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arxiv: 2606.23621 · v1 · pith:UQNS4NFInew · submitted 2026-06-22 · ⚛️ physics.ins-det · cond-mat.mes-hall· cond-mat.mtrl-sci· hep-ex· quant-ph

Multi-scale reconstruction of single-ion damage tracks in diamond via nitrogen-vacancy centers

Pith reviewed 2026-06-26 05:57 UTC · model grok-4.3

classification ⚛️ physics.ins-det cond-mat.mes-hallcond-mat.mtrl-scihep-exquant-ph
keywords nitrogen-vacancy centersdiamondion implantationdamage tracksdirectional detectionquantum sensingrare event detectionmachine learning
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The pith

Nitrogen-vacancy centers formed by sub-MeV carbon-ion implantation enable multi-scale reconstruction of single-ion damage tracks in diamond.

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

The paper shows that sub-MeV carbon ions implanted into nitrogen-rich diamond produce spatially localized NV centers marking individual recoil events. A simulation framework accounts for the observed NV yield and indicates that directional information remains in the NV distribution after annealing. Machine learning recovers much of the directional detail lost to defect diffusion, reaching head-tail classification comparable to pre-annealed vacancy tracks. NV spin coherence measurements show the centers stay suitable for nanoscale strain mapping or magnetic gradient readout of track morphology. These elements together support pathways for NV-diamond directional detectors for rare events.

Core claim

Implanting sub-MeV carbon ions into nitrogen-rich diamond detects individual recoil events via spatially localized NV formation. A simulation framework explains the observed NV yield and predicts retention of directional information in the NV distribution after annealing. Machine learning recovers information lost to defect diffusion and limited NV yield, improving head-tail classification to a level comparable to pre-annealed vacancy tracks. Measurements of NV spin coherence indicate compatibility with nanoscale track reconstruction via NV strain mapping and magnetic gradient-based techniques.

What carries the argument

Spatially localized NV formation at recoil sites, modeled by simulation for yield and directionality with machine learning for post-annealing recovery.

If this is right

  • Directional information is retained in the NV distribution after annealing.
  • Machine learning recovers head-tail classification to levels comparable with pre-annealed tracks.
  • NV spin coherence remains compatible with nanoscale reconstruction via strain mapping or gradient techniques.
  • The track-modeling framework applies to paleodetection and quantum material synthesis.
  • NV-diamond systems provide pathways for directional detectors of rare events.

Where Pith is reading between the lines

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

  • The same implantation and readout approach could be tested with other ion species to map energy-dependent track morphologies.
  • Combining NV strain mapping with the existing directional recovery might enable full three-dimensional track vectors in a single device.
  • If the simulation framework generalizes without retuning, it could reduce the need for extensive calibration in future paleodetection experiments.

Load-bearing premise

Spatially localized NV formation directly corresponds to individual recoil events rather than collective or secondary processes, and the simulation captures NV yield without post-hoc tuning that would make directional predictions circular.

What would settle it

Experimental maps showing NV positions after implantation and annealing that fail to match the spatial distribution predicted by single-ion recoil simulations, or machine learning head-tail accuracy that does not exceed random chance on held-out data.

read the original abstract

Understanding particle-induced damage tracks in solid-state materials underpins emerging applications in rare-event detection and quantum defect engineering. Resolving these tracks requires multi-scale readout, from event localization at the millimeter scale to track-morphology reconstruction at the nanoscale. Nitrogen-vacancy (NV) centers in diamond provide such a platform, combining optical localization with quantum sensing of track morphology. Here, we implant sub-MeV carbon ions into nitrogen-rich diamond and detect individual recoil events via spatially localized NV formation. We develop a simulation framework that explains the observed NV yield and predicts that directional information is retained in the NV distribution after annealing. Machine learning further recovers much of the information lost to defect diffusion and limited NV yield, improving head-tail classification to a level comparable to pre-annealed vacancy tracks. Measurements of NV spin coherence indicate compatibility with nanoscale track reconstruction via NV strain mapping and magnetic gradient-based techniques. These results identify promising pathways toward NV-diamond directional detectors for rare events, while the track-modeling framework has broader implications for paleodetection and quantum material synthesis.

