Generalized balanced power diagrams for 3D representations of polycrystals |
| |
Authors: | Andreas Alpers Andreas Brieden Peter Gritzmann Allan Lyckegaard Henning Friis Poulsen |
| |
Institution: | 1. Zentrum Mathematik, Technische Universit?t München, D-85747 Garching bei München, Germany.alpers@ma.tum.de;3. Fakult?t für Wirtschafts- und Organisationswissenschaften, Universit?t der Bundeswehr München, D-85579 Neubiberg, Germany.;4. Zentrum Mathematik, Technische Universit?t München, D-85747 Garching bei München, Germany.;5. Xnovo Technology, Galoche Allé 15, Dk- 4600 Koege, Denmark.;6. NEXMAP, Department of Physics, Technical University of Denmark, 2800 Kgs, Lyngby, Denmark. |
| |
Abstract: | Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its centre of mass position, its volume and, if available, and by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D X-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear programme it can be computed quite efficiently. Based on verified real-world measurements, we show that from the few parameters per grain (3, respectively, 6 in 2D and 4, respectively, 10 in 3D) we obtain excellent representations of both equiaxed and non-equiaxed structures. Hence our approach seems to capture the physical principles governing the forming of such polycrystals in the underlying process quite well. |
| |
Keywords: | power diagrams generalized balanced power diagrams tessellations linear programming grains polycrystals |
|
|