## 4 Conclusions  
A series of experiments were designed to investigate the classic Na\({}_{3}\)Zr\({}_{2}\)Si\({}_{2}\)PO\({}_{12}\) system based on the solid-state reaction (SSR) synthesis protocol (i.e., without considerations for optimizing electrical properties by controlling either the elemental composition or the grain boundaries in the crystalline lattice). Thus, sintering temperatures were maintained at the highest level of 1250 \({}^{\circ}\)C, which does not suppress excess zirconia contamination, and the evolution of the zirconia phase was carefully monitored. The main parameter that  
Figure 13: Parametric 2D and 3D phase-space mappings of the dissipation factor tan\(\delta\) of permittivity scanned over a broadband frequency range of 10\({}^{-1}\) to 10\({}^{11}\) Hz and for temperatures ranging from 200 \({}^{\circ}\)C to \(-\)100 \({}^{\circ}\)C. Scans for NASICON pellets assembled by applying pressure levels of (**a**) 245 MPa, (**b**) 345 MPa, and (**c**) 540 MPa are displayed. Phase-space mappings reveal the primary relaxation band as a diagonal ridge in direct association with the corresponding feature observed in conductivity mappings as well as a second relaxation band initiated at the transition temperature of the monoclinic-to-rhombohedral lattice structure for NASICON. Dissipation scales adhere to the common colormap on the right of figures. was evaluated was the applied isostatic pressure for converting the calculated NASICON powders into pellet form, right before the final sintering stage. Conductivity and dielectric permittivity measurements were conducted over broadband frequency and temperature scales, reaching near the cryogenic regime at \(-100\)\({}^{\circ}\)C. The overall analysis, enhanced by parametric 2D and 3D phase-space mappings, arrived at the following conclusions:  
* Precursor particle size (nano- vs. micron-sized particles) is not necessarily of critical importance, provided that ball-milling has been performed rigorously to arrive at monomodal but polydisperse distributions of NASICON precursors;
* Excess zirconia contamination can be modestly controlled, but not fully suppressed due to the high sintering temperature, by applying selected isostatic pressure levels during pellet formation in order to minimize the zirconia crystallite size; excessive pressure levels (>345 MPa) reverse this trend by dispersing zirconia particles over a wider phase distribution, although a higher packing order of the material is induced;
* Low pressure levels (<345 MPa) may cause inhomogeneity and mechanical stability issues due to zirconia accretion and poor packing order, reflecting negatively on the ionic conductivity of the system;
* Low pressure levels may also result in significant hysteresis between relaxation and ionic transport activation energies, with a lower energy barrier for relaxation causing early dissipation of energy and thus diminishing ionic conductivity;
* The high-frequency permittivity limit \(\varepsilon_{\infty}\) may be assessed by dielectric permittivity scans near the cryogenic regime without having to access high frequencies to negate dipole contributions to polarization;
* Phase-space mappings have identified a correlated high ionic conductivity band with its corresponding relaxation band in the dissipation factor spectra, both propagating diagonally in tandem frequency and temperature dependency; and
* Phase-space mappings of the dissipation factor revealed a secondary relaxation band that can be associated with the monoclinic-to-rhombohedral lattice transition. Future research will focus on investigating the optimized parameters for the main SSR synthesis in order to fully suppress zirconia contamination, and on extending the broadband scanning range to the cryogenic threshold at \(-160\)\({}^{\circ}\)C.  
Conceptualization, A.T. and A.M.; Methodology, M.I. and A.M.; Software, A.T.; Validation, A.T. and M.I. ; Formal analysis, A.T.; Investigation, A.T., M.I. and A.M.; Resources, A.M.; Data curation, A.T. and M.I.