## 3 Results and Discussion
### Raman Spectra of Neutron-Irradiated Diamonds
When comparing the level of radiation damage of neutron-irradiated diamonds and helium-implanted, it was taken into account that diamonds with a total helium dose of \(0.5\times 10^{17}\) cm\({}^{-2}\) recovered their crystal structure during high-temperature annealing. As can be seen in Figure 2, the position of maximum of \"1640\" band and the ratio of its amplitude to the amplitude of the boson peak can serve as good indicators of exceeding the critical level of radiation damage to diamond. It is important to note that both parameters in Figure 2 in the Raman spectra of diamonds implanted with helium ions at doses of \(1.0\times 10^{17}\) and \(2.5\times 10^{17}\) cm\({}^{-2}\) practically did not change during the subsequent annealing at temperatures at least to 500 \({}^{\circ}\)C until graphitization processes (appearance of the D band in the Raman spectra) of diamond implanted with helium ions with dose of \(2.5\times 10^{17}\) cm\({}^{-2}\) began. This indicates the possibility of using the dependences in Figure 2 for the non-destructive determination of the critical damage of diamonds in the case of their moderate heating during irradiation. The transformations of the Raman spectra during successive annealings (1 h at each temperature) were studied in order to confirm that the level of diamond radiation damage remains below the critical level under irradiation with fast neutrons with fluence of \(5\times 10^{20}\) cm\({}^{-2}\) (Figure 3). As the annealing temperature rises, the diamond peak is restored, and the bands are narrowed and shifted towards higher frequencies. The transformations of the \"1640\" band are of particular interest. This band has an asymmetric shape; after annealing at temperatures above 800 \({}^{\circ}\)C, several separate bands are spectrally resolved in it (as was observed in [55] in the Raman spectra of diamonds with a lower level of radiation damage), decreasing to the background level after annealing at temperatures above 1000 \({}^{\circ}\)C (Figure 3). The intensity of the two-phonon Raman band (2800-3500 cm\({}^{-1}\)) also significantly decreases after annealing at temperatures above 1000 \({}^{\circ}\)C (Figures 3 and 4). The spectral shape of the two-phonon Raman band for neutron-irradiated diamonds differs significantly both from the same spectrum for undamaged diamond with a maximum near 2335 cm\({}^{-1}\)[56], and from the spectra for a wide class of sp\({}^{2}\)-carbon materials, which dominate the band with a maximum near 2685 cm\({}^{-1}\)[79]. For example, the Raman spectrum of HOPG, treated graphite that displays the highest degree of three-dimensional ordering, consists of two main bands observed at 1581 and 2687 cm\({}^{-1}\), denoted as the G band and 2D (or G') band, respectively [80; 81]. The 2D band corresponds to the second-order Raman scattering of an in-plane transverse optical (TO) mode close to the Brillouin zone boundary \(K\) point [82]. Decomposition of the \"1640\" band into Lorentz contours (Figure 4) showed that it consists of at least three components with maxima near 1465, 1530, and 1620 cm\({}^{-1}\), and the four main components of the second-order band are presumably overtones of the \"1640\" band components with frequencies approximately equal to twice the first-order frequencies (2925, 3050 and 3230 cm\({}^{-1}\), respectively) and a combination of the 1530 + 1620 cm\({}^{-1}\) (\(\approx\) 3135 cm\({}^{-1}\)) components. In this case, it should be kept in mind that the lattice parameter of neutron-irradiated crystals is increased compared to unirradiated diamond [48; 74], which causes a shift of the bands in the Raman spectra to the low-frequency region [49; 54; 55; 67]. Thus, the data of Raman spectroscopy indicate that the level of radiation damage in natural diamonds irradiated with fast neutrons (\(F\) = 5 \(\times\) 10\({}^{20}\) cm\({}^{-2}\)) is below the critical value.