Thermodynamic Analysis of a Direct Mechanical to Electrical Energy Harvesting Cycle in Ferroelectric Crystals

Field induced phase transformations in ferroelectric crystals occur when the applied electrical or mechanical load exceeds a certain threshold. Mechanical cycling about these transformation field thresholds under varying open and closed circuit conditions has been shown to yield a near ideal mechanical to electrical energy harvesting technique. Numerical integration of experimentally measured stress – strain and electric field – electric displacement data has shown mechanical to electrical energy conversion efficiency near 60% for 0.24PIN-0.44PMN-0.32PT. In this work, the total irreversible energy is determined by the offset between the forward and reverse loading paths, equivalent to the hysteresis in the phase transformation behavior. This is equal to the available mechanical energy for conversion to electrical energy for harvesting. Following the ideal mechanical to electrical energy harvesting procedure, the total possible energy harvested is a direct function of the hysteresis area in the phase transformation and the electromechanical coupling factor. Efficiency is predicted to be equal to the electromechanical coupling factor, 0.596 (59.6%). Predicted results agree with experimental data from numerical integration. Energy densities are calculated up to 5 kJ/m³ with potential power densities of 10²–10³ kW/m³.