Internal defect reactions

Modifications in the Evaluation of Electrochemical Measurements Due to Internal Defect Reactions... 

It should be emphasized that the kinetics of the equilibration process after a change of the surrounding phase (e.g. a p(O2) change) requires the movement of defects and can be rather sluggish, particularly at lower temperatures. Therefore, non-equilibrated ionic solids with composition gradients can easily occur, and often the preparation conditions rather than the actual surroundings determine the defect concentrations (frozen-in compositions). On the other hand, internal defect reactions... 

More complex internal defect reactions involve association reactions or doping effects they will be considered later. (For more extensive treatments of defect chemistry see Ref.2)... 

J. Maier, Mass transport in the presence of internal defect reactions-concept of conservative ensembles I, Chemical diffusion in pure compounds. /. Am. Ceram. Soc., 76(5) (1993) 1212-1217 II, Evaluation of electrochemical transport measurements, ibid., 1218-1222 III, Trapping effect of dopants on chemical diffusion, ibid., 1223-1227 IV, Tracer diffusion and intercorrelation with chemical diffusion and ion conductivity, ibid., 1228-1232. 

Maier, J. Mass transport in the presence of internal defect reactions— Concept of conservative ensembles 1, Trapping effect of dopants on chemical diffusion./. Am. Ceram. Soc., 76,1223-1227 [1993). 

In this case, the intercalation process is essentially controlled by the Li concentration in the host lattice. As shown in Fig. 13.7b the thermodynamic factor, W, varies linearly with the degree of Li intercalation from 10 to 820 in the range 0.05 < X < 1.5. This x-dependence of W can be associated with the large decrease of the electronic mobility in Li MoOs film. Considering that M0O3 films are oxygen-deficient materials, the model of charge transport in internal defect compounds can be applied [14—18], Defects are Li interstitials, Li, and conductimi electrons, e. It has been shown [17] that, in a solid solution where no internal defect reactions... 

We have previously established (i) that, at finite temperatures, ionic and electronic point defects are required as local chemical excitations at equiUbrium, (ii) that we can write ideal mass action laws in all cases for low concentrations of defects, and (iii) that we know what parameters influence our mass action constants. We can now turn to a specific consideration of defect chemistry. Let us consider first internal defect reactions and pure single crystals By internal defect reactions in pure substances we mean processes that occur as a consequence of nonzero temperature in the otherwise perfect crystal without neighbouring phases being involved. (For two of these reaction tjrpes, however, we will need surfaces as sinks or sources of monomeric units, i.e. of lattice molecules.) In binary systems such processes leave the composition within the sohd undhanged. If we refer to the Dalton composition , we also speak of the intrinsic case. 

The anti-Prenkel reaction (F) is a third fundamental, internal defect reaction It describes a disorder variant analogous to type F but in the anionic sublattice (and is therefore also termed anion-FVenkel disorder). This typically occius in alkahne earth halides, particularly the fluorides here the anions are small enough (fluorides) or polarizable enough (in the case of the higher halides) to take up interstitial positions. In the building element notation and the structure element notation we formulate... 

Until now we have neglected cationic defects. On account of the isomorphy of the internal defect reaction, it is clear that analogous relationships result. Of course. 

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... 

TEMPERATURE HIGH Ambient Conditions Fouled or Failed Exchanger Tubes Fire Situation Cooling Water Failure Defective Control Valve Heater Control Failure Internal Fires Reaction Control Failures Heating Medium Leak into Process Faulty Instrumentation and Control... 

From eqs. (4-5) and (4-8) it can be seen that formal mass action equations may be written for the concentrations of defects in equilibrium when P, T, and the activity or partial pressure of a component are given. As has already been pointed out, the formulation of the reaction equation connecting the defect concentrations and the component activities is to some degree arbitrary, as long as the previously mentioned rules are properly obeyed. This results from the existence of internal defect equilibria which are always maintained if the crystal is in thermodynamic equilibrium. In the present case, for instance, we can write several other reaction equations. For example, we could write ... 

The defect formation may either occur internally in the solid or through reactions with the environment. In the following, the rules for formulating defect reactions will be described and applied to different defect stmcture systems, while in the next chapter, conditions for equilibrium and equations relating equilibrium defect concentrations to temperature, activities (partial pressures) of the components in a compound, impurity concentrations, etc., will be discussed. 

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