Iron (Fe) phase diagram up to Earth inner core conditions (dashed red box). Solid phase boundaries (α-bcc, γ-fcc, ε-hcp) and the melting curve are from Ref. 9 . There are uncertainties associated with the melting curve above 100 GPa as well as possible additional solid phases at very high pressures. The orange curve shows a range of possible temperatures for the Earth's interior. 12,68 The pressure-depth scale is obtained from the seismic Preliminary Reference Earth Model. 6 The Hugoniot 24 (purple curve) crosses the melting curve at ∼225-243 GPa. The blue curve shows the temperature rise associated with compression along the principal isentrope. This is a lower bound to the temperature achieved in ramp loading from ambient conditions as additional heating due to plastic work is expected. 69 In order to overdrive the α-ε transition and sample a wider range of P-T states, possible experimental paths showing an initial shock followed by isentropic compression (green and red curves) are also shown. For those paths, the temperature estimates were obtained from the Hugoniot temperature achieved in the initial shock 24 and by the temperature rise due to isentropic compression calculated using the Grüneisen parameter and its volume dependence for iron. 24
Target package for ramp compression experiments on iron at (a) Omega and (b) NIF. Laser beams were focused onto the inner walls of a Au hohlraum. The time-dependent laser intensity generates a near-blackbody distribution of x-rays with a characteristic radiation temperature, which increases as a function of time. Ablation of the diamond layer causes a time-dependent compression wave to be launched into the Fe sample. The VISAR velocity interferometer records the temporal history of the free-surface velocity, ufs(t), for each of the four Fe thicknesses.
(a) Raw VISAR data from Omega shot s58588. Fringe shifts are proportional to free-surface velocity. (b) Free surface velocity versus time profile for four thicknesses of Fe (shot s58588). The initial 2-ns portion of the laser pulse shape for this shot (shown as inset) was designed to launch a ∼50 GPa shock into the Fe sample before the onset of subsequent ramp compression. The thickness of each step is indicated. Light grey bars show agreement between two VISAR channels recording the free surface velocity. The horizontal dashed line indicates the free surface velocity in iron at the equilibrium phase transition pressure of ∼13 GPa. The “ramped” plateau at ∼3.0 km/s is due to the elastic wave in the diamond shaping the ramp drive applied to the Fe stepped sample. (c) For shot s58591, the laser power in the first 2 ns was increased to generate an ∼82 GPa steady initial shock. (d) NIF shot N120301. The first 8 ns of the laser pulse (inset) was designed to launch a steady 65 GPa shock into the multi-step Fe sample.
(a) Stress versus density for ramp compression shots with or without initial shock. For shot s58591 and N120301, the free surface velocity profiles (Figs. 3(c) and 3(d) ) where analyzed in two ways: (1) explicitly treating the initial steady shock (red and blue curves) (2) Assuming ramp compression throughout (orange and light blue curves). The results are nearly identical for the two cases within uncertainties. The grey curve shows the results from shot s58588 (since the designed 50-GPa shock launched in the iron is unsteady for this shot, we did not treat it as an initial steady shock in the analysis). The similarity between the results of shot s58588 and shot s58591 and N120301 above initial shock states implies that the time-dependent response due to the α-ε phase transition has a small effect on the stress-density state achieved at higher stress levels. Representative uncertainties for the ramp compression data are one standard deviation. The inset shows calculated Lagrangian sound velocities as a function of free surface velocity for the three experiments. The longitudinal and bulk sound speeds 70 are labeled as yellow and blue solid circles, respectively. (b) Stress versus density for weighted mean of all ramp compression of iron compared with experimental shock data, 19–23,60–63 room-temperature, 64,65 and high-temperature static data. 65 To obtain the weighted mean stress-density, we averaged all three shots in CL-u space following the procedure described in Ref. 50 . For CL < 10 km/s, no averaging was conducted and the values for shot s58588 were taken. For CL > 10 km/s, the weighted mean for all three shots was calculated. The results of these analyses are represented by the black curve. The error bars do not take into account the uncertainty from the Hugoniot initial shock state.
Free surface velocity profile for a single step (25.4-μm thickness) from shot s58588 extending to late times and showing the characteristic spall signature. The inset shows an enlargement of the wave profile in the spall region. Δufs is the change in free surface velocity and T is the oscillation period.
Spall strength versus strain rate. Solid symbols show our results including error bars. Open symbols are previous work. 66 The inset is the characteristics plot showing the stress state as a function of Lagrangian position and time for shot s58588. The arrow points to where the spall occurs (minimum stress state) in the sample. The color bar shows the calculated stress state in the sample.
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