Rayleigh behaviour and the threshold field in ferroelectric ceramics

The threshold field, E-t, values for various barium titanate and PZT-based ceramics have been determined by examination of the epsilon(r)'-E-0 and epsilon(r)"-E-0 relationships. The results obtained far both 'soft' and 'hard' PZT ceramics gave a good fit to the Rayleigh Law over a wide range of field amplitude for E-0>E-t. The linear increases in epsilon(r)' and epsilon(r)" as a function of field amplitude were attributed to a lossy ferroelectric domain wall translation mechanism, by analogy with similar behaviour in ferromagnetic materials. At high field levels approaching the coercive field, E-c, the measured epsilon(r)'-E-0 and epsilon(r)"-E-0 curves deviated from a linear relationship due to the onset of partial ferroelectric domain switching. Pure and Mn-doped barium titanate ceramics exhibited nonlinear epsilon(r)'-E-0 and epsilon(r)"-E-0 plots with a gradually increasing gradient. However, all of the materials studied yielded a linear epsilon(r)'-epsilon(r)" relationship, from which a critical field for the initiation of ferroelectric domain switching, E-SW, could be determined.