The Structure of Spinels: A Quantitative Assessment of the AB2X4 Family

Abstract

Compounds with the general formula AB2X4 crystallize with the atomic structure of the mineral spinel, MgAl2O4, described by three degrees of freedom: lattice parameter a, anion parameter u, and cation inversion parameter λ. Here, bond valence sum validation of 1244 ambient structures (338 compositions, 1915–2025) from the Inorganic Crystal Structure Database provides the first quantitative assessment. Cubic Fd 3̲$\underline{3} $m accounts for 86% of structures, tetragonal I41/amd for 8%, and B‐site cation‐ordered P4332 for 5%. Normal‐type ordering (A cation tetrahedral) is the majority arrangement (51%). The anion parameter is nearly invariant with cation disorder, shifting by only 0.002 across the full λ range, consistent with thermodynamic equilibrium rather than being a structural defect. The polyhedral volume ratio Voct/Vtet (median 2.9) is 27% below the ideal value, narrowing the tetrahedral–octahedral distinction and lowering the enthalpic cost of cation redistribution. A generalized anion parameter framework (ueff, Δu) is proposed to extend the single cubic anion coordinate to tetragonal and ordered structures for the first time. Oxides (88.9%) are well characterized; sulfides (10.0%) access nonclassical valence combinations at nearly double the oxide rate but remain undercharacterized. Prediction rules, benchmark data for 20 compositions, and refinement guidance are provided.