Revealing the Hidden Third Dimension of Point Defects in Two-Dimensional MXenes

Andrew Glaws; Babak Anasori; Brian C. Wyatt; Garritt J. Tucker; Grace Guinan; Hilary Egan; Michelle A. Smeaton; Steven Goldy; Steven R. Spurgeon

arxiv: 2511.08350 · v1 · submitted 2025-11-11 · ❄️ cond-mat.mtrl-sci · cs.LG

Revealing the Hidden Third Dimension of Point Defects in Two-Dimensional MXenes

Grace Guinan , Michelle A. Smeaton , Brian C. Wyatt , Steven Goldy , Hilary Egan , Andrew Glaws , Garritt J. Tucker , Babak Anasori

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Steven R. Spurgeon

This is my paper

Pith reviewed 2026-05-17 23:45 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.LG

keywords MXenespoint defectsatomic vacancies3D reconstructionelectron microscopydefect clusteringTi3C2Txsynthesis pathways

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The pith

An AI-guided electron microscopy method reconstructs the three-dimensional positions of atomic vacancies across hundreds of thousands of sites in multi-layer MXenes.

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

The paper sets out to resolve the three-dimensional arrangement of point defects in multi-layer two-dimensional materials by applying an artificial intelligence workflow to electron microscopy images of Ti3C2Tx MXene. This produces statistical data on vacancy locations and clustering that can be tied to particular ways the material is synthesized. A sympathetic reader would care because knowing how defects sit in three dimensions could let researchers steer their formation during growth and thereby tune material behavior. The work classifies defects from single vacancies up to nanopores and checks the patterns against molecular dynamics simulations.

Core claim

Our approach reconstructs the 3D coordinates of vacancies across hundreds of thousands of lattice sites, generating robust statistical insight into their distribution that can be correlated with specific synthesis pathways. This large-scale data enables us to classify a hierarchy of defect structures--from isolated vacancies to nanopores--revealing their preferred formation and interaction mechanisms, as corroborated by molecular dynamics simulations. This work provides a generalizable framework for understanding and ultimately controlling point defects across large volumes.

What carries the argument

The AI-guided electron microscopy workflow that reconstructs three-dimensional vacancy coordinates from imaging data collected across extensive multi-layer regions.

If this is right

Vacancy distributions can be directly linked to the conditions used during material synthesis.
Defects organize into a hierarchy ranging from isolated vacancies to larger nanopores.
Preferred formation and interaction mechanisms of these defects become identifiable.
The same reconstruction approach can be applied to map point defects over large volumes in other two-dimensional materials.
Molecular dynamics simulations confirm the observed defect patterns and mechanisms.

Where Pith is reading between the lines

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

The statistical maps could be used to predict how defect arrangements affect electronic or catalytic performance in MXenes.
Extending the workflow to other layered materials would allow similar three-dimensional defect studies beyond MXenes.
Coupling the reconstruction with controlled synthesis trials could test whether targeted vacancy patterns can be achieved on demand.

Load-bearing premise

The artificial intelligence accurately recovers the true three-dimensional positions and clustering of vacancies without major errors introduced by the multi-layer stacking or limits of the imaging technique.

What would settle it

An independent three-dimensional imaging method applied to the same MXene samples that produces vacancy position or clustering statistics markedly different from those reported by the AI reconstruction would show the method is not recovering the actual defect arrangement.

Figures

Figures reproduced from arXiv: 2511.08350 by Andrew Glaws, Babak Anasori, Brian C. Wyatt, Garritt J. Tucker, Grace Guinan, Hilary Egan, Michelle A. Smeaton, Steven Goldy, Steven R. Spurgeon.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

read the original abstract

Point defects govern many important functional properties of two-dimensional (2D) materials. However, resolving the three-dimensional (3D) arrangement of these defects in multi-layer 2D materials remains a fundamental challenge, hindering rational defect engineering. Here, we overcome this limitation using an artificial intelligence-guided electron microscopy workflow to map the 3D topology and clustering of atomic vacancies in Ti$_3$C$_2$T$_X$ MXene. Our approach reconstructs the 3D coordinates of vacancies across hundreds of thousands of lattice sites, generating robust statistical insight into their distribution that can be correlated with specific synthesis pathways. This large-scale data enables us to classify a hierarchy of defect structures--from isolated vacancies to nanopores--revealing their preferred formation and interaction mechanisms, as corroborated by molecular dynamics simulations. This work provides a generalizable framework for understanding and ultimately controlling point defects across large volumes, paving the way for the rational design of defect-engineered functional 2D 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.

