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 α and the cumulants of the vibrational amplitude that are measured in x-ray-absorption fine structure (XAFS), i.e., αrTσ2/σ(3)=1/2, where σ2 is the mean-square vibrational amplitude, σ(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 αrTσ2/σ(3)=[3z(1+z)ln(1/z)]/[(1-z)(1+10z+z2)], where z=exp(-ΘE/T), and ΘE 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.