Phase transitions and (p-T-X) behaviour of centrosymmetric perovskites: modelling with transformed crystallographic data.

A reversible transformation of the unit-cell parameters and atomic coordinates of centrosymmetric perovskites ABX3 into a Cartesian space is defined. Analytical expressions for the three vectors for the pseudocubic cell and three vectors for a BX6 octahedron are derived for space groups Pbmn, Cmcm, Ibmm, P4/mbm, P4/nmc, I4/mcm and R3c. The following structural parameters may be derived from these vectors: up to six pseudocubic parameters defining octahedral geometry; length- and angle-based octahedral distortion parameters λ and σ; inclination angles of tilted octahedra, θ1, θ2 and θ3; angles of tilt of octahedra; AX12:BX6 polyhedral volume ratio, VA/VB; parameters ηA and ηB defining the relative contraction of inner AX8 polyhedra and expansion of BX6 octahedra due to octahedral tilting. The application of these parameters is demonstrated by reference to published crystal structures. The variation of ηA and ηB with temperature in the compositional series SrxBa1-xSnO3 and SrxBa1-xHfO3, as well as the temperature series of BaPbO3 and CaTiO3, is related to the sequence of phases Pbmn → Ibmm→ Pm3m. Stabilization of the Cmcm phase is likewise interpreted in terms of these two parameters for NaTaO3 and NaNbO3. The pressure evolution of the structures of MgSiO3, YAlO3, (La1-xNdx)GaO3 (0 ≤ x ≤ 1) and YAl0.25Cr0.75O3 is modelled with the appropriate structural parameters, thereby also addressing the characteristics of the Pbmn → R3c transition. Simulation of MgSiO3 up to 125 GPa and of YAlO3 up to 52 GPa in space group Pbnm is carried out by using the Birch-Murnaghan equation of state. In both cases, full sets of oxygen coordinates assuming regular octahedra are generated. Octahedral distortion is also modelled in the latter system and predicted to have a key influence on structural evolution and the sequence of phase transitions. The core modelling procedures are made available as a Microsoft Excel file. open access.