Radiation-Induced Stable Radicals in Calcium Phosphates: Results of Multifrequency EPR, EDNMR, ESEEM, and ENDOR Studies

: This article presents the results of a study of radiation-induced defects in various synthetic calcium phosphate (CP) powder materials (hydroxyapatite—HA and octacalcium phosphate—OCP) by electron paramagnetic resonance (EPR) spectroscopy at the X, Q, and W-bands (9, 34, 95 GHz for the microwave frequencies, respectively). Currently, CP materials are widely used in orthopedics and dentistry owing to their high biocompatibility and physico-chemical similarity with human hard tissue. It is shown that in addition to the classical EPR techniques, other experimental approaches such as ELDOR-detected NMR (EDNMR), electron spin echo envelope modulation (ESEEM), and electron-nuclear double resonance (ENDOR) can be used to analyze the electron–nuclear interactions of CP powders. We demonstrated that the value and angular dependence of the quadrupole interaction for 14 N nuclei of a nitrate radical can be determined by the EDNMR method at room temperature. The ESEEM technique has allowed for a rapid analysis of the nuclear environment and estimation of the structural positions of radiation-induced centers in various crystal matrices. ENDOR spectra can provide information about the distribution of the nitrate radicals in the OCP structure.


Introduction
Nowadays, bone diseases, which are mainly caused by infections, defects, tumors, and injuries, are among the most common pathologies in clinical practices. It is certain that these defects require an appropriate bone treatment, without which irreversible consequences up to invalidity can occur. One of the most difficult but effective methods of treatment is surgery, with the subsequent replacement of the damaged area. One of the main aspects of bone treatment is the type and quality of materials used as a base for implants, which will determine the future successful healing of patients. Therefore, the creation and investigation of novel synthesized materials is gaining increasing interest in physics, biology, chemistry, and medicine [1][2][3][4].
Currently, there are a number of suitable materials for bone substitution such as inert metals (titanium-and tantalum-based alloys), polymers (polycaprolactone, cellulose, collagen), and ceramics (bioglass, gypsum, calcium carbonate) [2,5,6]. However, it is considered that calcium phosphate (CP)-based compounds are the most favorable choice behavior/origin of defects and their electron-nuclear interactions with the local ionic environment remain unexplored, requiring additional experimental methods.
One of the analytical, non-destructive tools for the investigation of CPs of both biogenic and synthetic origins is electron paramagnetic resonance (EPR) [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. The increased sensitivity, spectral and temporal resolution, along with the improved stability of modern commercial EPR spectrometers has opened new possibilities in the study of CPs during the last decade, taking a step towards in situ EPR imaging (EPRI) [44]. Pure, non-substituted CPs are EPR-silent. Consequently, conventional EPR can be used for the purity check of CP materials, for example, the presence of metal impurities [31]. A standard way of studying EPR-silent CPs is through the creation of certain types of defects with ionizing radiation such as X-, β-, γ-rays or ultraviolet light, and the investigation of their spectroscopic properties. Several radiation-induced paramagnetic species (anion radicals) located at hydroxyl or phosphate sites have been identified in synthetic HA, depending mainly on the nature of the biogenic materials and synthesis route/treatment of the artificial compounds as well as on the radiation conditions [45][46][47][48][49]. Among them, oxygen radicals O − , trapped atomic hydrogen centers, holes trapped on OH − and PO 2− 4 , carbonate radicals CO − 2 , CO − 3 , CO 3− 3 , and color centers have been observed. In burnt bones, coal-type C-radicals have been identified [41,50]. Besides material characterization, the spectroscopic and relaxation parameters of the observed paramagnetic centers can be used to track the radiation dose in HA-containing dental enamel [41], to follow the processes of calcification [29] and the doping/co-doping of synthetic materials with various ions [35,38]. The effect of diverse amino acids on the local microstructure of calcium-deficient hydroxyapatite was also tracked/confirmed by EPR spectroscopy [51].
