## 4 Conclusions  
This study aimed to investigate the formation of amorphous structures in Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) and Al\({}_{82}\)Fe\({}_{14}\)Mn\({}_{2}\)Ce\({}_{2}\) alloy powders via mechanical alloying. The primary goal was to determine if a fully amorphous phase could be achieved and to understand the underlying mechanisms. Our results confirm that a fully amorphous structure was successfully obtained in both alloys after 40 h of milling. This demonstrates the effectiveness of mechanical alloying in producing amorphous structures in these specific alloys.  
Initially, after 5 h of milling, both alloys exhibited an fcc solid solution formation alongside residual Al phases. The mixing enthalpies of Al-Ce (\(-\)38 kJ/mol) and Al-Fe (\(-\)11 kJ/mol), and the presence of Fe-Ce pairs with a positive mixing enthalpy (3 kJ/mol), did not hinder the amorphization process. This finding suggests that the appearance of Ce is a crucial factor in the amorphization mechanism, in conjunction with the three empirical rules of Inoue for bulk amorphous alloy fabrication. Additionally, factors like electron configuration and particle size of the raw powders were also found to influence the amorphization of Al-Fe-TM and Al-Fe-RE amorphous alloys.  
Furthermore, our study observed significant changes in magnetic properties during the milling process. The saturation magnetization (M\({}_{\text{s}}\)) values decreased dramatically from 29.5 and 24.69 emu/g to 1.53 and 1.41 emu/g for Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) and Al\({}_{82}\)Fe\({}_{12}\)Mn\({}_{2}\)Ce\({}_{2}\) alloys, respectively. The M\({}_{\text{s}}\) values decreased according to the transformation of the ferromagnetic phase content: starting with the formation of fcc solid solution and subsequently transforming into an amorphous phase. The coercivity (H\({}_{\text{c}}\)) of both alloys also displayed intriguing variations throughout the milling process. At first, H\({}_{\text{c}}\) decreased as milling time increased from 5 to 10 h, attributable to the reduction in the crystallite size of the alloys. However, upon extending the milling time to 20 h, H\({}_{\text{c}}\) values began to rise again due to the deformation of the powders. After 40 h of milling, the Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) and Al\({}_{82}\)Fe\({}_{14}\)Mn\({}_{2}\)Ce\({}_{2}\) alloys underwent a transformation from a solid solution to an amorphous state. This transformation resulted in their coercivity (H\({}_{\text{c}}\)) values reaching their lowest values, which were 156.69 Oe and 158.45 Oe for the Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) and Al\({}_{82}\)Fe\({}_{14}\)Mn\({}_{2}\)Ce\({}_{2}\) amorphous alloys, respectively.  
The amorphous powder of the Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) alloy exhibited a uniform particle size range of 1 \(\div\) 3 \(\upmu\)m with a nearly spherical particle shape, suggesting potential for consolidation into bulk samples.  
Conceptualization, N.H.H. and N.T.H.O.; methodology, N.H.H., N.H.V. and N.T.H.O.; software, N.H.V.; validation, N.H.H., N.H.V. and N.T.H.O.; formal analysis, N.H.V.; investigation, N.H.H. and N.H.V.; resources, N.H.H. and N.T.H.O.; data curation, N.H.V. and N.H.H.; writing--original draft preparation, N.H.H. and N.T.H.O.; writing--review and editing, N.H.V. and N.T.H.O.; visualization, N.H.V.; funding acquisition, N.H.H. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by Project B2022-BKA-16, Ministry of Education and Training of Vietnam, which the authors sincerely appreciate.  
Not applicable.