Quantitative evaluation of the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements: Tetragonal BaTiO3

A method is proposed for evaluating the potential piezoelectric response, that a ferroelectric material would exhibit after full poling, from elastic and dielectric measurements of the unpoled ceramic material. The method is based on the observation that the softening in a ferroelectric phase with respect to the paraelectric phase is of piezoelectric origin, and is tested on BaTiO3. The angular averages of the piezoelectric softening in unpoled ceramics are calculated for ferroelectric phases of different symmetries. The expression of the orientational average with the piezoelectric and dielectric constants of single crystal tetragonal BaTiO3 from the literature reproduces well the softening of the Young's modulus of unpoled ceramic BaTiO3, after a correction for the porosity. The agreement is good in the temperature region sufficiently far from the Curie temperature and from the transition to the orthorhombic phase, where the effect of fluctuations should be negligible, but deviations are found outside this region, and possible reasons for this are discussed. This validates the determination of the piezoelectric response by means of purely elastic measurements on unpoled samples. The method is indirect and, for quantitative assessments, requires the knowledge of the dielectric tensor. On the other hand, it does not require poling of the sample, and therefore is insensitive to inaccuracies from incomplete poling, and can even be used with materials that cannot be poled, for example, due to excessive electrical conductivity. While the proposed example of the Young's modulus of a ceramic provides an orientational average of all the single crystal piezoelectric constants, a Resonant Ultrasound Spectroscopy measurement of a single unpoled ceramic sample through the ferroelectric transition can in principle measure all the piezoelectric constants, together with the elastic ones.