Kinetics of structural change II - nucleation

We saw in Chapter 6 that diffusive transformations (like the growth of metal crystals from the liquid during solidification, or the growth of one solid phase at the expense of another during a polymorphic change) involve a mechanism in which atoms are attached to the surfaces of the growing crystals. This means that diffusive transformations can only take place if crystals of the new phase are already present. But how do these crystals - or nuclei - form in the first place  

There are two work terms to consider when a nucleus forms from the liquid. Equations (6.1) and (6.2) show that work of the type AH (T, - T)/T, is available to help the nucleus form. If AH is expressed as the latent heat given out when unit volume of the solid forms, then the total available energy is (4/3)ot AH (T, - T)/T, . But this is offset by the work 4 rr ysL needed to create the solid-liquid interface around the crystal. The net work needed to form the crystal is then 

This result has been plotted out in Fig. 7.1. It shows that there is a maximum value for Wjr corresponding to a critical radius r. For r r (dV /dr) is positive, whereas for r r it is negative. This means that if a random fluctuation produces a nucleus of size r r it will be unstable the system can do free work if the nucleus loses atoms and r decreases. The opposite is true when a fluctuation gives a nucleus with r r. Then, free work is done when the nucleus gains atoms, and it will tend to grow. To summarise, if random fluctuations in the liquid give crystals with r r then stable nuclei will form, and solidification can begin. 

This sort of nucleation - where the only atoms involved are those of the material itself - is called homogeneous nueleation. It cannot be the way materials usually solidify because (usually) an undercooling of 1°C or less is all that is needed. Flomogeneous nucleation has been observed in ultraclean laboratory samples. But it is the exception, not the rule. 

Normally, when a pond of water freezes over, or when a metal casting starts to solidify, nucleation occurs at a temperature only a few degrees below T, . Flow do we explain 

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