Obviously, if the above figure was our lattice, the hole would be the vacancy. Important points to note about vacancies:

* Important for diffusion and dislocation climb, creep, recrystalization

* Occurs in ceramics and metals

* Always present (except at 0K)

* Are equilibrium defects; they exist at equilibrium

* The proper number of vacancies lowers crystal energy

* Gibbs Free Energy: G = H – T*S (H is enthalpy, S is entropy). When dG/dnv = 0, the crystal is at equilibrium

* Gv = Hv – T*Sv where Hv = Nvw, Nv is the number of vacancies, w is the work required to break and recreate new bonds (for the new atom location). This is also called the ‘work of formation’ of vacancy

* S = -k*ln(j), where k is the Boltzman’s constant, and j is the number of configurations available with the same energy.

* The number of atoms plus the number of vacancies is the number of lattice sites. N = Na + Nv

* Gv = -Nv(w + k*T*[N*ln(N) + Na*ln(Na) + Nv*ln(Nv)]

* -w/(K*T) = ln[Nv/N]