## 3 Results and Discussion
### Evolution of Phase Composition and Microstructure
Visually, the volume fraction of the pores increases with increasing praseodymium content and reasonably decreases with increasing time and temperature of firing. The EDS analysis showed the accumulation of praseodymium near the surface of the pores. Again, the distribution of cations becomes more homogeneous with increasing temperature and duration of firing (Figure 3). Figure 3: SEM micrographs of polished Pr-substituted 5 YSZ ceramics with overlaid EDS elemental mapping. SEM inspection of the polished and thermally etched samples also revealed inhomogeneities in the grain size distribution (Figure 4). For lower T\({}_{\text{f}}\) and shorter t\({}_{\text{f}}\), larger grains (1-3 \(\upmu\)m) surround the pores, while small grains (0.2-1.2 \(\upmu\)m) fill the volume between the pores. The grain size distribution is correlated with praseodymium elemental distribution. As an example, Figure 5A shows the EDS spectra collected from different points of the P10-1450-4 sample. The results imply that the praseodymium concentration in the large grains is noticeably higher than in the small grains, which is in close agreement with the structural evidence of fluorite peak splitting (Figure 2), and increases drastically near the pore surface indicating the preferential location of the secondary pyrochlore Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\) phase. Increasing the time and temperature of firing promotes a more homogeneous distribution of the grain size and praseodymium concentration across the sample volume (Figures 3 and 4). Still, the accumulation of Pr near the pore surface is detectable by EDS analysis even in the samples with a longer firing at 1500-1550 \({}^{\circ}\)C (Figures 3 and 5B). Figure 4: SEM micrographs of polished and thermally etched Pr-substituted 5 YSZ ceramics. Thermal etching included heating in air to 1400 \({}^{\circ}\)C followed by immediate cooling (heating/cooling at 5 \({}^{\circ}\)C/min). Circles show that larger grain sizes are often associated with porosity. In combination, the XRD and SEM/EDS data suggest the following scheme of the phase evolution during direct firing. The pores in the ceramic samples may be due to poorer packing near praseodymium oxide agglomerates in the green powder mixture after ball-milling and compaction of the 5 YSZ + PrO\({}_{y}\) samples or due to hindered shrinkage as reactive firing proceeds. Independently of temperature, the solid-state reaction proceeds through the initial formation of the pyrochlore-type Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\) phase at the PrO\({}_{y}\)/5 YSZ contacts. This is followed by the diffusion of praseodymium from the formed layer of the pyrochlore phase into the bulk of the samples, under Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\)/(Zr,Y,Pr)O\({}_{2.8}\)/5 YSZ phase gradients inducing grain growth by Pr-enrichment and possibly also the onset of porosity by a Kirkendall-like effect, as demonstrated for interdiffusion in YSZ/YDC (YDC = yttria-doped ceria) [43]. In addition, local grain growth may hinder microstructural rearrangement, possibly combined with grain boundary pinning by Pr\({}_{2}\)Zr\({}_{2}\)O\({}_{7}\) particles, preventing the densification and elimination of the remaining porosity. Note also the irregular shape of this porosity (Figure 3). The phase evolution is well illustrated by the changes in the XRD peaks shape/splitting with increasing temperature of firing. The substitution by Pr into 5 YSZ is expected to increase the lattice parameters due to differences between the ionic radii of Pr\({}^{4+}\) (r\({}^{\text{VI}}\) = 0.85 A) and Pr\({}^{3+}\) (r\({}^{\text{VI}}\) = 0.99 A) relative to Zr\({}^{4+}\) (r\({}^{\text{VI}}\) = 0.72 A) and Y\({}^{3+}\) (r\({}^{\text{VI}}\) = 0.90 A) [35]. In addition to the fluorite (F) phase, the XRD pattern of the P05-1450-1 sample (Figure 2A) suggests  
Figure 5: EDS spectra collected from selected points of (**A**) P10-1450-4 and (**B**) P05-1550-4 ceramics showing the difference in Pr elemental distribution between small grains, large grains and pores surface.