Single-crystal Na2Ti6O13 nanorings formed by self-coiling of a nanobelt

Abstract

We presented, for the first time, the evidence of loop-by-loop self-coiling of a nanobelt to form single-crystal Na₂Ti₆O₁₃ nanorings with diameters of several micrometres. The winding nanobelts, with thickness of about 15 nm and widths of 100–500 nm, grow along their [010] crystallographic directions, and coherently match at ±(200) crystallographic planes. The driving force of such a coherent match is suggested to be the minimization of local electrostatic energy introduced by the cations and anions. We also discussed the dependence of the nanoring's yield on the thickness of the nanobelts, which affects the elastic deformation energy and misfit energy of the rings.