A note on grain topology-size relationship of three-dimensional polycrystalline microstructures

¹ School of Materials Science and Engineering, University of Science and Technology Beijing - 100083 Beijing, PRC
² Center for Advanced Structural Materials, Department of Mechanical and Biomedical Engineering, City University of Hong Kong - 999077 Hong Kong, PRC
³ State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing 100083 Beijing, PRC

^(a) junhluan@city.edu.hk
^(b) g.liu@ustb.edu.cn

Received: 18 April 2012
Accepted: 26 June 2012

Abstract

A grain topology-size equation for three-dimensional grains is suggested by considering the interactions of the nearest-neighbor grains, which indicates that the average grain size of a given topological class is determined by the difference between the grain face number and the average face number of nearest neighbors. In addition, a practical grain topology-size equation is presented. The two equations show good agreement with various experimental results. They are also verified by data of large-scale Potts model Monte Carlo simulation and Surface Evolver simulation.