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REVIEW 4 major objections 4 minor 64 references

Machine-learning-driven modelling of amorphous and polycrystalline BaZrS$_{3}$

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that one machine-learned interatomic potential, trained on DFT data, can model amorphous, grain-boundary, and polycrystalline BaZrS3, with simulated XRD and PDF patterns matching experiment best for a 50-grain model.

desk verdict Honest, transferable MLIP for BaZrS3 with genuinely new amorphous and grain-boundary results; the GB energy validation is slightly weaker than the headline suggests. read the letter →

arxiv 2506.01517 v1 pith:H33RJQP5 submitted 2025-06-02 cond-mat.mtrl-sci

Laura-Bianca Paşca , Yuanbin Liu , Andy S. Anker , Ludmilla Steier , Volker L. Deringer This is my paper
classification cond-mat.mtrl-sci
keywords BaZrS3chalcogenideperovskitemachine-learnedinteratomicpotentialatomicclusterexpansionamorphousphasegrainboundarypolycrystallinemodelpairdistributionfunction
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

BaZrS3, a lead-free chalcogenide perovskite being developed for thin-film photovoltaics, is usually made as polycrystalline films that grow from amorphous precursors. This paper sets out to show that a single bespoke machine-learned interatomic potential, built in the atomic cluster expansion (ACE) framework and trained on DFT data for crystalline, amorphous, and interface structures, can describe all three forms at the scale needed to compare with experiment. The authors validate the potential against DFT for grain-boundary formation energies, against EXAFS data for the amorphous phase, and against experimental XRD and pair-distribution functions for polycrystalline models. Their conclusion is that the experimental scattering data are matched best by a model containing 50 nanoscale grains, making realistic-scale simulations of this photovoltaic material feasible.

What carries the argument

The central object is a bespoke ACE (atomic cluster expansion) interatomic potential for BaZrS3, fitted with the pacemaker code to a DFT-labelled dataset of 2,781 structures spanning free atoms, dimers, random structures, high-temperature MD snapshots, crystalline phases, and crystalline–amorphous interfaces. Two fits of the same potential are used: a low-energy version (training structures below 1 eV/atom, energy RMSE 13.9 meV/atom) that produces all quantitative results, and a full-dataset version (RMSE 23.1 meV/atom) that is stable under the unphysically close contacts of initial Voronoi-tessellated polycrystalline cells. The machinery does its work by letting DFT accuracy be projected onto systems of hundreds of thousands of atoms, and by feeding relaxed structures into Debye scattering calculations that produce the XRD and PDF patterns compared with experiment.

What would settle it

Take a sample of relaxed grain boundaries from the 50-grain model, compute their formation energies with density-functional theory, and compare with the ACE potential's predictions; if several boundaries deviate by more than about 0.1 J/m2, or if the misranking seen for the 5.5° boundary becomes common, the claimed transferability to polycrystalline space is not established.

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Extended reading notes

Core claim

The central claim is that a single ACE potential for BaZrS3, iteratively trained on random-structure searches, melt-quench molecular dynamics, and crystalline–amorphous interfaces, reproduces the amorphous precursor, relaxes grain boundaries with formation energies close to DFT, and yields polycrystalline models whose simulated XRD and PDF patterns match experiment. In the authors' words, the experimental patterns 'are described best by the polycrystalline 50-grains model.' The potential's quantitative version has an energy RMSE of 13.9 meV/atom against DFT and places most relaxed grain-boundary formation energies within about 0.1 J/m2 of DFT values, with one 5.5° boundary misranked; the amorphous phase it produces has an average Zr coordination number of 5.9 and a density of 3.94 g/cm3. The paper also reports that the potential relaxes a 615,214-atom polycrystalline structure with six randomly oriented grains, and that the relaxed structure stays within the 'accurate extrapolation' region of its uncertainty metric.

Load-bearing premise

The load-bearing premise is that the potential's accuracy on amorphous and crystalline structures carries over to grain boundaries and polycrystalline arrangements, which were absent from its test set and partly relaxed with the less accurate model version.

Editorial extensions

If this is right

  • If the potential is as transferable as claimed, grain-boundary formation energies in BaZrS3 are now computable at near-DFT accuracy for many boundaries, enabling systematic studies of which orientations are stable.
  • The 50-grain model's match to experimental XRD and PDF implies that experimental nanoparticulate BaZrS3 samples can be interpreted as assemblies of nanoscale grains, consistent with the synthesis report the paper cites.
  • The amorphous model gives a concrete atomic picture of the precursor phase, including undercoordinated Zr sites and a density about 92.5% of the crystalline value, which can be used to study crystallisation mechanisms.
  • Because relaxation of a 600,000-atom polycrystalline structure takes minutes on a multi-core node, device-scale simulations of BaZrS3 films, including grain growth and annealing, become feasible.

