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Higher-order Landau-Devonshire theory for BaTiO3

The higher-order Landau-Devonshire theory for BaTiO3 is 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 eighth power when the three parameters vary in the experiment. We propose the tenth 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 tenth potential are in good agreement with experimental data on the spontaneous polarization, dielectric constants, dielectric susceptibility and piezoelectric coefficients versus the temperature and the electric field.