## 2 Experimental Part  
The purpose of this work is to obtain compounds with a set of specific physicochemical properties by performing a step-by-step synthesis of new phases from initial substances over a wide temperature range of 600-1200 \({}^{\circ}\)C. This involves multiple \"firing-grinding\" operations to ensure complete solid-phase interaction, while \"removing\" the reaction-inhibiting product layer from the surface of the reagents. The initial substances, Nd\({}_{2}\)O\({}_{3}\) (\"puriss. spec.\" grade, TU 48-4-523-90, 99.5%, Chem Craft, Kaliningrad, Russia), NiO (\"p.a.\" grade, TU 6-09-4125-80, 99.0%, LLC Granchem, Chelyabinsk, Russia), Mn\({}_{2}\)O\({}_{3}\) (\"p.a.\" grade, TU 6-09-2165-77, 99%, Yugraaktiv, Rostov-on-Don, Russia), Na\({}_{2}\)CO\({}_{3}\) (\"p.a.\" grade, GOST 83-79, 99.8%, BETATRADE, Ufa, Republic of Bashkortostan), and K\({}_{2}\)CO\({}_{3}\) (\"puriss.\" grade, GOST 4221-76, 99.0%, RossPolymer, Moscow, Russia) were pre- calcined at 400 \({}^{\circ}\)C for dehydration. The stoichiometric amounts, calculated to form the final product NdMeI\({}_{2}\)NiMnO\({}_{5}\) (MeI--Na, K), were carefully mixed and ground in an agate mortar. The thermal processing of mixtures to obtain nickel manganites includes the following steps. Transfer to crucibles and initial annealing: the mixtures are placed in alumina crucibles, pre-calcined at 600 \({}^{\circ}\)C, and annealed at the same temperature for 10 h. Annealing at various temperatures: 800 \({}^{\circ}\)C for 15 h; 1000 \({}^{\circ}\)C for 15 h; 1200 \({}^{\circ}\)C for 15 h. Cooling and reprocessing: after each temperature stage, the mixtures are cooled to room temperature. Then, mixing and grinding are performed to ensure uniform composition distribution. Low-temperature annealing: the samples are subjected to low-temperature annealing at 400 \({}^{\circ}\)C for 10 h. This multi-step process aims to achieve a stable structure and composition for samples of NdO-MeI\({}_{2}\)O-NiO-Mn\({}_{2}\)O\({}_{3}\) (MeI--Na, K) for further research. As a result of the reactions occurring through direct interaction between the particles of the initial solid substances, NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\) were obtained. The samples of nickel manganites NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\) are studied using experimental and computational X-ray diffraction methods. The identification of substances in the mixture was conducted based on their sets of interplanar spacings (d) and the relative intensities (I) of the corresponding lines on the X-ray diffractogram (Figure 1). Figure 1: The X-ray photographs of NdNa\({}_{2}\)NiMnO\({}_{5}\) (**a**) and NdK\({}_{2}\)NiMnO\({}_{5}\) (**b**). As a result of X-ray analysis performed to study the phase composition using the DRON-2.0 X-ray diffractometer (Manufacturer: NPP Burevestnik, St. Petersburg, Russia, 1989) and the X-ray diffractogram indication method, the type of crystal symmetry (syngony) and lattice parameters of the target products, neodymium nickel manganites NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\), were determined. The synthesized neodymium nickel manganites crystallize in a cubic syngony. Based on the analysis of the X-ray diffractograms of the samples, the following crystal lattice parameters were determined: NdNa\({}_{2}\)NiMnO\({}_{5}\) - a = 14.26 \(\pm\) 0.02 A, V\({}^{0}\) = 2899.74 \(\pm\) 0.06 A\({}^{3}\), a number of formula units in the cell Z = 4, volume of a lattice cell per formula unit V\({}^{0}\) = 724.93 \(\pm\) 0.01 A\({}^{3}\), a calculated X-ray density \(\rho_{\rm{roent. }}\) = 3.52 g/cm\({}^{3}\), a pycnometric density \(\rho_{\rm{pick. }}\) = 3.48 \(\pm\) 0.02 g/cm\({}^{3}\), determined using an organic liquid component as an indifferent liquid [15]. NdK\({}_{2}\)NiMnO\({}_{5}\) - a = 15.19 \(\pm\) 0.02 A, V\({}^{0}\) = 3504.05 \(\pm\) 0.07 A\({}^{3}\), Z = 4, V\({}^{0}\) = 876.01 \(\pm\) 0.02 A\({}^{3}\), \(\rho_{\rm{roent. }}\) = 3.15 g/cm\({}^{3}\), \(\rho_{\rm{pick. }}\) = 3.14 \(\pm\) 0.01 g/cm\({}^{3}\).