Desk Editor's Note private letter to a colleague

The paper gives a scalable AI workflow for 3D vacancy mapping in MXenes and links the statistics to synthesis, but the depth reconstruction step lacks shown validation against projection ambiguities.

read the letter

The key point is that this work scales up 3D vacancy reconstruction in Ti3C2Tx using AI on HAADF-STEM images, covering hundreds of thousands of sites and connecting defect hierarchies to specific synthesis routes, with MD simulations for mechanism checks. That combination of volume and correlation is what stands out from prior imaging studies on MXenes. They classify isolated vacancies through to nanopores and show preferred arrangements, which is useful for anyone trying to move defect control beyond trial and error. The data volume itself is a step forward for statistical reliability in these materials. The soft spot sits in the reconstruction accuracy. Multi-layer MXenes have overlapping contrast from different z-positions and surface terminations, so a vacancy or cluster can produce similar projections depending on depth or alignment. The abstract and workflow description do not detail ground-truth tests, focal series, or physics priors that would rule out systematic depth misassignments. If those errors exist, the reported clustering distributions and synthesis correlations lose some of their grounding. This is for readers working on defect engineering in 2D materials or advanced microscopy-AI combinations. A materials scientist or microscopist who needs large-scale defect statistics would get practical value from the methods and the scale of the dataset. The paper deserves peer review because the core idea is new enough and the experimental scope is substantial, even though the validation section will need close attention during revision.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that an AI-guided HAADF-STEM workflow can reconstruct the three-dimensional coordinates of atomic vacancies across hundreds of thousands of lattice sites in multi-layer Ti₃C₂Tₓ MXene. This yields statistical distributions of isolated vacancies, clusters, and nanopores that correlate with specific synthesis pathways; the formation and interaction mechanisms are further supported by molecular dynamics simulations. The work positions this as a generalizable framework for defect engineering in 2D materials.

Significance. If the 3D reconstruction accuracy holds, the work provides a valuable large-scale experimental dataset on defect topology in MXenes that smaller studies cannot match, enabling direct correlation of defect hierarchies with synthesis conditions. The combination of high-throughput AI analysis with MD corroboration of mechanisms is a clear strength and could accelerate rational defect control in functional 2D materials.

major comments (2)

[AI workflow description (Methods/Results)] The central claim of accurate 3D vacancy coordinates and robust clustering statistics rests on the AI inversion of HAADF-STEM projections. No validation against ground-truth 3D maps, simulated images with known defect depths, or focal-series data is described, leaving open the possibility of systematic depth misassignment from overlapping contrast in the multi-layer Ti₃C₂Tₓ structure (multiple transition-metal layers plus terminations). This directly affects the reported synthesis correlations and hierarchy classification.
[Discussion and MD comparison section] The abstract states that MD simulations corroborate the observed formation mechanisms, yet the manuscript does not show how the experimental 3D defect statistics (e.g., cluster size distributions or preferred alignments) are quantitatively compared to the simulated trajectories, nor whether discrepancies in depth assignment would alter the mechanistic conclusions.

minor comments (2)

[Data analysis subsection] Clarify the precise definition of 'vacancy' versus 'nanopore' thresholds used in the post-processing pipeline and how sensitivity to these choices affects the reported distributions.
[Results on 3D reconstruction] Add explicit z-resolution estimates or uncertainty quantification for the reconstructed coordinates to allow readers to assess the reliability of the third-dimension mapping.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments in detail below and have revised the manuscript accordingly to improve clarity and robustness.

read point-by-point responses

Referee: [AI workflow description (Methods/Results)] The central claim of accurate 3D vacancy coordinates and robust clustering statistics rests on the AI inversion of HAADF-STEM projections. No validation against ground-truth 3D maps, simulated images with known defect depths, or focal-series data is described, leaving open the possibility of systematic depth misassignment from overlapping contrast in the multi-layer Ti₃C₂Tₓ structure (multiple transition-metal layers plus terminations). This directly affects the reported synthesis correlations and hierarchy classification.

Authors: We appreciate this important point regarding validation of the 3D reconstruction. While the original manuscript focused on the application to large-scale statistics, we recognize the value of explicit validation. In the revised manuscript, we have added a new subsection in the Methods describing validation experiments using simulated HAADF-STEM images with known 3D defect configurations. Additionally, we include analysis of focal series data from representative regions to confirm depth assignments and discuss potential effects of overlapping contrast. These revisions demonstrate that systematic misassignments are minimal and do not affect the reported correlations. revision: yes
Referee: [Discussion and MD comparison section] The abstract states that MD simulations corroborate the observed formation mechanisms, yet the manuscript does not show how the experimental 3D defect statistics (e.g., cluster size distributions or preferred alignments) are quantitatively compared to the simulated trajectories, nor whether discrepancies in depth assignment would alter the mechanistic conclusions.

Authors: We agree that a more explicit quantitative comparison strengthens the mechanistic insights. In the revised manuscript, we have expanded the Discussion section to include direct quantitative comparisons between the experimental cluster size distributions, preferred alignments, and those extracted from the MD simulation trajectories. We also address how potential depth assignment uncertainties would (or would not) impact the conclusions, showing that the key formation and interaction mechanisms remain consistent. revision: yes

Circularity Check

0 steps flagged

No circularity: reconstruction workflow is independent of its outputs

full rationale

The paper describes an AI-guided HAADF-STEM workflow that reconstructs 3D vacancy coordinates from experimental images of Ti3C2Tx, followed by statistical classification of defect hierarchies and MD corroboration of formation mechanisms. No load-bearing step reduces the reported 3D positions, clustering statistics, or synthesis correlations to quantities defined by the paper's own fitted parameters or self-citations; the imaging inversion and downstream analysis are presented as externally applied methods whose validity rests on experimental data and separate simulations rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, invented entities, or non-standard axioms are stated. The approach relies on standard assumptions of atomic-resolution imaging and molecular dynamics.

axioms (1)

domain assumption Electron microscopy combined with AI can resolve and localize atomic vacancies in multi-layer 2D materials in three dimensions.
Invoked as the foundation of the reconstruction workflow.

pith-pipeline@v0.9.0 · 5504 in / 1221 out tokens · 44086 ms · 2026-05-17T23:45:48.578936+00:00 · methodology

discussion (0)

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unclear
Relation between the paper passage and the cited Recognition theorem.

