Anharmonic thermal vibrations of atoms in MgAl2O4 spinel at temperatures up to 1933 K

Abstract

Anharmonic thermal vibrations of atoms in MgA120 4 spinel (Fd3m, Z = 4) have been studied using sets of accurate X-ray diffraction intensities of Bragg reflections at temperatures up to 1933 K. The study was initiated by refining the temperature factor T(Q) of each atom in the form of the second-rank tensor/3~j, the ellipsoidal model of harmonic vibration being assumed. Difference Fourier maps based on the structure factors obtained from the refinements at 293 K (R=0.0197), 1503 K (R=0.0413), 1663 K (g = 0-0432) and 1933 K (R =0.0431) revealed residual electron densities around the atoms at the tetrahedral site A (point symmetry 43m) and octahedral site B (3m) and also around the O atoms (3m), the models of occurrence suggesting anharmonic atomic thermal vibration. The observed intensities lob s (=IBragg+ ITOS) were corrected for thermal diffuse scattering to extract the real intensities of the Bragg reflections. The correction was based on the one-photon and first-order acoustic vibration model. For the anharmonic refinement, a cumulant expansion of T(Q) in