Stereological reconstruction of polycrystalline materials

SUMMARY Laguerre tessellations are suitable models for many polycrystalline materials. In this work, we present a reconstruction‐based approach to fit a spatial Laguerre tessellation model to a plane section of a cellular material under the condition that one section of the model resembles the observed section of the material. To account for this special requirement, we introduce a novel Euclidean distance‐based criterion for the model fitting. The model fitting itself is based on Simulated Annealing. If the structure under consideration is a Laguerre tessellation, we found a nearly perfect reconstruction of its spatial cell characteristics in the model. Even for a real sample of a sintered alumina the observed section is captured quite well by the model. Lay Description A tessellations, that is, a subdivision of space in polyhedral cells, is a suitable model for many polycrystalline materials. In this work we present a reconstruction based approach to fit a three‐dimensional tessellation model to a two‐dimensional section of a cellular material under the condition that one section of the model looks exactly like the observed section of the material. To account for this special requirement, we introduce a novel criterion for the model fitting. The model fitting itself is based on a stochastic simulation. If the structure under consideration is a tessellation, we found a nearly perfect reconstruction of its three‐dimensional cell characteristics, like volume or surface area, in the model. Even for a real sample of a sintered alumina the observed section is captured quite well by the model.