Abstract
A new, efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual domains and their topology evolution in three-dimensional cellular structures. With this approach, we found a lot of new topological grain forms which are never reported before, i.e., there are total 8 and 32 topological forms for 7- and 8-faced grains respectively, other than the reported 7 and 27. This method is proved to be a practical tool to predict all possible grain forms efficiently. Moreover, a connectivity index of grain forms serves as a new convenient differentiator of different multicellular structures.
Highlights
A new, efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual domains and their topology evolution in three-dimensional cellular structures
We found a lot of new topological grain forms which are never reported before, i.e., there are total 8 and 32 topological forms for 7- and 8-faced grains respectively, other than the reported 7 and 27
We have introduced an efficient method to completely describe grain topologies. The application of this method to the grain form analysis has shown that the grain growth microstructure favors topological forms with large algebraic connectivity relative to the Poisson-Voronoi microstructure
Summary
A new, efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual domains and their topology evolution in three-dimensional cellular structures With this approach, we found a lot of new topological grain forms which are never reported before, i.e., there are total 8 and 32 topological forms for 7- and 8-faced grains respectively, other than the reported 7 and 27. Matzke characterized a large population of bubbles by recording the total number of faces and the number of edges of each face in each bubble By extending this method, E.A. Lazar et al.[10] introduced Weinberg vectors[11] and p vectors[12] to describe the grain topology and investigated the topological difference between Poisson-Voronoi and grain growth microstructures. It is necessary to develop a general, efficient method to describe the refined grain topology which can overcome these disadvantages of the above two methods
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