Generating SQS for a Ternary HCP Alloy (A-90%, B-6%, C-4%) with Extreme Concentration Skew

Alloy Theoretic Automated Toolkit (ATAT)
1

I am designing a ternary HCP alloy with a highly skewed composition: A-90%, B-6%, C-4%. For SQS generation key challenges are:
Minority Element Placement: Elements B (6%) and C (4%) are sparsely distributed. How can we ensure their random placement (e.g., avoiding B-B/C-C clustering) while enforcing pairwise probabilities (e.g., A-B: 10.8%, A-C: 7.2%)?
Dominance of A-A Correlations: A-A pairs dominate (81% probability). How do we prioritize A-A correlation accuracy while resolving minority contributions without introducing artificial periodicity?
HCP Lattice Constraints: How should correlation shells (e.g., 1st/2nd neighbors in HCP) be prioritized to minimize periodicity errors?

Request for Guidance:
What strategies, workflows:
Adjusting Monte Carlo parameters (e.g., temperature, swap rules) for sparse B/C placement.
Validating beyond pair correlations (e.g., triplet terms).
Addressing HCP symmetry challenges (e.g., supercell anisotropy).

Any insights or references to ternary SQS work with skewed compositions would be invaluable!

2

Avoiding clustering and periodicity artifacts are both accomplished by ensuring that pair correlations up to far enough distance match those of the disordered state. There is no separate algorithm to ensure this.
One word of caution: you cannot avoid all periodicity artifact with an SQS - you can only push them farther, at a distance where they shouldn’t matter.
Another caution: randomness does not imply complete absence of clustering.
Finally, the main problem with very low concentrations is that the SQS size might need to be very large. Multiple of 2% typically a supercell at least 50 times larger than the unit cell.
An hcp structure poses no special problems, other than typically requiring a larger SQS for the same matching quality, due to more symmetrically distinct clusters.