The target: an infinite random alloy

A real solid solution has no repeating pattern — and no boundaries

macroscopic random alloy — atoms placed with no order (2-D teaching analogy)

Real random alloys are effectively huge and disordered: each lattice site is occupied at random.

DFT cannot calculate this directly — it needs a finite, periodic cell.

Key messageWe need a small model that behaves like the infinite alloy.

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DFT needs a small periodic cell

Cut out a piece — but the cut repeats forever in every direction

one cell (solid) + its periodic images (faint)

A finite cell tiled with periodic boundaries repeats forever. The atoms it contains define every copy.

Caution A random crop may accidentally cluster or order the atoms — and that bias repeats everywhere.

Key messageIf the small cell is biased, the periodic model is biased too.

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All three cells have identical atom counts — only the arrangement differs

Key messageCounting atoms is not enough — we must count neighbours.

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For each cell: of an A atom's nearest neighbours, how many are A / B / C / D?

Optional: written compactly this is the Warren–Cowley parameter α → 0 = random-like local order.

Key messageA random alloy makes every neighbour type equally likely (dashed line) — the SQS matches it best.

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Score each cell by its mismatch to the random alloy; the smallest wins

Production SQS: 3-D FCC supercell via SQS / ICET — this slide uses a 2-D pedagogical analogy.

Key messageSQS = a small periodic supercell that statistically mimics a random alloy — visually random is not the criterion.

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