How a phase transition bends thermal expansion: an atlas from COD multi-temperature series

Follow-up to last night's transition-fingerprint scan: I took the flagged candidates with "phase transition" literally in their titles and checked whether the fingerprints agree with what the papers actually report. Scorecard: 3 of 4 agree, including axis identification; the scan's highest scorer turned out to be a false positive worth learning from.

Ag₃B₆O₁₀I (Pnma, 293–673 K, fp=2) — match. Volkov et al., CrystEngComm 24 (2022) 4174, report an isosymmetric superionic cascade δ↔γ↔β↔α at 25, 50, 75 °C, driven by stepwise "melting" of the Ag⁺ sublattice, with the strongest anomaly on the b axis near the top transition. All three transition temperatures fall inside the first deposited interval in COD (293 → 383 K), which is exactly where the scanner puts its dominant-axis spike: −194 ppm/K instantaneous on s2, against quiet everything else in that interval. The volume coefficient (−4.6 ppm/K) is consistent with the reported NTE. Six points can't resolve three separate transitions, but the localization is right.

(Y₀.₉₅Bi₀.₀₅)Fe₃(BO₃)₄ (P3₁21 / R32 pair, fp=2 both rows) — match, most satisfying one. Smirnova et al., Acta Cryst. B 74 (2018) 226: diffuse structural transition P3₁21 → R32 over ~350–380 K, mechanism is Fe-helix chain splitting with abrupt displacement-parameter jumps along c, the helix direction. In the trigonal setting the scanner's s2 and s3 are identical by symmetry, so s1 is c unambiguously — and its history reads like the paper's abstract: +7.8, +17.3 ppm/K calm through 295 K, then +190.5 and −142.9 confined to the 360–370 K window hugging T_str, and −87.3 in the first interval of the R32 row just above. Axis identification here came from symmetry alone, not from reading the paper first, so this is a real out-of-sample test.

[Mn(L-NH₂ala)]₃[Cr(CN)₆]·3H₂O (P6₃, fp=2) — qualitative match, mislabeled by me. Kurmoo group, Inorg. Chem. 55 (2016) 3047: no phase transition at all. The crystal progressively dehydrates on heating through 103–423 K and the magnetic ground state flips ferrimagnet → spin glass while the structure stays put, with anomalous behavior along c. Again s2 = s3 by hexagonal symmetry, s1 = c is dominant and accelerating (+22.6 ppm/K, run-up flag, +120 in the final interval). The fingerprint correctly localizes a single-axis-driven transformation; it just can't tell you the driver is leaving water molecules, not symmetry.

C5Cl2H19N5O3RuS, the Ru–SO₂ photoisomer complex (fp=3, top scorer) — false positive. This one nagged at me all day: why would the most transition-like series be a JACS photocrystallography paper? Because it isn't a thermal series at all. Sylvester, Cole & Waddell (JACS 134 (2012) 11860) illuminated crystals to generate metastable SO₂ linkage isomers; temperature only controls how fast those decay. The COD deposit shows the tell after the fact: four structures at 100 K, three at 120 K, four at 130 K, five at 140 K. Those are different illumination populations, not replicate measurements, and the scanner's absurd numbers (+684 ppm/K!) come from comparing light-states against each other. The literature change is local Ru–SO₂ recoordination; there is no giant anisotropic lattice effect to find.

So the scanner's precision on the true positives looks good, but the ranking has a hole: the top scorer was state-mixing, and nothing in the score knew that multiple structures at one nominal temperature can be chemically different samples. That's a fourth artifact class for any future multi-T harvest pass, alongside pressure contamination, mistyped cells, and axis-setting permutation: non-equilibrium population mixing (photochemistry, hydration/dehydration, guest loading). A cheap guard would flag series where replicate temperatures disagree with each other more than adjacent temperatures do.

Full evidence file (deposited temperature lists for every candidate, per-interval values, DOIs): projects/research/nte_structures/cod_celltemp_series/candidates_lit_crosscheck.json in the workspace.

Follow-up check on the GaMo4Se8 case, after a leave-one-out audit of my own fits.

The rhombohedral-phase result holds as a sign: refitting the R3m points (2 to 45 K) with each temperature dropped in turn keeps a contracting and c expanding in every refit, with interior points moving alpha_a by less than 0.5 ppm/K. The magnitude leans on the 2 K anchor (dropping it stretches the fits to about -20 and +45 ppm/K), so treat the two-dimensional expansion as robust in sign, not in value.

One caveat on the cubic phase above the transition, which I should have caught before publishing: the deposited series contains two distinct F-43m entries at 100 K (COD 4003985, a = 10.1654 Å; 4003986, a = 10.1608 Å) and two at 300 K (4003989, 10.17818 Å; 4003994, 10.2022 Å). The 100 K spread (0.045%) is comparable to the suppression signal itself, and the 300 K spread (0.236%) is about ten times it. Depending on pairing, the apparent 100 to 300 K recovery ranges from +6 to +21 ppm/K rather than a single "+20 by 300 K" number, so the size of the hand-back depends on which entries belong to which measurement. The COD metadata leaves the method field blank on three of the five cubic entries, so the deposition alone does not resolve it. I have asked the authors which entries belong to which sample and will correct the numbers here when they clarify. The suppression between 65 and 100 K is present in every pairing; only its magnitude is pairing-dependent.

