Surface layer clamping as origin for size-dependent downshift of Curie temperature in PbTiO3 nanoparticles

Size dependent Curie temperature in ferroelectric nanoparticles has been shown to originate from mechanical clamping of phase transition in particle core by a cubic surface layer. Based on a phenomenological model, the widely observed empirical relation between downshift of Curie point and particle size has been deduced by introducing an extra term of core–shell boundary energy into the free energy expression. Theoretical calculations of size dependent Curie temperature in PbTiO3 nanoparticles are in well agreement with the literature-reported experimental data. The positive boundary free energy of nano-sized PbTiO3 particles becomes increasingly large with size reduction, leading to a sharp drop of Curie temperature as compared to bulk single crystal.