Stress- and temperature-dependent scaling behavior of dynamic hysteresis in soft PZT bulk ceramics

Effects of electric field-frequency, electric field-amplitude, mechanical stress, and temperature on the hysteresis area, especially the scaling form, were investigated in soft lead zirconate titanate (PZT) bulk ceramics. The hysteresis area was found to depend on the frequency and field-amplitude with the same set of exponents as the power-law scaling for both with and without stresses. The inclusion of stresses into the power-law was obtained in the form of < A-A (sigma= 0) >alpha f - (0.25)E0 sigma (0.44) which indicates the difference in energy dissipation between the under-stress and stress-free conditions. The power-law temperature scaling relations were obtained for hysteresis area < A > and remanent polarization P-r, while the coercivity E-C was found to scale linearly with temperature T. The three temperature scaling relations were also field-dependent. At fixed field amplitude E-0, the scaling relations take the forms of < A >alpha T (-1.1024), P-r alpha T (-1.2322) and ( EC0 - E-C) alpha T.