PARAMETERIZATION OF CENTROSYMMETRIC ELPASOLITE-TYPE CRYSTAL STRUCTURES IN TERMS OF SYMMETRY-ADAPTED BASIS-VECTORS OF THE PRIMITIVE CUBIC ARISTOTYPE PHASE

摘要

Group-theory methods are used to decompose the crystal structures of centrosymmetric double perovskites, A_2BB'X_6, that exhibit zone-boundary tilting of octahedra and the rock-salt pattern of order of the B-site cations, typified by the mineral elpasolite, K_2NaAlF_6. For the twelve space-groups consistent with these phenomena, the associated structures are decomposed in terms of the magnitudes of an appropriate set of symmetry-adapted basis-vectors of the primitive cubic aristotype phase of perovskite at high-symmetry points of the Brillouin zone. The method is outlined using the example of Sr_2YNbO_6 in space group P2_1; full results that can be utilized in the decomposition of the other space-groups are tabulated. The advantages of decomposing elpasolite-structured phases in this way are further illustrated using the temperature dependence of the crystal structure of Ba_2SbBiO_6 between 4.2 and 625 K.