AB₂X₄ spinel structures: similarity and differences between the centrosymmetric, Fd3m, and noncentrosymmetric, F4₁32, space groups

Many compounds adopting the spinel AB 2 X 4 structure are technologically important owing to their tunable physical and chemical properties enabling diverse applications in energy storage, catalysis, magnetism, and functional ceramics. Most of them are traditionally assigned to the centrosymmetric space group Fd3m. However, the physical properties of some spinels are incompatible with centrosymmetry. This discrepancy is often accounted for by reducing the symmetry to the non-centrosymmetric space group F43m, allowing thus small atomic displacements from their original position in Fd3m. In this work, we demonstrate that the loss of the inversion symmetry can occur without any atomic displacements, since the centrosymmetric Fd3m and non-centrosymmetric F4 1 32 space groups are equivalent for structure determination and refinement based on X-ray diffraction data. If consistent with experiment, only the use of an anharmonic model of atomic displacements can distinguish these space groups. This study aims to clarify certain misconceptions regarding the structural symmetry and physical properties of spinel-type compounds.