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From mono- to hexa-interstitials: Computational insights into carbon defects in diamond

Nima Ghafari Cherati1,2, Arsalan Hashemi3,4, and Ádám Gali1,2,5,*

  • 1HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
  • 2Department of Atomic Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rakpart 3, H-1111 Budapest, Hungary
  • 3European Laboratory for Learning and Intelligent Systems (ELLIS) Institute Finland, Maarintie 8, 02150 Espoo, Finland
  • 4Department of Technical Physics, University of Eastern Finland, P.O. Box 1627, FI-70211 Kuopio, Finland
  • 5MTA-WFK Lendület “Momentum” Semiconductor Nanostructures Research Group, P.O. Box 49, H-1525 Budapest, Hungary

  • *Contact author: gali.adam@wigner.hun-ren.hu
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Phys. Rev. Research 8, 023088 – Published 29 April, 2026

DOI: https://doi.org/10.1103/kxgc-k5lq

Abstract

We present a comprehensive first-principles investigation of carbon self-interstitial defects in diamond, ranging from mono- to hexa-interstitial complexes. By density functional theory, empowered by interatomic potential models, we efficiently sample the complex configurational landscape and identify both known and previously unreported defect geometries. Our results reveal a pronounced energetic driving force for aggregation: The formation energy per interstitial decreases systematically from isolated split interstitials to compact multi-interstitial clusters, with the tetra-interstitial platelet emerging as a particularly stable structural motif. Additionally, charge analysis indicates that the predominantly covalent bonding in diamond becomes more polar within the defect centers. Analysis of defect energy levels shows that only the investigated mono-, di-, penta-, and hexa-interstitial complexes introduce in-gap electronic states, whereas the tri- and tetra-interstitial clusters are electronically inert. Vibrational spectroscopies further reveal that self-interstitials generate characteristic signatures. Short carbon-carbon bonds inside the defect cores give rise to high-frequency vibrational modes between 1375 and 1925cm−1, which are strongly infrared active but exhibit weak Raman activity. Through a systematic analysis of metastable configurations, we identify the 3H defect center as a neutral di-interstitial defect. Based on this identification, we further suggest that the TR12 center may arise from a 3H-containing defect like a metastable hexa-interstitial configuration. Taken together, these findings provide a coherent picture of the structural, electronic, and vibrational characteristics of carbon self-interstitials and establish a robust framework for their experimental identification.

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References (71)

