Formation of multiphase products

We deal in this section with quasi-binary systems in which more than one product phase A, B forms between the reactants A(=AX) and B(=BX) (Fig. 6-9). The more interfaces separating the different product phases, the more likely it is that deviations from local equilibrium occur (the interfaces become polarized during transport as indicated in Fig. 6-9, curve b). Polarization of interfaces is the theme of Chapter 10. If, however, we assume that local equilibrium is established during reaction, the driving force of each individual phase (p) in the product is inversely 

Adding the different A p s together, one obtains the total thickness 

Equation (6.41) states that the parabolic growth law also applies to the total thickness, and the relative thickness A J /,/ A p of compound p is independent of time. 

With these relations, we can perform quantitative calculations of the reaction kinetics. We start with Eqns. (6.35) and (6.36), which now contain Vp (= volume increase if one mole - or one equivalent — of species / is transported across the reaction layer p). In contrast to the growth of a single phase layer, however, transport occurs now in the two adjacent phases (p—1) and (p+ 1). This additional transport moves the interfaces p- )/p and p/(p+1) in addition to their shift due to the transport in p itself. Therefore, the kinetic differential equation for the growth of phase p has the following form 

In this context, it is again advisable to distinguish between rate constants of the first and second kind. kp, as introduced in Eqn. (6.41), obviously is the rate constant k of the first kind. It describes the growth of phase p when all the other phases form simultaneously. The rate constant kf] of the second kind describes the growth of phase p from phases (p- 1) and (p+ 1) only. 

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