Influence of ferroelectricity and dipole turning onelectrocaloric effect

In the three dimensional Landau-Devonshire ferroelectric theory, polarization is a variable of the Gibbs free energy function. The first derivative of the Gibbs free energy to polarization can be used to derive equilibrium values of the polarization and the energy level. When an external electric field ( E ) is applied, the derived polarization and energy level change according to angular degree between the polarization and the E , which can be derived by solving the Gibbs free energy function associated with the electric field. In the E direction the polarization increases with decreased Gibbs free energy level, in the anti- E direction the polarization decreases with increased Gibbs free energy level, and in the directions perpendicular to the E direction, polarization and the Gibbs free energy remain unchanged. If change in a Gibbs free energy level happens, the proportion of the dipole that forms the polarization will also change accordingly, which is derived by solving the Boltzmann distribution function via taking the Gibbs free energy as equilibrium energy level. The result demonstrates that proportion of the dipoles in the E direction increases, and proportions of the dipoles in other directions decrease. The changes in proportions of the dipoles between different directions can be described as turning of dipoles. This turning of dipoles to the E direction causes decrease in the entropy of dipole alignment, and the change in the entropy produces exothermal effect in adiabatic condition. On another aspect, a coupling effect will happen on the parallel aligned neighbor dipoles in the E direction by the action of the electric field to form reversible ferroelectric domains. When the E withdraws, the domains decouple. The coupling or decoupling of the reversible domains corresponds to exothermal effect or endothermal effect, respectively. As the coupling effect of dipoles causes electric hysteresis loop, the coupled thermal effects can be deduced from the polarization of the hysteresis loop which is associated with temperature and the electric field. The result shows that the change in entropy results in an exothermal peak, which shifts to higher temperature with the increase of E , even across the Curie temperature, under higher electric field. The coupling effect of the parallel aligned dipoles produces exothermal effect, decreasing with increase of temperature continuously. The present theoretic results can explain the relevant experimental results by numerical simulation of the derived equations.