## 3 Results and Discussion
### EDNMR Spectroscopy Analysis  
The significant anisotropy of \(g\)- and \(A\)-tensors and a relatively long transverse relaxation time (T\({}_{2}\) = 3 \(\upmu\)s) of the NO\({}_{3}^{2-}\) radical (see Figure 1a) allows us to carry out angular-selected EDNMR measurements at room temperature in the X-band frequency range. Signals corresponding to the Larmor frequencies of \({}^{31}\)P (\(\pm\)6 MHz) and \({}^{1}\)H (\(\pm\)14.8 MHz) nuclei are shown on the overview spectra at B\({}_{0}\)\(\approx\) 0.34 T (Figure 3). These signals are expected because hydrogen and phosphorus ions are structural elements of the HA and indicate that the studied nitrogen radical is located in the HA crystal lattice. The lack of additional structures (or splitting) for these nuclei indicates an insufficient spectral resolution of the EDNMR method (at least at room temperature in the X-band). The most interesting signals are those observed at v = \(\pm\)47.5 and \(\pm\)95 MHz. Given the theoretical calculations [58,59] for various electron-electron transitions as well as the known values of hyperfine structure \(A\) from EPR measurements (Figure 1a), it follows that these transitions are caused by the anisotropic hyperfine interaction from nitrogen nuclei. Due to the fact that the value of \(A\) exceeds the Larmor frequency of \({}^{14}\)N nuclei (I = 1, v\({}_{\text{Larmor}}\) = 1.04 MHz for B\({}_{0}\)\(\approx\) 0.34 T), this leads to the localization of the EDNMR signal in the range of the half (for single-quantum transitions with \(\Delta\)M\({}_{\text{I}}\) = \(\pm\)1) and whole (for double-quantum transitions with \(\Delta\)M\({}_{\text{I}}\) = \(\pm\)2) values of \(A\). A more detailed analysis of the spectrum at \(\Delta\)v > 0 (M\({}_{\text{I}}\) = \(-\)1) shows an additional splitting for the single-quantum transition exactly localized at the value \(A_{\perp}/2\) (Figure 4). Using the expression for single-quantum transitions [58]:  
\[\Delta\ =\ 2v_{Larmor}\pm 3P \tag{3}\]  
Figure 3: Total EDNMR spectra of HA according to the quantum number M\({}_{\text{I}}\): (a) M\({}_{\text{I}}\) = +1 at B\({}_{0}\) = B\({}_{1}\), (b) M\({}_{\text{I}}\) = \(-\)1 at B\({}_{0}\) = B\({}_{2}\) (see Figure 1a). Figure 2: EPR spectra of the nitrate radical in (a) HA and (b) OCP in the Q-band frequency range at room temperature. where \(\Delta\) is the splitting value of single-quantum transitions, and a choice of the sign \"\(\pm\)\" depends on the quantum number of \(\text{M}_{\text{I}}\) (\"+\" for \(\text{M}_{\text{I}}=-1\) and \"\(-\)\" for \(\text{M}_{\text{I}}=+1\)), we concluded that the observed splitting occurs due to the presence of a quadrupole interaction of the \({}^{14}\)N nuclei with a gradient of crystal field. Assuming that the tensors \(A\) and \(P\) are collinear, the value (and sign) of the quadrupole splitting can be calculated quite easily. Thus, we could establish that the value of quadrupole splitting \(P=1.2\) MHz. Due to the fact that the \(P\) value is comparable to the Larmor frequency of \({}^{14}\)N at \(\text{B}_{0}=340\) mT, splitting in the same orientation for \(\text{M}_{\text{I}}=+1\) is not observed. Additionally, EDNMR measurements were performed for an aluminum-doped hydroxyapatite within the frequency range of the single-quantum transitions. Although the substitution degree by aluminum ions was extremely high (up to 20%), the value of quadrupole splitting was not changed. This means that the local environment of the nitrogen radical, i.e., the electric (crystal) field gradient, does not change significantly. Consequently, aluminum-doped hydroxyapatite up to 20% retains its initial space group.