Bulk diffusion vacancies

Figure 28. Svensson s macrohomogeneous model for the i— 1/characteristics of a porous mixed-conducting electrode, (a) The reduction mechanism assuming that both surface and bulk diffusion are active and that direct exchange of oxygen vacancies between the mixed conductor and the electrolyte may occur, (b) Tafel plot of the predicted steady-state i— V characteristics as a function of the bulk oxygen vacancy diffusion coefficient. (Reprinted with permission from ref 186. Copyright 1998 Electrochemical Society, Inc.)...

Donor-doped BaTi03 and SrTi03 are relevant examples. There bulk diffusion is very slow because of the very low Vq concentration and the low mobility of the metal vacancies. If a perovskite ceramic,... 

Bulk Diffusion The flux of vacancy diffusion away from the neck... 

If the TPR profiles for the NM/CeOa catalysts and the bare support, also included in Figure 4.3, are compared, a common high temperature feature centred at 1090 K may be noted. This peak is generally interpreted as due to the bulk reduction of ceria (61, and references there in). In agreement with several earlier studies (73,110,283), the position of this peak does not seem to be modified by the presence of any supported metal. This observation is typically interpreted in terms of a kinetic model (205) which assumes that the high temperature reduction process is controlled by the slow bulk diffusion of the oxygen vacancies created at the surface of the oxide. 

Densification occurs by the bulk diffusion of vacancies away from the cylindrical pore channels toward the grain boundaries (curved arrows in Fig. 10.14/ ). 

Figure 10.15 Geometric constructions used to model porosity elimination, assuming (a) bulk diffusion, where the vacancies are assumed to be eliminated at the grain surface, and (6) grain boundary diffusion, where vacancies are restricted to diffusing along a grain boundary of width gb-...

Surface exchange reaction at the high p(02) interface (at the outer membrane surface) (ii) Simultaneous bulk diffusion of anionic oxygen (oxygen vacancy) and electrons (electron holes) in the bulk phase... 

Volume diffusion at room temperature is usually a slow process, but removal of the less noble metal atoms from the crystal lattice could possibly create a high vacancy concentration near the surface and thus lead to a higher diffusion rate than predicted from thermodynamic considerations. Injection of divacancies has also been considered to explain abnormally high solid-state diffusion rates [10]. Surface diffusion is generally faster than bulk diffusion and atoms should be able to rearrange more easily... 

Nabarro-Herring Creep, creep (q.v.) controlled by the diffusion of vacancies through the lattice (bulk diffusion). The creep rate is proportional to the square of the grain size. (F.R. Nabarro, Conference on the strength of solids, Bristol University 1947, and C. Herring J. Appl. Phys 21,1950, p437). 

Alternatively, if surface exchange and bulk diffusion can show a comparable resistance to the overall mass transfer, a generalized equation can be obtained by assuming that ionic conductivity rules the charge transfer within the membrane, and constant diffusion coefficient for vacancies. The well-known equation proposed by Xu and Thomson [34] can be then obtained by assuming that ionic diffusion proceeds according to Eq. (14.26) (i.e., v = 0) and that dy[Pg.322]

In diffusional processes, such as the classic Kirkendall effect of interdiffusion in a bulk diffusion couple of A and B, the atomic flux of A is not equal to the opposite flux of B. If we assume that A diffuses into B faster than B diffuses into A, we might expect that there will be a compressive stress in B, since there are more A atoms diffusing into it than B atoms diffusing out of it. However, in Darken s analysis of interdiffusion, there is no stress generated in either A or B. But Darken has made a key assumption that vacancy concentration is in equilibrium everywhere in the sample. To achieve vacancy equilibrium, we must assume that lattice sites can be created and/or annihilated in both A and B, as needed. Hence, provided that the lattice sites in B can be added to accommodate the incoming A atoms, there is no stress. The addition of a large number of lattice sites implies an increase in lattice planes if we assume that the mechanism of vacancy creation and/or annihilation is by dislocation climb mechanism. It further implies that lattice planes can migrate. 

In case of mixed control of the oxygen flux (bulk diffusion and surface exchange), the concentration of oxygen vacancies at both faces of the membrane is governed by the reaction ... 

Based on the stoichoimetric relationship between oxygen and vacancy, the oxygen bulk diffusion flux in the membrane can be given by... 

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