title: Matrix description of the complete topology of three-dimensional cells.
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.
authors.affiliation: School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.|School of Materials Science and Engineering, Liaoning Technical University, Fuxin 123099, People's Republic of China.
authors.forename: Weihua
authors.initials: W
authors.lastname: Xue
authors.affiliation: School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
authors.forename: Hao
authors.initials: H
authors.lastname: Wang
authors.affiliation: Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.|The State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, People's Republic of China.
authors.forename: Guoquan
authors.initials: G
authors.lastname: Liu
authors.affiliation: Beijing R&D Department, East China Branch of Central Iron and Steel Research Institute, Beijing 100081, People's Republic of China.
authors.forename: Li
authors.initials: L
authors.lastname: Meng
authors.affiliation: College of materials and metallurgy, Guizhou University, Guiyang 550025, People's Republic of China.
authors.forename: Song
authors.initials: S
authors.lastname: Xiang
authors.affiliation: Institute of Electrical and New Materials and Microelectronics, State Grid Smart Grid Research Institute, Beijing 102211, People's Republic of China.
authors.forename: Guang
authors.initials: G
authors.lastname: Ma
authors.affiliation: Department of Materials Engineering, The University of Tokyo, Tokyo 113-8656, Japan.
authors.forename: Wenwen
authors.initials: W
authors.lastname: Li
mesh_terms: D000465:Algorithms; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008434:Matrix Bands