Thermodynamic theory of intrinsic finite size effects in PbTiO₃ nanocrystals. II. Dielectric and piezoelectric properties

We compute the intrinsic dielectric and piezoelectric properties of single domain, mechanically free, and surface charge compensated PbTiO₃ nanocrystals (n-Pt) with no depolarization fields, undergoing a finite size induced first order tetragonal → cubic ferrodistortive phase transition. By using a Landau-Devonshire type free energy functional, in which Landau coefficients are a function of nanoparticle size, we demonstrate substantial deviations from bulk properties in the range < 150 nm. We find a decrease in dielectric susceptibility at the transition temperature with decreasing particle size, which we verify to be in conformity with predictions of lattice dynamics considerations. We also find an anomalous increase in piezocharge coefficients near ∼15 nm, the critical size for n-Pt.