The purpose of this study is to clarify the relationship between ionic conductivity and phase transformation of zirconia system codoped with scandium oxide $Sc2O3$ and ytterbium oxide $Yb2O3$. Aiming to achieve high ionic conductivity as well as high mechanical strength, the authors have also investigated the relationship between phase transformation and mechanical strength. The results have been discussed with respect to both the conductivity and the mechanical strength. The Sc- and Yb-codoped zirconia $(ZrO2)$ used as samples in this study were prepared by a standard solid-state reaction. X-ray powder diffraction (XRD) method was used to determine the crystal structures of the sintered samples. To detect any phase change between room temperature and $1273K$, thermal mechanical analysis (TMA) was conducted. To determine oxygen-ion conductivity in a temperature range from $873to1273K$ in air, impedance measurements were performed with alternating current (ac). Single-cell performance was confirmed under the condition of $26.2Pa$ partial hydrogen pressure. Finally, to measure bending strength, three-point bending tests were performed with a universal testing machine. The results of XRD and TMA showed that codoping of $Sc2O3$ and $Yb2O3$ into $ZrO2$ successfully stabilized the cubic phase when the average radius ratio of these two dopants in total was close to the ideal one for the eight-coordinate. The ac impedance measurement demonstrated that the cubic-phase stabilization achieved a high conductivity. Adequate amounts of dopants produced oxygen vacancies for high conductivity without complex defects: $ZrO2$ system doped with $1mol%$ of $Yb2O3$ and $8mol%$ of $Sc2O3$ showed the highest conductivity at $1273K$ and $0.30S∕cm$. The bending strength decreased with increasing the content of doped $Sc2O3$ from $7mol%to11mol%$, depending on the amount of the tetragonal phase, which contributes to strengthen materials. In the performance test, the $ZrO2$ system stabilized with doping $1mol%$$Yb2O3$ and $8mol%$$Sc2O3$ with thickness of $2.16mm$ showed maximum power density at $1273K$, that is, $210mW∕cm2$. From all the above tests, we recommend that, based on electrical and mechanical considerations, 1Yb8ScSZ is the present best option for an electrolyte material for a solid oxide fuel cell.

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