Wagner-Hebb polarization

Figure 42. Steady-state results of a Wagner-Hebb polarization of Y-doped Z1O2 or TI1O2 with the aid of the cell 0N2, Pt YSZ or YST air, Pt (left, current-voltage curve for Tho.9Yo.1Ch 95 (YST), right partial conductivities for Zro.9Yo.1O1.95 (YSZ)).232 Reprinted from L.D. Burke, H. Rickert, and R. Steiner, Z Phys. Chem. N.F., 74 (1971) 146-167. Copyright 1971 with permission from Oldenbourg Verlagsgruppe.

Figure 42 depicts steady-state results of a Wagner-Hebb polarization of (Y203-doped) Zr02 and Th02 for which the ideal Wagner-Hebb relation is valid.232... 

When performing a Hebb-Wagner polarization experiment one has to take the following aspects into careful consideration ... 

In the second case (limit of fast kinetics at the gas-solid interface), the film becomes entirely bulk transport limited, corresponding to the limit of Hebb— Wagner polarization. Since electronic conduction is fast, this situation yields a Warburg impedance for finite length diffusion ... 

Similar approaches are used for most steady-state measurement techniques developed for mixed ionic-electronic conductors (see -> conductors and -> conducting solids). These include the measurements of concentration-cell - electromotive force, experiments with ion- or electron-blocking electrodes, determination of - electrolytic permeability, and various combined techniques [ii-vii]. In all cases, the results may be affected by electrode polarization this influence should be avoided optimizing experimental procedures and/or taken into account via appropriate modeling. See also -> Wagner equation, -> Hebb-Wagner method, and -> ambipolar conductivity. 

Polarization method according to Hebb-Wagner (steady state)... 

Polarization Method According to Hebb-Wagner (Steady State)... 

Copper halides are good ionic conductors with values of O 0.1 - 1 S/cm and Oei Oj at 400°C. The ionic conductivity of copper is facilitated by Frenkel disorder on the cation sublattice. It was believed for many years, on the basis of the two-point Hebb-Wagner (H-W) polarization measurements (discussed in Section IV), that CuBr is a p-type MIEC. However, it was recently shown that CuBr decomposes quite rapidly and therefore... 

FIGURE 8.3. Cell arrangement for the measurement of the partial electronie conductivity according to the Hebb-Wagner method. Specifie example the MIEC conducts 0 ions and electrons/holes. The polarity of the... 

While in the experiments described so far both ionic and electronic species are transferred, it is also possible to determine the partial electronic conductivity by using ionically blocking electrodes to suppress the ionic transport so that only electrons and holes can pass. This technique is known as the asymmetric polarization or Hebb-Wagner technique. By using a chemically inert electronic conducting material, no ions will be delivered to the electrolyte when a voltage is applied with such a polarization that the mobile ions tend to be depleted at the inert electrode. An electrode used on the other side fixes the chemical potential of the mobile component of the electrolyte by the applied voltage at that phase boundary. 

The Hebb-Wagner polarization technique has been developed either for the determination of electron and hole conductivity in ionic conductors [Hebb, 1952 Joshi Wagner, 1975 Wagner, 1957] or for the measurement of ionic conductivity in MIECs [Riess, 1996 Wiemhofer et al., 2002]. Basically, the method consists in using a reversible electrode and blocking electrodes to suppress the predominant charge carrier and thus enable measurement of the minority sp>ecies. The main limitations of the method have been reviewed [Riess, 19%] and new experimental set-ups have been proposed. 

Fig. 18. (a) Two-point Hebb-Wagner polarization cell, C ion-blocking electrodes, M reversible electrode, MIEC MIEC containing positive mobile ionic defects (b) Two-point Hebb-Wagner polarization cell for the measurement of Oi in CU2O from [Riess, 1992b]. 

Riess, I. (1992). Four point Hebb-Wagner polarization method for determining the electronic conductivity in mixed ionic-electronic conductors. Solid State Ionics, Vol. 51, No 3-4, pp. 219-229... 

Riess, I. Safadi, R Tuller, H.L. (1994). Problems with Hebb-Wagner polarization measurements due to overpotentials and decomposition of the sample. Solid State Ionics, Vol. 72, pp. 3-6... 

Determination of hole and electron conductivities and transport numbers of oxide ion in LaGa03-based oxides were performed by the polarization method by Baker et al. [21], Yamajiet al. [35], and Kimand Yoo [36]. Kim et al. reported that Pq2 dependence of hole and electron conductivity is proportional to Pcn and respectively, and well obeys the Hebb-Wagner theory. The results... 

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