Semi-classical Anharmonic Correlated Einstein Model Debye–Waller Factors and EXAFS of Hcp Crystals

Abstract

A semi-classical anharmonic correlated Einstein model of hcp crystals is derived for the high-order expanded Debye–Waller factors and extended X-ray absorption fine structure. The many-body effect is included in this model based on the contributions of the first shell near neighbors of the absorber and backscatter atoms. The analytical expressions of Debye–Waller factors presented in terms of cumulant expansion up to the fourth order yield results based on the classical theory corrected for its absence of zero-point vibration. The anharmonic many-body effect effective potential is derived which includes the Morse potential for describing the single-pair atomic interactions. A method of providing all extended X-ray absorption fine structure quantities is created, correcting the absence of zero-point vibration in classical theory, combining it with the quantum one based on only the second cumulant. The derived model has the advantage of including both classical and quantum effects. The numerical results of all considered quantities of Zn (hcp) are found to be in good agreement with the experimental values.