Reading between the lines

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

  • A natural extension, not pursued in the paper, would be to apply the same training-and-two-fit recipe to related chalcogenide perovskites or mixed-anion alloys, where grain-boundary chemistry is likely to differ but the workflow should transfer.
  • The undercoordinated Zr environments in the amorphous model point to a testable electrocatalytic hypothesis: if amorphous or surface-amorphised BaZrS3 is active for oxygen or hydrogen evolution, the reactive sites may be exactly these five-coordinate Zr atoms.
  • The paper's reliance on the less-accurate full-dataset potential for polycrystalline relaxation suggests that actively adding grain-boundary structures to the training set and re-weighting them, which the authors note but do not implement, could reduce errors such as the misranking of the 5.5° boundary.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript reports a machine-learned interatomic potential (ACE) for BaZrS3, trained iteratively on DFT (PBEsol) data spanning crystals, random/amorphous structures, melt-quench trajectories, and crystalline–amorphous interfaces. Using this potential, the authors simulate a 10,240-atom amorphous model, relax coincidence-site-lattice grain boundaries and report formation energies against DFT, and build polycrystalline models with up to roughly 600,000 atoms whose simulated XRD and PDF patterns are compared with experiment. The central claim is that a single MLIP can cover amorphous, grain-boundary, and polycrystalline BaZrS3 and, in particular, that the experimental XRD and PDF data are described best by a 50-grain polycrystalline model.

Significance. If the central claim holds, this is a useful methodological contribution: it extends MLIP-based modelling to chalcogenide perovskite polycrystals and provides a path to device-scale structural models. The paper has genuine strengths: the training-data construction is detailed and iterative; the authors explicitly disclose limitations (one misranked grain boundary, quench-rate dependence in Table S3, and two potential versions with different accuracies); and the data are made available on GitHub. The comparisons to EXAFS, XRD, and PDF anchor the simulations to experiment. However, the quantitative grain-boundary formation energies rest on validation against DFT single-point energies at MLIP-relaxed geometries, with no fully DFT-relaxed grain-boundary benchmark, and the test set explicitly excludes grain boundaries; this makes the central quantitative claim less secure than the paper's tone suggests.

