## 3 Results and Discussion
To have a more overarching view, one should focus on the general trends visible in Figure 3. To improve the glass forming ability, or to at least destabilize the solid solution and to introduce structural disorder, the content of the elements with a large atomic radius, and preferably with a large negative heat of mixing with Fe (e.g., Zr), should be further increased at the expense of the Fe and Si content. The change in \(\Delta H^{\text{am-ss}}\) sign (for about 15 at.% of Zr, Ce, and Nd) marks the change in phase preference (Figure 3). To extend the analysis, the composition dependence of the normalized mismatch entropy was also calculated (Figure S1). Most of the compositions exhibited \(S_{\sigma}/k_{\text{B}}\) values higher than 0.1. This is the minimum value for the achievement of considerable glass forming ability [30]. Normalized mismatch entropy reflects the effect of atomic radii mismatch between the main constituents and, as expected due to the large atomic radius difference between Zr, Ce, Nd, and Si, reaches the highest values for Fe-free compositions. The lowest value of \(S_{\sigma}/k_{\text{B}}\) among the alloys of interest (Table 2) was determined for ZrFe\({}_{12}\) and was equal to 0.11. The highest mismatch reflected in the \(S_{\sigma}/k_{\text{B}}\) value of 0.44 was reached for Ce\({}_{2}\)Fe\({}_{15}\)Si\({}_{2}\) and Nd\({}_{2}\)Fe\({}_{15}\)Si\({}_{2}\). As expected, the results indicate a beneficial effect of the presence of largely mismatched atomic radii elements on the possibility of the formation of a disordered structure. Figure 2: Compositional dependences of the formation enthalpies of the solid solution \(\Delta H^{\text{ss}}\) of ternary (Zr, Ce, and Nd)-Fe-Si systems. Key composition regions are marked in grey (2:17-type phases) and black (1:12-type phases). Black solid lines are \(\Delta H\) = 0 indicators. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\Delta H^{\mathbf{am}}\) & \(\Delta H^{\mathbf{ss}}\) & \(\Delta H^{\mathbf{am-ss}}\) & \(S_{e}/k_{\mathbf{B}}\) & \(\Delta P_{HS}\) \\  & **(kJ/mol)** & **(kJ/mol)** & **(kJ/mol)** & **(kJ/mol)** & **(kJ/mol)** \\ \hline ZrFe\({}_{12}\) & \(-2.0\) & \(-2.8\) & \(0.8\) & \(0.11\) & \(-0.9\) \\ \hline CeFe\({}_{12}\) & \(7.2\) & \(5.9\) & \(1.3\) & \(0.31\) & \(0.3\) \\ \hline NdFe\({}_{12}\) & \(6.5\) & \(5.9\) & \(0.6\) & \(0.31\) & \(0.1\) \\ \hline ZrFe\({}_{10}\)Si\({}_{2}\) & \(-17.5\) & \(-18.2\) & \(0.7\) & \(0.14\) & \(-3.5\) \\ \hline CeFe\({}_{10}\)Si\({}_{2}\) & \(-8.9\) & \(-10.3\) & \(1.4\) & \(0.36\) & \(-5.8\) \\ \hline NdFe\({}_{10}\)Si\({}_{2}\) & \(-9.3\) & \(-10.0\) & \(0.7\) & \(0.36\) & \(-6.0\) \\ \hline Zr\({}_{2}\)Fe\({}_{17}\) & \(-4.6\) & \(-3.6\) & \(-1.0\) & \(0.14\) & \(-1.6\) \\ \hline Ce\({}_{2}\)Fe\({}_{17}\) & \(7.4\) & \(7.8\) & \(0.4\) & \(0.40\) & \(0.6\) \\ \hline Nd\({}_{2}\)Fe\({}_{17}\) & \(6.5\) & \(7.8\) & \(-1.3\) & \(0.40\) & \(0.1\) \\ \hline Zr\({}_{2}\)Fe\({}_{15}\)Si\({}_{2}\) & \(-16.6\) & \(-15.7\) & \(-0.9\) & \(0.17\) & \(-4.0\) \\ \hline Ce\({}_{2}\)Fe\({}_{15}\)Si\({}_{2}\) & \(-5.1\) & \(-5.0\) & \(-0.1\) & \(0.44\) & \(-5.3\) \\ \hline Nd\({}_{2}\)Fe\({}_{15}\)Si\({}_{2}\) & \(-5.7\) & \(-4.7\) & \(-1.0\) & \(0.44\) & \(-5.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Enthalpies of the formation of amorphous phase \(\Delta H^{\mathbf{am}}\), of solid solution \(\Delta H^{ss}\), their difference \(\Delta H^{am-ss}\), normalized mismatch entropy \(S_{e}/k_{\mathbf{B}}\), and glass forming ability parameter \(\Delta P_{HS}\) calculated for the chosen binary and ternary 1:12-type and 2:17-type compositions. Figure 3: Compositional dependences of difference of two quantities, of formation enthalpies of amorphous phase and solid solution \(\Delta H^{am-ss}\) of ternary (Zr, Ce, and Nd)-Fe-Si systems. Key composition regions are marked in grey (2:17-type phases) and black (1:12 type phases). Black solid lines are \(\Delta H=0\) kJ/mol indicators (negative \(\Delta H^{am-ss}\) values indicate a lower enthalpy of formation of amorphous phase).