## 3 Results
### MnAl-C Powders after Annealing  
XRD patterns (not shown here) of (Mn\({}_{\text{25}}\)Al\({}_{\text{45}}\))\({}_{\text{100}\times\text{C}_{\text{x}}}\) powders before and after annealing reveal the mixed phases of \(\beta\), \(\gamma_{\text{2}}\), C, Al\({}_{\text{4}}\)C\({}_{\text{3}}\), AlMn\({}_{\text{3}}\), \(\kappa\)(AlMn\({}_{\text{3}}\)C), and \(\varepsilon\)-MnAl, as well as \(\tau\)-MnAl. The ferromagnetic \(\tau\) phase is indexed by the diffraction 29 angles at 24.6\({}^{\circ}\), 41.1\({}^{\circ}\), 46.5\({}^{\circ}\), 53.3\({}^{\circ}\), and 89.2\({}^{\circ}\), respectively, from: (0,0,1); (1,0,1); (1,1,0); (1,1,1); and (2,0,2) planes (JCPDS 01-078-2655 and 00-048-1831). The c/a ratio of \(\tau\)-MnAl is around 1.3, whereas the nonmagnetic \(\varepsilon\)-MnAl has a higher value of 1.6. From the Rietveld refinement, the variations in \(\tau\), \(\varepsilon\), \(\kappa\) phase compositions with C doping and annealing are plotted in Figure 1. From every condition, the \(\tau\)-MnAl in Figure 1a of less than 45% is much lower than those obtained in previous reports [12; 13; 14; 15; 16; 17; 18; 19; 20]. The induction heating without re-melting may yield a lower \(\varepsilon\) phase to begin with, and the \(\varepsilon\rightarrow\tau\) phase transformation can only be moderately increased by extending the annealing time to 2 h [21]. Figure 1 may not exhibit a clear phase variation with C doping, but some trends are observed. First of all, other crystalline and amorphous phases around 10% are present in every sample, as shown in Figure 1d. A total of 90% composition of \(\tau\), \(\varepsilon\), and \(\kappa\) is varied depending on the level of C doping. In Figure 1c, the maximum phase over 20% in MnAl-C3 indicates that the largest C doping promotes the formation of AlMn\({}_{\text{3}}\)C. By contrast, the phase is less than 10% when the C doping is lowered and becomes minimal in the case of MnAl-C2. The remaining phase compositions show the trade-off between \(\tau\)-MnAl in Figure 1a and the decrease in \(\varepsilon\)-MnAl in Figure 1b. The trend is consistent with the \(\varepsilon\rightarrow\tau\) phase transformation upon annealing at around 450-550 \({}^{\circ}\)C [10; 11; 23; 24; 25]. In the case of the MnAl-C3, the intensity of the major \(\tau\)-MnAl peak is significantly reduced, but the minor peak at 53.3\({}^{\circ}\) is increased. The effect of annealing temperature is observable. Without C doping (MnAl-C0), the highest amount of \(\tau\) phase and the lowest amount of \(\varepsilon\) phase are clearly observed after the annealing at 500 \({}^{\circ}\)C. In contrast, the amounts of \(\varepsilon\)-MnAl are still higher than \(\tau\)-MnAl compositions in MnAl-C1 and MnAl-C2 after the annealing. For the highest C doping (MnAl-C3), the \(\varepsilon\) phase is at the lowest in Figure 1b and monotonically decreases with increasing annealing temperature. On the other hand, the \(\tau\) phase reaches the maximum by annealing at 550 \({}^{\circ}\)C. Hence, the C doping not only shifts the \(\varepsilon\rightarrow\tau\) phase transformation to a higher temperature, but also inhibits the decomposition of \(\tau\) phase [10; 11; 25]. The annealing clearly influences the crystallite size, as shown in Figure 2. For all C doping, crystallite sizes of the main MnAl phase are comparable, and the growths are clearly observed after annealing at 550 \({}^{\circ}\)C. However, the largest crystallite in MnAl-C3 is obtained from the annealing at 450 \({}^{\circ}\)C because of the different phase compositions in the as-melted alloys. Figure 1: Weight ratio of (**a**) \(\tau\) phase; (**b**) \(\varepsilon\) phase; (**c**) \(\kappa\) phase; (**d**) other remaining phases in (MnSAl\({}_{5}\))\({}_{100\times}\)C\({}_{\times}\) powders computed from XRD spectra by the Rietveld refinement. After melting in the induction heating tube, MnAl–C0 (x = 0), MnAl–C1 (x = 1), MnAl–C2 (x = 2), and MnAl–C3 (x = 3) samples were annealed at 450, 500, and 550 \({}^{\circ}\)C for 20 min under argon atmosphere.