  1. R. Kalish, Diamond as a unique high-tech electronic material: Difficulties and prospects, J. Phys. D: Appl. Phys. 40, 6467 (2007).
  2. R. J. Nemanich, J. A. Carlisle, A. Hirata, and K. Haenen, CVD diamond—Research, applications, and challenges, MRS Bull. 39, 490 (2014).
  3. J. Zhang, J. Wang, G. Zhang, Z. Huo, Z. Huang, and L. Wu, A review of diamond synthesis, modification technology, and cutting tool application in ultra-precision machining, Mater. Des. 237, 112577 (2024).
  4. D. S. Misra, Nitrogen centers in single crystal diamond grown by chemical vapor deposition, J. Vac. Sci. Technol. A 41, 042703 (2023).
  5. A. Zaitsev, N. Kazuchits, V. Kazuchits, K. Moe, M. Rusetsky, O. Korolik, K. Kitajima, J. Butler, and W. Wang, Nitrogen-doped CVD diamond: Nitrogen concentration, color and internal stress, Diam. Relat. Mater. 105, 107794 (2020).
  6. C. M. Breeding and J. E. Shigley, The “type” classification system of diamonds and its importance in gemology, Gems Gemol. 45, 96 (2009).
  7. J. Rovny, Z. Yuan, M. Fitzpatrick, A. I. Abdalla, L. Futamura, C. Fox, M. C. Cambria, S. Kolkowitz, and N. P. de Leon, Nanoscale covariance magnetometry with diamond quantum sensors, Science 378, 1301 (2022).
  8. G. Wolfowicz, F. J. Heremans, C. P. Anderson, S. Kanai, H. Seo, A. Gali, G. Galli, and D. D. Awschalom, Quantum guidelines for solid-state spin defects, Nat. Rev. Mater. 6, 906 (2021).
  9. G. Zhang, Y. Cheng, J.-P. Chou, and A. Gali, Material platforms for defect qubits and single-photon emitters, Appl. Phys. Rev. 7, 031308 (2020).
  10. G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, Nanoscale imaging magnetometry with diamond spins under ambient conditions, Nature (London) 455, 648 (2008).
  11. J. Foglszinger, A. Denisenko, T. Kornher, M. Schreck, W. Knolle, B. Yavkin, R. Kolesov, and J. Wrachtrup, TR12 centers in diamond as a room temperature atomic scale vector magnetometer, npj Quantum Inf. 8, 65 (2022).
  12. K. Iakoubovskii and G. Adriaenssens, Optical study of some interstitial-related centres in CVD diamond, Phys. Status Solidi A 181, 59 (2000).
  13. J. H. N. Loubser and J. A. van Wyk, Electron spin resonance in the study of diamond, Rep. Prog. Phys. 41, 1201 (1978).
  14. C. D. Clark, R. W. Ditchburn, and H. B. Dyer, The absorption spectra of natural and irradiated diamonds, Proc. R. Soc. Lond. A 234, 363 (1956).
  15. J. Walker, An optical study of the TR12 and 3H defects in irradiated diamond, J. Phys. C 10, 3031 (1977).
  16. G. Davies, C. Foy, and K. O’Donnell, The TR12 vibronic band in diamond, J. Phys. C 14, 4153 (1981).
  17. L. Allers, A. T. Collins, and J. Hiscock, The annealing of interstitial-related optical centres in type II natural and CVD diamond, Diam. Relat. Mater. 7, 228 (1998).
  18. B. Naydenov, R. Kolesov, A. Batalov, J. Meijer, S. Pezzagna, D. Rogalla, F. Jelezko, and J. Wrachtrup, Engineering single photon emitters by ion implantation in diamond, Appl. Phys. Lett. 95, 181109 (2009).
  19. S. P. Turaga, H. Jin, E. J. Teo, and A. A. Bettiol, Cross-sectional hyperspectral imaging of proton implanted diamond, Appl. Phys. Lett. 115, 021904 (2019).
  20. X. Chai, H. Liang, C. Yang, V. X. Ho, E. J. Teo, Z. Pastuovic, and A. Bettiol, High sensitivity spin defects in carbon implanted diamond, Adv. Opt. Mater. 13, 2500397 (2025).
  21. G. Davies, Properties and Growth of Diamond, EMIS Datareviews Series (INSPEC, the Institution of Electrical Engineers, London, 1994).
  22. M. Newton, B. Campbell, D. Twitchen, J. Baker, and T. Anthony, Recombination-enhanced diffusion of self-interstitial atoms and vacancy–interstitial recombination in diamond, Diam. Relat. Mater. 11, 618 (2002).
  23. S. J. Breuer and P. R. Briddon, Ab initio investigation of the native defects in diamond and self-diffusion, Phys. Rev. B 51, 6984 (1995).
  24. J. P. Goss, B. J. Coomer, R. Jones, C. J. Fall, P. R. Briddon, and S. Öberg, Extended defects in diamond: The interstitial platelet, Phys. Rev. B 67, 165208 (2003).
