XAFS and Thermal Averaging

Abstract
XAFS measures ρ(r), the distribution of the magnitude r of the relative vector displacement f between a center probe atom and its neighbors. The related ρ(r^→) of the distribution of the vector distance between the probe atom and its neighbors defines a pair potential V(r^→) which is thermally averaged over the position of all of the other atoms in the material being investigated. It is shown that there are subtle differences between ρ(r) and p(r^→) which lead to a new correction term to XAFS measurements necessary to obtain the correct thermal expansion of interatomic distances. Besides measuring ρ(r), XAFS allows the determination of both ρ(r^→) and V(r^→) which include σ²_⊥ addition to the usual σ²_x, the mean squared vibrational disorder perpendicular and along the line between the average position of the pair of atoms, respectively.