Magnetic resonance tracking of fluorescent nanodiamond fabrication

3.1.1. General view spectra.

Figure 2 shows the raw (non-processed) experimental EPR spectra of all samples under study recorded within the field scan range of 1 T at incident microwave power P_MW = 20 mW and 100 kHz magnetic field modulation amplitude A_mod = 1 mT. These spectra are the typical EPR signatures of each sample. In general, each spectrum of non-irradiated samples (both intact and milled) consists of some broad line(s) with g_eff > 2.00 and intense narrow lines within the region of g = 2.00. Irradiation/annealing adds additional low intense spectral features in the half-field region g = 4 to these lines, as well as satellite lines (marked by arrows in figure 2) symmetrically located on both sides of the intense g = 2.00 lines. Each line (group of lines) was further recorded separately at the experimental setup, providing the best spectral resolution and signal-to-noise ratio available. It should be noted that all of the EPR spectra and spectra parameters found for the coarser fraction of the FND sample (cFND) practically repeat the corresponding spectra and parameters of its precursor FND, except for the increased content of magnetic impurities. Thus, hereinafter these spectra and their description will be omitted from the experimental section. On the other hand, tables 2 and S1 in the supplemental material (stacks.iop.org/JPhysD/48/155302) also include data on cFND samples.

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Table 2. Concentrations of EPR active defects in the diamond samples under study.

Sample	Particle size (nm)	Concentration of S = 1/2 defects NS = 1/2 (spins/g)a	Concentration of triplet NV− defects NNV− (spins/g)a	Relative concentration of magnetic impurities Nimp (arb. units/mg)b
MD	150  ×  103	4.9  ×  1018	≈0	41c
FMD	150  ×  103	3.6  ×  1018	5.4  ×  1017	483
ND	<100	8.8  ×  1018	≈0	10
FND	<100	8.1  ×  1018	3.6  ×  1017	3
cFND	<100	8.9  ×  1018	3.8  ×  1017	7
fFND	<20	1.6  ×  1019	5.4  ×  1016	2

^aErrors in determination of N_S, N_NV⁻ do not exceed ±15%. ^bError in determination of N_imp does not exceed ±30%. ^cAveraged over the three batches.

After recent EPR studies on diamond powders [22, 23, 26], the following attributions of the features observed can be made:

• (a)  
  The intense EPR lines in the region of g = 2.00 are attributed to the primary paramagnetic defects with S = 1/2;
• (b)  
  The broad EPR lines with g > 2.00 are attributed to para- and ferro-magnetic impurities (probably surface weakly-bonded adsorbates) contained in the intact initial sample or appearing/disappearing during irradiation treatment, annealing, milling, and purification. Doubly integrated intensity of these lines (DI) indicates the total amount of magnetic impurities in a diamond sample. The impurity content in starting MD samples was found to be strongly inhomogeneous and varies several times from batch to batch. The relative concentrations of magnetic impurities (in arbitrary units per unit weight) are listed in table 2;
• (c)  
  The EPR lines in the half-field (HF) region (g = 4) appearing in all of the samples passed through high-energy electron irradiation and subsequent annealing. Following [22, 23], these lines are attributed to 'forbidden' transitions in the EPR spectra of triplet (S = 1) paramagnetic centers, like NV⁻ (g = 4.26) and the multi-vacancies (g = 4.00);
• (d)  
  The satellite lines observed aside of intense g = 2.00 lines and separated by ~100 mT and ~200 mT are attributed to 'allowed' transitions in EPR spectra of triplet NV⁻ centers [23].

