Pressure-Dependent Anharmonic Correlated Einstein Model Extended X-ray Absorption Fine Structure Debye–Waller Factors

Abstract

A pressure-dependent anharmonic correlated Einstein model is derived for extended X-ray absorption fine structure (EXAFS) Debye–Waller factors (DWFs), which are presented in terms of cumulant expansion up to the third order. The model is based on quantum thermodynamic perturbation theory and includes anharmonic effects based on empirical potentials. Explicit analytical expressions of the pressure-dependent changes in the interatomic distance, anharmonic effective potential, thermodynamic parameters, first, second, and third EXAFS cumulants, and thermal expansion coefficient have been derived. This model avoids the use of extensive full lattice dynamical calculations, yet provides good and reasonable agreement of numerical results for Cu with experimental results of X-ray diffraction (XRD) analysis and pressure-dependent EXAFS. Significant pressure effects are shown by the decrease in the pressure-induced changes in the interatomic distance, EXAFS cumulants and thermal expansion coefficient, as well as by the increase in the pressure-induced changes in the interatomic effective potential, effective spring constant, correlated Einstein frequency, and temperature.