The effective dielectric, piezoelectric, and elastic constants of polycrystalline ferroelectric materials are calculated from single-crystal data by an advanced method of effective medium, which takes into account the piezoelectric interactions between grains in full measure. For bulk BaTiO3 and PbTiO3 polarized ceramics, the dependences of material constants on the remanent polarization are reported. Dielectric and elastic constants are computed also for unpolarized c- and a-textured ferroelectric thin films deposited on cubic or amorphous substrates. It is found that the dielectric properties of BaTiO3 and PbTiO3 polycrystalline thin films strongly depend on the type of crystal texture. The influence of two-dimensional clamping by the substrate on the dielectric and piezoelectric responses of polarized films is described quantitatively and shown to be especially important for the piezoelectric charge coefficient of BaTiO3 films. (C) 1998 American Institute of Physics. [S0021-8979(98)01815-5].
Pertsev, N. A., Zembilgotov, A. G., & Waser, R. (1998). Aggregate linear properties of ferroelectric ceramics and polycrystalline thin films: Calculation by the method of effective piezoelectric medium. Journal of Applied Physics, 84(3), 1524–1529. https://doi.org/10.1063/1.368218