ELSEVIER Journal of Non-Crystalline Solids 202 (1996) 290-296 ]OURNAL OF Avrami exponents for transformations producing anisotropic particles Michael C. Weinberg *, Dunbar P. Birnie III Arizona Materials Laboratory, Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85712, USA Received 18 December 1995 Abstract The behavior of Avrami exponents (AE) for systems which produce anisotropic particles (for which shielding effects and phantoms occur) is examined. Probabilistic arguments used in previous studies are applied to derive expressions for the AE as a function of time or the extent of transformation. Numerical calculations for the one dimensional (1D) cases of site saturation and continuous nucleation show that blocking effects produce a minimum in plots of AE versus extent of transformation. The influence of growth rate anisotropy upon the magnitude of the reduction in the AE is also examined and certain features of the behavior of the AE for 2D and 3D systems are discussed. I. Introduction The goal of the 'formal theory of transformation kinetics' [1] for nucleation and growth transforma- tions is the description of the fraction of material transformed at a given time in terms of the rates of the latter processes. The Johnson-Mehl-Avrami- Kolmogorov (JMAK) theory [2-6] is generally used for this purpose. Furthermore, JMAK theory has been used extensively for the interpretation of crys- tallization experiments and for inferring crystalliza- tion mechanisms from the results of such experi- ments. Quite often these analyses have relied upon the use of the Avrami exponent (AE) described below. * Corresponding author. Tel.: + 1-520 621 6070; fax: + 1-520 621 8059; e-mail: migs@ccit.arizona.edu. For a class of isothermal crystallization processes the fraction of material crystallized after a time t, X(t), can be written as X(t) = 1 - exp{-kt"}, (1) where k is a constant and n is the AE. The value of n depends upon the crystallization mechanism. For example, for continuous nucleation and 3D crystal growth n = 4. Other cases are discussed in Ref. [1]. Thus, if one determines X(t) experimentally and uses the data to construct a plot of In{ - In[1 - X(t)]} versus In t, then from Eq. (1) it should be linear and possess a slope given by the AE. From the determi- nation of the AE the crystallization mechanism is inferred. Eq. (1) is only valid for isothermal crystallization although it has been invoked frequently for the inter- pretation of non-isothermal DTA/DSC experiments. Furthermore, it is known that Eq. (1) must be modi- fied (or is totally erroneous) for certain types of isothermal crystallization processes, too. Examples 0022-3093/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0022-3093(96)003 89-4