On the Use of Laguerre Tessellations for Representations of 3D Grain Structures

Accurate descriptions of 3D grain structures in polycrystalline materials are of key interest as the grain structure is closely correlated to the macroscopic properties of the material. In the present study, we investigate the accuracy of using Laguerre tessellations to represent 3D grain structures from only the spatial center of mass location and the volume of the grains. The ability of Laguerre tessellations to describe accurate grain shapes and topologies of real 3D grain structures are revealed by direct comparison to 3D reconstructions of an un‐deformed meta‐stable β ‐titanium alloy obtained by phase‐contrast micro‐tomography. This study reveals that (volume weighted) Laguerre tessellations are superior to classical Voronoi tessellations when it comes to providing accurate representations of real 3D grain structures. Furthermore, although the Laguerre tessellations were only able to correctly describe the local arrangements of grains (i.e., the grain neighbors and number of grain facets) for 31.8% of the investigated grains, the Laguerre tessellations were able to accurately describe statistical grain characteristics such as grain size distributions and grain neighbor distributions. The representation of 3D grain structures by tessellation is studied. Representing the 3D grain structure from a meta‐stable β‐ titanium alloy obtained by phase‐contrast micro‐tomography with both the classical Voronoi tessellation and the Laguerre tessellation (see figure) shows that the Laguerre is superior when the ability to reconstruct the grain shape as well as the topology is considered. In addition, statistical grain characteristics such as grain size distributions and grain neighbor distributions is improved when choosing the Laguerre tessellation over the Voronoi tessellation.