As mentioned above, the EPR method is a well-established approach for the study of disordered materials such as CPs. However, we should accept the fact that this method has several limitations (low spectral resolution and technical restrictions) that do not allow us to resolve weak hyperfine interactions. The main problems arise from line broadening and signal overlapping. Therefore, important information about the local nuclear environment remains unexplored. More complicated approaches in hardware and better physical understanding have led to the advancement of magnetic resonance techniques. However, methods based on double resonance techniques for the study of disordered materials are still not used as widely as would be expected. In this article, we will demonstrate that there are a number of interesting techniques, which are targeted to the study of weak hyperfine splittings, allowing us to study local atomic (nuclear) surroundings. Such methods as electron spin echo envelope modulation (ESEEM), electron nuclear double resonance (ENDOR), and electron-electron double resonance (ELDOR) detected NMR (EDNMR) provide information that is related to the NMR spectroscopy approach and obviously cannot be obtained by conventional EPR. The corresponding experimental data (Larmor frequencies of nuclei, the values of hyperfine and quadrupole interactions with angularselected measurements) significantly complement and deepen the existing understanding of the structural behavior of CP materials.
The diverse field of pulse EPR spectroscopy allows us to obtain a complete set of spectroscopic and dynamic parameters for the radiation-induced centers in calcium phosphate materials. The parameters of the spin Hamiltonian (anisotropic g-factor, hyperfine A and quadrupole P interaction matrices) reflect the local symmetry of the defect position. The extent of anisotropy and principal values of the tensors depend on the electron density, the distribution of nearby ions, and the local gradients of electric fields. Additional quantum chemical methods can be employed to calculate the listed energy characteristics, which are determined by the structural features of defects as well as the localization of impurity ions in the vicinity. Thus, a comparative analysis of experimental data from pulse EPR spectroscopy with further theoretical calculations is crucial for a more complete understanding of the structural features of the crystal lattice of calcium phosphate materials. The explicit identification of certain paramagnetic centers is important for biphasic materials (HA + TCP), which are now generating great interest in dentistry [52]. For the successful Appl. Sci. 2021, 11, 7727 4 of 14 characterization of biphasic compounds, a comprehensive understanding of structural nuances in single-phase materials is required.
The experimentally obtained data in this article (anisotropic g-factors, hyperfine A and quadrupole P interaction values) for different impurity centers can be used as a reference point for further theoretical calculations based on quantum chemistry (e.g., the density functional theory-DFT approach), which would allow for the acquisition of additional structural information about the features of the doped crystal lattice.

Sample Synthesis
HA powders were synthesized by precipitation from aqueous solutions according to the reaction (Equation (1)), using reactants of analytical grade (Labtech, Russia) and deionized water: 10Ca(NO 3 ) 2 + 6(NH 4 ) 2 HPO 4 + 8NH 4 OH →Ca 10 (PO 4 ) 6 (OH) 2 + 20NH 4 NO 3 + 6H 2 O (1) The ammonium phosphate solution was added dropwise into a calcium nitrate solution during the stirring. The pH of the reaction mixture was maintained at a value of 11.0-12.0 by adding aqueous ammonia. After the synthesis, the mixture was ripened for 21 days for the crystallization of the precipitate [53].
The powder of OCP was synthesized by hydrolysis of the initial DCPD powder in a buffer solution. A total of 10 g of DCPD powder was immersed in 1000 mL of 1.5 M sodium acetate aqueous solution, with a pH value of 8.8 ± 0.2. The powder was kept in the solution for 24 h, with a constant stirring rate at 35 • C, and then thoroughly washed in distilled water and dried overnight at 37 • C.
The jawbone material of a Vietnamese mini-pig (a mineral phase that consists mainly of hydroxyapatite) was extracted by removing an implant with small bone fragments of peri-implant tissues. The corresponding preparation of the jawbone sample for EPR measurements was carried out by separating it from the implant and sawing it into blocks. All requirements and relevant ethical standards for interventionary studies involving animals were rigorously followed according to the Local Ethics Committee of the Federal State Budgetary Educational Institution "Kazan State Medical University" of the Ministry of Health of the Russian Federation.
The studied samples were in dry powder form, which facilitated sample preparation before experiments. Standard quartz flasks were used for all types of EPR spectroscopy measurements at different frequency ranges. Since the Bruker Elexsys spectrometers use a resonator system (the dimensions of which are proportional to the microwave length), the sizes of the flasks (cylindrical sample holders) for each range were different: 7 mm, 3 mm, and 0.6 mm for the X, Q, and W-bands, respectively. The volume/mass of each sample corresponded to a fully filled resonator, ensuring a fill factor of K = 1. A quantitative assessment of the radiation-induced center concentration was not carried out; therefore, the specific mass of the samples was not relevant. For X-ray and γ irradiation, the powder samples were packaged in plastic containers and plastic bags, and irradiated in air at room temperature.

