The bounds of electrostrictive coefficients of relaxor-based ferroelectricceramics

Two extreme approximations, namely the Voigt- and Reuss-type approximations , have been used to estimate the effective electrostrictive coefficients of isotropic or anisotropic (as in the de electric-field-blase piezoelectric mode) relaxer-based ferroelectric ceramics. It is shown that, for a dense c eramic with cubic crystallites, both simple approximations give very simila r results and can be used for such estimates. However, for common ceramics containing pores, the Voigt and Reuss approximations yield only extreme upp er and lower bounds respectively, and a more appropriate approach is needed .