3.1.2. EPR of primary paramagnetic defects with S = 1/2.

The most intense EPR signal in the initial sample MD (figure 3(a), black trace) demonstrates a well-resolved polycrystalline hyperfine pattern. This hyperfine pattern originates in the paramagnetic centers coming from a single unpaired electron anisotropically interacting with the ¹⁴N nucleus (I = 1) in diamond, the so-called P1 (or N0) [27]. The EPR parameters determined for these P1 centers by simulation are g_iso = 2.0024(2), A_zz = 4.06(2) mT, A_xx = A_yy = 2.91(2) mT, individual line width ΔH_pp^Lorentz = 0.12 mT. The total concentration of paramagnetic centers N_{S = 1/2} in MD is estimated as 4.9  ×  10¹⁸ spins/g (within 15% experimental error, see table 2)⁶. The EPR spectrum of the ND sample, obtained by milling of MD, results in a similarly complicated EPR signal (figure 3(a) green trace) consisting of the same two independent unlike components which saturate at different microwave power levels (an example of the typical decomposition of such a signal may be found in figure 2(d) of [26]). At low microwave power P_MW (P_MW ≤ 200 μW), when no component is saturated, the experimental spectrum (figure 3(a), green trace) is a superposition of two intense signals: the signal of the P1 centers and a singlet Lorentzian line, which overlaps with the central transition of the P1 spectrum. The singlet line has the same (unresolved within the experimental error) g-factor, line width ΔH_pp ~ 0.9 mT, and its DI is ~50% of the total signal intensity, which corresponds to N_{S = 1/2} = 8.8  ×  10¹⁸ spins/g. As is clearly seen in figure 3(a), the amount of observable P1 centers in ND remains practically the same as in the initial MD. Thus, the increase in the total amount of S = 1/2 defects is due to the new Lorentzian signal attributed to dangling bonds in diamond edges [26]. Figure 3(b) illustrates the EPR spectrum after high-energy electron irradiation and subsequent annealing of MD. The EPR spectrum of the fluorescent FMD sample (red trace in figure 3(b)) demonstrates a noticeable reduction of the P1 signal (N_{S = 1/2} = 3.6  ×  10¹⁸ spins/g) and its broadening (ΔH_pp^Lorentz = 0.2 mT), in comparison with the spectrum of starting MD (figure 3(b), black trace). Figure 3(c) illustrates changes in the EPR spectrum due to milling of the fluorescent FMD sample. The milled fluorescent FND sample shows (figure 3(c), blue trace) a significant increase of the surface-originated dangling bond signal evidenced by signal broadening ΔH_pp ~ 1 mT (by WIN-SimFonia simulation), together with the newly appearing relatively narrow (ΔH_pp = 0.23 mT) Lorentzian-like line contributing to ~70% of the total signal intensity. The latter corresponds to N_{S = 1/2} = 8.1  ×  10¹⁸ spins/g. Extraction of the fine fraction from the FND sample leads to a drastic decrease of the low- and high-field hyperfine components of the P1 signal in the EPR spectrum of fFND (figure 3(d) magenta and purple traces). Thus, the spectrum of the fFND sample represents the superposition of two Lorentzian lines: a relatively broad line with ΔH_pp ~1.1 mT (~80% of total intensity) and a narrow one with g = 2.0026(2) and ΔH_pp ~0.3 mT. The total concentration of S = 1/2 spins in fFND shows a twofold increase in comparison with its precursor FND (N_{S = 1/2} = 1.6  ×  10¹⁹ spins/g). Data on electron relaxation found for both P1 and dangling bond components show a reduction of T_SLe in the result of any treatment of the initial MD sample whereas the T_SSe values remain quite short and are practically unchanged. The spin-lattice relaxation times of both types of defects are strongly affected by milling and depend on the mean particle size of the resulting product obtained by fractionation. For further detail see the supplemental materials (stacks.iop.org/JPhysD/48/155302).

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3.1.3. EPR spectra in the HF region (g = 4).

The initial micron sized sample MD shows no signals within the HF region. The same is correct for the milled sample ND—see the overlapping black and green traces in figure 4. On the other hand, irradiated and annealed MD, as well as its milled derivatives, show intensive characteristic signals with g = 4.26(1) in that region—see figure 4(a), red trace. The spectra of FMD and FND also show a weak line with g = 4.19(1)⁷. Milling of the FMD sample to FND causes a ~30% reduction of the characteristic g = 4.26 signal, as well as smoothening of the quasi-crystalline features—see figures 4(a) and (b), blue traces. The coarse fraction of the FND sample (cFND) provides the same (within the experimental error) HF signals (not shown). The fine fraction of the FND sample (fFND) shows a further considerable (about an order of magnitude) reduction of the g = 4.26 signal, the practical disappearance of g = 4.19 signal and all quasi-crystalline features, and the rise of the new signal with g = 4.00(1), in which the intensity at those partially saturated excitation conditions becomes comparable with the intensity of the g = 4.26 signal—see figures 4(a) and (b), magenta trace. Unfortunately, the low signal-to-noise ratios for both HF signals in fFND do not allow a reliable evaluation of the electron relaxation times. Saturation dependencies measured for FMD and FND coincide and provide estimated values T_SLe ~ 10⁻⁵ s and T_SSe ~ 10⁻⁸ s. Figure 5(b) shows HF EPR spectra of fluorescent diamond powders FMD, FND, and fFND recorded at relatively low P_MW = 2 mW power. Comparing the spectrum of fFND (figure 5(b), magenta trace) with the corresponding spectrum in figure 4(b) recorded at tenfold P_MW reveals that the g = 4.26 signal saturates at a lower P_MW than the g = 4.00 one signal, indicating a longer T_SLe for defects responsible for the g = 4.26 signal.

