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

TL;DR

This work presents a comprehensive first-principles survey of carbon self-interstitial defects in diamond, extending from mono- to hexa-interstitial clusters. Using a multiscale workflow that combines Frenkel-pair generation, neural-network and empirical potential pre-optimization, and hybrid functional DFT, the authors map structural, electronic, and vibrational properties of all viable interstitial configurations. They find a strong thermodynamic drive toward aggregation, with the tetra-interstitial platelet emerging as a particularly stable motif, and identify two distinct electronic classes: some defects host in-gap states and multiple charge states, while tri- and tetra-interstitials are electronically silent. Importantly, none of the lowest-energy neutral interstitials reproduces the two isolated in-gap states required to explain the TR12 center, indicating that TR12 is unlikely to arise from neutral carbon self-interstitial clusters. The vibrational fingerprints, especially high-frequency IR-active modes localized on defect bonds, offer practical signatures for experimental identification and help establish a robust framework for defect engineering in diamond.

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. 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.

Figures (5)

• Figure 1: Optimized geometries of carbon self-interstitial configurations, ordered by increasing energy, together with their corresponding structural symmetries. Panels: $\mathrm{C}^{a}_{\mathrm{1i}}$ and $\mathrm{C}^{b}_{\mathrm{1i}}$ mono-carbon interstitials; $\mathrm{C}^{a}_{\mathrm{2i}}$ - $\mathrm{C}^{c}_{\mathrm{2i}}$ di-carbon; $\mathrm{C}^{a}_{\mathrm{3i}}$ - $\mathrm{C}^{e}_{\mathrm{3i}}$ tri-carbon; $\mathrm{C}^{a}_{\mathrm{4i}}$ and $\mathrm{C}^{b}_{\mathrm{4i}}$ tetra-carbon; $\mathrm{C}^{a}_{\mathrm{5i}}$ and $\mathrm{C}^{b}_{\mathrm{5i}}$ penta-carbon; and $\mathrm{C}^{a}_{\mathrm{6i}}$ and $\mathrm{C}^{b}_{\mathrm{6i}}$ hexa-carbon.
• Figure 2: The integrated crystal orbital Hamilton population (ICOHP) values for the most stable of each interstitial defect versus their bond lengths. Each data point represents one C$-$C bond.
• Figure 3: Formation energy of the interstitial defects depicted in Fig. \ref{['fig:geo_inter']} as a function of the position of the Fermi level. The valence level energy is aligned to zero for the sake of simplicity. The conduction level energy is set at 5.4 eV.
• Figure 4: (a) Electronic structure for the ground states of the neutral defects using HSE06 functional. Kohn-Sham levels are represented by spin-up ($\uparrow$) and spin-down ($\downarrow$). The valence band (VB) and conduction band (CB) are depicted in brown and cream, respectively. (b) Representation of Kohn-Sham orbitals of the relevant states. The light cyan and yellow lobes exhibit negative and positive isovalues. The isosurface absolute value is set to $7 \times 10^{-7}$ Å$^{-3}$.
• Figure 5: (a) First-order Raman spectra for defect complexes $\mathrm{C}^{a}_{\mathrm{1i}}$ to $\mathrm{C}^{a}_{\mathrm{6i}}$. Pentagram symbols mark Raman-active modes that are predominantly localized on the defect centers. Each spectrum is normalized to its own maximum (arbitrary units). The black line shows the contribution of the defect atoms to the total spectrum, which are eligible in Raman cases. (b) Infrared (IR) spectra of the corresponding defects, where pronounced defect-localized modes are numbered and visualized in (c). (c) Atomic displacement patterns of the selected IR-active modes, where only the defect atoms are active. Red arrows indicate the direction of atomic motion, and their lengths are scaled by the displacement magnitude.