Theoretical X-Ray Absorption Debye-Waller Factors

TL;DR

This paper presents a theoretical approach to calculating Debye-Waller factors in x-ray absorption spectra using density functional theory and cumulant expansion, accounting for thermal effects and anharmonicity.

Contribution

It introduces a novel method combining DFT and cumulant expansion to accurately compute Debye-Waller factors, considering anharmonic effects and exchange-correlation sensitivities.

Findings

Results agree with experimental data for several materials.

The method captures thermal expansion and vibrational asymmetry.

Sensitivity to lattice constants affects Debye-Waller factor calculations.

Abstract

An approach is presented for theoretical calculations of the Debye-Waller factors in x-ray absorption spectra. These factors are represented in terms of the cumulant expansion up to third order. They account respectively for the net thermal expansion $\sigma^{(1)}(T)$, the mean-square relative displacements $\sigma^2(T)$, and the asymmetry of the pair distribution function $\sigma^{(3)}(T)$. Similarly, we obtain Debye-Waller factors for x-ray and neutron scattering in terms of the mean-square vibrational amplitudes $u^2(T)$. Our method is based on density functional theory calculations of the dynamical matrix, together with an efficient Lanczos algorithm for projected phonon spectra within the quasi-harmonic approximation. Due to anharmonicity in the interatomic forces, the results are highly sensitive to variations in the equilibrium lattice constants, and hence to the choice of exchange-correlation potential. In order to treat this sensitivity, we introduce two prescriptions: one based on the local density approximation, and a second based on a modified generalized gradient approximation. Illustrative results for the leading cumulants are presented for several materials and compared with experiment and with correlated Einstein and Debye models. We also obtain Born-von Karman parameters and corrections due to perpendicular vibrations.