## 2 Materials and Methods  
The Al-Mg-Si alloys were produced using gravity casting with 99.8 wt.% commercial pure Al, a 98.5 wt.% Si pellet, and 99.9 wt.% pure Mg. The alloys were comprised of different Mg and Si contents, and their compositions are shown in Table 1; the composition of Al-1.1 Mg\({}_{2}\)Si alloys is located in the hypo-eutectic field on the Al-Mg\({}_{2}\)Si phase diagram [20]. The Al-1.9 Mg\({}_{2}\)Si alloy was designed for the eutectic composition in the Al-Mg\({}_{2}\)Si system. The Al-1.9 Mg\({}_{2}\)Si alloy is located in a hyper-eutectic field on the phase diagram. The chemical compositions of the alloys were investigated through spark emission spectroscopic analysis. Gas bubbling filtration treatment was performed at 750 \({}^{\circ}\)C for 15 min with high purity (99.9%) Ar gas in the melt. The melt was stabilized for 15 min prior to casting. The melt was then poured into a permanent mold which was preheated to 95 \({}^{\circ}\)C after stabilization.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Alloys** & **Al** & **Si** & **Mg** & **Fe** & **Mg\({}_{2}\)Si** \\ \hline Al-1.1 Mg\({}_{2}\)Si & 98.80 & 0.39 & 0.73 & 0.10 & 1.1 \\ Al-1.9 Mg\({}_{2}\)Si & 97.91 & 0.67 & 1.32 & 0.11 & 1.9 \\ Al-3.5 Mg\({}_{2}\)Si & 96.30 & 1.22 & 2.36 & 0.11 & 3.5 \\ \hline \end{tabular}
\end{table}
Table 1: The chemical compositions of studied alloys.  
The samples were heat treated at 590 \({}^{\circ}\)C for 30 min in the solution treatment, then quenched in water (at approximately 80 \({}^{\circ}\)C) in order to form a supersaturated solid solution. The samples were then aged at different temperatures from 180 to 240 \({}^{\circ}\)C. In addition, Al-1.9 Mg\({}_{2}\)Si was aged at 340 \({}^{\circ}\)C so as to observe the Mg\({}_{2}\)Si precipitate. The Mg\({}_{2}\)Si precipitate was observed using an optical microscope (OM), a scanning electron microscope (SEM), and a transmission electron microscope (TEM) after the aging treatment.  
Thermal diffusivity was measured using a laser flash apparatus (LFA 457, NETZSCH, Selb, Germany). The samples were cut to a diameter of 12.7 mm and a thickness of 2.5 mm for the thermal diffusivity measurements. The samples were coated using a carbon spray prior to analysis in order to prevent the laser from reflecting on the surfaces of the samples. The LFA test was performed at a temperature range from 25 to 500 \({}^{\circ}\)C five times.  
A differential scanning calorimetry (DSC) device (DSC 404 F1, NETZSCH, Selb, Germany) was used to investigate the microscale phase transformation by heat treatment condition. The samples were cut into cylindrical shapes of 6 mm diameter and 1 mm thickness. The DSC analysis was performed at a temperature range from 20 to 530 \({}^{\circ}\)C at a rate of 10 \({}^{\circ}\)C/min in a 99.999% N\({}_{2}\) atmosphere. The gas flow was fixed at 50 mL/min and a pre-vacuum sequence was performed in order to prevent oxidation of the samples.  
An X-ray diffraction (XRD) device (X'pert Pro, PANalytical, Amelo, The Netherlands) was used to investigate the diffraction pattern of as-quenched Al-1.9 Mg\({}_{2}\)Si; the sample was also analyzed after DSC measurement. The sample was then used to identify the dissolution and precipitation of the Mg\({}_{2}\)Si phase in Al-Mg\({}_{2}\)Si alloy. Cu K\(\alpha\) radiation was used to define the sample precipitates.