Interface Motion During Phase Transformation

To complete the set of kinetic equations we observe that ub = (A/ /Ac)b where Acb can be expressed in terms of 5 ,b. Finally, the requirement of mass conservation yields a further equation. Considering the inherent nonlinearities, this problem contains the possibility of oscillatory solutions as has been observed experimentally. Let us repeat the general conclusion. Reactions at moving boundaries are relaxation processes between regular and irregular SE s. Coupled with the transport in the untransformed and the transformed phases, the nonlinear problem may, in principle, lead to pulsating motions of the driven interfaces. 

Proceeding systematically, diffusion controlled a-fi transformations of binary A-B systems should be discussed next when a and / are phases with extended ranges of homogeneity. Again, defect relaxations at the moving boundary and in the adjacent bulk phases are essential for their understanding (see, for example, [F. J. J. van Loo (1990)]). The morphological aspects of this reaction type are dealt within the next chapter. 

Interface control of the solid state reaction A+B = AB (e.g., at the AB/B boundary) means inter alia that the chemical potential of reactant A in AB is n°K instead of a + AG°ab at the AB/B interface (Fig. 10-10). It thus seems as if a negative virtual pressure AG°AB/Vm is dragging the interface into the A supersaturated region of B (Fig. 10-10c). From the steady state condition of the moving AB/B interface, we have vh = v°A = y A/cA(B), which gives 

This shows how the steady state velocity of the interface is related to some characteristic parameters of the reacting solids if interface control prevails. 

Sometimes, one has independent information on r. Let us consider an interface controlled spinel formation (A0+B203 = AB204). We assume that the rate limiting interface is AB204/A0 and also that the spinel product is a so-called normal spinel in which the A cations are situated on tetrahedral sites. Therefore, in the super- 

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Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

A vast number of engineering materials are used in solid form, but during processing may be found in vapor or liquid phases. The vapor— solid (condensation) and liquid—>solid (solidification) transformations take place at a distinct interface whose motion determines the rate of formation of the solid. In this chapter we consider some of the factors that influence the kinetics of vapor/solid and liquid/solid interface motion. Because vapor and liquid phases lack long-range structural order, the primary structural features that may influence the motion of these interfaces are those at the solid surface. 

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