“…We first consider the series of glasses with varying Si/Al ratio [(80 − x)SiO 2 − x Al 2 O 3 − 5 B 2 O 3 − 15 Na 2 O with x = 0, 1, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, and 20], for which hardness data have already been reported (Zheng et al, 2012b). Figure 1 shows the composition dependence of the experimentally determined hardness values and those calculated based on Eqs 1 and 2 with the analyzed chemical compositions and 11 B and 27 Al magic angle spinning (MAS) NMR data as input (Zheng et al, 2012a).…”