Nonclassical Models for the Critical Nucleus

An extensive formulation of classical and nonclassical models for homogeneous nucleation, as well as experimental tests of their validity, have been carried out for the Co-Cu precipitation system in which coherent Co-rich nuclei form [15]. 

The nucleation rate is also sensitive to the magnitude of the driving energy since, according to Eq. 19.4, AQc is proportional to the inverse square of this quantity. When the temperature is changed and the system becomes metastable, the driving force increases with continued temperature change until the rate of nucleation increases explosively, as indicated in Fig. 19.11. 

It is often useful to estimate values of AQc that may be required to produce an observable nucleation rate. For example, for the nucleation of a solid in a liquid, Eq. 19.33 applies and reasonable values for the various factors in the equation are (A c/3ttA/ fcT)1/2 10 1 zcX% 102 vc 1013 s 1 N 1023 cm 3 exp[—G /(kT) ss 10—3 and J ss 1 cm-3s-1. Therefore, AQC 76kT and AQc must be no larger than approximately 76/cT for observable rates of nucleation to occur. 

The explosive onset of nucleation has made the experimental measurement of nucleation rates difficult, as measurable rates can be obtained only under a very limited range of experimental conditions. An additional difficulty has been counting the actual number of particles formed, since substantial concurrent particle coarsening often occurs (see Fig. 19.1). A common procedure has therefore been to find the driving force (which is relatively easy to quantify) that is necessary to produce 

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