## 3 Results and Discussion
### Refinement Mechanism of B\({}_{4}\)C Addition  
The results obtained from microstructure and thermal analysis clearly demonstrate that addition of B\({}_{4}\)C particles to Al-Mg\({}_{2}\)Si composite caused partial refinement of the Mg\({}_{2}\)Si particles. The appropriate refinement has been obtained with addition of 5 wt% B\({}_{4}\)C. Figure 8 illustrates the SEM microgrpah of primary Mg\({}_{2}\)Si particles including dark particle in its center with corresponding line scanning spectra analysis. As seen, the EDS analysis reavled that the dark color particle in the centre of primary Mg\({}_{2}\)Si is B\({}_{4}\)C. The existance of this particle in the center of Mg\({}_{2}\)Si crystal propose that B\({}_{4}\)C particle may provide favorable nucleation substrates for the Mg\({}_{2}\)Si particles precipitation. In order to find out whether the refining effect is related to the role of B\({}_{4}\)C particles as heterogeneous nucleation sites for primary Mg\({}_{2}\)Si, the crystal structures of Mg\({}_{2}\)Si and B\({}_{4}\)C were compared and the lattice misfit between these crystal structures was calculated. The crystal structures of B\({}_{4}\)C and Mg\({}_{2}\)Si are shown in Figure 9. It can be clearly observed that the atoms distributed on the B\({}_{4}\)C and Mg\({}_{2}\)Si planes are in a different manner. In addition, the calculated lattice misfit between the B\({}_{4}\)C and Mg\({}_{2}\)Si is 43.6%. According to [PERSON]'s two-dimensional lattice misfit theory, if the mismatch between two planes is below 15%, one phase can act as a heterogeneous nucleation substrate for another [29]. Thus, it is observed that B\({}_{4}\)C particles is not likely to meet the character of heterogeneous nucleation substrates for primary Mg\({}_{2}\)Si crystals. Figure 7: Duration of primary Mg\({}_{2}\)Si particles to nucleate and grow as a result of B\({}_{4}\)C additions. Figure 8: (**a**) SEM micrograph of primary Mg\({}_{2}\)Si crystal including B\({}_{4}\)C particle, (**b**) corresponding elemental mapping analysis. Figure 9: Comparison of crystal structures of Mg\({}_{2}\)Si and B\({}_{4}\)C crystals. In addition, Figure 6 depicts that with the addition of B\({}_{4}\)C particles to Al-Mg\({}_{2}\)Si composite, the nucleation temperature (T\({}_{\rm N}\)) of primary Mg\({}_{2}\)Si was reduced. It has been reported that provision of heterogeneous nucleation substrates for primary Mg\({}_{2}\)Si particles through addition of refiners occurred at higher nucleation temperatures which results in a refined microstructure of the composites [30,31]. Hence, it can be concluded that the refinement of Mg\({}_{2}\)Si particles as a result of B\({}_{4}\)C addition is related to the growth stage rather than nucleation. The possible reason for refinement of primary Mg\({}_{2}\)Si particles is the presence of the B\({}_{4}\)C particles that act as a physical barrier during the growth of the primary Mg\({}_{2}\)Si phase during solidification. According to the particle pushing phenomenon, the B\({}_{4}\)C particles are rejected by the solidification front and finally stuck in grain boundary areas [32]. It was expected that with the addition of higher content of B\({}_{4}\)C particles (10 wt%) to Al-20%Mg\({}_{2}\)Si composite, the size of the primary Mg\({}_{2}\)Si decreases. However, as shown in Figures 3 and 4, addition of 10 wt% B\({}_{4}\)C results in a reverse trend as the mean size of primary Mg\({}_{2}\)Si particles increased. In fact, in Al-20%Mg\({}_{2}\)Si-10%B\({}_{4}\)C hybrid composite, the B\({}_{4}\)C particles are agglomerated in some areas in the matrix with non-uniform distribution throughout the composite matrix; therefore, they cannot effectively hinder the growth of primary Mg\({}_{2}\)Si particles in the preferred Mg\({}_{2}\)Si growth directions, which results in an increase in the particles size.