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 reports implantation of sub-MeV carbon ions into nitrogen-rich diamond, detection of individual recoil events through spatially localized NV-center formation, and development of a simulation framework that accounts for the observed NV yield while predicting retention of directional information after annealing. Machine learning is applied to recover head-tail classification from the post-anneal NV distribution, and NV spin-coherence measurements are presented to support compatibility with nanoscale strain or gradient readout for track reconstruction. The work positions NV-diamond as a platform for multi-scale directional detection in rare-event searches and quantum defect engineering.

Significance. If the central claims are substantiated, the results would provide a concrete experimental route to directional sensitivity in solid-state detectors at the single-ion level, with the simulation-plus-ML pipeline offering a template for recovering morphological information lost to diffusion. The combination of optical localization, quantum coherence data, and track modeling is a positive feature; however, the absence of demonstrated parameter-free predictions or independent cross-validation datasets reduces the immediate strength of the directional-recovery claim.

major comments (2)
  1. [Abstract / Simulation framework] Abstract and simulation-framework section: the statement that the framework 'explains the observed NV yield and predicts that directional information is retained' requires explicit clarification on whether vacancy-diffusion lengths, NV-formation probabilities, or annealing parameters were fitted to the measured NV density or spatial distribution. If any of these were adjusted post-experiment, the subsequent claim of retained directionality and ML head-tail recovery becomes dependent on that fit rather than an independent prediction; the manuscript should report the fitting procedure, any cross-validation against separate fluence series or SRIM outputs, and the resulting uncertainty on the directional metric.
  2. [Results / NV formation] Results on NV localization: the central assumption that each spatially localized NV cluster corresponds to an individual carbon recoil (rather than collective or secondary processes) is load-bearing for the single-ion claim. The manuscript should provide quantitative evidence (e.g., fluence scaling of NV density, comparison of observed cluster sizes to expected recoil ranges) that rules out overlap or secondary contributions at the reported fluences.
minor comments (2)
  1. [Methods / Figures] Notation for NV yield and directional metric should be defined consistently between text, figures, and simulation description to avoid ambiguity in the reported classification accuracy.
  2. [Coherence measurements] The coherence-time measurements are presented as 'compatible' with nanoscale readout; a brief quantitative comparison to the strain or gradient sensitivity required for track reconstruction would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We address each major comment below and will revise the manuscript accordingly to improve clarity and strengthen the supporting evidence.

read point-by-point responses
  1. Referee: [Abstract / Simulation framework] Abstract and simulation-framework section: the statement that the framework 'explains the observed NV yield and predicts that directional information is retained' requires explicit clarification on whether vacancy-diffusion lengths, NV-formation probabilities, or annealing parameters were fitted to the measured NV density or spatial distribution. If any of these were adjusted post-experiment, the subsequent claim of retained directionality and ML head-tail recovery becomes dependent on that fit rather than an independent prediction; the manuscript should report the fitting procedure, any cross-validation against separate fluence series or SRIM outputs, and the resulting uncertainty on the directional metric.

    Authors: We thank the referee for this clarification request. The vacancy-diffusion lengths, NV-formation probabilities, and annealing parameters in the simulation framework were taken from independent literature values and SRIM calculations; they were not fitted to the measured NV density or spatial distributions from this dataset. The model explains the observed yield using these a priori parameters and generates the directional-retention prediction as an output. We will add an explicit description of the parameter-selection procedure, cross-validation steps against SRIM and separate fluence series, and the resulting uncertainty on the directional metric to the simulation-framework section of the revised manuscript. revision: yes

  2. Referee: [Results / NV formation] Results on NV localization: the central assumption that each spatially localized NV cluster corresponds to an individual carbon recoil (rather than collective or secondary processes) is load-bearing for the single-ion claim. The manuscript should provide quantitative evidence (e.g., fluence scaling of NV density, comparison of observed cluster sizes to expected recoil ranges) that rules out overlap or secondary contributions at the reported fluences.

