The Rayleigh law in piezoelectric ceramics

The direct longitudinal piezoelectric effect (d(33)) in lead zirconate titanate, barium titanate, bismuth titanate and strontium bismuth titanate ceramics was investigated with respect to the dependence on the amplitude of an alternating pressure. At low alternating pressure amplitudes, the behaviour of the piezoelectric charge and the piezoelectric coefficient may be explained in terms of the Rayleigh law originally discovered for magnetization and magnetic permeability in ferromagnetic materials. The charge versus pressure hysteresis loops measured for piezeoelectric ceramics may similarly be described as the Rayleigh loops. The results presented show that the Rayleigh law can be applied to irreversible displacement of several types of non-180 degrees ferroelectric domain walls and imply universal validity of the Rayleigh law for displacement of ferromagnetic, ferroelastic and ferroelectric domain walls.