## 4 Summary and Conclusions  
In this paper, we have presented a comprehensive study of the Mg-Zn-Si alloys' microstructure in 3D using X-ray Computed Tomography, electron microscopy, and computational image analyses. The quantification of the complex morphology of intermetallic particles is a challenging task and has significant implications for the micromechanical properties of the alloys. However, 2D characterization techniques and simple 3D morphometric parameters based on 3D particle volume and aspect ratios often fall short in capturing the complex 3D morphology of these intermetallics. Therefore, with a focus on the quantification of morphologies of the MgZn intermetallic particles in 3D, we presented two 3D particle morphology parameters--particle-to-convex hull volume ratio and convex hull sphericity--to quantify the complex morphology of the MgZn intermetallic particles in the biocompatible Mg-Zn-Si alloys. Furthermore, we have presented data on the correlation between particle morphology and particle size, using these new parameters, and showed that both cooling rate and Zn content only slightly influence particle morphology distribution within the analyzed parameters. The main findings of the study are as follows:  
1. The results demonstrate a tendency for the formation of a greater number of large particles with complex interconnected morphologies as the cooling rate decreased and Zn content increased. Cooling rate and Zn content very slightly influence the particle morphology distribution of MgZn eutectic particles within the analyzed parameters;
2. SEM and EDS analysis also revealed that these MgZn particles consist of the eutectic microconstituent Mg-MgZn, rather than solely MgZn as previously reported in the literature. This discovery offers a new perspective on the composition of MgZn particles in these alloys;
3. A novel particle-to-convex hull ratio (\(p\)) was used to quantify the morphology of the different MgZn eutectic particles captured. Smaller particles were found to have simpler morphologies (high \(p\) value), while larger particles were found to have more complex morphologies (low \(p\) values). Furthermore, it was found that the drop in the \(p\) value for the alloys studied in this paper always occurred in the 1000-10,000 \(\upmu\)m\({}^{3}\) volume range;
4. In addition to p, the sphericity of the convex hull(\(s\)) of the particles was also quantified to understand the overall shape anisotropy of the network of MgZn particles in the microstructure. A trend of decrease in the sphericity of the convex hull of particles(\(s\)) was observed in the 1000-10,000 \(\upmu\)m\({}^{3}\) particle volume range with an increase (decrease in anisotropy) observed for particles larger than 10,000 \(\upmu\)m\({}^{3}\);
5. The branching behavior of MgZn particles and their spatial distribution during the early stages of particle formation demonstrated that increasing the Zn content and maintaining low cooling rates facilitate branching. This branching behavior initiates the interconnected network observed in the literature through particle interconnection, underscoring the critical role of particle morphology in network formation. 6. Similar trends for \(p\) and \(s\) versus particle size were observed in particle morphology at different cooling rates and could be attributed to the similarity of dendritic structures within the cooling rate range of 0.44 \({}^{\circ}\)C/s to 1.44 \({}^{\circ}\)C/s, as indicated by the minimal variation in dendritic spacing. The findings presented here open further avenues of research into the 3D microstructure of cast alloys. The findings and tools developed for this study can be applied to other alloy systems, beyond the biocompatible alloys presented in this paper, to understand the complex 3D microstructure of alloys and the impact of microstructure on the mechanical properties. Conceptualization, N.C., J.E.S., E.G. and G.L.d.G. ; methodology, G.L.d.G., E.G. and N.C.; writing--original draft preparation, E.G. and G.L.d.G.