Are the survey's best alloys really stable, or does another crystal structure beat them?

EXPERIMENTS.md · lines 2839–2886

E54 — The three qualifiers are on the wrong lattice; the expansion cannot see what beats them

The design-space survey found exactly three compositions meeting the service window, all Hf/V/Zr-rich near-binaries, all qualifying by staying ordered above 1000 K. A literature review of single-phase refractory stability came back with a specific objection: in the Hf-V and Zr-V corner the phase that actually forms is the cubic C15 Laves, HfV2 and ZrV2, which does not sit on a bcc lattice and therefore cannot appear anywhere in a bcc cluster expansion - not as a competitor, not as an instability, not at all.

That is checkable here, so it was checked. MACE-MPA-0, full relaxation of cell and positions, C15 built from the MgCu2 prototype against the bcc solid solution at the same composition:

The bcc figure is the mean of three random 54-atom occupancies. The C15 cells were confirmed as Fd-3m (227) before and after relaxation, and relax to a = 7.292 and 7.355 A against experimental 7.39 and 7.44 A - 1.3 per cent low, the ordinary underbinding of a PBE-trained model, which is what says the structure is the one intended.

The margin is 21 times the expansion's own cross-validation error of 5.67 meV/atom. It is larger than the entire ordering effect the expansion exists to measure. At these compositions bcc is not an approximation that costs a little accuracy; it is the wrong lattice, and the transition temperature reported there is the ordering temperature of a structure that never forms.

So the survey's three hits are withdrawn. They are not marginal results awaiting a better rung - they are answers to a question about a phase that loses by a fifth of an electron volt per atom.

What this says about the guard added the same day. Leverage against the design matrix was introduced to mark compositions where the expansion is extrapolating, and it does that correctly: it puts a 70/30 binary at 0.76 of the training edge and a 4:1 at 1.07. But it would not have caught this. Leverage measures distance from the training set within the hypothesis space, and every training structure was bcc, so a composition can sit comfortably inside the fitted region and still be on the wrong lattice. The two failures are independent: one is about where the parameters were constrained, the other about what the model is able to express. A guard against the first is not a guard against the second, and reporting only leverage would have dressed this result in a reassuring number.

The missing rung. The ladder's three rungs are the same expansion with more seeds and more sweeps, so none of them can overturn a lattice assumption they all share - they agree with each other and are wrong together. The rung that answers this is off-lattice and it is cheap: the two comparisons above took about four minutes each on one CPU.