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Thermodynamics and Kinetics in Materials ScienceA Short Course$
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Boris S. Bokstein, Mikhail I. Mendelev, and David J. Srolovitz

Print publication date: 2005

Print ISBN-13: 9780198528036

Published to Oxford Scholarship Online:

DOI: 10.1093/oso/9780198528036.001.0001

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Kinetics of heterogeneous processes

Kinetics of heterogeneous processes

Chapter:
(p.189) 11 Kinetics of heterogeneous processes
Source:
Thermodynamics and Kinetics in Materials Science
Author(s):

Boris S. Bokstein

Mikhail I. Mendelev

David J. Srolovitz

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198528036.003.0013

Most practical reactions that occur in synthesizing or processing materials are heterogeneous. These include oxidation, reduction reactions, dissolution of solids in liquids, and most solid-state phase transformations. Consider the oxidation of a metal by exposure of a solid metal to an atmosphere with a finite partial pressure of oxygen. In order for oxidation to occur, molecular oxygen must dissociate into atomic oxygen on the metal surface. In some cases, atomic oxygen diffuses into the metal and reacts to form an internal oxide, while in others, the reaction occurs at the surface. In the latter case, thickening of the oxide layer requires either metal or oxygen diffusion through the growing oxide layer. This example demonstrates that heterogeneous processes commonly involve several steps. The first step is usually the transport of a reactant through one of the phases to the interface. The second is the adsorption (segregation) or chemical reaction on the interface. Finally, the last third step is the diffusion of the products into the growing phase or the desorption of the product. Since the entire heterogeneous process is a type of complex reaction, there is usually one step that controls the rate of the process, that is, is the rate-determining step. Recall that the rate-determining step is the slowest (fastest) step for a consecutive (parallel) reaction (see Sections 8.2.1 and 8.2.2). Consider the case of a consecutive heterogeneous reaction in which one of the reactants is transported through the fluid phase to the solid–fluid interface, where a first-order reaction takes place. The reaction rate ωr in such a case is ωr=kcx, where cx is the concentration of the reactant on the interface. Since the reactant is consumed at the interface, cx is smaller than the reactant concentration far from the interface, c0. It is usually easier to measure the reactant concentration in the bulk fluid. Therefore, it is convenient, to rewrite the reaction rate in terms of the bulk concentration in the fluid and an effective rate constant . . . ωr = kcx = keffc0. (11.1) . . . It is easiest to see the relation between keff and k by considering the steady-state case.

Keywords:   kinetics-limited process, mass-transfer coefficient, transport-limited process

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