Temperature dependence of the polarization and the dielectric constant near the paraelectric-ferroelectric transitions in BaTiO3

Temperature dependences of the spontaneous polarization and the dielectric constant are calculated near the paraelectric-ferroelectric (cubic-tetragonal) transition in BaTiO₃ using our mean field model. By expanding the free energy in terms of the spontaneous polarization (order parameter), expressions for the temperature dependence of the spontaneous polarization and the dielectric constant are derived. By considering the temperature dependence of the Raman frequencies for the lattice mode (～310 cm^?1) which is related to the spontaneous polarization, the experimental data from the literature is analyzed near the first order paraelectric-ferroelectric transition in BaTiO₃. The dielectric constant is then calculated as a function of temperature for the cubic-tetragonal transition in BaTiO₃. Our results show that the observed behavior of the spontaneous polarization in the ferroelectric phase (TC) and that of the dielectric constant in both paraelectric (T>T_C) and ferroelectric phases, can be described adequately by the mean field model studied here for BaTiO₃.