VASP Computing Generalized Stacking Fault Energy of Au
VASP: Genearlized Stacking Fault Energy of Au
Input files
Here are the basic input files required for VASP calculation. Some of the files need to be changed since we need to perform a large number of calculations.
INCAR
System = fcc Au LWAVE = .FALSE. ENCUT = 400 ISMEAR = 1 SIGMA = 0.1 ISIF = 2
KPOINTS
test convergence 0 0 = automatic generation of k-points Monkhorst 7 7 11 0 0 0
POSCAR
POSCAR for FCC Au (created manually) 4.0605 1.22474487139159 0 0 0 1.73205080756888 0 0 0 0.70710678118655 6 Cartesian (real coordinates r) 0 0 0 0.40824829046386 0.57735026918963 0 0.81649658092773 1.15470053837925 0 0.61237243569579 0 0.35355339059327 1.02062072615966 0.57735026918963 0.35355339059327 0.20412414523193 1.15470053837925 0.35355339059327
You also need to put the LDA pseudopotential file as POTCAR in this directory.
Results
Perfect crystal
The following table shows energy convergence with k-points. (Reference value from Au_bulk calculation: E = -4.39 eV/atom.)
| KPOINTS | E (eV/atom) | optimal number of CPUs | computational time (second) |
|---|---|---|---|
| 3x3x3 | -4.4735468 | -- | -- |
| 5x5x5 | -4.4121563 | -- | -- |
| 7x7x7 | -4.4043722 | -- | -- |
| 7x7x11 | -4.3981093 | 16 | 341 |
| 7x5x13 | -4.3974777 | 16 | 291 |
Unrelaxed stacking fault energy
From now on, we fix KPOINTS at 7x5x13, for which the energy of perfect crystal is E0 = -4.3974777 (eV/atom).
To create a stacking fault, we shift the repeat vector b in the x-direction by sqrt(6)/6. The new POSCAR file is (notice the change in 3rd line).
POSCAR for FCC Au (created manually) 4.0605 1.22474487139159 0 0 0.40824829046386 1.73205080756888 0 0 0 0.70710678118655 6 Cartesian (real coordinates r) 0 0 0 0.40824829046386 0.57735026918963 0 0.81649658092773 1.15470053837925 0 0.61237243569579 0 0.35355339059327 1.02062072615966 0.57735026918963 0.35355339059327 0.20412414523193 1.15470053837925 0.35355339059327
| Unrelaxed stacking fault energy | |
|---|---|
| E1 (raw data) | -26.343752 (eV) |
| E0 (perfect crystal) | -4.3974777 (eV/atom) |
| Ex (excess) = (E1-E0*6) | 0.0411142 (eV) |
| Area | 14.27873 (angstrom^2) |
| Esf (unrelaxed) = Ex / Area | 0.0028794 (eV/angstrom^2) = 46.128 (mJ/m^2) |
The result can be compared with previous calculations Esf = 59 (mJ/m^2) (Rosengaard and Skriver, PRB, 47, 12865, 1993) and experimental value of Esf = 42 (mJ/m^2) (Devlin, J. Phys. F: Metal Phys. 4, 1865, 1974).
Relaxed stacking fault energy
We now displace the y-component of the repeat vector b and find the minimum energy.
| Relaxed stacking fault energy | |
|---|---|
| E1 (min) | ?? (eV) |
| E0 (perfect crystal) | -4.3974777 (eV/atom) |
| Ex (excess) = (E1-E0*6) | ?? (eV) |
| Area | 14.27873 (angstrom^2) |
| Esf (unrelaxed) = Ex / Area | ?? (eV/angstrom^2) = ?? (mJ/m^2) |
Unrelaxed generalized stacking fault energy
The unrelaxed generalized stacking fault energy is obtained by displacing the x-component of the repeat vector b (while keeping y-component of b fixed).
(Insert unrelaxed GSF curve here)
Relaxed generalized stacking fault energy
The relaxed generalized stacking fault energy is obtained by displacing the x-component of the repeat vector b, while allowing the y-component of b to relax. This means for every value of we will need to a set of calculations with different values of .
(Insert relaxed GSF curve here)