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 occu r via nucleation and growth and which produce anisotropic particles. T he derivation, which is coached in terms of aggressor and blocker part icles, accounts for shielding effects and is more easily generalizable to more complex situations than a previous derivation for X(t) for th is problem. Since this 1-D problem is equivalent to the 2-D case in th e limit of low seeding density, the accuracy of our resulting formula for X(t) is assessed by illustrative calculations using elliptically s haped particles. It is found that the derived expression is nearly pre cise. In addition, we examine the influence of particle growth rate an isotropy and particle shape on the importance of shielding effects. We conclude that for growth rate anisotropies (ratio of major to minor a xis growth rates) smaller than 5, shielding effects are not very signi ficant. Also, particle shape appears to have a small effect on transfo rmation kinetics.