  In the paper, the description of the dielectric and ferroelectric properties
of BaTiO_3 single crystals using Landau thermodynamic potential is 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, \beta (the coefficient of P^4_i terms), are required to adequately
reproduce the nonlinear dielectric behavior of the paraelectric phase and the
electric field induced ferroelectric phase, 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 BaTiO_3. In addition,
the fourth-power coefficients, \beta and \xi (the coefficient of P^2_i P^2_j
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. 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.
