Effect of a Two-Dimensional Pressure on the Curie Point of Barium Titanate

Abstract

By hydraulic means, a single crystal of barium titanate in the shape of a flat circular disk was subjected to a pressure exerted on its edges and not on its faces. A very slight pressure removed all domains that were not normal to the disk. The stress system then consisted of equal pressures on the two $a$ axes, and no pressure on the $c$ axis. The transition temperature increased with the square of the two-dimensional pressure, while, according to Merz, a hydrostatic pressure produces a linear drop. Using Devonshire's expansion for the free energy and the appropriate Legendre transformation, the free energy, depending on polarization and pressure, was obtained for both two-dimensional and hydrostatic stress systems. This yielded a purely linear-pressure dependence, and it was, therefore, necessary to supplement Devonshire's expansion with higher terms in order to obtain a quadratic effect.Although it was too difficult to evaluate the effect of pressure on the transition temperature itself when higher terms were included, it was easy to determine the effect on the Curie-Weiss temperature ${T}_{0}$. This is the temperature at which the inverse susceptibility of the cubic phase extrapolates to zero, and its pressure dependence will be the subject of a future paper. For both two-dimensional and hydrostatic pressures, the linear part of the shift of the Curie-Weiss temperature was found to depend only on the lower terms in the free energy, and provide two independent relations for determining the two $g$ coefficients. The quadratic shift of the Curie-Weiss temperature depends on the higher terms with which Devonshire's expansion was supplemented, and a reasonable interpretation of these higher terms gave an upward direction to the quadratic shift of the Curie-Weiss temperature.