Nano-scale equilibrium crystal shapes

The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including the free energy of step formation and inverse-square step–step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a constant of integration, which we call the shape parameter c. The total crystallite free energy, including interface energy, is minimized for c = 0, yielding in all cases the traditional Pakrovsky–Talapov shape. Solutions of the crystal shape for c ≠ 0 are presented and discussed in the context of meta-stable states due to the energy barrier for nucleation. Explicit scaled relationships for the ECS and meta-stable states in terms of the measurable step parameters and the interfacial energy are presented.