Polar properties and local piezoelectric response of ferroelectric nanotubes - Morozovska, A.N.; Svechnikov, G.S.; Shiskin, E.I.; Shur, V.Y. (Semiconductor Physics Quantum Electronics & Optoelectronics, 2008)
We consider the polar properties of the ferroelectric nanotubes within the framework of Landau-Ginzburg-Devonshire phenomenology. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on the radii of nanotube, polarization gradient, extrapolation length, elastic stresses and strains arising from surface tension and thermal expansion mismatch, and electrostriction coefficient was derived. We calculated effective local piezoresponse of the ferroelectric nanotube within decoupling approximation of electric and elastic problem. Obtained results explain the ferroelectricity conservation in Pb(Zr,Ti)O₃ and BaTiO₃ nanotubes observed by using Piezoelectric Force Microscopy