Ferro-electric phase transitions

The quasiharmonic approximation studied in Sects.5.2,3 gives reasonable results for the thermodynamic properties of crystals in which the anhar-monicity is weak and the force constants are renormalized by thermal expansion only. In crystals with very strong enharmonic interactions, however, this approximation breaks down. Examples are the vibrations in rare-gas solids, in particular solid helium, soft modes in ferro-electric phase transitions and melting processes. For these cases a method has been developed, the self-consistent harmonic approximation (SCHA), which allows a qualitative description of the effects of strong anharmonicity. 

The soft mode concept can be extended to all distortive phase transitions (transitions with relatively small atomic displacements), even if they are only close to second order. In the case of a ferro-distortive transition, as for example in BaTiOs or KDP, the order parameter is proportional to the spontaneous electric polarization Fj. d F/ dp is not only proportional to co, but also to the dielectric susceptibility. This does not, however, mean that all components of the order parameter eigenvector must contribute to Ps. 

In a crystal of polar molecules it may well be as easy to reverse a molecule in its site as to form any other defect. This reversal will cost less in energy the more disorder is already present, and this co-operative effect may give rise to a dear order-disorder transition. The ordered phase may in particular be ferro- or antiferro-electric. The ferroelectric transition in thiourea is essentially of this nature. 

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