A general mechanism of grain growth—Ⅰ. Theory

The behaviors of grain growth dominate the formation of the microstructure inside polycrystalline materials and thus strongly influence their practical performances. However, grain growth behaviors still remain ambiguous and thus lack a mathematical formula to describe the general evolution despite decades of efforts. Here, we propose a new migration model of grain boundary (GB) and further derive a mathematical expression to depict the general evolution of grain growth in the cellular structures. The expression incorporates the variables influencing growth rate (e.g. GB features, grain size and local grain size distribution) and thus reveals how the normal, abnormal and stagnant behaviors of grain growth occur in polycrystalline systems. In addition, our model correlates quantitatively GB roughening transition with grain growth behavior. The general growth theory may provide new insights into the GB thermodynamics and kinetics during the cellular structure evolution.