Surface energies of non-centrosymmetric nanocrystals by the inverse Wulff construction method

The Wulff construction is a well-known method for studying the morphologies of nanocrystal particles. The underlying Gibbs-Wulff theorem relies on Wulff points or particle centers, which are invalid for non-centrosymmetric crystals. In this study, we extend the method of inverse Wulff construction to study surface free energies of non-centrosymmetric crystals. A nonpolar (4[combining macron]3m) and a polar crystal system (6mm) are selected to show the difficulties and constraints caused by the lack of inversion centers. In addition to analytical and numerical results, we also present a general four-parameter function to simplify calculations of surface free energies from observed micro- or nanoparticle morphologies. The results reveal that non-centrosymmetric crystal morphologies entail the surface thermodynamics of coupling polar surfaces, with certain limitations originating from the combination of geometrical shapes and crystal symmetries.

Shape control of inorganic nanoparticles from solution

Inorganic materials with controllable shapes have been an intensely studied subject in nanoscience over the past decades. Control over novel and anisotropic shapes of inorganic nanomaterials differing from those of bulk materials leads to unique and tunable properties for widespread applications such as biomedicine, catalysis, fuels or solar cells and magnetic data storage. This review presents a comprehensive overview of shape-controlled inorganic nanomaterials via nucleation and growth theory and the control of experimental conditions (including supersaturation, temperature, surfactants and secondary nucleation), providing a brief account of the shape control of inorganic nanoparticles during wet-chemistry synthetic processes. Subsequently, typical mechanisms for shape-controlled inorganic nanoparticles and the general shape of the nanoparticles formed by each mechanism are also expounded. Furthermore, the differences between similar mechanisms for the shape control of inorganic nanoparticles are also clearly described. The authors envision that this review will provide valuable guidance on experimental conditions and process control for the synthesis of inorganic nanoparticles with tunable shapes in the solution state.