| With the development of electronic engineering, piezoelectric materials have been widely spread as many applications. Piezoelectricity can be obtained by piezoelectric materials only after being poled, and the performance is the key factor to the reliability and the scope of application. In order to calculate the intrinsic properties of poled piezoelectric materials, we propose a probability density function of orientation(PDFO) model to study the domains inside the materials. Main works and results are as follows:1. Eulerian angles are introduced to study the domain orientations as well as the Reuss assumptions and domain switching criterion are applied in the research of tetragonal(4mm), rhombohedral(3m) and orthorhombic(mm2). We show the domain switching distributions for these three phases and with the PDFO after saturated/unsaturated poling, we calculate the distribution of orientations for all domains, remnant polarization, macroscopic dielectricity and piezoelectricity. Misleading results led by other researchers via pole/inverse pole figures or orientation distribution functions are also rectified.2、We introduce Landau-Devonshire free energy function to study the stability of the tetragonal and rhombohedral phases, as well as the coexistence of them. With the polarization of single crystals we define a ‘ratio of polarizations A’ to depict the relationship between these two phase. The range of ‘A’ is divided into three parts and we calculate mole percentage of each phase and relative properties via PDFO in each for the whole range of ‘A’. The results are generalized and only have relationships with ‘A’. When studying one specific material it‘s only necessary to find the relative ‘A’ and substitute the generalized results.3、With the inner stress and the Eshelby model, the piezoelectric material model is global linkage. We calculate the intrinsic d33 with Landau-Devonshire free energy function and an example for barium titanate is also included. |
PDF Full Text Request