Influence of phonons on the pair distribution function deduced from neutron powder diffraction

Abstract

The widths of the peaks in the pair distribution function (PDF) contain information on the phonons of a material. At large interatomic distances r the width of the peaks is fully determined by the thermal parameters. For low r, however, correlation effects reduce the width significantly, depending on the shape of the phonon dispersion curves. We have studied the sensitivity of the PDF with respect to the phonons by means of computer simulations based on various lattice dynamical models. The peak widths were calculated both in the one-phonon approximation as well as by a real space approach using displacement correlation functions. Exemplary results are presented for Ni, Rh, Nb, Ge, and ${\mathrm{CaF}}_{2}.$ We find that the PDF is rather insensitive to details in the phonon dispersion curves. Therefore, there is little hope to extract more information on the lattice vibrations from an experimental PDF than is contained in the thermal parameters. This finding contradicts a claim recently made by Dimitrov, Louca, and R\"oder [Phys. Rev. B 60, 6204 (1999)].