Gaseous reduction of solids

A voluminous literature exists on the kinetics of gaseous reduction of solids in connection with industrial applications. In particular, that of iron oxides has been comprehensively reviewed by Manning and Philbrook [1] As these authors evaluate the situation Although the science of iron ore reduction is nearly a hundred years old, it is still best characterized by uncertainty, by inconsistent experimental data and by conflicting theories . This evaluation seems to us quite adequate (except, perhaps, that a case could be made for replacing a hundred years by three thousand years ), and the statement is applicable to reductions of other solids. 

As is common to general topochemical reactions involving solids, the observed rate of reduction, R, can usually be expressed in terms of a rate r per unit area of reaction interface, multiplied by a surface area, S, which may evolve in many possible ways in time, t, viz. 

T is temperature and C, s are concentrations of reactants, intermediates and products. Very occasionally, in the entire field of solid—gas reactions, intermediates are formed in such a way that reaction rate is not proportional to surface area and eqn. (1) is violated. This has been observed in halide—halogen reactions (Sect. 4) but not in reductions. The specific rate, r, may be controlled by chemical reaction at the reaction interface, or by diffusion of reactants and products through either the gas phase or the solid reacted zone. Therefore, numerous expressions for r are 

The behaviour of S as a function of time t can be crudely classified into two cases. The first corresponds to formation of nuclei of the product and their growth. As shown schematically in Fig. 1, the reaction interface increases until growing nuclei overlap extensively and then decreases, resulting in a sigmoidal dependence of the extent of reaction, a, on time t. When diffusion is not significant, the early stage of the nucleation is described by a power law dependence of a on t 

Usually, n 3. When nuclei start to overlap, the extent of reaction depends on time via the Avrami—Erofeev—Mampel expression 

---