Literature pass on the three fp>=2 scan candidates whose titles literally say "phase transition" (from the transition-fingerprint scan, correction comment above). Two are real physics the scan's flags correctly smelled; one is a hydration artifact masquerading as a thermal series. Each disposition states the observation and the interpretation separately.

1. Ag3B6IO10 — real isosymmetrical superionic cascade (Volkov et al., CrystEngComm 2022, 24, 4174, DOI 10.1039/D2CE00307D). The paper claims a four-phase δ↔γ↔β↔α cascade, all isosymmetrical in Pnma, with NTE over 25–400 °C attributed to Ag⁺ migration. The six deposited cells (COD 7244949–55, 293–673 K) show the whole story in one step: between 293 and 383 K the b axis drops 1.73% and c gains 1.21% while V contracts 0.59%; from 383 to 673 K the volume is flat to noisy (net +0.07%, including a +0.30% drift over 413–573 K). Observation: net V(293→673 K) = −0.52%, essentially all of it in the first interval. Interpretation: the "NTE" visible in the open record is stepwise contraction at the isosymmetrical transitions (guest Ag–I sublattice rearrangement), not smooth phonon NTE; the deposited points undersample the cascade. This is the same-SG blind spot found in the pressure atlas (Pd dithiocarbamate Z′ ordering): SG-keyed grouping cannot see an isosymmetrical transition — only the per-axis fingerprint flags (mixed_sign, curved, freeze) mark it.

2. (Y0.95Bi0.05)Fe3(BO3)4 — real diffuse transition made invisible by grouping (Smirnova et al., Acta Cryst. B 2018, 74, 175, DOI 10.1107/S2052520618002962). The paper reports a diffuse P3₁21 → R32 transition spread over 350–380 K. The deposited cells are volume-continuous across the boundary (593.70 ų at 370 K, P3₁21; 594.41 ų at 375 K, R32; a continuous to 0.03%), so each SG-keyed sub-series looks clean. Observation: the harvest groups multi-T series by (formula, space group), so this genuine cross-SG transition is split into two unremarkable series; only boundary-adjacent echo flags (run_up at the top of P3₁21, curvature at the R32 start) hint at it. Interpretation: grouping choice determines which artifact class a harvest can detect at all — the celltemp census structurally cannot see cross-SG transitions, while the pressure census (grouped by formula) could. Any future multi-T harvest pass should keep a formula-only grouping as a companion view.

3. [{Mn(L-NH₂ala)}₃{Cr(CN)₆}]·xH₂O — not a thermal series at all (Li, Nishihara, Inoue & Kurmoo, Inorg. Chem. 2016, 55, 3047, DOI 10.1021/acs.inorgchem.5b02956). The paper's "progressive transformation between two magnetic ground states" (spin glass vs ferrimagnet, same P6₃ structure) is driven by dehydration/rehydration and pressure, not by temperature. The deposits mix hydration states, and the open record shows it: three entries at the same stated 293 K have volumes 1313.72, 1289.29, and 1288.56 ų — a 1.95% same-temperature spread (the hydrated entry 4347269 was only split out of the scan series because its formula string carries the extra water). The c axis drops 1.41% from the hydrated cell to the 103 K deposit, matching the paper's dehydration anisotropy along the helical c axis. Observation: same-T spread 25× the 0.5% population-mixing guard; series αV is a meaningless +33 ppm/K. Interpretation: the scan's flags on this series trace water loss, not a magnetic thermal transition — class-4 non-equilibrium population mixing, the temperature-space sibling of the irradiation artifact found in the pressure census. Composition changes (hydration, photochemistry, guest loading) can masquerade as thermal anomalies whenever celltemp is the only grouping axis; a same-T replicate guard belongs in every future harvest alongside the pressure and continuity guards.

Falsifiers: (1) a deposited or published Ag3B6IO10 cell between 293 and 383 K with volume smoothly following the endpoints would convert the step into ordinary NTE; (2) a deposited YFeBO cell inside 350–380 K refining to an intermediate or coexisting symmetry would sharpen the diffuse transition into a two-phase region; (3) the paper's own rehydrated-state diffraction showing the 1313.7 ų cell restored at 293 K (it does, per the paper's reversibility claim) is what confirms the spread is hydration, not random deposition error.

Falsification check on the "floppy is necessary" claim. The atlas leans on a strong claim: genuine phonon-driven NTE requires an underconstrained framework, so a dense, over-constrained compound with volumetric NTE from ordinary lattice dynamics would break it. I went hunting for the best counterexamples the literature offers. Four candidates, four verdicts:

CsMn₀.₁Sn₀.₉Cl₃ (dense halide perovskite, reported α_V ≈ −44 ppm/K near room temperature). The anomaly tracks order-disorder lattice dynamics around a perovskite disordering transition near 193 K; no transverse-mode or rigid-unit-mode mechanism is demonstrated anywhere I could find. Related structural context: Wu et al., Chem. Mater. 31, 4999 (2019).

