Efficient Evaluation of Temperature‐Dependent <scp>EXAFS</scp> Debye–Waller Factor of Au Using a Classical Correlated Einstein Model

ABSTRACT The temperature‐dependent Debye–Waller (DW) factor in extended X‐ray absorption fine structure (EXAFS) for gold (Au) is investigated by explicitly accounting for thermal disorder effects. The theoretical model is constructed by combining classical statistical theory with the correlated Einstein model and the anharmonic effective potential to describe correlated local Au–Au vibrations. Within this framework, analytical closed‐form expressions for thermodynamic EXAFS parameters are derived, explicitly incorporating atomic correlation and anharmonicity arising from nearest‐neighbor interactions. Numerical results for Au reproduce the temperature‐ and wavenumber‐dependent attenuation of the EXAFS amplitude and remain consistent with the reported experimental trends and uncertainties, particularly in the temperature region where the classical approximation is valid. The validity range of the classical treatment is quantified by the relative deviation between the quantum and classical mean‐square relative (MSR) displacements, yielding a temperature threshold condition T ≥ 0.912 θ E , where θ E is the correlated Einstein temperature. A sensitivity analysis of the Morse potential parameters shows that the anharmonic force constants and EXAFS DW damping at high wavenumbers are especially sensitive to the potential‐width parameter, whereas the overall temperature‐ and wavenumber‐dependent behaviors remain robust. The analysis demonstrates that the present calculation model provides a physically transparent and computationally efficient framework for modeling temperature‐dependent EXAFS DW factor in Au under thermal disorder. Because MSR displacement is obtained analytically from the AE potential and the statistical formalism, the present model can be incorporated into standard EXAFS fitting procedures as a physically constrained description of thermal damping in Au and related metallic systems.