Cation counterdiffusion

In the classical cation counterdiffusion experiment, oxygen gas is excluded from the interfaces and rM = 0 (Fig. 6-6 a). Thus the coupling condition is simply... 

Figure 5.22 Formation of metal oxide films (a) parallel diffusion of cations and electrons (b) counterdiffusion of cations and holes (c) counterdiffusion of anions and electrons (d) parallel diffusion of anions and holes and (e) counterdiffusion of anions and cations.

Many metal oxides are insulators. In these cases oxidation can only occur if charge neutrality is maintained by way of a significant counterdiffusion of cations and anions (Fig. 5.22e). Once again, mobilities will be equalized by the Nemst field set up when one species moves faster than the other. When counterdiffusion of ions is involved, the oxide film grows at both the inner and outer surfaces. 

Saveant and co-workers have shown that the kinetics for C—C cleavage of radical cations of NADH model compounds fall into this pre-equilibrium regime. Similarly, the slope of log(A obs) vs. AG°ab for a number of C—C containing ion radicals also is about -1/(2.303/ 7 ). The first clear demonstration of the transition from activation to counterdiffusion control was found in a study of the fragmentation of anion radicals of a-aryloxyacetophenones (ArC(0)CH20Ar ). This study used a combination... 

Inert markers have been used to obtain additional information regarding the mechanism of spinel formation. A thin platinum wire is placed at the boundary between the two reactants before the reaction starts. The location of the marker after the reaction has proceeded to a considerable extent is supposed to throw light on the mechanism of diffusion. While the interpretation of marker experiments is straightforward in metallic systems, giving the desired information, in ionic systems the interpretation is more complicated because the diffusion is restricted mainly to the cation sublattice and it is not clear to which sublattice the markers are attached. The use of natural markers such as pores in the reactants has supported the counterdiffusion of cations in oxide spinel formation reactions. A treatment of the kinetics of solid-solid reactions becomes more complicated when the product is partly soluble in the reactants and also when there is more than one product. 

NiO is a cation deficient semiconductor. The fraction of its cation vacancies and compensating electron holes depends on the oxygen potential as discussed in Section 2.3. The isovalent Ca2+ ions can replace Ni2+ ions in the cationic sublattice of the fee matrix by chemical interdiffusion. TiOz and NiO form NiTi03 which dissolves to some extent in the fee matrix of NiO as Ti and Vmc. The counterdiffusion of Ti02 and CaO in the NiO solvent leads to the encounter of the different solute cations (Fig. 9-12a). With increasing overlap of their concentration profiles, the concentration of the product will eventually surpass the solubility limit (and the nucleation barrier). Precipitation of the rather stable CaTi03 compound as an internal reaction product in the NiO matrix is the result. 

To treat solid-solid reactions, Wagner introduced the concepts of local equilibrium and counterdiffusion of cations between the solids. The latter concept forms the basis for Darken s subsequent introduction of the interdiffusion coefficient, which was discussed in Section 2.4. To maintain a state of local equilibrium, the exchange fluxes across the interface must be large compared to the net transport of matter across the boundary. This is analogous to the criterion that the forward and reverse reaction rates be the same, or nearly so, for a reversible reaction to be considered at thermodynamic equilibrium. 

The nature of the cations present in a zeolite can have a marked effect upon the rate of intracrystalline counterdiffusion, as shown by studies with several selected aromatic hydrocarbons in a series of ion-exchanged forms of the type Y zeolite. For 1-methylnaphthalene diffusing from type Y into bulk cumene, the desorptive diffusion coefficients vary by 2 orders of magnitude over different ion-exchanged forms in the order ... 

The results are interpreted in terms of the size of the diffusing molecule and the effect of the cation upon the pore size of the zeolite. Counter diffusion of the molecules studied occurs readily in the various forms of type Y zeolite, but molecule-molecule interactions between the counterdiffus-ing molecules have a pronounced effect upon the diffusion rate. 

