Surface tension and Curie temperature in ferroelectric nanowires and nanodots

The effect of surface tension associated internal pressure on the Curie phase transition in ferroelectric nanowires and nanodots has been investigated using a modified Landau-Ginzburg-Devonshire phenomenological approach. Based on experimental data on the size- dependent phase transition in freely suspended single-crystalline ferroelectric nanocrystals, bulk surface tension coefficients for BaTiO3 and PbTiO3 have been determined to be of the order of 1-2 N/m. The present theoretical study reproduces the size dependence of the transition temperature experimentally acquired in individual BaTiO3 single-crystalline nanowires. In the case of PbTiO3 single-crystalline nanodots, however, in order to fit the theoretically calculated size-dependent ferroelectric transition with the experimental data, an effective surface tension coefficient has been introduced, which is size dependent and can be much higher than the bulk value.