Grain-size effect on ferroelectric Pb(Zr_1−xTi_x)O₃solid solutions induced by surface bond contraction

Bond contraction in the surface layers induces a compressive stress on the inner part of a grain and results in a size effect for ferroelectric materials in the nanometer size range. By using the Landau-Ginsburg-Devonshire free energy approach, the phase transitions and intrinsic ferroelectric properties of the lead zirconate titanate solid solution system have been studied theoretically. It is found that, due to the surface bond contraction, the phase stability is affected by grain size and the size-dependent properties show differences in different phases.