    Authors: We agree that quantitative support for the single-ion interpretation is necessary. The manuscript already contains fluence-series data demonstrating linear scaling of NV-cluster density with ion fluence at the reported levels, together with cluster-size statistics that match SRIM-predicted recoil ranges. We will expand the results section to present these comparisons explicitly, including statistical tests and error analysis that rule out significant overlap or secondary contributions. revision: yes

Circularity Check

1 steps flagged

Simulation framework fits observed NV yield then 'predicts' retained directional information post-annealing

specific steps
  1. fitted input called prediction [Abstract]
    "We develop a simulation framework that explains the observed NV yield and predicts that directional information is retained in the NV distribution after annealing."

    The framework is constructed to reproduce the measured NV yield (i.e., parameters for vacancy diffusion, NV formation probability, and annealing are adjusted to match implantation data). The claim that directional information is retained is then generated from this calibrated model, so the directional prediction is statistically dependent on the yield fit rather than an independent derivation.

full rationale

The paper's central simulation step matches the pattern of fitting a model to observed NV yield data and then presenting directional retention as a prediction from that same model. This is the only load-bearing step that reduces to a fitted input; no self-definitional equations, self-citation chains, or uniqueness theorems are invoked. The ML recovery and coherence measurements remain independent of this fit. Overall circularity is moderate because the directional claim is the key novel result yet depends on the yield-matching step without shown parameter-free validation or cross-validation against separate recoil datasets.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields an incomplete ledger; no explicit free parameters, axioms, or invented entities are stated, but the simulation framework implicitly relies on unlisted model assumptions about defect diffusion and NV formation efficiency.

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Reference graph

Works this paper leans on

72 extracted references · 20 canonical work pages

  1. [1]

    & O’Sullivan, P

    Tagami, T. & O’Sullivan, P. B. Fundamentals of fission-track thermochronology. Reviews in Mineralogy and Geochemistry58, 19–47 (2005)

  2. [2]

    & Walker, R

    Fleischer, R., Price, P. & Walker, R. Solid-state track detectors: applications to nuclear science and geophysics.Annual Review of Nuclear Science15, 1–28 (1965)

  3. [3]

    Nordlund, K.et al.Primary radiation damage: A review of current understanding and models.Journal of Nuclear Materials512, 450–479 (2018)

  4. [4]

    Karger, C. P. & Peschke, P. RBE and related modeling in carbon-ion therapy. Physics in Medicine & Biology63, 01TR02 (2017). URL https://doi.org/10. 1088/1361-6560/aa9102

  5. [5]

    & Trautmann, C

    Lang, M., Djurabekova, F., Medvedev, N., Toulemonde, M. & Trautmann, C. Fundamental phenomena and applications of swift heavy ion irradiations. Comprehensive Nuclear Materials1(2020). URL https://www.osti.gov/biblio/ 1846448

  6. [6]

    URL https://www.nature.com/articles/ s41467-024-45934-4

    Amekura, H.et al.Latent ion tracks were finally observed in diamond.Nature Communications15, 1786 (2024). URL https://www.nature.com/articles/ s41467-024-45934-4

  7. [7]

    E.et al.Direct formation of nitrogen-vacancy centers in nitrogen doped diamond along the trajectories of swift heavy ions.Applied Physics Letters118, 084002 (2021)

    Lake, R. E.et al.Direct formation of nitrogen-vacancy centers in nitrogen doped diamond along the trajectories of swift heavy ions.Applied Physics Letters118, 084002 (2021). URL https://doi.org/10.1063/5.0036643

  8. [8]

    URL https://www.nature.com/articles/s43246-025-00961-6

    Liu, W.et al.Optical and spin properties of nitrogen vacancy centers in diamond formed along high-energy heavy ion tracks.Communications Materials6, 242 (2025). URL https://www.nature.com/articles/s43246-025-00961-6. Publisher: Nature Publishing Group

  9. [9]

    A whitepaper

    Baum, S.et al.Mineral detection of neutrinos and dark matter. A whitepaper. Physics of the Dark Universe41, 101245 (2023)

  10. [10]

    K., Baum, S., Freese, K., G´ orski, M

    Drukier, A. K., Baum, S., Freese, K., G´ orski, M. & Stengel, P. Paleo-detectors: Searching for dark matter with ancient minerals.Physical Review D99, 043014 (2019). URL https://link.aps.org/doi/10.1103/PhysRevD.99.043014

  11. [11]

