Concurrent Nucleation and Growth

A discontinuous transformation generally occurs by the concurrent nucleation and growth of the new phase (i.e., by the nucleation of new particles and the growth of previously nucleated ones). In this chapter we present an analysis of the resulting overall rate of transformation. Time-temperature-transformation diagrams, which display the degree of overall transformation as a function of time and temperature, are introduced and interpreted in terms of a nucleation and growth model. 

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The remainder of the book treats discontinuous transformations. Nucleation, which is necessary for the production of a new phase, is treated in Chapter 19. The growth of new phases under diffusion- and interface-limited conditions is treated in Chapter 20. Concurrent nucleation and growth is treated in Chapter 21. Specific examples of discontinuous transformations are discussed in detail these include solidification (Chapter 22), precipitation from solid solution (Chapter 23), and martensite formation (Chapter 24). 

The theory of the kinetics of concurrent nucleation and growth reactions has a rich history that includes work by Kolmogorov [1], Johnson and Mehl [2], Avrami [3-5], Jackson [6], and Cahn [7]. Cahn s time-cone method for treating a class of these problems is the most general of these, with the most transparent assumptions, and is presented here. The method of Johnson, Mehl, and Avrami is covered in Section 4 of Christian s text [8]. 

Time-Cone Analysis of Concurrent Nucleation and Growth... 

Before seeking a morphological model, it is possible to direct research in a certain number of cases. The problem arises primarily for the transformations producing a new solid phase in which it is interesting to know whether a one-process model with only nucleation or growth or a two-process model with concurrent nucleation and growth will be necessary as a morphological model. We have for that a test that is still based on the switch method. 

The structural and morphological features that evolve are the result of the crystallization mechanisms which can, in principle, be elucidated by crystallization kinetic studies. Despite the complex structure of the melt, where the chains are intertwined and entangled, polymer crystallization can be formally treated as a concurrent nucleation and growth process. The classical analysis of Goler-Sachs and Avrami apply. The only modification necessary for polymers is to account for the fact that the transformation is rarely if ever complete. The extent of the transformation, or level of crystallinity that is attained, is very dependent on molecular weight and chain structure. 

Crystallization is a two step process, requiring first nucleation and then crystal growth. In practice, as discussed below in Section V, the two steps occur concurrently, but their explanation is simplified by first considering them separately. Supersaturation is necessary for both nucleation and growth, but its effect is different in the two steps. 

Structural control in sol-gel processes is complicated because many and diverse variables affect concurrent reactions differently. Inductive and steric factors contribute to the reaction rates. pH is probably the single most important variable in these reactions. It accounts for differences when DCCAs are used and for the rapid gel times in Si(OAc)4 sols, as well as differences in the two predominant growth mechanisms nucleation and growth and cluster-cluster aggregation. 

At intermediate SAN contents of 30 wt%, a fully dispersed SAN phase can be detected, leading to an optimum of cell growth in the SAN phase and stabilization by the PPE/PS phase. The lower phase size of the dispersed SAN phase restricts the formation of larger foam cells, while the high SAN particle density and the concurrent nucleation in the PPE/PS matrix induce high cell densities. 

Abyaneh, M. and Fleischmann, M. (1991) General models for surface nucleation and three dimensional growth the effects of concurrent redox reactions and of diffusion. Joutnal of The Electrochemical Society, 138, 2491. 

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