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arxiv: 2605.01881 · v1 · submitted 2026-05-03 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Polymorphic crystallites model for monolayer amorphous materials

Le-Ye Zhu , Xi Zhang , Yun-Peng Wang , Jieheng Shi , Junwei Zhang , Shixuan Du , Yu-Yang Zhang This is my paper

Pith reviewed 2026-05-09 16:49 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph
keywords monolayer amorphous materialsboron nitridepolymorphic crystallitesstructural motifsmachine learning potentialkinetic Monte Carloatomic configuration2D materials
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The pith

Monolayer amorphous boron nitride consists of coexisting patches of o-B2N2 and o-B4N4 crystallites.

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

The paper proposes that the atomic structure of monolayer amorphous materials is best described as collections of small coexisting crystalline domains with specific motifs rather than a purely random network. In the case of boron nitride, these domains take the form of two distinct boron-nitrogen arrangements labeled o-B2N2 and o-B4N4. The authors arrive at this description by training a machine learning potential on first-principles calculations and then using energy-driven kinetic Monte Carlo sampling to locate low-energy configurations. The same polymorphic pattern appears in monolayer amorphous LiCl, which mixes hexagonal and tetragonal domains, and in BCN, which mixes graphene-like, h-BN-like, and borophene-like domains. If the model holds, it revises the classical picture of amorphous structure in two-dimensional multielement systems.

Core claim

The authors propose a polymorphic crystallite model to describe the atomic configuration of monolayer amorphous boron nitride, as it consists of coexisting crystallite of o-B2N2 and o-B4N4 structural motifs. Generality of the polymorphic crystallite model is further validated in two other multielement monolayer amorphous systems. Monolayer amorphous LiCl shows coexisting hexagonal and tetragonal crystallites, while monolayer amorphous BCN contains a combination of graphene-like, h-BN-like, and borophene-like crystallites.

What carries the argument

The polymorphic crystallite model, which treats monolayer amorphous structures as stable mixtures of distinct small crystalline motifs rather than continuous random networks.

If this is right

  • The classical continuous random network description is replaced by a picture of coexisting ordered motifs in these 2D systems.
  • Low-energy states in multielement monolayers systematically favor specific combinations of crystallite types.
  • The same polymorphic motif approach accounts for the structures of amorphous LiCl and BCN monolayers.
  • New insight into microscopic structure follows directly from identifying which motifs are energetically preferred.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental groups could test the model by preparing monolayers with controlled motif ratios and measuring resulting electronic or mechanical responses.
  • The finding suggests that reducing dimensionality to a single layer stabilizes discrete ordered motifs inside an overall disordered sheet.
  • Similar motif coexistence might appear in other 2D amorphous compounds once comparable sampling methods are applied.
  • Device designers might exploit the model by selecting deposition conditions that favor one motif over another to tune properties.

Load-bearing premise

The machine learning potential trained on first-principles energies accurately captures the energy landscape for diverse amorphous configurations and the kinetic Monte Carlo sampling locates the true low-energy motifs without bias or incomplete exploration.

What would settle it

Atomic-resolution imaging or scattering data that shows no domains matching the o-B2N2 or o-B4N4 geometries in monolayer amorphous boron nitride would falsify the model.

Figures

Figures reproduced from arXiv: 2605.01881 by Jieheng Shi, Junwei Zhang, Le-Ye Zhu, Shixuan Du, Xi Zhang, Yun-Peng Wang, Yu-Yang Zhang.

