Hidden Truchet Architecture in Zinc $p$-Hydroxybenzoate

Andrew L. Goodwin; Guy Greenbaum; Hunter J. Windsor; Tristan N. Dolling; Yevheniia Kholina

REVIEW 3 major objections 5 minor 44 references

Hidden Truchet Architecture in Zinc $p$-Hydroxybenzoate

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper argues that the apparently random disorder in the metal-organic framework Zn(hba) is actually governed by ice-like coordination rules and one-dimensional ligand order, and that a Truchet-tile model captures the material's local c

desk verdict Plausible and elegant structural reinterpretation of Zn(hba) with a Truchet/ice model, but the MC validation is partly circular and visual; deserves review with a request for quantitative comparison. read the letter →

arxiv 2607.22307 v1 pith:UCE5TVYQ submitted 2026-07-24 cond-mat.mtrl-sci

Hunter J. Windsor , Guy Greenbaum , Tristan N. Dolling , Yevheniia Kholina , Andrew L. Goodwin This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords Zn(hba)Truchettilingcorrelateddisorderdiffusescatteringmetal–organicframeworksquareiceMonteCarlosimulationVoronoidecomposition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Zn(hba), a metal–organic framework long thought to contain partially occupied sites and a doubled c-axis, actually owes its apparent messiness to correlated, not random, disorder. This paper shows that the material's diffuse X-ray scattering is governed by two local rules: every Zn2+ ion forms two short and two long bonds to its four ligand donors, and every row of hba2− ligands has a uniform polarity. These rules force one-dimensional ordering along each ligand chain and weak antipolar correlations between chains—exactly the two-in-two-out constraint of the square-ice model. A Truchet-tile representation, built by decorating Voronoi cells of the average structure, turns these rules into matching conditions, and Monte Carlo simulations produce models that reproduce both the average crystal structure and the diffuse scattering. If this model is right, the previously published c-doubled, partially occupied structure is a misinterpretation of diffuse scattering as Bragg intensity.

What carries the argument

The key mechanism is the Voronoi decomposition of the average crystal structure into node and linker tiles, followed by chemical decoration that lowers tile symmetry. The decorated tiles—four orientations for the Zn node, two for the hba linker—must pack according to matching rules derived from the two-short-two-long coordination and uniform chain polarity. These rules are equivalent to the two-in-two-out constraint of the square-ice model, which forces correlations that are strong along one dimension but only weak (antipolar) between rows; Monte Carlo simulation of these tile packings, with harmonic bond springs for displacements, yields configurations whose computed diffuse scattering matc

What would settle it

Decisive experiment: a high-dynamic-range single-crystal diffraction measurement at l = odd in the (h0l) plane. If the features at l = (2n+1)/2 remain broad with a ~50 Å correlation length, the Truchet-tile model is supported; if they sharpen to instrument-limited Bragg peaks as the crystal grows, they are true superstructure reflections and the c-doubled model stands. Independently, Zn K-edge EXAFS or total-scattering PDF would show whether Zn–O bonds are two-short, two-long or four nearly equal.

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Extended reading notes

Core claim

The central claim is that the correlated disorder in Zn(hba) is a physical realisation of a Truchet tiling governed by ice-like coordination rules. Each Zn2+ centre is displaced along one of four ⟨110⟩ directions and connects to two carboxylate (short) and two phenoxide (long) donors; each chain of hba ligands must have a single polarity because reversing polarity would break the two-short-two-long rule or distort the coordination. These constraints yield four distinguishable node-tile orientations and two linker-tile orientations, and the matching rules between tiles generate one-dimensional order along ligand rows, weak antipolar order between rows, and a ~50 Å correlation length along the

Load-bearing premise

The entire model rests on transferring the local coordination rules of the ordered lithium analogue Li(inox) to disordered Zn(hba): every Zn2+ must form two short and two long Zn–O bonds, and every ligand chain must have uniform polarity; if either local rule is violated, the correlated-disorder model collapses.

