Localversusaverage structure: a study of neighborite (NaMgF3) utilizing the pair distribution function method for structure determination

The temperature-dependent local structure (< 2 nm) of neighborite (NaMgF3) is probed through least-squares refinement of structure models fit to the pair distribution function [G(r)] derived from the total high-energy X-ray scattering of sample powders. In contrast to previous temperature-dependent structure models obtained through Rietveld refinement and statistical modelling of powder diffraction data, it is found that the average Mg—F bond length, corresponding to a ∼2 Å peak in theG(r), increases between 323 and 1123 K. At each temperature, asymmetry in this peak is consistent with an orthorhombic (Pbnm) perovskite local structure, allowing three unique Mg—F values and deformation of MgF6octahedra. Defined by the three orthogonal Mg—Mg distances, the pseudo-cubic unit cell of local structure models becomes metrically tetragonal and cubic at temperatures greater than ∼623 and 1038 K, respectively. A discontinuity in the temperature dependence of the fluorine atomic displacement parameters at 1038 K suggests thermal activation of new vibrational modes in NaMgF3at high temperature, consistent with transverse vibration of the bridging fluorine atoms (Mg—F—Mg).