## 3 Results and Discussion  
### Preliminary Material Characterization: Effects of Processing Parameters  
#### 3.1.1 Particle Size Distribution, Microporosity, and Thermal Profiles  
According to recent studies [54; 55], particle size distribution for the precursor materials can have an effect on the upper limit for ionic conductivity, making a distinction between materials in the nanoparticle range (<100 nm for ZrO\({}_{2}\), and 10 to 20 nm for SiO\({}_{2}\)) vs. macro-precursors (5 \(\upmu\)m for ZrO\({}_{2}\), and 216 \(\upmu\)m for SiO\({}_{2}\)). However, such claims may not be universal, primarily because (i) the applied ball-milling procedure may be considered anemic (wet-milling at 120 RPM for 2 h, followed by calcination at 400 \({}^{\circ}\)C and pressing into pellets, manual grinding, calcination at 1100 \({}^{\circ}\)C, and wet-milling at 120 RPM for 3 h; no sequencing of ball diameters mentioned for fine grinding [54]), which can be remedied by subsequent jet-milling [55]; and (ii) pre-sintered powders originating from nano- and macro-precursors both displayed the exact same bimodal particle size distribution with peaks at 5 \(\upmu\)m and 90 \(\upmu\)m [54], albeit at relatively different frequencies, thus rendering the effect of initial particle size essentially negligible as smaller particles agglomerated into the same size scales during thermal processing. In this study, starting from macro-precursors (5 \(\upmu\)m for ZrO\({}_{2}\), and 200 to 500 \(\upmu\)m for SiO\({}_{2}\)), a noticeably finer grade of particles was achieved by applying a rigorous and highly energetic ball-milling procedure to gradually reduce and homogenize particle sizes. After ball-milling concluded, the precursor mix displayed an average particle size in the low micrometric range (\(\sim\)1.7 \(\upmu\)m), which was conserved after sintering with particles of larger diameters (\(<\)5 \(\upmu\)m) accumulating due to thermally induced aggregation--the latter was also evident in the numerical frequencies of the cumulative distributions shifting toward the larger diameters after thermal treatment (Figure 1). Submicronic particles (\(\geq\)480 nm) occurring after thermal treatment most possibly originated from the thermal decomposition of the more volatile phases of the precursor constituents (melting point of NH\({}_{4}\)H\({}_{2}\)PO\({}_{4}\) at 190 \({}^{\circ}\)C). Table 1 presents the statistical metrics for the particle size distributions before and after sintering of NASICON powders, obtained by dynamic light scattering (DLS) measurements conducted in static mode to account for micronic particles and verified for the sub-micronic range in dynamic mode. \(D_{mole}\) and \(D_{average}\) correspond to the mode and the average hydrodynamical diameter of the distributions, respectively; the \(D_{A}\) metrics signify the diameter value corresponding to the cumulative curve at \(A\)% (e.g., \(D_{50}\) corresponds to the median); \(CV\) is the covariance of the sample; \(PI\) is the polydispersity index, where \(PI=(D_{90}-D_{10})/D_{50}\); and \(RMS\)  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Processing Stage** & \(D_{mole}\) [nm] & \(D_{average}\) [nm] & \(D_{10}\) [nm] & \(D_{50}\) [nm] & \(D_{90}\) [nm] & \(CV\) [nm] & \(PI\) [\%] &  
is the root mean square. Analysis revealed that the sintered NASICON powders were polydispersed (_PI_ >> 70%) compared to the monodispersed pre-sintered material, while both distributions were monomodal. Polydispersity occurs as a consequence of thermally induced aggregation at the high temperatures of sintering; modality, however, is strictly dependent on the effectiveness of ball-milling, and is conserved before and after thermal processing. Surface area and microporosity analyses of pre-sintered NASICON samples were conducted by BET and BJH, respectively (Figure 2), based on nitrogen adsorption caused by intrinsic surface energies (i.e., non-selective and reversible physical adsorption between gas molecules and the exposed surface of the porous material).