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arXiv:2512.06167

From Mono- to Hexa-Interstitials: Computational Insights into Carbon Defects in Diamond

Nima Ghafari Cherati, Arsalan Hashemi, Ádám Gali

cond-mat.mtrl-sciquant-phSubmitted Dec 5, 2025• Announced Dec 9, 2025• Revised Mar 12, 2026 (v2)
v1 · Dec 5, 2025v2 · Mar 12, 2026
arXivHTMLPDF

Abstract

We present a comprehensive first-principles investigation of carbon self-interstitial defects in diamond, ranging from mono- to hexa-interstitial complexes. By quantum mechanical 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 1925 cm$^{-1}$, which are strongly IR-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.

Journal reference
Phys. Rev. Research 8, 023088 (2026)
DOI
10.1103/kxgc-k5lq
Comments
18 pages, 8 figures, 2 tables

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Hexagonal diamond, often called lonsdaleite, is an exotic allotrope of carbon, predicted to be harder than cubic (conventional) diamond with a wider bandgap. Due to its pure sp3^33 bonded lattice, it should be expected to host sub-bandgap defect centres (colour centres). Here we perform \textit{ab initio} modeling of nitrogen-vacancy (NV) colour centres in hexagonal diamond nanocrystals; for both the neutral and negatively charged species (NV0^00 and NV−^-−). We identify three distinct configurations for the NV center: two of which are analogous to NV in diamond, and one which is a configuration that can only exist in the hexagonal form. The diamond-like NV systems comprise three symmetry equivalent centers which reside on the same carbon plane, and one defect that is split across two planes and replaces a carbon-carbon bond. There is an additional NV centre where the N and V each have four nearest neighbour carbon atoms. The presence of this latter configuration would provide an unambiguous determination of the hexagonal nature of lonsdaleite. Quantum chemical analysis show all derivatives to be thermochemically stable, and each with their own unique photophysical properties, spectral profiles, and magneto-optical characteristics. By assuming that the ground state properties of the NV−^-− in hexagonal diamond are comparable to those of NV−^-− in cubic diamond, albeit with increased strain, we predict ground state fine structure splitting for two of the centres of 2.74~GHz and 4.56~MHz, compared with 2.87~GHz for cubic diamond. The possibility of optically detected magnetic resonance with NV−^-− in lonsdaleite would provide a new carbon-based quantum sensing system, and an unambiguous method to resolve outstanding issues around the structure of lonsdaleite as hexagonal diamond.
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Abstract We present a high throughput and systematic method for the screening of colour centres in diamond with the aim of searching for and reproducibly creating new optical centres down to the single defect level, potentially of interest for a wide range of diamond-based quantum applications. The screening method presented here should, moreover, help to identify some already indexed defects among hundreds in diamond (Zaitsev 2001 Optical Properties of Diamond (Berlin: Springer)) but also some promising defects of a still unknown nature, such as the recently discovered ST1 centre (Lee et al 2013 Nat. Nanotechnol . 8 487; John et al 2017 New J. Phys . 19 053008). We use ion implantation in a systematic manner to implant several chemical elements. Ion implantation has the advantage of addressing single atoms inside the bulk with defined depth and high lateral resolution, but the disadvantage of producing intrinsic defects. The implanted samples are annealed in vacuum at different temperatures (between 600 °C and 1600 °C with 200 °C steps) and fully characterised at each step in order to follow the evolution of the defects: formation, dissociation, diffusion, re-formation and charge state, at the ensemble level and, if possible, at the single centre level. We review the unavoidable ion implantation defects (such as the GR1 and 3H centres), discuss ion channeling and thermal annealing and estimate the diffusion of the vacancies, nitrogen and hydrogen. We use different characterisation methods best suited for our study (from widefield fluorescence down to sub-diffraction optical imaging of single centres) and discuss reproducibility issues due to diamond and defect inhomogeneities. Nitrogen is also implanted for reference, taking advantage of the considerable knowledge on NV centres as a versatile sensor in order to retrieve or deduce the conditions and local environment in which the different implanted chemical elements are embedded. We show here the preliminary promising results of a long-term study and focus on the elements O, Mg, Ca, F and P from which fluorescent centres were found.
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