Higher-order Landau phenomenological models for perovskite crystals based on the theory of singularities: a new phenomenology of BaTiO3

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Abstract
The higher-order Landau phenomenological models for perovskite crystals based on the theory of singularities are proposed. The structural stabilities of some Landau potentials proposed for the phenomenology of BaTiO3 until now are discussed in the framework of the singularity theory. We confirm that the structurally stable Landau potential has to contain at least all the invariants up to the eighth power when the three parameters vary in the experiment. We propose the 10th-order Landau potential for adequate description of the various experimental data for BaTiO3 crystal. We show that the results of the phenomenology based on the 10th potential are in good agreement with the experimental data on spontaneous polarization, dielectric constants, dielectric susceptibility and piezoelectric coefficients versus the temperature and the electric field.

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