallel and perpendicular to the surface, and which phonons contribute to the correlated motion of neighbouring atoms. We have compared the spectral densities with phonon dispersion curves obtained from slab calculations, and have examined the usefulness of spectral density in interpreting the results of electron energy loss spectroscopy experiments. In this paper we present a brief description of the method, and the results for tungsten, rhodium, nickel, and for oxygen adatoms on nickel.

Recently there have been several papers dealing with atom dynamics at metal surfaces in which a continued fraction technique is employed. This technique allows one to calculate spectral densities and mean square displacements. It has been used by Black, Laks and Mills¹to study atom motion at the W(100) surface, by Mosteller and Landman² to study atom motions at a step on the Pt(111) surface, and by Black³ to study motion of adatoms on the Ni(111) surface.

It is the intention of this paper to concentrate on what can. be achieved with the application of the continued fraction method. We begin with a discussion of the theory of the method, and the accuracy to be expected. This is followed by an examination of spectral density and mean square displacement obtained for a number of metals, and for various models of the interaction between atoms. In the third section of the paper prominent peaks in the spectral density are interpreted using dispersion curve data obtained by means of slab calculations.⁴

In the fourth section of the paper we examine the application of the method to the study of atom correlations in the surface. Then in the fifth section we apply the method to the motion of adatoms at the nickel (111) surface. We conclude with a comparison of our data with the electron energy loss spectra obtained by Ibach and Bruchmann⁵ and Ibach⁶, and with a few remarks about future applications of the continued fraction method.

On leave of absence from Physics Department, Brock University, St. Catharines, Ontario L2S 3Al, CANADA.

UCI Technical Report #80–56.