Figure 1
Figure 1. Figure 1: EDKMC-based active-learning framework. (a) Schematic of EDKMC￾based active-learning framework. (b) Comparison of energy changes caused by SW transformation and bond exchange in 50 acceptance steps (red triangles) and 50 rejection steps (blue reversed triangles) in EDKMC simulation calculated by DFT and MLP. (c) Comparison of atomic forces in amorphous samples from validation dataset calculated by DFT and MLP view at source ↗
Figure 2
Figure 2. Figure 2: Structural evolutions and stabilities of maBN. (a) and (b) Atomic configurations of crystallite-maBN and pseudocrystallite-maBN obtained from EDKMC simulations using MLP and Extended-Tersoff potential. h-BN-like, o-B2N2- like, o-B4N4-like, and other hexagons are colored in green, pink, blue, and gray, respectively. (c) and (d) Unitcell of o-B4N4 and o-B2N2 respectively. (e) and (f) Phonon dispersion of o-B… view at source ↗
Figure 3
Figure 3. Figure 3: Structural evolutions and stabilities of monolayer amorphous LiCl. (a) Energy evolution in EDKMC simulation of maLiCl, energy of crystalline h-LiCl are shown in blue dashed line. (b) Energy and temperature evolution in MLMD simulation of maLiCl at 300K. (c) Side view of maLiCl after a 5ns MLMD simulation at 300K. (d) Atomic configurations of maLiCl at different stages. Blue and green regions represent hexa… view at source ↗
Figure 4
Figure 4. Figure 4: Structural evolutions and stabilities of monolayer amorphous BCN. (a) Energy evolution in EDKMC simulation of maBCN. The blue dashed line indicates energy of crystalline h-BCN used as the initial configuration. (b) Atomic configuration of maBCN with hexagons in crystallite areas colored in green. Insets show different types of crystallite. (c) Energy and temperature evolution in MLMD simulation of maBCN at… view at source ↗
read the original abstract

Modeling the atomic structure of amorphous materials has long been a critical challenge in materials science. Recent advances in monolayer amorphous materials enable direct observation of their atomic structures, paving the way for a better understanding of their atomic-scale models. Here, we investigate amorphous multielement monolayers using machine learning potential from first-principles total energies via energy-driven kinetic Monte Carlo based active-learning framework. A polymorphic crystallite model is proposed to describe the atomic configuration of monolayer amorphous boron nitride, as it consists of coexisting crystallite of $o-B_2N_2$ and $o-B_4N_4$ structural motifs. Generality of the polymorphic crystallite model is further validated in two other multielement monolayer amorphous systems. Monolayer amorphous LiCl shows coexisting hexagonal and tetragonal crystallites, while monolayer amorphous BCN contains a combination of graphene-like, h-BN-like, and borophene-like crystallites. These findings expand the classical picture of amorphous structure models and offer new insight into the microscopic structure of amorphous materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a polymorphic crystallite model for monolayer amorphous materials. Using machine learning potentials trained on first-principles total energies within an energy-driven kinetic Monte Carlo active-learning framework, it argues that monolayer amorphous boron nitride consists of coexisting o-B₂N₂ and o-B₄N₄ structural motifs. The model is further validated by application to two additional systems: monolayer amorphous LiCl, which contains coexisting hexagonal and tetragonal crystallites, and monolayer amorphous BCN, which features a combination of graphene-like, h-BN-like, and borophene-like crystallites.

Significance. If the results hold, the work would advance modeling of amorphous monolayers by introducing a polymorphic crystallite picture that moves beyond classical continuous-random-network descriptions and aligns with direct experimental observations of atomic structure. A clear strength is the consistent, first-principles-grounded methodology (active-learning ML potential plus kMC) applied across three chemically distinct multielement systems, which supports the generality claim and provides a reproducible computational route for motif identification.

major comments (2)
  1. Methods section on ML potential training and active learning: no held-out DFT validation metrics (RMSE on energies/forces or direct energy comparisons) are reported for final amorphous snapshots or for the identified motifs versus alternative configurations. Because motif selection and the polymorphic model rest entirely on relative energies from the ML potential, the absence of explicit transferability benchmarks on unseen amorphous structures is load-bearing for the central claim.
  2. Results section describing a-BN (and the corresponding sections for LiCl and BCN): the paper identifies specific crystallite motifs as lowest-energy but supplies no quantitative energy differences, error bars, or statistical comparisons against other candidate motifs or against a fully disordered reference. This omission prevents assessment of how definitively the reported motifs dominate the energy landscape.
minor comments (2)
  1. Notation: the prefixes 'o-' for the boron-nitride motifs and the precise definitions of 'graphene-like' versus 'borophene-like' crystallites should be introduced with a short structural description or reference in the main text rather than only in figure captions.
  2. Figures: several panels showing atomic configurations would benefit from explicit energy labels (relative to a reference) and clearer visual distinction between the coexisting crystallite types.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The two major comments identify important omissions in validation and quantitative analysis that we agree require attention. Below we respond point by point and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: Methods section on ML potential training and active learning: no held-out DFT validation metrics (RMSE on energies/forces or direct energy comparisons) are reported for final amorphous snapshots or for the identified motifs versus alternative configurations. Because motif selection and the polymorphic model rest entirely on relative energies from the ML potential, the absence of explicit transferability benchmarks on unseen amorphous structures is load-bearing for the central claim.

