## 3 Results and Discussion
### Microstructural Observation  
In the as-cast state of alloy A(0.1 Zr) and alloy B(0.05 Sc), the dendrite structures inside the grains can be clearly observed in Figure 2a,b, respectively. Most of the dendritic structures were eliminated through the one-stage homogenization heat treatment (470 \({}^{\circ}\)C * 24 h) as shown in Figure 2c,d. Similarly, the dendrite structures in the as-cast state were fully eliminated through the two-stage homogenization heat treatment (410 \({}^{\circ}\)C * 3 h + 470 \({}^{\circ}\)C * 20 h). The grain diameter was measured by the intercept method, as shown in Figure 2e,f. The average grain diameters of alloy A(0.1 Zr) and alloy B(0.05 Sc) were approximately 54.0 \(\upmu\)m (standard deviation was 10.3 \(\upmu\)m) and 49.0 \(\upmu\)m (standard deviation was 8.5 \(\upmu\)m), respectively. Figure 2: The optical microscope images of (**a**) as-cast alloy A(0.1 Zr); (**b**) as-cast alloy B(0.05 Sc); (**c**) 1-Hom. alloy A(0.1 Zr); (**d**) 1-Hom. alloy B(0.05 Sc); (**e**) 2-Hom. alloy A(0.1 Zr); (**f**) 2-Hom. alloy B(0.05 Sc). By the measurement of the intercept method, after one-stage and two-stage homogenization heat treatments, the grain diameters of the A(0.1 Zr) alloys were about 58.0 \(\upmu\)m (standard deviation was 12.2 \(\upmu\)m) and 55.0 \(\upmu\)m (standard deviation was 9.5 \(\upmu\)m), respectively; the grain diameters of the B(0.05 Sc) alloys were about 54.0 \(\upmu\)m (standard deviation was 7.5 \(\upmu\)m) and 51.0 \(\upmu\)m (standard deviation was 14.3 \(\upmu\)m), respectively. Therefore, it can be seen that the grain refining of alloy B(0.05 Sc) was better than that of alloy A(0.1 Zr), and that the grains of both alloy A(0.1 Zr) and alloy B(0.05 Sc) were smaller after the two-stage homogenization heat treatment than those after the one-stage homogenization heat treatment. The aluminum alloys containing trace transition elements such as Zr and Sc were prone to precipitate thermally stable dispersed phases (Al\({}_{3}\)Zr, Al\({}_{3}\)Sc) [5]. The TEM microstructures of alloy A(0.1 Zr) and alloy B(0.05 Sc) after the one-stage homogenization heat treatment are shown in Figure 3a,b, respectively. The dispersed precipitation phases of the spherical grains of alloy A(0.1 Zr) and alloy B(0.05 Sc) in the aluminum matrix can be seen. Through the TEM-EDS analysis, the components were Al\({}_{3}\)Zr and Al\({}_{3}\)Sc, respectively, as shown in Figure 3e,f; Figure 3c,d are the TEM microstructures of alloy A(0.1 Zr) and alloy B(0.05 Sc), respectively, after the two-stage homogenization heat treatment. Figure 3: \(Cont.\)  
Comparatively, as shown in Figure 3a,c, after different homogenizations, the grain diameters of the Al\({}_{3}\)Zr dispersed phases of Zr-containing alloy A(0.1 Zr) can be observed through the image software (Image) analysis. The Al\({}_{3}\)Zr after the two-stage homogenization was smaller than that after the one-stage homogenization, and the diameters were about 54 nm and 34 nm, respectively, with a difference of about 40%. In a lower magnification observation, the Al\({}_{3}\)Zr distribution after the two-stage homogenization was denser than that after the one-stage homogenization treatment; however, although the grain diameters of the Al\({}_{3}\)Zr dispersed phases of the Sc-containing alloy B(0.05 Sc) after the two-stage homogenization treatment was smaller than that after the one-stage homogenization (Figure 3d), their diameters were about 81 nm and 72 nm respectively, only with a difference of about 10%. To sum up, the different values of the B(0.05 Sc) alloys are not as obvious as those of the A(0.1 Zr) alloys, and there were no great differences between the levels (81 nm and 72 nm) of the distribution density of the grains precipitating in the B(0.05 Sc) alloys. The phenomena probably occurred because the precipitation temperatures of Al\({}_{3}\)Sc and Al\({}_{3}\)Zr were between 250 \({}^{\circ}\)C-350 \({}^{\circ}\)C [21] and 350 \({}^{\circ}\)C-410 \({}^{\circ}\)C [9], respectively.