Size dependence of the ferroelectric transition of small BaTiO3 particles: Effect of depolarization.

摘要: A theory has been developed to examine the depolarization effect on ferroelectric transition of small ${\mathrm{BaTiO}}_{3}$ particles. To reduce energy, a crystal would break up into domains different polarization. In this study, we consider cubic particles with alternating separated by 180\ifmmode^\circ\else\textdegree\fi{} domain walls. The energy and domain-wall were incorporated Landau-Ginzburg free-energy density. Assuming hyperbolic tangent polarization profile across wall, \ensuremath{\gamma} half thickness \ensuremath{\xi} can be obtained minimizing respect \ensuremath{\xi}. account for not being perfect insulator, Schottky space charge layer beneath particle surface that shields interior from field was considered. equilibrium P width D total density both D. results calculations show temperature substantially lower than bulk as result effect. Consequently, at below temperature, dielectric constant \ensuremath{\epsilon} peak certain cube size L. These agree existing experimental observations. Finally, also applied other materials such ${\mathrm{KH}}_{2}$${\mathrm{PO}}_{4}$ or ${\mathrm{PbTiO}}_{3}$.