A Stochastic Optimization for the Optimal Texture of Ferroelectrics for Piezoelectric Applications

A stochastic optimization procedure incorporating a continuum modelling is used to identify the optimal texture (orientation distribution) parameters of ferroelectrics (FEs) for piezoelectric applications. FE polycrystals differ significantly from single crystals because of the presence of variously oriented crystallites. The orientation of FE 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 texture of crystallites is unlimited. Crystallographic orientation in FEs is characterised through Euler angles . The macroscopic properties of a ceramic FE, differ significantly from those of single crystals mainly due to the imperfect alignment of the crystallographic axes of the constituent domains or crystallites. This suggests that piezoelectric properties can be tailored by a proper choice of the parameters which control the orientation distribution. Nevertheless, this choice is complicated and it is impossible to analyze all possible combinations of the distribution parameters or the angles themselves. Stochastic optimization combined with a generalized Monte Carlo scheme optimizes the objective functions, the effective piezoelectric coefficients . Objective functions are calculated using the homogenization method at each orientation configuration chosen by the optimization algorithm. A modified simulated annealing is employed to describe the stochastic optimization. Here we have simulated the texture of polycrystals using a simple model with a Gaussian distribution. Optimal design variables that enhance the macroscopic piezoelectricity are identified.