Here's a technical explanation.[1] But here's an example of triggering crystal formation in a supersaturated solution.[2] Classic high school chemistry experiment. Dropping a solid crystal into the supersaturated solution causes the whole liquid to turn into a solid in seconds.

That's the basis of single-crystal casting. The solidification process relies on operating very close to the melting point of the material. The idea is to create an alloy mixture that's ready to crystallize, then starting the process by dropping in a crystal and letting the liquid crystallize in a very controlled way. The heated zone is moved through the liquid, as in zone refining (or the solid is pulled from the heated zone, or gas cooling is used) so that the crystal growth takes place in only a narrow layer.

This is decades old, and one of the reasons jet engines last a long time now.

[1] http://www.asminternational.org/documents/10192/6019788/amp1... [2]