K. P. Jayachandran

Piezoelectricity enhancement in ferroelectric ceramics due to orientation

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.

Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

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 ...

Homogenized electromechanical properties of crystalline and ceramic relaxor ferroelectric 0.58Pb(Mg1/3Nb2/3)O3–0.42PbTiO3

A modelling framework that incorporates the peculiarities of microstructural features, such as the spatial correlation of crystallographic orientations and morphological texture in piezoelectrics, is established. The mathematical homogenization theory of a piezoelectric medium is implemented using the finite element method by solving the coupled equilibrium electrical and mechanical fields. The dependence of the domain orientation on the macroscopic electromechanical properties of crystalline as well as polycrystalline ceramic relaxor ferroelectric 0.58Pb(Mg1/3Nb2/3)O3–0.42PbTiO3 (PMN–42% PT) is studied based on this model. The material shows large anisotropy in the piezoelectric coefficient ejK in its crystalline form. The homogenized electromechanical moduli of polycrystalline ceramic also exhibit significantly anisotropic behaviours. An optimum texture at which the piezoceramic exhibits its maximum longitudinal piezoelectric response is identified.

Enhancement of the electromechanical response in ferroelectric ceramics by design

It is demonstrated based on continuum mechanics modeling and simulation that it is possible to obtain polycrystalline ceramic ferroelectric (FE) materials which beggar single crystals in electromechanical properties. The local inhomogeneities at the FE domain-scale level due to spontaneous polarization and the underlying anisotropy are taken into consideration in the framework of mathematical homogenization of physical properties in FE materials. The intrinsic randomness of the spatial distribution of polarization is shown to be judiciously employed for the design of better polycrystalline FEs. The noncollinear rotation of the net polarization vectors embedded in crystallites of the ceramic FEs is demonstrated to play the key role in the enhancement of physical properties.

Effect of Microstructure and Texture on the Macroscopic Piezoelectric Response of Ferroelectric Barium Titanate and PZN—PT Films

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.

A Stochastic Optimization Procedure Applied to Ferroelectrics for Piezoelectric Applications

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.

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.

Optimization of Ferroelectric Ceramics by Design at the Microstructure Level

Ferroelectric materials show remarkable physical behaviors that make them essential for many devices and have been extensively studied for their applications of nonvolatile random access memory (NvRAM) and high‐speed random access memories. Although ferroelectric ceramics (polycrystals) present ease in manufacture and in compositional modifications and represent the widest application area of materials, computational and theoretical studies are sparse owing to many reasons including the large number of constituent atoms. Macroscopic properties of ferroelectric polycrystals are dominated by the inhomogeneities at the crystallographic domain/grain level. Orientation of grains/domains is critical to the electromechanical response of the single crystalline and polycrystalline materials. Polycrystalline materials have the potential of exhibiting better performance at a macroscopic scale by design of the domain/grain configuration at the domain‐size scale. This suggests that piezoelectric properties can be opti...

Macroscopic Electromechanical Behavior of Polycrystalline Piezoelectric Materials BaTiO3 and PbTiO3; a 3D Analysis

The present work establishes a finite element based solution for the rigorous homogenization problem to quantify the microstructural features such as crystallographic orientation and spatial distribution of domains on the global piezoelectric response of single‐crystalline and polycrystalline ferroelectric materials. The crystal orientation dependences of the macroscopic electromechanical properties of single‐crystal as well as polycrystalline ferroelectrics BaTiO3, and PbTiO3 are studied based on this method. Both the materials show large anisotropy in the piezoelectric strain djK in its single‐crystal form. The homogenized electromechanical properties of polycrystalline system also exhibit significant anisotropic behaviours. An optimum texture, at which the piezoelectric response of both the polycrystalline material is maximised, is identified. Piezoelectric performance characteristics like the electromechanical coupling coefficients at various textures are evaluated for polycrystals of both the materials.