Extended x-ray-absorption fine-structure Einstein frequency and moments of the phonon spectrum: An experimental and theoretical study

Extended x-ray-absorption fine-structure measurements of the nearest-neighbor mean-square relative displacements (MSRD) for the fcc materials Ni, Cu, Yb, Pt, Au, Pb, and Th are presented. It is shown experimentally that the temperature dependence of the MSRD is well characterized by a single parameter ${\omega }_E$, the Einstein frequency. This frequency was found to be equal to the square root of the second moment of the phonon density of states 〈${\omega }^2$ ${〉}^{1/2}$ in all cases studied. Theoretical calculations are presented which show that if nearest-neighbor interactions dominate, ${\omega }_E$ should equal 〈${\omega }^2$ ${〉}^{1/2}$ to within 5%.