Study of Tricalcium Phosphate Ceramics Doped with Gadolinium Ions with Various EPR Techniques

Abstract

Tricalcium phosphate (TCP)-based materials, such as β-Ca₃(PO₄)₂ doped with rare earth ions (RE), have shown applications as biomaterials, lighting emitting materials, scintillating materials, in vivo imaging probes, and thermoluminescent dosimeters. Their properties are found to be dependent on the distribution of RE³⁺ on Ca²⁺ sites that can be controlled by pulsed electron paramagnetic resonance (EPR) and electron spin echo envelop modulation (ESEEM) experiments. The main spectroscopic parameters (spin Hamiltonian values) of Gd³⁺ and nitrogen impurity centers are quantitatively determined (g-factor, the fine structure parameters D and E, the hyperfine constants A) as well as dynamic characteristics: spin–lattice T₁ and spin–spin T₂ relaxation times. Based on the analysis of the EPR datasets, the interatomic distance between Gd³⁺ and ³¹P was estimated in the dipole–dipole approximation. Two structurally nonequivalent Gd³⁺ positions in the β-TCP structure have been identified. The obtained valuable results demonstrate applicability of modern EPR techniques to characterize Gd-TCP systems despite the powder structure of the material and high electron spin S = 7/2 of Gd³⁺ ions.

1. Introduction

During the last decade, materials based on calcium phosphate (CaP) have been widely used to create composite compounds that serve as substitutes for bone tissue as an alternative to allotropic transplants. CaP-based biomaterials are successfully used in dental, craniofacial, and orthopedic surgery, as well as drug transporters in targeted drug delivery [1,2]. The main advantage of the development of biomaterials based on CaP is their similarity in chemical and elemental composition and appropriate properties with bone mineral. However, some weaknesses, such as the unpredictable (uncontrolled) rate of degradation (resorption), limited osteoinduction still do not fully satisfy clinical tasks (medical requirements) [3]. Therefore, for the development of multifunctional materials, CaPs are systematically doped with various cations and anions (magnesium Mg²⁺, strontium Sr²⁺, copper Cu²⁺, cobalt Co²⁺, silicon Si²⁺, manganese Mn²⁺, iron Fe³⁺, etc.) [4,5,6,7]. Substitutions in the CaP structure are also used to improve biocompatibility, biological activity of the implant, its antibacterial, anti-inflammatory, and angiogenic stimulation of the proliferation and differentiation of osteoblasts, induction of gene expression, and local microenvironment, as well as catalytic properties [3].

Rare earth (RE) dopants in CaP [8] can act as contrast agents for magnetic resonance imaging, also as phosphor centers used in the form of optical markers. In addition, due to suitable biocompatibility and excellent biological effects, the RE ions are gradually involved in research and development in biomedical fields, such as biometrics, drug delivery, diagnosis, and treatment of diseases [9,10,11], etc. The main material for the treatment of damaged hard tissues and joints is beta-tricalcium phosphate (β-TCP, Ca₃(PO₄)₂), which has stoichiometry similar to amorphous biological precursors of bone mineral with a molar ratio of Ca/P = 1.5 [12]. Various investigations, including clinical ones, have shown that synthetic β-TCP is a highly promising, osteoconductive, and osteoinductive material with a high biocompatibility with human bone tissue [13,14].

Owing to the ionic radius close to the radius of Ca²⁺ ions and a higher number of charges, RE ions (i.e., Gd³⁺) have a significant affinity with Ca²⁺ sites on biomolecules [15]. This feature, combined with their inherent biological properties, provides RE ions with advantages in materials for bone restoration, such as: improving physical properties, providing luminescence to materials for visualization, interaction with cells, induction of gene expression, regulation of the local microenvironment, etc. RE-CaPs elements (Eu³⁺ and Ln³⁺, respectively) were developed [16,17] and their luminescent and dielectric properties were investigated.

Gd³⁺-substituted β-TCP compounds are promising biomaterials for bone engineering, since they allow the control and tracking of the degree of bone tissue regeneration using imaging methods introduced into medical practice (radiography, computed tomography (CT), and magnetic resonance imaging (MRI)). Trivalent gadolinium (Gd³⁺) is a key rare earth ion due to its excellent magnetic, optical, and electrical properties [18]. Gadolinium-based materials have been used in oncotherapy, cancer diagnosis, and orthopedic implants [19]. It was shown in [20] that the addition of Gd³⁺ to magnesium-based implants significantly improves the mechanical properties and corrosion resistance of orthopedic implants. Positive osteogenic effects of Gd³⁺ addition and developed Gd³⁺-based Gd-MCR/CTS frameworks for bone defect healing were found in the paper [21].

