## 3 Results and Discussion
### Influence of B\({}_{4}\)C Addition on Cooling Curves  
Figure 5 demonstrates the cooling curve of Al-20%Mg\({}_{2}\)Si composite with the first and second derivative curves corresponds to different contents of B\({}_{4}\)C. The peaks on the first and second derivative curves represent distinct phase transformations that occurred during solidification. According to the binary phase diagram of Al-20%Mg\({}_{2}\)Si, the first phase is the primary Mg\({}_{2}\)Si, while the second phase is the formation of eutectic Al-Mg\({}_{2}\)Si. It is observed that the addition of B\({}_{4}\)C altered the solidification behavior of the Al-20%Mg\({}_{2}\)Si composite by changing the solidification temperatures (nucleation temperature (T\({}_{\rm N}\)), growth temperature (T\({}_{\rm G}\))) of primary Mg\({}_{2}\)Si phase that is correlated with the microstructures of the composites, as observed in Figure 3.  
Figure 6 shows the nucleation temperature (T\({}_{\rm N}\)) and growth temperature (T\({}_{\rm G}\)) of the primary Mg\({}_{2}\)Si phase which correspond to the various additions of B\({}_{4}\)C. The plotted graph of T\({}_{\rm N}\) has the same pattern as T\({}_{\rm G}\) of primary Mg\({}_{2}\)Si, representing the same influence of the B\({}_{4}\)C on these temperatures. Based on the result, it can be observed that the T\({}_{\rm N}\) of primary Mg\({}_{2}\)Si decreased when the B\({}_{4}\)C addition was introduced from 2.5 to 10 wt%. The same trend of graph is also observed for the T\({}_{\rm G}\) of primary Mg\({}_{2}\)Si phase. From the temperature of 659.2 \({}^{\circ}\)C for base Al-20%Mg\({}_{2}\)Si composite, T\({}_{\rm N}\) of primary Mg\({}_{2}\)Si decreased to 659 \({}^{\circ}\)C, 657 \({}^{\circ}\)C, and 655.8 \({}^{\circ}\)C after the addition of 2.5, 5, and 10 wt% B\({}_{4}\)C respectively.  
Figure 4: Characteristics of primary Mg\({}_{2}\)Si particles in Al-20%Mg\({}_{2}\)Si composite treated with various content of B\({}_{4}\)C.  
Figure 7 depicts the duration (\(\Delta\)t) of primary Mg\({}_{2}\)Si particles formation. The t\({}_{\rm G}\)Mg\({}_{2}\)Si-t\({}_{\rm N}\)Mg\({}_{2}\)Si is used to indicate the time needed for the primary Mg\({}_{2}\)Si to nucleate and grow  
Figure 5: Cooling curves with first and second derivative curves of the Al-20%Mg\({}_{2}\)Si composite added with various B\({}_{4}\)C concentrations: (**a**) 0, (**b**) 2.5, (**c**) 5, and (**d**)10 wt%.  
Figure 6: Nucleation temperature (T\({}_{\rm N}\)) and growth temperature (T\({}_{\rm G}\)) of primary Mg\({}_{2}\)Si phase correspond to different B\({}_{4}\)C additions.  
until complete solidification before the beginning of the eutectic cells. In the base Al-20%Mg\({}_{2}\)Si composite, the duration of primary Mg\({}_{2}\)Si to grow is about 13.82 s. The duration is reduced to 12.59 and 10.32 s as the composite was added with 2.5 and 5 wt% B\({}_{4}\)C, respectively. Nonetheless, the duration of primary Mg\({}_{2}\)Si particles formation increased to 12.42 s when the composite is treated with 10 wt% B\({}_{4}\)C. The difference between the duration is small, which is no more than 3.5 s. It is probable that B\({}_{4}\)C addition plays a role in controlling the growth of Mg\({}_{2}\)Si particles, which results in the changing particle size. The obtained results demonstrate that when Al-20%Mg\({}_{2}\)Si composite is added with 5%B\({}_{4}\)C particles, the duration of primary Mg\({}_{2}\)Si formation is less than other B\({}_{4}\)C additions, which is consistent with the results in Figures 3 and 4, in which the addition of 5%B\({}_{4}\)C to Al-20%Mg\({}_{2}\)Si composite caused the most refinement effect on primary Mg\({}_{2}\)Si particles.