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.

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Anharmonic effective potential, Extended X-ray Absorption Fine Structure (EXAFS) and its parameters of hcp crystals have been theoretically and experimentally studied. Analytical expressions for the anharmonic effective potential, effective local force constant, three first cumulants, a novel anharmonic factor, thermal expansion coefficient and anhamonic contributions to EXAFS amplitude and phase have been derived. This anharmonic theory is applied to analyze the EXAFS of Zn and Cd at 77 K and 300 K, measured at HASYLAB (DESY, Germany). Numerical results are found to be in good agreement with experiment, where unnegligible anharmonic effects have been shown in the considered theoretical and experimental quantities.

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.

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