Size effects in PbTiO ₃ nanocrystals: Effect of particle size on spontaneous polarization and strains

The spontaneous polarization (Ps) and spontaneous strains (xi) in mechanically unclamped and surface charge compensated PbTiO3 nanocrystals were determined as a function of particle size in the range <150 nm by differential scanning calorimetry and x-ray powder diffraction, respectively. Significant deviations from bulk order parameters (P, xi) have been observed as the particle size decreased below ~100 nm. The critical size (rc) below which the ferroelectric tetragonal phase transforms to the paraelectric cubic phase was determined as ~15 nm. The depression in transition temperature with particle size is 14 °C at 28 nm. No change in the order of m3m→4mm ferrodistortive phase transition is observed. A simple analysis showed that Δ Htr (kB T) ~ 103 at 25 °C for r=16 nm, indicating that the stabilization of the cubic phase at rc cannot be linked to an instability in dipolar ordering due to thermal agitations. Comparison of the spontaneous volumetric strains with the strain induced by surface stress indicated that the effect of surface stress on ferroelectric phase stability was negligible. Anomalies in electrostrictive properties were determined for r→ rc. The observed size dependence of PS is attributed to the reduced extent of long-range dipole-dipole interactions that arise due to the changes in bonding characteristics of ions with decreasing particle size in the perovskite lattice, in conformity with a recent study by Tsunekawa [Phys. Rev. Lett. 85 (16), 4340 (2000)].