Experimental Setup
Conventional (continuous wave-CW) and pulsed EPR measurements were performed, exploiting the abilities of Bruker Elexsys 580/680 spectrometer in X-(ν MW = 9-10 GHz), Q-(ν MW = 33-34 GHz), and W-band (ν MW = 94-95 GHz) ranges. At CW mode, experimental parameters (amplitude modulation, power of mw-source, and integration times) were chosen to avoid any distortion and saturation of absorption signals. Electron spin echo (ESE)-detected EPR spectra were recorded using a standard Hahn echo sequence with π = 32 ns and τ = 300 ns for the X-band, and π = 64 ns and τ = 240 ns for the W-band, unless otherwise specified in the text. Relaxation time measurements were taken using a 2-pulse Hahn echo sequence and an inversion-recovery 3-pulse sequence for the spin-spin T 2 and spin-lattice T 1 relaxation times, respectively.
Electron Spin Echo Envelope Modulation (ESEEM) was implemented using a wellknown two-pulse Hahn sequence: π/2 − τ − π, where the length of π was 32 ns, and τ was equal to 200 ns. In this method, the integral intensity of the electron spin echo (ESE) was recorded, depending on the time interval τ between two pulses at a fixed magnetic field. This parameter was increased to the required value (before the loss of information on nuclear modulations). To increase the sensitivity and spectroscopic resolution, the smallest possible step, t = 4 ns, was chosen and the ESE was integrated only at its peak with an integration time of t = 4 ns. Further spectral analysis of obtained results involved a Fourier transform using the program OriginPro.
Electron nuclear double resonance (ENDOR) experiments were conducted using special (for nuclei and electron) cavities and a scheme of simultaneous electron-nuclear excitations called the Mims pulse sequence: π/2 − τ − π/2 − T − π/2, with an additional radiofrequency (RF) π-pulse inserted between the second and third microwave π/2 pulses, where the length of π/2 was 64 ns, τ = 250 ns, T = 20 µs, and for the RF pulse, π = 18 µs. Since the Larmor frequency of the nuclei is less than for an electron by about 2000 times, and is consequently in the radio frequency range, an additional RF-source with a wide frequency range (1-200 MHz) was used to stimulate the NMR transitions. To increase the spectroscopic resolution and separate close nuclear frequencies or overlapping splitting from each other in the RF-scale, experiments were performed in the high-field part of the spectrometer (W-band, ν MW = 94 GHz). Due to method requirements for T 1 time measurements, the experiments were performed at a low temperature, T = 50 K.
The ELDOR-detected NMR (EDNMR) method for the electron-nuclear study is based on the electron-electron double resonance (ELDOR) approach. The additional ELDOR module E580-400U, and a dielectric ring resonator ER 4118X-MD5, were used to investigate double electron-electron transitions. In this case, the initial (main) source of microwave radiation acts as the observation frequency (v mw1 or v obs ) at a fixed value (ν MW = 9.59 GHz). At the same time, module E580-400U is necessary for generating and varying the second independent microwave frequency (v mw2 or v pump ) in the range from 9.3 to 10 GHz. Owing to its adjustable Q-factor, the ER 4118X-MD5 resonator allows for the optimization of the bandwidth of resonant frequencies in accordance with the specific requirements of the experiment. The duration of the selective pulse t sel was chosen to be 6 µs, which corresponds to the excitation band in the EPR spectrum, with ∆B = 7.2 µT and the length of the detection pulse equal to 300 ns (∆B = 144 µT). All of these tuning parameters allow for the recording of the spectra at a high resolution.
To create stable paramagnetic centers in the nominal pure material, X-ray irradiation of the synthesized powders was provided by a URS-55 source (U = 55 kV, I = 16 mA, W anticathode) at room temperature for 30 min, with the estimated dose of 10 kGy.
