Dear Wun-Fan,

In reality both formulas are equivalent. The more general formula includes the chemical potential whose energy is to be calculated (as well as a charge contribution that depends on the Fermi level). For example, for a vacancy in a pure crystal, assuming no charge (electronic) effects and zero temperature, the chemical potential can be expressed as Ev/(N-1). If you operate with the resulting formula, you get the expression that you refer to above.

I'd say that for non charged defects, this is the way to go.

Jaime

It depends on what you wish to use as 'basin' (and physicist or chemist inclination:) I guess). Let's assume a different type of defect : an oxygen vacancy in CeO2.

Then you can either take:

Ed=Ef - Ei + 0.5 EO2

(Ed= defect formation energy, Ef= total energy of cell with vacancy, Ei= Total energy of cell wo vacancy, EO2 binding energy of O2)

or

Ed=Ef - Ei + µO

(with µO the chemical potential of O)

In the latter case you need to find/choose this chemical potential, which is based on the assumption that the formation of an oxygen vacancy requires a different amount of energy depending on the chemical environment (is there O2 gas present) Then the O rich environment leads to µO=0.5EO2. For the O poor environment one looks at the heat of formation of Ce2O3, and distills a µO out of this, as a result your Ed now becomes a linear function of µO.

As you can see the first equation is merely one extreme case of the latter. The latter equation allows you to compare different systems that can be in competition, and may provide you with "environmental conditions"(=oxygen rich/poor) where one competing system will be better than the other and vice versa. This can be very usefull, however, if you are comparing systems where the chemical potential term is the same for all your systems, you will just end up with parallel lines (making the first equation the most efficient one)