Effective elastic properties for unpoled barium titanate

Piezoelectric devices with complex electrode geometries may contain regions of ferroelectric material that remain unpoled. It is desirable to account for these non-piezoelectric regions for device optimization, since the unpoled and poled material properties differ. The lack of published elastic properties for unpoled ferroelectrics, specifically the numerous commercial PZT compositions, reflects the difficulty of experimental measurement. In this work, a method was developed to predict unpoled properties from more commonly available poled material data. Barium titanate was chosen for study as a representative ferroelectric, with both single crystal and polycrystalline (ceramic) properties available. Finite element micro-mechanical models were created with a focus on computational economy. This allowed larger ensembles of results to be computed, providing accurate effective compliances when averaged. The modelling methodology predicted the elastic properties for unpoled barium titanate to within ∼10% of measured experimental values.