γ-ray irradiation was performed on a cyclic electron accelerator for 15 and 90 min (with the estimated doses of 4 and 25 kGy, respectively) at room temperature. Irradiation was carried out on a cyclic electron accelerator "Microtron-cT". The irradiation parameters were as follows: the electron energy was 21 MeV, the electron beam current was up to 5 µA, the pulse repetition rate was 200 Hz, the pulse duration was 3 µs, the gamma-quantum flux was 5 × 10 13 s −1 cm −2 . The duration of sample irradiation was 15 and 90 min at an electron beam current of 4 µA, with the estimated absorbed doses of about 4 and 25 kGy, respectively. The details of irradiation are provided in our paper [54].

EPR Spectroscopy
There are no paramagnetic centers in nominally pure samples (HA and OCP); therefore, no EPR signals in CP materials can be observed. An X-ray or γ-irradiation procedure performed on the samples leads to the formation of radiation centers that can be successfully detected by EPR ( Figure 1). As we can see, the acquired EPR spectra from the irradiated samples have quite a strong anisotropy, with a characteristic splitting into hyperfine structures. Powder spectra of the radiation-induced centers (nitrate radicals) in CPs are very often described by a Spin-Hamiltonian of axial symmetry: where g || and g ⊥ are the main components of the g tensor, A || and A ⊥ are the main components of the hyperfine tensor, B i , S i , and I i are the projections of the external magnetic field strength, electronic (S = 1/2), and nuclear (I = 1) spins, respectively, onto the i = {x, y, z} coordinate axis, and β is the Bohr magneton.
The Spin-Hamiltonian parameters for the same center may differ significantly, depending on the type of sample. The spectra of the CP samples synthesized from the nitrogen-containing reagents (see Equation (1)) can be described with the parameters that are shown in Table 1.  (5) The shape of the EPR line and the splitting values for HA and OCP are very different. This may be due to the different atomic environments, the degree of distortion of the crystal lattice, or the level of delocalization of the paramagnetic center [55]. Differences in the parameters of the Spin-Hamiltonian should be useful for further analysis of crystal structures of samples doped with various cations. It should be noted that the EPR spectra of CP samples differ in the degree of anisotropy in the experiment on the high-frequency part of the spectrometer (Figure 1b). Experimental measurements in two or more different frequency ranges allow for a description of the obtained results more accurately, i.e., unequivocally identify the paramagnetic centers and determine the parameters of the main interactions. The W-band EPR spectrum of The Spin-Hamiltonian parameters for the same center may differ significantly, depending on the type of sample. The spectra of the CP samples synthesized from the nitrogen-containing reagents (see Equation (1)) can be described with the parameters that are shown in Table 1.  (5) The shape of the EPR line and the splitting values for HA and OCP are very different. This may be due to the different atomic environments, the degree of distortion of the crystal lattice, or the level of delocalization of the paramagnetic center [55]. Differences in the parameters of the Spin-Hamiltonian should be useful for further analysis of crystal structures of samples doped with various cations.
It should be noted that the EPR spectra of CP samples differ in the degree of anisotropy in the experiment on the high-frequency part of the spectrometer (Figure 1b). Experimental measurements in two or more different frequency ranges allow for a description of the obtained results more accurately, i.e., unequivocally identify the paramagnetic centers and determine the parameters of the main interactions. The W-band EPR spectrum of OCP is more difficult to interpret, despite the fact that the values of the hyperfine interaction (A || or A ⊥ ) are the smallest for the calcium phosphates group. It was concluded that in the irradiated HA samples, EPR is mainly due to the stable NO 2− 3 ions, preferably substituting one distinct PO 3− 4 position in the HA structure (substitution of the B-type), while there are several non-equivalent positions for the nitrate radical in the OCP structure. In our paper [55], we found that the distribution of A ⊥ for TCP is larger than that of the HA. We suggested that it could be due to the three different positions for PO 4 group substitution in the TCP structure, as well as due to the various mechanisms for charge compensation.
