Phenomenological theory of size effects in ultrafine ferroelectric particles of lead titanate

A new phenomenological model is proposed and discussed to study size effects on the first-order ferroelectric phase transition of lead titanate ferroelectric particles. This model, by taking size effects on the phenomenological Landau-Ginzburg-Devonshire coefficients into consideration, can successfully explain the observed size effects on the Curie temperature, $c/a$ ratio, and thermal and dielectric properties of lead-titanate-type ferroelectric particles. Theoretical and experimental results for ${\mathrm{PbTiO}}_3$ fine particles are compared and discussed. The relationship between the current model and the model of Zhong et al. [Phys. Rev. B 50, 698 (1994)] is also discussed.