Fig. 1 Laser shock experiment of shot 35286. (A to C) Schematic experimental setup and typical measurements by a velocimeter [velocity interferometer system for any reflector (VISAR)] (B) and a pyrometer [streaked optical pyrometer (SOP)] (C). The driving laser was GEKKO XII (Osaka University). VISARs give direct measurements of shock velocities in forsterite and quartz under extreme conditions. The particle velocity in forsterite was calculated using the known shock velocity–particle velocity relation of quartz. This method provides a precise Hugoniot determination of forsterite. A single crystal of forsterite with a thickness of 20 or 50 μm was used as a sample. A typical equation-of-state (EOS) target assembly consisted of polypropylene (CH), aluminum (Al), crystalline α-quartz (SiO2), and forsterite (Mg2SiO4). The CH polymer with a thickness of 15 or 30 μm was used as an ablator to generate a shock wave and to minimize hard x-ray radiations in the laser-plasma interaction region. The aluminum (40 μm thick) and quartz (50 μm thick) were used as the reference materials for the impedance mismatching analysis. The brightness temperature was determined using the gray-body Planck spectrum observed by a calibrated pyrometer (SOP). For details, see the Supplementary Materials.
Fig. 2 Hugoniot relationships for forsterite single crystals. (A) Shock velocity (Us) and particle velocity (up). (B) Pressure and density. Note the remarkable discontinuities around ~350 and ~450 GPa in (B) that correspond to particle velocities at up of ~7 and 9 km s−1 in (A), respectively. Experimental setup of target is illustrated in fig. S1, and experimental data are listed in Table 1. Three previous data sets from Jackson and Ahrens (3) (for red diamonds), Marsh (4) (for violet diamonds), and Mosenfelder et al. (7) (for brown diamonds) are compared. The dot dashed lines in (A) and (B) indicate the extended Hugoniot relations given by Us (km s−1) = 2.93 + 1.82 up (km s−1) applicable for a range of up of 4.1 to 6.9 km s−1, which is almost the same as the prediction by de Koker et al. (8).
Fig. 3 Phase diagram for MgO, Mg2SiO4 (Fo), and MgSiO3 (En). The present data of pressure and temperature on Fo Hugoniot are shown by solid circles with error bars, and the wide gray curve illustrates a possible path along Fo Hugoniot based on the present study. Phase boundaries for the transition of B1 MgO and B2 MgO and for the liquidus and melting curves of compounds Fo, En, and MgO are illustrated together with linearly extended Hugoniots (8) of Fo represented by Fo melt (line 1), liquid MgSiO3 + B1 MgO (line 2), and postperovskite MgSiO3 + B1 MgO (line 3). Shock temperatures of Fo measured by Luo et al. (28) are shown in squares. Boundaries for B1-B2 transition (9–11, 14, 29) and melting of MgO, solidus (10, 14) of MgSiO3, and demixing phase boundary (14) for MgSiO3 (liq) = MgO (solid) + SiO2 (liq) as MgSiO3 liquidus are illustrated for comparison.
- Table 1 Shock compression data of single-crystal forsterite (initial density of 3.226 ± 0.004 g cm−3).
Shot number Shock velocity (km s−1) Particle velocity (km s−1) Pressure (GPa) Density (g cm−3) Temperature (103 K) Reflectivity 33552 14.00 ± 0.42 6.00 ± 0.39 271.0 ± 18.1 5.65 ± 0.40 7.12 ± 0.36 0.0145 ± 0.0023 35283 14.21 ± 0.27 6.22 ± 0.21 285.2 ± 10.3 5.74 ± 0.24 9.43 ± 0.68 0.0174 ± 0.0016 33676 15.70 ± 0.34 6.80 ± 0.23 344.3 ± 12.6 5.69 ± 0.24 8.44 ± 0.49 0.0527 ± 0.0050 37817 16.12 ± 0.17 7.90 ± 0.16 410.9 ± 8.5 6.33 ± 0.18 12.49 ± 0.46 0.0541 ± 0.0103 37779 16.54 ± 0.15 8.74 ± 0.20 466.3 ± 10.8 6.84 ± 0.24 13.88 ± 0.89 0.0987 ± 0.0153 37767 17.74 ± 0.20 9.21 ± 0.22 527.3 ± 12.9 6.71 ± 0.25 16.80 ± 0.64 0.1072 ± 0.0161 36755 17.96 ± 0.29 9.49 ± 0.30 549.7 ± 18.0 6.84 ± 0.36 20.63 ± 2.60 0.183 ± 0.0161 35314 19.99 ± 0.50 10.73 ± 0.37 692.0 ± 26.2 6.96 ± 0.48 — — 35286 22.63 ± 0.19 13.35 ± 0.23 974.4 ± 17.5 7.87 ± 0.29 33.98 ± 5.48 0.213 ± 0.0324
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/8/e1600157/DC1
fig. S1. Hugoniot and phase boundaries.
fig. S2. The phase relations and Gibbs free energies as functions of pressure and temperature.
fig. S3. A typical profile of decay for shot 37767.
table S1. Measured quartz shock velocities and inferred Al states based on the impedance mismatching analysis.
Additional Files
Supplementary Materials
This PDF file includes:
- fig. S1. Hugoniot and phase boundaries.
- fig. S2. The phase relations and Gibbs free energies as functions of pressure and temperature.
- fig. S3. A typical profile of decay for shot 37767.
- table S1. Measured quartz shock velocities and inferred Al states based on the impedance mismatching analysis.
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