On the validity of Avrami formalism in primary crystallization

Abstract

Articles you may be interested in Molecular dynamics of polymer crystallization revisited: Crystallization from the melt and the glass in longer polyethylene J. Chem. Phys. 139, 054903 (2013) Calorimetric data of primary crystallization is usually interpreted in the framework of the Kolmogorov ͓Dokl. Akad. Nauk SSSR 1, 355 ͑1937͔͒, Johnson and Mehl ͓Trans. AIME 135, 416 ͑1939͔͒, and Avrami ͓J. Chem. Phys. 7, 1103 ͑1939͒; 8, 212 ͑1940͒; 9, 177 ͑1941͔͒ ͑KJMA͒ theory. However, while the KJMA theory assumes random nucleation and exhaustion of space by direct impingement, primary crystallization is usually driven by diffusion-controlled growth with soft impingement between the growing crystallites. This results in a stop of the growth before the space is fully crystallized and induces nonrandom nucleation. In this work, phase-field simulations are used to check the validity of different kinetic models for describing primary crystallization kinetics. The results show that KJMA theory provides a good approximation to the soft-impingement and nonrandom nucleation effects. Moreover, these effects are not responsible of the slowing down of the kinetics found experimentally in the primary crystallization of glasses.

The effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation

“…It is known that in polymorphic transformations, the competition between crystals are purely geometric and they stop growing due to direct hard impingement. 54 However, in the multicomponent solution studied here, soft impingement may be of primary importance due to the significant concentrating effect by the growth of the two competing iceballs (i.e., depletion of water molecules in the same region). In other words, the growth of two adjacent iceballs should be stopped by the dramatically elevated concentration of the solution layer commonly depleted by them, instead of the direct physical contact.…”

A new model for diffusion-controlled precipitation reactions using the extended volume concept

“…(Note that this is different from some other models, notably [13].) The present model focusses on the diffusion fields in the parent phase, and the fraction transformed is thus obtained from the concentrations in the parent phase, through Eq.…”

“…109-119 3 Some of the users of KW model have described this treatment of impingement as 'a simple response equation ' [12], i.e. it is an approximation for which the accuracy is as yet unproven and it has been suggested that the mean field approach underestimates impingement because it ignores a geometrical component to the impingement process [13]. The contribution of a geometrical component has been investigated in [13,14].…”

“…[13,33,34]) can reveal many details at the level of single precipitates, but are computationally expensive to the extend that simulation of impingement is rarely attempted (see [13,35] for rare examples of a phase field model with impingement).…”

“…it is an approximation for which the accuracy is as yet unproven and it has been suggested that the mean field approach underestimates impingement because it ignores a geometrical component to the impingement process [13]. The contribution of a geometrical component has been investigated in [13,14].Benefits of the KW approach are that basic capillarity effects can be included and that, in principle and at some computational costs, the numerical scheme can be implemented to model different groups of precipitates and (in principle 1 ) incorporate coarsening [7,8]. The models described by Svoboda, Fisher and co-workers [15,16] applying the thermodynamic extremal principle (first described by Onsager [17]) employ a mean field approach that is equivalent to the KW approach (see [16]).…”