Structural Diversity of Ordered Pyrochlores

Pyrochlores belong to a numerous family of crystalline materials with a rich variety of technologically important functional properties and developed structural diversity of possible transformations including isosymmetric, reconstructive, and phase transitions of second order (and first order close to second order). Here, using a combination of group-theoretical and crystallographic analysis, we report a uniform classification of 343 types of possible ordered phases, which are theoretically derived from only one initial A2B2X6Y pyrochlore structure by different specific physical mechanisms (order parameters or its combinations) and show a hierarchical relationship between them. A symmetry analysis of the intrinsic relationships between structural degrees of freedom and atomic order in pyrochlore crystals made it possible to highlight six nominal classes of atomic order depending on the ordered sublattice, and by taking into account the role of the improper ordered parameters, only four classes remain: X, XY, ABX, and ABXY. For each of these abstract classes of atomic order the modified Bärnighausen tree, illustrating the symmetry pathways of group–subgroup relation and participation of relevant order parameters, was constructed. Three fundamental structural features of the ordered pyrochlores have been established: (a) the impossibility of "pure" (not accompanied by atomic displacements) cation ordering at the A and B pyrochlore sublattices (16d and 16c Wyckoff positions, respectively); (b) the impossibility of "pure" ordering of anions at the X sublattice (48f Wyckoff position); (c) atomic ordering in the A sublattice which is always accompanied by atomic ordering in the B sublattice. A brief review of experimentally known ordered pyrochlores consistent with our structural predictions is given. Finally, the main directions of the theoretical results application including interpretation of the phase transition origins, experimental property predictions, the choice of a model for structural refinement or for materials design as a starting point for energy calculations, and a classification of the hierarchical relationship between phases are discussed. This study provides a symmetry guide for the extensive family of ordered pyrochlores and shows the origin of its structural diversity.