III. RESULTS AND DISCUSSION

Figure 2 shows the XRD results of the Al–x% Mg₂Si (x = 16, 25) composites, indicating that both composites consist of Al and Mg₂Si phases. Figures 3(a) and 3(b) show the cooling curves of the Al–16% Mg₂Si melt at different positions. As can be found, position A has a faster cooling rate than position B, and position C exhibits the slowest cooling rate and near equilibrium solidification. Average cooling rates can be estimated by^{Reference Li, Gill and Varin23,Reference Xu, Wang, Qiu, Yang and Jiang24}

(1)$${V_{{\rm{average}}}} = {{\left( {{T_{\rm{a}}} - {T_{\rm{b}}}} \right)} / {\Delta t}}\quad ,$$

where V _average is the average cooling rate of the Al–Mg₂Si melt, T _a is the initial temperature of the melt, T _b is the final temperature of the melt, and Δt is the time that the temperature decreases from T _a to T _b. Based on the cooling curves, T _b is selected as 550 °C. The average cooling rates of the melt are 32.1, 12.4, and 1.1 °C/s at the positions of A, B, and C, respectively. Figure 4 shows the morphology evolution of the primary Mg₂Si from octahedral to truncated octahedral shapes in the Al–16% Mg₂Si composite. With a slow cooling rate of 1.1 °C/s, the solidification process of position C is near equilibrium solidification. In this case, the {100} faces with the fastest growth rate will disappear while the {111} faces with the slowest growth rate be retained as the Mg₂Si crystal surfaces. Therefore, octahedral Mg₂Si is obtained in the final microstructure [Figs. 4(c) and 4(f)].

FIG. 2.

XRD patterns of (a) Al–16% Mg₂Si and (b) Al–25% Mg₂Si.

FIG. 3.

(a) Cooling curves of the Al–16% Mg₂Si melt with different positions, (b) local enlarged image of (a); (c) cooling curves of the Al–25% Mg₂Si melt with different positions, (d) local enlarged image of (c).

FIG. 4.

Morphology evolution from octahedral to truncated octahedral Mg₂Si in Al–16% Mg₂Si composite with various cooling rates (a) position A; (b) position B; (c) position C; evolution schemes from octahedral to truncated octahedral Mg₂Si (d) position A; (e) position B; (f) position C.

With an intermediate cooling rate of 12.4 °C/s, the solidification process of position B deviates from the equilibrium solidification. The Mg₂Si crystal exhibits truncated octahedron morphology [Figs. 4(b) and 4(e)]. The increase of the cooling rate restricts the growth rates of the 〈100〉 directions and results in morphology evolution of the primary Mg₂Si. With a fast cooling rate of 32.1 °C/s, the solidification process of position A further deviates from the equilibrium solidification. The growth of the 〈100〉 directions is further restricted. Therefore, the primary Mg₂Si shows the truncated octahedron with the extended {100} faces [Figs. 4(a) and 4(d)].

When the coarsening time is relatively long at position C, the solidification process of the Al–Mg₂Si composite is near equilibrium solidification. In the Al–16% Mg₂Si composite, the primary Mg₂Si follows a typical faceted growth pattern, which forms an octahedral shape due to the high growth rate of 〈100〉 directions and the low growth rate of 〈111〉 directions. With the reduction of the coarsening time, the growth rate of 〈100〉 directions is restricted and the {100} faces are retained finally. As a result, the primary Mg₂Si transforms from octahedron to truncated octahedron shape.

Figures 4(d)–4(f) schematically show the morphology evolution of the primary Mg₂Si from octahedron to truncated octahedron shape. The {100} faces of the Mg₂Si crystal appear and extend with the increasing cooling rate. The morphology of the primary Mg₂Si is determined by the ratio of growth rates along the 〈100〉 and 〈111〉 directions, i.e., R = V _〈100〉/V _〈111〉. If $R \ge \sqrt 3$, a dendrite and an octahedron can be obtained; whereas if 1 < R ≤ $\sqrt 3$, a truncated octahedron can be achieved; if ${{\sqrt 3 } / 3}$ < R ≤ 1, a truncated cube can be prepared, and if R = ${{\sqrt 3 } / 3}$, a cube can be formed.^{Reference Wang, Lu and Hogan25} With increasing cooling rate, the primary Mg₂Si transforms from octahedron to truncated octahedron crystal and the ratio of growth rate (R) decreases. Therefore, the growth of the 〈100〉 directions is restrained effectively and the {100} faces are retained finally.

