Topology-dependent description of grain growth

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
³ College of Materials Science and Engineering, Key Laboratory of Advanced Functional Materials, Ministry of Education of China, Beijing University of Technology - Beijing 100124, PRC

^a g.liu@ustb.edu.cn

Received: 22 July 2011
Accepted: 9 September 2011

Abstract

A growth equation for individual grains is suggested by considering the interactions of the nearest-neighbor grains, which indicates that the average grain growth rate of a given topological class depends on the difference between the number of faces and the average number of faces of the nearest neighbors. For the convenience of its application, a practical equation is also proposed. They have been verified by the data of β-titanium grains, dry 3D foams, Monte Carlo Potts model simulation, vertex model simulation, and surface evolver simulation.