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Sweep concentration ranges

Enumerate across a band of concentrations in a single call using ConcentrationRange. Internally, the range decomposes at each supercell volume into a list of integer-multiplicity "partitions" (possible stoichiometries consistent with the concentration range); enumerate runs the fixed-concentration algorithm once per partition.

Setup

julia> using Enumlib

julia> p = ParentLattice([0.0 0.5 0.5; 0.5 0.0 0.5; 0.5 0.5 0.0]);    # FCC primitive

julia> sites = Sites([Site([0.0, 0.0, 0.0], [0, 1])]);               # binary

A bounded range

Specify per-species (min, max) fractional bounds. The example below restricts each species to the 40–60% range — a typical "near-equiatomic" sweep (say, for high-entropy alloys):

julia> cr = ConcentrationRange([(2//5, 3//5), (2//5, 3//5)]);     # 40%-60% on each species

julia> e = enumerate(p, sites; supercells = VolumeRange(8:8), concentration = cr);

julia> length(e)
94

At n=8 with bounds 40–60%, only (4, 4) fits (counts must be integers); (3, 5) and (5, 3) are outside the range. So the result equals the HF 2012 reference for 50/50 FCC at n=8: 94 structures.

A sparse / dilute regime

Restrict the first species to 1 or 2 of 12 atoms — this is where ConcentrationRange shines, because the unrestricted enumeration at n=12 would visit 7140 structures across all concentrations, while this dilute band visits only 216 across 2 partitions:

julia> cr_dilute = ConcentrationRange([(1//12, 2//12), (10//12, 11//12)]);

julia> e = enumerate(p, sites; supercells = VolumeRange(12:12), concentration = cr_dilute);

julia> length(e)
216

The partition-count limit

If a ConcentrationRange decomposes into many partitions per supercell, the cost can balloon. The default limit refuses the request when the partition count exceeds 100 at any single volume:

julia> cr_wide = ConcentrationRange([(0//1, 1//1), (0//1, 1//1)]);   # totally unrestricted

julia> try
           enumerate(p, sites; supercells = VolumeRange(12:12),
                     concentration = cr_wide, partition_threshold = 5)
       catch e
           e isa PartitionExplosionError ? :refused : rethrow()
       end
:refused

In the example above we drop the threshold to 5 to trigger the limit on a small case. To override at production scale, pass on_partition_overflow = :warn (warns but proceeds) or :ignore (silent), or raise partition_threshold explicitly. See PartitionExplosionError for the full message text and mitigation list.

See also