The effects of crystallographic texture and microstructure are analyzed for polycrystalline tetragonal BaTiO 3 , pseudotetragonal PZN-PT, and cubic BaTiO 3 . For tetragonal BaTiO 3 and pseudotetragonal PZN-PT, we demonstrate that a high anisotropy of the single-crystal properties induces an apparent enhancement in the macroscopic piezoelectric response. For tetragonal BaTiO 3 , the predicted macroscopic piezoelectric constants d 31 and d 33 are enhanced with respect to its single-crystal value at the expense of the spatial contributions from d 15 . For samples possessing fiber texture, an optimal response is predicted for samples that are not perfectly textured. Similarly, an apparent enhancement of the macroscopic value of d 15 is predicted for PZN-PT. For cubic BaTiO 3 , the low anisotropy of the underlying crystal properties induces a uniform decrease of the macroscopic electrostrictive constant, Q 11 , with decreasing texture. A completely random polycrystal provides 0.8570.05 times its single-crystal response.
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A model and numerical framework is developed for piezoelectric materials. The model treats the piezoelectric and electrostrictive effects by incorporating orientation-dependent, single-crystal properties. The method is implemented in Object Oriented Finite Element program, a public domain finite element code, so it can be applied to arbitrary two-dimensional microstructures with crystallographic anisotropy. The model is validated against analytic solutions. Consistency of the method for known cases permits application of the technique to more complicated twodimensional systems. The piezoelectric and electrostrictive response is determined for a few simple device geometries and provides insight for design and convergence criteria.
J ournalThe polarization vector is related to the applied electric fieldẼ and total polarizationD by:where E 0 is the permittivity of vacuum. z Because this is an expansion about a stable state, it is implicit that hysteretic effects, domain wall motion, charge separation, mass diffusion, and other irreversible kinetic effects cannot be operative, thus these equations apply. In a ferroelectric, there may be irreversible phase transitions that include switching events and local motion of domains.
We propose a new type of ordered colloid, the "ionic colloidal crystal" (ICC), which is stabilized by attractive electrostatic interactions analogous to those in atomic ionic materials. The rapid self-organization of colloids via this method should result in a diversity of orderings that are analogous to ionic compounds. Most of these complex structures would be difficult to produce by other methods. We use a Madelung summation approach to evaluate the conditions where ICC's are thermodynamically stable. Using this model, we compare the relative electrostatic energies of various structures showing that the regions of ICC stability are determined by two dimensionless parameters representing charge balance and the spatial extent of the electrostatic interactions. Parallels and distinctions between ICC's and classical ionic crystals are discussed. Monte Carlo simulations are utilized to examine the glass transition and melting temperatures, between which crystallization can occur, of a model system having the rocksalt structure. These tools allow us to make a first-order prediction of the experimentally accessible regions of surface charge, particle size, ionic strength, and temperature where ICC formation is probable.
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