Nanoparticle shapes by using Wulff constructions and first-principles calculations

Abstract

Summary Background: The majority of complex and advanced materials contain nanoparticles. The properties of these materials depend crucially on the size and shape of these nanoparticles. Wulff construction offers a simple method of predicting the equilibrium shape of nanoparticles given the surface energies of the material. Results: We review the mathematical formulation and the main applications of Wulff construction during the last two decades. We then focus to three recent extensions: active sites of metal nanoparticles for heterogeneous catalysis, ligand-protected nanoparticles generated as colloidal suspensions and nanoparticles of complex metal hydrides for hydrogen storage. Conclusion: Wulff construction, in particular when linked to first-principles calculations, is a powerful tool for the analysis and prediction of the shapes of nanoparticles and tailor the properties of shape-inducing species.

Equilibrium Morphologies of Faceted GaN under the Metalorganic Vapor‐Phase Epitaxy Condition: Wulff Construction Using Absolute Surface Energies

“…Due to crystal symmetry, the SAG on the lateral direction, which consists of (0001), , and planes, can also be considered. Details of the equilibrium Wulff construction are explained elsewhere . Furthermore, it is well known that the MOVPE condition, such as growth temperature, partial pressure, and carrier gas, is crucial for the equilibrium crystal shape in GaN nanostructures.…”

“…Details of the equilibrium Wulff construction are explained elsewhere. [20,24,25] Furthermore, it is well known that the MOVPE condition, such as growth temperature, partial pressure, and carrier gas, is crucial for the equilibrium crystal shape in GaN nanostructures. In this study, these parameters are taken into account by constructing surface phase diagrams among various orientations as functions of growth temperature and partial pressure.…”

Two-Dimensional Colloidal Nanocrystals

“…Historically, in 1874, 38 Gibbs suggested that the shape of a crystal is dictated by the minimization of the total surface energy. Therefore, the shape of crystals (and nanocrystals, as it has been shown that the equilibrium shapes of the macroscopic crystals and nanocrystals are the same when they have the same chemical composition 39,40 ) is therefore not dictated by the minimum total surface (which is a sphere), but depends strongly on crystalline facets. The final equilibrium shape will be dominated by the facets with the lowest surface energies.…”

Effects of surface stability on the morphological transformation of metals and metal oxides as investigated by first-principles calculations

“…First-principles investigations have been recognized as effective for studying the morphology and surface properties of a wide variety of crystals and NCs [52][53][54]. Our group has developed a working methodology, which has been applied to the study of different morphologies in different metal oxides such as SnO 2 [55][56][57], PbMoO 4 [58], and CaWO 4 [59].…”