Atomic order in the spinel structure - a group-theoretical analysis

Group-theoretical methods of the Landau theory of phase transitions are used to investigate the structures of ordered spinels. The possibility of the existence is determined of 305 phases with different types of order in Wyckoff position 8a (including seven binary and seven ternary cation substructures), 537 phases in Wyckoff position 16d (including eight binary and 11 ternary cation substructures), 595 phases in Wyckoff position 32e (including seven binary and four ternary anion substructures) and 549 phases with simultaneous ordering in Wyckoff positions 8a and 16d (including five substructures with binary order in tetrahedral and octahedral sublattices, two substructures with ternary order in both spinel sublattices, and nine substructures with different combined types of binary and ternary order). Theoretical results and experimental data are compared. Calculated structures of the spread types of ordered low-symmetry spinel modifications are given.