  25. A. Gali, Ab initio theory of the nitrogen-vacancy center in diamond, Nanophotonics 8, 1907 (2018).
  26. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  27. J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
  28. J. Bernholc, A. Antonelli, T. M. Del Sole, Y. Bar-Yam, and S. T. Pantelides, Mechanism of self-diffusion in diamond, Phys. Rev. Lett. 61, 2689 (1988).
  29. J. P. Goss, B. J. Coomer, R. Jones, C. J. Fall, C. D. Latham, P. R. Briddon, and S. Öberg, Small aggregates of interstitials and models for platelets in diamond, J. Phys.: Condens. Matter 12, 10257 (2000).
  30. J. Goss, B. Coomer, R. Jones, T. Shaw, P. Briddon, and S. Öberg, Interstitial aggregates in diamond, Diam. Relat. Mater. 10, 434 (2001) .
  31. J. P. Goss, B. J. Coomer, R. Jones, T. D. Shaw, P. R. Briddon, M. Rayson, and S. Öberg, Self-interstitial aggregation in diamond, Phys. Rev. B 63, 195208 (2001).
  32. F. Colasuonno, F. S. Gentile, W. Mackrodt, A. M. Ferrari, A. Platonenko, and R. Dovesi, Interstitial defects in diamond: A quantum mechanical simulation of their EPR constants and vibrational spectra, J. Chem. Phys. 153, 024119 (2020).
  33. A. Komarovskikh, DFT investigation of 100-split interstitial paramagnetic centers in diamond, Diam. Relat. Mater. 146, 111235 (2024).
  34. S. Salustro, Y. Nöel, C. M. Zicovich-Wilson, P. Olivero, and R. Dovesi, The V + I defects in diamond: An ab initio investigation of the electronic structure, of the Raman and IR spectra, and of their possible recombination, J. Chem. Phys. 145, 184701 (2016).
  35. A. Mainwood, A. T. Collins, and P. Woad, Isotope dependence of the frequency of localized vibrational modes in diamond, in Defects in Semiconductors 17, Materials Science Forum (Trans Tech Publications Ltd., Aedermannsdorf, Switzerland, 1993), Vol. 143, pp. 29–34.
  36. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  37. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  38. J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber, and J. G. Ángyán, Screened hybrid density functionals applied to solids, J. Chem. Phys. 124, 154709 (2006).
  39. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
  40. Z. Fan, Z. Zeng, C. Zhang, Y. Wang, K. Song, H. Dong, Y. Chen, and T. Ala-Nissila, Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport, Phys. Rev. B 104, 104309 (2021).
  41. P. Erhart and K. Albe, Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide, Phys. Rev. B 71, 035211 (2005).
  42. Z. Fan, Y. Wang, P. Ying, K. Song, J. Wang, Y. Wang, Z. Zeng, K. Xu, E. Lindgren, J. M. Rahm, A. J. Gabourie, J. Liu, H. Dong, J. Wu, Y. Chen, Z. Zhong, J. Sun, P. Erhart, Y. Su, and T. Ala-Nissila, GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
  43. Y. Wang, Z. Fan, P. Qian, M. A. Caro, and T. Ala-Nissila, Density dependence of thermal conductivity in nanoporous and amorphous carbon with machine-learned molecular dynamics, Phys. Rev. B 111, 094205 (2025).
  44. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81, 3684 (1984).
  45. J. E. Northrup, R. Di Felice, and J. Neugebauer, Energetics of H and NH2 on GaN(101¯0) and implications for the origin of nanopipe defects, Phys. Rev. B 56, R4325 (1997).
  46. C. Freysoldt and J. Neugebauer, First-principles calculations for charged defects at surfaces, interfaces, and two-dimensional materials in the presence of electric fields, Phys. Rev. B 97, 205425 (2018).
  47. R. Nelson, C. Ertural, J. George, V. L. Deringer, G. Hautier, and R. Dronskowski, LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory, J. Comput. Chem. 41, 1931 (2020).
  48. K. Huang and A. Rhys, Theory of light absorption and non-radiative transitions in F-centres, Proc. R. Soc. Lond. A 204, 406 (1950).
  49. A. Alkauskas, B. B. Buckley, D. D. Awschalom, and C. G. V. de Walle, First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centres, New J. Phys. 16, 073026 (2014).
