Experiments · E45
Partly. Titanium lowers it, as published, but weakly (rank correlation −0.149); niobium lowers it most (−0.478); temperatures span 150–1225 K.
In the log: A short-range-order and transition-temperature map, and it reproduces a trend
book/assets/diagrams/exp/E45.svg).No result paragraph for this entry was found in the log.
Date 2026-09-13 · Question The deliverable is where these alloys order and at what
temperature. What does the design space look like? · Provenance scripts/odt_map.py,
runs/odt_map/map.jsonl
219 compositions, each with four independent Monte Carlo runs down an 18-point ladder from 1800 K at 128 sites, across the bounded design space of section 4f-bis. Roughly ninety seconds each, run overnight on this machine at no cost.
The spread. Transitions from 150 to 1225 K, median 550, with one composition at a ladder edge - so the range covers the space. Short-range-order strength 0.68 to 1.71, median 1.14. That the transition swings by a factor of eight across compositions is consistent with Sobieraj et al., who report 300 to 1400 K across theirs.
Which pairs order, across the whole space:
| pair | times dominant | mean alpha |
|---|---|---|
| V-Zr | 92 | -2.79 |
| Ta-W | 44 | -3.28 |
| Ti-Zr | 26 | -3.00 |
| Mo-Ta | 21 | -2.43 |
| Ta-V | 8 | -2.59 |
| Nb-V | 5 | -2.50 |
Ta-W and Mo-Ta are precisely the pairs the two independent papers identify - Sobieraj et al. flag Ta-W as one of the two most influential in Cr-Ta-Ti-V-W, Nguyen-Manh et al. find Mo-Ta strongest in MoNbTaVW. Both emerge here without being sought.
Element trends, and one is a reproduction.
| element | Spearman with transition | |
|---|---|---|
| Nb | -0.478 | lowers it, decisively (p < 1e-12) |
| Ti | -0.149 | lowers it, marginally (p ~ 0.03) |
| Zr | +0.238 | raises it (p ~ 4e-4) |
| V | +0.228 | raises it |
| Hf | +0.170 | raises it |
| Ta, W | +0.00 | no detectable effect |
Sobieraj et al. report that increasing titanium significantly decreases the order-disorder temperature. The same sign appears here across 219 compositions from an expansion never fitted to their data - though at p ~ 0.03 it is a weak reproduction, and is reported as such rather than as agreement.
New, and not in either published system. V-Zr dominates more often than any other pair and niobium lowers the transition more strongly than titanium does. Neither Cr-Ta-Ti-V-W nor MoNbTaVW contains zirconium, so neither could have seen the first; and Nb's effect is three times titanium's here.
The limitation, stated with the result. Each individual transition carries +/- 173 K (median across four runs) - the Monte Carlo scatter established in E41, which more training data cannot reduce. The trends over 219 compositions are far better determined than any single entry, and only the trends should be quoted. Individual compositions in this map are candidates for a careful determination, not determinations themselves.
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