Landau thermodynamic potential for BaTiO3.

In this paper the description of the dielectric and ferroelectric properties of BaTiO₃ single crystals using the Landau phenomenological thermodynamic potential was addressed. Our results suggest that when using the sixth-power free energy expansion of the thermodynamic potential, remarkably different values of the fourth-power coefficient, β (the coefficient of P_i⁴ terms), are required to adequately reproduce the nonlinear dielectric behavior of the paraelectric phase and the electric field induced ferroelectric phase (E_b|[001]), respectively. In contrast, the eighth-power expansion with a common set of coefficients enables a good description for both phases at the same time. These features, together with the data available in literature, strongly attest to the necessity of the eighth-power terms in Landau thermodynamic potential of BaTiO₃. In addition, the fourth-power coefficients, β and ξ (the coefficient of P_i²P_j² terms), were evaluated from the nonlinear dielectric responses along [001], [011], and [111] orientations in the paraelectric phase. Appreciable temperature dependence was evidenced for both coefficients above T_C. Further analysis on the linear dielectric response of the single domain crystal in the tetragonal phase demonstrated that temperature dependent anharmonic coefficients are also necessary for an adequate description of the dielectric behavior in the ferroelectric phase below T_C. As a consequence, an eighth-power thermodynamic potential, with some of the anharmonic coefficients being temperature dependent, was proposed and compared with the existing potentials. In general the potential proposed in this work exhibits a higher quality in reproducing the dielectric and ferroelectric properties of this prototypic ferroelectric substance. [ABSTRACT FROM AUTHOR]