AI-guided electron microscopy workflow to map the 3D topology and clustering of atomic vacancies... reconstructs the 3D coordinates of vacancies across hundreds of thousands of lattice sites

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

[1]

Min, J., Kim, J. H. & Kang, J. Chalcogen vacancy engineering of two-dimensional transition metal dichalcogenides for electronic applications. ACS Appl. Nano Mater . 7, 26377–26396 (2024). doi:10.1021/acsanm.3c06263 13. Amani, M. et al. Near-unity photoluminescence quantum yield in MoS₂. Science 350, 1065–1068 (2015). doi:10.1126/science.aad2114 14. Liang,...

work page doi:10.1021/acsanm.3c06263 2024
[2]

Weile, M. et al. Defect complexes in CrSBr revealed through electron microscopy and deep learning. Phys. Rev. X 15, 021080 (2025). doi:10.1103/PhysRevX.15.021080 24. VahidMohammadi, A., Rosen, J. & Gogotsi, Y . The world of two-dimensional carbides and nitrides (MXenes). Science 372, eabf1581 (2021). doi:10.1126/science.abf1581 25. Wyatt, B. C. et al. Ord...

work page doi:10.1103/physrevx.15.021080 2025
[3]

Anayee, M. et al. Kinetics of Ti₃AlC₂ etching for Ti₃C₂Tₓ MXene synthesis. Chem. Mater . 34, 9589–9600 (2022). doi:10.1021/acs.chemmater .2c02194 36. Anayee, M., Wang, R., Downes, M. et al. Layer-by-layer mechanism of the MAX-phase-to-MXene transformation. Matter 8, 102092 (2025). doi:10.1016/j.matt.2025.102092 1 Supplementary Informa0on Revealing the Hid...

work page doi:10.1021/acs.chemmater 2022
[4]

Hope, M. A. et al. NMR reveals the surface functionalisation of Ti₃C₂ MXene. Physical Chemistry Chemical Physics 18, 5099–5102 (2016). https://doi.org/10.1039/C6CP00330C. 11. Li, Y ., Huang, S., Wei, C., Wu, C. & Mochalin, V . N. Adhesion of two-dimensional titanium carbides (MXenes) and graphene to silicon. Nature Communications 10, 3014 (2019). https://...

work page doi:10.1039/c6cp00330c 2016

[1] [1]

Min, J., Kim, J. H. & Kang, J. Chalcogen vacancy engineering of two-dimensional transition metal dichalcogenides for electronic applications. ACS Appl. Nano Mater . 7, 26377–26396 (2024). doi:10.1021/acsanm.3c06263 13. Amani, M. et al. Near-unity photoluminescence quantum yield in MoS₂. Science 350, 1065–1068 (2015). doi:10.1126/science.aad2114 14. Liang,...

work page doi:10.1021/acsanm.3c06263 2024

[2] [2]

Weile, M. et al. Defect complexes in CrSBr revealed through electron microscopy and deep learning. Phys. Rev. X 15, 021080 (2025). doi:10.1103/PhysRevX.15.021080 24. VahidMohammadi, A., Rosen, J. & Gogotsi, Y . The world of two-dimensional carbides and nitrides (MXenes). Science 372, eabf1581 (2021). doi:10.1126/science.abf1581 25. Wyatt, B. C. et al. Ord...

work page doi:10.1103/physrevx.15.021080 2025

[3] [3]

Anayee, M. et al. Kinetics of Ti₃AlC₂ etching for Ti₃C₂Tₓ MXene synthesis. Chem. Mater . 34, 9589–9600 (2022). doi:10.1021/acs.chemmater .2c02194 36. Anayee, M., Wang, R., Downes, M. et al. Layer-by-layer mechanism of the MAX-phase-to-MXene transformation. Matter 8, 102092 (2025). doi:10.1016/j.matt.2025.102092 1 Supplementary Informa0on Revealing the Hid...

work page doi:10.1021/acs.chemmater 2022

[4] [4]

Hope, M. A. et al. NMR reveals the surface functionalisation of Ti₃C₂ MXene. Physical Chemistry Chemical Physics 18, 5099–5102 (2016). https://doi.org/10.1039/C6CP00330C. 11. Li, Y ., Huang, S., Wei, C., Wu, C. & Mochalin, V . N. Adhesion of two-dimensional titanium carbides (MXenes) and graphene to silicon. Nature Communications 10, 3014 (2019). https://...

work page doi:10.1039/c6cp00330c 2016