Diffusion of Oxygen Atoms

Let s consider the electrode system O2, Pt Zr(Y)02 j/2 at the diffusion of oxygen atoms on metal with the following two assumptions the electrode represents itself the dense platinum stripe with width 2xq, attached to the zirconia electrolyte, and the coefQcient of oxygen diffusion in the adsorption layer is independent from the oxygen concentration. We will deduce an equation of polarization curve for this system. 

The solution ofEquations (1.51) and (1.52) carries out at the following boundary conditions  

For the second stage of the electrode process, using Pick s second law and the ionization reaction O -t 2e - 0 , the local current density on the ME interface can be written considering that the activity of oxygen ions in zirconia is a constant value  

FIGURE 1.20 Polarization curves of the oxygen electrode at the surface diffusion of oxygen atoms digits on curves represent ho. 

Both correlations (1.54) and (1.58) are related to the electrodes with the uniform structure, when the width of both gas-metal and metal-zirconia surfaces is much bigger than the values for and A e. In the case of correspondence of their values, the speed of the electrode process will be predominantly determined by the exchange reactions, and Equation (1.58) will be as follows  

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It can be concluded that the formation of the voids in the center of SnOi particles is mainly a result of the Kirkendall effect [8] associated with a faster outward diffusion of Sn atoms as compared to the inward diffiision of oxygen atoms in the process of the surface oxide layer formation. This produces high density of vacancies at the metal side of the metal/oxide interface. Vacancies transform to vacancy clusters which then aggregate into holes. It might be expected from this model that the increase of oxygen content in the ambiance will result in the promotion of an inward diffusion of oxygen atoms into the Sn particles, and therefore, suppress the formation of holes. 

Exposed to an unlimited supply of gas phase particles characterized by the applied pressures and temperature, the surface will adapt on time scales set by the kinetic limitations. Already these time scales could be sufficiently long to render corresponding metastable states interesting for applications. In fact, the classic example is a slow thickening of oxide films due to limitations in the diffusion of oxygen atoms from the surface to the oxide-metal interface or in the diffusion of metal atoms from the interface to the surface [37,38]. Directly at the surface a similar bottleneck can be the penetration of oxygen, which... 

Mass transfer, basically taking place by the diffusion on the interphase surfaces, stipulates the transfer of electrochemically active components from the places of adsorption to the places of the electrochemical reaction. A scheme of the electrode process development allows various scenarios determined by the combination of the separate stages. For example, elechode system M,021variants, considering the extension of the reaction zone in the contact of the TPB by the surface diffusion of oxygen atoms, subions (O), and electron (holes), come to the following (scheme for anodic reaction) ... 

There is no doubt that the variants described above cannot comprehend aU the possible ways of the reaction zone extension, even for the relatively simple electrode system. It is possible that some of the electrode processes can take place simultaneously on the gas-electrolyte, gas-metal, and metal-electrolyte interfaces. The removal of oxygen in the second variant, for instance, can be represented by the following reactions diffusion of subions along the metal-electrolyte interface, and diffusion of oxygen atoms on the gas-metal interface. Prior to this, the oxidation reaction of subion to atom O should take place with the transfer of electrons into the metal. 

Figure 11. Pressure dependence of the diffusivity of oxygen atoms at 4000 K. Three kinds of symbols and lines correspond to three types of potential parameters type I ( , a solid line), type n ( , a dashed line) and type III (o, a dotted line), where the size of the symbols approximates the error bars. The lines are the results of the least-square fitting with eq.(8). Pc s for each potential are denoted with arrows.

Finally it should be stressed that the interatomic potential, which is reliable enough to reproduce the pressure dependence of the enthalpy of the polymorphs of silica, is an essential ingredient of the present investigation. The realistic interatomic potential combined with moderate control of the potential parameter has first enabled us to clarify the close relation between the diffusivity of oxygen atoms in molten state and the relative stability of the polymorphs of silica. 

The oxygen reduction reaction at the cathode (Eq. 4) can be broken down into several steps gas-phase diffusion, oxygen adsorption and dissociation at the cathode surface, surface or bulk diffusion of oxygen atoms, and incorporation into the electrolyte [4,5]. Any of these steps can limit the rate of cathodic reaction. The reaction site distributes three dimensionally aroimd the triple-phase boimdary (TPB) of electrode, electrolyte, and gas phase, as illustrated in Figme 2. In practical applications, LSM is often used as a composite with YSZ particles to increase the electrochemical reaction site. As YSZ can make a separate ionic path, the reaction site is made three dimensionally inside the electrode layer [6]. 

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