Since hydroxyapatite is an inorganic mineral component of bone tissue, we studied the biogenic material after X-ray irradiation. As an example, the jawbone of a Vietnamese mini-pig was chosen for the EPR study. This sample, like synthetic hydroxyapatite, does not contain its own paramagnetic centers. However, after X-ray exposure, radiation-induced centers are formed. The EPR spectra of samples in two frequency ranges are shown in Figure 1. The signal is attributed to the stable carbonate radical, which is identified by the degree of rhombic anisotropy (shape of line) and the values of the g-factor (see Table 1). As we can see, all three values of the g-factor can be accurately determined due to the high spectroscopic resolution (at W-band), while for the X-band, it is possible to distinguish only perpendicular (g xx = g yy = g ⊥ ) and parallel orientations (g zz = g || ). At the same time, there is no evidence of a nitrate radical. Figure 1 clearly shows that the presence of free radicals in the irradiated sample depends on the type of biomaterial under study.
Relaxation characteristics were also investigated for the CP samples. The obtained data are shown in Table 2. As we can see, the relaxation times T 1 (spin-lattice or longitudinal relaxation) and T 2 (spin-spin or transverse relaxation) differ depending on the type of CP material. This difference may indicate that the radiation-induced centers occupy various positions in the crystal lattices of HA, OCP, and biogenic compounds (jawbone of a Vietnamese mini-pig). Because of the difference in spin-spin relaxation times, we can conclude that there is an unequal distribution of free radicals for various CP materials. Therefore, a full set of spectroscopic values and dynamic characteristics of radiationinduced centers will allow us to unambiguously determine the nature of EPR signals in poorly studied CP materials (amorphous, biphasic, and doped materials). Table 2. Relaxation characteristics of radiation-induced paramagnetic centers in different matrices at room temperature T = 297 K, in the X-band frequency range ν MW = 9.6 GHz. Values for CP materials were measured at B 0 (see Figure 1a).

Type of Material
Spin-Lattice Relaxation T 1 (µs)

Spin-Spin Relaxation T 2 (µs)
HA 28.5(5) 3.0(1) OCP 60.7(8) 0.68(5) jawbone of a mini-pig 17.7(2) 1.31 (8) Samples irradiated by X-ray and γ-radiation were additionally explored in the Q-band microwave range. Experimental results are presented only in continuous wave mode at room temperature. Figure 2 shows the difference in the EPR spectra between the types of irradiation for the same type of material. The nature of the paramagnetic centers can be dependent on the type of radiation exposure. The influence of the type of radiation (and other radiation characteristics) on the EPR spectrum was extensively discussed in the literature [56,57]. However, for the OCP sample, the difference in the EPR spectra according to the type of irradiation is not observed. It may serve as additional proof to the conclusion made in ref. [54] that, in contrast to HA, the radiation-induced radicals in OCP are stabilized not in the apatite, but in the hydrated layers of OCP.
The results obtained in the Q-band frequency range provide additional information about the spectroscopic values of the spin system. But as we can see in the case of irradiated calcium phosphates, not all available frequency ranges are suitable for the analysis of powdered materials. The anisotropy of the g-factor for nitrate radicals in high magnetic fields is comparable to or even greater than the hyperfine interaction splitting, while at the X-band, the converse can be observed. Therefore, measurements of the nitrogen radical in an intermediate frequency range lead to the formation of a complex EPR spectrum that is difficult to interpret. Nevertheless, in other cases, a comparison of the EPR spectra makes it possible to clearly determine the origin of the radiation-induced paramagnetic centers and calculate the parameters of the Spin-Hamiltonian. Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 15 The results obtained in the Q-band frequency range provide additional information about the spectroscopic values of the spin system. But as we can see in the case of irradiated calcium phosphates, not all available frequency ranges are suitable for the analysis of powdered materials. The anisotropy of the g-factor for nitrate radicals in high magnetic fields is comparable to or even greater than the hyperfine interaction splitting, while at the X-band, the converse can be observed. Therefore, measurements of the nitrogen radical in an intermediate frequency range lead to the formation of a complex EPR spectrum that is difficult to interpret. Nevertheless, in other cases, a comparison of the EPR spectra makes it possible to clearly determine the origin of the radiation-induced paramagnetic centers and calculate the parameters of the Spin-Hamiltonian.

EDNMR Spectroscopy Analysis
The significant anisotropy of g-and A-tensors and a relatively long transverse relaxation time (T2 = 3 μs) of the NO radical (see Figure 1a) allows us to carry out angularselected EDNMR measurements at room temperature in the X-band frequency range.
