Publisher Summary Solid-state phase transformations are a central topic in physical metallurgy because almost all industrial alloys are heat-treated after casting to improve their properties. Two main types of phase transformation are found: polymorphous changes and precipitation reactions. In a polymorphous change—for example in iron, cobalt, or titanium—there is a change of the metal's crystal structure. This affects all the atoms in the alloy and has a tremendous scope for changing the microstructure of the alloy. In a precipitation reaction, which is crucial in alloys based on aluminum, copper, and nickel having the same crystal structure up to the melting temperature, the main method of modifying the microstructure is to alloy with elements that are soluble in the base metal at high temperature but which come out of solution at lower temperatures. The particles of the new phase are called “precipitates.” In all polymorphous and most precipitation reactions, there is a migration of an interface between two crystalline phases and there are two possible modes of interface migration. In the first of these modes, atoms make thermally activated random jumps across the interface—a “diffusive” mechanism. In the second mode, the daughter crystal grows into the parent by a coordinated shear-type (martensitic) motion of all the atoms at the interface.