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

In the classical limit, a simple relation has been shown to exist between the thermal expansion coefficient and the cumulants of the vibrational amplitude that are measured in x-ray-absorption fine structure (XAFS), i. e. , ^2/^ (3) =1/2, where ^2 is the mean-square vibrational amplitude, ^ (3) 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 ^2/^ (3) =3z (1+z) ln (1/z) / (1-z) (1+10z+z^2), where z=exp (-₄/T), and ₄ 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.