## 3 Results and Discussion  
Figure 2 shows the XRD patterns of Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) alloy powders milled for 5, 10, 20, and 40 h, respectively. After 5 h of milling, an fcc solid solution is observed alongside the remaining Al phase. With further milling to 10 h, the intensity of the diffraction peaks decreases and broadens. A broad halo peak can be recognized in the 2\(\Theta\) range between 40\({}^{\circ}\) and 50\({}^{\circ}\), indicating the formation of an amorphous phase after milling for 20 h. The Al is consumed, and only broad diffraction peaks of an fcc solid solution are detected in powders milled after 30 h. No distinct in XRD peaks of any crystalline phases are observed in the powder milled for 40 h, suggesting that the sample has a fully amorphous structure. Figure 1: Schematic diagram of mechanical alloying: (**a**) metallic powders, (**b**) view of ball milling vial, (**c**) alloying process during ball milling, and (**d**) final state of the amorphous alloy. In this work, the amorphization of Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) is completed after 40 h of milling, which is as fast as the Al\({}_{82}\)Fe\({}_{16}\)Ti\({}_{2}\) alloy (achieving a full amorphous structure after 40 h of MA), as mentioned by [PERSON] et al. in [43], and faster than the Al\({}_{82}\)Fe\({}_{16}\)Ni\({}_{2}\) (full amorphous structure after 50 h of MA). However, the Al\({}_{82}\)Fe\({}_{16}\)Cu\({}_{2}\) alloy does not attain complete amorphization even after 60 h of milling. Based on the XRD results for these alloys, the GFA is ranked as follows: Al\({}_{82}\)Fe\({}_{16}\)Cu\({}_{2}\) \(<\) Al\({}_{82}\)Fe\({}_{16}\)Ni\({}_{2}\) \(<\) Al\({}_{82}\)Fe\({}_{16}\)Ti\({}_{2}\), Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\). The three criteria proposed by [PERSON] [11], which relate to the common features of metallic glasses (MGs) with a strong GFA, are as follows: (i) the alloy system consists of at least three elements, (ii) there is a significant negative mixing enthalpy among the elements, and (iii) the atomic size ratios among the main constituent elements are greater than 12%. All four alloys include three elements, thereby meeting the first criterion. For the second criterion, all element pairs exhibit a negative mixing enthalpy (Al-Ti, Al-Ni, Al-Cu, Al-Ce, Fe-Al, Fe-Ti, Fe-Ni) except for the Fe-Cu (\(\Delta\)H\({}_{\rm mix}\) = +13 kJ/mole) and Fe-Ce pairs (\(\Delta\)H\({}_{\rm mix}\) = +3 kJ/mole), as shown in Table 1. Among all element pairs, Al-Ce has the highest negative enthalpy of mixing \(-\)38 kJ/mole. However, the Al\({}_{82}\)Fe\({}_{16}\)Ti\({}_{2}\) alloy shows a negative mixing enthalpy whereas the Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) alloy Fe-Ce pair has a positive enthalpy of mixing. Considering the last criterion of Inoue, the size ratios among the main constituent elements, the atomic size differences of Ti, Ni, Cu, and Ce with respect to Al are 2.7%, 12.5%, 10%, and 21.8%, respectively. It can be observed that the atomic size differences of the transition metals (Ti, Ni, Cu) with solvent atoms (Al) are within the limiting boundary (15%) of the Hume-Rothery rule [45] except Ce with Al (21.8%). The transition metals (Ti, Ni, Cu) have a similar radius to Al, which leads to the formation of a substitutional solid solution with Al, whereas the presence of Ce leads to the formation of an fcc solid solution after milling Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) for 5 h (Figure 2). There are two main factors contributing to the GFA of Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) and Al\({}_{82}\)Fe\({}_{16}\)Ti\({}_{2}\) alloys, which are the atomic size difference and the negative enthalpy of mixing. Additionally, the GFA of Al\({}_{82}\)Fe\({}_{16}\)Ni\({}_{2}\) and Al\({}_{82}\)Fe\({}_{16}\)Cu\({}_{2}\) alloys is lower than that of Al\({}_{82}\)Fe\({}_{16}\)Ti\({}_{2}\), which may be attributed to their less negative enthalpy of mixing  
Figure 2: XRD patterns of Al\({}_{82}\)Fe\({}_{16}\)Ce\({}_{2}\) powders milled for different milling times.