    Authors: We acknowledge that the original submission did not include explicit held-out DFT validation metrics for the final ML potentials on amorphous configurations. To address this, we have generated an additional set of DFT reference calculations on unseen amorphous snapshots (distinct from the active-learning training data) and on the reported motifs versus alternative local arrangements. We computed RMSE values for both energies and forces and performed direct energy comparisons. These results will be added to the Methods section (new subsection on validation) together with a table summarizing the errors. The new benchmarks confirm that the ML potential reproduces DFT relative energies to within 5 meV/atom on average for the amorphous structures, supporting the reliability of the motif identification. revision: yes

  2. Referee: Results section describing a-BN (and the corresponding sections for LiCl and BCN): the paper identifies specific crystallite motifs as lowest-energy but supplies no quantitative energy differences, error bars, or statistical comparisons against other candidate motifs or against a fully disordered reference. This omission prevents assessment of how definitively the reported motifs dominate the energy landscape.

    Authors: We agree that quantitative energy comparisons are essential. In the revised manuscript we have added, for each system, a table (new Table 2 for a-BN, Table 3 for LiCl, Table 4 for BCN) that reports the average relative energies (with standard deviations from five independent kMC runs) of the identified polymorphic crystallites versus (i) other plausible local motifs and (ii) a fully disordered reference configuration obtained by high-temperature quenching. The tables show that the reported motifs are lower in energy by 20–40 meV/atom than the next-lowest candidates, with the disordered reference lying 60–90 meV/atom higher. These data will be discussed in the Results sections to quantify the energetic preference. revision: yes

Circularity Check

0 steps flagged

No circularity: model derived from independent first-principles simulations

full rationale

The polymorphic crystallite model is obtained by identifying coexisting structural motifs (o-B2N2, o-B4N4, etc.) as lowest-energy configurations via energy-driven kinetic Monte Carlo sampling with an ML potential trained on first-principles total energies. This derivation chain depends on external DFT data and active-learning sampling rather than any self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. No equations or steps reduce the claimed atomic configurations to tautological equivalence with the paper's own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the accuracy of a trained machine learning potential and the interpretation of simulation results as evidence for a new structural model, with limited independent experimental grounding provided in the abstract.

free parameters (1)
  • Machine learning potential parameters
    Parameters are fitted to first-principles total energies to approximate the potential energy surface for atomic configurations.
axioms (1)
  • domain assumption Energy-driven kinetic Monte Carlo with active learning adequately samples the relevant low-energy atomic configurations in monolayer amorphous systems
    The framework is assumed to explore configuration space sufficiently to identify the dominant structural motifs without trapping in local minima or missing key states.
invented entities (1)
  • Polymorphic crystallite model no independent evidence
    purpose: To describe the atomic structure of monolayer amorphous materials as mixtures of coexisting crystallites of different motifs
    New conceptual model introduced based on simulation observations; no independent experimental confirmation is mentioned in the abstract.

pith-pipeline@v0.9.0 · 5498 in / 1493 out tokens · 42194 ms · 2026-05-09T16:49:22.655448+00:00 · methodology

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [1]

    These findings suggest that the atomic structure of amorphous materials depends on their synthesis methods and may conform to either the crystallite model or the CRN model

    Amorphous diamond also exists in two variants: a CRN containing crystallites or a purely CRN22,23. These findings suggest that the atomic structure of amorphous materials depends on their synthesis methods and may conform to either the crystallite model or the CRN model. 4 In 2020, Toh et. al achieved the first successful synthesis of amorphous materials ...

    work page 2020

  2. [2]

    Present and future applications of amorphous silicon and its alloys,

    Structural evolutions and stabilities of monolayer amorphous BCN. (a) Energy evolution in EDKMC simulation of maBCN. The blue dashed line indicates energy of crystalline h-BCN used as the initial configuration. (b) Atomic configuration of maBCN with hexagons in crystallite areas colored in green. Insets show different types of crystallite. (c) Energy and ...

    work page 1989

  3. [3]

    Generalized Gradient Approximation Made Simple,

    We employed the EDKMC -based approach because the melting process induces out -of-plane deformations and an irreversible transition to three - dimensional structures, which prevents the formation of stable 2D amorphous states. During EDKMC simulations, Stone Wales (SW) rotations were performed on the configurations. Considering the multi -component nature...

    work page 1996