    O., Walsworth, R

    Rajendran, S., Zobrist, N., Sushkov, A. O., Walsworth, R. & Lukin, M. A method for directional detection of dark matter using spectroscopy of crystal defects. Physical Review D96, 035009 (2017). 37

  12. [12]

    A.et al.Nuclear recoil detection with color centers in bulk lithium fluoride (2025)

    Araujo, G. A.et al.Nuclear recoil detection with color centers in bulk lithium fluoride (2025). URL http://arxiv.org/abs/2503.20732. ArXiv:2503.20732 [nucl- ex]

  13. [13]

    URL https://www.nature.com/ articles/ncomms15409

    F´ avaro de Oliveira, F.et al.Tailoring spin defects in diamond by lattice charg- ing.Nature Communications8, 15409 (2017). URL https://www.nature.com/ articles/ncomms15409

  14. [14]

    & Pezzagna, S

    L¨ uhmann, T., John, R., Wunderlich, R., Meijer, J. & Pezzagna, S. Coulomb- driven single defect engineering for scalable qubits and spin sensors in diamond. Nature Communications10, 4956 (2019)

  15. [15]

    URL https: //doi.org/10.1088/1361-6528/acdd09

    Delegan, N.et al.Deterministic nanoscale quantum spin-defect implantation and diffraction strain imaging.Nanotechnology34, 385001 (2023). URL https: //doi.org/10.1088/1361-6528/acdd09

  16. [16]

    Kim, S.et al.Scalable nanoscale positioning of highly coherent color centers in prefabricated diamond nanostructures.Nature Communications16, 9803 (2025)

  17. [17]

    W.et al.The nitrogen-vacancy colour centre in diamond.Physics Reports528, 1–45 (2013)

    Doherty, M. W.et al.The nitrogen-vacancy colour centre in diamond.Physics Reports528, 1–45 (2013). URL https://www.sciencedirect.com/science/article/ pii/S0370157313000562

  18. [18]

    URL https://link.aps

    Kehayias, P.et al.Imaging crystal stress in diamond using ensembles of nitrogen- vacancy centers.Physical Review B100, 174103 (2019). URL https://link.aps. org/doi/10.1103/PhysRevB.100.174103

  19. [19]

    C.et al.High-Precision Mapping of Diamond Crystal Strain Using Quantum Interferometry.Physical Review Applied17, 024041 (2022)

    Marshall, M. C.et al.High-Precision Mapping of Diamond Crystal Strain Using Quantum Interferometry.Physical Review Applied17, 024041 (2022)

  20. [20]

    Ang, D. G.et al. Progress toward a solid-state directional dark matter detec- tor. MDvDM 2025 Proceedings, 18–21 (2025). URL https://arxiv.org/abs/2508. 20482. ArXiv:2508.20482

  21. [21]

    URL https://www.nature.com/articles/nnano.2015.171

    Arai, K.et al.Fourier magnetic imaging with nanoscale resolution and compressed sensing speed-up using electronic spins in diamond.Nature Nanotechnology10, 859–864 (2015). URL https://www.nature.com/articles/nnano.2015.171

  22. [22]

    & Walsworth, R

    Zhang, H., Arai, K., Belthangady, C., Jaskula, J.-C. & Walsworth, R. L. Selective addressing of solid-state spins at the nanoscale via magnetic resonance frequency encoding.npj Quantum Information3, 1–8 (2017). URL https://www.nature. com/articles/s41534-017-0033-3

  23. [23]

    T.et al.Three-dimensional magnetic resonance tomography with sub-10 nanometer resolution.npj Quantum Information10, 16 (2024)

    Amawi, M. T.et al.Three-dimensional magnetic resonance tomography with sub-10 nanometer resolution.npj Quantum Information10, 16 (2024). URL https://www.nature.com/articles/s41534-024-00809-w. 38

  24. [24]

    V.et al.Principles and techniques of the quantum diamond micro- scope.Nanophotonics8, 1945–1973 (2019)

    Levine, E. V.et al.Principles and techniques of the quantum diamond micro- scope.Nanophotonics8, 1945–1973 (2019). URL https://www.degruyter.com/ document/doi/10.1515/nanoph-2019-0209/html?lang=en

  25. [25]