Editorial extensions

If this is right

The average structure of Zn(hba) is the higher-symmetry P42/mmc cell halved along c; the previously reported c-doubled structure with partially occupied sites is an artifact of integrating diffuse scattering as Bragg intensity.
Because the disorder follows square-ice rules, its configurational entropy is subextensive: the number of configurations grows with the square root of the number of nodes, so a crystal's information content is carried by binary 'barcodes' along the a and b axes.
Subextensive entropy makes the degree of disorder size-dependent: smaller crystals should show quantitatively different diffuse scattering than larger ones.
The four distinct pore-channel types, differing in ligand orientation, break the local point symmetry and should have different host–guest interactions, offering a route to bias specific disordered or ordered daughter configurations.
Chemical substitution controls the disorder: the aliphatic hca2− ligand gives an ordered analogue (Zn(hca)) while the aromatic hba2− favours disorder, and Co-substituted variants exist, so the configurational landscape appears navigable by synthesis.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

We infer that the Truchet-tile formalism is likely to apply beyond these two frameworks: any network whose average node and linker sites have higher point symmetry than the chemical fragments themselves could hide analogous tile structure, which would be revealed by the same combination of Voronoi decomposition and diffuse-scattering analysis.
The 'barcode' picture suggests a concrete information-storage scheme: if edge orientations determine the bulk pattern, then controlling the ligand orientation at crystal edges during growth could program a specific global configuration, effectively writing data into the crystal.
A testable extension: total scattering or pair-distribution-function analysis of Zn(hba) should show the two-short-two-long Zn–O bond distribution; if instead a four-equal-bond environment is observed, the transfer of local rules from the ordered analogue fails.
The ~50 Å correlation length along c implies that nanocrystals of Zn(hba) should appear nearly ordered; comparing diffraction from microcrystals and nanocrystals would test the subextensive-entropy prediction directly.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is worth reading. It does something genuinely useful: it reinterprets the Zn(hba) structure, showing that the previously reported doubled-c cell with partial occupancies is likely an artifact of treating diffuse scattering as Bragg intensity. The new average structure in P4_2/mmc with c≈6 Å is supported by well-resolved rocking curves that distinguish Bragg from diffuse. The Truchet-tile model, with its mapping to square ice and the subextensive entropy point, is elegant and chemically motivated. The connection to Li(inox) is plausible, and the local two-short/two-long rule is physically reasonable.

The soft spots are real but not fatal. The Monte Carlo validation is more illustrative than quantitative. T_MC = 2J is chosen to give 'weak antipolar correlations implied by experiment,' and the odd number of layers is introduced to mimic the ~50 Å correlation length measured from the same diffuse scattering. So the model is not independently predicted; it is parameterized to reproduce the observations. The comparison in Fig. 9 is visual — no residuals or line-profile fits. You could imagine a different local-rule model also giving 'lumpy rods' and half-integral maxima. Also, the transfer of Li(inox) bonding rules to Zn(hba) is stated as an expectation. That is a reasonable chemical guess, but it isn't directly measured (e.g., by total scattering or EXAFS). If that rule were wrong, the ice-like correlations would collapse.

That said, the average-structure correction alone is a solid contribution. The authors are transparent about the unverified size-effect claim ('We have not yet explored this point experimentally'), and they do not overclaim DFT-level accuracy. The paper is a good candidate for peer review. A serious referee should ask for a quantitative diffuse-scattering comparison — even a simple R-factor along a few reciprocal lines would help — and a clearer statement of which parameters are fitted versus predicted. The Li(inox) transfer could be probed by showing the local coordination is consistent with the refined displacement parameters or by a small systematic study with related ligands.

Recommendation: engage with the paper. Send it to referees. It deserves a proper review, but the authors will need to strengthen the evidence before it is convincing to a skeptical crystallographer.

Referee Report

3 major / 5 minor

Summary. The paper reports a redetermination of the average crystal structure of the disordered metal–organic framework Zn(hba) from single-crystal X-ray diffraction, explicitly separating Bragg reflections from structured diffuse scattering. The authors reinterpret the previously reported doubled-c-axis model with partially occupied sites as a mis-assignment of diffuse scattering as Bragg intensity, and propose instead a higher-symmetry P4_2/mmc average structure. Using crystal-chemical arguments transferred from the ordered analogue Li(inox), they develop a Truchet-tile description in which Zn nodes and hba linkers obey two-short/two-long Zn–O bonding and uniform ligand polarity along each chain. They then generate atomistic configurations via a two-step Monte Carlo simulation and calculate diffuse scattering that is compared visually with experiment. The central claim is that the same model simultaneously accounts for the local chemistry, the crystallographic average structure, and the observed diffuse scattering, and that this Truchet-tile formalism may apply generally to correlated disorder in framework materials.

