The crystal chemistry of synthetic potassium-bearing neighborite, (Na_{1− x} K _x )MgF₃

Abstract

 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 (Na_{1− 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 [110] and [001] 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 [001] axis of the cubic subcell (φ) ranging from 4.5° to 4.8° (determined from the atomic coordinates). The solid solution (Na_{1− 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.