2.2. Characterization

The density (ρ) values of the as-prepared and post-treated glasses were determined by Archimedes’ principle of buoyancy. The weight of each sample (at least 1.5 g) was measured 10 times in ethanol.

An ultrasonic thickness gauge (38DL Plus, Olympus, MA, USA), equipped with 20 MHz delay line transducers for the determination of the longitudinal V₁ and transversal wave velocities V₂, was used to determine the elastic properties of the glasses. Based on these velocity and density values, we calculated Young’s modulus E, bulk modulus B, and shear modulus G as well as Poisson ratio ν using the relations for isotropic materials.

We also calculated the atomic packing density (C_g). To do so, we assumed four-fold coordination for Si, six-fold coordination for Ca, two-fold coordination for O, while the speciation for boron and aluminum was based on previous structural data for the CABS glasses [6]. C_g is defined as the ratio between the theoretical molar volume provided by the ions and the effective molar volume of the glass. The atomic packing density (C_g) can then be calculated as,

where Vi=43πN(xrA3+yrB3) represents the molar volume of an oxide A_xB_y with the molar mass M_i and the molar fraction f_i, N is the Avogadro number, and r_A and r_B are the ionic radii [28,29,30].

Micro-indentation measurements were carried out with a Nanovea CB500 hardness tester to determine the Vickers hardness (H_V) and crack resistance (CR). On each sample, 20 indentations with a maximum load of 4.9 N (1 kgf) were generated to determine H_V, with a loading duration of 15 s and a dwell time of 10 s. We then used an optical microscope to analyze the residual imprints and calculate the H_V. CR, i.e., the resistance of the glass to the initiation of cracks in the corners upon indentation, was determined using two different diamond indenters, namely, the 136° four-sided pyramid Vickers tip and the three-sided pyramid cube corner tip with mutually perpendicular faces. For the same glass, the sharper cube’s corner tip leads to higher residual stress, less densification, and easier crack initiation compared to the Vickers tip. In both cases, we used increasing loads (from 4.8 to 30 N for Vickers and from 0.1 to 0.9 N for cube corner) and counted the numbers of corner cracks 2 h after unloading (see Figure S2). CR was calculated based on the method of Wada [31]. That is, the probability of crack occurrence (PCI) was defined as the ratio between the number of corner cracks and the total number of corners on all indents. CR is a load that generates 2 or 1.5 cracks (PCI = 50%) on average for Vickers and cube corner, respectively. At least 30 indents were performed on each sample using a loading duration and dwell time of 15 s and 10 s, respectively. Measurements were performed under laboratory conditions (room temperature, relative humidity ~37% RH).

To better understand the indentation deformation mechanism (i.e., the relative propensity for densification vs. shear flow) in the different glasses, we explored the recovery of the indent side length. This analysis consists of recording images of the indent site before treatment and after a thermal treatment at 0.9 T_g for 2 h [32], and then measuring how much the side length of the indent cavity shrinks after the annealing treatment. Such side length recovery is in turn related to the degree of densification upon indentation, as the densified region will recover during the 0.9 T_g annealing but not the displacement due to shear flow. We explored at least 10 indents with the load of 4.9 N for each specimen, loading duration of 15 s, and dwell time of 10 s. The side length recovery (L_SR) can then be calculated as,

where L_s,i is the indentation side length as defined from the optical microscope before the treatment and L_s,f is the indentation side length after annealing at 0.9 T_g for 2 h.