Can one energy model cover twelve elements without losing accuracy on the original eight?

EXPERIMENTS.md · lines 4697–4797

E85 — Twelve elements: prediction before fitting

The expansion is widened from nine to twelve - the eight refractory metals plus Cr, Co, Cu and Ni - so the fly can propose across the space the hull of E84 already covers. Everything else is held: the same fixed lattice at 3.2935 A, the same cutoffs, shared-lattice references, corners as training points at weight 10.

The four new anchors, measured:

Every one is at or above vanadium's 505, which was the largest of the original eight, and cobalt is more than twice it. Copper and chromium sit at nearly the same bcc spacing yet differ by 470 meV/atom, which is stiffness rather than size - the expansion now has to span a range roughly twice what it did.

Predicted:

1. CV RMSE between 10 and 20 meV/atom, from 7.41 at nine elements and 5.68 at eight.
2. All twelve corners pin to within the new CV error. They are training points whose targets are zero by definition, and this held at nine.
3. The refractory predictions survive. On the 120 nickel-free relaxation-survey compositions the twelve-element fit stays within about 15 meV/atom of the eight-element one, as the nine-element fit did (it shifted by 3).

Prediction 3 is the one that decides the architecture. If it fails, one expansion cannot serve both the refractory work and the wider space, and the twelve elements need their own fit rather than a widened one - which is a real cost, because every recorded refractory result would then live on a different model from any new work.

Outcome. Predictions 1 to 3 hold; the hull of E84 is wrong and is withdrawn.

The twelve-element expansion fits: CV RMSE 9.09 meV/atom against 7.41 at nine and 5.68 at eight, just below the predicted 10-to-20 band. All twelve corners pin within 2 meV/atom. On the 120 refractory relaxation-survey compositions the twelve-element fit reads MAE 19.3 against the eight-element 19.1, a mean shift of 3.9 - so one expansion serves both, and the architecture question prediction 3 was posed to settle is settled in the easy direction.

But wiring it to the E84 hull turned every refractory answer positive. MoNbTaW went from -114 to +15 meV/atom and Mo0.62Ta0.38 from -149 to +38. That is not a widening of the search, it is the headline result of the project being overturned, so it was traced rather than accepted.

The 434 observed phases changed the refractory verdict by nothing at all. The entire 120 meV swing rests on one entry: MoTa [jarvis], a two-atom Pm-3m cell at -11.5358 eV/atom, 191 meV/atom below the Mo/Ta linear average - in a system the assessed phase diagram calls a continuous bcc solid solution.

It is B2. A bcc lattice with the two species alternating. And that is the error, which is mine and not the database's: the off-lattice hull exists to hold phases the expansion cannot see - hcp, omega, Laves, fcc - because those are the rivals a bcc cluster expansion can never lose to (E56). A B2 structure is a bcc superstructure. It is exactly what the expansion does describe, and whether it forms is the ordering question, which T_od and the Monte Carlo already answer.

Putting bcc orderings into the hull makes the screen ask whether a disordered solid solution lies below its own ordered state. At 0 K it never does. Every composition in the system therefore screens positive, and it looks like a discovery rather than a double count.

So E84's hull is withdrawn as built. What survives from E84 is the method and the nickel result: the databases really do supply the Ni-Ti, Ni-Nb, Ni-Ta and Ni-V compounds that hand- picked prototypes missed, and those are genuinely off-lattice. What must change is the filter. A structure earns a place on the off-lattice hull only if its underlying lattice - with the decoration ignored - is not bcc.

The filter is right in principle and too strict in practice; the twelve-element hull is not yet trustworthy and is not in use for anything recorded.

Classifying all 936 relaxed structures by their bare lattice removed 241 bcc superstructures, MoTa [jarvis] among them, correctly identified as Im-3m with a one-atom primitive cell. MoNbTaW improved from +15 to +6 meV/atom - and it should be -57.

The census of what survives says why. Of the refractory-only binaries kept, 58 are I4/mmm, against 46 Fm-3m, 45 P6_3/mmc and 29 Fd-3m. The last three are fcc, hcp and C15 Laves: genuinely off-lattice, exactly what the hull is for. I4/mmm is very often a tetragonally distorted bcc superstructure, and a test that demands exact Im-3m cannot see one. TaW2, MoNb2, MoTa2 and Mo2Ta - the four Alexandria phases now doing the damage - are of that kind.

So the discriminator has to be geometric rather than symmetric. Coordination number is the honest one and is indifferent to distortion: bcc has eight nearest neighbours, fcc and hcp have twelve, and Laves has twelve and sixteen. Counting neighbours inside about 1.15 times the nearest-neighbour distance separates bcc-derived from close-packed whether or not the cell has relaxed off cubic. That is the next change and it is not made here.

Nothing recorded is affected. build() still loads offlattice_hull.json for any eight-element expansion, so every result in this file stands on the hull it was measured against; only the twelve-element path touches offlattice_hull12.json, and no verdict has been taken from it.