Time-Cone Analysis of Concurrent Nucleation and Growth

1 Time-Cone Analysis of Concurrent Nucleation and Growth 

Probability that a Point r will not be Transformed at Time t. The probability that a point Fin the sample will be untransformed at the time t is obtained by computing the probability that no nuclei had formed at any location r and any previous time t that could have grown and led to prior transformation at f and t. This is accomplished in three steps  

The probability that exactly zero events occurs is given by Eq. 21.1 as 

In the context of nucleation and growth kinetics, the quantity p corresponds to the nucleation rate, J the product pt corresponds to the number of nucleation events, (N)c, in the time cone and the probability that exactly zero nucleation will have occurred within the time cone is equal to the untransformed volume fraction at time t, 1 — (, giving the relation 

Equation 21.4 forms the basis of the theory for the kinetics of concurrent nu-cleation and growth transformations. Specific cases can be formulated by deriving appropriate expressions for the quantity N)c. 

---