A new subgroup approach to the thermo-dynamic (Landau) theory of continuous phase transitions in structurally complex crystals

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Abstract
A brief review is given of the usual Landau theory. In the present work it is assumed that the free energy functional of a structurally complex crystal is a sum of sublattice free energies plus a small interaction term. The analysis is then reformulated in terms of the relevant effective sub-space groups of the sublattices: the order parameters, the subduction criteria, and the other conditions on admissible transitions are related to the effective subspace groups. It is found that a transition can be “nearly second order,” i.e. second order with respect to the subgroup but really first order with respect to the actual full space group for similar order parameters. The approach is illustrated on the A-15 compounds especially the transitions O h 3 → D4 5 and O h 3 → C7 4v produced by “strain-like” order parameters.