Mobile vacancy concentration

At this point, it is instructive to examine both components of this equation and the likely contribution to the tracer diffusion coefficient for these perovskite materials. Here the term [F ] refers to the mobile vacancy concentration, which may be different from the stoichiometric vacancy concentration (i.e., that determined by the oxidation states of the constituent cations) because of vacancy trapping, as observed in the fluorite oxides [2], or due to vaeaney ordering [5]. contains the terms relevant to mobility of the vacancies, i.e., the ease with which the oxygen atoms can jump from an adjacent lattice site into a vacancy. Mizusaki et al. [6] have previously shown that data for D, the vacancy diffusivity, show remarkably little variation for a number of perovskite materials. This is a very interesting observation and one to which we return later. It is thus important to understand the changes that occur in the vacancy concentration in these materials and how this affects the oxygen self-diffusion coefficient. 

AHf affects the stoichiometric vacancy concentration whereas AH a affects the mobile vacancy concentration and A// only enters into the vacancy diffusion coefficient. Thus, if we can determine the stoichiometric vacancy concentration (or, more accurately, the mobile vacancy concentration), then we can extract the value of Dv, leading to a value for AHm. 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

Diffusion of K+ ions in KCl occurs by interchange of the potassium ions with cation vacancies (see Figure 4.40d). It makes sense, then, that the diffusivity of potassium ions in KCl, Dk,ci is both a function of the potassium ion mobility, A. and the cation vacancy concentration, [V[ ... 

Figure 4.46 Schematic representation of the variation of metal ion diffnsivity as a fnnction of (a) oxygen pai tial pressnre and (b) temperatnre, and (c) the metal ion vacancy concentration and (d) mobility with temperatnre. From W. D. Kingery, H. K. Bowen, and D. R. Uhhnann, Introduction to Ceramics. Copyright 1976 by John Wiley Sons, Inc. This material is nsed by permission of John Wiley Sons, Inc.

Ceria-based catalysts are intensively used because of their high chemical and physical stability, high oxygen mobility and high oxygen vacancy concentrations, which are characteristic of fluorite-type oxides. The possibility of cycling easily between reduced and oxidized states (Ce Ce" ) permits the reversible addition... 

Figure 13.10 shows the chromatogram calculated for the same set of experimental conditions as used for Figure 13.9, except for the concentrations of the analytes, which are Cq,i = Cq,2 = 0.01 M, instead of 0.0001 M. The matrix f (Eq. 13.11a) of this system is a 4x4 matrix and the mobile phase concentration is represented by a 2 X1 vector. The injection of the vacancy pulse causes two perturbations, one for each component. Each of these perturbations involves two peaks. 

The oxygen mobility in the lattice is needed for this mechanism to be possible. This is consistent again with the correlation observed between vacancy concentration (which facilitates oxygen mobility) and catalytic activity as estimated from NO conversion. 

The wustite phase, FeO, is a p-type metal-deficit semiconductor which can exist over a wide range of stoichiometry, from Feo.950 to Feo.ggO at 1000 °C according to Engell. With such high cation-vacancy concentrations, the mobilities of cations and electrons (via vacancies and electron holes) are extremely high. 

The intrinsic part is not usually observed because an impurity concentration of between 1 in 10 and 1 in 10 is sufficient to control the vacancy concentration. There is another complication we should consider as we saw in Section 11.8, there is attraction between [Cak] and [Vy that results in defect complexes. The concentration of these complexes depends on the strength of this attraction formation of these complexes will probably reduce the mobility of the point defects and thus decrease diffusion rates. 

Figure 5.4 Plot of [OH"] (mobile proton concentration) versus water vapour pressure (hydration isotherm) for a material with 10mol% vacancies and K = 2.0...

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