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Since piezoelectric ferroelectric materials including perovskite ceramics (e.g. PZT) have been widely used in electro-mechanical transform devices, studies on the properties of these materials have been attracted attention of many researchers. The saturated polarization and strain are important properties of ferroelectric materials. The saturated domain orientation texture can determine the upper limit of electric and mechanical properties of the polycrystalline ferroelectrics.
Recently, researchers of Institute of Advanced Science at
In the past, many studies have been performed to estimate saturated strain of polycrystalline ferroelectrics materials. In 1995, a researcher obtained strain and polarization hysteresis curve of Pb-La-Zr-Ti(PLZT) by loading a strong electric field and determined relative saturated strain. In 1999, it was analyzed thermodynamically analyzed 90° and 180° polarization switching by using oriented distribution function (ODF) for PZT ferroelectric ceramics. In 2004, it was calculated saturated polarization of polycrystalline ferroelectrics of tetragonal crystals with a microscopic electro-dynamical simulation and obtained the results of maximum tensile remanent strain and maximum compressive remanent strain. In 2007, A researcher analytically estimated saturated domain orientation texture of single phase polycrystalline ferroelectrics of tetragonal, rhombohedral and orthorhombic ferroelectrics by using one-dimensional ODF and obtained the saturated strains. In 2008, it was suggested the inverse-pole-figure (IPF) model to evaluate the saturated polarizations and saturated strains for tetragonal and rhombohedral single-phase polycrystalline ferroelectrics by analytical integral on an imaginary sphere.
However, in fact, many ferroelectric materials including PZT-like ceramics are polycrystalline ferroelectrics which contain different morphotropic phase boundaries (MPBs) where two or more crystal systems coexist. Enhancement of electrical and mechanical response near the MPBs was probed to be caused by coexistence of different crystalline phases. The IPF method was also applied to analyze domain switching near the MPBs where tetragonal phase and rhombohedral phase coexist in ferroelectric ceramics. Recently, the IPF model was generalized to analyze domain switching of various MPBs and was used to analyze the saturated polarization and equilibrium composition near the MPBs in polycrystalline ferroelectrics.
In this study, we have analytically calculated the saturated strain near tetragonal-rhombohedral MPB of polycrystalline ferroelectrics by using the generalized IPF model.
Firstly, saturated strains are calculated for single phase tetragonal and rhombohedral polycrystalline ferroelectrics by the generalized IPF method. Single phased polycrystalline ferroelectric system has the equivalent easy axes, so the IPF spherical surface can be divided into congruent regular spherical polygons. For example, the IPF surfaces of tetragonal polycrystalline ferroelectric systems can be divided into 6 spherical squares by projecting a regular hexahedron on the concentric IPF surface. Similarly, the IPF surface of rhombohedral polycrystalline ferroelectric systems can be divided 8 eight spherical regular triangles by projecting a regular octahedron on the concentric IPF surface.
For tetragonal polycrystalline system and rhombohedral polycrystalline system, the saturated strains are 0.5513 and 0.6366, respectively. The results are in perfect agreement with those from the former studies by theoretical modeling and experimental measuring, confirming exactness of the generalized IPF method in analyzing saturated strain of polycrystalline ferroelectrics.
And then, the general formula to analytically calculate relative saturated strain near MPB has been derived and relative saturated strain (~0.7890) near tetragonal-rhombohedral MPB has been calculated. The result shows enhanced saturated strain near tetragonal-rhombohedral MPB in comparison with those for single phase tetragonal and rhombohedral polycrystalline systems.
We published the results of this study in SCI journal entitled "Analytical calculation of saturated strain near morphotropic phase boundary of polycrystalline ferroelectrics by the generalized inverse-pole-figure model" (https://doi.org/10.1140/epjb/e2019-90559-2) in SCI Journal "European Physical Journal B" (2019, Vol.92, No.2, pp. 48(1-5)).