Counterdiffusion of cumene and 1-MN occurred readily in type Y zeolite, as shown by several studies. The 1-MN is selectively adsorbed relative to cumene thus, when the zeolite was initially saturated with cumene and placed in 1-MN, essentially 100% of the cumene diffused out but when the zeolite was saturated with 1-MN and placed in cumene, only about 74% of the 1-MN diffused out. The same end point was also reached when SK-500 saturated with cumene was placed in a mixture of 1-MN and cumene in the proper ratio. This selective adsorption equilibrium value was essentially independent of temperature and, except for the cerium form of type Y, was independent of the nature of the cation... 

The ramifications of these findings are many. Unlike Knudsen difusion, the rate of diffusion in one direction is affected markedly by the opposite flux. Adsorption or desorption measurements cannot be used to approximate counter diffusion rates these must be determined independently. They are a function of the nature of the zeohte, the type of cation within the pore structure, and the nature of the counterdiffusing species. 

J. R. Katzer No, we have not studied counterdiffusion in the type X zeolite, but I am now in the process of doing so. The effect appears to be produced by the cations within the pore structure and resting near the pore apertures. Olson (Olson, D. H., J. Phys. Chem. 1968, 72, 4366) indicated that structural variations occurred in the CaX form which careful examination shows could reduce the pore aperture. However, he has recently indicated (Olson, D. H., personal communication, 1970) that the pore aperture remains essentially the same upon exchange from the... 

Cations A and B counterdiffuse independently, with self-diffusion coefficients Z)yv+ and >b+, respectively, that are not functions of composition. 

Electroneutrality is maintained by having the counterdiffusing cation fluxes coupled. Note that for this to happen, the system must be predominantly an ionic conductor, that is, t < // — if not, decoupling of the fluxes will occur (see below). 

The mechanism for such reactions, as proposed by Wagner, is the counterdiffusion of cations. It has been found that this mechanism does occur for purely ionic materials. Counterdiffusion of cations in ionic systems is dictated by charge-balance considerations rather than cation mobilities. Thus significant deviations from the predicted balance may occur when electronic carriers (i.e., electrons and holes) are present. 

These processes are summarized in Figure 25.12. Mechanisms 1 and 2 require that diffuse, which may not be likely, or that electrons can move, which may be the case in semiconducting oxides unless it is prevented. The third mechanism is the counterdiffusion of cations. 

In this case, the most likely mechanism is the counterdiffusion of cations, i.e., the mechanism of Fig. 3.3c, where the electroneutrality is maintained by the coupling of flux of the cations. When the formation rate of the product is controlled by diffusion through the layer of the product, the thickness of the product layer will follow a parabolic growth law, which is given by ... 

In practice, one can say that the transport coefficients of the individual ions are generally rather different from one another. In oxide spinels, the diffusion of oxygen is negligible compared to the cationic diffusion. Therefore, we can eliminate a number of the mechanisms shown in Fig, 6-3. Furthermore, if ideal contact is maintained at the phase boundaries so that the gas phase cannot enter, then the only remaining probable reaction mechanism is the counterdiffusion of cations. In this mechanism, the two cation fluxes in the reaction product are coupled through the condition of electroneutrality. 

In practice, the diffusion coefficients of the ions differ widely. For example, in spinels, diffusion of the large ions is rather slow when compared to cationic diffusion so that the mechanisms in Fig. 2.14d and e can be eliminated. Furthermore, if ideal contact occurs at the phase boundaries so that transport of O2 molecules is slow, then the mechanisms in Fig. 14a and b are unimportant. Under these conditions, the most likely mechanism is the counterdiffusion of... 

Several investigations have reported a parabolic growth rate for the reaction layer, which is usually taken to mean that the reaction is diffusion controlled (32). The reaction between ZnO and FeiOs to form ZnFe204 is reported to occur by the counterdiffusion mechanism in which the cations migrate in opposite directions and the oxygen ions remain essentially stationary (33,34). The reaction... 

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