Defect-chemical reactions

As basic ambipolar theory210 225 shows (cf. Part I2, Section VI.3.iv), in the interior of the sample the flux densities /k are a combination of an ohmic term and a stoichiometry term. In the case of a mixed (O2 /e") conductor (in the absence of internal defect chemical reactions), jk (k = eon,ion) is given by... 

The situation is equivalent to the formation of H30+ ( proton interstitial ) and OH ( proton vacancy ) in water where the endothermic formation enthalpy of the water dissociation reaction is also compensated by the gain of configuration entropy [61]. In both cases, defect chemical reactions can be formulated the dissociation reaction in water... 

The defect concentrations in ionic solids can be enhanced by doping with aliovalent ions if, for example, Cd2+ ions replace Ag+ ions in AgCl, additional positive charges are introduced that are compensated by negative silver vacancies (Fig. lb). In terms of a defect chemical reaction the doping can be written as ... 

We begin by noting that the bulk stoichiometry of an oxide is a function of the temperature and composition of the surrounding atmosphere [46]. For a hypothetical metal oxide (MO), we can write the appropriate defect chemical reactions in Kroger-Vink notation and equilibrium constants for congruent evaporation (k o). the production of vacancies by evaporation (k and ko), and Shottkey defect formation (kg) ... 

The incorporation of Sr thus leads to cheirge compensation by the formation of Fe ions, which is in accord with the Verwey principle of controlled ionic valency [162]. The extent of oxygen non-stoichiometry is established by the following defect chemical reactions. 

The concentrations of point defects in ionic compoxmds vary with the concentration of dopants. The defect concentrations can be predicted using defect chemistry where each defect species is considered to be a chemical species and the reactions among defects are expressed as chemical reaction equations. In expressing defect chemical reactions, some basic principles are applied. 

In additimi to foreign cation and anion dopants, native point defects are also usually present in the material. Examples are vacancies, interstitials, or substituents. These defects can have a similar influence on the optical, electrical, and catalytic properties as dopants. They are formed by intrinsic defect-chemical reactions, or by a change in the lattice stoichiometry due to exchange of, e.g., oxygen with the gas phase. Since virtually every defect affects the performance of the material in some way, the ability to understand and predict the relatiruiship between dopants and defect concentrations is of paramoimt importance for designing efficient photoelectrodes. 

Fig. 2.7 Diagram summarizing the key elements of the Kroger-Vink notation for point defects in ionic solids. The formation of defects can be described with defect-chemical reactions and corresponding equilibrium constants...

Consider a perfect crystal of an elemental solid E with N atoms as starting material. Let ny vacancies be formed according to the defect-chemical reaction... 

The working principle will be described on the TiO example because the stoichiometry of this material may change continuously in a large range, from x = 1.5 to x = 2, as a function of oxygen pressure. In a simple model, the defect chemical reaction can be written as... 

While conductivity measurements are evaluated by determining a flux, in the case of tracer diffusion and chemical diffusion it is simpler to use concentration changes for analysis . Let us consider the volume section in Fig. 6.21 and assume onedimensional geometry. It is evident that the increase in concentration can only occur in two ways (i) by more flowing into the volume than out of it (oc —(Jx+ax—jx)/Ax) (ii) by the presence of internal sources or sinks, i.e. (defect) chemical reactions in the... 

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