Analysis of EXAFS Spectra of Crystalline Copper using Classical Anharmonic Correlated Einstein Model

Abstract

In this work, the temperature dependence of extended X-ray absorption fine structure (EXAFS) of the crystalline copper structure was calculated and analyzed using the anharmonic correlated Einstein model and the classical statistical theory. The thermodynamic parameters of a system are derived from an anharmonic effective potential that has taken into account the influence of all nearest neighbors of absorbing and backscattering atoms in the crystal lattice with thermal vibrations, where the Morse potential is assumed to characterize the interactions between each pair of atoms and the function of anharmonic EXAFS spectra presented in terms of the cumulant expansion up to the fourth-order. Analytical expressions for the first four cumulants and their contribution to amplitude reduction and phase shift obtained in the simple form of the mean-square relative displacement or the correlated Einstein frequency. The numerical results for crystalline copper were in good agreement with those obtained by the other theoretical procedures and experiments at several temperatures. The analytical results show that this calculation model is useful to reduce measurement and data analysis of experimental EXAFS spectra.