Continuous Sound Velocity Measurements along the Shock Hugoniot Curve of Quartz

We report continuous measurements of the sound velocity along the principal Hugoniot curve of $\alpha$ quartz between 0.25 and 1.45 TPa, as determined from lateral release waves intersecting the shock front as a function of time in decaying-shock experiments. The measured sound velocities are lower than predicted by prior models, based on the properties of stishovite at densities below $\sim 7\mathrm{g}/{\mathrm{cm}}^3$, but agree with density functional theory molecular dynamics calculations and an empirical wide-regime equation of state presented here. The Grüneisen parameter calculated from the sound velocity decreases from $\gamma \sim 1.3$ at 0.25 TPa to 0.66 at 1.45 TPa. In combination with evidence for increased (configurational) specific heat and decreased bulk modulus, the values of $\gamma$ suggest a high thermal expansion coefficient at $\sim 0.25–0.65\mathrm{TPa}$, where ${\mathrm{SiO}}_2$ is thought to be a bonded liquid. From our measurements, dissociation of the molecular bonds persists to $\sim 0.65–1.0\mathrm{TPa}$, consistent with estimates by other methods. At higher densities, the sound velocity is close to predictions from previous models, and the Grüneisen parameter approaches the ideal gas value.

Figure 1

(a) Experimental geometry: 4 beams of the SGIII (prototype) laser focused on the CH ablator produce an unsupported shock in the Al pusher. The quartz sample has a free side (shown at bottom of quartz sample) introducing a lateral release wave incident into the shock wave. The solid black curves indicate the shock front at different times, $U_s$ is the shock wave velocity, $U_p$ the particle velocity, and $Cb$ the bulk sound velocity. The bent shock front below the red-dashed line scatters the reflected beam away from—rather than returning it to—the streak camera. (b) Line-imaging VISAR record for continuous sound-speed measurement from side release between shock incidence and breakout. The solid green curve shows the velocity of the shock front, and the red crosses (shifted downward by $20\mu \mathrm{m}$) indicate the points at which the shock front bends and are used to extract the sound velocity along the Hugoniot curve.

Figure 2

Measured bulk sound velocity (red and blue filled circles with error bars) is in good agreement with DFT-MD calculations (solid black curve with green background), as well as our empirical EOS model (black dashed line). Subscript $H$ means the Hugoniot state, $b$ means bulk sound velocity, $L$ means longitudinal sound velocity, and $c$ means the cold state. Sound velocity from the analytic model (Knudson and Desjarlais [12], half-shaded circle) and previous data of Pavlovskii [22] (open squares), McQueen [23] (stars), and Zha [24] (dash-dot-dot curve) are indicated together with results from the cold curve [31, 32] (dash-dotted curve) and the Hugoniot curve of stishovite [10, 33] (short-dashed curve).

Figure 3

Calculated Grüneisen parameter of ${\mathrm{SiO}}_2$ decreases with compression, and approaches 0.66 at densities above $7.0\mathrm{g}/{\mathrm{cm}}^3$. The solid closed circles (red and blue) give the present measurements, the dark blue dash-dot curve is the average value (${\overline{\gamma }}_{FQ}$) between the Hugoniot curves of fused silica [14] and quartz [12], and the olive dashed curve is the average value (${\overline{\gamma }}_{QS}$) between the quartz Hugoniot curve [12] and the stishovite cold curve [31, 32]. The black solid curve with green shading shows the DFT-MD result. Inverted triangles show the effective gamma in the KD model [12]. The black solid and open symbols on the left side are data for solid stishovite [35], and gray triangles are data for liquid fused silica [7]. The solid cyan gives the calculated thermal expansion coefficient ($\alpha$). Reflectivity ($R$) measured from the shock front using the VISAR probe laser (blue $\times \mathrm{s}$ and red bars) and the Hugoniot temperature ($T$, purple short dash) calibrated by Millot et al. [10] are also shown.