## 3 Results and Discussion
### Microstructural Analyses Using X-ray Computed Tomography (XCT)
For example, parameters such as the equivalent spherical diameter (diameter of a sphere with the same volume as that of the particle), the bounding box (smallest cuboidal that encompasses the entire particle) volume, and Feret diameter (distance between two parallel planes bounding the particles) can capture the size of the particle; however, the complex network-like morphology is elusive to these parameters [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 41; 43]. Figure 7: After the acquisition of XCT data, it was critical to separate the Zn-rich phases from the rest of the microstructure of the alloys: (**a**) after initial filtration using non-local means filtration, the Zn-rich phase was segmented using a (**b**) simple greyscale thresholding technique, following which the individual Zn-rich intermetallic particles were (**c**) visualized in 3D and then individually separate following a (**d**) 3D watershed-based analyses, and then the separated particles were further analyzed to derive size and shape parameters (different colors in (**d**) are only used to represent the individual MgZn intermetallic particles following the watershed analyses). To better capture the shape and morphology of the particles, consider the concept of a convex hull. For a set of points on a plane, the convex hull is the smallest polygon that completely encompasses the points [51]. For a 3D particle, the convex hull is defined as the smallest convex polyhedron (all interior angles are less than 180\({}^{\circ}\)) that encloses the entire particle. In the context of the complex particle shown in Figure 8b, it represents the \"volume of influence\" of the particle to an extent. Furthermore, unlike the bounding box, the convex hull can more accurately capture the volume of the matrix that the particle influences (either mechanically or chemically). For a simple particle such as a sphere or an ellipse, similar to the particle shown in Figure 9a, the convex hull is very similar to the outer surface of the particle. In contrast, for the complex particle shown in Figure 9b, the convex hull takes the form of a large surface that encompasses a volume much larger than that of the particle itself. Figure 8: Particle morphologies within the alloys: after watershed analyses, the different particles within the alloys were extracted and it was observed that there were two extremes of particle morphologies present in the microstructure; (**a**) highly spherical particles tend to be smaller in size, while (**b**) larger particles tend to have a complex 3D network morphology. Figure 9: The convex hull (shown in red) as a function of the anisotropy of the spread of particles (shown in black): (**a**) spherical particles have a convex hull very close to the outer surface of the particles, hence the convex hull sphericity (_s_) is a close approximation of the sphericity of the particle itself; in contrast, for the case of (**b**), a particle with complex morphology with a more anisotropic spatial distribution will have a lower sphericity of convex hull (_s_); further, (**c**) a complex particle with more isotropic spatial distribution will have a higher sphericity of convex hull. Therefore, an elegant approach to distinguishing the smaller particle, with the more simple morphology, from the larger particle, with the more complex morphology, would be to take the ratio (\(p\)) of the particle volume to the volume encompassed by the convex hull [43]. The larger particles with the more complex morphology will have a small value of \(p\), whereas the smaller particle with a simpler morphology will have a large (close to 1) value of \(p\). Furthermore, if we consider the shape of the convex hull--as quantified by the sphericity of the convex hull (\(s\))--we can also derive an indication of the anisotropy of the shape of the complex particles. Sphericity is a measure of how closely the shape of an object resembles the shape of a sphere. It is defined as the ratio of the surface area of a sphere with the same volume as the object to the surface area of the object [52].