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 ABX (3) into a Cartesian space is defined. Analytical expressions for the three vectors for the pseudocubic cell and three vectors for a BX (6) octahedron are derived for space groups Pbmn, Cmcm, Ibmm, P4/mbm, P4/nmc, I4/mcm and R 3 c. 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, θ(1), θ(2) and θ(3); angles of tilt of octahedra; AX (12):BX (6) polyhedral volume ratio, V ( A )/V ( B ); parameters η( A ) and η( B ) defining the relative contraction of inner AX (8) polyhedra and expansion of BX (6) octahedra due to octahedral tilting. The application of these parameters is demonstrated by reference to published crystal structures. The variation of η( A ) and η( B ) with temperature in the compositional series Sr (x) Ba(1–x )SnO(3) and Sr (x) Ba(1–x )HfO(3), as well as the temperature series of BaPbO(3) and CaTiO(3), is related to the sequence of phases Pbmn → Ibmm→ Pm 3 m. Stabilization of the Cmcm phase is likewise interpreted in terms of these two parameters for NaTaO(3) and NaNbO(3). The pressure evolution of the structures of MgSiO(3), YAlO(3), (La(1–x )Nd (x) )GaO(3) (0 ≤ x ≤ 1) and YAl(0.25)Cr(0.75)O(3) is modelled with the appropriate structural parameters, thereby also addressing the characteristics of the Pbmn → R 3 c transition. Simulation of MgSiO(3) up to 125 GPa and of YAlO(3) 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.