New extended volume treatment of nucleation and growth in a thin layer between two interfaces

The extended volume concept used in the Kolmogorov-Johnson-Mehl- Avrami (KJMA) model is revised to analyse the nucleation-and-growth behaviour in a thin layer between two interfaces. In this layer, nucleation occurs homogeneously at a constant rate and growth stops at the interfaces. The limitation of the extended volume concept is examined in two previous models: the KJMA model and the Tobin model. In the KJMA model, the extended volume fraction P_ex, of the phantom crystallites (phantoms), is completely included in the extended volume fraction while, in the Tobin model, P_ex is completely subtracted from the extended volume fraction. The use of the KJMA model causes a serious problem in that the transformed fraction is overestimated because the phantoms in the KJMA model partly protrude from the crystallites. In the Tobin model the transformed fraction is underestimated because the contribution of the phantoms is completely neglected. Then the true extended volume fraction Q_ex of the phantoms is expressed as 0 < Q_ex < P_ex. The present model is thus derived by introducing a contribution factor which accounts for the effective size of the phantoms. The contribution factor is more than zéro and less than unity in the present model, while it equals unity in the KJMA model and zero in the Tobin model. The simplified analytic solution of the present model is in much better agreement with the numerical simulations than are the analytic solutions of the KJMA model and the Tobin model.