Surface tension and size effect in ferroelectric nanotubes

Using a thermodynamic model, linear stability analysis is performed on the associated dynamic Ginsburg-Landau equation for a ferroelectric nanotube. Analytic expressions of the transition temperature and Curie-Weiss relation are derived. The ferroelectric properties of the tube are found to generally depend on its dimensions through effects of the surface tension and near-surface eigenstrain relaxation. Our results also show that the transition temperature and polarization are both enhanced due to the dominance of the effective radial pressures induced by the surface tension, resulting in a remnant polarization and coercive field that may become larger than the bulk values.