## 3 Results and Discussion
### Transport Numbers in SZY Membranes  
#### 3.2.1 Transport Numbers of Oxygen Ions in the Bulk and Film SZY Membranes  
It is known that the transport number of species \(i\) in a mixed-conducting material is determined as:  
\[t_{i}=\frac{\sigma_{i}}{\sigma} \tag{2}\]  
where \(\sigma_{i}\) and \(\sigma\) denote the partial conductivity of species \(i\) and the total conductivity. The effective transport numbers of oxygen ions were determined for both the bulk and film SZY membranes exposed to a gradient in the chemical activity of oxygen. The anode and cathode gas chambers of the concentration cells were fed with humid hydrogen and humid air, respectively, at a  
Figure 3: SEM images of the thermally etched surface of SZY pellet (**a**), surface (**b**) and fractured cross-section of NiO-YSZ supported SZY film (**c**). flow rate of 2 L h\({}^{-1}\). The values of humidity of the gases were equal (\(p\)H\({}_{2}\)O = 3365 Pa) to eliminate proton defects transport. After reaching a stationary state, the measurements of OCV, IS and CV characteristics were performed. A transport number of oxygen ions, \(t_{\text{O}^{2-}}\), in a membrane exposed to \(p\)O\({}_{2}\) gradient may be determined as:  
\[t_{\text{O}^{2-}}=\frac{E_{\text{m}}}{E_{\text{N}}} \tag{3}\]  
where \(E_{\text{m}}\) is a measured value of OCV and \(E_{\text{N}}\) is a theoretical EMF for an oxygen concentration cell. \(E_{\text{N}}\) is determined by the Nernst equation:  
\[E_{\text{N}}=\frac{RT}{nF}\ln\frac{p\text{O}_{2}(1)}{p\text{O}_{2}(2)} \tag{4}\]  
where \(n\) is the number of electrons transferred in the cell reaction (\(n\) = 4 for oxygen), \(p\)O\({}_{2}\)(1) and \(p\)O\({}_{2}\)(2) are the oxygen partial pressures at the opposite sides of the membrane, \(F\) is the Faraday's constant, \(R\) is the universal gas constant and \(T\) is the temperature. However, the ratio of OCV to the Nernst EMF can differ noticeably from the ionic transport number if polarization resistance of a concentration cell is significant. Measuring the impedance of a gas concentration cell, in addition to OCV measurements, was suggested for taking into consideration the cell polarization [34; 35]. In this case, the ionic transport number may be calculated as  
\[t_{\text{O}^{2-}}=1-\frac{R_{\text{E}}}{R_{\text{T}}}(1-\frac{E_{\text{m}}}{ E_{\text{N}}}) \tag{5}\]  
where \(R_{\text{E}}\) and \(R_{\text{T}}\) are an electrolyte resistance and a total cell resistance which can be determined from the impedance spectrum [34]. In the electrode-supported cells with a thin-film electrolyte, the electrode polarization can be significant because of the increase of the electrode thickness. That is why [PERSON]'s approach was applied for the determination of the effective transport numbers in the present study. The values of \(E_{\text{m}}\), \(R_{\text{E}}\) and \(R_{\text{T}}\) were obtained from the measurements of OCV, IS and CV on gas concentration cells. In the air/H\({}_{2}\) gradient, the measurements were carried out for both bulk membrane and Ni-YSZ-supported film, whereas in oxidizing atmospheres only bulk membrane was studied as NiO-YSZ does not act as the electrode at high \(p\)O\({}_{2}\). Impedance spectra of Cells 1 and 2 exposed to \(p\)O\({}_{2}\)(air)/\(p\)O\({}_{2}\)(H\({}_{2}\)) gradient in the Nyquist representation are depicted in Figure 4. Humidity levels in air and hydrogen were equal (\(p\)H\({}_{2}\)O = 3365 Pa) to prevent proton transport in the membrane. The Nyquist plots for Cell 1 exhibit a fragment of a high-frequency arc and a low-frequency semicircle (Figure 4a). The impedance has been fitted to the equivalent circuit \(R_{\text{b}}(R_{\text{gb}}Q_{\text{gb}})(R_{\text{el}}Q_{\text{el}})\) composed of \(R_{\text{b}}\) resistor and two parallel \(RQ\) elements (\(Q\) is a constant phase element) connected in series using the software EQUIVCRT 4.51. The value of \(R_{\text{b}}\) corresponds to the grain bulk resistance of the electrolyte.