How a Special Quasirandom Structure (SQS) is built

Watch a finite cell rearrange until its short-range order matches the ideal random alloy.

What you are watching: a 2-D close-packed (111)-style patch of a 5-element alloy. A Monte-Carlo / simulated-annealing search swaps atoms to drive the Warren–Cowley parameters α(shell) → 0 — i.e. it forces the small cell's pair statistics to match a truly random alloy. This is a teaching analog; the paper's production SQS used ICET, a 3-D FCC cell, 256 atoms, then was cut to a 4×4×6 (111) slab (96 atoms) with a pure-Pt skin.
Phase 1 — clustered start: like atoms sit together, so order is high.
1st-shell short-range order  mean |α1|
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target for a random alloy: α → 0
2nd-shell |α2|
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unlike-bond frac.
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anneal temperature  ·  objective
composition (equiatomic, 20% each)
MC steps · accepted
0 / 0 ok
speed

From bulk SQS to the Pt-skin (111) slab used in the study

Take the converged random arrangement as the bulk, cut a (111) slab, then replace the outermost layer with pure Pt.

→
Pt skin (top layer) gives a Pt-like surface.
Subsurface layers keep the high-entropy Fe–Co–Ni–Cu–Pt mix from the SQS — the buried tuning handle.

Production model: 4×4×6 (111) slab · 96 atoms · 6 layers (top 3 relaxed, bottom 3 fixed) → H adsorbed on 96 hollow sites.
The goal

Mimic randomness, cheaply

A truly random alloy is infinite — we can't put it in DFT. An SQS is a small periodic cell chosen so its correlation functions match the random alloy for the most important short-range clusters.

The objective

Drive α to zero

The Warren–Cowley parameter αij = 1 − P(j|i)/cj measures deviation from random neighbours. Clustering gives α>0; ordering gives α<0. The search minimizes Σ α² over the nearest shells.

The search

Anneal, don't guess

Metropolis Monte Carlo swaps two atoms and accepts good moves (and occasionally bad ones while "hot"). Cooling the temperature locks in the best-mixed, lowest-α configuration — the SQS.

Companion to the TICC 2026 talk · ← back to slides · units: eV, potentials V vs RHE