Higher-order thermal motion tensor analysis and atom disorder in cubic melanophlogite

Abstract

The structure of the high temperature form of melanophlogite (MEP) at 84 °C was refined by using a least squares refinement that was based on the Gram-Charlier expansion of the atomic probability density functions (PDF) up to the fourth-order terms. The refinements of 95 variable parameters on the space group Pm3n converged to R = 0.0275 (R_w = 0.0313) for the 607 observed reflections in single crystal X-ray diffraction. The PDFs for three types of O atom (in total, there were four types, O₁ to O₄) were both broad and strongly distorted from an ellipsoidal shape: unimodal for O₁, bimodal for O₂, and concave-spheroidal for O₄. Their zero-contours covered areas with radii of 0.75-1.0 Å in sections perpendicular to the shortest axes of thermal ellipsoids. The characteristic appearance of the PDF is interpreted as arising from disordered atoms in the 12 domains of low MEP. The tetragonal cell of low MEP, which is a (2 × 2 × 1)-superstructure of high MEP, is three-fold rotationally twinned around [111] (of the cubic cell) and, then antiphase translation in [100], [010] and [110] generates antiphase domains to result into a cubic average structure.