Surface energy and surface stress

By cutting a piece of material in two one can create two fresh surfaces and it is evident that they represent an increase of the energy of the system because bonds between atoms or molecules have been broken. Admittedly, the energy may then decrease somewhat by relaxation in the surface layer. The net effect can be defined as the surface energy or rather surface free energy or surface Gibbs energy under the usual isobarothermal conditions. We shall simply use the term surface energy and apply the same term to real surfaces as well as interfaces. Specific surface energy, i.e. the energy per surface area, will be denoted by σ.

However, the energy of the system may decrease further by minimizing the surface area. Primarily, there would be a tendency of the two new pieces to minimize the surface area by a shape change of the material and for an isotropic material the final shape would be spherical. That could happen quickly if the material is liquid but it could be an extremely slow process for a piece of solid material. The decrease of energy during the shape change is easily calculated for an isotropic material because its specific surface energy, σ, the energy per area, is constant.

Secondarily, the surface could contract further without a shape change by compressing the material in the sphere. It will thus be put under an increased pressure, formally caused by a stress in the surface.