## 3 Results and Discussion
### Zr-Nb-Fe (Laves Phases)  
The first example we will consider is the Zr-Nb-Fe system. The phase diagram of this system is shown in Figure 5, after the work of [PERSON] _et al._[14] and the compilation in [15]. The phase of interest is the Laves phase, which exists in its three polymorphic structures, C15, C14, and C36. The transformation of one structure into another along the section joining ZrFe\({}_{2}\) and NbFe\({}_{2}\) when Nb substitutes Zr is quite common and this type of transformation occurs in many different systems. What is less common, and more interesting, is the ability that Nb has to also substitute for the Fe in ZrFe\({}_{2}\), giving rise to an extended \(C14\) homogeneity range Zr(Fe\({}_{1-x}\)Nb\({}_{x}\))\({}_{2}\) extending towards a metastable ZrNb\({}_{2}\). One can therefore appraise the double extension of the Laves phases from ZrFe\({}_{2}\) parallel to both the Nb-Fe and Zr-Nb axes, rather similar to what has been drawn in Figure 2. It is already strange to have  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Strukturbericht** & **Phase Name** & \
\begin{tabular}{c} **Structure** \\ **Type** \\ \end{tabular} &
\begin{tabular}{c} **Pearson** \\ **Symbol** \\ \end{tabular} & **Space Group** & \(n\) & **Inequivalent Sites** & **CN** \\ \hline C14 & Laves phase & MgZn\({}_{2}\) & \(hP12\) & \(P6_{3}/mmc\) & 3 & \(4f\) & \(16\) \\  & & & & & \(6h\) & \(12\) \\ \hline C15 & Laves phase & MgCu\({}_{2}\) & \(cF24\) & \(Fd\overline{3}m\) & 2 & \(8a\) & \(16\) \\  & & & & & \(16d\) & \(12\) \\ \hline C36 & Laves phase & MgNi\({}_{2}\) & \(hP24\) & \(P6_{3}/mmc\) & 5 & \(4f\) & \(16\) \\  & & & & & \(6g\) & \(12\) \\  & & & & & \(6h\) & \(12\) \\ \hline \(A12\) & \(\chi\) phase & \(a\)Mn & \(cJ58\) & \(l\overline{4}3m\) & 4 & \(2a\) & \(16\) \\  & & & & \(8c\) & \(16\) \\  & & & & & \(24g\) & \(13\) \\  & & & & & \(24g\) & \(12\) \\ \hline \(D_{\rm 8b}\) & \(\sigma\) phase & CrFe & \(tP30\) & \(P4_{2}/mmm\) & 5 & \(2a\) & \(12\) \\  & & & & & \(4f\) & \(15\) \\  & & & & & \(8i\) & \(14\) \\  & & & & & \(8i\) & \(12\) \\  & & & & & \(8j\) & \(14\) \\ \hline \end{tabular}
\end{table}
Table 1: List of the phases discussed in the following sections, with major crystallographic information.  
the Zr\({}_{2}\)Fe homogeneity domain in one direction (parallel to the Zr-Nb axis) and the C14 domain in another direction (parallel to the Fe-Nb axis). Even stranger is the fact that this is now the same phase extending in two different directions. Noteworthy is the fact that this phenomenon also causes a miscibility gap inside the intermetallic phase with an observed equilibrium between two C14 structures (two phase domain marked C14 + C14), instead of a complete solubility domain.  
In order to better understand this phenomenon, DFT calculations have been carried out in this system. Figure 6 presents the ground state at 0 K of the \(C14\) structure in the form of a ternary phase diagram. The figure clearly evidences the V-shape of the \(C14\) phase extending from ZrFe\({}_{2}\) to both ZrNb\({}_{2}\) and NbFe\({}_{2}\) compositions. One may also note the stability of the configu  
Figure 4: Structure drawing of the phases discussed in the following.  
Figure 5: Isothermal section at 800 \({}^{\circ}\)C of the Zr–Nb–Fe system (redrawn from [14,15]). The red triangle shows the three ordered stable or metastable compositions of the Laves phase: ZrNb\({}_{2}\), ZrFe\({}_{2}\), and NbFe\({}_{2}\), as in Figure 2 (solid lines: normal substitution, dashed line: site reversal).  
composition Zr(Fe\({}_{0.25}\)Nb\({}_{0.75}\))\({}_{2}\) and the miscibility gap in the C14 phase between the two arms of the V. These two features reproduce what is observed in the experimental determination.