Ionic transference numbers

Because the ionic transference number for zirconia material is taken as being unity, then this equation reduces to the Nernst equation " ... 

From Eqns. (8.56) and (8.57), we can obtain the electrical conductivity of the crystal and also the ionic transference number. 

Deviations from Eq. (77) that are due to surface effects should allow conclusions on effective surface rate constants). The more detailed derivation has been given in Section II.2 (Eq. (35)). In Eq. (77) the ionic transference number has been averaged over the P0-range covered. A more precise evaluation involves the explicit... 

An alternative electrolyte material, lanthanum-doped barium indium oxide, (Ba,La)In205+3, has been proposed. This new material has been shown to have an ionic transference number of 1.0 with an oxygen ion conductivity better than that of YSZ. 

Conductivity The materials must have an ionic transference number close to unity i.e., the electronic conductivity in the electrolyte must be sufficiently low in order to minimize internal shorting and provide high energy conversion efficiency. The electrolyte materials should also possess high oxygen ion conductivity to minimize the ohmic losses in the cell. 

When there is the same electrolyte MA with different concentrations on the two sides of the interface, Eu (a) may be described by a relatively simple equation [41-43] and is dependent on ionic transference numbers and the electrolyte concentration in both solvents. Obviously, if the activity of the electrolyte in both solvents is identical, then (a) drops to zero. 

This tendency for reduction restricts the range of oxygen partial pressures over which the ionic transference number remains close to unity. For example, at 800°C, the oxygen partial pressure in the lower limit is restricted to partial pressures over 10 atm. This lower limit has been extended with no loss in conductivity to 10" atm at 700°C in ceria doped with 20 mol% GdaOs by replacing 3% of the gadolinium with praseodymium. 

Fig. 10.7. (a) Defect and (b) conductivity diagram for ceria-doped YSZ at 1000°C. The relevant parameters to construct the diagrams are given in Ref. [119]. The theoretical dependence of ionic transference number tionand oxygai permeability /02 are given in (c). Dashed lines in (c) refer to YSZ. Fm (YzrO represents the aliovalent dopant used. Reproduced (slightly adapted) from Marques et al. 

The electrolyte dissociation from the lower partial pressure side does not initially result in the decrease of em/for cell (1.20) because the average ionic transference number plays the crucial role and can be given as follows [26] ... 

It can be observed from Equation (1.27) that the average ionic transference number indicates on the m/deviation of the electrochemical cell (1.20) from the thermodynamic cm/at the presence of electronic conductivity in solid electrolytes. 

As long as we have an equilibrium between electrons on the local levels and electrons in the conductivity zone, that is, F = the ionic transference number (t ) can be described by the foUowing equation ... 

These reactions determine the apparent potential of the zirconia-based sensor. Since the raw exhaust gas at automotive and combustion applications constitutes a nonequilibrium gas mixture, thermodynamic equilibrium has to be achieved at the SE surface of the zirconia-based sensor before monitoring the potential. Consequently, such sensors contain catalytically active materials and are operated at temperatures above 600°C, when the average ionic transference number % > 0.99. For less active materials or temperatures below 600°C the apparent em/starts to deviate significantly from the value under equilibrium conditions due to insufficient catalytic activity. Earlier research of the YSZ-based sensors was focused on the electrode materials with high exchange currents and high catalytic activity for the desired electrode reactions. Pt electrodes were found to be the most suitable for this type of application. 

Low values of the parameter pe (ionic transference number, is 0.5) indicate low contributions of partial electronic conductivity to the total conductivity, which result in higher ionic conductivities (k) according to the equation... 

FIGURE 4.7 Ionic transference number as a function of oxygen concentration for the sensor based on a zirconia single crystal at400°C. (From Zhuiykov, S., Zirconia single crystal analyser for low-temperature measurements, Proc. Control and Quality 11 (1998) 23-37. With permission.)... 

Figure 4.7 illustrates the ionic transference number as a function of oxygen concentration in molten Ga in the range 10" -100 ppm for a sensor, shown in Figure... 

Let s consider 4, within the above-mentioned ranges of temperatures and pressures. The true ionic transference number based on [10] can be expressed according to the following equation ... 

As has been shown above, the average ionic transference number t at the above-mentioned ranges of oxygen pressures and temperatures is equal to 1, and conse-qnently, this error, stipnlated by the nonionic component of condnctivity (8Pi92(I))e2. can also be ignored. 

---