A new method to determine the un-poled elastic properties of ferroelectric materials

Piezoelectric devices with complex electrode geometries often contain ferroelectric regions that experience little or no electric field and remain unpolarised. Since the un-poled and poled material properties differ it is desirable to account for these regions in a device when developing predictive models or to design piezoelectric transducers. The lack of published data on the elastic properties for un-poled ferroelectrics, specifically the numerous commercial compositions such as lead zirconate titanate, reflects the difficulty of experimental measurement. In this work, a method for predicting un-poled properties from more commonly available poled data has been developed. A new method of calculating these properties is presented which provides a rapid and practical solution to the problem of evaluating the isotropic stiffness and Poisson’s ratio for an un-poled ferroelectric material. The way in which this calculation has been derived and validated is presented and detailed comparisons are made with alternative methods and experimental data.