Signals corresponding to the Larmor frequencies of 31 P (±6 MHz) and 1 H (±14.8 MHz) nuclei are shown on the overview spectra at B0 ≈ 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 ν = ±47.5 and ±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

EDNMR Spectroscopy Analysis
The significant anisotropy of gand A-tensors and a relatively long transverse relaxation time (T 2 = 3 µs) of the NO 2− 3 radical (see Figure 1a) allows us to carry out angularselected EDNMR measurements at room temperature in the X-band frequency range.
Signals corresponding to the Larmor frequencies of 31 P (±6 MHz) and 1 H (±14.8 MHz) nuclei are shown on the overview spectra at B 0 ≈ 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 ν = ±47.5 and ±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   A more detailed analysis of the spectrum at ∆ν > 0 (MI = −1) shows an additional splitting for the single-quantum transition exactly localized at the value A⊥/2 ( Figure 4). Using the expression for single-quantum transitions [58]: where ∆ is the splitting value of single-quantum transitions, and a choice of the sign "±" depends on the quantum number of MI ("+" for MI = −1 and "−" for MI = +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 A more detailed analysis of the spectrum at ∆ν > 0 (M I = −1) shows an additional splitting for the single-quantum transition exactly localized at the value A ⊥ /2 ( Figure 4). Using the expression for single-quantum transitions [58]: where ∆ is the splitting value of single-quantum transitions, and a choice of the sign "±" depends on the quantum number of M I ("+" for M I = −1 and "−" for M 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 B 0 = 340 mT, splitting in the same orientation for M 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.
1, x FOR PEER REVIEW 10 of 15   However, it should be noted that the hyperfine A and quadrupole P tensors are not collinear (the principal/canonical axes of the tensors do not match), which are based on the simple calculation and analysis of the angular dependencies of the A and P values. Earlier, a similar mutual behavior of tensors was observed in oil samples [60]. The possibility of detecting resolved EDNMR spectra is due to the good localization of the nitrogen center (in the position of phosphate, see [37,38]), which leads to the absence of local variations of g, A, and the electric field gradient. Such measurements make it possible to establish unequivocally the presence of a nitrogen atom in the free radical. The EDNMR method easily copes with cases when A is much larger than 2νLarmor, which is almost impossible to achieve with other methods (ESEEM and ENDOR).

Hyperfine Interaction Spectroscopy (ESEEM and ENDOR Methods)
There are several approaches for the analysis of hyperfine interactions that cannot be registered in EPR spectra due to the small value of splitting. This section is dedicated to One of the proofs that the splitting of the line for the single-quantum transition is actually caused by a quadrupole interaction is the presence of an angular dependence of the P value: The anisotropic EPR spectrum of the nitrate radical ( Figure 1a) and a rather narrow microwave excitation band make it possible to conduct angular selected measurements of the quadrupole splitting. Indeed, in our experiments, we can clearly observe that the value of splitting significantly depends on the B 0 , confirming the aforementioned assumption (see Table 3). Therefore, the presence of the splitting in the EDNMR spectrum (by quadrupole interaction for a single quantum transition and by 2ν Larmor Larmor frequency of 14 N for a double quantum transition), as well as the localization of obtained signals near A, clearly indicate that the radiation-induced center is related to the nitrogen radical NO 2− 3 . Furthermore, this nitrogen radical can surely be used as a spin probe.
However, it should be noted that the hyperfine A and quadrupole P tensors are not collinear (the principal/canonical axes of the tensors do not match), which are based on the simple calculation and analysis of the angular dependencies of the A and P values. Earlier, a similar mutual behavior of tensors was observed in oil samples [60]. The possibility of detecting resolved EDNMR spectra is due to the good localization of the nitrogen center (in the position of phosphate, see [37,38]), which leads to the absence of local variations of g, A, and the electric field gradient. Such measurements make it possible to establish unequivocally the presence of a nitrogen atom in the free radical. The EDNMR method easily copes with cases when A is much larger than 2ν Larmor , which is almost impossible to achieve with other methods (ESEEM and ENDOR). Table 3. Quantitative values of quadrupole interaction, depending on the external magnetic field values.

