A theoretical method to calculate the surface free energies of crystals

An ideal density of dangling bonds and the surface free energy (SFE) of ( 1 x 1)-( hk1) surface of cubic crystals are calculated by using a broken-bond model. The results show that the SFE( gamma) can be expressed as gamma= f( hkl)center dot (E-b/d(0)(2)) where f( hkl) is a periodically convergent function, E-b and d(0) are respectively the bond energy and the bond length. The f( hkl) is related to the crystal structure. The anisotropy of the SFE and the equilibrium form (EF) of the crystal can be readily determined by using the results. It is found that the EFs of the crystals of fee and bee are truncated octahedron and rhombic dodecahedron, respectively, which are coincident with the corresponding crystals' three dimensional first Brillouin zones, respectively.