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An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differs significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus, a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterized by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. The optimization procedure applied to the single crystalline phase compares well with the experimental data. Apparent enhancement of piezoelectric coefficient d33 is observed in an optimally oriented BaTiO3 single crystal. Based on the good agreement of results with the published data in single crystals, we proceed to apply the methodology in polycrystals. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO3 is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centered around 45°. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal. Our optimization model provide designs for materials with enhanced piezoelectric performance, which would stimulate further studies involving materials possessing higher spontaneous polarization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

A two-dimensional (2D) plane-strain finite element method (FEM) model of polycrystalline film wherein the film thickness is much greater than the microstructure is presented. A finite element based solution for the rigorous homogenization problem to quantify the microstructural features, such as orientation and spatial distribution of crystallographic grains on the global piezoelectric response of unclamped polycrystalline ferroelectric films is implemented. The homogenized material parameters of the piezoelectric films are calculated using the FEM by the solution of the coupled equilibrium electrical and mechanical fields in the linear domain. The dependence of macroscopic electromechanical properties on domain orientation and texture of single-crystalline as well as polycrystalline ferroelectric BaTiO3 and PZN-PT films are demonstrated based on this model. The orientation dependent anisotropy of homogenized electromechanical moduli of polycrystalline and single-crystalline films are examined. The polycrystalline films can be improved in their out-of-plane global piezoelectric behavior by engineering microstructures that favor {111} texture in the case of BaTiO3 and {001} texture in the case of PZN-PT. [ABSTRACT FROM AUTHOR]

A continuum model simulation, explicitly incorporating anisotropic grain-level features, based on homogenization of materials predicts an enhancement of piezoelectricity in ferroelectric ceramics better than oriented single crystals. Incorporation of randomness in the orientation of polarization associated with the grains is demonstrated to offer great prospect in the design of ceramic ferroelectric materials such as BaTiO3. [ABSTRACT FROM AUTHOR]