The Ginzburg interval in soft-mode phase transitions: consequences of the rigid unit mode picture

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Abstract
In soft-mode structural phase transitions the Ginzburg temperature interval in which fluctuations and the interactions between them become important is often observed to be small on the scale of the transition temperature. We consider the size of the Ginzburg interval (GI) in framework and 'cogwheel' structures using the concept of 'rigid unit modes'. Such materials, as well as being very displacive, i.e. close to the soft-mode limit, have an extremely anisotropic phonon spectrum. Modelling these two properties with a suitable effective Hamiltonian for the degrees of freedom driving the transition we find that the GI can range from very small to large, depending on the balance between displaciveness and anisotropy. For the two perovskites SrTiO3 and LaAlO3 and the 'cogwheel' structure K2SeO4, we obtain values of the model parameters describing displaciveness and anisotropy from experimentally measured phonon dispersions and find, for the size of the GI, quantitative agreement with experiment. We also estimate typical values for the model parameters and the size of the GI for framework silicates, using quartz and cristobalite as examples. Finally, we use computer simulations to confirm the results of our theoretical analysis over a wider range of model parameters.