In the Al–Mg₂Si composite, octahedral Mg₂Si is often observed. In some other work, the formation of hollows has been investigated in the {111} faces of octahedral Mg₂Si,^{Reference Li, Wu, Li and Liu21,Reference Qin and Li26} but the growth before the formation of hollows is not clear.

Figures 5(a)–5(e) show the morphologies of the octahedral Mg₂Si at different growth stages. Figure 5(a) reveals the early transition morphology of the octahedral Mg₂Si before the hollows form in the {111} faces. There are deficiencies on the edge center of the octahedral skeleton due to relatively low concentration of Mg and Si atoms, and no complete hollow forms in the center of the {111} faces. As it grows, the Mg and Si atoms gradually fill the deficiencies on the edge centers of the octahedral skeleton. The edges of the octahedral skeleton have the priority to grow and then the {111} faces start to form in Fig. 5(b). Meanwhile, the hollows start to form but have irregular edges in the centers of the {111} faces. Then, the complete hollows form and show regular edges [Fig. 5(c)]. With the successive growth of the octahedral Mg₂Si, the hollow transforms to round shape with lower interface energy [Fig. 5(d)]. Finally, complete octahedral Mg₂Si forms in Fig. 5(e).

FIG. 5.

(a)–(e) Transition morphologies of octahedral Mg₂Si at different growth stages; (f)–(k) schematic illustration of the different growth stages of octahedral Mg₂Si.

Figures 5(f)–5(k) show the schematic illustrations of the different growth stages of the octahedral Mg₂Si. At the starting growth stage, the composition segregation and the various undercoolings result in that the primary Mg₂Si grows preferentially in the positions with higher undercooling degree or larger concentrations of Mg and Si atoms in the Al–Mg₂Si melt. Analogously, the microsegregation of Si atoms in the melt results in easier nucleation of primary silicon.^{Reference Wang, Bian, Qin and Syliusarenko27} Figure 5(f) shows that some bulges rapidly grow on the crystal surface and form the first branches along the preferential 〈100〉 direction. Owing to the concentration gradient around the advancing tips of the first branches, the secondary branches are produced along the 〈110〉 directions in Fig. 5(g). However, there are sunken deficiencies on the edge centers of the octahedral skeleton (the 〈110〉 directions). Figures 6(a)–6(c) show the deficiency evolution on the edge center of the octahedral skeleton. First, the secondary branches preferentially grow on the advancing tips of the first branches [Fig. 6(a)]. Then, the deficiencies form on the edge centers of the octahedral skeleton [Fig. 6(b)]. Subsequently, the growth of the 〈110〉 directions finishes and these adjacent secondary branches connect each other and form the octahedral skeletons [Fig. 6(c)]. After the growth of the 〈110〉 directions finishes and the deficiencies disappear, the hollows form in the {111} faces and show incomplete and irregular edges in Fig. 5(h). With the successive growth of the {111} faces, the hollows shrink gradually and exhibit regular edges in Fig. 5(i). As a result of the decrease of interface energy, the hollows transform to round shape in the {111} faces of octahedral Mg₂Si [Fig. 5(j)] and disappear finally, which leads to the formation of the complete {111} faces and the perfect octahedron Mg₂Si [Fig. 5(k)].

FIG. 6.

(a)–(c) Deficiency evolution on the edge center of octahedral skeleton.

In the early growth stage of the Mg₂Si crystal, the aluminum atoms easily diffuse into a large body of melt on the corners and edges of the octahedron Mg₂Si. However, the aluminum atoms are relatively difficult to diffuse in the center of the surfaces, which results in that Mg and Si atoms concentrate in front of the corners and edges. This factor restricts the growth of the {111} faces and induces the formation of hollows in the {111} faces. Moreover, Xu et al. have suggested that the increase of impurity concentrations in the center of {111} faces terminated the growth of the {111} faces of primary silicon,^{Reference Xu, Wang, Liu and Jiang28} which is another factor to restrict the growth of the {111} faces of octahedral Mg₂Si.

