Schematic cross-section of diamond anvils and sample, with the drive laser that creates the shock wave entering from the left. Supports for the anvils are shown in purple, and, as described in the text, current laser systems require the anvil on the shock-entry side to be thin. The sample is indicated, along with a stepped shock-wave standard, and diagnostics described in the text [VISAR and pyrometry (not shown)] record the dynamic compression of the sample through the second anvil.

Impedance matching solution for the Hugoniot pressure (P_H) and particle velocity (u_p) in the sample, as determined from the shock velocity U_S measured across the sample that by Eq. 5 defines the slope of the red line (P₁ is ignored here). The intersection with the equation of state of the standard (blue curve), reflected about the pressure–particle velocity state achieved in the standard (blue point), defines the common state (red point) behind the forward- and backward-traveling waves in the sample and standard. In a mechanical-impact experiment, u₀ would correspond to the impact velocity of the standard into the sample.

Schematic of diamond-anvil cell (Left and Center), showing both a cross-section (blue arrow indicates direction of incoming, shock-wave generating laser beams) and a pulled-apart view, and photograph (Right) of a diamond cell as a laser-induced shock is being generated during an experiment at the Omega laser facility (University of Rochester, Rochester, NY).

Internal energy as a function of pressure corresponding to Fig. 5, showing the isentrope and the Hugoniots for initially uncompressed (red) and precompressed samples (thin red, green, light blue). Approximate dimensional values for the axes are indicated assuming V₀ ≈ 5 cm³ per mol of atoms and K_0S = 10¹¹ Pa; a typical precompressed sample size is ≈400 μm diameter by 10 μm thick, or ≈300 nmol of atoms. Note that the pressure dependence of the Hugoniot energy for the linear U_S − u_p relation (Eq. 7) (black) is similar to that derived from the Mie–Grüneisen analysis (Eq. 9).

Predicted contours of electrical conductivity (thin gray solid and dashed curves) for He as a function of pressure and temperature, showing that metallic properties can be induced either by high P or high T. These influences can be separately documented by varying the initial density of the sample: colored dot-dash curves trending from lower left toward upper right indicate Hugoniots for different degrees of precompression (1- to 7-fold initial compression, as indicated by the color scale). Electrical conductivity can be experimentally inferred from optical absorption and reflectivity (see Fig. 7), and the contours shown here are based on thermodynamic and semiconductor models (24–26). A model isentrope for Jupiter's interior is shown for comparison (dashed black curve).

VISAR record from a laser-shock experiment through a precompressed sample (14), showing velocity fringes as a function of time (horizontal axis) obtained from an optical streak camera imaging light reflected off the stepped-Al shock standard across the ≈300-μm width of the sample area (vertical axis). Fringe positions are proportional to velocity of the reflecting surface, so shifts in fringes (e.g., at breakout) indicate changes in velocity. Curvature in breakout times indicate that the shock fronts are not exactly planar, and the stepped breakout at the center of the image shows the difference in travel time through the thin and thick Al steps (Fig. 2).

VISAR records of shock-loaded H₂O (precompressed to ≈1 GPa) showing the transition from transparent behavior at P ≈ 50 GPa and T < 3,500 K (Left: reflection of diamond-sample interface is visible through the shock-compressed sample, before and after first breakout); to opaque at P ≈ 100 GPa and 3,500 < T < 9,000 K (Center: reflection disappears on breakout); to reflecting at P > 150 GPa and T > 9,000 K (Right: new reflection appears from shock front, as evident from time-dependent (curved) fringes after breakout) (14). Time and distance across the sample are along the horizontal and vertical axes, respectively, and red (vs. blue) colors indicate higher recorded intensity of light.

Predicted pressure–density equations of state for condensed matter, caused by isentropic compression (isentrope: heavy dark blue curve), shock compression (Hugoniot: heavy red curve, ρ₁/ρ₀ = 1.0), and shock compression of samples precompressed to initial densities of ρ₁/ρ₀ = 1.1, 1.5, 2.0, and 3.0 (thin red, green, turquoise, and blue curves, respectively) assuming K′_0S = 4, γ₀ = 1.5, and γ_e = 0.2 (see text). Pressure and density are normalized to the zero-pressure bulk modulus and density, respectively, and the Mbar (= 100 GPa) and Gbar (= 100 TPa) pressure regimes are indicated based on a typical value of K_0S ≈ 10¹¹ Pa; corresponding central pressures for Earth, Jupiter, and supergiant planets are indicated on the right. The Hugoniot for the linear U_S − u_p relation (Eq. 7) and the density dependence of the electron–gas pressure, P_EG ≈ ρ^5/3 (ref. 9; only the slope, not the absolute value, has meaning here) are shown by thin black and gray lines. Because c in Eq. 7 is the zero-pressure bulk sound velocity, (K_0S/ρ₀)^1/2, its value is absorbed in our pressure normalization; in accord with K′_0S = 4 for the finite-strain calculations, we set s = 5/4 (17). Conditions near zero pressure are shown on a linear plot (Inset) to complement the log–log plot of the main figure.