Shape of free and constrained group-IV crystallites: Influence of surface energies

The equilibrium crystal shapes of the group-IV materials diamond, Si, and Ge are constructed based on surface energies obtained by means of ab initio calculations. The same method is applied to constrained crystallites with a pyramidal shape and a fixed orientation of the basal plane. Trends of shape are discussed versus the constraints and the orientation of facets using only energetical arguments.