Figures 3(c) and 3(d) show the cooling curves of the Al–25% Mg₂Si melt at different positions. According to Eq. (1), the average cooling rates of the melt are 25.8, 9.8, and 0.6 °C/s at the positions of A, B, and C, respectively. In the Al–25% Mg₂Si composite, the Mg₂Si dendrites were observed at a low cooling rate [Figs. 7(a) and 7(b)]. Based on the discussion above, it is known that the growth rate of the Mg₂Si crystal is greater for 〈100〉 than for 〈111〉 and its growth rate is encouraged by the supersaturation of Mg and Si. First, the first branch (primary dendrite) forms along the preferential 〈100〉 growth directions. Many growth units grow and stretch themselves to the bugles on the primary Mg₂Si dendrite, as shown in Fig. 7(a). Then, the bugles grow into the secondary dendrites in the 〈100〉 directions perpendicular to the primary dendrite, as shown in Fig. 7(b). These growth units of the secondary dendrites produce quickly. In this case, the following growth of the secondary dendrites is strongly limited by the simultaneous growth of its neighbors, and many secondary dendrites overlap or connect to reveal the inconspicuous crystallographic features.

FIG. 7.

Three-dimensional shapes of the extracted primary Mg₂Si in the Al–25% Mg₂Si alloy at low cooling rate: (a) primary dendrite; (b) primary and secondary dendrites; (c) truncated octahedron connecting; (d)–(h) growth process schematics of connected Mg₂Si phases.

In addition, with the low cooling rate, the truncated octahedron Mg₂Si crystals mutually connect to form the complicated crystal structure, as shown in Fig. 7(c). Figures 7(d)–7(h) show the growth process of the connected Mg₂Si phases. The initial Mg₂Si nuclei are likely to be rounded or spherical, as shown in Fig. 7(d). They are inclined to connect and form fluted structure because of the low undercooling and high concentrations of Mg and Si atoms [Fig. 7(e)]. With the subsequent growth and the undercooling variation, the growth manner of the Mg₂Si crystal transforms to faceted and the skeleton of the truncated octahedron Mg₂Si starts to form [Figs. 7(f) and 7(g)]. Finally, the hollows in the {111} faces vanish gradually and the Mg₂Si phases exhibit connected shape in Fig. 7(h).

Figures 8(a) and 8(b) show the morphology of the primary Mg₂Si with the high cooling rate (25.8 °C/s at position A). The primary Mg₂Si exhibits truncated octahedron morphologies in the Al–25% Mg₂Si composite. The primary Mg₂Si dendrite and the complete octahedron Mg₂Si cannot be observed in the composite. Moreover, the truncated octahedron with the round hollow is observed in Fig. 8(b). It suggests that the 〈111〉 directions still have relatively low growth rates compared with those of the 〈100〉 directions.

FIG. 8.

Different three-dimensional shapes of the extracted primary Mg₂Si in the Al–25% Mg₂Si alloy at high cooling rate: (a) truncated octahedron; (b) truncated octahedron with hollow; (c)–(f) growth process schematics of truncated octahedron Mg₂Si phases with and without hollows.

Figures 8(c)–8(f) show the growth process of the truncated octahedron Mg₂Si. With the increase of the cooling rate, the initial Mg₂Si nuclei are difficult to connect each other and separately grow in the melt [Figs. 8(c) and 8(d)]. The subsequent growth process of the Mg₂Si crystal is similar to that of the octahedron Mg₂Si as shown in Fig. 5. Owing to higher concentrations of Mg and Si atoms in the Al–25% Mg₂Si composite, Mg and Si atoms are easier to concentrate in the {111} faces of the Mg₂Si crystal. It increases the growth rate of the 〈111〉 direction and decreases the ratio of growth rates along the 〈100〉 and the 〈111〉 directions, i.e., R = V _〈100〉/V _〈111〉. When 1 < R ≤ $\sqrt 3$, the truncated octahedron can be achieved. Figures 8(e) and 8(f) show the separate growth processes of the truncated octahedron Mg₂Si with and without the hollow. The high cooling rate restrains the cluster and aggregation of the initial Mg₂Si nuclei, which effectively affect the morphology of the primary Mg₂Si in the final microstructure.

In the Al–25% Mg₂Si composite, the higher concentrations of Mg and Si and wider solidification range effectively promote the growth of the primary Mg₂Si at different directions. The primary Mg₂Si exhibits coarse and dendritic morphologies with the long coarsening time (position C). The reduction of the coarsening time restrains the cluster and aggregation of the initial Mg₂Si nuclei so that they are difficult to connect. Therefore, the primary Mg₂Si transforms from complicated dendrite to truncated octahedron morphology.