## 3 Results and Discussion
### Ionic Conductivity and Dielectric Relaxation Investigations
#### 3.2.1 Broadband Ionic Conductivity Measurements
Finally, overall temperature dependency was monitored by obtaining Poincare sections from the phase-space mappings at different frequency intervals; these are displayed as Arrhenius plots of the real component \(\sigma^{\prime}\) of conductivity against scaled reciprocal temperature in Figure 10. Temperature dependency manifests as linearity in the high-frequency region, which becomes distorted at lower frequencies due to polarization dominance. Overall, conductivity increased with temperature, with low-temperature conduction being associated with bipolar hopping mechanisms and high-temperature conduction being attributed to thermally activated polaron hopping [56]. Figure 9: Fitting parameters to the frequency series data according to the Jonscher power law, obtained by the nonlinear Levenberg–Marquardt iteration algorithm and transposed over scaled reciprocal temperature, showing the (**a**) bulk dc electrical conductivity, \(\sigma_{dc}\); (**b**) ac conductivity coefficient, \(A\); (**c**) frequency exponent of the mobile ions, \(n\); and (**d**) derived crossover frequency, \(\omega_{p}\). Parameter fittings correspond to \(R^{2}\) values ranging from 0.99 to 0.94. Demarcated values correspond to room temperature (RT) conditions. In review, conductivity measurements can be readily associated with observations established in the material characterization stage of the analysis: zirconia contamination remains a critical factor, limiting ionic conductivity in comparison to the commercial reference throughout the temperature and frequency scanning ranges. This is evident in the contaminated samples prepared at 540 MPa and 245 MPa, implying that applied pressure acts in conjunction with zirconia contamination by influencing its local distribution. This, in turn, affects the degree of connectedness of long-range ion-hopping pathways and the extent of tortuosity, and is reflected in both frequency and temperature-dependent factors of the Jonscher power law by transposing their global inflection points alongside their values. Divergence compared to the reference becomes more pronounced as the crystallite size of zirconia contaminants increases, as porous pathways for ion hopping are blocked by enlarged zirconia partitions and defects. At this point, it is not clear if and how packing order and mechanical stability induced by applied pressure can affect conductivity, but the comparably larger deviation in power law factors displayed by the 245 MPa sample may lend support to this interpretation. Finally, it is noteworthy that the values of power law factors diverge considerably as the temperature dropped near the cryogenic scale, although the deviations in temperature-dependent dc conductivity and activation energies remained relatively stable. This implies that thermally activated polaron hopping acts as the main  
Figure 10: Arrhenius plots of the real component \(\sigma^{\prime}\) of conductivity against reciprocal temperature, obtained as Poincaré sections at the frequency domains of (**a**) \(10^{7}\) Hz; (**b**) \(10^{5}\) Hz; (**c**) \(10^{3}\) Hz; and (**d**) \(10\) Hz. Comparative scans include all in-lab prepared NASICON pellets over different levels of applied pressure versus the commercial NASICON as the reference. Inlets portray the temperature interval in the vicinity of RT, with displayed conductivity readings for RT at the corresponding scanning frequency. Temperature dependency manifests as linearity in the (**a**,**b**) high-frequencies scans. Temperature dependency becomes distorted at the lower (**c**,**d**) frequency intervals due to polarization dominance. conduction mechanism, which diminishes considerably in low temperature regimes where bipolar hopping mechanisms instead dominate. The marked difference between the in-lab prepared samples and the commercial reference is again associated with the degree of connectedness of long-range ion-hopping pathways, which is hampered by the extent of zirconia contamination.