## 2 Materials and Methods
### Measurement Description  
The electrical conductivity of the bulk SZY sample was measured using two-probe AC impedance spectroscopy (Parstat 2273-SVS, USA) across the frequency range of 0.1 Hz-1 MHz, using an amplitude of 30 mV. For the electrical measurements, symmetrical Pt electrodes were made on opposite sides of the pellet by painting a platinum paste and firing at 1000 \({}^{\circ}\)C for 1 h. The impedance measurements were carried out in wet air (\(p\)H\({}_{2}\)O = 3365 Pa) and wet hydrogen (\(p\)H\({}_{2}\)O = 3365 Pa) in the temperature range of 300-800 \({}^{\circ}\)C. The required humidity was achieved by bubbling the gas through a water bath with a temperature of 26 \({}^{\circ}\)C. The samples were equilibrated with the ambient gas for 24 h before the measurements. The measured Nyquist plots were fitted using the software EQUIVCRT 4.51 [31; 32]. For the transport numbers determination, gas concentration cells with separated gas chambers were fabricated. The cell testing apparatus is schematically shown in Figure 1. SZY pellets with a thickness of 0.12 cm and NiO-YSZ supported SZY film with a thickness of 2.5 \(\upmu\)m were studied. The platinum paste was symmetrically applied to each side of SZY and SZY-film/NiO-YSZ pellets along with current collectors made out of platinum wire and fired at 1000 \({}^{\circ}\)C for 1 h. Then the pellets were fixed to the tube made of YSZ electrolyte using spring-loaded rods. For the film sample study, the film-coated side of NiO-YSZ pellet faced YSZ tube. The contact between the sample and the tube was filled with a glass possessing a softening temperature of 950 \({}^{\circ}\)C. The sealing glass was used to avoid gas leakage through the contact. Then the testing assembly was placed into a tubular furnace. The inner gas chamber was confined inside the YSZ tube, while the furnace tube confined the outer chamber. After heating to 950 \({}^{\circ}\)C, the furnace was dwelled for 5 minutes to soften the glass, and then cooled down to 800 \({}^{\circ}\)C for testing. Before the electrical measurements on the film membrane, NiO-YSZ substrate was reduced in-situ in a hydrogen atmosphere as follows. It is known that during the reduction process, the initial volume of NiO phase is reduced by about 40% creating pores. To prevent the film cracking or delamination because of the growing substrate's porosity, the outer gas compartment was fed with Ar-H\({}_{2}\) gas mixtures with a stepwise hydrogen content increase (10% H\({}_{2}\), 20% H\({}_{2}\),..., 100% H\({}_{2}\)) at a flow rate of 2 L h\({}^{-1}\) and duration of 1 h for each step, and holding isothermal at 800 \({}^{\circ}\)C in hydrogen atmosphere until achieving a constant value of OCV on the concentration cell. The gas flows were controlled using the mass flow controllers RRG-12 and the electronic control unit BUIP-3 (Eltochpribor, Moscow, Zelenograd, Russia). Measurements of OCV, IS and CV characteristics of the concentration cells Gas1, Pt/SZY/Pt, Gas2 (Cell 1) and Gas1, Pt/Ni-YSZ/SZY-film/Pt, Gas2 (Cell 2) were performed using Potentiostat-Galvanostat  
Figure 1: A schematic representation of the apparatus for electrochemical testing of concentration cells. P-45X (Elins, Zelenograd, Russia). Impedance measurements were carried out across the frequencies from 0.1 Hz to 500 kHz. The applied amplitude was 30 mV. The oxygen gradient across the SZY membranes was established between atmospheric air (\(p\)O\({}_{2}\) = 21 kPa, Gas 2), and a lower value (Gas 1) obtained by passing of argon or wet hydrogen. The gases were supplied at a flow rate of 2 L h\({}^{-1}\). The residual \(p\)O\({}_{2}\) in Ar was 10 Pa. The values of \(p\)O\({}_{2}\) in wet hydrogen were determined using the equilibrium constant of the water formation reaction. The water content in the gases was varied by passing gas flows through the column with zeolite beads (\(p\)H\({}_{2}\)O \(\approx\) 40 Pa), or by bubbling through a water bath with a temperature of 0, 26 or 30 \({}^{\circ}\)C (\(p\)H\({}_{2}\)O = 610, 3365 and 4240 Pa, respectively).