Dependence of cumulants and thermodynamic parameters on temperature and doping ratio in extended X-ray absorption fine structure spectra of cubic crystals

The thermodynamic properties and anharmonic perturbation factor of orderly doped crystals are described in terms of the cumulants in extended X-ray absorption fine structure (EXAFS) spectra. The thermodynamic parameters and cumulants are studied based on the anharmonic correlated Einstein model. We derive analytical expressions for the dispersion relation, the correlated frequency and Einstein temperature, and the EXAFS cumulants. Parameters of the Morse potential, thermal expansion coefficient due to effect of anharmonicity, anharmonic factor, the EXAFS phase including the anharmonic effects depend on doping ratio of cubic-structure crystals are considered. The derived anharmonic effective potential includes the contributions of all the nearest neighbors of the absorbing and scattering atoms to account for three-dimensional interactions and the parameters of the Morse potential to describe single-pair atomic interactions. Numerical results for face-centered cubic (fcc) crystals of copper (CuCu) and silver (AgAg) and their compound AgCu agree reasonably with experiments and other theories.