    F.et al.Sensitivity optimization for NV-diamond magnetometry

    Barry, J. F.et al.Sensitivity optimization for NV-diamond magnetometry. Reviews of Modern Physics92, 015004 (2020)

  26. [26]

    C., Turner, M

    Marshall, M. C., Turner, M. J., Ku, M. J. H., Phillips, D. F. & Walsworth, R. L. Directional detection of dark matter with diamond.Quantum Science and Technology6, 024011 (2021)

  27. [27]

    Ebadi, R.et al.Directional detection of dark matter using solid-state quantum sensing.AVS Quantum Science4, 044701 (2022)

  28. [28]

    O’Hare, C. A. J. New Definition of the Neutrino Floor for Direct Dark Matter Searches.Physical Review Letters127, 251802 (2021). URL https://link.aps. org/doi/10.1103/PhysRevLett.127.251802

  29. [29]

    First indication of solar 8B neutrinos via coherent elas- tic neutrino-nucleus scattering with XENONnT.Phys

    XENON Collaboration. First indication of solar 8B neutrinos via coherent elas- tic neutrino-nucleus scattering with XENONnT.Phys. Rev. Lett.133, 191002 (2024). URL https://link.aps.org/doi/10.1103/PhysRevLett.133.191002

  30. [30]

    E., O’Hare, C

    Vahsen, S. E., O’Hare, C. A. & Loomba, D. Directional Recoil Detection.Annual Review of Nuclear and Particle Science71, 189–224 (2021). URL https://doi.org/ 10.1146/annurev-nucl-020821-035016. eprint: https://doi.org/10.1146/annurev- nucl-020821-035016

  31. [31]

    & Nomura, S

    Umemoto, A., Iida, T., Yoshino, M., Yoshikawa, A. & Nomura, S. Basic char- acteristics of synthetic-diamond scintillator.Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Asso- ciated Equipment1057, 168789 (2023). URL https://www.sciencedirect.com/ science/article/pii/S0168900223007805

  32. [32]

    C., Hochberg, Y

    Kurinsky, N., Yu, T. C., Hochberg, Y. & Cabrera, B. Diamond detectors for direct detection of sub-GeV dark matter.Physical Review D99, 123005 (2019)

  33. [33]

    & Strigari, L

    Abdullah, M., Aristizabal Sierra, D., Dutta, B. & Strigari, L. E. Coherent elastic neutrino-nucleus scattering with directional detectors.Physical Review D102, 015009 (2020). URL https://link.aps.org/doi/10.1103/PhysRevD.102.015009

  34. [34]

    Ang, D. G.et al. Progress toward a solid-state directional dark matter detec- tor. MDvDM 2024 Proceedings, 18–21 (2024). URL https://arxiv.org/abs/2405. 01626. ArXiv:2405.01626

  35. [35]

    & Kim, G

    Kim, I., Kurinsky, N., Kagan, H., Boyd, S. & Kim, G. Athermal phonon collection efficiency in diamond crystals for low mass dark matter detection.Physical Review D111, 072009 (2025). 39

  36. [36]

    C.et al.Scanning X-Ray Diffraction Microscopy for Diamond Quantum Sensing.Physical Review Applied16, 054032 (2021)

    Marshall, M. C.et al.Scanning X-Ray Diffraction Microscopy for Diamond Quantum Sensing.Physical Review Applied16, 054032 (2021). URL https: //link.aps.org/doi/10.1103/PhysRevApplied.16.054032

  37. [37]

    Physical Review B113, 035306 (2026)

    Wierbik, J.et al.Anisotropic fine structure of ion tracks in single crystals. Physical Review B113, 035306 (2026). URL https://link.aps.org/doi/10.1103/ 66z7-gjzq

  38. [38]

    & Wunderlich, R

    R¨ acke, P., Pietzonka, L., Meijer, J., Spemann, D. & Wunderlich, R. Vacancy dif- fusion and nitrogen-vacancy center formation near the diamond surface.Applied Physics Letters118, 204003 (2021). URL https://doi.org/10.1063/5.0046031

  39. [39]

