## 5 Discussion and Conclusions  
According to our past calculations [3, 4], replacing most of Co with Fe in the SmCo\({}_{5}\) magnet and using Ni as a thermodynamic mediator results in an SmFe\({}_{3}\)CoNi magnet that has extraordinary magnetic properties, such as a very high Curie temperature, robust magnetic anisotropy about twice that of the Nd\({}_{2}\)Fe\({}_{14}\)B magnet, and a big maximum energy product (an estimated 70.5% of the record maximum energy product of the Nd\({}_{2}\)Fe\({}_{14}\)B magnet), which should be about 56% larger than that of the SmCo\({}_{5}\) precursor. However, even if we substitute a relatively expensive metal Co (283 RMB/kg) by cheaper Ni (99 RMB/kg) and Fe (3 RMB/kg), the cost of the suggested SmFe\({}_{3}\)CoNi magnet is still mostly defined by the relatively expensive RE samarium metal (450 RMB/kg). Thus, in this paper, we expand on the fundamental idea of refs. [3, 4] by using nickel metal as the stabilizing material in the YCo\({}_{5}\) magnet (Y is almost half the price of Sm [5]) in order to accommodate the maximum amount of iron metal to favor a very high magnetization. We find a significant difference between the regions of stability of the YFe\({}_{3}\)(Ni\({}_{1\text{-}x}\)Co\({}_{5}\))\({}_{2}\) and SmFe\({}_{3}\)(Ni\({}_{1\text{-}x}\)Co\({}_{x}\))\({}_{2}\) alloys. In order to stabilize the SmFe\({}_{3}\)(Ni\({}_{1\text{-}x}\)Co\({}_{x}\))\({}_{2}\) alloys, one should have at least half of the 2c-type sites to be occupied by Ni atoms. The extreme case is the SmFe\({}_{3}\)CoNi magnet, where Fe atoms occupy all 3g-type sites, and Ni and Co atoms occupy the 2c-type sites with equal probability, which has been suggested in refs [3, 4]. For the YFe\({}_{3}\)(Ni\({}_{1\text{-}x}\)Co\({}_{x}\))\({}_{2}\) alloys, it is possible to have the stable solutions until approximately all Ni atoms are substituted by Co atoms. Our ab initio heat of formation predictions are confirmed by CALPHAD modeling at 298 K (Figure 2a). The combination of negative heat of formation and extended solubility limits experimentally observed in the YTM\({}_{5}\) (TM = Co, Fe, Ni) magnets (i.e., complete solubility from YCo\({}_{5}\) to YNi\({}_{5}\) at 1073 K and 1273 K; solubility of \(\sim\)20 at.% Fe in Y(Co,Fe)\({}_{5}\) at 1323 K [94]; solubility of \(\sim\)30 at.% Fe in Y(Fe,Ni)\({}_{5}\) at 873 K [95]) is promising for experimentalists who would like to synthesize these new magnets. Based on a thorough literature review, theoretical calculations, and preliminary CALPHAD works presented in this study, an in-depth CALPHAD assessment of the Y-Co-Fe-Ni system has been initiated and will provide guidance on how to make these new magnets. Meanwhile, a specific example from this work is the YFe\({}_{3}\)Co\({}_{2}\) magnet for which we calculated the Curie temperature, _Tc_, which is equal to 1097.7 K and the maximum energy product, \((BH)_{max}(YFe_{3}Co_{2})\), as \(\sim\)365 kJ/m\({}^{3}\), which is \(\sim\)71% of the record maximum energy product of the Nd\({}_{2}\)Fe\({}_{14}\)B magnet, \((BH)_{max}=512\) kJ/m\({}^{3}\). Here, the maximum energy products of YFe\({}_{3}\)Co\({}_{2}\) and YFe\({}_{3}\)CoNi magnets are estimated using the calculated total magnetic moments of YFe\({}_{3}\)Co\({}_{2}\), YFe\({}_{3}\)CoNi, and YCo\({}_{5}\) magnets as well as the experimental values of the saturated magnetization and the maximum energy product of the YCo\({}_{5}\) magnet. Calculations are performed in the same fashion as for the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet (see Section 4). According to our calculations, the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet has a Curie temperature \(T_{c}\)\(\sim\)900 K that is relatively close to the calculated Curie temperature of the YCo\({}_{5}\) magnet, \(T_{c}\)\(\approx\) 892 K. In addition, the maximum energy product of the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet is significantly improved compared to the YCo\({}_{5}\) magnet (\(\sim\)57% larger).