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.

晶粒生长的行为主导了多晶材料内部微观结构的形成，从而强烈影响了它们的实际性能。然而，尽管经过了几十年的努力，晶粒生长行为仍然不明确，因此缺乏描述一般演变的数学公式。在这里，我们提出了一种新的晶界迁移模型（GB），并进一步推导出一个数学表达式来描述细胞结构中晶粒生长的一般演变。该表达式结合了影响生长速率的变量（例如 GB 特征、晶粒尺寸和局部晶粒尺寸分布），从而揭示了多晶系统中晶粒生长的正常、异常和停滞行为是如何发生的。此外，我们的模型将 GB 粗糙化转变与晶粒生长行为定量相关。