  50. A. Gali, E. Janzén, P. Deák, G. Kresse, and E. Kaxiras, Theory of spin-conserving excitation of the N−V− center in diamond, Phys. Rev. Lett. 103, 186404 (2009).
  51. U. von Barth and L. Hedin, A local exchange-correlation potential for the spin polarized case. I, J. Phys. C 5, 1629 (1972).
  52. D. C. Hunt, D. J. Twitchen, M. E. Newton, J. M. Baker, T. R. Anthony, W. F. Banholzer, and S. S. Vagarali, Identification of the neutral carbon 〈100〉-split interstitial in diamond, Phys. Rev. B 61, 3863 (2000).
  53. C. Weigel, D. Peak, J. W. Corbett, G. D. Watkins, and R. P. Messmer, Carbon interstitial in the diamond lattice, Phys. Rev. B 8, 2906 (1973).
  54. D. J. Twitchen, M. E. Newton, J. M. Baker, O. D. Tucker, T. R. Anthony, and W. F. Banholzer, Electron-paramagnetic-resonance measurements on the di-〈001〉-split interstitial center (R1) in diamond, Phys. Rev. B 54, 6988 (1996).
  55. B. Coomer, J. Goss, R. Jones, S. Öberg, and P. Briddon, Interstitial aggregates and a new model for the I1/W optical centre in silicon, Physica B 273–274, 505 (1999).
  56. R. Jones, T. Eberlein, N. Pinho, B. Coomer, J. Goss, P. Briddon, and S. Öberg, Self-interstitial clusters in silicon, Nucl. Instrum. Methods Phys. Res. Sect. B 186, 10 (2002).
  57. P. J. Fallon, L. M. Brown, J. C. Barry, and J. Bruley, Nitrogen determination and characterization in natural diamond platelets, Philos. Mag. A 72, 21 (1995).
  58. A. L. Görne and R. Dronskowski, Covalent bonding versus total energy: On the attainability of certain predicted low-energy carbon allotropes, Carbon 148, 151 (2019).
  59. G. Henkelman, A. Arnaldsson, and H. Jónsson, A fast and robust algorithm for Bader decomposition of charge density, Comput. Mater. Sci. 36, 354 (2006).
  60. S. Prawer, K. Nugent, and D. Jamieson, The Raman spectrum of amorphous diamond, Diam. Relat. Mater. 7, 106 (1998).
  61. A. A. El-Azhary and H. U. Suter, Comparison between optimized geometries and vibrational frequencies calculated by the DFT methods, J. Phys. Chem. 100, 15056 (1996).
  62. G. P. Srivastava, The Physics of Phonons, 2nd ed. (CRC Press, Boca Raton, FL, 2022).
  63. T. Shimanouchi et al., Tables of Molecular Vibrational Frequencies (U.S. Government Printing Office, Washington, DC, 1973).
  64. D. Twitchen, M. Newton, J. Baker, W. Banholzer, and T. Anthony, Optical spin polarization in the di-〈001〉-split interstitial (R1) centre in diamond, Diam. Relat. Mater. 8, 1101 (1999).
  65. J. Steeds, T. Davis, S. Charles, J. Hayes, and J. Butler, 3H luminescence in electron-irradiated diamond samples and its relationship to self-interstitials, Diam. Relat. Mater. 8, 1847 (1999).
  66. J. Gräfenstein, E. Kraka, M. Filatov, and D. Cremer, Can unrestricted density-functional theory describe open shell singlet biradicals? Int. J. Mol. Sci. 3, 360 (2002).
  67. G. Thiering and A. Gali, Complexes of silicon, vacancy, and hydrogen in diamond: A density functional study, Phys. Rev. B 92, 165203 (2015).
  68. A. V. Ivanov, Y. L. A. Schmerwitz, G. Levi, and H. Jónsson, Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations, SciPost Phys. 15, 009 (2023).
  69. N. Ghafari Cherati, I. Abdolhosseini Sarsari, A. Hashemi, and T. Ala-Nissila, Boron isotope effects on Raman scattering in bulk BN, BP, and BAs: A density functional theory study, Phys. Rev. B 111, 205204 (2025).
  70. I. Vlasov, V. Ralchenko, and E. Goovaerts, Laser-induced transformation of 3H defects in diamond, Phys. Status Solidi A 193, 489 (2002).
  71. N. Ghafari Cherati, From mono- to hexa-interstitials: Computational insights into carbon defects in diamond (ARP, 2026).

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Phys. Rev. Research 8, 023088– Published 29 April, 2026
  • Received 9 December 2025
  • Accepted 23 March 2026
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