Thermal expansion and x-ray-absorption fine-structure cumulants

Abstract

In the classical limit, a simple relation has been shown to exist between the thermal expansion coefficient α and the cumulants of the vibrational amplitude that are measured in x-ray-absorption fine structure (XAFS), i.e., αrT${\mathrm{\sigma }}^2$/${\mathrm{\sigma }}^{\mathrm{}\left(3\right)\mathrm{}}$=1/2, where ${\mathrm{\sigma }}^2$ is the mean-square vibrational amplitude, ${\mathrm{\sigma }}^{\mathrm{}\left(3\right)\mathrm{}}$ the third cumulant, T the absolute temperature, and r the equilibrium bond length. We generalize this relation to the quantum case using a correlated Einstein model and thermodynamic perturbation theory, and find αrT${\mathrm{\sigma }}^2$/${\mathrm{\sigma }}^{\mathrm{}\left(3\right)\mathrm{}}$=[3z(1+z)ln(1/z)]/[(1-z)(1+10z+${\mathit{z}}^2$)], where z=exp(-${\mathrm{\Theta }}_{\mathit{E}}$/T), and ${\mathrm{\Theta }}_{\mathit{E}}$ is the Einstein temperature. This result is found to be in agreement with the measured thermal expansion coefficient and XAFS cumulants in RbBr at 30 K and 125 K.