High-order EXAFS cumulants of diamond crystals based on a classical anharmonic correlated Einstein model

Abstract

The temperature dependence of high-order cumulants in extended X-ray absorption fine structure (EXAFS) of the diamond crystal structure was calculated and analyzed on the basis of the anharmonic correlated Einstein model and the classical statistical method. Thermodynamic parameters of a system were derived from the high-order anharmonic effective potential, where the Morse potential was used to characterize the interaction between each pair of atoms in expansion up to the fourth order. Analytical expressions for the first four cumulants and their contribution to amplitude reduction and phase shift were obtained in the simple form of the mean-square relative displacement or the correlated Einstein frequency. Numerical results for crystalline germanium were in good agreement with experimental values and values calculated by the quantum statistical method and other methods, especially with the values in the high-temperature range. The analytical results show that this method is useful to reduce measurement and data analysis of experimental EXAFS spectra.