## 3 Results and Discussion
### Microstructural Analyses Using X-ray Computed Tomography (XCT)
#### 3.2.1 Impact of Composition  
Figure 10a shows the correlation between the particle-to-convex hull volume and the particle volumes for the two alloy compositions studied in this paper. The cooling rate for the two compositions is kept the same (0.44-0.48 \({}^{\circ}\)C/s) to enable a fair comparison. From the plot in Figure 10a, we can see that for very small particle volumes (<1000 \(\upmu\)m\({}^{3}\)), the particle-to-convex hull volume ratio (\(p\)) is quite high. This is indicative of very simple particle morphologies (ellipsoidal or spherical), like the one shown in Figure 10a. However, as we consider particles with volume in the range of 1000 to 10,000 \(\upmu\)m\({}^{3}\) we see a gradual drop in the \(p\) ratio--indicating that the particles are becoming more complex and the volume of influence of the particle is becoming much larger than the volume of the particle itself. Furthermore, note that despite the difference in the composition of the particles, the range in which the \(p\) drops, as well as the range to which the \(p\) drops, is comparable for the two compositions. The alloy with 3 wt.% Zn has larger particles, which is expected due to the larger weight fraction of Zn. The different morphologies of particles corresponding to the different size ranges for the 2 wt.% and 3 wt.% Zn alloys are shown in Figure 10b,c. As hypothesized, the smaller particles in the distribution (~1000 \(\upmu\)m\({}^{3}\)) are mostly simple in shape and exist as ellipsoids or spheres. In the transition zone (1000 to 10,000 \(\upmu\)m\({}^{3}\)), we see that the particles show an increased affinity for branching and a general increase in complexity of the network. Finally, for larger particles (>10,000 \(\upmu\)m\({}^{3}\)), we see a stabilization of the \(p\) ratio to 0.05-0.1 with the particles forming very complex networks, as indicated by the examples in Figure 10b,c. The trend of decrease in \(p\) clearly indicates that larger MgZn particles in the alloy form more complex morphologies than simpler ones (spheres and ellipses). This trend can be explained as a direct outcome of the solidification path of the alloys studied in this research. Solidification in this case begins with the crystallization of Mg in the form of dendrites. This is followed by the segregation of Zn and Si into the liquid phase. Subsequently, the eutectic microconstituents (Mg + Mg\({}_{2}\)Si) form in the interdendritic regions, starting from the Mg dendrites that serve as substrates for the onset of solidification. Finally, the last portions of the liquid phase reach the eutectic composition (Mg-Zn + Mg), leading to the formation of MgZn eutectic particles. Therefore, the complex morphology of the MgZn eutectic particles is influenced by the previously solidified dendritic structures of Mg and the eutectic components formed in the interdendritic regions. In contrast to the \(p\) values, which give information about the complexity of the particle morphology, if we consider the sphericity of the convex hull around the particle, we can get insights into the spatial distribution of the complex network of the MgZn particles. For example, if the sphericity of the convex hull is low (<0.5), it may indicate that the MgZn particle had developed in an anisotropic manner (i.e., in the present case, the liquid phase in between the Mg dendrites was more anisotropically distributed). However, if the sphericity of the convex hull is high (>0.5), it may indicate that the particle had developed in a more isotropic manner--either because the particle was small or because the liquid phase in between the Mg dendrites was more isotopically distributed. Consider the schematic shown in Figure 9. The particle shown in Figure 9 has a high sphericity of convex hull compared to the particle shown in Figure 9. In the case of the particle in Figure 9, we can see that the particle has developed in a more isotropic manner, while in the other case, we can see that the particle with the complex morphology has developed in a more anisotropic manner.