Bragg Institute, Australian Nuclear Science and Technology Organisation
Today relative stability of different modifications of perovskite structure type can be estimated with wide range of methods from simple geometric considerations based on the concept of ionic radii (tolerance factor) and bond valence approach (SPUDS) to energy calculations. However, in general these methods rely on tabulated values of radii, bond valence parameters, interatomic potentials, etc which are well established for room temperature but often unknown for non-standard conditions (high pressure, low/high temperature, etc).
Using a novel analytical approach we investigated crystallographic data for ~1800 perovskites ABX3 contained in the ICSD (release 2005-2). We show that parameterless method based on the analysis of M-X-M angles and A- and B- site polyhedra volume ratio (VA/VB) calculated directly from experimental results under any conditions can be used for (a) a unified description of crystal structure evolution during phase transitions according to group-theoretical analysis by Howard&Stokes and (b) estimating critical values at which phase transitions will occur in parametric studies (composition, temperature, pressure, etc). Comparison to other existing approaches and examples will be presented.