Shielding effects in 1-D transformation kinetics

A new derivation is presented for the fraction of material transformed as a function of time, X(t), for 1-D phase transformations which occur via nucleation and growth and which produce anisotropic particles. The derivation, which is coached in terms of aggressor and blocker particles, accounts for shielding effects and is more easily generalizable to more complex situations than a previous derivation for X(t) for this problem. Since this 1-D problem is equivalent to the 2-D case in the limit of low seeding density, the accuracy of our resulting formula for X(t) is assessed by illustrative calculations using elliptically shaped particles. It is found that the derived expression is nearly precise. In addition, we examine the influence of particle growth rate anisotropy and particle shape on the importance of shielding effects. We conclude that for growth rate anisotropies (ratio of major to minor axis growth rates) smaller than 5, shielding effects are not very significant. Also, particle shape appears to have a small effect on transformation kinetics.