Transient Nucleation in Devitrification
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ABSTRACT A review is given of transient crystal nucleation in glassy or amorphous solids. The types of behaviour are surveyed. It is shown that the kinetics can be quantitatively modelled and that the matching of experiment and theory provides an important test of the classical theory. Examples are considered of homogeneous nucleation (affecting glass formation), heterogeneous nucleation, and nucleation at an interphase interface. While the emphasis is on transient effects of the kind implicit in the classical theory, it is shown that transients can arise for other reasons as well, thus potentially complicating the interpretation of experiments.
1. INTRODUCTION In the classical theory of nucleation attention is often focused on the critical clusters of the nucleating phase, i.e., those clusters which are in unstable equilibrium with the parent phase. Clusters larger than the critical size can grow spontaneously, and the nucleation frequency at any instant can be taken to be proportional to the population of critical clusters. But a further important element of the theory is that all clusters of the nucleating phase (pre-critical, critical and postcritical) are assembled molecule-by-molecule, and do not arise by single large fluctuations. During nucleation, then, there exists a distribution of cluster sizes; the nucleation frequency can be in steady state only when the steady state size distribution can be established. Attaining the steady state cluster size distribution cannot be instantaneous, and for this reason transient effects arise in nucleation. In many cases, however, such transient effects are negligible, either because transformation of the sample occurs from only a few nucleation events or because the nucleation kinetics themselves are so rapid. A good example is crystal nucleation in the solidification of liquid metals. This typically occurs at low undercooling on a few heterogeneous sites, which cause transformation of the entire sample. Even if nucleation kinetics were important in the overall transformation, it is estimated that steady state nucleation (homogeneous or heterogeneous) would be established after (negligible) times of the order of 1 pis given the large atomic mobilities near the melting point. In devitrification, on the other hand, transient nucleation effects are particularly important. Slow crystal growth means that nucleation kinetics are important in the transformation. Large numbers of nuclei and the ability to interrupt the transformation at any degree of transformation mean that the nucleation kinetics can be accurately determined. Furthermore, the kinetics can be determined under isothermal conditions. Low atomic mobility in the glassy or amorphous state can lead to very substantial times before steady state nucleation is established. The simplest type of transient nucleation effect to consider is that of an effective time-lag before any nucleation is observed. If the glassy or amorphous state were to be produced with no (or a negligible population of) clusters of any kind, then
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