A thermodynamic model for the shape and stability of twinned nanostructures

Although thermodynamically metastable, planar defects are often observed in many faceted nanomaterials including nanocrystals, nanorods, and nanowires, even after annealing. These planar defects include contact twins and (intrinsic or extrinsic) stacking faults, and are usually neglected by most analytical models. For example, many bulk metals have the face-centered cubic structure, but small nanocrystals and nanorods of the same material often exhibit various structural and morphological modifications such as single or multiple symmetric twinning, as well as 5-fold cyclic twinning resulting in decahedral and truncated decahedral nanostructures. Presented here is a general analytical model for the investigation of nanomaterials of arbitrary shape, and with any configuration of planar defects. The model is tested for the case of twinning in unsupported gold nanocrystals and nanorods, and is shown to give results in excellent agreement with experimental and computational studies reported in the literature.