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


  • The authors thank Stefan Othmar Poulsen for assistance with the image analysis and doing the manual segmentation of the grain boundaries and the European Synchrotron Radiation Facility for provision of beam time. A.L., E.M.L., W.L., and H.F.P. acknowledge the Danish National Research Foundation and the Danish Natural Science Research Council (via DANSCATT) for supporting the Center for Fundamental Research: Metal Structures in 4D, within which part of this work was performed and E.M.L. and R.W.F. furthermore acknowledge the support jointly sponsored by the Office of Naval Research and DARPA as part of the Dynamic 3-D Digital Structure Program (Grant numbers N00015-05-1-0510 & N00014-08-WX20726).


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.