Separation of nonlinear and friction-like contributions to the piezoelectric hysteresis

Based on direct and converse piezoelectric measurements, our results for relaxor-ferroelectric solid solutions 0.5 Pb(Zr,Ti)O/sub 3/-0.5 Pb(Ni/sub 1/3/Nb/sub 2/3/)O/sub 3/ (PNN-PZT) show that piezoelectric hysteresis can be better described by a coupled Rayleigh-frictional model rather than by either model separately. The nonlinear parameters yielded by such loop analysis are in a good agreement with the ones obtained from piezoelectric nonlinearity, constituting a new validation of Rayleigh-inspired models for the piezoelectric response in ferroelectrics. Finally, the possible mechanisms leading to hysteresis formation are discussed.