Mechanism of energy conversion of ferroelectric in pyroelectric cycle

Abstract

<p indent="0mm">“Waste heat” in the environment can be converted into electric energy by the Seebeck effect of semiconductor and pyroelectric effect of ferroelectrics ascribed to induction effect of polarization by electric field applied, energy conversion originates from the difference of polarization hysteresis electric field (<italic>P-E</italic>) loops between two different temperatures. Two isothermal processes and two iso-electric field processes form a pyroelectric cycle. By absorbing and releasing heat between two thermal reservoirs, a ferroelectric change its polarization successively so as to convert heat into electricity in a thermal-electric cycle, similar to the Carnot cycle. Output electric energy is the area enclosed by the cycle. For a constant high temperature environment, how to design a ferroelectric with proper Curie temperature and how to set cycling condition to match the temperatures to enlarge the area of a cycle are the two crucial problems. Experiment researches on pyroelectric energy conversion have been performed since the 1960s. The theoretic research was limited on simple expressions due to the difficulty on solving <italic>P-E</italic> loop. The <italic>P-E</italic> loop of ferroelectrics stems from rotation of dipoles and polarization hysteresis. In three-dimensional ferroelectrics, Gibbs free energies in the orientation directions of dipoles change with applied electric field differently, which causes changes in probabilities of dipole in different directions, i.e., rotation effect of dipoles. By introducing a coupling factor in the parallel dipoles the hysteresis effect was solved. The above solutions are extended to pyroelectric cycle to solve the problems referring to two isothermal processes and two iso-electric field processes with different initial condition. By combining the rotation effect and coupling effect that the coupling strength between dipoles is proportional to the rotated dipoles in the field direction during the field increasing process and persists to the same value in the field withdrawing process, mechanisms of polarization hysteresis are derived as several formulae. By editing a software program, numerical simulation method is used by setting values to the parameters to obtain evolution of polarization in the four processes of a cycle. Simulated result provides path of a cycle, depending on the maximal electric field (<italic>E</italic>_max). For a <italic>P-E</italic> loop in the first quadrant, there is a middle-curve rises from zero point to the top point of the loop, and an up-curve reduces from the top point to the remnant polarization at the zero field. In a cycle for a large enough <italic>E</italic>_max, the iso-low temperature process passes along the up-curve in the opposite direction, while for a smaller <italic>E</italic>_max, the process starts between the middle-curve and the up-curve and then transforms to the up-curve with the increase in the field because of impact of the small remnant polarization produced by <italic>E</italic>_max. The efficiency of pyroelectric cycling depends on cycling temperatures relative to Curie temperature and magnitude of the fields. High temperature is set above or below Curie temperature, and low temperature is set much below Curie temperature. Results show that when the low temperature is closer to Curie temperature, and high temperature is slightly higher than Curie temperature, pyroelectric energy conversion efficiency is higher and stable. When the high and low temperatures are close to the Curie temperature, the maximum pyroelectric conversion efficiency is obtained, but it decreases with the increase of the high temperature rapidly. A scaled efficiency, the efficiency relative to the Carnot cycle, decreases with the increase of temperature.