XAFS and thermal averaging

XAFS measures p(r), the distribution of the magnitude r of the relative vector displacement r̄ between a center probe atom and its neighbors. The related p(r̄) of the distribution of the vector distance between the probe atom and its neighbors defines a pair potential V(r̄) 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 p(r) and p(r̄) which lead to a new correction term to XAFS measurements necessary to obtain the correct thermal expansion of interatomic distances. Besides measuring p(r), XAFS allows the determination of both p(r̄) and V(r̄) which include σ²_⊥ in addition to the usual σ²_z, the mean squared vibrational disorder perpendicular and along the line between the average position of the pair of atoms, respectively.