A New Global Parameterization of Perovskite Structures

A new method is proposed for the quantitative description of all perovskite structures, ABX 3 . It extends earlier work on the relationship between polyhedral volume ratio V A /V B and octahedral tilt angles [Thomas (1996 a ). Acta Cryst. B 52 , 16–31] by defining additional parameters, Γ_i, which describe the planes formed by chains of octahedral stalks. The number of parameters required to define a particular perovskite structure, i.e. the number of structural degrees of freedom (d.o.f.), may be deduced from its atomic coordinates and cell parameters. Relationships between space group and these d.o.f. are examined for all known space groups, with particular attention paid to the group Pnma (No. 62), which is commonly found. Here the variation of the eight anion-related d.o.f. with V A /V B is investigated for: (i) different compositions; (ii) NaMgF 3 at different temperatures; (iii) MgSiO 3 at different pressures. Furthermore, the ability of the volume ratio V A /V B to act as a structural determinant permits a prediction of the structures ( i.e. cell parameters and atomic coordinates) of novel chemical compositions. It is anticipated that this method of predicting structures will find application in deriving good starting models for Rietveld refinements.