Experiments · E242

Does the chosen alloy really stay disordered when checked with DFT?

Not yet. The DFT is still running; the model's own check on Mo–Ta passed, ordering at 1149 ± 114 K as expected.

In the log: the survivor at DFT: does Mo₅₁Ti₃₈W₃Ta₃ order? (pre-registered 2026-09-23 22:0x)

runningDate 2026-09-23 22:0x, as written in the logrung 4 · DFT4 predictions · 2 result paragraphsEXPERIMENTS.md lines 16291–16308, line 16309, lines 16311–16320
exp E242 diagram
What E242 did and how it came out, drawn from this record and the files it names (book/assets/diagrams/exp/E242.svg).

Pre-registration

  1. (1)
    e6's own ΔE_order on these two cells is < 5 meV/atom (its rung 1 finds no transition down to 60 K; by E222's Bragg–Williams scaling ~20–30 K per meV).
    no verdict written against it
  2. (2)
    Decisive: DFT ΔE_order ≤ 5 meV/atom → e6's ordering energetics confirmed at this composition and the find stands as the ladder's first full pass; 5–15 → not established (a transition could sit at ~100–400 K), reported as such; > 15 → e6 is wrong here and the find FAILS. The e6 ground state is the lowest state the MODEL finds, so a small DFT ΔE_order is a lower bound that cannot rule out a different DFT-preferred order — stated, not hidden.
    no verdict written against it
  3. (3)
    The random cell's DFT formation energy is within 15 meV/atom of e6's (with E239's open Ti-reference caveat: the old-label frame may carry ~x_Ti·30 meV).
    no verdict written against it
  4. (4)
    Known answer for e6's rung 1 (runs in parallel on the Mac): equiatomic Mo–Ta through the production path (ECEVerifier, e6 ensemble mean, exact evaluator) must show a transition inside the sweep between 500 and 2600 K (published CE+MC 2020 ± 545 K; v5 985 K on the same sampler); "no transition" there would void E240.
    no verdict written against it
The pre-registration, as written

E242 — the survivor at DFT: does Mo₅₁Ti₃₈W₃Ta₃ order? (pre-registered 2026-09-23 22:0x)

E222's design on E241's survivor. The e6 model (seed 0; the ensemble re-evaluates) is annealed from five starts to its 54-atom ground state at the survivor's composition (ground_state.py), and a seed-fixed random decoration of the same composition is written (random_cell.py); both at ideal bcc sites and the Vegard constant, QE at the rung-4 standard (60/720 Ry, k 4³, MV 0.02), on the A100 through the spin-aware ladder. ΔE_order = E(random) − E(ground), per atom. Predictions. (1) e6's own ΔE_order on these two cells is < 5 meV/atom (its rung 1 finds no transition down to 60 K; by E222's Bragg–Williams scaling ~20–30 K per meV). (2) Decisive: DFT ΔE_order ≤ 5 meV/atom → e6's ordering energetics confirmed at this composition and the find stands as the ladder's first full pass; 5–15 → not established (a transition could sit at ~100–400 K), reported as such; > 15 → e6 is wrong here and the find FAILS. The e6 ground state is the lowest state the MODEL finds, so a small DFT ΔE_order is a lower bound that cannot rule out a different DFT-preferred order — stated, not hidden. (3) The random cell's DFT formation energy is within 15 meV/atom of e6's (with E239's open Ti-reference caveat: the old-label frame may carry ~x_Ti·30 meV). (4) Known answer for e6's rung 1 (runs in parallel on the Mac): equiatomic Mo–Ta through the production path (ECEVerifier, e6 ensemble mean, exact evaluator) must show a transition inside the sweep between 500 and 2600 K (published CE+MC 2020 ± 545 K; v5 985 K on the same sampler); "no transition" there would void E240.

Results

EXPERIMENTS.md · line 16309

E242 addendum (2026-09-24 00:08, before any DFT result) — the cells' actual composition. Both 54-atom cells round the survivor's nine-element x to whole atoms: Mo₂₈Ti₂₁Ta₂W₂Zr₁ (runs/e242_random/Mo51Ti38W3Ta3_random/random_cell.json), i.e. Mo 51.9, Ti 38.9, Ta 3.7, W 3.7, Zr 1.9 at.%. Cr, Hf, Nb and V (0.63 at.% each in x, 0.34 atoms each) are absent. The name Mo₅₁Ti₃₈W₃Ta₃ is x's four largest shares; ΔE_order is measured on the rounded cell, and the verdict applies to that composition. Predictions unchanged.

