As is know, for a pure element, the equilibrium vacancy concentration can be calculated with the vacancy formation energy and temperature:
Nv/N = exp(-Qv/k*T)
However, for a solid solution (A-B system), how to calculated the equilibrium vacancy concentration with the vacancy formation energy for various atoms (Qv_A and Qv_B )?
To calculate the equilibrium vacancy concentration per atom you should use:
C=C0 exp-(Q/kT).
Since you have the enthalpy of formation Q in eV, this value is for 1 vacancy. Consequently you should use the Boltzmann-Constant k instead of R (R is for 1 mol; k is for 1 Atom: R=k x N)
C0 is not temperature dependent and is defined by the local change of entropy if 1 vacancy is formed. C0 should be taken from experimental literature, since it is not easy to calculate theoretically.
To calculate the vacancy concentration per atom is quite useful, because one gets a feeling for the relation between atoms and the un-occupied places (vacancies). To calculate the absolute number of vacancies, you shoud multiply your result per atom with the number of atoms per mol (Avogadro-Constant). bit easier because you do not need to think about k and R.
. If Q is in eV, then it is easier to convert the temperature to eV also. The rule is simple, 1eV = 11600 K. So 1000 K = 1000/11600 eV = 0.0862 eV, and Q/T = 0.9/0.0862 = 10.44.
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