## 3 Results and Discussion
### Microstructural Analyses Using X-ray Computed Tomography (XCT)  
A cross-sectional view of the 3D tomography data is shown in Figure 7a, where the brighter regions represent the MgZn phases, while the darker regions represent the Mg matrix (and the Mg\({}_{2}\)Si intermetallics). As in the SEM image, the XCT data clearly show the MgZn phase; however, unlike the SEM data, the XCT technique provides important 3D tomographic data for the MgZn phase. Once the 3D tomographic data were captured using the XRM, they were further analyzed to separate the MgZn intermetallics from the matrix using a simple grey-scale thresholding technique to make a binary (black and white) image, as shown in Figure 7b. The binary image shows the MgZn intermetallics in white and the Mg matrix and Mg\({}_{2}\)Si phase in black. Figure 7c shows a 3D rendering of the MgZn particles in blue; in the 3D rendering, we can clearly see the complex interconnected networks of MgZn intermetallic particles that dominate the microstructure of the alloy. After the binarization, a watershed-based segmentation process [43; 44; 48] followed to obtain individual MgZn particles in the scanned samples in 3D, as shown in Figure 7d. These individual particles appear as large, separated networks of MgZn intermetallics within the alloy. The different colors in Figure 7d are only used to represent the individual MgZn intermetallic particles. These individual particles were then further analyzed to obtain the novel morphological parameters discussed in the subsequent sections. When seen individually, the MgZn eutectic intermetallic particles show a wide range of particle morphologies. Figure 8 shows extreme examples of the MgZn particles that are found in the samples. Smaller MgZn intermetallic particles exist in the form of spherical particles \(\sim\)5-20 \(\upmu\)m in diameter, while larger particles exist in the form of a complex 3D network of nodes and branches. When casting these alloys, the morphology of these intermetallics becomes quite important [43]. Consider a large particle, such as the one shown in Figure 8b. Such a complex particle can influence a large region in the matrix--volumetrically much larger than the particle itself. Furthermore, consider, for example, the effect of a large versus a small particle on the corrosion resistance of the alloy. The acceleration of galvanic corrosion occurs near the interface between the Mg and MgZn phases. This can lead to increased local corrosion and reduced corrosion resistance if these interfaces are abundant and interconnected throughout the material. For smaller particles, such as the one shown in Figure 8a, local interfacial corrosion is expected, which may result in the separation of the  
Figure 6: Detailed image of the MgZn microconstituent observed through SEM-BSE in sample Mg-0.6 Si-3 Zn (at a cooling rate of 0.44 \({}^{\circ}\)C/s) showing the eutectic shape of the MgZn particles and the composition of the MgZn particle and surrounding matrix. intermetallic from the Mg matrix without significant damage to the matrix. However, as the complexity of MgZn particles increases, a larger interconnected interfacial area comes in contact with the matrix. This interconnection enhances localized corrosion in regions where these more complex phase morphologies occur [7; 22; 27; 28; 29; 49; 50]. Therefore, to quantify the spread of the MgZn intermetallic particles, and their complex morphology, a suitable parameter is needed. While there are many 3D particle shape parameters available in the literature [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41], these often fall short in capturing the complex morphology and spread of the particles.