Generalization of the Aboav-Weaire law
1 School of Materials Science and Engineering, University of Science and Technology Beijing - 100083 Beijing, PRC
2 State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing 100083 Beijing, PRC
Received: 3 October 2012
Accepted: 26 November 2012
How cells are arranged in a three-dimensional celluar network is one of the classic problems of physics, biology and materials science. Based on the topological analyses on steady-state grain-growth structure, a generalization of the Aboav-Weaire law to layers beyond the first is suggested that the average number of faces per grain, mj(f), is related to the number of grains, qj(f), in thej-th layer of a center grain with f faces (on average). This result is verified by the data from the curvature flow simulation and assists in better understanding the arrangement of cells in three dimensions.
PACS: 81.10.Jt – Growth from solid phases (including multiphase diffusion and recrystallization) / 81.10.Aj – Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation / 61.82.Bg – Metals and alloys
© EPLA, 2012