Bulk diffusion limitations and phase boundary kinetics inferred using specimen resistance change
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T H E kinetics of the following distinct types of gas/solid chemical reactions can be conveniently studied by monitoring the electrical r e s i s t a n c e - t i m e behavior of a solid specimen upon exposure to gaseous reactants: a) Volatile Reaction Product(s). When the specimen is not m e r e l y a catalyst, its d i m e n s i o n s will change during the c o u r s e of reaction, thereby causing its electrical resistance, R (measured at constant t e m p e r a ture), to continuously increase. A simple example would be the oxidation of tungsten filaments at elevated temperatures 1 b) Condensed Reaction Product of Negligible E l e c t r i cal Conductivity. Here the specimen resistance again increases due to a continuous reduction in the unreacted c r o s s - s e c t i o n . Examples involving a sharp p r o d u c t / r e actant phase boundary would be the sulfidation of iron, 2 or the carbonization of high-temperature tungsten when exposed to simple hydrocarbon vapors. 3 c) Reactant Dissolution. If the reactant, or an element in the reactant, goes into solution in the solid (without causing either the formation of a new phase, o r volatile reaction products), 4 and the specimen r e s i s t ivity is sufficiently sensitive to solute concentration, then resistance changes can be used as a measure of the extent of solution. ~-9 Simple examples of this type would be the nitrogen " e n g a s s i n g " of niobium and tantalum filaments. 8'9 In each of the above limiting cases,* isothermal *Two (or more) of these processes frequently occur simultaneously.
R(l)-data comprise the starting point for the inference of kinetic p a r a m e t e r s describing the rate of the r e l e vant phase-boundary reaction. 6-1~ These overall rate p a r a m e t e r s , in turn, provide general information conDANIELE. ROSNERis Associate Professor of Engineering and Applied Science, Chemical Engineering Group, Yale University, New Haven, Conn. Manuscript submitted January 17, 1972. METALLURGICAL TRANSACTIONS
cerning elementary (atomic level) events at the phase boundary.* *Special care must be taken in performing engassing/degassingkinetic experiments to avoid contamination of the surface by foreign elements present either in the feed gas mixture, or initially present in the specimen bulk.
The relation between such R(t)-measurements and amount of reaction is particularly straightforward in c a s e s (a) and (b) since the effect is a purely geometric one, becoming trivial for elongated specimens with a high degree of s y m m e t r y (e.g., circular filaments or flat ribbons). For case (c), however, the interpretation of R(t)-data is simple only if the electrical resistivity is a single-valued function of solute concentration, and concentration gradients within the specimen are negligible at all times. This latter condition is a particulaxly stringent one, frequently dictating the use of very thin, hence fragile, specimens. Moreover, the question of how thin is "sufficiently" thin (to cause a prescribed e r r o r in the inferred kinetic constant
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