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3.1.4. EPR spectra of satellite lines.

Low intensity satellite lines are observed only in the irradiated/annealed FMD sample and its derivatives (FND, cFND and fFND). Neither the initial MD nor the milled ND samples show any EPR lines in the corresponding magnetic field regions. The black traces in figure 5(a) show the zoomed satellite lines in the EPR spectra of FMD, which are recorded at low P_MW (intense EPR signals in the g = 2.00 region are not plotted here). The red traces in figure 5(a) represent the simulated polycrystalline spectrum of triplet (S = 1) paramagnetic centers obtained using WIN-SimFonia software and the following spin-Hamiltonian (SH) parameters: ΔH_pp^Lorentz = 1 mT; g_iso = 2.003 and zero field splitting parameters D = 0.0950 cm⁻¹ and E = 0.0003 cm⁻¹. Figure 6(c) demonstrates the evolution of satellite lines in the process of milling and further fractionation of the FMD sample. Comparison of the same evolution in the HF g = 4.26 lines (figure 5(b)) with the corresponding satellite lines (figure 5(c)) reveals that upon milling, and especially the extraction of the fine fraction, the reduction of the peak-to-peak intensities (and, respectively, signal-to-noise ratios) of the satellite lines is more pronounced than that of the HF lines.

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RT ¹³C spectra ((stacks.iop.org/JPhysD/48/155302), figure S4(a)) reveal symmetric narrow singlet lines with chemical shift 35 ppm characteristic of sp³ carbons of diamond [28]. The sample treatment causes a decrease in the line width, an increase in spin-spin relaxation time T_2n(¹³C), and a shortening of the ¹³C NMR spin-lattice relaxation times: T_1n(¹³C) vary from 98 to 6.7 s ((stacks.iop.org/JPhysD/48/155302), figure S4(b), table S1), which correlates with the increase in the density of paramagnetic defects [28]. This correlation as well as the stretched exponential character of the relaxation are attributed to the interaction of nuclear spins with paramagnetic defects, both inherent P1 and processing-driven dangling bonds detected by EPR.

RT ¹H NMR measurements reveal a noticeable difference in the proton spectra within this series of samples. While initial larger particle size samples MD and irradiated/annealed FMD show no observable proton signal, the milled ND sample (figure S4(c) and table S1) shows a relatively broad line at 8.6 kHz (stacks.iop.org/JPhysD/48/155302). FND, cFND, and fFND samples reveal narrow symmetric singlets ((stacks.iop.org/JPhysD/48/155302), figure S4(c)), which is characteristic of mobile water molecules adsorbed on the nanodiamond surface [28]. More details on ¹³C and ¹H NMR spectra and relaxation in the studied samples can be found in the supplemental material (stacks.iop.org/JPhysD/48/155302).

EPR data allow the direct tracking of the presence of magnetic contaminations in polycrystalline diamond samples. The initial commercial samples of MD demonstrate a moderate level of magnetic (both para- and ferro-magnetic) impurities (see figure 2 and table 1). These contaminations originate most probably from the HPHT synthesis. The irradiation/annealing process introduces additional magnetic contamination. Thus, the total intensity of the magnetic signal per unit mass in the fluorescent FMD sample is an order of magnitude larger than the same in the initial sample. The presence of a significant amount of ferromagnetic impurities is sufficient to explain both the broadening of the ¹³C NMR line and the shortening of the ¹³C spin-lattice relaxation time (see supplemental material (stacks.iop.org/JPhysD/48/155302), figures S4(a) and (b)). In contrast, the total amount of the main intrinsic EPR spectrum broadening agent—inherent paramagnetic defects—shows a ≈30% reduction in the FMD sample in comparison with the initial MD sample. It is reasonable to suppose that these contaminations come from the irradiation accessories or from the annealing chamber. On the other hand, diamond samples which passed through milling and subsequent fractionation processes (ND, FND, cFND and fFND, respectively) show quite low contamination levels (figure 2 and table 2), which is in a good agreement with the corresponding treatments, including special decontamination procedures in which metallic impurities are removed, among others (see table 1 and supplemental material (stacks.iop.org/JPhysD/48/155302)).

