Electron transport number

A key factor in the possible applications of oxide ion conductors is that, for use as an electrolyte, their electronic transport number should be as low as possible. While the stabilised zirconias have an oxide ion transport number of unity in a wide range of atmospheres and oxygen partial pressures, the BijOj-based materials are easily reduced at low oxygen partial pressures. This leads to the generation of electrons, from the reaction 20 Oj + 4e, and hence to a significant electronic transport number. Thus, although BijOj-based materials are the best oxide ion conductors, they cannot be used as the solid electrolyte in, for example, fuel cell or sensor applications. Similar, but less marked, effects occur with ceria-based materials, due to the tendency of Ce ions to become reduced to Ce +. 

Electron transport number, re . Nd2Eu203F6 , Nd2Ce203F6 , Nd2Gd203F6 (reproduced with permission from J. Fluorine Chem., 87 (1998) 229 [39]). 

Fig. 23. The transport number of various rare-earth fluoride stabilized zirconias. Oxide ion transport number, tO2 --------- Electron transport number, re-------- ...

A key factor in the possible application of oxygen ion conducting ceramics is that, for use as solid electrolyte in fuel cells, batteries, oxygen pumps or sensors, their electronic transport number should be as low as possible. Given that the mobilities of electronic defects typically are a factor of 1000 larger than those of ionic defects, a band gap of at least 3 eV is required to minimize electronic contributions arising from the intrinsic generation of electrons and holes. 

The rate of oxidation with rate-determining diffusion in the scale is calculated from this equation. This is the maximum oxidation rate for a gas-tight protective layer. The equation applies for the oxidation, sulfurization, nitriding, and halogenation of a metal (X2 = O2, N2, halogen). Two border cases can be differentiated with the equation. For Ui + U2 = 1, (the ion conductor), k is determined by the parameter U, the electron transport number. For Uj, 1, (the electron conductor), k is determined by (f/i + Uq). 

Furthermore, for the tarnishing of divalent transition metals (to form NiO, CoO, FeO, etc.), the electronic transport number can be set equal to one. The practical rate constant is then ... 

Although oxides have a wide range of catalytic applications their transport properties are most obviously critical when they are used in the form of a membrane within a chemical or electrochemical reactor. As such their ionic conductivity must be high if they are going to support a reasonable ion flux. Such materials fall broadly into two classes those materials that exhibit a very low electronic conductivity and, if the electronic transport number is <0.01, are generally termed solid electrolytes (solid electrolytes are covered in a separate chapter) and those materials that exhibit an appreciable or high electronic conductivity as well as ionic conductivity and are hence termed mixed conductors. In the rest of this chapter we will focus on such mixed ionic and electronic conducting (MIEC) materials. First, we will address transport in MIEC membranes from a theoretical perspective... 

It should be noted that the emf developed across the membrane depends upon A fie. Equation (3.81) can therefore, on integration, be used to calculate the emf. This is simply performed if the ionic and electronic transport numbers are constant and results in. 

We now assume that the electron transport number approaches unity. Substituting for electrochemical potential, in the absence of a gradient in electrical potential, in terms of p02 with the electron transport number at unity gives. 

To apply Faraday s law, the voltage at which the above reactions occirr must be compatible with the electrolytic domain of the SIC. When this condition is not ftilfilled, an electronic conductivity, either n or p type, will appear. Generally, with an electronic transport number of a few percent, the faradaic efficiency is close to one and the error is less disastrous than for potentiometric devices. 

This method can be considered as a fast and simple screening tool. It should be pointed out that the technique is convenient for electronic transport numbers higher than 1 % and when there is an oxygen partial pressure domain in which the conductivity is purely ionic. 

Determination of nonstoichiometry in oxides is a key point in the search for new materials for electrochemical applications. In recent decades, owing to their current and potential applications (electrodes in fuel cells, insertion electrodes, membranes of oxygen separation, gas sensors, catalytic materials, etc.), various methods of precise characterization of MfECs have been proposed, either the measurement of the defect concentrations and the stoichiometric ratio as functions of the oxide composition, of the surroxmding oxygen pressure and of temperature, or the transport properties. There are different methods to determine the electrical properties of MIECs and, more specifically, the ionic and electronic contributions. The most appropriate method depends on different parameters, i.e., the total electrical conductivity of the studied oxides, the ionic and electronic transport numbers, the... 

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