I've learned that in general steel and other metals tend to have smaller grains when cooled quickly and larger grains when cooled slowly and that at higher temperatures, the grain size grows even if there is no phase transformation. My question is why does the grain size turn from large at high temperatures to small when rapidly cooled? I've looked online and couldn't find any explanations or pictures of the grains during the cooling process thank you
Grain boundaries cost energy—the bonding quality is worse there—so there's always a driving force to form one giant grain. However, slow kinetics limit this process, so we generally encounter only polycrystalline metals.
As for the grain size, we've got two competing processes: nucleation and growth. With slight undercooling below the phase-change temperature, there's not much driving force for nucleation, as the free-energy release scales up linearly with increasing undercooling. However, the diffusion kinetics are fast, as diffusion scales exponentially with temperature. As a result, the few number of nucleated grains of the new phase grow relatively rapidly to consume the original phase. This produces a final structure of a few large grains.
With strong undercooling, there's a large driving force for nucleation, but the many nucleated grains are very slow to grow. This produces a final structure of many small grains.