Grain Growth Kinetics under Triple-Junction Drag: Phase-Field Simulations in Two and Three Dimensions

Grain growth kinetics in polycrystalline materials can be governed by either grain boundary mobility or triple-junction mobility. Boundary-controlled growth follows parabolic kinetics (growth exponent n = 2), while junction-controlled growth exhibits linear kinetics (n = 1). Predicting the dominant growth mode for a given material is crucial for microstructural control, yet the specific transition criteria between these regimes remain unclear, particularly for practically relevant three-dimensional systems. Using large-scale phase-field grain growth simulations with explicit triple-junction drag incorporation, we investigated this transition in both two-dimensional and three-dimensional systems containing initially 500,000 grains. By systematically varying the triple-junction mobility, we analyzed grain growth exponent n as a function of the dimensionless drag parameter Λ, which represents the ratio of boundary to junction mobilities scaled by grain size. Results demonstrate that junction-controlled growth (n ≈ 1) occurs when Λ ≲ 0.1, while boundary-controlled growth (n ≈ 2) dominates when Λ ≳ 5–10. Remarkably, despite geometric differences between triple junctions in two dimensions (points) and three dimensions (lines), the variation of n with Λ follows approximately the same trend in both dimensions, suggesting dimensionally invariant transition criteria. Grain size distributions under junction drag continuously evolve without reaching steady states because the drag effect progressively weakens as grain size increases. These findings provide quantitative criteria for predicting growth modes in fine-grained materials, where the volume fraction and influence of triple junctions become significant.