Dependence on the temperature and doped ratio of the cumulants and thermodynamic parameters in XAFS of cubic crystals
DOI:
https://doi.org/10.51453/2354-1431/2017/153Keywords:
Phi Ä‘iá»u hòa; XAFS; Cumulants; Nhiệt Ä‘á»™ng; Tham số; Tá»· lệ.Abstract
Thermodynamic properties and anharmonic perturbation factor of orderly doped metal crystals has described throught by terms of cumulants expansion up to the fourth-order in X-ray absorption fine structure (XAFS) spectra, which have been studied base on anharmonic correlated Einsten model. Analytical expressions for dispersion relation, correlated frequency Einstein and temperature Einstein, and the XAFS cumulant up to the fourth level have been derived, the first cumulant or net thermal expansion coefficient, the second cumulant or mean square relative displacement (MSRD) or Debye-Waller factor (DWF) to describe the attenuation of x-ray scattering or coherent neutron scattering caused by thermal motion, the third cumulant and the fourth cumulant describe asymmetry for interactive potential of atoms in crystals at high temperatures, thermodynamic parameters and anharmonic perturbation factor inclusion the anharmonic effects contributions. Derived anharmonic effective potential includes contributions of all nearest neighbors of absorbing and scattering atoms to take into account three-dimensional interaction and Morse potential parameters for description single
pair atomic interaction. This research aims further away, the thermodynamic parameters and cumulants not only temperature dependence but also depend on the ratio of orderly dopants crystals. Numerical results are found to be in good and reasonable agreement with those of other theories.
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