Abstract
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.
Highlights
A reversible transformation of the unit-cell parameters and atomic coordinates of centrosymmetric perovskites ABX3 into a Cartesian space is defined
It is likely that the imminent phase transition to post-perovskite at 125 GPa is triggered by the strong OÁ Á ÁO repulsions that will be associated with this degree of octahedral tilting
The ability of the method to analyse experimental structural data and the sequences of phase transitions between space groups has been demonstrated in x3 and x4
Summary
Synthetic perovskite-related compounds continue to attract the attention of many scientists and technologists, irrespective of whether they are working, for example, on the development of lead-free piezoelectric ceramics (Shrout & Zhang, 2007) or on organolead halide ABX3 nanocrystals for photochemical cells (Jena et al, 2019). Tamazyan & van Smaalen (2007) subsequently argued that inclination angles 1, 2 and 3 defined by Thomas (1996) were unnecessarily influenced by octahedral distortion They proposed an alternative method of calculating tilt angles, this was at the expense of losing the simple link to polyhedral volume ratio expressed by equation (1). The conflict between geometrical, i.e. crystal-chemical and group-theoretical methods in describing perovskite structures is somewhat contrived, since both have legitimate fields of application and have similar aims This was made clear in seminal work by Knight (2009), who utilized grouptheoretical methods to develop a general parameterization of centrosymmetric perovskites based on symmetry-adapted basis vectors of the Pm3m phase. Details of these methodological improvements are given
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