Thermodynamic parameters depend on temperature with the influence of doping ratio of the crystal structure metals in extended X-Ray absorption fine structure

Abstract

The effects of the doping ratio and temperature on the cumulants andthermodynamic parameters of crystal structure metals and their alloys wasinvestigated using the anharmonic correlated Einstein model, in extended X-ray absorption fine structure (EXAFS) spectra. We derived analytical expressions for the EXAFS cumulants, correlated Einstein frequency, Einstein temperature, and effective spring constant. We have considered parameters of the effective Morsepotential and the Debye-Waller factor depend on temperature and the effects of the doping ratio of face-centered-cubic (fcc) crystals of copper (Cu-Cu), silver (Ag-Ag), and hexagonal-close-packed (hcp) crystal of zinc (Zn-Zn), and their alloys of Cu-Ag and Cu-Zn. The derived anharmonic effective potential includes the contributions of all the nearest neighbors of the absorbing and scattering atoms. This accounts for three-dimensional interactions and the parameters of theMorse potential, to describe single-pair atomic interactions. The numericalresults of the EXAFS cumulants, thermodynamic parameters, and anharmonic effective potential agree reasonably with experiments and other theories.