Application of the Landau theory to elastic phase transitions

The Landau theory of phase transitions has been applied to elastic phase transitions pertaining to crystals belonging to each of the 32 crystallographic point groups. Investigation of the Landau free-energy expansions provides information about: (i) the order of the possible transitions, (ii) the associated acoustic mode (which for a second-order transition should soften completely at the transition temperature) and (iii) the higher-order elastic constant contributions to thermal expansion only. Emphasis has been placed on finding the form of third-order invariants (the fourth-order terms also have been obtained for cubic crystals), which are needed in any quantitative assessment of the applicability of the Landau theory to elastic phase transitions in which the order parameter is just a strain tensor component. Application of the theory to the f.c.c. to f.c.t., transition in In-TI alloys is discussed.