## 3 Results
### Numerical Study of the Loss Tangent of Dielectric Materials
Numerical calculations of the theoretical graphs \(\mathrm{tg}\mathrm{g}_{\mathrm{th}}^{(\mathrm{v})}(\mathrm{T})\) and molecular parameters of the relaxators \(\zeta_{\mathrm{th}}=\left\{\mathrm{U}_{0,\mathrm{th}};\mathrm{v}_{0,\mathrm{ th}};\mathrm{t}_{0,\mathrm{th}};\mathrm{s}_{0,\mathrm{th}};\mathrm{a}_{i, \mathrm{th}}\right\}\) were carried out using the same comparison function minimization method (MCF-method) [73; 171; 172]. A detailed description of the elements and components of these studies is provided in the captions accompanying Figure 10.  
The experimental graph 1 was obtained from measurements on Onot talc crystal \(\mathrm{Mg}_{3}(\mathrm{Si}_{4}\mathrm{O}_{10})(\mathrm{OH})_{2}\) pre-calined at \(\mathrm{T}_{\mathrm{ac}}=923\) K, at a polarization temperature T = 300 K and an alternating field frequency \(\mathrm{v}=7\) MHz. Theoretical graphs (2-5) were calculated near the frequencies corresponding to maxima on the experimental graph 1, using the quasi-classical kinetic theory methods (from expression (151), with parameters (120)-(122) as described in this article). Additionally, theoretical graphs (2\({}^{\prime}\)-5\({}^{\prime}\)) were computed using direct quantum-mechanical calculations based on the model equations (from expression (27) in [4]), combined with the comparison function minimization method (MCF-method) [73; 171; 172]. The theoretical maximum 6\({}^{\prime}\) has not yet been experimentally identified. As shown in Figure 10, the theoretical graphs (2-5), calculated using the quasi-classical kinetic theory (from expression (151), with parameters (120), (121), (122) in this article), have amplitudes slightly lower than the corresponding experimental maxima. Meanwhile, the theoretical graphs 2\({}^{\prime}\)-5\({}^{\prime}\), computed using direct quantum-mechanical calculations (from expression (27) in [4]), exhibit amplitudes slightly higher than their corresponding experimental maxima. In both cases, the calculated values \(\mathrm{tg}\mathrm{g}_{\mathrm{th},i,\mathrm{max}}^{(\mathrm{v})}(\zeta_{ \mathrm{th},i})\) all within the confidence interval of the numerical values of the measured maxima amplitudes \(\mathrm{tg}\mathrm{g}_{\mathrm{exp},i,\mathrm{max}}^{(\mathrm{v})}(\zeta_{ \mathrm{exp},i})\). Here, the index \(i\), as previously noted, corresponds to the number of the experimental maximum. A total of four measured maxima are shown in Figure 10, at temperatures 160 K, 220 K, 265 K, and 310 K [1; 4]. Figure 10: Temperature spectra of the dielectric loss tangent in onotsky talc crystals. The comparison function minimization scheme applied to the theoretical and experimental values of the studied function \(\text{tg}\delta_{i}^{(\
u)}(\text{T})\) near the point \(\text{T}_{\text{exp},i,\text{max}}\) allows, using the methods described in [73; 171; 172], the calculation of a theoretical temperature \(\text{T}_{\text{th},i,\text{max}}\rightarrow\text{T}_{\text{exp},i,\text{max}}\). At this temperature, there exists an optimized set of molecular parameter values for the \(i\)-th relaxator \(\zeta_{i,\text{th}}=\left\{\text{U}_{0,i,\text{th}};\text{$\
u$}_{0,i,\text{ th}};\text{Figure 8:0}_{0,i,\text{th}};\text{Figure 8:1}_{0,i,\text{th}};\text{Figure 8:2}_{i,\text{th}}\right\}\) such that the distance between the theoretical and experimental maxima:  
Figure 8:3  
reaches its minimum: \(\left|\text{tg}\delta_{\text{exp},i,\text{max}}^{(\
u)}\big{(}\zeta_{\text{ exp},i}\big{)}-\text{tg}\delta_{\text{th},i,\text{max}}^{(\
u)}(\zeta_{\text{th},i}) \right|\rightarrow\text{min}\). The parameters calculated using this numerical scheme for each type of relaxator in Onot talc crystals are presented in Figure 8:4  
A distinctive feature of the spectra depicted in Figure 10 is the presence of a low-temperature theoretical maximum \(6^{\prime}\), which has not yet been experimentally detected due to the low resolution of the measuring setup [73; 171].