Stochastic Optimization of Electromechanical Coupling in Ferroelectric Materials

Abstract

Polycrystalline ferroelectrics differ significantly from single crystals because of the presence of variously oriented grains or crystallites. The orientation of ferroelectric crystals plays a critical role in the anisotropy of their piezoelectric properties. The set of combination of variables, known as solution space, which dictates the orientation distribution of grains is unlimited. Thus a stochastic optimization combined with homogenization is employed for the identification of the optimal granular configuration of the ferroelectric ceramic microstructure with optimum electromechanical coupling suitable for applications such as transducers and actuators. The effective macroscopic electromechanical coupling k are calculated at every iteration using the mathematical homogenization method. The configuration of crystallites at each step is chosen by the optimization algorithm. The single crystal ferroelectrics are also investigated in an effort to compare the performance characteristics with that of polycrystals. A configuration constraining the orientation distribution of the c-axis (polar axis) of the crystallites is identified. This grain configuration would optimize the figures of merit such as dh and kh of the ferroelectric material.