High-order expanded XAFS Debye–Waller factors of HCP crystals based on classical anharmonic correlated Einstein model

Abstract

In this paper, high-order expanded anharmonic effective potential and Debye–Waller factors in X-ray absorption fine structure (XAFS) of hcp crystals have been studied based on classical anharmonic correlated Einstein model. Here XAFS Debye–Waller factors are presented in terms of cumulant expansion up to the fourth order and their analytical expressions have been derived based on classical statistical theory. They contain the parameters of a derived high-order anharmonic effective potential that takes into account all nearest neighbors of absorber and backscattering atoms, where Morse potential is assumed to describe interatomic interaction included in this derived anharmonic effective potential. The dependence of the derived cumulants on atomic vibrations is described by their proportionality to the correlated Einstein frequency. This model avoids full lattice dynamical calculations yet provides good agreement of numerical results for Zn and Cd with experiment at several temperatures.