## 3 Results and Discussion
### Raman Spectra of Neutron-Irradiated Diamonds
At the same time, the intensity of a broad band of unidentified nature with a maximum near 720 cm\({}^{-1}\) increases (Figure 1). It is possible that the band at 720 cm\({}^{-1}\) is associated with a feature of the vibrational density of states activated by the disorder of the sp\({}^{2}\) phase [69]. The position, relative amplitude, and FWHM of the band around 1600-1640 cm\({}^{-1}\) are most sensitive to the neutron fluence (Figure 1). As the neutron fluence increases from 3 \(\times\) 10\({}^{18}\) to 5 \(\times\) 10\({}^{20}\) cm\({}^{-2}\), the relative intensity of this band increases significantly, and its maximum shifts to low frequencies up to 1574 cm\({}^{-1}\) (Figures 1 and 2). The position of the \"1640\" band is higher than the graphitic mode at 1580 cm\({}^{-1}\) (G peak) [70], which is doubly degenerate (TO and LO) phonon mode (\(E_{2g}\) symmetry) at the center of the Brillouin zone. The nature of the \"1640\" band in diamonds with a damage level below the critical level is complex. The measurements were performed on ion-implanted and fast neutron-irradiated diamonds [55], and the \"1640\" band consists of several peaks, which shift to higher frequencies and become narrower with decreasing in the radiation damage level. The decomposition of the \"1640\" band showed that it consists of at least six Gaussian peaks (FWHM of 6-10 cm\({}^{-1}\)), which shift to lower frequencies and become wider with increasing in the radiation damage level [55]. These peaks appear to refer to various irradiation-induced defects. The observed sharpness of the peaks indicates that they originate from well-defined local rather than extended defects. As the level of radiation damage increases, the concentration of defects of this type and tensile stresses increase, and their structure can change, which leads to a low-frequency shift and broadening of the corresponding bands in the Raman spectra (Figures 1 and 2). Figure 2: Position (left axis) of the “1640” band and ratio “1640”-to-boson peaks (right axis) in Raman spectra of natural diamonds irradiated with fast neutrons or He-implanted as functions of radiation damage. Dashed lines are guides to eyes. Yellow circles show the position of the “1640” band and ratio “1640”-to-boson peaks corresponding to the critical level of radiation damage of diamond. Multiple-energy implantation of helium ions makes it possible to receive the uniform distribution of radiation defects in ion-implanted areas in diamonds, including those with a level above the critical level [62] (two upper spectra in Figure 1). Radiation damage to diamonds above the critical level abruptly changes the mechanical and physicochemical properties of diamond [62], while the Raman spectra change almost monotonously. The features associated with phonon confinement in diamond disappear in them [13], and the maximum of the most intense band shifts from 1574 cm\({}^{-1}\) (at \(F\) = 5 \(\times\) 10\({}^{20}\) cm\({}^{-2}\)) to 1567 and 1542 cm\({}^{-1}\) in the spectra of natural diamonds implanted with helium ions with a total dose of 1 \(\times\) 10\({}^{17}\) and 2.5 \(\times\) 10\({}^{17}\) cm\({}^{-2}\), respectively [62]. Radiation damage of diamonds during multiple-energy helium implantation [62] with total dose of 1 \(\times\) 10\({}^{17}\) cm\({}^{-2}\) approximately corresponds to the degree of disorder achieved when they are irradiated with fast neutrons [52] with fluence of 1 \(\times\) 10\({}^{21}\) cm\({}^{-2}\). Thus, the intensity and position of the maximum of the \"1640\" band can serve as an indicator of the degree of radiation damage to the diamond. The selection for magnetic measurements of natural diamond grains irradiated with fast neutrons was carried out according to Raman scattering data on the basis of the intensity criterion and the spectral position of the \"1640\" band (see Figure 2), i.e., having the highest subcritical level of radiation damage.