major comments (4)
  1. [Grain boundaries, Fig. 3a] The grain-boundary formation energies are validated only against DFT single-point energies computed at the MLIP-relaxed geometries (SI: “single-point energies predicted by DFT at the PBEsol level”), not against fully DFT-relaxed grain-boundary structures. Because the test set explicitly excludes grain boundaries and the production potential was filtered to structures below 1 eV/atom, this validation checks the energy at the MLIP-chosen geometry but not whether that geometry is the DFT equilibrium structure. The misranked 5.5° grain boundary and the need to use the less accurate full-dataset potential for the polycrystalline relaxation show that extrapolation to grain-boundary configurational space is not fully controlled. I ask the authors to relax the smaller grain-boundary supercells (Σ25, Σ31, Σ35; roughly 800–1,200 atoms) fully with DFT and compare both energies and atomistic geometries, or otherwise demonstrate that the MLIP-relaxed grain-boundary geometries are local minima of the DFT potential-energy surface; this is necessary to support the reported grain-boundary energies and the S-deficient-boundary conclusion.
  2. [Numerical validation, Supplementary Information] The SI states that the test set “contains all configuration types relevant for the present study, excluding grain boundaries.” As a result, the quoted energy RMSE of 13.9 meV/atom does not measure accuracy in the grain-boundary region, and the extrapolation-grade analysis in Fig. S5 is applied to the 3D polycrystalline model but not to the 2D CSL grain-boundary supercells. The extrapolation grade is a useful heuristic, but it is not a substitute for a direct accuracy test on grain-boundary configurations. I recommend reporting D-optimality extrapolation grades for the grain-boundary supercells and, ideally, including a small set of grain-boundary structures in the training or test data so that the grain-boundary RMSE can be evaluated directly.
  3. [Polycrystalline structures, Fig. 4] The claim that the experimental XRD and PDF patterns “are described best by the polycrystalline 50-grains model” is based on visual comparison only; no quantitative goodness-of-fit metric is reported, and the simulations depend on choices such as the Debye–Waller factor (0.3 Ų), the Q range, and the grain-size distribution. These models were also relaxed with the less accurate full-dataset ACE potential (RMSE 23.1 meV/atom). I ask for a quantitative comparison (for example, a residual or R-factor over the experimental range) and a sensitivity test with respect to the Debye–Waller factor and potential version, so that the reader can judge whether the 50-grains model is genuinely preferred over the other models.
  4. [Amorphous BaZrS3, Table S3] The melt–quench protocol is characterized by a strong quench-rate dependence: Table S3 shows that changing the 1,500→300 K quench rate from 10^13 to 10^15 K/s changes the density from 3.94 to 3.63 g/cm³ and the average Zr coordination number from 5.88 to 5.15, with a drastically different CN distribution. The main text presents one 10^13 K/s trajectory as representing the amorphous precursor and compares it to EXAFS, but it does not discuss whether the structural descriptors in Fig. 2 are robust across the protocol or whether the chosen rate is representative of experimental deposition conditions. Please add a discussion of this sensitivity and, if possible, show that the conclusions (undercoordinated Zr, preserved ZrS6-like motifs, comparison to EXAFS) hold for the range of quench rates.
minor comments (4)
  1. [Grain boundaries, Eq. (1)] The equation for the grain-boundary formation energy is displayed but unnumbered; numbering it would make it easier to reference in the text and in future work.
  2. [Amorphous BaZrS3, EXAFS comparison] In the comparison with EXAFS, the simulated Zr–S bond length (2.575 Å) and CN (5.9) are called “qualitatively” consistent with experiment (2.593 Å, 5.2); reporting the numerical differences and the effect of the coordination cutoff (3.1 Å vs the experimental determination) would make the comparison more transparent.
  3. [Polycrystalline structures, Fig. 4] The main text discusses grain-size effects on XRD broadening without specifying the approximate average grain diameters in the 8-grain and 50-grain models; giving these values would help connect the simulated broadening to the Scherrer equation.
  4. [Supplementary Information, Table S2] The units for the regularisation parameters σ_E, σ_F, and σ_v in Table S2 are not specified in the table header; please add the units (likely eV, eV/Å, and eV, respectively).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MLIP is fitted to DFT data, but every central quantity is benchmarked against independent DFT or experimental data.

full rationale

The ACE potential is a fitted surrogate for DFT, which is the standard and transparent role of an MLIP; no reported quantity is a refit of a target observable. The amorphous-phase results (density, Zr–S bond lengths, coordination numbers) are generated by melt–quench MD and checked against independent EXAFS data (Table S4 and Ref. 10), not against training labels. Grain-boundary formation energies from Eq. (1) are compared with DFT single-point energies on MLIP-relaxed geometries (Fig. 3a), an external benchmark; the test set explicitly excludes grain boundaries, so this is extrapolation rather than interpolation of fitted values. Polycrystalline XRD/PDF patterns are compared with experimental data (Ref. 52) without fitting any scattering parameter to the experiment. Self-citations appear only as methodological context (e.g., RSS protocols and interface-training recipes from the same group) and are not load-bearing for the central claims. The skeptic's concern that DFT single-point checks do not verify fully DFT-relaxed GB geometries is a correctness/extrapolation risk, not a circularity: no equation reduces to its own input and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the accuracy and transferability of the ACE potential, which is trained on DFT data with several hand-chosen hyperparameters and simulation protocols. No new physical entities are introduced. The dominant assumptions are that PBEsol-DFT is a reliable reference, that ACE can interpolate it in the relevant configurational space, and that the chosen melt-quench and scattering-simulation protocols produce structures and patterns comparable to experiment.