The EPR clearly indicates that the main paramagnetic defect in the initial synthetic sample MD is the P1 center originating from a single isolated substitutional nitrogen [27]. The non-saturated (at P_MW = 2 μW) width of the central Δm_I = 0 hyperfine line ΔH_pp = 0.12(1) mT corresponds to ~100 at. ppm of paramagnetic impurities [29]. This number is in perfect agreement with the total amount of paramagnetic centers estimated by EPR as 4.9  ×  10¹⁸ spins/g. It is worth mentioning here that, according to the manufacturer of the initial MDs, the nitrogen content in these Ib type samples does not exceed 150 at. ppm. This means that most of the nitrogen in the MD takes part in the creation of isolated substitutional defects P1. Of course, P1 is not the only paramagnetic defect in MD: analysis of saturation curves indicates the presence of some carbon-inherited defect like dangling bonds. Moreover, P1 spectra recorded at high incident power (P_MW > 1 mW) reveal an additional weak doublet signal with the splitting between the doublet lines of 3.2 mT (not shown), which saturates at much higher P_MW levels than P1. Strong differences in the saturation curve behavior of hyperfine components as well as estimated relative intensities make the attribution of these lines to the P1 centers associated to naturally abundant ¹⁵N (I = 1/2, ~0.34%) irrelevant. Thus, this doublet indicates the presence of paramagnetic centers of other types than P1 or dangling bonds in these MDs. However, the prevailing intrinsic defect in MD is P1.

Irradiation/annealing treatment does not make new S = 1/2 defects appear, but it does affect the initial P1 signal. Figure 3(b) clearly indicates both the reduction of the amount of P1 centers and an about twofold broadening of P1 center hyperfine lines in the fluorescent FMD sample. The electron spin-lattice relaxation time also drops (figure S4(c), (stacks.iop.org/JPhysD/48/155302)). Moreover, the ¹³C NMR measurements of this sample also shows line broadening and reduction of nuclear spin-lattice relaxation time (figures S5(a) and (b), (stacks.iop.org/JPhysD/48/155302)). It is known that the presence of paramagnetic defects is the main factor affecting electron and nuclear relaxation in diamonds [26, 28, 29]. Thus, the reduction of the number of paramagnetic defects observed in the FMD sample contradicts the broadening of EPR and NMR lines, as well as the shortening of relaxation times found in FMD. It may be suggested that irradiation/annealing changes the structural properties of MDs, directly affecting both nuclear and electron relaxation. The reduction of P1 defects in FMD may be due to the cumulative effect of high-energy irradiation and subsequent high temperature annealing.

Milling affects the basic paramagnetic properties of synthetic MDs much more seriously than irradiation/annealing. Thus, from the EPR spectra of milled ND one may infer that the total amount of S = 1/2 paramagnetic defects increases by almost a factor of two compared to MD (figure 3(a)). Considering that the P1 content remains practically the same, the new dangling bond signal (which was practically not observed in the initial MD sample) becomes the evident feature in the EPR spectrum. In this sample, the amount of dangling bond-type defects is comparable to that of P1. In contrast to the FMD case, these fabrication-driven defects are responsible for shortening EPR and NMR spin-lattice relaxation times. The same is observed for the milled and processed irradiated/annealed sample FND: the total amount of paramagnetic defects here is practically the same as in ND, but since the amount of P1 in its starting FMD sample is lower than in initial non-irradiated MD, the dangling bond signal is the prevailing feature in the EPR spectrum of FND (figure 3(c)). ¹³C nuclear relaxation times in ND, FND and cFND sample are found to be the same within the experimental error, which perfectly corresponds to practically the same densities of main paramagnetic defects in these samples. On the other hand, both FND and cFND demonstrate a noticeable reduction of the electron spin-lattice relaxation in the P1 centers ((stacks.iop.org/JPhysD/48/155302), figure S3(c)). This occurs due to the combined effect of the structural changes that originate in irradiation/annealing (one of the factors affecting line width and relaxation in the ND sample) and the increasing spin-lattice relaxation rates that are due to the new paramagnetic defects induced by milling. The suggested location of the dangling bond defects are at the surface and interface layer of ND particles.

