Effects of Positive Feedback on Crystallization Kinetics and Recalescence
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Effects of Positive Feedback on Crystallization Kinetics and Recalescence Sven Bossuyt1, A. Lindsay Greer2 1 Vrije Universiteit Brussel, Department of Mechanics of Materials and Constructions, VUB—TW—MeMC, Pleinlaan 2, B—1050 Brussels, Belgium. 2 University of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge CB2 3QZ, UK. ABSTRACT In bulk metallic glasses cooled at nearly the critical cooling rate for glass formation, nucleation is observed to be spatially localized; nanocrystals are clustered together in spherical regions. This implies that a positive feedback mechanism locally increases the nucleation rate in the vicinity of other nucleation events. Linear stability analysis and computer simulation of differential equations describing crystal nucleation and growth are used to theoretically examine the plausibility of different potential feedback mechanisms. It is shown that interactions between different crystallizing phases can lead to counter-intuitive composition dependence of the crystallization kinetics in the case of non-polymorphic crystallization. INTRODUCTION In a series of alloys in the Cu-Ni-Ti-Zr system, with compositions close to the bulk glass forming alloy Cu47Ni8Ti34Zr11 (Vit101) reported by Lin et al. [1], the nucleation density has been shown to be spatially inhomogeneous; in an amorphous matrix there are spherical clusters with a high density of nanocrystals [2,3]. The implied positive feedback in the nucleation rate was analyzed in terms of a recalescence instability, where the latent heat released upon crystallization causes the nucleation rate to increase locally, if the nucleation rate is an increasing function of temperature and thermal diffusivity is low enough to avoid distributing the heat evenly over the sample. In deeply undercooled liquids, the first of these requirements is satisfied, but the second requirement may not be. There are, however, other mechanisms by which the nucleation rate could be enhanced in the vicinity of other crystals. In principle, any change in the material can affect crystallization kinetics, sometimes drastically. When the change in the material is caused by the crystallization itself, this amounts to feedback in the crystallization mechanism. Every conceivable effect of crystallization on the remaining material could change any of the parameters in the crystallization kinetics, so there are myriad possible feedback paths. Some of these, e.g. the reduction of the remaining material free to crystallize accounted for by the Kolmogorov-Johnson-Mehl-Avrami analysis [4], are well known. Most are usually ignored because it is difficult to gather relevant experimental data. Moreover, different feedback mechanisms often have very similar effects, making it virtually impossible to know which ones should be taken into account and which parameters would allow quantitative analysis of the effects, if those parameters could be measured. However, since feedback results in behavior fundamentally different from that in the absence
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