Meaning
Analytical frameworks governing crystal interface movement assume uniform atom attachment across atomically rough solid-liquid boundaries without nucleation barriers. In solidification theory, the continuous growth model calculates interface velocity as a function of thermal undercooling. The model applies to diffuse or rough interfaces and ceases to hold when step-flow or lateral nucleation controls growth on faceted surfaces.
Attachment Speed
Kinetic attachment rates dictate how rapidly liquid atoms incorporate into the solid phase under thermodynamic driving forces. Solidification front advance proceeds proportionally with interface undercooling when structural barriers to atomic attachment are absent. Non-planar growth morphology develops when heat extraction rates fail to remove latent heat released at the advancing boundary.
Thermal Undercooling
Atomic movement across the solid-liquid boundary depends on activation energy barriers for self-diffusion. Higher thermal driving forces accelerate transition rates, driving rapid interface migration during quenching operations. At extreme cooling rates, kinetic resistance at the interface limits growth speed below pure diffusion predictions.
Growth Breakdown
Planar growth breaks down into cellular or dendritic structures when local thermal gradients invert near the solidifying front. Alloy composition influences this transition by establishing constitutional supercooling zones ahead of the boundary. High velocity solidification bypasses traditional nucleation steps, producing homogeneous microstructures suitable for high performance metallic powders and silicon anode precursors.
When interface velocity reaches critical limits, solute trapping suppresses dendritic branching entirely, yielding supersaturated single-phase solid solutions.