free parameters (4)
  • Energy filter threshold for potential split = 1 eV/atom
    Structures with DFT energies above 1 eV/atom were excluded from the low-energy ACE version used for quantitative results, while the full-dataset version (including these structures) was used for polycrystalline relaxation. This choice affects the accuracy-stability trade-off across all reported simulations.
  • Melt-quench cooling rate (1500 K to 300 K) = 10^13 K/s
    Used to generate the amorphous BaZrS3 structure. Table S3 shows density and coordination numbers vary with quench rate; the chosen rate is several orders of magnitude faster than experimental cooling.
  • Debye-Waller factor for XRD simulation = 0.3 A^2
    Applied as an isotropic atomic displacement factor in DebyeCalculator; directly affects peak broadening and thus the visual comparison of simulated and experimental XRD patterns.
  • Coordination cutoffs for CN and bond lengths = 3.1 A (Zr-S), 3.8 A (Ba-S)
    Used with OVITO to compute coordination numbers and bond lengths for comparison with EXAFS. Different cutoffs would change the reported CN values.
assumptions (5)
  • domain assumption DFT with the PBEsol functional provides accurate reference energies and forces for BaZrS3.
    All MLIP training and validation labels come from PBEsol calculations; any systematic DFT error is inherited by the potential.
  • domain assumption The atomic cluster expansion (ACE) framework can accurately interpolate the DFT potential-energy surface within the trained configurational space.
    This is the foundational assumption of all MLIP methods; the paper provides RMSE values but they are averages, not guarantees for all local environments.
  • ad hoc to paper The melt-quench protocol at 10^13 K/s produces an amorphous structure representative of experimentally deposited amorphous precursor phases.
    The paper uses this protocol without evidence that it reproduces the experimental preparation conditions; Table S3 shows significant quench-rate dependence.
  • domain assumption Comparing static (0.1 K) simulated XRD/PDF patterns, with an isotropic Debye-Waller factor of 0.3 A^2, to room-temperature experimental data is meaningful.
    Standard practice in the field, but the temperature mismatch and simplified B-factor introduce unquantified uncertainty.
  • standard math Coincidence site lattice theory enumerates the relevant stable grain boundaries for the orthorhombic BaZrS3 structure.
    The paper constructs GB models from CSL misorientation angles following King and Singh (Ref 53); this is a standard crystallographic tool.

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Pith. "Pith review of Machine-learning-driven modelling of amorphous and polycrystalline BaZrS$_{3}$." pith.science (2026). https://pith.science/paper/H33RJQP5

@misc{pith2026250601517,
  author       = {Pith},
  title        = {Pith review of: Machine-learning-driven modelling of amorphous and polycrystalline BaZrS$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H33RJQP5}},
  note         = {Machine review of arXiv:2506.01517}
}
abstract

The chalcogenide perovskite material BaZrS$_{3}$ is of growing interest for emerging thin-film photovoltaics. Here we show how machine-learning-driven modelling can be used to describe the material's amorphous precursor as well as polycrystalline structures with complex grain boundaries. Using a bespoke machine-learned interatomic potential (MLIP) model for BaZrS$_{3}$, we study the atomic-scale structure of the amorphous phase, quantify grain-boundary formation energies, and create realistic-scale polycrystalline structural models which can be compared to experimental data. Beyond BaZrS$_{3}$, our work exemplifies the increasingly central role of MLIPs in materials chemistry and marks a step towards realistic device-scale simulations of materials that are gaining momentum in the fields of photovoltaics and photocatalysis.

Figures

Figures reproduced from arXiv: 2506.01517 by the authors.

Figure 1
Figure 1. A machine-learned interatomic potential for crystalline and amorphous BaZrS3. (a) Schematics of the different approaches used in training dataset construction, showing examples of the different configuration types sampled. Structural images were created using OVITO. 24 (b) Evolution of the training dataset, visualised in a style similar to Ref. 25. Each slice provides a two￾dimensional representation (using the UMAP… view at source ↗
Figure 2
Figure 2. Amorphous BaZrS3. (a) The atomistic structure of the simulated amorphous phase (10,240-atoms) and manually-chosen close-ups showing the range of geometries and connectivity types between the coordination polyhedra of the A- and B-site cations. (b) Histogram plot showing the distribution of coordination numbers around Zr atoms in the amorphous and crystalline phases, respectively. (Note that environments with CN < 0.… view at source ↗
Figure 3
Figure 3. Grain boundaries. (a) The grain-boundary (GB) energy prediction for relaxed GB structures of BaZrS3 using the MLIP model compared with the single-point energies predicted by DFT at the PBEsol level of theory. (b) Optimisation of the Σ31[001]/(001) GB geometry, where high-energy atoms with energies higher than 1 eV/atom (red) are relaxed to a lower-energy structure using the ML potential. (c) Relaxation of a 615,214-… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Effect of grain size on the X-ray diffraction (XRD) patterns and pair distribution func￾tions (PDFs) of crystalline BaZrS3. (a) A single-crystal 10,240-atom model (top) and its simulated PDF [G(r); bottom]. (b) A polycrystalline model with a simulation box side length …

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.