Nucleation During a Non-isothermal Process

Under non-isothermal conditions, temperature dependency of key parameters such as nucleation driving force, solute diffusivities and solute concentrations, etc., have been taken into account, and are updated automatically during a simulation.

Another important parameter that depends on thermal history is the incubation time, defined by

[Eq. 1]         

for an isothermal condition. In a non-isothermal process, the exact calculation of the incubation time requires a solution to the Fokker-Planck equation. In the Precipitation Module, an approximation approach has been employed to deal with the transient nucleation, which gives the incubation time as an integral form of past thermal history [2004Jou] as in

[Eq. 2]         

where

is the incubation time, is the impingement rate for solute atoms to the critical cluster as defined in

[Eq. 3]         

and is the Zeldovich factor, previously defined in

[Eq. 4]         

but now as a function of derived from temperature change.

The starting point of the integral is either the starting time if there is an initial nucleation driving force, or the latest time when the nucleation driving force is vanished.

Reference

[2004Jou] H.-J. Jou, P. Voorhees, G. B. Olson, Computer simulations for the prediction of microstructure/property variation in aeroturbine disks. Superalloys, 877–886 (2004).