Hyperfine Interaction Spectroscopy (ESEEM and ENDOR Methods)
There are several approaches for the analysis of hyperfine interactions that cannot be registered in EPR spectra due to the small value of splitting. This section is dedicated to ESEEM (X-band) and ENDOR (X-and W-band) spectra recorded at the field positions corresponding to the maximum of echo intensity. Taking into account the wide excitation bandwidth of short microwave pulses (approx. 50 MHz) and significant spectra overlapping between signals of different paramagnetic centers, current X-band ENDOR measurements cannot be used to selectively address the paramagnetic centers. Nevertheless, important information can be gathered from the analysis.
The crystal lattice of CP samples contains ions with magnetic nuclei ( 1 H and 31 P both with I = 1/2). Therefore, if the radiation-induced center is localized near these ions, we can register the corresponding signal of the electron-nuclear interaction. In the spectrum for the X-ray irradiated HA sample (Figure 5a), only signals from phosphorus nuclei ( 31 P, ν z ≈ 5.9 MHz at B 0 = 340 mT) are observed, although the material also contains hydrogen atoms. This result may indicate that for the HA material, the carbonate radical occupies positions near the phosphorus groups PO 4 . The ESEEM spectrum of the irradiated OCP sample (Figure 5b) was registered for the nitrate radical at B 0 = 341.8 mT (see Figure 1a). The ESEEM spectrum contains a complete set of signals from all magnetic nuclei ( 1 H, ν z ≈ 14.2 MHz), which indicates the position of the nitrate radical directly in the crystal lattice of the OCP sample. Consequently, in further investigations, the nitrate radical can be successfully used as a spin probe for analyzing the concentration dependences of samples doped with various impurity ions. However, the presence of a sufficiently intense signal from the hydrogen nuclei and the existence of the second harmonic of 1 H (2ν z ) may indicate the localization of the nitrate radical near the hydrogen layers of OCP. The nitrogen radical in the CP structure can also provide the possibility of using the ENDOR method for a more detailed analysis of the nuclear environment. It is worth noting that due to the insufficient spectroscopic resolution of the method, we could not observe the additional splitting of the lines.
In contrast to other methods of measuring hyperfine interactions with neighboring magnetic ligands, the ENDOR method allows for the direct registration of NMR transitions, which significantly increases the spectral resolution. In the ENDOR spectrum of the irradiated OCP with fixed B 0 = 341 mT, signals at the Zeeman frequencies corresponding to protons (ν z ≈ 14.8 MHz) and phosphorous 31 P (ν z ≈ 5.9 MHz) nuclei are observed ( Figure 6). Only one broad signal for 31 P is detected, which can be simulated as a convolution of Gaussian and Lorentzian lines with the line widths of 1.6 MHz and 0.4 MHz; however, in HA, a 31 P splitting of 0.5-1.0 MHz can be observed [35,36,58]. The absence of well-structured ENDOR and ESEEM signals from phosphorous and hydrogen nuclei may be explained by the irregularity of the incorporation of several distinct (R1-R3) defects [54] into the lattice (it is either because of preferential localization in the disordered hydrated layer or due to a large variety of incorporation sites in the apatite layer). Most probably, in line with the discussion on the EPR parameters given above, this means that the radical(s) are not located in the majority of apatite crystallites (A-or B-type substitution) but in the hydrated layers [61].