The properties of TCP-based materials are found to be dependent on the distribution of RE ions on Ca²⁺ sites and the TCP crystal structure [22]. Therefore, reliable analytical tools should be applied to investigate the defects introduced with incorporation of RE ions. Electron paramagnetic resonance (EPR) is known as a powerful non-destructive method of studying the magnetic properties and symmetry of the crystal field of various compounds with RE dopants [23,24,25,26,27,28]. Advanced EPR techniques have repeatedly demonstrated their effectiveness in the precise characterization of different CaP systems doped with 3d-metals [29]. In contrast, investigations of RE-CaP powder systems are quite rare, though the other analytical techniques are broadly exploited for those purposes (see the references cited above). For example, the properties of TCP powders doped with Gd³⁺ ions were studied by conventional EPR only in paper [23] where the parameters of the zero field splitting were defined.

In the presented research, we, for the first time to the best of authors’ knowledge, demonstrate the abilities of various (not only conventional) EPR techniques to comprehensively study the Gd³⁺-CaP powder systems (ceramics) on example of β-TCP. We have applied different EPR approaches to obtain unique information about the structural and magnetic changes with the RE ions incorporation (concentration), as well as unique fundamental knowledge about the localization, spin–orbit, spin–lattice, and electron–nuclear interactions depending on the temperature, magnetic field, and gadolinium concentration. Those derived from the EPR values can be used for the qualitative and quantitative control of incorporation of gadolinium into the TCP structure and serve as the basis for quantum-chemical simulations of the crystal lattice and Gd-TCP physical/chemical properties to construct the materials with the desired functionality.

2. Materials and Methods

2.1. Synthesis

The synthesis procedures were described in detail in paper [4]. Briefly, TCP containing gadolinium was synthesized by precipitation from aqueous solutions of salts. The initial components for the syntheses were calcium nitrate (chemical grade, Chimmed, Moscow, Russia), diammonium phosphate (analytical grade, Chimmed, Moscow, Russia), gadolinium chloride (chemical grade, Chimmed, Moscow, Russia), and 25% aqueous ammonia solution (analytical grade, Chimmed, Moscow, Russia). The synthesis of Gd-substituted TCP was performed according to reaction (1):

3 − xCa(NO₃)₂ + xGdCl₃ + 2(NH₄)₂HPO₄ + 2NH₄OH → Ca_3−xGd_x(PO₄)₂ + +3xNH₄Cl + +(6 − 2x)NH₄NO₃ + 2H₂O

(1)

where x = 1.3; 0.13; 0.0013.

The resulting powders were subjected to heat treatment at 900 °C for 1 h. The corresponding ceramics were prepared by uniaxial pressing of the powders in a steel mold at a pressure of 100 MPa, followed by sintering the compacts in an air atmosphere in a muffle furnace at 1100 °C for 2 h.

2.2. Characterization

2.2.1. XRD Analysis

The phase composition was determined by X-ray diffractometry (XRD) using Rigaku D/MAX 2500 (Cu Kα, θ/2θ geometry). The XRD data were derived at T = 297 K in the 2θ range from 10° to 60° with a step of 0.02° and a scan rate of 3°/min. Le Baile decomposition [30] implemented in a JANA2006 software program was applied to define the unit cell volume as well as the parameters. The phase analysis was carried out using the Crystallographica Search-Match program (version 2.0.3.1) and the JCPDS PDF-2 and PDF-4 databases. The Rietveld technique was utilized for quantitative phase analysis by using the JANA2006 [31]. More technical details are provided in paper [4].

2.2.2. Conventional EPR Spectroscopy

The EPR spectra in conventional continuous wave (CW) mode were recorded at T = 297 K in the X-band microwave range (v_MW = 9.6 GHz) on a Bruker spectrometer Elexsys E580. The modulation amplitude, integration time, and microwave power were set in such a way as to avoid over-modulation, distortion, or saturation of the EPR signal, respectively (modulation amplitude 0.01 mT at 100 kHz, microwave power P = 2 µW). The recording time of the full spectrum was 3 min. A satisfactory signal-to-noise ratio (better than 1:20) could be achieved using single-scan registration. The sample was placed in a resonator (ER 4118X-MD5) with an extremely high quality factor (Q ≈ 10,000) using a quartz flask, which ensured sensitivity to a small amount of impurities.

