## Materials and Methods  
The nominal compositions were formulated as [(ZrO\({}_{2}\))\({}_{0.95}\)(Y\({}_{2}\)O\({}_{3}\))\({}_{0.05}\)]\({}_{1-x}\)[PrO\({}_{y}\)]\({}_{x}\) with \(x\) varying between 0.05 and 0.15. Table 1 lists the nominal cation compositions recalculated to give the fractions of binary oxides and the cation ratio in the fluorite-type AO\({}_{2}\) formula unit. The samples were prepared using 5 mol.% yttria partially stabilized zirconia (SYSZ, Innovano, Portugal, d\({}_{50}\) = 500 nm) and praseodymium oxide Pr\({}_{6}\)O\({}_{11}\) (Alfa Aesar, 99.5% purity). Praseodymium oxide was preliminarily annealed at 1000 \({}^{\circ}\)C for 2 h to remove adsorbates and slowly cooled (2 \({}^{\circ}\)C/min) down to room temperature. The powders of initial reagents were mixed in the appropriate proportions and ball-milled with ethanol for 4 h at 150 rpm using nylon containers, Tsooh tetragonal zirconia milling media and Retsch S1 planetary mill. After drying the milled powders, green disk-shaped samples (O 18 mm, thickness \(\sim\) 1.5 mm) were compacted by uniaxial pressing at 40 MPa. The generic firing schedule included controlled heating/cooling at 5 \({}^{\circ}\)C/min with the firing temperature T\({}_{\text{f}}\) in the range 1450-1550 \({}^{\circ}\)C and the firing time t\({}_{\text{f}}\) in the range 1-9 h. The experimental plan was designed employing the Taguchi method [31] and is detailed in Table 2. The firing of samples was done using alumina plates as supports covered with alumina cups; each sample was placed on a bed of powder of identical cation composition. Dense 5 YSZ and 8 YSZ ceramics samples for comparative studies were prepared using commercial powders (5 YSZ, Innovano, Portugal, and 8 YSZ, Tsooh, Japan) and sintered at 1600 \({}^{\circ}\)C for 10 h.  
The electrical conductivity (\(\sigma\)) was determined by AC impedance spectroscopy (Agilent 4284A precision LCR meter, frequency range 20 Hz-1 MHz) using bar-shaped ceramic samples with applied porous Pt electrodes (Heraeus CL-11-5349 platinum paste, sintering at 1000 \({}^{\circ}\)C for 30 min). The conductivity was calculated as \(\sigma\) = L/(A \(\times\) R) where L and A are the length and cross-sectional area of the sample, respectively, and R is the total ohmic resistance of the sample extracted from the impedance spectroscopy data. The measurements were done in air in the temperature range 500-1050 \({}^{\circ}\)C in a stepwise cooling regime (25\({}^{\circ}\) step, with \(\geq\)20 min equilibration at each step) or isothermally on redox cycling between air and 10%H2-N2 atmosphere at 900 \({}^{\circ}\)C. The average oxygen ion transference numbers (\(\overline{\text{t}_{\text{O}}}\)) under air/O2 gradients were determined at 700-900 \({}^{\circ}\)C by the electromotive force (EMF) technique modified to take the electrode polarization into account ([PERSON]'s modification [32; 33; 34]). In the classical EMF method, the average \(\overline{\text{t}_{\text{O}}}\) of oxide sample with negligible electrode polarization resistance is obtained as a ratio of measured EMF (E\({}_{\text{exp}}\)) and theoretical Nernst voltage (E\({}_{\text{theor}}\)) of concentration cell:  
\[\overline{\text{t}_{\text{O}}}\ =\ \text{E}_{\text{exp}}/\text{E}_{\text{theor}}\ =\ \text{R}_{\text{e}}/\left(\text{R}_{\text{O}}+\text{R}_{\text{e}}\right), \tag{1}\]  
where \(\text{R}_{\text{O}}\) and \(\text{R}_{\text{e}}\) are the partial oxygen ionic and electronic resistance of the sample, respectively. Non-negligible electrode polarization (\(\text{R}_{\text{\eta}}\)) leads to underestimated \(\overline{\text{t}_{\text{O}}}\) values. [PERSON]'s modification [32; 33; 34] is based on the measurement of EMF of the cell as a function of external resistance (\(\text{R}_{\text{M}}\)) closing the circuit.