## 4 Conclusions  
The transport numbers of oxygen-ion conduction in the bulk and 2.5 \(\upmu\)m-thick Ni-cermet supported Sr\({}_{0.98}\)Zr\({}_{0.95}\)Y\({}_{0.05}\)O\({}_{3-\delta}\) (SZY) membranes were studied. The film fabricated via a multi-step chemical solution deposition and synthesized at 1000 \({}^{\circ}\)C showed a nanogenized morphology with grains of 100-200 nm. The bulk sample obtained by a soft chemistry route followed by sintering at 1650 \({}^{\circ}\)C possessed a dense microstructure with grains of up to 4-5 \(\upmu\)m. It was found that the Ni-cermet supported film contains nickel due to the diffusional interaction with the substrate. Despite Ni diffusion, the 2.5 \(\upmu\)m-thick membrane operating in the fuel cell mode was found to possess highly effective transport numbers of oxygen ions close to those of the bulk membrane (0.97 and 0.99 at 550 \({}^{\circ}\)C, respectively). The high transport numbers of ionic conduction in the thin Ni-cermet supported electrolyte indicates that the diffusional interaction with the supporting electrode, which is expected to be more intensive during the film synthesis at 1000 \({}^{\circ}\)C and less intensive during the cell operation (500-800 \({}^{\circ}\)C) does not lead to electrolyte degradation, and therefore this combination of materials is appropriate for application in SOFCs. The effective proton transport number of 0.87 was reached in the bulk SZY membrane operating in humid air at temperatures from 500 to 600 \({}^{\circ}\)C.  
The film conductivity was shown to be one order of magnitude smaller than that of the bulk membrane. The difference is caused by a larger contribution of the grain boundary resistance of the nanogenized film. To improve the film conductivity, the temperature of the film sintering is to be increased. The next step of our research will involve a study to reveal the effect of the film sintering temperature on the electrochemical performance of Ni-cermet supported cells. Using the data on the effective conductivity and the effective transport numbers of oxygen ions in SZY membrane operating in the fuel cell mode and oxidizing conditions, and assuming the conventional model of defect formation in acceptor doped oxides, the relationship between the total conductivity of SZY and the oxygen partial pressure was derived. The good agreement of the calculated conductivity values with the experimentally obtained data indicates the reliability of the applied approach. The following are available online at [[http://www.mdpi.com/2076-3417/10/7/2229/s1](http://www.mdpi.com/2076-3417/10/7/2229/s1)]([http://www.mdpi.com/2076-3417/10/7/2229/s1](http://www.mdpi.com/2076-3417/10/7/2229/s1)), Figure S1: The area specific values of \(R_{\rm E}\) (a) and \(R_{\rm T}\) (b) as functions of inverse temperature for the gas concentration cells air/H\({}_{2}\) and air/Ar with the bulk and film SZY membranes, Figure S2: Temperature dependences of \(\rm E_{m}\) and \(E_{\rm N}\) for the gas concentration cells: (a) air/H\({}_{2}\), (b) air/Ar, Figure S3: The area specific values of \(R_{\rm E}\) (a) and \(R_{\rm T}\) (b) as functions of inverse temperature for the gas concentration cells pH\({}_{2}\)O/, Pt/SZY/Pt, pH\({}_{2}\)O/ in air at \(pH_{2}\)O = 40 Pa and pH\({}_{2}\)O/ = 4240, 3365 and 610 Pa, Figure S4: Temperature dependences of \(\rm E_{N}\) and \(\rm E_{m}\) for the gas concentration cell pH\({}_{2}\)O/, Pt/SZY/Pt, pH\({}_{2}\)O/ in air at \(pH_{2}\)O/ = 40 Pa and pH\({}_{2}\)O/ = 4240, 3365 and 610 Pa.  
Conceptualization, A.K. and L.D. ; methodology and validation, A.K. and L.D. ; formal analysis, A.K. ; investigation, A.K. and A.P. ; resources, L.D. ; data curation, L.D. ; writing--original draft preparation, A.K. ; writing--review and editing, L.D. ; visualization, A.K. and L.D. ; supervision, L.D. ; project administration, L.D. ; funding acquisition, L.D. All authors have read and agreed to the published version of the manuscript. This research was funded by Ural Branch of the Russian Academy of Sciences, project number 18-10-3-42.