Mobile species

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

The tlrermodynamic activity of nickel in the nickel oxide layer varies from unity in contact with tire metal phase, to 10 in contact with the gaseous atmosphere at 950 K. The sulphur partial pressure as S2(g) is of the order of 10 ° in the gas phase, and about 10 in nickel sulphide in contact with nickel. It therefore appears that the process involves tire uphill pumping of sulphur across this potential gradient. This cannot occur by the counter-migration of oxygen and sulphur since the mobile species in tire oxide is the nickel ion, and the diffusion coefficient aird solubility of sulphur in the oxide are both vety low. 

The primary question is the rate at which the mobile guest species can be added to, or deleted from, the host microstructure. In many situations the critical problem is the transport within a particular phase under the influence of gradients in chemical composition, rather than kinetic phenomena at the electrolyte/electrode interface. In this case, the governing parameter is the chemical diffusion coefficient of the mobile species, which relates to transport in a chemical concentration gradient. 

Whereas in many metals with relatively simple and isotropic crystal structures the parameter / has values between 0.5 and 1, it can have much more extreme values in materials in which the mobile species move through much less isotropic structures with 1-D or two-dimensional (2-D) channels, as is often the case with insertion reaction electrode materials. As a result, radiotracer experiments can provide misleading information about self-diffusion kinetics in such cases. 

The flux by diffusion is described by the diffusivity Di and the migration by the conductivity cr-. The conductivity is proportional to the product of the mobility and the concentration of the mobile species. The diffusivity and mobility are related by the Nernst-Einstein relation [3J. The flux is in general given by... 

Making use of Eq. (25), the maximum conductivity of a solid electrolyte with monovalent mobile species is given by... 

Evidence concerning the identity of the mobile species can be obtained from observation [406,411—413] of the dispositions of product phases and phase boundaries relative to inert and immobile markers implanted at the plane of original contact between reactant surfaces. Movement of the markers themselves is known as the Kirkendall effect [414], Carter [415] has used pores in the material as markers. Product layer thickness has alternatively been determined by the decrease in intensity of the X-ray fluorescence from a suitable element which occurs in the underlying reactant but not in the intervening product layers [416]. 

Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [111] has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. 

In low density reactant compacts, the reaction is believed to involve gas phase oxygen diffusion whereas under conditions of improved contact, in high-density material, the mobile species is identified as Fe2+. The metal catalyzes decomposition of the oxidant (KMn04), an effect that is inhibited by small quantities of certain additives (e.g. NaF). There is a large and specialist literature devoted to self-heating reactions. 

Equations (3.16) and (3.17) describe the dissociative adsorption and, recombination of oxygen on a donor D. The transfer between the donor D and acceptor A is described by eq. (3.18). The spillover oxygen (O) is a mobile species which is present on the acceptor surface without being associated with a particular surface site. The mobile spillover species can interact with a particular surface site B forming an active site C (eq. 3.19). Eq. (3.20) represents the deactivation of the active site C by interaction with a reactant E. 

Similar films are obtained from powdered molecular sieves loaded with organic molecules Zeolite Y microparticles embedded into a polystyrene film and loaded with appropriately sized transition metal complexes allow selective electron exchange reactions between trapped and mobile species in the film... 

Countercurrent electrophoresis can be nsed to split a mixtnre of mobile species into two fractions by the electrical analog of elntria-tion. In such countercurrent electrophoresis, sometimes termed an ion still, a flow of the suspending flnid is maintained parallel to the direction of the voltage gradient. Species which do not migrate fast enough in the applied electric field will be physically swept out of the apparatus. An apparatus based mainly on this principle bnt nsing also natural convection currents has been developed (Bier, Electrophoresis, vol. II, Academic, New York, 1967). 

In liquid Ne, evidence has been found for a high-mobility species, which may be a delocalized electron, that converts to a low-mobility species in several tens of nanoseconds (Sakai et al, 1992). Field dependence of the low-mobility species is supralinear, but the lifetime of the high-mobility species increases with the field strength and decreases with temperature from -2 to -100 ns. 

Just as in the case of (16), an equation of the form (20) applies to any other association-dissociation reaction in which one of the dissociated species is mobile, the other fixed. When the two species are distinct but both mobile, as for hydrogen combining with, say, an interstitial silicon, a similar line of reasoning, whose details we omit, leads to equations of the same form as (16) and (20) but with D+ replaced by the sum of the diffusion coefficients of the two species. When the two mobile species are the same, as for the reaction H° + H° 5H2, it turns out that nA and n+ should each be replaced by the monatomic density n, D+ by the monatomic diffusion coefficient, and 4ir by 8tt in (16) but not in (20). 

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