An intrinsic-transport model for solid-solid reactions involving a gaseous intermediate
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INTRODUCTION
HIGHtemperature reactions between two solids of the type A(s) + B(s) ~ aB(s) are important industrially and as subjects for the study of kinetics and reaction mechanisms. They are usually carried out in powder compacts or in beds of granular solids. Direct, purely solid-solid reactions are slow. Many solid state reactions actually occur via a liquid or gaseous intermediate. 1 A few well-known reactions where this has been shown or assumed to be the case are summarized in Table I. Consider a mixture of solid reactants A and B in which reactant A is volatile or forms a volatile intermediate compound and assume that reaction proceeds by the volatile species diffusing through the pore space to the B/gas interface and reacting to form ABe on the particles of B: A(g) + aB(s) = ABe(s)
[1]
In the limit, only three distinct rate-controlling mechanisms are of concern in the large majority of such reactions. In the first case, shown in Figure 1, a coherent product layer of the solid AB~ forms on the particles of B and the reaction proceeds by solid-state diffusion of ions through the growing layer of ABe. This diffusional step is slow and is the rate-limiting step. The chemical reactions at the A/gas and/or AB,/gas interfaces, as well as the transport of A(g) to the latter interface, are rapid. This case is quantitatively described by the equations developed by Jander 2 and later by Ginstling 3 and Carter;4 their rate equations are given in Table II. The second case is illustrated in Figure 2. In this morphology the product grows in the form of protuberances (sometimes whiskers) on the surface while much of the surface of B remains exposed to the gas phase. In this case the overall rate is controlled by the rate of chemical reaction at a surface of B. The solid state and/or surface diffusion required to maintain nucleation and growth of the noncoherent AB~ phase 5 as well as transport of A(g) to the B/gas J.R. WYNNYCKYJ is Professor, Department of Chemical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1. W.J. RSUKIN is Principal Research Scientist, CSIRO Division of Mineral Engineering, Clayton, Victoria, 3168, Australia. Manuscript submitted February 17, 1986.
METALLURGICALTRANSACTIONSB
interface are rapid. The formalism for the rate of reaction for surface-reaction control is also given in Table II. 6 The third limiting case, which is also illustrated by Figure 2, is where the supply of the reactant A to the B/gas interface is rate limiting. This means that the gas-phase diffusion, of the intermediate through the pore space of the reacting mixture indicated by appropriate arrows in the figure, is slow while all other steps are fast. The ratecontrolling diffusional step is henceforth referred to as "intrinsic transport". A particularly apparent case where this might occur is at an advanced stage of the reaction where the AB layer, in Figure 2, though porous, is thick and diffusion must occur through it. The more general case is one where the partial pressure of the diffusing intermedia
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