Abstract

The application of group theoretical methods to the study of phase transitions has been greatly facilitated by the implementation of these methods in computer programs such as ISOTROPY . Structures arising from the application of any specified distortion (irrep) or combination of distortions to a given parent structure can be listed, group-subgroup relationships established, and the nature of the transitions that might occur between the different structures assessed.

The methods have been applied to establish structural hierarchies for perovskites, which in turn have proved invaluable in assisting experimental investigations. The methodology will be illustrated by reference to diffraction studies of the temperature-induced phase transitions in SrZrO3, the discovery of a new high temperature phase in WO3 , and elucidation of the temperature-composition phase diagram for (Ca,Sr)TiO3. More recent applications will also be presented.

[1] H. T. Stokes, D. M. Hatch, and B. J. Campbell (2007). ISOTROPY , stokes.byu.edu/isotropy.html. [2] C.J. Howard and H.T. Stokes (2005), ‘Structures and Phase Transitions in Perovskites – A Group Theoretical Approach’, Acta Cryst. A61 , 93-111. [3] M.A. Carpenter, C.J. Howard, K.S. Knight and Z. Zhang (2006), ‘Structural Relationships and a Phase Diagram for (Ca,Sr)TiO3 Perovskites’, J. Phys.: Condens. Matter 18, 10725-10749.