Triple Hysteresis Loops and the Free-Energy Function in the Vicinity of the 5°C Transition in BaTiO3

Abstract

The effect of an electric field on the transition between the orthorhombic and tetragonal states in single crystals of BaTi${\mathrm{O}}_{3}$ has been investigated. With zero bias the tetragonal to orthorhombic transition occurs near 5\ifmmode^\circ\else\textdegree\fi{}C and the inverse transition at 11\ifmmode^\circ\else\textdegree\fi{}C, exhibiting a temperature hysteresis of about 6\ifmmode^\circ\else\textdegree\fi{}C. As expected, an external field in the direction of the polarization in the tetragonal state lowers both transition temperatures. Measurements show that the temperature depression varies linearly with the field. A strong field (>20 kv/cm) can lower both transition temperatures below the 5\ifmmode^\circ\else\textdegree\fi{}C transition at zero field. Thus at a constant temperature, in a small temperature range below 5\ifmmode^\circ\else\textdegree\fi{}C, the crystal can be switched reversibly between the two states by means of an electric field. Since the spontaneous polarization is smaller in the orthorhombic state, this phenomenon can be displayed as a "triple loop" in the familiar polarization vs electric field hysteresis plot. The dielectric constant has been measured as a function of temperature, and as a function of field at fixed temperatures. Transitions between states are sharp whether the transition is produced by varying the temperature or the electric field, provided the faces are completely electroded.Numerical coefficients for various terms in the free-energy expansion for BaTi${\mathrm{O}}_{3}$, have been determined from certain of the experimental measurements. Calculations for various physical properties based upon the free-energy expansion agree reasonably well with these properties determined experimentally.