2.2.3. Pulsed EPR

The experiments in the pulsed mode were carried out in the low Q-factor mode of the resonator (Q = 200) to decrease the dead time so that the subsequent pulse sequences work correctly. To measure the EPR spectra in the pulsed mode, the method of detecting the integral intensity of the electron spin echo (ESE) during the sweep of the magnetic field B₀ was used. Two-step phase cycling was used to prevent the superposition of the pulse signal on ESE and the subsequent distortion of the EPR signal.

The relaxation measurements were conducted at T = 25 K using a helium flow cryostat. The stable value of the sample temperature was maintained using a temperature controller and monitoring of the helium flow level (Oxford Instrumentation). The spin–spin (dephasing) relaxation time T₂ was measured by tracking the primary amplitude of the ESE with the same pulse durations π/2–π with a change of τ. The relaxation curves were recorded in a multi-scan mode with a rapid sweeping in time to exclude heating of the electronic circuits of the spectrometer and, as a consequence, signal distortion. The spin–lattice relaxation time T₁ was extracted from inversion-recovery studies by applying the pulse sequence π–T (delay)–π/2–τ–π, while the delay T varied. The stable value of the sample temperature was maintained using a temperature controller and monitoring of the helium flow level (Oxford Instrumentation).

The electron–nuclear interactions were analyzed using a three-pulse Electron Spin Echo Envelope Modulation (ESEEM) sequence (π/2–π/2–π/2–ESE), with a change in both distances (τ and T) from 180 ns to 1204 ns. The sweep step was chosen to be optimal at 32 ns for capturing the majority of the numbers of magnetic nuclei. The current ESEEM spectroscopy experiment was performed at T = 12 K. The three-pulse sequence was chosen for several reasons, including: (i) to increase the spectroscopic resolution, since the time T₁ is several times longer than the time T₂ and (ii) to suppress the cross-resonant nuclear frequencies (sum and difference), which complicate the interpretation of the results. The obtained ESEEM results in the time range were further processed by the Origin Pro 2017 program by subtracting the exponential curve to obtain nuclear modulations and the subsequent Fourier transform.

2.2.4. X-ray Irradiation

To investigate the radiation-induced paramagnetic species, X-ray irradiation of the materials was performed using a URS-55 source (U = 50 kV, I = 15 mA, W-anticathode) at T = 297 K for 1 h with a calculated dose of 15 kGy.

3. Results and Discussion

3.1. XRD Analisys

According to XRD data (Figure 1), β-TCP is the main crystalline phase in the synthesized samples after calcination. It is important to note that two impurity phases were also found in the species under investigation [4]: chlorapatite (Ca₁₀(PO₄)₆Cl₂, Cl-AP-phase) and β-calcium pyrophosphate (β-Ca₂P₂O₇) which can also be studied by EPR techniques [32,33]. The formation of the Cl-AP phase is associated with the use of GdCl₃ as a precursor [34]. A small amount of impurity phases (<5%) causes it to be unlikely to detect EPR signals from them compared to the main phase of β-TCP at the experimental conditions described in Section 2.2.

Generally, TCP has three modifications: β-TCP, α-TCP, and α’-TCP. α’-TCP is of no practical interest as it only exists at temperatures above 1430 °C and is almost instantly converted to α-TCP upon cooling. Despite the same chemical composition, α- and β-TCP differ significantly in their structure, density, and solubility. The α-TCP phase can be maintained at room temperature in a metastable state [35] and its stability range is strongly affected by ionic substitutions. α-TCP is as biocompatible as β-TCP but more soluble and rapidly hydrolyzes to calcium-deficient hydroxyapatite. [36] α-TCP crystallizes in a monoclinic crystal system and belongs to the space group P2 ₁/a [37]. To the best of the authors’ knowledge, only 3d-ions doped α-TCP (such as Mn²⁺) were examined by EPR so far [38], opening up endless horizons for the use of EPR for the study of α-TCP with RE doping.

