## 3 Thermodynamics Properties of the Y(Co-Fe-Ni)\({}_{5}\) Alloys
Later on, [PERSON] and [PERSON] [94] re-assessed the Y-Ni system to make it compatible with the three sublattice model used for the Y-Co assessment. This last work was also modified by [PERSON] et al. [129] to fit the Y-Al-Ni system. Finally, [PERSON] and [PERSON] [130] assessed the Y-Ni system using the modified quasichemical model to consider the prevalence of short-range ordering in the liquid phase. In the present study, the initial assessment of [PERSON] and [PERSON] [127] is considered as it agrees with most experimental data [32; 131; 132]. In particular, the heat of formation of YNi\({}_{5}\) (\(-\)29.58 kJ/mole and \(-\)31.05 kJ/mole at 298 and 1000 K, correspondingly) [127] is in accord with the experimental data of \(-\)34.1 kJ/mole (298 K) [32] and \(-\)21.28 \(\pm\) 0.42 kJ/mole (average between 887 and 1224 K) [131] and the calculated value of \(-\)30.09 kJ/mole (= \(-\)22.91 mRy/atom, present study). The resulting CALPHAD model presented in Table 2 for the YTM\({}_{5}\) phase can now be used to calculate the heat of formation of the pseudo-binary YFe\({}_{3}\)(Ni\({}_{1\text{-}}\)Co\({}_{\text{x}}\))\({}_{2}\) alloys with reference to hcp-Y, hcp-Co, bcc-Fe, and fcc-Ni at 298 K. As observed in Figure 2a, the CALPHAD results at 298 K are in excellent agreement with the ab initio predicted values at 0 K. Considering that the CALPHAD database is a combination from various sources (i.e., Y-Co re-assessed from [92], Y-Fe from [126] with new _ab inito_ input, and Y-Ni from [127]), this agreement highlights both the predictive capability of ab initio methods and the flexibility and reliability of the CALPHAD method. The CALPHAD work performed in the present study on the Y-containing binary systems reveals a negative heat of formation across almost the entire YFe\({}_{3}\)(Ni\({}_{1\text{-}}\)Co\({}_{\text{x}}\))\({}_{2}\) pseudo-binary, confirming the great potential of stabilizing a YFe\({}_{3}\)(Ni\({}_{1\text{-}}\),Co\({}_{\text{x}}\))\({}_{2}\) magnet. However, additional assessments are required to include the experimental data gathered on the ternary Y-Co-Ni [91; 95], Y-Fe-Ni [95], and Y-Co-Fe [94; 95] systems to consistently represent the Gibbs energy landscape of the entire Y-Co-Fe-Ni composition space and propose alloy \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Model** & **Reference** \\ \hline \(\text{Y}_{2}\text{TM}_{17}\) & \multicolumn{2}{c}{Sublattice model: (Co,Fe,Ni)\({}_{17}\)(Y)\({}_{2}\)} \\ \hline \(\text{G}_{m}^{Co_{y}Y_{2}}=-282934.050+44.6925387\text{+}17^{0}G_{Co}^{hcp}+2 0G_{Y}^{hcp}\) & This work \\ \hline \(\text{G}_{c}^{Co_{y}Y_{2}}=+1167\) & \\ \hline \(\text{G}_{m}^{Co_{y}Y_{2}}=+27.8\) & \\ \hline \(\text{G}_{m}^{Fe_{3}Y_{2}}=-237121+97\text{+}\text{T}+17^{0}G_{Fe}^{kcc}+20G_{Y} ^{hcp}\) & [126] \\ \hline \(\text{G}_{c}^{Fe_{3}Y_{2}}=+318\) & \\ \hline \(\text{G}_{m}^{Fe_{3}Y_{2}}=+1.98\) & \\ \hline \(\text{G}_{m}^{Ni_{3}Y_{2}}=-386087+61.742\text{+}\text{T}+17^{0}G_{Ni}^{fcc}+20G_{Y} ^{hcp}\) & [121] \\ \hline \(\text{YTM}_{5}\) & Sublattice model: (Co,Fe,Ni)\({}_{5}\)(Y)\({}_{1}\) & \\ \hline \(\text{G}_{m}^{Co_{5}Y}=-117345.473+14.9230313\text{+}\text{T}+5^{0}G_{Co}^{hcp}+0G_{Y} ^{hcp}\) & This work \\ \hline \(\text{G}_{m}^{Fe_{3}Y}=+5000+5^{0}G_{Fe}^{hcp}+0G_{Y}^{hcp}\) & This work \\ \hline \(\text{G}_{m}^{Ni_{3}Y}=-186706+31.187\text{ }\text{ }\text{T}+5^{0}G_{Ni}^{fcc}+0G_{Y}^{hcp}\) & [121] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized thermodynamic parameters of Y\({}_{2}\)TM\({}_{17}\) and YTM\({}_{5}\) compounds with TM = Co, Fe, Ni (l/mole). compositions and thermal treatments to stabilize the Fe-rich Y(Co,Ni,Fe)\({}_{5}\) magnet. The goal of the current paper is to examine the stabilizing outcomes (enthalpy) of adding nickel to the Y(Co\({}_{1-x}\)Fe)\({}_{5}\) alloys and its impact on magnetic properties (Section 4); this additional CALPHAD work will be presented in a follow up paper.