Was the 2.2-fold gap to published ordering temperatures a real physics problem?

EXPERIMENTS.md · lines 2769–2834

E53 — The 2.2x was three things, none of them the physics; and every mixing energy was half wrong

The scale gap against the literature is largely a yardstick problem. The published table used for validation (Lederer, Toher, Vecchio and Curtarolo) reports two columns and they disagree with each other by about a factor of two; the comparison in E52 used the higher one throughout. Against the lower column the same alloys give ratios of 1.19, 0.56, 1.08 and 1.05 - scattered about one.

MoNbTaW settles it, being the one alloy in this family with several independent determinations:

Ours sits inside the spread of converged Monte Carlo and 12% below the closest comparison

• Koermann's unrelaxed 717 K - which is the right one, our model being unrelaxed too. This is the first time any part of this pipeline has been checked against an external number rather than against itself.

The ordering-blindness hypothesis is refuted. Compared within a composition across enumerated decorations of the same cell at the same volume, where references and volume cancel exactly, the expansion reproduces DFT ordering energies at slope 0.73-0.84, Pearson 0.85-0.90. An expansion that had never seen ordering would sit below 0.5. It compresses ordering by about 15%, worth 1.2x in transition temperature, not 2.2x. The fixed lattice is ruled out again by the same test (own-volume against fixed-lattice slope 1.05).

An estimator bias, found and fixed. The coldest rungs of a temperature ladder are the hardest to equilibrate, and the variance of a trace that is still sliding measures the slide rather than the fluctuation - so an unsettled cold rung reports a large excess heat capacity and drags the transition onto itself. It sat on one of the three coldest rungs for 30 of 75 alloys. CEThermo.integrate now reports each rung's drift and order_disorder refuses those beyond one standard deviation. On MoNbTaW across five seeds: 606 +/- 30 K becomes 631 +/- 22 K - higher, as the bias was downward, and a third tighter.

So: yardstick 1.5-2x, ordering compression 1.15-1.3x, estimator 1.1-1.2x, which multiplies to the 2.2x observed. Nothing was wrong with the physics.

Separately, and worse: the elemental references were strained. build_ce.py referenced every element at the shared lattice of 3.2935 A. An element held away from the constant it adopts carries elastic energy it never pays in its own crystal, and that energy is charged to the alloy:

Across the design space that is 226 +/- 43 meV/atom, against mixing energies of a few hundred - the correction is the same size as the quantity. Every mixing energy this project has reported is that much too negative; the best alloy quoted at -465 meV/atom is nearer -239. Rankings move little, the correction varying by only +/- 43 meV, but no absolute value stands. References are now each element's own equilibrium, found by a parabola through its energy-volume curve.

Ordering, short-range order and every transition temperature are untouched: a reference cancels in any difference taken at fixed composition.