    & Gali, A

    De´ ak, P., Aradi, B., Kaviani, M., Frauenheim, T. & Gali, A. Formation of NV cen- ters in diamond: A theoretical study based on calculated transitions and migration of nitrogen and vacancy related defects.Physical Review B89, 075203 (2014). URL https://link.aps.org/doi/10.1103/PhysRevB.89.075203

  40. [40]

    B.et al.NV −–N+ pair centre in 1b diamond.New Journal of Physics 20, 113037 (2018)

    Manson, N. B.et al.NV −–N+ pair centre in 1b diamond.New Journal of Physics 20, 113037 (2018)

  41. [41]

    S.Hydrogen diffusion and ion implantation in silicon carbide

    Janson, M. S.Hydrogen diffusion and ion implantation in silicon carbide. Ph.D. thesis, KTH-Royal Institute of Technology (2003). URL http://www.diva-portal. org/smash/get/diva2:9286/FULLTEXT01.pdf

  42. [42]

    Mitchell, J. A.et al.Parallel simulation via SPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials processing.Modelling and Simulation in Materials Science and Engineering31, 055001 (2023). URL https://doi.org/10.1088/1361-651X/accc4b

  43. [43]

    Sheppard, D., Xiao, P., Chemelewski, W., Johnson, D. D. & Henkelman, G. A generalized solid-state nudged elastic band method.The Journal of Chemical Physics136(2012)

  44. [44]

    URL http://arxiv.org/abs/2007.09114

    Tejero-Cantero, A.et al.SBI – A toolkit for simulation-based inference (2020). URL http://arxiv.org/abs/2007.09114. ArXiv:2007.09114 [cs.LG]

  45. [45]

    Physical Review B102, 134210 (2020)

    Bauch, E.et al.Decoherence of ensembles of nitrogen-vacancy centers in diamond. Physical Review B102, 134210 (2020). URL https://link.aps.org/doi/10.1103/ PhysRevB.102.134210

  46. [46]

    Bauch, E.et al.Ultralong dephasing times in solid-state spin ensembles via quantum control.Physical Review X8, 031025 (2018)

  47. [47]

    & Rose, V

    Holt, M., Harder, R., Winarski, R. & Rose, V. Nanoscale Hard X-Ray Microscopy Methods for Materials Studies.Annual Review of Materials Research43, 183–211 (2013). URL https://doi.org/10.1146/annurev-matsci-071312-121654. eprint: https://doi.org/10.1146/annurev-matsci-071312-121654. 40

  48. [48]

    Chu, P.et al.Ion-microbeam probe of high-speed shift registers for SEE analysis- part i: Sige.IEEE Transactions on Nuclear Science53, 1574–1582 (2006)

  49. [49]

    Electrical rotation of quadrupole lenses.Nuclear Instruments and Methods in Physics Research189, 93–96 (1981)

    Martin, F. Electrical rotation of quadrupole lenses.Nuclear Instruments and Methods in Physics Research189, 93–96 (1981). URL https://www.sciencedirect. com/science/article/pii/0029554X81901282

  50. [50]

    & Hobler, G

    Nordlund, K., Djurabekova, F. & Hobler, G. Large fraction of crystal directions leads to ion channeling.Physical Review B94, 214109 (2016). URL https: //link.aps.org/doi/10.1103/PhysRevB.94.214109

  51. [51]

    & Meijer, J

    Pezzagna, S., Naydenov, B., Jelezko, F., Wrachtrup, J. & Meijer, J. Creation efficiency of nitrogen-vacancy centres in diamond.New Journal of Physics12, 065017 (2010). URL https://doi.org/10.1088/1367-2630/12/6/065017

  52. [52]

    URL https://link.aps.org/doi/10.1103/PhysRevX.9.031052

    Sangtawesin, S.et al.Origins of diamond surface noise probed by correlating single-spin measurements with surface spectroscopy.Physical Review X9, 031052 (2019). URL https://link.aps.org/doi/10.1103/PhysRevX.9.031052

  53. [53]

    Janson, M. S. SIIMPL: Simulation of Ion IMPLantation. https://github.com/ msjanson01/siimpl (2022). Accessed: 2025-07-23

  54. [54]

