Boson mode, Medium Range Structure and Intermediate Phase (IP) in (Na$_{2}$O)$_{x}$(B$_{2}$O$_{3})_{1-x}$ glasses

Raman scattering of titled glasses are examined using a T64000 Dispersive system. Scattering strengths of the Boson mode (40 cm$^{-1}$, 70 cm$^{-1})$ and the Boroxyl ring (BR) mode (808 cm$^{-1})$ are found to decrease with increasing x at the same rate in the 0 $<$ x $<$ 20{\%} soda range. Apparently, the 2D character of BRs embedded in a 3D network gives rise to the Boson mode.\footnote{M. Flores-Ruiz and G. Naumis, PRB, 2011. \textbf{83}: p. 184204} The triad of modes (705, 740, 770 cm$^{-1})$ near the 808 cm$^{-1}$ mode are found to display a maximum in scattering strength near x = 37{\%} (705 cm$^{-1})$, 33{\%} (740 cm$^{-1})$ and 25{\%} (770 cm$^{-1})$, suggesting that these are also ring modes of Na-tripentaborate (STPB), Na-diborate (SDB) and Na-triborate (STB) super-structures. Variations in Raman scattering strengths also suggest that STB percolate near x = 20{\%}, the \textit{stress} transition, while the STPB and SDTB percolate near x = 40{\%}, the \textit{rigidity} transition. These transitions were inferred from m-DSC experiments that show an intermediate phase in the 20{\%} $<$ x $<$ 40{\%} range in dry and homogeneous glasses.