CRYSTALLIZATION KINETICS AND THE JMAK EQUATION

In the present work the application of the Johnson-Mehl-Avrami-Kolmogo rov (JMAK) theory for the calculation of the volume fraction crystalli zed is discussed for several particular cases of isothermal transforma tions. In particular, the following three situations, for which the JM AK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and ( 3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle forma tion, finite size effects and non-uniform nucleation lead to a reducti on of the crystallization rate. Furthermore, transformations which pro duce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK t(4) law arising from time dependent nucleation must include size-dep endent growth effects to obtain a logically consistent result. (C) 199 7 Elsevier Science B.V.