## 3 Results and Discussion
Substitution of Fe by Si strongly influences enthalpy values, which are negative also for Ce and Nd. The most negative value of \(\Delta H^{am}\) among the analyzed compositions was found for the ZrFe\({}_{10}\)Si\({}_{2}\) alloy, confirming the beneficial influence of the Zr and Si substitutions. One should bear in mind that kinetic parameters were not taken into account in the calculations and the formation of the amorphous phase would be more probable with specific methods (e.g., for high cooling rates). Moreover, the determined \(\Delta H^{am}\) values did not include any information on other phases (intermetallics and solid solution) that were competing during solidification process. To have a full picture, one needs to compare all of them. Therefore, another paragraph is devoted to the formation enthalpy of solid solutions. The contour maps of the enthalpies of formation of solid solutions in Zr-Fe-Si, Ce-Fe-Si, and Nd-Fe-Si (Figure 2) are similar to the respective contour maps calculated for the amorphous phases (presented in Figure 1). The most negative values were reached for low Fe-content and for Zr-containing alloys. When we take a closer look at (Zr, Ce, Nd)Fe\({}_{12-x}\)Si\({}_{x}\) (0 \(\leq\) x \(\leq\) 2) and (Zr, Ce, Nd)\({}_{2}\)Fe\({}_{17-x}\)Si\({}_{x}\) (0 \(\leq\) x \(\leq\) 2) compositions, rare earth alloys exhibited higher values of \(\Delta H^{ss}\) (as already reported also for \(\Delta H^{am}\)). The enthalpy of formation of solid solution \(\Delta H^{ss}\) was equal to \(-2.8\) kJ/mol, 5.9 kJ/mol, and 5.9 kJ/mol, for ZrFe\({}_{12}\), CeFe\({}_{12}\), and NdFe\({}_{12}\), respectively. Si-substituted compositions exhibited lower values of \(\Delta H^{ss}\) than Si-free counterparts mentioned above. \(\Delta H^{ss}\) is equal to \(-18.2\) kJ/mol, \(-10.3\) kJ/mol, and -10.0 kJ/mol, for ZrFe\({}_{10}\)Si\({}_{2}\), CeFe\({}_{10}\)Si\({}_{2}\), and NdFe\({}_{10}\)Si\({}_{2}\), respectively. All of the \(\Delta H^{am}\) and \(\Delta H^{ss}\) values listed above are gathered in Table 2 along with the data for 2:17-type phases (believed to be the main competing phases). The \(\Delta H^{am}\) and \(\Delta H^{ss}\) values calculated for Zr\({}_{2}\)Fe\({}_{17}\) were more negative than those determined for the ZrFe\({}_{12}\) phase. Inverse dependence was observed for Ce and Nd substitutions, where both enthalpies were higher for 2:17-type phases. Si substitution plays a crucial role in all cases, reducing the enthalpy values significantly. To have a clear comparison of the \(\Delta H^{am}\) and \(\Delta H^{ss}\), the difference between both values (\(\Delta H^{am-ss}\)) is presented in Figure 3 in the form of a contour map. This gives us a more reliable way to show the phase formation preferences for each composition. The \(\Delta H^{am-ss}\) data specific for 1:12 and 2:17 compositions are shown in Table 2. The positive values point out compositions for which the formation of the solid solution is thermodynamically preferred over an amorphous phase. This is the case for all 1:12-type compositions gathered in Table 2. In turn, for all 2:17-type phases, except Ce\({}_{2}\)Fe\({}_{17}\), the amorphous phase is preferred. If we take into account the influence of the structural  
Figure 1: Compositional dependences of formation enthalpies of amorphous phase \(\Delta H^{am}\) of ternary (Zr, Ce, 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. enthalpy term (exact values discussed in the Calculations section), this preference should even be slightly strengthened. The most negative value of \(\Delta H^{\text{am-ss}}=-1.3\) kJ/mol was calculated for the Nd\({}_{2}\)Fe\({}_{17}\) composition.