The crystal chemistry of synthetic potassium-bearing neighborite, (Na1− x K x )MgF3
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A series of fluoride perovskites related to neighborite was investigated using X-ray and neutron diffraction techniques, and Rietveld profile refinement of powder diffraction data. The series (Na1− x K x )MgF3 comprises orthorhombic (Pbnm, a ≈ \(\), b ≈ \(\), c ≈ 2a p , Z=4) perovskites in the compositional range 0 ≤ x ≤ 0.30, tetragonal perovkites (P4/mbm, a ≈ \(\), c ≈ a p , Z=2) in the range 0.40 ≤ x ≤ 0.46, and cubic phases (Pm3¯m, Z=1) for x > 0.50. The structure of the orthorhombic neighborite is derived from the perovskite aristotype by rotation of MgF6 octahedra about the  and  axes of the cubic subcell. The degree of rotation, measured as a composite tilt Φ about the triad axis, varies from 18.2° at x=0 to 11.2° at x=0.30 (as determined from the fractional atomic coordinates). Orthorhombic neighborite also shows a significant displacement of Na and K from the “ideal” position (≤0.25 Å). The tetragonal members of the neighborite series exhibit only in-phase tilting about the  axis of the cubic subcell (φ) ranging from 4.5° to 4.8° (determined from the atomic coordinates). The solid solution (Na1− x K x )MgF3, shows a regular variation of unit-cell dimensions with composition from 3.8347 Å for the end-member NaMgF3 (reduced to pseudocubic subcell, a p ) to 3.9897 Å for KMgF3. This variation is accompanied by increasing volumes of the A-site polyhedra, whereas the volume of MgF6 octahedra initially decreases (up to x=0.40), and then increases concomitantly with K content. The polyhedral volume ratio, V A /V B , gradually increases towards the tetragonal structural range, in agreement with diminishing octahedral rotation in the structure. The P4/mbm-type neighborite has an “anomalous” polyhedral volume ratio (ca. 5.04) owing to the critical compression of MgF6 polyhedra.
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