Significance. If the central claim is upheld, this would be an important demonstration that the Truchet-tile concept extends beyond TRUMOF-1 and that a previously published doubled-c-axis structure was an artifact of misinterpreting diffuse scattering as Bragg scattering. The manuscript has real strengths: a fresh single-crystal dataset, a quantitative rocking-curve distinction between Bragg and diffuse features, an ordered analogue (Li(inox)) that provides physically motivated local rules, a second ordered analogue (Zn(hca)) that supports the idea of chemical control over order/disorder, and the use of 3D-ΔPDF to visualise correlations. The model Hamiltonian is transparent and the simulation details are described sufficiently for reproduction. However, the validation is currently qualitative: the Monte Carlo parameters are set from the same diffuse data that the simulation is said to reproduce, and agreement is shown visually, not through a residual or line-profile analysis. The local-rule transfer from Li(inox) is stated as an expectation rather than directly measured in Zn(hba). These issues are load-bearing for the paper's strongest claim, so the present version is defensible but not yet con

major comments (3)

[Monte Carlo simulations and diffuse scattering calculations, Eq. (1) and Methods] The Monte Carlo validation is partly circular as presented. T_MC=2J is chosen because it gives 'weak antipolar correlations implied by experiment,' and an odd number of layers introduces 'a single stacking fault ... mimicking the ~50 Å correlation length identified above.' The agreement in Fig. 9(a) is visual only; no quantitative residual, R-factor, or line-profile comparison is reported. Please provide such a comparison (e.g. integrated diffuse intensity along [h00] and [00l], or an R-factor on the diffuse scattering volume) and show the sensitivity of the simulated patterns to T_MC and to the stacking-fault construction. This is necessary to support the central claim that the same model accounts for the observed diffuse scattering.
[Results, 'Average structure: then and now' and 'Voronoi decomposition and Truchet tiling'] The local-rule transfer from Li(inox) is explicitly presented as an expectation ('Our expectation is that the disordered Zn(hba) structure contains the same local bonding rules...'). The two-short/two-long coordination rule and the uniform chain-polarity rule are the load-bearing constraints that generate the one-dimensional order and ice-like correlations. The average structure being 'consistent with' these rules is not the same as establishing that they hold locally, because the refined occupancies and displacement ellipsoids are compatible with many local configurations. The authors should either provide direct experimental or computational evidence for these rules in Zn(hba) (e.g. EXAFS, total scattering, or DFT on representative local fragments) or demonstrate that the diffuse scattering is uniquely sensitive to the Li(inox)-derived rules by allowing variations in the MC constraints
[Monte Carlo simulations and diffuse scattering calculations, Fig. 9(b)] The statement that collapsing the MC supercell 'recovers the experimentally-determined average structure' is supported only by a visual inset. A quantitative comparison is needed: for example, the refined fractional occupancies of the four Zn positions and the two hba orientations in the collapsed MC cell versus the P4_2/mmc refinement, and a comparison of positional/thermal parameters. Without this, the simultaneous consistency with the average structure is not quantitatively established.

minor comments (5)

[Author list] The author names contain stray spaces ('T ristan', 'Y evheniia'); these should be cleaned up.
[References] Reference 14 is incomplete (journal volume and article number are missing). Also, please check the spelling in Reference 19: 'Mémoir' → 'Mémoire' and 'combinasions' → 'combinaisons'.
[Fig. 3 and Fig. 9] The comparison between experimental and calculated diffuse scattering would be aided by using the same colour scale and orientation in the two figures. Currently the experimental data are shown in (hk0) and (h0l), while the calculated pattern is shown in (hk0) and (0kl); please make the plane labelling consistent.
[Monte Carlo simulations, Eq. (2)] The claim that 'Our results do not depend on the specific value of this constant' is not demonstrated. Even if the qualitative pattern is robust, a brief sensitivity test (e.g. k = 1, 3, 10 eV Å⁻²) would make the claim credible.
[Conclusions] The statement about subextensive entropy and crystal-size effects is interesting, but the sentence 'We have not yet explored this point experimentally' is an explicit limitation. Consider softening the claim or moving it more clearly into the outlook section.

