Diffusion coefficient chemical, ambipolar

From the formation reaction of protonic defects in oxides (eq 23), it is evident that protonic defects coexist with oxide ion vacancies, where the ratio of their concentrations is dependent on temperature and water partial pressure. The formation of protonic defects actually requires the uptake of water from the environment and the transport of water within the oxide lattice. Of course, water does not diffuse as such, but rather, as a result of the ambipolar diffusion of protonic defects (OH and oxide ion vacancies (V ). Assuming ideal behavior of the involved defects (an activity coefficient of unity) the chemical (Tick s) diffusion coefficient of water is... 

Other definitions of chemical diffusion coefficients were also suggested for various particular cases (e.g., see [iii, vi-viii]). In all cases, however, their physical meaning is related either to the ambipolar diffusion or to diffusion in non-ideal systems where the activity coefficients differ from unity. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

The chemical diffusion coefficient includes, as we know from the formal treatment in Section VI..3iv., both an effective ambipolar conductivity and an effective ambipolar concentration. The latter parameter is determined by the thermodynamic factor which is large for the components but close to unity for the defects. 

Since this equation is in the form of Pick s first law, it follows that the chemical or ambipolar diffusion coefficient responsible for oxidation is... 

Relationships Between Self-, Tracer, Chemical, Ambipolar, and Defect Diffusion Coefficients... 

Exposing a binary compound to a chemical potential gradient of one of its components results in a flux of that component through the binary compound as a neutral species. The process, termed ambipolar diffusion, is characterized by a chemical diffusion coefficient Z)chem which is related to the defect and electronic diffusivities by... 

Exposing a binary compound as a whole to a chemical potential, i.e., for diiy[x/dx 7 0, results in the ambipolar migration of both constituents of that compound down that gradient. The resulting ambipolar diffusion coefficient for an MO oxide is given by... 

In the literature, there are diffusion coefficients that have been used to describe the diffusion characteristics of a particular species, such as atom, interstitial, or vacancy, a particular diffusion path, such as lattice, grain boundary, or surface diffusion, or a particular process, such as chemical diffusion or ambipolar diffusion. 

The multitude of transport coefficients collected can thus be divided into self-diffusion types (total or partial conductivities and mobilities obtained from equilibrium electrical measurements, ambipolar or self-diffusion data from steady state flux measurements through membranes), tracer-diffusivities, and chemical diffusivities from transient measurements. All but the last are fairly easily interrelated through definitions, the Nemst-Einstein relation, and the correlation factor. However, we need to look more closely at the chemical diffusion coefficient. We will do this next by a specific example, namely within the framework of oxygen ion and electron transport that we have restricted ourselves to at this stage. 

The equilibration process in oxide systems can be monitored by changes in a bulk crystal property that is nonstoichiometiy sensitive, such as weight, Aw, electrical conductivity, Ao, or thermopower, AS. The kinetics of the re-equilibration process, provoked by isothermal changes of p(02), are schematically illustrated in Figure 4.25. The rate of the equilibration is determined by chemical diffusion involving the transport of defects under a gradient of chemical potential (ambipolar diffusion). Chemical diffusion coefficients may be determined from the relevant solutions of Pick s second law for long and short times, respectively... 

The conductivity factor can be determined also by measuring the (ambipolar) chemical diffusion coefficient >. However, D includes the thermodynamic factor W that must be determined separately, as... 

Two diffusion coefficients are of interest in MIECs the component diffusion coefficient, Dk, and the chemical diffusion coefficient, D. The component diffusion coefficient reflects the random walk of a chemical component. It is therefore equal to the tracer diffusion coefficient, except for a correlation factor which is of the order of unity. It is also proportional to the component mobility as given by the Nemst-Einstein relations. The chemical diffusion coefficient, I), reflects the transport of neutral mass under chemical potential gradients. In MIECs mass is carried by ions, and transport of neutral mass occurs via ambipolar motion of ions and electrons or holes so that the total electric current vanishes. b can be determined from steady-state permeation measurements, as mentioned in Section IV.H. However, D is usually determined from the time dependence of a response to a step change in a parameter, e.g., the applied current. Alternatively, D is determined from the response to an ac signal applied to the MIEC. 

The most important diffusion coefficient for chemistry and materiab science is the chemical diffusion coefficient which characterizes the diffusion kinetics of composition changes. This is formally a diffusion of neutral components, and, for ionic compounds, a charge-neutral ambipolar diffusion of at least two chemically different charged particles . A relevant example is the cheinge in stoichiometry of the oxide M2O (Fig. 6.17c) in the sense of... 

Many other cases of combined transport coefficients are in use, e.g. the combined (additive) transport of oxygen and metal ions commonly that we shall address later (and exemphfy by the high temperature oxidation of metals), the combination of two diffusivities involved in interdiffusion (mixing) processes, and the mass transport in creep being rate hmited by the smallest out of cation and anion diffusivities in a binary compound. As some of these sometimes are referred to as ambipolar or chemical diffusivities, we want to stress the above simple definition of ambipolar transport coefficients as relevant for membrane applications using mixed conductors. 

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