PARAMETERIZATION OF THE CRYSTAL STRUCTURES OF CENTROSYMMETRIC ZONE-BOUNDARY-TILTED PEROVSKITES: AN ANALYSIS IN TERMS OF SYMMETRY-ADAPTED BASIS-VECTORS OF THE CUBIC ARISTOTYPE PHASE

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The methods of group theory have been used to decompose the crystal structures of centrosymmetric perovskites, ABX 3 , that exhibit zone-boundary tilting of the BX 6 octahedra. For the fourteen 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 on the surface of the Brillouin zone. The advantage of this parameterization is twofold; firstly, octahedron tilt angles can be determined precisely and independently of the effects of octahedron distortion, and secondly, the degrees of freedom required by the perovskite structure can be rigorously derived. The method is outlined using the results of a neutron-diffraction investigation of CaTiO 3 in space group Pbnm , an example where the structural degrees of freedom are found to be one less than that required by the space group. Full results that can be very simply utilised in the decomposition of the other thirteen space-groups are tabulated. The advantages of decomposing perovskite-structured phases in this way are further illustrated using the temperature dependence of the crystal structure of KCaF 3 between 4.2 and 542 K.