Orientation of (1×1)-surface free energies of crystals

The free energy of a (1×1)-surface, with no relaxation and no adsorption, is calculated using a bond-breaking mode in which the potential energy of the crystal is treated as the sum of the energy of the bonds connecting pair-wise atoms. Based on a purely geometrical model, the number of broken bonds or dangling bonds per atom is calculated on the surface of the crystal when an atomically flat plane h(hkl ) is created. The results provide a general expression of the surface free energy in terms of Miller indices hkl. The anisotropy of the surface free energy is completely described in the expression. Considering nearest-neighboring bonding only, the orientation dependence of the surface free energy is discussed for simple cubic (sc) and cubic tetrahedral (cth) crystals, respectively. Wulff plots and the equilibrium forms for the sc and the cth crystals are obtained on the basis of their expressions of the surface free energy, implying the cube and the octahedron are the equilibrium forms for the sc and the cth crystals, respectively. Furthermore a predicted anisotropy of fcc metals is discussed. © 1998 Elsevier Science B.V. All rights reserved.