Interface Control

Interface Control的核心是速度瓶颈再界面原子交互，与时间无关，而仅与过冷度$\Delta T$和Dislocation有关，规律最稳定.

分为两种生长模式：

• Continuous: 对Rough
• Crosswise: 对Smooth

Scenarios of occurance

Pure materials (no diffusion needed)

• 热力学条件

纯物质的相变平衡温度为熔点$T_m$，实际相变需过冷（$T<T_m$），此时液态（母相）自由能高于固态（产物相），提供驱动力$\Delta G<0$

• 动力学特征

无溶质成分变化，无需长程溶质扩散

界面原子迁移速率直接决定生长快慢

Alloys at temperatures below $T_m$

• 热力学条件

$T_m$：Equilibrium Phase Transtion Temperature，相变平衡温度；在此温度下，$G_{parent}=G_{product}$,相变驱动力$\Delta G=0$，系统处于动态平衡，宏观上无相变发生

• 动力学特征

溶质分配系数（$k=\frac{c_S}{C_L}<1$）导致界面附近溶质堆积，但温度低于$T_0$时，溶质扩散系数($D$)极低

界面处的原子迁移（如固液界面的连续生长）成为唯一限速步骤

Interface Structure & Corresponding Growth Modes

Atomically Rough Interface

Atomically Smooth Interface

Defect-Assisted Growth (Faster than 2D Nucleation)

For materials with defects, growth is easier.

• Screw Dislocation Growth: Atoms attach to the “spiral” edge of a screw dislocation (no need for 2D nucleation)
• Growth rate rule:

1. For small $\Delta T_k$: $R \propto \Delta T_{k}^{2}$
2. For large $\Delta T_k$: $R \propto \Delta T_{k}$

• Result: A “growth spiral” forms on the interface.

Diffusion Control

Diffusion control means the growth rate (R) is determined by how fast heat or solute diffuses over long distances (not the interface).

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Diffusionless Transformations

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