The structure of spinels: a quantitative assessment of the AB2X4 family

Compounds with the general formula AB 2 X 4 crystallize with the atomic structure of the mineral spinel, MgAl 2 O4 , described bythree degrees of freedom: lattice parameter a, anion parameter u, and cation inversion parameter λ. Here, bond valence sumvalidation of 1244 ambient structures (338 compositions, 1915–2025) from the Inorganic Crystal Structure Database provides the firstquantitative assessment. Cubic Fd3m accounts for 86% of structures, tetragonal I4 1 /amd for 8%, and B-site cation-ordered P4 3 32for 5%. Normal-type ordering (A cation tetrahedral) is the majority arrangement (51%). The anion parameter is nearly invariantwith cation disorder, shifting by only 0.002 across the full λ range, consistent with thermodynamic equilibrium rather than beinga 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 remainundercharacterized. Prediction rules, benchmark data for 20 compositions, and refinement guidance are provided.