β-TCP has a rhombohedral syngony with space group R3c with a = b = 10.4352(2) Å, c = 37.4029(5) Å, V = 3527.26 Å. The unit cell contains 21 formula units [Ca₃(PO₄)₂] as for whitlockite, (Ca₁₈Mg₂H₂(PO₄)₁₄) [39]. The structure of β-TCP can be described as broken layers of PO₄ tetrahedra with calcium ions in their centers. One unit cell of β-TCP contains 63 calcium atoms and 42 PO₄ groups. The calcium atoms are located in five different Ca positions, the distinguishing feature is that the Ca(4) position is three-fold, coordinated by oxygen atoms, and has a partial calcium filling factor of 0.5 [12]. In contrast, Ca(1), Ca(2), Ca(3), and Ca(5) are each completely occupied by one calcium atom and these positions are coordinated to seven, eight, eight, and six oxygen atoms, respectively. The structure of β-TCP consists of two planar repeating domains, one of which has a molar ratio of Ca/P 60/42 = 1.429 and the other Ca/P 66/42 = 1.571 [40].

3.2. CW EPR

The vast majority of EPR spectra are recorded in CW (continuous wave) mode, using a magnetic field sweep, which is created by an electromagnet, at a constant frequency of microwave radiation [41]. Figure 2 shows the EPR spectra of the TCP-Gd sample with different concentrations of gadolinium recorded at room temperature (T = 297 K). The EPR signals consist of the asymmetric wide line (from 0 to 600 mT) with a weakly resolved structure. In low magnetic field region, it is possible to distinguish resonant absorptions corresponding to the effective g-factor g_eff = 2.8 and additional unresolved low-field components at g_eff = 5.9. The main intensity contribution of the EPR spectrum are concentrated at g = 2.0 related to typical 3d/4f metal ions with predominantly spin paramagnetism in powder form of the samples.

The crystal lattice of pure tricalcium phosphate does not contain ions with non-zero electron spin, consequently, the material is EPR silent. The observed absorption lines for doped TCP samples in Figure 2 refer to the Gd³⁺ centers. Separately noteworthy and well-known signals from trivalent Gd³⁺ ions in disordered polycrystalline matrices (for example, in fluoride glasses) are three signals with an effective g-factor of 5.9, 2.8, and 2 [42]. Owing to the presence and the characteristic low-field EPR signals with effective g-factors (g_eff = 5.9, g_eff = 2.8, and g = 2), it is possible to produce unambiguous conclusions that, firstly, the gadolinium ion has a valence of 3+ and, secondly, it is embedded in the TCP crystal lattice into one of the calcium positions Ca²⁺.

The RE gadolinium ion Gd³⁺ with a 4f⁷ configuration in the main ⁸S_7/2 state is paramagnetic and has an electron spin S = 7/2 with a zero orbital moment L = 0. The spectrum of this spin system should contain 2*S = 7 different magnetic transitions, which provide seven lines in the EPR spectrum with the center of gravity of the spectrum at g ≈ 2.0, because there is no orbital magnetic moment. β-TCP crystallizes in the rhombohedral space group R3c. Due to the low symmetry, a gradient of the internal crystalline (electric) field is formed, which leads to the appearance of a “zero field splitting” (ZFS) of the spin sublevels. As a result, we observe fine structure lines in the spectrum. The TCP-Gd sample under study is in the form of a powder, therefore, all equally probable orientations of nanocrystals relative to the external magnetic field B₀ are present in the EPR spectrum. The energy values of the ZFS depend on the relative position of the main axis of the nanocrystal c with the lines of force of the magnetic induction vector of the external magnetic field B₀. Thus, the components of the fine structure have an angular dependence, which causes mutual overlapping and the broadening of the available resonant absorptions. The formation of low-field singularities, despite the powder phase of the sample and the high spin S = 7/2 of the impurity center, arises due to the unusual behavior orientation dependence of the spin levels. In this paper, the fine structure values are approximately commensurate with the Zeeman energy. This condition leads to the fact that the spin sublevels are entangled, i.e., they are the superposition of two or more neighboring spin levels. Such systems are characterized by a situation in which the low-field EPR absorption lines are weakly or almost independent of the orientation of the nanocrystals in the magnetic field (isotropic condition), which leads to mutual superposition and correspondingly to increase the signal intensity. A similar picture with the observation of low-field hyperfine structures was demonstrated for the TCP doped by Mn²⁺ ions [43]. There are multiple cases of observation of a signal from trivalent iron Fe³⁺ in the region g = 4.27 due to the similar reason [44,45].

