Hi all,
I am trying to calculate segregation energy for an impurity atom X using its solution energies at grain boundary and in the bulk of an element Y. The problem is that the pure grain boundary cell of Y has 2 more atoms than its pure bulk cell. I can't make the number of atoms same in these supercells.
Eseg= E(X)+E(Y) - E(X+Y) - Eperfect cell
E(X) is the energy of perfect Y cell with one X atom at an interstitial site; 18 + 1 atoms
E(Y) is the energy of pure Y grain boundary(GB) cell; 20 atoms
E(X+Y) is the energy of the GB cell with one X atom; 20 + 1 atoms
Eperfect is the energy of perfect cell; 18 atoms
Would the segregation energy be erroneous as the cell energies have been computed for cells with different number of atoms ? If so, how should I rectify this error ?
Dear colleague,
Your definition of the segregation anergy as the difference between the solvation energy of the impurity at the grain boundary and in the bulk material is correct in my opinion.
Your question concerns the reliability of the numerical results you obtain for these two quantities, given that you use supercells with a different number of atoms for the two situations. I suppose that your calculation takes into account the deformation of the host lattice around the impurity atom!
On the basis of your calculations alone, nothing can be said. What you need to do in both cases, and I hope your computer facilities will allow that, is to repeat the two sets of calculations for larger supercellls. Ideally you would like to have at least three sets of results, and see how the individual solvation energies change with supercell size. You can then extrapolate to the limit of infinite dilution, which is your case of interest.
Best regards
René Monnier
I think you should refer this article too : https://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.245406
All the best
mohan
Your definition is correct as long as the supercells are large enough for the interaction between impurity images to be small. From what you say, your supercells are pretty small, with ~20 atoms. Because you are using supercells of different sizes (and probably different shapes too) you don't get the benefit of the cancellation of the impurity interaction contribution between the GB and the bulk models. That will introduce an error in the calculation.
As René Monnier pointed out, you can get an estimate of the error by using larger and larger supercells. But if you can afford a much larger supercell, the best approach might be to have a "bulk-like" region within your GB model. Then you can just compare the two energies resulting from putting an atom at two different places within the same cell. This approaches gives the optimal cancellation of errors.
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