## 3 Results and Discussion
### The SROC Model in Bismuth Borate Glasses
Thus, for x = 0.25, the \(\underline{\mathrm{M}}\) node, \(X_{\underline{\mathrm{M}}}(0.25)=1\), and the structure should consist exclusively of metaborate-type units, namely \(\mathrm{B}\mathcal{O}_{4}\)\({}^{-}\) and \(\mathrm{B}\mathcal{O}_{2}\)O\({}^{-}\). Their molar fractions are unknown, but we can use the NMR value \(X_{4}=0.37\) from ref. [45] and, consequently, \(X_{2}=0.63\) for x = 0.25. At this point, we have all the information needed for nodes \(\underline{\mathrm{N}}\), \(\underline{\mathrm{M}}\), and \(\underline{\mathrm{P}}\) and the results for the components of the corresponding SROCs, following Equation (6), are reported in \[A(x)=\frac{3x+3(1-x)}{2(1-x)}=\frac{1.5}{1-x}\]0  
The molar fractions of the borate entities for the SRO structure of bismuth borate glasses can be easily derived by applying Equation (13a,b). The results are depicted in \[A(x)=\frac{3x+3(1-x)}{2(1-x)}=\frac{1.5}{1-x}\]1 In the same figure, the data from our previous experimental study are also included [43]. Inspection of Figure 3 shows that for x = 0.2 and x = 0.4 the SROC model agrees perfectly with the experimentally derived data, as expected. In fact, for x = 0.2 this agreement was already mentioned and served as our starting point for the SROC of the \(\underline{\mathrm{M}}\) node, while for x = 0.4, the corresponding SROC \(\underline{\mathrm{P}}\) used the experimental data as input. On the contrary, for the x = 0.3 glass composition, there is a clear divergence between the SROC model and the experimentally calculated data. The main discrepancy concerns the molar fractions of pyro- and orthoborate units. It is surprising, though, that while the SROC model predicts the presence of orthoborate units with a molar fraction of ca. 0.13, derived for the data in Figure 3, the experimental infrared absorption coefficient spectra of the x = 0.3 glass strongly suggest the absence of orthoborate triangles, as shown in Figure 3 of ref. [43]. To trace the origin of these deviations, we observe that in the SRO structure of the glass with the nominal pyroborate composition x = 0.40, pyroborate units constitute the minority species, with a molar fraction of 0.14, while metaborate tetrahedra and orthoborate units are the majority structural entities, both having a molar fraction of 0.43. This observation, which is in contrast to the stoichiometric considerations, strongly supports the occurrence of the disproportionation reaction of pyroborate units into metaborate tetrahedra and orthoborate moieties:  
\[2\mathrm{B}\mathcal{O}\mathrm{O}_{2}\)\({}^{2-}\)\(\rightleftarrows\)\(\mathrm{B}\mathcal{O}_{4}\)\({}^{-}\)\(+\)\(\mathrm{B}\mathrm{O}_{3}\)\({}^{3-}\)  
The aforementioned reaction fully explains the values of the molar fractions reported in Table 1 for the SRO structure of the x = 0.40 glass, with the nominal pyroborate stoichiometry. If we assume that initially there are only pyroborate triangles in the melt, then the onset of reaction (14) will result in equal populations of \(\mathrm{B}\mathcal{O}_{4}\)\({}^{-}\) tetrahedra and \(\mathrm{B}\mathrm{O}_{3}\)\({}^{3-}\) orthoborate triangles, in agreement with their equal molar fractions of 0.43. Moreover, this value of 0.43 dictates that pyroborate units participate in this reaction with a molar fraction of 0.86, thus leaving pyroborate units with a molar fraction of 0.14 in the glass structure. It is worthwhile to note that inspection of Table 1 evidences that the aforementioned disproportionation reaction is not active in the glass with x = 0.30 since there are no orthoborate triangles in the SRO structure. In other words, the onset of reaction (14) lies somewhere in the composition range above x = 0.30 and below x = 0.40. With this observation in mind, we try to reconciliate the deviations between the original SROC model and the experimental findings by adding an additional node in the SROC model, as analytically discussed in the forthcoming section.