The simulation of the EPR spectrum was carried out in the MatLab software, using the EasySpin package [46]. The spin Hamiltonian of the gadolinium center is described by the following set of parameters:

$$Ĥ=g\beta H_0{Ŝ}_z+B_2^0{O}_2^0+B_4^0{O}_4^0+B_6^0{O}_6^0$$

(2)

where g—g-factor, β—Bohr magneton, S = 7/2—electronic spin, $B_k^q$—crystal field parameters, $O_k^q$—Stevenson operators, and D = $B_2^q$, E = ($b_2^2$/3)—fine structure parameters.

In order to describe the EPR spectrum obtained in the CW mode, we assumed that gadolinium Gd³⁺ is embedded in the crystal structure of TCP and use the corresponding spin Hamiltonian (2) and theoretical simulations in the powder averaging mode. An acceptable approximation was obtained using two contributions with a different set of parameters, which indicates the presence of two different positions of Gd³⁺ ions in the TCP structure. We have obtained a set of parameters related to axial symmetry as for Ca(4) position (

Table 1. The zero-field (fine structure) parameters of Gd³⁺ spin–Hamiltonian.

	${\mathit{B}}_{\mathbf{2}}^{\mathbf{0}}$	${\mathit{B}}_{\mathbf{2}}^{\mathbf{2}}$	${\mathit{B}}_{\mathbf{4}}^{\mathbf{0}}$	${\mathit{B}}_{\mathbf{6}}^{\mathbf{0}}$
Ca(x)	1.9 GHz	-	15.2 MHz	0.69 MHz
Ca(4)	530 MHz	50 MHz	-	-

). Ca(x) site possesses a lower symmetry, since the second part of EPR intensity contribution described by a higher order of parameters of the crystal field of the spin Hamiltonian. As it was already pointed out in Section 3.1, in reference [4] using XRD and IR spectroscopy, it was found that the studied TCP-Gd samples contain mainly one phase (>90%). Therefore, based on the simulation of EPR spectra, we unequivocally conclude that the EPR signals from two gadolinium positions in the crystal lattice of β-TCP are observed.

3.3. Pulse EPR

The EPR spectrum was recorded using a two-pulse Hahn sequence with different times τ between pulses π/2 and π, in order to determine the presence of other different contributions. The black line in Figure 3 shows the EPR spectrum at the minimum time between π/2 and π pulses τ = 0.18 µs. The resulting spectrum corresponds to the spectrum of the powder sample with a broad line, without separately expressed signals. The measurements of the decay of the transverse magnetization revealed two exponential curves. The mathematical processing of the resulting EPR spectrum causes it to be possible to separate the spectrum into two components with a fast T₂ = 0.19 ± 0.01 µs and a slower T₂ = 1.0 ± 0.05 µs. To confirm the presence of two different processes, an EPR spectrum was recorded with an extended time τ between π/2 and π pulses τ = 0.54 µs (green line in Figure 3). As can be seen, with increasing time τ, a strong decrease in the spectrum component with a short relaxation time is observed against the background of the spectrum component with a longer time, which confirms the existence of two types of centers. Thus, the difference between the black and green EPR spectrum arises due to the redistribution of intensities.

At a temperature of 25 K, the spin–lattice relaxation rate was measured for both centers, at a magnetic field value of B₀ = 344.3 mT, in which both types of center contribute, and B₀ = 118.2 mT, where there is a contribution from only the second center. The spin–lattice relaxation rate of Gd³⁺ for both centers turned out to be rather short T₁ = 30 ± 2 μs, which corresponds to gadolinium relaxation in other crystals [47]. To distinguish the dynamic characteristics of both centers to each other the additional measurements of the relaxation rates were carried out at T = 12 K, the results shown in

Table 2. Relaxation times obtained at T = 12 K.

	T1 (μs)	T2 (μs)
B0 = 344 mT	157 ± 3	0.2 ± 0.01
B0 = 118 mT	173 ± 5	1 ± 0.05

.

