“…Hardness is a measure of the mean contact stress for the formation of a permanent deformation and it is typically quantified by permanently deforming the glass with a sharp indenter (e.g.,Vickers diamond indenter), where hardness (H ) is given by the load (P) divided by the project area (A) as H = P/A. Hardness is a function of chemical composition and different models and approaches have been proposed to predict the composition dependence of glass hardness (Georoff and Babcock, 1973;Yamane and Mackenzie, 1974;Calleja et al, 2002;Smedskjaer et al, 2010a). Relationships between H and various macroscopic properties have also been proposed (Liu and Cohen, 1989;Sehgal and Ito, 1999;Gao et al, 2003;Hand and Tadjiev, 2010), but there is an intrinsic difference in the scaling between hardness and, e.g., elastic moduli.…”