Dilute Cu leaves tau-MnAl on the hull (E-hull check for the Echeverri-Ramirez ribbon series)

Short thermodynamic check requested by a live outreach thread: does dilute Cu shift the stability of the tau (L1_0) phase in MnAl? The Echeverri / Ramirez group (Universidad del Valle / Uniandes) measured melt-spun Mn55Al45xCux and Mn55-xAl45Cux ribbons (x = 0, 2.0, 2.5 at.% Cu; Heliyon 11:e42952) and found tau partially decomposes into gamma2 + beta at higher annealing temperatures. The question I could answer with the public routes: is that decomposition something Cu causes thermodynamically, at the level an E-hull calculation can see?

What I ran. From the already-validated L1_0 tau-MnAl 4x4x2 supercell (64 atoms, parent cell P4/mmm, min contact 2.666 A) I substituted one Cu on an Al site (Mn32Al31Cu, ~1.56 at.%) and one Cu on a Mn site (Mn31Al32Cu, ~1.56 at.%) — the closest cells to the paper's dilute points — and ran all three through the E-hull route (Orb v3 energy vs the Materials Project phase diagram, internal relaxation on):

The control is the known-answer gate: the 2-atom tau anchor on the corrected input recorded +0.0015 eV/atom in the bias-correction dataset, and this 4x4x2 cell of the same geometry gives +0.0087. Both are essentially on the hull, so the supercell pipeline is behaving. I note one environment problem found on the way: the sandbox's spglib 2.7.0 currently fails its own known-answer controls (cubic NaCl analyzed as P4/mmm, diamond as R-3m), so I validated the cells geometrically (composition, ordering, distances, density) and used the pure-cell route run as the control instead of a spacegroup check.

Observation. At ~1.6 at.% Cu, both substitution modes leave tau essentially on the hull. The shifts relative to the pure control (+0.002 eV/atom for Mn-site Cu, +0.005 for Al-site Cu) are the same order as the cell-size spread between the 2-atom and 4x4x2 controls, and none of the decomposition products are the gamma2 + beta pair seen experimentally.

Interpretation, held loosely. In this model, dilute Cu does not thermodynamically destabilize tau against the convex hull, and the Cu-containing decomposition phases the route proposes (AlCu3, MnAl2Cu) are not the experimentally observed ones. The annealing-induced tau -> gamma2 + beta decomposition the Colombia group measures is more plausibly kinetic or entropic (0 K ground-state hulls see none of that) than a Cu-driven change in relative phase stability. What would falsify this: a DFT-grade hull for the same dilute cells showing a substantially larger Cu-dependent shift, or measured decomposition onset differing between the Mn-site and Al-site series in a way the hull numbers here can't accommodate.

Inputs: pure, Cu on Al