The effect of the milling to fine fractions on paramagnetic defects seems to be more complicated. The total amount of main paramagnetic defects in fFND grows almost twice in comparison with its precursor FND—up to 1.6  ×  10¹⁹ spins/g. However, the analysis of EPR signals line shapes points out some transformations of EPR signals observed in the precursor. On the one hand, the EPR spectrum of fFND (red trace in figure 2(d)) shows subsequent increase of the broad Lorentzian line due to dangling bonds. At the same time, the hyperfine Δm_I = 1 components of the P1 signal, which are found to be practically unchanged after irradiation/annealing and milling (see figure 3(c)) almost disappear in fFND. Only zooming the spectrum (purple trace in figure 3(d)) reveals some traces of these components. Interestingly, the remaining hyperfine P1 components in fFND are not broadened in comparison with the same signals in FND or cFND. Thus, the real decrease of the conventional P1 signal is observed here. On the other hand, a new narrow Lorentzian signal with g = 2.0026(2) and ΔH_pp ~ 0.3 mT emerges in the spectrum. After decomposition into two Lorentzians, we infer that the narrow signal contributes to ~20% of the total DI, which corresponds well with the contribution of the P1 signal into the spectrum of the precursor FND. One may suggest that in the fine fraction, extracted from FND, the characteristic P1 signal transforms into the narrow Lorentzian line, originating from the same P1 defects. Indeed, the P1 defects are intrinsic ones and are located in the bulk of MDs and, most probably, are hardly affected by the milling process. For instance, milling practically does not affect the P1 content (figure 3(c)). It is worth mentioning that this ND sample is the only one containing an enormous (over 1  ×  10¹⁹ spins/g) density of paramagnetic dangling bonds. Thus, both the dipole-dipole and the exchange interactions of the P1 defects with dangling bonds confined in the nanoparticle become the main factor determining the line shape of the EPR signal, as has been recently observed in detonation NDs [22]. In this case the exchange averaging of the hyperfine structure causing the so-called exchange narrowing may form a new signal of the same P1 defects: the narrow Lorentzian line observed in the EPR spectrum of fFND. Following this hypothesis, the residual weak hyperfine lines observed in the EPR spectrum of fFND at higher gain may be due to P1 centers in diamond crystallites of larger sizes (>40 nm), naturally occurring in fine ND powders in small but not vanishing quantities (<0.3 wt. %) (see figure S3(c) for the population mode with smallest sizes, which characterizes isolated single crystallites, (stacks.iop.org/JPhysD/48/155302)). A detailed study of the line shape dependence of P1 polycrystalline EPR spectrum on diamond particle size will be reported elsewhere.

Recent studies [22, 23] allow unambiguous attribution of the HF line with g = 4.26, accompanied by the satellite lines (symmetrically located on both sides of the g = 2.00 transitions and separated by ~100 mT and ~200 mT), to negatively charged triplet (S = 1) nitrogen vacancies NV⁻. This attribution is based on the solid ground of the specific line shape of the polycrystalline EPR spectrum as well as the SH parameters determined both directly from the spectrum and by simulations. Thus, following these signals provides researchers with a reliable tool to track the appearance and evolution of NV⁻ centers, as well as to estimate their content in samples under study. EPR data allow us to conclude that both initial synthetic MD and its milled derivative ND contain no NV⁻ centers traceable by EPR—see the overlapping black and green traces in figure 4. These samples also show no pronounced fingerprints of NV⁻-type photoluminescence. Irradiation/annealing turns the initial MD sample into the fluorescent sample (FMD). This transformation is accompanied by the clear appearance of new features in the EPR spectrum of FMD: a strong narrow (non-saturated line width ΔH_pp = 0.5 mT) HF line with g = 4.26 due to 'forbidden' ΔM_S = 2 transitions in polycrystalline EPR spectrum of NV⁻ centers (red trace in figures 4 and 5(b)) and a set of low- and high-field satellite lines with ΔH_pp ~ 1.5 mT due to 'allowed' ΔM_S = 1 transitions in the same spectrum (figure 5(a) and (c)).

