Mean-Square Displacements of Surface Atoms in the Continuum Approximation

Abstract

The mean-square displacement of an atom on a crystal surface is investigated using a model which approximates the lattice by an isotropic elastic continuum with a stress-free surface. Mean-square displacements both parallel and perpendicular to the surface are calculated for atoms on the surface and in the interior. The relative contributions of the various types of modes are shown as a function of temperature. The results of the continuum analysis are compared with lattice-dynamical calculations. Qualitative agreement is obtained both in relative magnitude and temperature dependence. Theoretical estimates for the high-temperature limit of the mean-square displacement perpendicular to the surface are in reasonable agreement with experimental values reported for tungsten.