Energy density of a free surface or an interface

In the preceding discussion, the early stages in the growth of a film from a vapor were considered in a qualitative way in terms of the behavior of atoms. Many of the inferences drawn can also be made in terms of surface energy and interface energy of solid materials. These quantities are macroscopic measures attributable to the discreteness of the material. However, they represent only ensemble averages of behavior at the atomistic level and do not incorporate discreteness of the material in any direct way. In many 

Many additional observations can be made on the basis of the same construction (Herring 1951). Among the most useful of these concerns the possibility of a macroscopically fiat surface assuming a corrugated or peak- 

Like free surfaces, interface surfaces at which materials are joined can also be represented macroscopically as discrete surfaces and can be characterized by an interface surface energy per unit area. The physical origin of this energy is essentially the same as that of a free surface. The energy density of an interface is presumably less than the sum of the free surface energies of the two materials joined at that interface, and greater than the energy densities within either of the materials at interior points remote from the interface. 

Up to an additive of constant, the free energy change associated with island formation is 

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