Double integration of the entire NV⁻-related spectrum (i.e. all 'allowed' and 'forbidden' lines excluding the g = 2.00 region of very strong main paramagnetic signals, which in the simulated EPR spectrum of NV⁻ contributes to the total DI less than 10%) provides an estimation of NV⁻ content in FMD as 5.4  ×  10¹⁷ spins/g which, making simple volume/mass calculations, corresponds to ~3  ×  10¹² NV⁻ centers per each 150 μm FMD particle. Milling of fluorescent MDs leads to a weak broadening of all NV⁻-related lines in the EPR spectra of the FND and cFND samples (ΔH_pp = 0.6 mT and 2 mT for the 'forbidden' and 'allowed' line, correspondingly) and about 30% reduction of DI of that characteristic g = 4.26 line (blue trace in figure 5). Following the aforementioned procedure, a double integration of all NV⁻-related lines provides NV⁻ content in FND as 3.6  ×  10¹⁷ spins/g corresponding to ~660 NV⁻ centers per each 100 nm FND particle. Extraction of the fine fraction (the fFND sample, average particle sizes below 20 nm) reveals a more pronounced broadening of EPR lines (magenta traces in figures 5, 6(b) and (c), ΔH_pp = 0.7 mT and ~4 mT for the 'forbidden' and 'allowed' lines) as well as a drastic decrease in the NV⁻ centers content down to 5.4  ×  10¹⁶ spins/g. The latter number corresponds to a single NV⁻ center per 3 ÷ 4 (assuming 15 nm mean size) diamond nanoparticles. It could be suggested that, likewise in the case of the P1 signals described above, the EPR signals of NV⁻ centers observed for the fFND sample originate from single nanocrystallites of larger sizes (>40 nm, like those in FND). However, a significant line broadening of all of the NV⁻-related EPR signals registered in the fFND vote against such a model. Thus, one can suppose that NV⁻ centers in small (size <20 nm) fFND particles are infrequent defects.

It should be noted that changes in DI of the 'forbidden' line agree quite well with the changes in the NV⁻ content obtained by the correct procedure of double integration of the entire NV⁻-related EPR spectrum. Thus, the EPR spectrum of 'forbidden' line in the HF region may be used as a reliable tool for comparative estimations of the NV⁻ content in fluorescent NDs, even in those cases when weak 'allowed' transitions are not (or hardly) observed (see, for instance, [22]).

Let us analyze the evolution of the NV⁻ content in the diamond samples under study. NV⁻ centers do not exist in the non-irradiated samples: both initial and milled ones. The EPR features attributed to NV⁻ appear only in the FMD sample and its pulverized derivatives, i.e. in the samples passed through the corresponding irradiation/annealing treatment. The highest density of NV⁻ is observed in the micron-sized sample FMD. Upon milling to 100 nm (FND, cFND), this density decreases by one third. This means that 30% of NV⁻ defects, most probably located within or closer to the interface layers, were quenched by milling, which is usually accompanied by excessive heating, formation of paramagnetic dangling bonds etc. Other NV⁻ centers in this sample (as well as in the irradiated/annealed FMD sample) are located in the bulk of the diamond particle and, thus, are almost unaffected (not quenched) by the treatment.

The above findings seem to disagree with the fluorescence microscopy observation combined with atomic-force microscopy size measurement [13]. The optical study reports that in the sample analogous to fFND (mean particle size of ~8 nm) ~25% of the particles carry at least one NV color center. Let us point out that the photoluminescence reported in [13] also includes the contribution from the neutral NV⁰ centers. It was recently reported that, due to the larger influence of surface electron traps in smaller particles, the proportion of negatively charged NV⁻ defects, with respect to its neutral counterpart NV⁰, decreases with the size of the ND [15]. These observations were done on isolated FND spincoated on a cover glass. However, in our EPR experiment the inter-particle interactions could also play a role. In order to rule out the effect of inter-particle interactions on the surface electron trapping process, we carried EPR measurements on the diluted cFND:SiO₂ and fFND:SiO₂ samples to allow light to be shed on the effect of inter-particle interactions on the surface electron trapping process. Upon dilution by SiO₂, the NV⁻-related EPR features for both coarser and fine nanoparticles behave exactly in the same manner as the features responsible for the main paramagnetic defects: no changes in SH parameters and line width, just a proportional reduction of the signals intensities. In a case where inter-particle interactions have played a role, one would have observed deviations from the proportional reduction for the fine sample. Such a deviation is not observed and so we can exclude the involvement of inter-particle interactions in the process of surface induced charge state conversion of single NV defects hosted in NDs, which solely comes from surface electron traps.

