## 3 Results
### SEM with Microanalysis EDX Results  
Figure 4 shows SEM micrographs taken to study the microstructure and morphology of fabricated glass-ceramic composite samples, melted at 1000 \({}^{\circ}\)C in ceramic crucibles, cooled at 1000 RPM (Figure 4a) and 800 RPM (Figure 4b), and polycrystalline material obtained from the batch melted in the PtIr crucible at 1000 \({}^{\circ}\)C, cooled at 1000 RPM (Figure 4c). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Structure** & **Space Group** & \ \begin{tabular}{c} **Lattice** \\ **Constants [Å]** \\ \end{tabular}  & \begin{tabular}{c} **Rwp** \\ \end{tabular}  & **Factor [\%]** \\ \hline Twin rollers, 1000 RPM & Fluorite & Fm3m & a = 5.537 & 7.91 \\ Ceramic crucible & Fluorite & Fm3m & a = 5.541 & 6.50 \\ \hline Free cooling & Fluorite & Fm3m & a = 5.537 & 6.78 \\ Ceramic crucible & & & & \\ \hline Twin rollers, 1000 RPM & \multirow{2}{*}{Monoclinic} & \multirow{2}{*}{P21/c} & a = 5.849 & \multirow{2}{*}{9.62} \\ PtIr crucible & & & & \\ \cline{4-4} \cline{5-5}  
Materials melted in the ceramic crucible (Figure 4a,b) are characterized by a homogeneous grain distribution and a structure without visible cracks and pores. The grains are of nanometric size and do not have clearly defined boundaries, which probably confirms the significant contribution of the amorphous matrix in the structure of the glass-ceramic composite, revealed in the XRD results as amorphous contribution. It should be noted, however, that individual grains are often composed of several agglomerated much smaller crystallites. The morphology of the material obtained by cooling with twin rollers of the batch from the PtIr crucible (Figure 4c) differs significantly from the previously described samples. The grains are much larger, with sharply defined boundaries, which may indicate a negligible contribution of the amorphous part in the sample, a result that is consistent with the shape of the diffractograms for these materials. The structure of the sample is heterogeneous--it is possible to observe solid grains of micrometric size with nanometric partially separated precipitates on them, as well as areas where crystallites of less than 100 nm in size are agglomerated. Many cracks and pores are also visible. Figure 3: (**a**) Thermal evolution of XRD patterns of a sample prepared in ceramic crucible at 1000 \({}^{\circ}\)C and quenched by twin rollers method (1000 RPM) during heating up to 800 \({}^{\circ}\)C; (**b**) thermal evolution of the same sample during cooling down from 800 \({}^{\circ}\)C to room temperature. Blue and gray colors correspond to \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) type phase (fluorite structure); turquoise color indicates phase transition to \(\gamma\)-like phase; orange and maroon colors correspond to \(\gamma\)-like phase stability range. To further analyze the grain size distribution and the occurrence frequency of crystallites of each size, a statistical analysis was performed on the SEM micrographs shown in Figure 4 using an algorithm in MATLAB software. The resulting histograms are presented in Figure 5.  
It is very important to notice that the value obtained from XRD is the crystallite size, while the one obtained from the SEM is the grain size. Grain can consist of several crystallites. Nevertheless, based on this method, the determined average grain size for the samples from ceramic crucibles cooled by twin rollers at 1000 RPM and 800 RPM is 50 nm and 64 nm, respectively, which is in fairly good agreement with the values determined by the Scherrer equation. Histogram 5c differs greatly from those of Histograms 5a,b because it relates to the microstructure of the \(\alpha\)-Bi\({}_{2}\)O\({}_{3}\) sample obtained from the PtIr crucible. This difference clearly shows that only in the ceramic crucible is it possible to obtain \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) by the twin rollers method. The large sample inhomogeneity described earlier, which may significantly affect the shape of the diffractograms, is most likely responsible for such a remarkable discrepancy.