## 3 Results and Discussion
Nevertheless, it has been reported by [PERSON] and [PERSON] [18] for (Sm, Zr, and Ce)Fe\({}_{10}\)Si\({}_{2}\) that the combination of three rare earth site substitutions resulted in the stabilization of a 1:12 structure with an improved hard magnetic performance (in comparison with stable alloys with the mixture of two elements on rare earth site) and simultaneously with a low content of critical rare earth elements. A more exact comparison requires the consideration of the values of the enthalpies of formation of amorphous phases, solid solutions, and intermetallics. Because of the coexistence of many various types of phases, e.g., tetragonal 1:12-type (space group \(I4/mmm\)) or hexagonal (space group \(P6_{3}/mmc\)) and rhombohedral (space group \(R3\)m) 2:17-type phases in the region of interest in the phase diagram, and the limitations of [PERSON]'s model-based semi-empirical approach, the enthalpies of formation of intermetallic compounds were taken from theoretical works based on more sophisticated methods, e.g., ab initio calculations. The general conclusion, which can be drawn from the literature data, is the improvement of 1:12-type phase stability by the substitution of Fe by various stabilizing elements, as reported for SmFe\({}_{12}\) and SmFe\({}_{11}\)(Co, Ti, V, and Ga) [45]. The lowering of the enthalpy of formation for the substituted SmFe\({}_{11}\)(Co, Ti, V, Ga) samples resembledthe variation of enthalpies of formation of solid solutions reported in the present paper (Table 2). While the energy of formation for SmFe\({}_{12}\) was approximately equal to 2 kJ/mol, it decreased for Co, Ti, V, and Ga substitutions and reached a value lower than -5 kJ/mol for SmFe\({}_{11}\)Ti [45]. The recent study by [PERSON] et al. [46] showed that nickel can also play a role as a stabilizer in the 1:12-type structure. Comparing these values with the formation energies reported in the paper by [PERSON] et al. [11] shows us a general picture about the relative stability of various intermetallic phases. At first, the value of the formation energy of SmFe\({}_{12}\) was determined to be equal to approx. 0.2 eV. Recalculation of this value to kJ/mol provided a much higher value than the 2 kJ/mol calculated in [45]. Nevertheless, the overall picture remained consistent. The formation energy of 1:12-type phase increased with increasing the atomic radius on the rare earth site. The energy of formation of ZrFe\({}_{12}\) was strongly negative (approx. \(-\)0.25 eV). It also remained negative for Lu, Tm, Er, Ho, and Dy. A further increase in the atomic radius made the formation of the 1:12-type phase unfavorable. For NdFe\({}_{12}\), the formation energy was highly positive and doubled the value determined for SmFe\({}_{12}\). When comparing these values with the enthalpies of formation reported in Table 2, it is clear that the energy of formation of intermetallics always had a higher absolute value. It means that in the case of compositions of interest, the formation of intermetallic phases was preferred in respect to the solid solution and amorphous phase. Nevertheless, one has to bear in mind that any deviation from ideal stoichiometry and growing chemical disorder could reverse this situation. Finally, we compared the formation energy values for the competing 2:17-type and 1:12-type phases. As opposed to the enthalpies of formation of solid solutions (Table 2), the energies of formation of rhombohedral Th\({}_{2}\)Zn\({}_{17}\) and hexagonal Th\({}_{2}\)Ni\({}_{17}\) were 0.04-0.16 eV lower than the energy of formation of tetragonal ThMn\({}_{12}\) phase for all of the analyzed rare earth site substitutions (Hf, Zr, Sc, Lu, Tm, Er, Ho, Dy, Y, Gd, Sm, Nd, Pr, and La) [11]. In conclusion, the utilization of Zr as the main rare earth site substitution had the highest impact on the lowering of the enthalpy of formation of all types of phases, intermetallics (as already reported in [11]), solid solutions, and amorphous.