Circularity Check

2 steps flagged · score 6.0 of 10

MC validation of diffuse scattering is partly circular: T_MC and the inserted stacking fault are chosen from the same diffuse data the model is then said to reproduce, so the agreement is partly by construction.

fitted input called prediction [Results, "Monte Carlo simulations and diffuse scattering calculations" (paragraph following Eq. 1)]
"Carrying out these simulations at an effective Monte Carlo temperature T MC = 2J gave row polarisations with weak antipolar order (note the coupling term J was positive). This temperature places the system well within the disordered regime while retaining the weak antipolar correlations implied by experiment."

The MC temperature is the parameter that controls the strength of antipolar row correlations. It is selected specifically to match the weak antipolar correlations inferred from the diffuse maxima at the midpoints between Bragg reflections. The simulated (hk0) diffuse scattering is then presented as reproducing those same experimental maxima, so the agreement is set by construction rather than independently predicted.
fitted input called prediction [Methods, "Monte Carlo Simulations"]
"Seven layers were used to form a 8×8×7 configuration. The odd number of layers introduced a single stacking fault into the otherwise antipolar stacking sequence, mimicking the∼50 Å correlation length inferred from the experimental diffuse scattering."

The ~50 Å correlation length was read off from the width of the l=(2n+1)/2 diffuse features. Encoding that same correlation length via an odd number of layers with a single stacking fault directly builds the observed correlation into the simulation box. The calculated (0kl) broad maxima at l=(2n+1)/2, shown as a successful reproduction, are therefore forced by the input construction.

full rationale

The circularity is confined to the Monte Carlo validation step, not to the whole paper. The redetermination of the average structure (c ≈ 6 Å, P4_2/mmc) and the distinction between Bragg (l = 2n) and diffuse (l = 2n+1) scattering using rocking curves is independent experimental work. The two-short/two-long coordination rule is grounded in the ordered analogue Li(inox) and is consistent with the refined Zn(hba) average structure; this is a legitimate external input, though the paper itself calls the transfer an 'expectation' rather than a measured fact. The Truchet-tile description is a re-framing of the local coordination chemistry and the ice-like chain-polarity rules; that is not circular in itself. However, the two key parameters of the MC model — T_MC = 2J and the odd-layer stacking fault — are chosen from the same diffuse-scattering observations that the model is then claimed to reproduce. Consequently, the statement that 'the same model accounts simultaneously for the local chemistry, the crystallographic average structure, and the observed diffuse scattering' is only partially supported as an independent prediction: the diffuse-scattering part is a consistency check with input correlation lengths built in, not a parameter-free validation. The paper also acknowledges limitations (no DFT optimisation, no experimental exploration of size effects), and no quantitative residual or R-factor comparison is reported, so the agreement remains visual. These issues warrant a score of 6 rather than 0: the central diffuse-scattering validation reduces in part to its own inputs, while the average-structure and local-chemistry components retain independent content.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. Truchet tiles, Voronoi tiles, and 'barcodes' are representational devices, not new forces/particles/fields.

free parameters (3)

Monte Carlo temperature T_MC relative to coupling J = T_MC = 2J (J > 0; absolute scale not given)
Chosen so that Eq. (1) produces the weak antipolar row-polarisation correlations 'implied by experiment' (Results, MC Simulations). This is a hand-set value targeting the observed diffuse-scattering lumpiness.
Stacking fault (odd layer count) = 7 layers, one stacking fault in an 8×8×7 box
Inserted deliberately to mimic the ~50 Å correlation length inferred from the half-integer diffuse maxima along l (Methods: MC Simulations). This encodes the target observation into the model.
Zn–O harmonic force constant k = 3 eV Å^-2
Selected to give 'physically sensible displacements' at 300 K; authors state the results do not depend on its precise value (Methods). Not central, but still a hand-set number.