Extrapolation of the data presented in [15] indicates that in NV containing NDs with sizes smaller than 10 nm, the NV⁰ centers are about 50% of total NV-related defects. It should be noted that, in spite of its spin singlet origin (S = 1/2 ground state) the NV⁰ center is practically EPR silent due to the dynamic Jahn–Teller coupling, which broadens the EPR lines, dramatically reducing detection sensitivity [30]. Therefore, these centers do not contribute to any (especially NV⁻ related) EPR signals. Hence, it may be concluded that just ~12% of the fFND particles carry at least one EPR active NV⁻ center. This estimation is in a good agreement with the EPR findings reported above.

Figure 4(a) clearly shows that, in addition to the characteristic NV⁻-originated g = 4.26 signal, another two HF signals appear during irradiation/annealing and milling of the initial sample. These are the g = 4.19 signal, observed in FMD and coarse ND fractions (FND, cFND), as well as the weak g = 4.00 signal observed in both coarse and fine fractions. In the fine fraction fFND the intensity of the latter signal becomes comparable with the intensity of the g = 4.26 signal—see figure 4(b), magenta trace. Neither the g = 4.19 nor the g = 4.00 lines are accompanied by observable 'allowed' lines—most probably due to the low abundance of these triplet centers. Following the attribution of all narrow HF signals to 'forbidden' ΔM_S = 2 transitions in polycrystalline EPR spectra of some triplet centers [22, 23], one may suggest that the weak additional HF features found in this study belong to other triplet centers with SH parameters differing from those for the NV⁻ defects. One may ascribe the g = 4.19 line to triplet defects with a D-value smaller than that for the NV⁻ center (0.0950 cm⁻¹). Spectra simulations provide that the g = 4.19 position corresponds to D ~ 0.08 cm⁻¹. Detailed study of the irradiation induced centers of this type in other irradiated diamond samples will be reported elsewhere. The same considerations for the g = 4.00 signals provide D ~ 0.03 cm⁻¹. Recently, similar signals were found in HF EPR spectra of NDs manufactured by detonation and other dynamical synthesis techniques [22], and attributed to some triplet defects TR2, which do not relate to atomic nitrogen substitutions in the diamond lattice and are, therefore, caused solely by carbon-inherited defects, namely intrinsic multivacancy defects [22]. Strengthening of the g = 4.00 signals just in the EPR spectra of the fine fraction fFND supports the hypothesis proposed in [22]. Indeed, the fine fraction fFND is characterized by the enormous content of the milling induced singlet paramagnetic defects which, in turn, increases the probability of these defects coupling.

Shames et al [22] reports on thorough but unsuccessful attempts to observe any traces of EPR lines which could be attributed to 'allowed' transitions in EPR spectra of polycrystalline NDs obtained by dynamic synthesis techniques (detonation, laser ablation etc.). On the other hand, characteristic HF signals with g = 4.26 attributed to 'forbidden' transitions in EPR spectra of NV⁻ centers [23] were registered for all of the above mentioned ND samples. It was suggested that some specific broadening of just the 'allowed' lines causes such a puzzling situation [22]. Some speculations on the mechanisms responsible for the disappearance of 'allowed' lines in EPR spectra of NDs have been discussed in this reference. Careful analysis of the data reported in this study promises to shed light on this problem. Figures 6(a)–(c) illustrate changes in EPR parameters of g = 4.26 'forbidden' line and one (low field) of the 'allowed' satellite lines, obtained from the experimental spectra of the diamond series under study (figures 5(b) and (c)). It is found that DI of both 'allowed' and 'forbidden' lines drop down equally on milling—see figure 6(a). On the other hand, as a result of this milling, the peak-to-peak intensity I_pp of the 'forbidden' line undergoes a less dramatic decrease than the same of the 'allowed' line (figure 6(b)). The drop in the 'allowed' line intensity is accompanied by a strong broadening of just this line (figure 6(c)), which correlates with the DI changes found for both lines. Thus, the main reason for the disappearance of EPR lines corresponding to the 'allowed' transitions in EPR spectra of NV⁻ containing NDs is the stronger broadening of the 'allowed' lines in comparison with the broadening affecting the lines attributed to 'forbidden' transitions. Let us speculate on the mechanisms which could be responsible for such a selective broadening. Figure 6(d) presents the g = 4.26 'forbidden' lines and low field 'allowed' ones obtained by XSophe simulation of the polycrystalline EPR spectrum of NV⁻ centers in diamond (SH parameters—in figure caption) as a function of the homogeneous broadening of individual Lorentzian lines. Here it is clearly seen that both lines are broadened in the same manner, providing the same drop in peak intensities. Thus, the origin of the asymmetry in line broadening may be found in the mechanisms responsible for inhomogeneous EPR line broadening in the spectra of a disordered (or partially ordered) system. Among the possible mechanisms of such a disorder one can consider the so-called D-strain—distributed zero field interaction [31] or, in other words, slight differences in zero field splitting parameters in SH of NV⁻ centers in various micro- and nano-crystallites. These differences may be either intrinsic or induced by processing, such as milling or surface treatment. Figure 6(e) shows changes in the above mentioned simulated EPR spectra as a function of D-strain, ΔD, obtained at fixed individual line width ΔH_pp^Lorentz = 0.57 mT. Figure 6(e) shows that appearance of D-strain broadens the 'allowed' line and, correspondingly, decreases its peak intensity more effectively than the 'forbidden' one. By comparing the experimental spectra of figures 6(b) and (c) with those extracted from the simulations, one can find that in the starting irradiated/annealed FMD sample the distributed zero-field splitting is ΔD ~ 0.0010 cm⁻¹.

