The Electric and Optical Behavior of BaTi${\mathrm{O}}_3$ Single-Domain Crystals

The dielectric constants, the spontaneous polarization, and the optical properties of BaTi${\mathrm{O}}_3$ single-domain crystals have been measured as a function of temperature. It is shown that the deformation of the crystal in the tetragonal state is proportional to the square of the spontaneous polarization, in analogy to the behavior of the other ferroelectrics, and that the temperature dependence of the birefringence is proportional to the square of the spontaneous polarization. The change of the polarization at the two lower transition points is consistent with the assumption that the Ti ions in the oxygen octahedra are displaced from the [001] to the [011] and later to the [111] direction.