assumptions (4)

domain assumption Zn(hba) follows the same two-short/two-long Zn–O coordination rule as the ordered analogue Li(inox).
Stated explicitly in Results: 'Our expectation is that the disordered Zn(hba) structure contains the same local bonding rules as observed in Li(inox).' The whole chain-polarisation constraint depends on this transfer.
domain assumption Within any hba–Zn2–hba chain, all ligand polarisations must be identical to preserve the coordination geometry.
Argued from crystal chemistry around Fig. 4(b): reversing a ligand would break two-short/two-long bonding or heavily distort geometry. This one-dimensional ordering is the origin of the ice-like correlations.
domain assumption Decorated Voronoi tiles and their matching rules exhaust the physically allowed local configurations of Zn and hba.
The Truchet construction assumes that the only relevant disorder is tile orientation subject to matching rules; other relaxation modes are folded into the later harmonic-spring MC stage.
domain assumption The square-ice two-in-two-out statistical mechanics (and its subextensive entropy) applies to the layer-by-layer row-polarisation variables of Zn(hba).
Asserted in Conclusions via analogy to Refs 28-30; the paper does not derive the mapping rigorously for the finite 3D stacking-faulted crystal.

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Cite this review

Pith. "Pith review of Hidden Truchet Architecture in Zinc $p$-Hydroxybenzoate." pith.science (2026). https://pith.science/paper/UCE5TVYQ

@misc{pith2026260722307,
  author       = {Pith},
  title        = {Pith review of: Hidden Truchet Architecture in Zinc $p$-Hydroxybenzoate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UCE5TVYQ}},
  note         = {Machine review of arXiv:2607.22307}
}

abstract

We redetermine the structure of the disordered metal-organic framework Zn(hba) (hba$^{2-}$ = the dianion of 4-hydroxybenzoic acid). Using single-crystal X-ray diffraction measurements, we characterise the structured diffuse scattering that is experimentally observed for this material and which is characteristic of strongly correlated disorder. We use geometric and crystal chemical arguments to propose a general model for correlated disorder in Zn(hba), and then relate this model to a specific realisation of so-called Truchet tilings. Using Monte Carlo simulations, we proceed to show that the model so developed is simultaneously consistent with both the average crystal structure solution described previously, and the structured diffuse scattering reported here. The existence of ordered analogues with different, but related, chemistry suggests scope for control over correlated disorder in this family of metal-organic frameworks. Our study illustrates the potential for a Truchet-tile formalism to help describe and understand more generally the correlated disorder that occurs in framework materials - even amongst those that are chemically and crystallographically dissimilar.

Figures

Figures reproduced from arXiv: 2607.22307 by the authors.

**Figure 1.** Truchet tilings arise when high-symmetry tiles are decorated to lower their symmetry. Here, the simple diagonal decoration distinguishes four orientations of a square tile. Enforcing matching rules generates complex patterns that are neither ordered nor random. 1 arXiv:2607.22307v1 [cond-mat.mtrl-sci] 24 Jul 2026 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** (a) (hk0) (top) and (h0l) (bottom) sections of the single-crystal X-ray diffraction patterns of Li(inox) (left) and Zn(hba) (right). Structured diffuse scattering is evident in the latter but not in the former. This diffuse scattering is transverse polarised in the (hk0) plane; i.e. vertical streaks are strongest in a horizontal direction, and vice versa. In the (h0l) plane, the diffuse scattering appears as weak Br… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: (a) The process of assigning to a MOF structure a corresponding tiling involves first identifying the (average) node and linker positions and then calculating the corresponding Voronoi decomposition. Note that, by design, the Voronoi tiles so obtained inherit the sa…

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: Representations of a fragment of one possible realisation of the Zn(hba) structure, with connectivity determined by applying the Truchet-tile rules developed in the text. Note the sensible coordination geometries and local connectivities of both Zn2+ and hba2− ions. i…

**Figure 9.** Figure 9: (a) Single-crystal X-ray diffraction patterns calculated from the Truchet-tile Zn(hba) configurations relaxed using direct Monte Carlo simulation. Note the presence of transverse-polarised diffuse scattering in the (hk0) plane and broad maxima at l = (2n + 1)/2 in the…

**Figure 10.** Figure 10: (a) The square ice model developed in Ref. 28 consists of a square array of nodes connected by vectors that obey the two-in-two-out constraint derived from hydrogen-bonding rules in water ice. The chain polarisations in Zn(hba) obey the same rules. (b) The ligand or…

**Figure 11.** Figure 11: Representation of the crystal structure of Zn(hca), viewed in perspective away from the c axis. chemical intuition or additional knowledge regarding local structure. In the present study, we have used the availability of an ordered analogue (viz. Li(inox)) to infer th…

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