According to the analysis of the dynamic characteristics provided in Table 2, the presence of two different paramagnetic centers was confirmed. This result indicates that the Gd³⁺ ion at low concentrations occupies at least two structurally nonequivalent Ca²⁺ positions. The difference in relaxation times for each type of center is associated with a different local environment, which affects the longitudinal relaxation, as well as a different interatomic distance between gadoliniums, leading to a change in the transverse (spin–spin) relaxation time.

3.4. ESEEM Experiment

ESEEM (Electron Spin Echo Envelop Modulation) is a spectroscopy method aimed to detecting weak electron–nuclear interactions in paramagnetic systems with the presence on magnetic nuclei. The ESEEM method serves as a way to determine the anisotropic hyperfine structure from the modulation of the decay curve T₂. The integrated intensity of the electron spin echo (ESE) is recorded depending on the time interval (τ) between two pulses in a fixed magnetic field (B₀) [41]. In this work, we used a three-pulse ESEEM technique: π/2–τ–π/2–T–π/2–τ–echo. The first two π/2 pulses create nuclear coherence, including nuclear frequencies, during the evolution time T, the nuclear coherence accumulates a phase and decays with the transverse relaxation time T₂. The third π/2 pulse converts the nuclear coherence back to the observed electron coherence and causes the intensity of the stimulated echo to be modulated by nuclear frequencies, which causes it to be possible to measure the last ones. The modulation occurs due to the fact that the second π-pulse not only inverts the phase of electron coherence, but also redistributes this coherence between all allowed and forbidden transitions. The coherence is maximum for nearby nuclei, the nuclear magnetic moment of which has a large magnetic dipole–dipole interaction with an unpaired electron [48]. The Fourier transform of the modulations provides a frequency spectrum in which the frequencies of the nuclear–spin transitions are visible and one can further interpret the hyperfine interactions.

ESEEM modulation (harmonic oscillations in the decay curve of transverse magnetization) occurs when the Gd³⁺ center is coupled to the surrounding nucleus through an anisotropic dipole–dipole interaction. The used three-pulse echo sequence, where the second π/2-pulse shifts a part of the magnetization to the z-axis, while it already decays only due to a relatively longer spin–lattice relaxation, causes it to be possible to register a greater number of oscillations and, accordingly, the spectral resolution increases. When this magnetization is returned to the transverse plane by the third π/2 pulse, a “stimulated echo” occurs and will have a peak height greater than the two-pulse Hahn echo at the same τ. In the conditions, where the electron spin is coupled to the magnetic nucleus via a hyperfine dipole coupling, it causes periodic modulation. An analysis of the frequencies of these modulations helps in identifying the nuclei type near the unpaired electron, as well as in estimating the distance between the nucleus and the unpaired electron (³¹P and Gd³⁺).

The magnitude of the above interaction is related to the distance through an anisotropic dipole–dipole approximation and is expressed by the formula [41]:

$$A_{d-d }~ \frac{g_n{g}_e{\mathsf{\mu }}_n{\mathsf{\mu }}_e}{{\mathrm{r}}^3}$$

(3)

where g_n = 2.2632 nuclear g-factor of phosphorus, g_e = 2.004—electron g-factor.

The presence of magnetic nuclei in CaPs samples often leads to the appearance of modulations in the decay curves of transverse magnetization. The type of modulation data (its frequency and magnitude) depends on the sample and paramagnetic probe. Such experimental data are presented in Figure 4. The observation of modulations in most cases immediately indicates the presence of the ESEEM effect. This effect is caused by neighboring nuclei, information about which can be obtained from the Fourier transform, which connects the time characteristic of a spin system with its frequency spectrum. The form of modulation depends on the interatomic distances, the magnitude of the magnetic moments, and the degree of mixing of the spin wave functions, which affects the probability of forbidden transitions. The most informative results of ESEEM spectroscopy in the frequency domain after appropriate signal processing are shown in Figure 4 (right). The spectra show a ³¹P signal centered at the Larmor frequency for the field B₀ = 344 mT, the frequency ν_Larm (³¹P) = 6 MHz, and for B₀ = 118 mT, respectively, ν_Larm (³¹P) = 2.1 MHz. However, this information already indicates that the paramagnetic center is located in the structure of the sample and can be successfully used as a spin label in further studies.

