Recrystallization nucleation rate
The number of new, stress-free crystallites formed per unit time in a previously deformed microstructure. It decisively determines the final grain size.
In short, when welding, the structure in the heat-affected zone is deformed and heated. During cooling, new grains form – that's recrystallization. How fine or coarse the grain becomes depends strongly on the cooling rate and the prior deformation. If you cool too fast, the grain becomes fine, but stresses and hardening cracks can occur. If you cool too slowly, the grain grows and the material becomes softer and tougher, but loses strength. In practice, this means: don't quench the weld with water, but let it cool as evenly as possible. If you see a coarse structure, the heat input was too high or the cooling too slow. A fine, uniform grain is usually the goal – you achieve that with a clean, controlled weld without overheating.