If the screen credits alloys whose atoms are too slow to move, does the search diversify?

EXPERIMENTS.md · lines 5113–5194

E91 — Carrying kinetics into the screen: calibrating a four-millisecond activation energy

E90 established that the screen the generator learns from asks about thermodynamic stability at 90 K, where a five-element alloy's mixing entropy is worth about 16 meV/atom, and that this is why every element added makes the score worse. The requirement is not that, it is that nothing happens anywhere between 90 and 1000 K, and what makes a high-entropy alloy an engineering material is that decomposition is unreachable rather than unfavoured.

The ladder already answers this - it is what rescues MoNbTaW in E74 - but the kinetics cost twenty minutes, from a MACE vacancy formation energy and a climbing-image barrier, and the screen has four milliseconds. So the screen needs an activation energy it can afford.

The candidate is the oldest rule in diffusion: Q is proportional to the melting point. For body-centred cubic metals Q/(k_B T_m) sits near 17, and the rule-of-mixtures melting point is already computed as a descriptor in microseconds.

This is calibrated before it is used, against the four activation energies the ladder measured properly: Mo0.62Ta0.38 4.93 eV, Ta0.39Mo0.34W0.18Nb0.08 5.20, Mo0.50Ta0.33W0.15 5.03, Ta0.53Mo0.47 4.60.

Predicted: the rule reproduces those four within 0.5 eV, which is the spread the ladder itself quotes on Q and is small against the 4.6 to 5.2 eV range. If it does, the screen can carry a kinetic term; if it does not, the term has to come from somewhere else, because a Q wrong by an electron volt is a diffusion distance wrong by orders of magnitude at 1000 K.

Falsified if the four disagree by more than 0.5 eV, or if the ordering of the four is wrong - a rule that gets the absolute scale right and the ranking backwards is worse than none, because ranking is what the generator uses.

Outcome. The rule ranks correctly and the screen, given the requirement as written, explores.

The melting-point rule reproduced the four measured activation energies to 0.53 eV at the textbook constant - marginally outside the 0.5 predicted, and one-signed, always under - and to 0.31 eV at a fitted 18.4. It ranked all four correctly, which was the stated criterion. Four points is thin and the constant is the weakest number in the method; it is recorded as such in the code.

The screen now asks the requirement rather than a proxy for it. Across twelve temperatures spanning the window, the driving force is taken where atoms can actually travel the couple of nanometres a nucleus needs. A probability saturates - five of eight test alloys returned exactly 1.000 - so the headline stays in meV/atom: the worst driving force among reachable temperatures, or, if nothing is reachable anywhere, the hot driving force credited 200 meV/atom for being frozen.

The monotonic penalty on element count is gone, and it was not removed by hand. MoNbTaW, the one alloy in this system with an experiment behind it, now ranks first - ahead of every binary - because it is the alloy whose vacancies do not move. Two real Senkov alloys that the 90 K screen called unstable are now placed correctly. NbTiVZr and the twelve-element equiatomic remain the only compositions where decomposition is reachable, and they stay rejected.

And the generator explores. Identical seeds, identical budget, four objectives:

All twelve elements now appear, against nine; the mean composition holds four elements rather than two and a half; a third of what it finds is a five-element alloy or larger, against two per cent. It also found more compositions, not fewer, so nothing was traded for the diversity.

The earlier diagnosis in E90 was right and the earlier fix was wrong. Changing what the generator was paid - optimistic instead of pessimistic - did nothing, because the problem was never the uncertainty term. It was that the screen asked about 90 K thermodynamics while the requirement is about a window and about whether anything can happen inside it. Given the question it was actually meant to answer, the search explores without being told to.