Preferential crystallographic growth planes are influenced to a large
extent by the shape of the microcrystals that nucleate the growth. In
contrast with macroscopic crystals, for nanometer scale microcrystals
the energies associated with edges and vertices play a crucial role in
determining an energetically favourable shape. We present a model for
the computation of edge and vertex energies within the framework of s
emi-empirical quantum chemical calculations for atomic clusters. For t
wo diamond crystallite shapes, both terminated by hydrogen saturated (
111) surfaces, energy coefficients for the bulk and surface as well as
two types of edges and vertices are obtained. The values are consiste
nt with measurements. Size dependent effects are investigated by calcu
lating the energy per atom for arbitrary sizes of a given shape, from
the coefficients. It is found that even for this simple example, there
is an energy cross-over at small crystallite size.