How would you report the lattice parameters of an alloy, modelled using a supercell

Question

There is a whole lot of literature behind ab initio modelling of alloys with statistical site occupancies. These include VCA, SQS, CPA, supercell approach, etc. This question does not aim to compare these approaches, but it rather assumes a case where the supercell approach is used to model a new alloy using the DFT framework.

Consider some alloy $\ce{A_{0.33}B_{0.67}C3}$. A supercell of size 1x1x3 (it's small, but for the sake of understanding) is generated and the geometry optimisation is performed.

Now, I have two questions.

1. During the supercell generation, the space group symmetry of the original alloy can be (is probably) lowered, because the supercell may not support the same amount of symmetry operations. Therefore, how plausible is it to report the symmetry of the optimised supercell as the final relaxed symmetry of the original alloy? Are there any strategies to go back to the original unit cell from a relaxed supercell?
2. What is the convention when reporting the optimised lattice parameters? Do you report the parameters as they are for the supercell ~(a, b, 3c), or do you take the average ~(a, b, c_avg)?

Answer 1

By making a supercell and modifying it in some way, you are creating an entirely new structure which you hope can give you some insight by being compared to the original structure. Any of the conclusions you draw from your calculations will come from the modified supercell, rather than a version where you have converted it back into the primitive cell. Some software packages, like pymatgen, are able to describe structures with partial occupancies, but I do not think it is possible to systematically convert a relaxed supercell to a primitive cell without losing information.

For this reason, it is most logical to report the geometry, symmetry and other properties of the supercell. This is what I have observed to be the convention in the literature. Reporting the raw data based on the supercell is also important to make your work as transparent and reproducible as possible.

Depending on what you are trying to show, it may be possible to report properties normalized per atom. For example, instead of reporting the lattice parameters of your 1x1x3 supercell in the primitive cell by "averaging" the c lattice parameter, it might be equally effective for your application to compare the volume of the primitive and supercells per atom.