General Semiclassical Theory of Gas—Surface Scattering

Abstract

Owing to the short-range nature of the interatomic pair potential, the non-stationary part of the atom-surface interaction is assumed to be mainly contributed by the first layer of surface atoms. The instant configuration of this layer is described by the displacement u _k of kth atom from its equilibrium position R _k . It is convenient to express u _k through the amplitudes a _l of phonon modes l = (q,j) with wave vectors q and polarizations j (the system of units with ħ = 1 is used throughout this review):

$$ u_k = \sum\limits_l {\frac{{e_l }} {{\sqrt {2\omega _l MN} }}[\exp (iqR_k )a_l + exp( - iqR_k )a_l^* ],} $$

(1.1.1)

here M is the mass of crystal atom, N is the number of atoms in the crystal block; dispersion w _l and polarization vectors e _l are determined by the structure of both bulk and surface phonon modes.