Elastic moduli of hexagonal diamond and cubic diamond formed under shock compression

The relative stiffnesses and strengths of hexagonal diamond and cubic diamond constitute long-standing unresolved issues, because relevant experimental results are lacking. Laser interferometry was used to experimentally determine the longitudinal sound speeds and moduli in hexagonal diamond and cubic diamond formed during the shock compression of graphite. The hexagonal diamond longitudinal moduli are significantly larger than the cubic diamond longitudinal moduli, and even exceed averaged cubic diamond single crystal values. The measured hexagonal diamond longitudinal moduli, combined with high-pressure bulk moduli for cubic diamond single crystals, show that shock-formed hexagonal diamond shear moduli are larger than the shear moduli for cubic diamond single crystals.

Figure 1

Front-surface impact experimental approach. (a) Experimental configuration. (b) An $h-t$ plot showing wave propagation. Solid lines indicate shock waves and dashed lines indicate release waves. (c) Idealized center probe particle velocity history obtained at the graphite/LiF interface.

Figure 2

Particle velocity histories obtained at the graphite/LiF interface for HOPG (a) and PG (b). Experiments 1–4 are on ZYB-grade HOPG and experiment 8 is on ZYH-grade HOPG. The particle velocity history for experiment 6 utilized PDV measurements due to VISAR contrast loss. All other profiles were obtained from VISAR measurements.

Figure 3

Eulerian sound speeds. Sound speeds determined for each experiment are shown as solid symbols and previous sound speeds reported for shock compressed HOPG [27] and PG [39] are shown as open symbols. For comparison with the experimental results, the dashed line shows ambient cubic diamond (CD) sound speed along the [100] orientation and the solid black lines show the ambient sound speeds corresponding to the Voigt (upper bound) and Reuss (lower bound) averaged CD elastic moduli. The ambient hexagonal diamond (HD) sound speed calculated from an average [22] of theoretical elastic constants along the orientation observed in XRD experiments ($\left[10\overline{1}0\right]$) is shown as a blue line.

Figure 4

Longitudinal moduli. Experimentally determined diamond moduli are shown as solid symbols and moduli reported for HOPG below the transition [27] are shown as open symbols. For comparison with the present experimental results, the dashed line shows cubic diamond (CD) [100] moduli calculated from second and third order elastic constants. Solid lines show the moduli corresponding to the Voigt (upper) and Reuss (lower) averaged CD elastic moduli scaled with increasing stress (and hence density) assuming a linear elastic response. The blue line is a linear fit for visual reference, with the intercept fixed at the ambient hexagonal diamond (HD) modulus along $\left[10\overline{1}0\right]$, calculated from an average [22] of theoretical elastic constants.