Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals

Abstract

In this work, the temperature dependence of the extended x-ray absorption fine structure (EXAFS) amplitude and phase of the first shell of face-centered cubic crystals was studied using the anharmonic correlated Einstein model and quantum statistical theory with first-order perturbation. 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. The analytical expressions of the temperature dependence of the first four EXAFS cumulants were calculated and evaluated in both low-temperature and high-temperature limits. The numerical results for crystalline copper were in good agreement with those obtained by the other theoretical procedures and experiments at several other temperatures. The analytical results of the contributions of the EXAFS cumulants to the amplitude reduction and phase shift of the EXAFS spectra discovered the role and meaning of high-order cumulants in the analysis of the temperature dependence of the EXAFS spectra.