EXPERIMENTS.md · line 16311

E242 (4) RESULT (22:4x) — e6's rung 1 passes the Mo–Ta known answer. Equiatomic Mo–Ta through the production path (ECEVerifier, three-member e6 mean, exact evaluator): T = 1149 ± 114 K by the energy-slope channel, α₁(Mo–Ta) = −1.00 on cooling (perfect B2) — inside the pre-registered 500–2600 K (published CE+MC 2020 ± 545 K; v5 985 K). E240 is not void. Caveat it exposes: the fluctuation channel peaks at 80 K here — a spurious low-temperature peak from energy still drifting where the sampler freezes, while the true transition sits at 1149 K. Both channels therefore have cold-end artefacts. The 2026-09-23 fix uses the fluctuation channel only when the slope channel found no peak, and the five finds it failed had mid-range fluctuation peaks (331–575 K), not cold-end ones; failing an ambiguous find is the safe direction, but those five are "not established", not proven to order. runs/e242_mota_known_answer.json.

The full record

This entry is written in 3 separate places in the log, shown here in log order.

EXPERIMENTS.md · lines 16291–16308

E242 — the survivor at DFT: does Mo₅₁Ti₃₈W₃Ta₃ order? (pre-registered 2026-09-23 22:0x)

E222's design on E241's survivor. The e6 model (seed 0; the ensemble re-evaluates) is annealed from five starts to its 54-atom ground state at the survivor's composition (ground_state.py), and a seed-fixed random decoration of the same composition is written (random_cell.py); both at ideal bcc sites and the Vegard constant, QE at the rung-4 standard (60/720 Ry, k 4³, MV 0.02), on the A100 through the spin-aware ladder. ΔE_order = E(random) − E(ground), per atom. Predictions. (1) e6's own ΔE_order on these two cells is < 5 meV/atom (its rung 1 finds no transition down to 60 K; by E222's Bragg–Williams scaling ~20–30 K per meV). (2) Decisive: DFT ΔE_order ≤ 5 meV/atom → e6's ordering energetics confirmed at this composition and the find stands as the ladder's first full pass; 5–15 → not established (a transition could sit at ~100–400 K), reported as such; > 15 → e6 is wrong here and the find FAILS. The e6 ground state is the lowest state the MODEL finds, so a small DFT ΔE_order is a lower bound that cannot rule out a different DFT-preferred order — stated, not hidden. (3) The random cell's DFT formation energy is within 15 meV/atom of e6's (with E239's open Ti-reference caveat: the old-label frame may carry ~x_Ti·30 meV). (4) Known answer for e6's rung 1 (runs in parallel on the Mac): equiatomic Mo–Ta through the production path (ECEVerifier, e6 ensemble mean, exact evaluator) must show a transition inside the sweep between 500 and 2600 K (published CE+MC 2020 ± 545 K; v5 985 K on the same sampler); "no transition" there would void E240.

EXPERIMENTS.md · line 16309

E242 addendum (2026-09-24 00:08, before any DFT result) — the cells' actual composition. Both 54-atom cells round the survivor's nine-element x to whole atoms: Mo₂₈Ti₂₁Ta₂W₂Zr₁ (runs/e242_random/Mo51Ti38W3Ta3_random/random_cell.json), i.e. Mo 51.9, Ti 38.9, Ta 3.7, W 3.7, Zr 1.9 at.%. Cr, Hf, Nb and V (0.63 at.% each in x, 0.34 atoms each) are absent. The name Mo₅₁Ti₃₈W₃Ta₃ is x's four largest shares; ΔE_order is measured on the rounded cell, and the verdict applies to that composition. Predictions unchanged.

EXPERIMENTS.md · lines 16311–16320

E242 (4) RESULT (22:4x) — e6's rung 1 passes the Mo–Ta known answer. Equiatomic Mo–Ta through the production path (ECEVerifier, three-member e6 mean, exact evaluator): T = 1149 ± 114 K by the energy-slope channel, α₁(Mo–Ta) = −1.00 on cooling (perfect B2) — inside the pre-registered 500–2600 K (published CE+MC 2020 ± 545 K; v5 985 K). E240 is not void. Caveat it exposes: the fluctuation channel peaks at 80 K here — a spurious low-temperature peak from energy still drifting where the sampler freezes, while the true transition sits at 1149 K. Both channels therefore have cold-end artefacts. The 2026-09-23 fix uses the fluctuation channel only when the slope channel found no peak, and the five finds it failed had mid-range fluctuation peaks (331–575 K), not cold-end ones; failing an ambiguous find is the safe direction, but those five are "not established", not proven to order. runs/e242_mota_known_answer.json.

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