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Abstract
A stochastic optimization procedure incorporating a continuum modelling is used to identify the optimal orientation distribution of ferroelectrics (FEs) for piezoelectric applications. The orientation of ferroelectric crystals plays a critical role in the anisotropy of their piezoelectric properties. Crystallographic orientation is inextricably related to the piezoelectric properties of FEs and is characterised through Euler angles (φ, θ, ψ). Ferroelectric single crystal in general exhibit orientation dependent piezoelectricity. The macroscopic properties of a ceramic FE, in general, 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. The set of combination of variables, known as solution space, which dictates the orientation distribution of crystallites is unlimited. Stochastic optimization combined with a generalized Monte Carlo scheme optimizes the objective functions, the effective piezoelectric coefficients d jν and the electromechanical coupling. These objective functions are calculated using the homogenization method at each orientation configuration chosen by the optimization algorithm. A modified simulated annealing is employed to optimize the objective functions described in the optimization. Polycrystalline ferroelectric materials are shown to have the potential of exhibiting better performance at a macroscopic scale by the design of the grain configuration at the micro scale.
Acknowledgments
KPJ acknowledges the award of Ciência 2007 by the FCT, Portugal.