Phonons from neutron powder diffraction

Abstract

The spherically averaged structure function $S(|\mathbf{q}|)$ obtained from pulsed neutron powder diffraction contains both elastic and inelastic scattering via an integral over energy. The Fourier transformation of $S(|\mathbf{q}|)$ to real space, as is done in the pair density function (PDF) analysis, regularizes the data, i.e., it accentuates the diffuse scattering. We present a technique which enables the extraction of off-center $(|\mathbf{q}|\ensuremath{\ne}0)$ phonon information from powder diffraction experiments by comparing the experimental PDF with theoretical calculations based on standard interatomic potentials and the crystal symmetry. This procedure [dynamics from powder diffraction] has been successfully implemented as demonstrated here for two systems, a simple metal fcc Ni and an ionic crystal ${\mathrm{CaF}}_{2}.$ Although computationally intensive, this data analysis allows for a phonon based modeling of the PDF, and additionally provides off-center phonon information from neutron powder diffraction.