## 3 Results and Discussion
To combine both, the enthalpy of formation and the mismatch entropy, the glass forming ability parameter \(\Delta P_{HS}\) (Figure S2) was also calculated as a product of \(S_{\sigma}/k_{\rm B}\) and chemical enthalpy (basic term in the expression for enthalpy of formation for both, amorphous phase and solid solution). The obtained results were comparable to those of the formation enthalpy of the amorphous phase. The most negative values indicating the highest glass forming ability were reached again for the Fe-free compositions. Large negative interfacial enthalpies and an atomic radii difference between (Zr, Ce, and Nd) and Si are believed to be crucial here, as already stated in the case of \(\Delta H^{am}\). However, \(\Delta P_{HS}\) reached the most negative values for the 1:12-type phases, \(-5.8\) kJ/mol for CeFe\({}_{10}\)Si\({}_{2}\) and \(-6.0\) kJ/mol for NdFe\({}_{10}\)Si\({}_{2}\). To conclude the first part of our research, one should expect that the substitution of Fe simultaneously by the elements with larger and smaller atomic radii, as in the case of (Zr, Ce, Nd) and Si substitutions, will promote the vitrification process. The minimum content of Zr, Ce, and Nd (equal to 15 at.%), determined on the basis of \(\Delta H^{am-ss}\), should be taken as an estimation only, as kinetic factors of synthesis process can be decisive. We can be more precise when comparing systems with various substitutions for similar compositions, and the data gathered in Table 2 can be treated as a guide. Nevertheless, qualitative and quantitative agreement of the calculated enthalpies with existing data can be found. For example, when one compares the \(\Delta H^{am-ss}\) contour map of the Nd-Fe-Si system with the experimental data reported in [39] (Nd\({}_{90\times}\)Fe\({}_{x}\)Si\({}_{10}\) amorphous alloys were successfully synthesized in the range of \(20\leq\) x \(\leq 50\)), it is evident that the very broad glass forming range confirmed here for the low Si content converged well with the literature. Planning future experimental works, we should compare the calculated values of the enthalpies of formation of amorphous alloys and solid solutions to those of intermetallic compounds apparently also competing during the synthesis process. There is experimental evidence on the formation of the phase of interest (ThMn\({}_{12}\)-type) in (Zr, Ce)Fe\({}_{10}\)Si\({}_{2}\) and similar systems. [PERSON] et al. [40] showed that the ThMn\({}_{12}\)-type phase crystallized (along with relatively small amount of \(\alpha\)-Fe) in Nd\({}_{1\times}\)Zr\({}_{x}\)Fe\({}_{10}\)Si\({}_{2}\) (x = 0.25, 0.5 and 0.75), indicating the atomic radius of the rare earth site element as a controlling factor. Moreover, it has been reported that the changes in the cooling rate in a rapid quenching process influenced the phase constitution. The ThMn\({}_{12}\)-type structure has been stabilized in the samples quenched with a roll velocity of 10 m/s for Sm, Gd, and Er substitutions, while for 30 m/s, Zr and Nd also favored its formation [40]. Other studies have confirmed the stability of the tetragonal structure in (REE)Fe\({}_{10}\)Si\({}_{2}\) for rare earth site elements having an atomic radius equal or smaller than 0.181 nm [20; 41; 42]. CeFe\({}_{10}\)Si\({}_{2}\) and NdFe\({}_{10}\)Si\({}_{2}\) preferably crystallize in the Th\({}_{2}\)Zn\({}_{17}\)-type structure [21]. The stabilization of the 1:12 structure in such alloys can be obtained through the substitution of larger (REE) atoms with smaller Zr [21; 43; 44]. To date, there is no direct evidence on the stability of 1:12-type phase in the alloys containing a combination of Nd, Zr, and Ce atoms.