Articles you may be interested in Tailoring 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 BiFeO 3 -(K 0.5 Bi 0.5 )TiO 3 -PbTiO 3 system. At room temperature, a mechanistic explanation of the correlation between crystal symmetry, i.e., tetragonal spontaneous strain, x s , and the Rayleigh relations using Landau theory is provided. The intrinsic response was found to be heavily dependent upon the tetragonal x s , 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 d init of 183 Â 10 À12 m/V and Rayleigh coefficient of 59 Â 10 À18 m 2 /V 2 were measured, resulting in the largest piezoelectric charge coefficients. The piezoelectric charge coefficient d 33 , 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, d init , 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. V C 2014 AIP Publishing LLC.