Inspired by the crystallization process, a optimal cooling rate would be one of the following:
- linear cooling
- non-linear cooling: slow first, rapid later
- isothermal crystallization: maintaining the temperature near the melting point
Intuitively, thinking in an extreme way, when the termperature is too high, crystallization will not happen. When the temperature is too low, the atoms cannot acquire energy to escape a local minimum. Thus only an appropriate temperature is useful.
Idealy, the kinetic energy should be just enough for the system to escape a local minimum, but not engough for the system to escape a global minimum, meaning there is a neighbourhood around the melting point to be extra critical. In practice this is hard to control, especially given the random nature of the kinetic energy.