Numerical study of the minimum of the thermodynamic potential of a ferroelectric barium titanate

The macroscopic polarization is the most essential concept in any phenomenological description of dielectric media. The presence of a spontaneous macroscopic polarization is the defining property of a ferroelectric material that is central to whole physics of ferroelectrics. Based solely on symmetry considerations, Landau theory can provide a reliable description of a system equilibrium behavior near a phase transition. This phenomenological approach allows giving relations between measurable quantities using a minimal set of input parameters that can be determined by comparison with physical experiment or numerical first-principles calculation. Now, the problem of true presentation of Landau-Devonshire potential for different materials is outstanding. The properties of Landau-Devonshire thermodynamic potential (TP) for ferroelectric materials in this article is investigated on the example of barium titanate. The previously approved topological method of research of nonlinear properties of ferroelectrics is applied. The cellular complexes approach use for interpretation of TP extremes. The new representation of the 8-order polynomial TP compared with previously used 6-order representation. For the 8 order potential the structure of metastable states for barium titanate is presented in the vicinity of first-order phase transition point at T = 5°C. New method proposed for the qualitative description of the metastable states structure that TP generates. Based on the method the temperature regions are pointed where the 6 and 8 order potentials predicting for the metastable states are qualitatively different.