Local versus average 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 the G(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 MgF₆ octahedra. 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 NaMgF3 at high temperature, consistent with transverse vibration of the bridging fluorine atoms (Mg - F - Mg).