Mechanisms Of Pyroelectric Coefficients In Intrinsic Mode And Electric Field Enhancement Mode For Ferroelectrics

A ferroelectric has a primary property of symmetry dipole distribution in its possible orientation directions. As pyroelectric coefficient of a ferroelectric is the derivative of the polarization with respect to temperature, caused by the change in temperature, a ferroelectric has not pyroelectric effect in absence of electric field, because when temperature changes, the change in polarizations due to the corresponding dipoles in each orientation direction is same. However, if the ferroelectric is polarized in strong electric field to cause irreversible domain, the polarized ferroelectrics or pyroelectrics has an intrinsic mode of pyroelectric effect. On the other hand, during a reversible polarization process by an externally applied electric field (E), the ferroelectric will have electric field enhancement mode of pyroelectric effect due to two aspects: The rotation of dipoles towards E-direction, and the changes in polarizations of the E-direction and of its opposite direction. In this paper, the theoretical formulae of pyroelectric coefficient of the two modes are derived by introducing the dipole coupling on the basis of the Landau-Devonshire ferroelectric phenomenologic theory by considering two different responses of the two polarizations in these two opposite directions, along and anti- the E-direction. The two responses of the two opposite polarizations were described by two Gibbs free energies combined with the E. The orientation probabilities of dipoles in all possible orientation directions follows the Boltzmann statistic distribution. The changes in the orientation probabilities of dipoles can be considered as rotations of dipoles. With the increase in E, valley of the opposite Gibbs free energy rises. When the E increases to a critical value, the valley of the Gibbs free energy disappears, accompanying by the re-distribution of dipoles, resulting in a sudden explosive increase of the rotation of the dipoles to the E-directions. This critical behavior in polarization causes various critical phenomena, such as polarization, dielectric constant, and pyroelectric coefficient. For the temperature far below the Curie temperature, the critical electric field is very large and critical behavior is rather small. By deducing the derivative of the orientation probabilities with respect to temperature, the contribution of the dipole rotation for the pyroelectric effect is derived. By deducing the derivative of the polarizations of the two opposite directions with respect to temperature, the contribution of the polarization for the pyroelectric effect is also derived. The numerical simulation for the intrinsic mode of the pyroelectrics shows that the pyroelectric coefficient increases with rising temperature, sharply in proximity to the Curie temperature. For the E-enhancement mode of ferroelectrics, the pyroelectric coefficient is ascribed to the temperature effects of the rotation effect of the dipole and of the E-induced polarization. In the low temperature region far from the Curie temperature, pyroelectric coefficient is produced mainly by the dipole rotation mode by exhibiting a peak in the low electric field, and then with the increase of the electric field, pyroelectric coefficient shows a flat variation due to the E-induced polarization. When temperature rises, the peak of the pyroelectric coefficient due to the dipole rotation moves towards high electric field direction. In paraelectric phase, the E-induced polarization dominates pyroelectric effect.For a constant electric field, the pyroelectric coefficient shows peak, which shifts to high temperature with the increase of the electric field. The basic method to maintain temperature stability for the high pyroelectric coefficient of ferroelectrics is to increase electric field if temperature rises.