14.2 MHz), which indicates the position of the nitrate radical directly in the crystal lattice of the OCP sample. Consequently, in further investigations, the nitrate radical can be successfully used as a spin probe for analyzing the concentration dependences of samples doped with various impurity ions. However, the presence of a sufficiently intense signal from the hydrogen nuclei and the existence of the second harmonic of 1 H (2νz) may indicate the localization of the nitrate radical near the hydrogen layers of OCP. The nitrogen radical in the CP structure can also provide the possibility of using the ENDOR method for a more detailed analysis of the nuclear environment. It is worth noting that due to the insufficient spectroscopic resolution of the method, we could not observe the additional splitting of the lines. In contrast to other methods of measuring hyperfine interactions with neighboring magnetic ligands, the ENDOR method allows for the direct registration of NMR transitions, which significantly increases the spectral resolution. In the ENDOR spectrum of the irradiated OCP with fixed B0 = 341 mT, signals at the Zeeman frequencies corresponding to protons (νz ≈ 14.8 MHz) and phosphorous 31 P (νz ≈ 5.9 MHz) nuclei are observed ( Figure  6). Only one broad signal for 31 P is detected, which can be simulated as a convolution of Gaussian and Lorentzian lines with the line widths of 1.6 MHz and 0.4 MHz; however, in HA, a 31 P splitting of 0.5-1.0 MHz can be observed [35,36,58]. The absence of well-structured ENDOR and ESEEM signals from phosphorous and hydrogen nuclei may be explained by the irregularity of the incorporation of several distinct (R1-R3) defects [54] into the lattice (it is either because of preferential localization in the disordered hydrated layer or due to a large variety of incorporation sites in the apatite layer). Most probably, in line with the discussion on the EPR parameters given above, this means that the radical(s) are not located in the majority of apatite crystallites (A-or B-type substitution) but in the hydrated layers [61]. . X-band ENDOR spectra detected at B0 (see Figure 1a) and T = 100K of the OCP sample after X-ray irradiation.
Other features of the ESEEM and ENDOR spectra can be ascribed to the interaction with 23 Na nuclei (νz ≈ 3.9 MHz at B0 = 340 mT, I = 3/2 and, therefore, quadrupolar). The presence of a signal from 23 Na nuclei is probably due to the incorporation of sodium into the OCP lattice during the synthesis stage. Similar results without deep analysis have been reported in some papers devoted to apatite investigations (see [61], for example). Frequently, the quadrupolar interaction makes the 23 Na spectra too complicated for analysis. Using the EasySpin procedure salt for ENDOR spectra simulations and assuming an isotropic interaction, we were able to estimate A23Na = 1.5 MHz and e 2 Qq/h = 3.3 MHz ( Figure  6).

Conclusions
In this paper, we studied calcium phosphate materials using diverse magnetic resonance approaches. The powders under study were exposed to X-ray/gamma radiation to create paramagnetic centers (free radicals). The EPR method makes it possible to distinguish the types of radiation-induced paramagnetic centers in different samples through the values of the Spin-Hamiltonian parameters and dynamic (relaxation) characteristics. Methods targeted to the analysis of weak hyperfine interactions (EDNMR, ESEEM, and ENDOR) demonstrated their advantage in the characterization of synthetic calcium phosphate powder samples. The EDNMR method allows for the determination of the value of the quadrupole interaction for the nitrogen radical, which is a sensitive parameter of the Figure 6. X-band ENDOR spectra detected at B 0 (see Figure 1a) and T = 100K of the OCP sample after X-ray irradiation.
Other features of the ESEEM and ENDOR spectra can be ascribed to the interaction with 23 Na nuclei (ν z ≈ 3.9 MHz at B 0 = 340 mT, I = 3/2 and, therefore, quadrupolar). The presence of a signal from 23 Na nuclei is probably due to the incorporation of sodium into the OCP lattice during the synthesis stage. Similar results without deep analysis have been reported in some papers devoted to apatite investigations (see [61], for example). Frequently, the quadrupolar interaction makes the 23 Na spectra too complicated for analysis. Using the EasySpin procedure salt for ENDOR spectra simulations and assuming an isotropic interaction, we were able to estimate A 23Na = 1.5 MHz and e 2 Qq/h = 3.3 MHz (Figure 6).

Conclusions
In this paper, we studied calcium phosphate materials using diverse magnetic resonance approaches. The powders under study were exposed to X-ray/gamma radiation to create paramagnetic centers (free radicals). The EPR method makes it possible to distinguish the types of radiation-induced paramagnetic centers in different samples through the values of the Spin-Hamiltonian parameters and dynamic (relaxation) characteristics. Methods targeted to the analysis of weak hyperfine interactions (EDNMR, ESEEM, and ENDOR) demonstrated their advantage in the characterization of synthetic calcium phos-phate powder samples. The EDNMR method allows for the determination of the value of the quadrupole interaction for the nitrogen radical, which is a sensitive parameter of the local gradient of the electric (crystal) field. It is possible to identify the various nuclear environments and estimate the position of the radiation-induced centers by ESEEM spectroscopy, while ENDOR provides extensive information about local structural changes caused by the introduction of even non-paramagnetic ions.