As one can see in Figure 4 (right panel), the ESEEM pattern depends on the magnitude of the external magnetic field. This means that there are at least two non-identical types of Gd³⁺ paramagnetic centers in the studied samples with different nuclear environments. Thus, we revealed the presence of two structurally nonequivalent Gd³⁺ positions in the TCP lattice. From the linewidth at half-height, the distance from Gd³⁺ to ³¹P was calculated in the dipole–dipole approximation using Equation (3). The results are presented in

Table 3. Distance between calcium and phosphorus as derived from the analysis of ESEEM peaks exploiting Equation (3).

	rexp (Å)	rtheor (Å) [43]
B0 = 344 mT	4.0 ± 0.2	4.059
B0 = 118 mT	4.3 ± 0.2

.

3.5. Radiation-Induced Centers

The standard way to study EPR silent CaPs is to create radiation defects and study their spectroscopic properties. Several radiation-induced paramagnetic particles (radical anions) located in hydroxyl or phosphate centers have been identified in CaPs [45]. The studied TCP-Gd samples were irradiated with an X-ray source at ambient conditions. The EPR spectra (Figure 5) were recorded in a pulsed mode using the Hahn sequence at room temperature (T = 297 K).

The TCP contains impurities of the nitrate anion (a by-product). This nitrate anion occupies the phosphorus position. Such an anion is used as a probe for the analysis of the local environment. The spin probe is one of the effective methods for studying the structural features of the local environment of an impurity center. The nitrate anion itself is not paramagnetic; therefore, we irradiate the sample under study with X-ray radiation of the order of 15 kGy. At different concentrations of gadolinium, the spectrum is not distorted, so we can conclude that TCP retains its original symmetry group. A simulation was also carried out using the EasySpin [46] and the main spectroscopic parameters were determined by using the spin Hamiltonian of the nitrogen radical possessing S = 1/2, I = 1:

H = g_∥βB_zS_z + g_⊥(B_xS_x + B_yS_y) + A_∥S_zI_z + A_⊥(S_xI_x + S_yI_y)

(4)

with corresponding values: g_∥ = 2.005, g_⊥= 2.009, A_∥ = 6.68 mT, A_⊥ = 3.75 mT for ${\mathrm{NO}}_3^{2-}$ radical in TCP [45,49].

The dynamic characteristics (electron relaxation times T₁, T₂) of the nitrogen radical at B = B₀ were also measured, which are presented in

Table 4. Electron relaxation times of the nitrogen radical at T = 297 K.

Sample	T1 (μs)	T2 (μs)
TCP	24.3 ± 2	4.16 ± 0.4
TCP + 0.01 Gd	23.0 ± 2	2.55 ± 0.2
TCP + 0.13 Gd	22.6 ± 2	2.4 ± 0.2
TCP + 1.3 Gd	38.8 ± 4	0.8 ± 0.1

.

The relaxation time T₂ decreases due to the interaction between gadolinium ions and the nitrogen radical. The nitrogen radical “feels” the magnetic field created by gadolinium, which is a rare earth element, and the relaxation times shortens. These fast relaxations create strong fluctuating fields. This process leads to additional dephasing of the magnetization of the ${\mathrm{NO}}_3^{2-}$ radical [49].

4. Conclusions

The structural and fundamental features of the TCP-Gd spin system were analyzed by electron paramagnetic resonance spectroscopy. A comprehensive study enabled it to be possible to reveal the presence of two structurally nonequivalent positions of gadolinium ions in the crystal lattice of the TCP sample. For each Gd³⁺ center, the main parameters of the spin Hamiltonian (g-factors, zero-field splitting, and hyperfine constant) with dynamic (T₁ and T₂ relaxation) characteristics were determined. Based on the ESEEM spectroscopy from electron–nuclear interaction analysis, the interatomic distance between Gd³⁺ and ³¹P was estimated in the dipole–dipole approximation. The introducing of Gd³⁺ ions in the TCP crystal lattice does not lead to significant distortions and the material retains its spatial symmetry (space group) without the formation of side phases (by-products) of synthesis. It has been established that the paramagnetic Gd³⁺ ions affect the dynamic characteristics of stable nitrogen radicals. Thus, nitrogen radicals can serve as a sensitive probe for the track of the incorporation chemical procedure of gadolinium ions into the TCP structure. The obtained results will be a fundamental basis for the studying of structurally disordered systems (S ≥ 1) and have an additional applied value in the field of clinical industry.