· Consider the introduction of n vacancies into a lattice with N lattice sites and (N - n) atoms

· For the defect free crystal the Gibbs function has the value: G₀= H₀ - TS₀

· Introducing one vacancy increases the enthalpy by H_v and: G₁ = H₀ + H_v - TS₁

· For a crystal with n non-interacting vacancies the introduction of the vacancies increases the enthalpy by nH_v and the Gibbs function has the value: G_n = H₀ + nH_v - TS_n

· The creation of these vacancies also increases the configurational entropy of the lattice; an entropy of mixing : S_n = k Ln W

where k = Boltzmann's constant, W = Number of different configurations of n Vacancies and (N - n) Atoms on N Lattice sites.