Solidification: nucleation and grain growth

Solidification is the change of a metal from liquid to solid. It occurs in two steps: nucleation of tiny solid particles (nuclei) and growth of these nuclei into grains.

Cooling curve of a pure metal

 T
 |\
 | \  liquid cools
 |  \
 Tm |---\  /---------------\     <- arrest at Tm (freezing)
 |     \/                  \
 |  undercooling dT,         \   solid cools
 |  then recalescence          \
 +-----------------------------------> time

A pure metal freezes at a constant temperature $T_m$. The liquid cools to slightly below $T_m$ (undercooling $\Delta T$), nuclei form and release the latent heat of fusion, the temperature rises back to $T_m$ (recalescence), and it stays constant until solidification is complete.

Nucleation

• Homogeneous nucleation: nuclei form in the pure liquid by random clustering of atoms. A cluster of radius $r$ has a free-energy change $\Delta G = \tfrac43\pi r^3\Delta G_v + 4\pi r^2\gamma$. Only clusters with $r > r^*$ (the critical radius) are stable. A large undercooling is needed.
• Heterogeneous nucleation: nuclei form on mould walls, impurities or added inoculants. The surface-energy barrier is lower, so only a small undercooling (0.1-10 K) is needed. This is the usual case in castings; grain refiners (Ti, B in aluminium) exploit it.

Grain growth and dendrites

Nuclei grow as atoms attach to them. When the liquid ahead of the interface is undercooled, small protrusions grow into the liquid faster than the flat front, giving a tree-like crystal called a dendrite (primary, secondary and tertiary arms). The arms thicken until they meet, and the remaining liquid fills the gaps. Each dendrite becomes one grain, and grains meet at grain boundaries.

     |   /|\   dendrite arm
   --+--/-+-\--
     | /  |  \
     |/   |   \

Effect of cooling rate

Fast cooling gives more nuclei, hence fine grains with higher strength and toughness; slow cooling gives coarse grains.