Suppose that I have crystalline system made of 2 species, let say A and B (e.g. NaCl). I've built a supercell and I want to substitute individual element C in place of A or B (only one atom at a time, in different sites of A or B). How to calculate the most stable (in terms of energy) substitution site (or how to compare energies of different substitutions)?
This is not so obvious because elements A and B give different contribution to total energy, so when I substitute element C in place of A or B, I will get different energies and their simple comparison is wrong idea.
You could calculate the binding energy Ebind = Etot,combined - sumi Ei with i being an index for the different atom types and Ei being the total energy of your individual atoms. This would cancel out the different contributions to the total energy of your subtituents and give you a quantity which you can compare between the different systems. If the binding energy of a certain compound is lower then the one of another compound, it is "more stable".
So, if I understand correctly: first I need to do calculation of total energy for single A, single B and single C (Ei), then for my structures with C substituted on different sites (this is the Etot,combined) and then use eq. You provided to compare thus computed energies.
Great, thanks.
yes, you understand correctly. start from single element calculation (or from bulk) to get the formation (sublimation) energy of your AB. then you replace A/B with C. the energy (of formation) is then : deltaE=E(abc)-N_a.E_A-N_b.E_B-N_c.E_C . Fair enough. now, you need to compute different configuration to compare the energy. this is the laborious part as you have to calculate: C on A, C on B, interstitial position, then check whether antisite defects are presents (if C on A and at the same time A on B leaving B deficient) etc. There are publications out that may help you to get the concept of such calculation, sending link to a very useful publication: http://www.sciencedirect.com/science/article/pii/S0921452611012701
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