## 3 Results and Discussion
Next, the dependence \(\lg R\)-\(f(1/T)\) shown in Figure 10b for NdNa\({}_{2}\)NiMnO\({}_{5}\) in the temperature range of 423-483 K is described by the equation:  
\[lgR=0.6656+\frac{1946}{T}, \tag{16}\]  
then, taking Equation (12) into account, the activation energy of conductivity (\(\Delta E_{a}\)) is equal to 0.336 eV. The linear dependence \(\lg R\)-\(f(1/T)\) for NdK\({}_{2}\)NiMnO\({}_{5}\) is shown in Figure 11.  
The dependence \(\lg R\)-\(f\)(1/\(T\)), shown in Figure 11a for NdK\({}_{2}\)NiMnO\({}_{5}\) in the temperature range of 293-403 K, is described by the equation:  
\[lgR=-7.0237+\frac{3972}{T}, \tag{17}\]  
Taking Equation (12) into account, the activation energy of conductivity (\(\Delta E_{a}\)) for NdK\({}_{2}\)NiMnO\({}_{5}\) was found to be 0.683 eV. The dependence \(\lg R\)-\(f\)(1/\(T\)), shown in Figure 11b for NdK\({}_{2}\)NiMnO\({}_{5}\) in the temperature range of 443-463 K, is described by the equation:  
\[lgR=1.7343+\frac{1130}{T}, \tag{18}\]  
From this, considering Equation (12), the activation energy of conductivity (\(\Delta E_{a}\)) is calculated to be 0.191 eV. The analysis of the calculated activation energies of conductivity for NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\) offers insights into the processes taking place in these materials across different temperature ranges. For NdNa\({}_{2}\)NiMnO\({}_{5}\), in the temperature range of 293-353 K, the activation energy is 0.382 eV; in the range of 423-483 K, the activation energy decreases to 0.336 eV. This decrease in activation energy with increasing temperature might indicate a transition to another conductivity regime, characterized by the dominance of a different conduction mechanism. It could also be linked to changes in defect types or the occurrence of second-order phase transitions. For NdK\({}_{2}\)NiMnO\({}_{5}\), in the range of 298-403 K, the activation energy is 0.683 eV; at higher temperatures (443-463 K), the activation energy significantly decreases to 0.191 eV. The higher activation energy observed in the 298-403 K range compared to NdNa\({}_{2}\)NiMnO\({}_{5}\) may suggest greater resistance to electrical conductivity at lower temperatures, likely involving polaronic or ionic conduction mechanisms. The sharp drop in activation energy in the higher temperature range could indicate structural changes or a transition to another phase, reducing the energy barrier for charge transfer. Comparative observations: NdNa\({}_{2}\)NiMnO\({}_{5}\) exhibits smaller variations in activation energy across the studied temperature ranges, implying a more stable conduction structure. In contrast, NdK\({}_{2}\)NiMnO\({}_{5}\) shows more pronounced changes in activation energy, highlighting significant structural or phase transformations. These differences could be attributed to the distinct nature of the cations (Na and K) and their effects on the lattice structure and defect states. A higher activation energy reflects a greater energy barrier for charge transport, while its reduction may signify shifts in conduction mechanisms or phase transitions. The bandgap widths (\(\Delta E_{g}\)) for NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\) were calculated. The bandgap width of the studied substances was determined using the formula:  
\[R_{nn}=R_{0}e^{\frac{\Delta E_{n}}{2R^{2}}}. \tag{12}\]0  
where \(k\) is the Boltzmann constant equal to 8.617302 \(\times\) 10\({}^{-5}\) eV. K\({}^{-1}\), \(R_{1}\) is the resistance at \(T_{1}\), and \(R_{2}\) is the resistance at \(T_{2}\). For example, for LaNa\({}_{2}\)NiMnO\({}_{5}\) semiconductor regions in the range 293-353 K, \(T_{1}\) = 293 K, \(T_{2}\) = 353 K; \(R_{1}\) = 6.02, and \(R_{2}\) = 4.76 Om. For compound LaNa\({}_{2}\)NiMnO\({}_{5}\), in the range 293-353 K, the bandgap width is 0.87 eV; at 423-483 K, the bandgap width increases to 1.53 eV. An increase in the band gap during the transition to a higher temperature range may indicate a phase transition or changes in the electronic structure of the material.