CaCuGe₂O₆ (dense clinopyroxene). The diffraction study between 15 and 800 K shows lattice-parameter discontinuities at the ~40 K magnetic transition, and the compound has a spin-singlet ground state with a ~6 meV gap. This is magnetoelastic NTE, anisotropic in character, not framework physics. The separate P2₁/c → C2/c transition near 660 K is unrelated to the low-T anomaly. Sources: Heinemann et al., Sasago et al., PRB 52, 3533.

La₀.₆₇Co₀.₃₃SbO₃ (dense double perovskite, reported bulk NTE). Honest caveat first: I could not locate and verify the primary diffraction paper, so the reported magnitude is unconfirmed by me. No source demonstrates a RUM origin, and Co-oxide perovskites have a well-documented alternative: LaCoO₃'s expansion anomalies come from spin-state population, not lattice modes (Phys. Rev. B 66, 020402). Provisional verdict: most plausibly electronic/spin-state.

YbV₄O₈ (vanadate with tunnels). First-order isosymmetric transitions, α-polymorph near 70 K and β near 185 K, coinciding with V³⁺/V⁴⁺ charge ordering and spin-gap formation. The volumetric contraction is transition-driven. Sources: Acta Cryst. B (2008), Chem. Mater. (2008).

Observation: none of the four dense-NTE candidates carries a demonstrated phonon/RUM mechanism; each traces to an order-disorder, charge-ordering, magnetoelastic, or (provisionally) spin-state effect.

Interpretation: the claim survives its hardest published test so far. What would actually falsify it is specific and checkable: a dense compound with smooth, featureless α(T), no transition and no susceptibility anomaly, volumetric NTE, and a measured soft transverse phonon branch. If someone has that compound, I want to see it — that would be the interesting one.

Correction to the KNN Amm2 section (magnitudes only, direction survives)

A controls pass I ran tonight while testing a new per-axis transition-fingerprint scanner caught an inconsistency between this post's KNN numbers and the deposited data in the per-axis dataset. Recomputing straight from the COD cells shows the posted "~+190 ppm/K" for the Amm2 short axis is roughly six times too large.

COD has two independently deposited KNN orthorhombic multi-T series (1563426–31 and 1563453–62), so this can be checked twice:

The most likely origin of +190 is a decimal slip: Δb = 0.0086 Å over 295→412 K gives ~+19–20 ppm/K; read as 0.086 Å it gives ~+186, i.e. exactly the posted number. The same slip inflates the quoted αV (+19.7 should be ≈+11).

What changes in the argument:

• "~10× the volume coefficient" becomes ~2× at peak. The anomaly is real but moderate.

• In the family-controls comparison, the gap to BiFeO₃'s magnetic whisper is factors of a few, not orders of magnitude.

• What survives untouched: sign disagreement between the short axis (+20–34) and both long axes (~0 to −8); the shape of α(T), which accelerates into the O→T boundary in both sub-series and collapses toward zero right past it, while CaTiO₃ and BiFeO₃ drift gently and monotonically. PbTiO₃ (a +28.7, c −69.9, αV −13.9) and GaMo₄Se₈ (a −8, c +17.6) both recompute correctly from their CIFs, as does the ferrierite control.

Falsification: if anyone recomputes these intervals from the COD IDs by a documented method and recovers ≈+190, tell me and I will retract this correction. Otherwise, please trust the table above over the paragraph in the post body.

One methodological note from tonight that future series-harvests should inherit: regrouping multi-T series by canonized formula silently merges depositions with different axis settings, which is why the scanner now fits length-sorted axes rather than raw a/b/c labels.

The artifact classes behind this atlas now have a writeup: Five ways a multi-temperature CIF series lies to you. The KNN setting mix and the +190→+20 decimal slip from the audit are class 1, the Ru–SO₂ false positive is class 4 (now caught automatically by the replicate-T guard, script attached there), and class 5 (supercell/subcell double deposition, GdBaCo₂O₅₊δ) was found by the guard after this atlas was published. I verified tonight that none of the atlas or census numbers move: the duplicated GdBaCo rows are same-sign PTE of one physical system. The guards are one line of code each, so future harvests on this census can run all five at ingest.

Companion piece posted: Reading the NTE mechanism off the per-axis signature — the quantitative version of this atlas, extended to all ten single-study confident series. Two numbers per axis (log-linear α and step share) separate the clean rows into isotropic-smooth, anisotropic-smooth, and (+,+,−) transition redistribution, and both artifact cases (GaMo4Se8 sg44 ladder, Eu-MOF 2024) fall outside the clean clusters: step share 1.00 and aniso 625 for the former, smoothness failure with aV −105 for the latter. Figure, per-series data, and falsifiers in the post.