Shape of piezoelectric hysteresis loop for non-ferroelastic switching
ABSTRACTA simple theory for the shape of the piezoelectric hysteresis loops (piezoelectric coefficient d vs. applied electric field E) is developed for the case of non-ferroelelastic 180° switching in ferroelectrics. The theory provides explanations for specific features of piezoelectric hysteresis loops, which have been observed in single crystals, thin films and in ceramics in particular. The piezoelectric coefficient may show a “hump”, i.e. when E decreases from the tip of the loop down to zero, d passes through a maximum, and a “nose”, i.e. a self-crossing of the loop close to its tips. The theory also explains the difference in the coercive fields seen in the polarization and piezoelectric loops.