Is negative defect formation energy reasonable?

[zhu]

Dear all,
I calculated the defect formation energy of CuI, using VASP 5.2. The exchange correlation potential is GGA-PBE. However, the formation energy of neutral copper vacancy is negative (-0.4eV). Is it reasonable? I have checked the input parameters. All the results are well converged. The formation energy is the total energy of defective supercell minus that of perfect supercell and plus that of bulk copper (FCC structure). I don?t calculate the total energy of the perfect supercell. The supercell (3*3*3) contains 27 times atom as primitive cell. I replace it with 27 times of the energy of primitive cell. Will it cause error? What is the matter?
Thank you
The following are the INCAR files.

INCAR of primitive cell

ISTART=0
ICHARG=2
ISPIN=2
PREC=Accurate
NELM=80
ALGO=V
LREAL=.F.
EDIFF=1E-6
IBRION=2
NSW=100
ISIF=3
ENCUT=355
EDIFFG=-1E-2
ISMEAR=-5
SIGMA=0.1

INCAR of supercell

ISTART=0
ICHARG=2
ISPIN=2
PREC=Accurate
NELM=80
ALGO=V
LREAL=Auto
EDIFF=1E-6
IBRION=2
NSW=100
ISIF=4
ENCUT=355
EDIFFG=-1E-2
ISMEAR=-5
SIGMA=0.1

[alex]

Hi zhu,

I'd suggest some sanity checks:
a) check literature if you can find the heat of formation of bulk CuI and compare
b) do the perfect supercell calculation and compare

Cheers,

Alex

[dyc_2008]

Dear ZHU

Based on thermodynamics, G=H-TS, when there is a defect,T and S will increase simultaneously. So, it is reasonable to get a negative defect formation energy.

But, Based on VASP, the temperature is 0k. so, I it is unreasonable to get a negative defect formation energy.

I am confused by this problem .
please Somebody tell me how to solve this problem.

[zhu]

Dear all,
Thank you for your advice. The experimental cohesive energies of bulk Cu (FCC) and bulk CuI (FCC) are -3.49eV and -5.32eV. Our theoretical total energies are -3.723eV and -5.5598eV. Their dispersions are not very much.
The total energy of perfect supercell is -150.14eV, which is very close to 27 times of the energy of the primitive cell (-150.11eV).
I think that the negative formation energy will not definitely lead to the collapse of the lattice. It only considers the thermodynamic equilibrium condition. The vacancy atom cannot diffuse freely in the lattice due to the energy barrier.

[zhu]

Any suggestions?

[alex]

Hi zhu, some more questions.

You state 'However, the formation energy of neutral copper vacancy is negative (-0.4eV)'.

Does neutral mean you remove Cu(0) for removing a neutral Cu atom? What is the reaction you put this energy for?

Cheers,

Alex

[zhu]

Hi alex,
One copper atom is removed in POSCAR for copper vacancy, regardless its charge state. For neutral charge state, the number of electron is just the same as that total electron of the atoms in POSCAR (NELECT=default). For positive (negative) charge state, an extra electron is removed (added) by changing NELECT (NELECT=default-1 or default+1).
The following is the defect reaction of copper vacancy.
O=Vcu(neutral)+Cu(bulk)

[alex]

What exactly are you doing in terms of chemistry? Put an equation like a+b -> c+d and the total energies for each compound/(super)cell. As well as possible charges on the cells.

Thx,

Alex

[zhu]

The defect reaction is as follow.
perfect supercell=defect supercell with copper vacancy(neutral) + copper atom.
In copper-rich limit, the energy of copper atom in CuI is equal to the energy of the atom in bulk copper. The energy is -150.11ev, -146.83ev and -3.72ev for the three terms. The enthalpy of the reaction is -0.44ev.

[alex]

Like that:

(CuI)_n -> (CuI)_(n-1)-I + Cu^0, Delta E = -0.44 eV

?

[zhu]

YES.

[Neutrino]

I highly suspect this result. The defect formation energy is positive, while the Gibbs free energy of formation is negative. At 0 Kelvin (without any extra phonon calculations ) what you calculate is the formation "energy" and hence it has to be positive. On the other hand for a charged defect you may obtain a negative formation energy if you arbitrarily vary the electron chemical potential (Fermi Level) within the band gap. In reality such values of Fermi level that leads to negative formation energies are not accessible experimentally.

Suggestions:
1- Are you comparing calculations withe same K-point density? Gamma Point Sampling is NOT sufficient for defects in an ionic material.
2- Can you increase the energy cutoff to say 500 eV to check the convergence of your results?
<span class='smallblacktext'>[ Edited Sun Nov 27 2011, 12:00AM ]</span>

[zhu]

Thank you.
Yes, I have checked the convergence of k-point (4*4*4), size of supercell, and energy cutoff (350 eV).
Dose this problem originate from DFT itself? I just guess.

[Neutrino]

You may consult this paper to benchmark your findings:

"Native p-type transparent conductive CuI via intrinsic defects"
J. Appl. Phys. 110, 054907 (2011); doi:10.1063/1.3633220