Nanoparticle shapes by using Wulff constructions and first-principles calculations

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.