How Is Chemical Potential Determined in Defect Formation Energy Calculations?

[muonneutrino91]

When determining the formation energy associated with a point vacancy in say a monoatomic crystal - when the total energies of both perfect and defected crystals are known - how exactly is the chemical potential determined?

Formation Energy should be given by expression

E_form = E_defect - E_perfect - nμ
where ;
n = number of added/removed atoms, μ = chemical potential

I would anticipate that given the total energies of the perfect crystal are known, the chemical potential would be given as the energy per ion of the perfect crystal.
Otherwise, I would expect that it would be given by the total energy of either a single atom of the same species, or the total energy of a single unit cell of the crystal.

Help with this will set me right on track.

Edit: I am pretty sure that it is my first anticipation: calculating the defect-free supercell energy per atom

 

[Asim Riaz]

. The chemical potential, μ, is the energy per atom of the perfect crystal (Eperfect/N) where N is the number of atoms in the crystal. This represents the energy cost of adding or removing an atom to/from the crystal. To calculate the formation energy, you then subtract this energy cost from the total energy of the defective supercell (Edefect), and add or subtract the energy associated with adding or removing n atoms (nμ).