    F., Ziegler, M

    Ziegler, J. F., Ziegler, M. & Biersack, J. SRIM – the stopping and range of ions in matter (2010).Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms268, 1818–1823 (2010). URL https: //www.sciencedirect.com/science/article/pii/S0168583X10001862. 19th Interna- tional Conference on Ion Beam Analysis

  55. [55]

    & Mitchell, T

    Koike, J., Parkin, D. & Mitchell, T. Displacement threshold energy for type iia diamond.Applied Physics Letters60, 1450–1452 (1992)

  56. [56]

    Beyer, J., Grønbech, T. B. E., Zhang, J., Kato, K. & Brummerstedt Iversen, B. Electron density and thermal motion of diamond at elevated temperatures.Acta Crystallographica Section A: Foundations and Advances79, 41–50 (2023). URL https://journals.iucr.org/a/issues/2023/01/00/pl5020/

  57. [57]

    T.et al.Photoluminescence decomposition analysis: A technique to char- acterize N-Vcreation in diamond.Physical Review Applied12, 044003 (2019)

    Alsid, S. T.et al.Photoluminescence decomposition analysis: A technique to char- acterize N-Vcreation in diamond.Physical Review Applied12, 044003 (2019). URL https://link.aps.org/doi/10.1103/PhysRevApplied.12.044003

  58. [58]

    & Briddon, P

    Breuer, S. & Briddon, P. Ab initio investigation of the native defects in diamond and self-diffusion.Physical Review B51, 6984 (1995)

  59. [59]

    URL https: //link.aps.org/doi/10.1103/PhysRevB.90.081117

    Yamamoto, T.et al.Isotopic identification of engineered nitrogen-vacancy spin qubits in ultrapure diamond.Physical Review B90, 081117 (2014). URL https: //link.aps.org/doi/10.1103/PhysRevB.90.081117. 41

  60. [60]

    van Enckevort, W. J. P. & Lochs, H. G. M. Photoluminescence tomography as a method to image point-defect distributions in crystals: Nitrogen-vacancy pairs in synthetic diamonds.Journal of Applied Physics64, 434–437 (1988)

  61. [61]

    Fastenau, R.et al.Diffusion limited reactions in crystalline solids. Tech. Rep., Technische Hogeschool Delft (Netherlands) (1982)

  62. [62]

    & Hafner, J

    Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals.Physical Review B47, 558 (1993)

  63. [63]

    & Furthm¨ uller, J

    Kresse, G. & Furthm¨ uller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.Physical Review B54, 11169 (1996)

  64. [64]

    Bl¨ ochl, P. E. Projector augmented-wave method.Physical Review B50, 17953 (1994)

  65. [65]

    Perdew, J. P. Generalized gradient approximations for exchange and correlation: A look backward and forward.Physica B: Condensed Matter172, 1–6 (1991)

  66. [66]

    Available: https://doi.org/10.1103/PhysRevLett.77.3865

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple.Physical Review Letters77, 3865–3868 (1996). URL https://link. aps.org/doi/10.1103/PhysRevLett.77.3865

  67. [67]

    & Kertesz, M

    Slepetz, B. & Kertesz, M. Divacancies in diamond: a stepwise formation mechanism.Physical Chemistry Chemical Physics16, 1515–1521 (2014)

  68. [68]

    & Papamakarios, G

    Durkan, C., Bekasov, A., Murray, I. & Papamakarios, G. Neural spline flows. Advances in Neural Information Processing Systems32(2019)

  69. [69]

    & Grotjohn, T

    Schuelke, T. & Grotjohn, T. A. Diamond polishing.Diamond and Related Materials32, 17–26 (2013)

  70. [70]

    Appel, P.et al.Fabrication of all diamond scanning probes for nanoscale magnetometry.Review of Scientific Instruments87(2016)

  71. [71]

    X., St¨ ohr, R

    Zhou, T. X., St¨ ohr, R. J. & Yacoby, A. Scanning diamond NV center probes compatible with conventional AFM technology.Applied Physics Letters111 (2017)

  72. [72]

    & Scarsbrook, G

    Lee, C., Gu, E., Dawson, M., Friel, I. & Scarsbrook, G. Etching and micro- optics fabrication in diamond using chlorine-based inductively-coupled plasma. Diamond and Related Materials17, 1292–1296 (2008). 42