Temperature dependence of the intrinsic and extrinsic contributions in BiFeO₃-(K₀.₅Bi₀.₅)TiO₃-PbTiO₃ piezoelectric ceramics

This contribution focuses on the use of modified Rayleigh law as a technique for determining the intrinsic and extrinsic (reversible/irreversible) contributions to the piezoelectric effect up to 150 ?C across a broad compositional space, augmenting previous understanding of the BiFeO3- (K0.5Bi0.5)TiO3-PbTiO3 system. At room temperature, a mechanistic explanation of the correlation between crystal symmetry, i.e., tetragonal spontaneous strain, xs, and the Rayleigh relations using Landau theory is provided. The intrinsic response was found to be heavily dependent upon the tetragonal xs, whereby an optimisation between polarization and permittivity was elucidated, leading to enhanced piezoelectric charge coefficients. A c/a ratio of ?1.041 was identified at which the room temperature intrinsic and extrinsic effects were at a maximum; a dinit of 183?10?12m/V and Rayleigh coefficient of 59?10?18m2/V2 were measured, resulting in the largest piezoelectric charge coefficients. The piezoelectric charge coefficient d33, intrinsic and extrinsic contributions of these materials were all found to increase up to 150 ?C while adhering to the Rayleigh model. The reversible extrinsic component of the total reversible response, dinit, was calculated to be relatively minor, 4.9% at room temperature, increasing to 12.1% at 150 ?C, signifying its increasing influence to the piezoelectric effect, as domain wall motion is thermally activated. Hence, the phenomenological interpretation provided here may be used as a roadmap to elucidate the origins of the temperature dependence of the piezoelectric effect.