Interfacial energy is the interfacial excess free energy. Hence, it can be written in terms of enthalpy and entropy as follows:
 |
(4) |
where,  and  are the enthalpy and entropy associated with the boundary. Further, if one considers a solid-vapour interface in which a solid is in contact with its vapour, the enthalpy  can be replaced by internal energy associated with the boundary,  .
Consider a temperature that is low enough that the entropy contribution to the execess free energy can be neglected. In such a solid-vapour interface, almost all the interfacial energy contribution comes from the internal energy of the boundary. One can estimate the internal energy contribution using a simple bond-breaking model in such a system as follows.
Let us consider a crystalline solid. In the bulk, each atom has a certain number neighbours with which it bonds. For example, an atom in the bulk fcc structure bonds with 12 of its neighbours; an atom in the bulk bcc structure bonds with 8 of its neighbours; an atom in a simple cubic structure bonds with 6 of its neighbours and so on. However, if an atom is on the surface, certain number of its neighbours are missing; hence, the bonds are not satisfied; such dangling bonds are the ones which contribute to the internal energy of the system.
In a crystalline solid, obviously, surface formed with different planes will have different energies because the number of broken bonds per unit areas are different on different planes. Hence, the interfacial energy is also anisotropic in crystalline solids. This anisotropy is more prominent at lower temperatures. As temperatures rise, the entropy contribution becomes dominant and makes the interfacial energy less anisotropic. |
