PACS 81.10.Jt -Growth from solid phases (including multiphase diffusion and recrystallization) PACS 61.82.Bg -Metals and alloys PACS 81.10.Aj -Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientationAbstract -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.

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.Aj -Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation PACS 64.30.Ef -Equations of state of pure metals and alloys 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.

No abstract