This is the natural D-strain resulting from irradiation/annealing. Milling induces intensification of the D-strain to ~0.0020 cm⁻¹. However, for smaller nano-particles obtained by fractionation—fFND sample, the D-strain model stops working. Indeed, in spite of an almost threefold broadening (in comparison with the starting FMD sample) of the 'allowed' line, the 'forbidden' line remains quite narrow—see figure 6(c). One can suppose that in small (size <20 nm) nano-particles carrying, in addition to NV⁻ centers, dozens of other paramagnetic centers (like dangling bonds) and other mechanisms of inhomogeneous line broadening take place.

The absence of NMR-detectable proton signals in the initial MD and irradiated/annealed FMD samples undoubtedly indicates that both the surface and bulk of these micro-diamond particles contain bound hydrogen in quantities below the detection threshold of the solid state NMR machine in use. It should be noted that surface of these micron-sized crystallites seems to be hydrophobic and can even contain no detectable water molecules, which usually provide relatively narrow (and, thus, easily observed) ¹H NMR lines. On the other hand, samples which have undergone milling and subsequent processing/fractionation do show well observable ¹H NMR signals, which indicates a modification of their surfaces. Thus, the surfaces of FND, cFND and fFND show clear hydrophilic properties—they adsorb water molecules, which are responsible for the narrow ¹H NMR lines in figure S4(c), (stacks.iop.org/JPhysD/48/155302) (blue and magenta traces, correspondingly) as well as for the single exponential magnetization recovery. This hydrophilic character is likely to come from carboxylic groups produced during the chemical decontamination procedure. The same treatment also produces hydroxyl groups, which together with carboxylic groups are necessary to stabilize aqueous NDs suspension. In contrast to FND, cFND, and fFND, ND displays a broad ¹H NMR line in the sample, indicating the presence of dipole–dipole coupling of proton spins, which means that the surface of this nanodiamond is partially terminated by hydrogen atoms forming rigid hydrocarbon and hydroxyl groups. This ¹H NMR line broadening is characteristic of NDs, in which hydrogen atoms at the surface are irregularly positioned, presumably forming more hydrogenated spots of limited sizes alternating with less hydrogenated or nearly non-hydrogenated zones [28]. Moreover, the width of the ¹H NMR line in the ND sample is found to be dependent on the delay between the echo pulses (τ_d) and decreases with increasing τ_d—see the green and olive traces in figure S4(c), (stacks.iop.org/JPhysD/48/155302). Such a behavior of the NMR spectrum may be described in terms of the superposition of a variety of components showing different widths and T₂. For the long τ_d, the broad components with short T₂ are dephased and are thus not observed in the experiment [32]. The contribution of the long T₂ proton species to the entire NMR signal is relatively small: the long τ_d spectrum (olive trace) in figure S4(c), (stacks.iop.org/JPhysD/48/155302) was recorded at tenfold increased number of coherent acquisitions compared to the spectrum measured with short τ_d. By comparing proton NMR data in the ND and FND samples of the same particle sizes (they passed through the same micronization), one can conclude that the surfaces in these samples are different. We suggest that this difference is due to the FND irradiation/annealing treatment. This treatment somehow reconstructs the surface of the diamond particles, making them more hydrophilic, i.e. with a higher (comparing to ND) content of carboxylic group, and receptive to ambient humidity.