Description of the 3d Morphology of Grain Boundaries in Aluminum Alloys Using Tessellation Models Generated by Ellipsoids

Parametric tessellation models are often used to approximate complex grain morphologies of polycrystalline microstructures. A big advantage of such models is the substantial reduction in disk space required to store large, three-dimensional data sets, especially when compared with voxel-based alternatives. By selection of an appropriate tessellation model, a reasonably small loss of information on the real grain shapes can usually be achieved. Special attention has recently been devoted to models based on ellipsoidal approximations fitted to each grain. Faces of these tessellations are portions of quadric surfaces whose parameters can be derived easily. In this paper, we deal with geometric features of the structure, notably curvatures and dihedral angles, which are closely related to the kinetics of grain growth. These characteristics are computed for ellipsoidbased tessellations fitted to two different aluminum alloys with nominal composition Al-3 wt% Mg-0.2 wt% Sc and Al-1 wt% Mg. The results are then compared with estimations based on meshed empirical data. We observe that the model offers more consistent estimations of grain shape characteristics than do the meshed empirical data. Precise description of grain boundaries by the model is also promising with respect to possible applications of these tessellations in stochastic space-time modeling of grain growth.