A classical mechanics model for the interpretation of piezoelectric property data

In order to provide a means of understanding, the relationship between the primary electromechanical coefficients and simple crystal chemistry parameters for piezoelectric materials, a static analysis of a 3 atom, dipolar molecule has been undertaken to derive relationships for elastic compliance s^E, dielectric permittivity ε^X, and piezoelectric charge coefficient d in terms of an effective ionic charge and two inter-atomic force constants. The relationships demonstrate the mutual interdependence of the three coefficients, in keeping with experimental evidence from a large dataset of commercial piezoelectric materials. It is shown that the electromechanical coupling coefficient k is purely an expression of the asymmetry in the two force constants or bond compliances. The treatment is extended to show that the quadratic electrostriction relation between strain and polarization, in both centrosymmetric and non-centrosymmetric systems, is due to the presence of a non-zero 2nd order term in the bond compliance. Comparison with experimental data explains the counter-intuitive, positive correlation of k with s^E and ε^X and supports the proposition that high piezoelectric activity in single crystals is dominated by large compliance coupled with asymmetry in the sub-cell force constants. However, the analysis also shows that in polycrystalline materials, the dielectric anisotropy of the constituent crystals can be more important for attaining large charge coefficients. The model provides a completely new methodology for the interpretation of piezoelectric and electrostrictive property data and suggests methods for rapid screening for high activity in candidate piezoelectric materials, both experimentally and by novel interrogation of ab initio calculations