Hardness and elastic recovery measurement

Indentation hardness and elastic recovery were derived from the load-displacement curves established by the three-sided pyramidal Berkovich diamond indenter (Keysight Nano Indenter G200). The indenter parameters were first calibrated against hard materials with a wide hardness range, including fused quartz, Al₂O₃, and SiC. The measured hardness for these materials was consistent with the referenced data. The applied standard loading time to peak load was 15 s, the peak holding time was 10 s, and the unloading time was 15 s. In addition, the indentation measurements were also carried out with varying loading, holding, and unloading times. The applied time has no significant effect on the elastic modulus, elastic recovery, and hardness (see fig. S9). The applied loads were 0.98 to 9.8N for the GCs, Si, SiO₂, MgO, and Al₂O₃, whose hardness and elastic recovery had little change with the loads, especially above 4.9 N. The applied loads were 0.49 to 4.41 N for Cu and Al, and the obtained hardness and elastic recovery were almost unchanged with the loads. The standard shore hardness test block of the HD-29 rubber is too soft; thus, we had to use a small load of 0.049 N to obtain a standard load-displacement curve. When larger loads were used, the hops were not anticipated to appear on the curve, possibly due to the breaking of rubber. In addition, the hardness and elastic recovery of steel, TiNi, and bulk metallic glass were estimated from the previous research. For the nanoindentation method, the hardness was estimated by the peak load and projected area of indentation determined by the indenter displacement (that is, indentation depth) at peak load and the indenter geometries. The reduced modulus E_r was determined by the contact stiffness and project area. By assuming a Poisson’s ratio of 0.2 for all GCs, their Young’s moduli were estimated. The indentation elastic recovery was calculated using the ratio of area integrals under the unloading and loading curves, respectively.

The standard Vickers hardness (H_v) measurement was also carried out, and the indentation experiments were performed on the polished samples using a four-sided pyramidal diamond indenter. The loading force of the microhardness tester was 4.9 N. The loading and dwell times were both 15 s. Under each sample, six indentations were made. H_v is defined as the applied load P(N) divided by the surface area of the impression after unloading: H_v = 1854.4P/d², where d is the arithmetic mean of the two diagonals of the indent in micrometers (μm).

The hardness characterization of compressed GC was also carried out with a qualitative scratch test (that is, Mohs hardness test). The edge of the Com.GC-3 sample rod readily scratched the (0001) crystal planes of Al₂O₃ (Mohs scale, 9) and SiC single crystals (Mohs scale, 9.5) (see fig. S12). This means that the hardness of Com.GC-3 is comparable to or even higher than those of Al₂O₃ and SiC. The hardness of (0001) crystal planes of Al₂O₃ and SiC single crystals we measured are 22 and 33 GPa, respectively, which are consistent with other reports.