Daniel H. Kalantar - Lawrence Livermore National Laboratory Presented by Thomas Lorenz 8 th International Workshop on the Physics of Compressible Turbulent Mixing Pasedena, CA - December 9-14, 2001 J. Belak, J. D. Colvin, M. Kumar, K. T. Lorenz, K. O. Mikaelian, S. Pollaine, B. A. Remington, S. V. Weber, L. G. Wiley (LLNL), J. S. Wark, A. Loveridge, A. M. Allen (University of Oxford), M. A. Meyers, M. Schneider (UCSD) This work was performed under the auspices of the US DOE by UC LLNL under contract No. W-7405-48-Eng. Supported in part through the Science Use of Nova Program, DOE Grants program, and NLUF program (OMEGA). Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Outline � Introduction — Solid-state experiments at high pressure on a laser � High pressure strength — RT instability in solid Al at high pressure to infer Y(P) � Dynamic material response — Dynamic x-ray diffraction of the lattice level response in Si and Cu � Wave profile and residual deformation — VISAR measurement, sample recovery and characterization Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
The high pressure response of materials is of interest for many reasons; lasers provide a way to access high pressures and strain rates � The core of the earth is Fe at 3 Mbar, both solid and liquid — Long time scale, diamond anvil experiments � Survivability of passengers in a car crash depend on the material response of the car — ms-µs time scale, Hopkinson bar and gun experiments � Space station wall integrity from space debris, dust, micro-asteroids — µs time scale, gun and high explosives experiments Lasers Lasers access unique high Pressure pressure, high strain rate Gas gun regime of material response Hopkinson to test the limits of theories bar and scaling laws Strain rate Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Example - strength measurements at high pressure using a high explosive drive and modulated Al plate � Shockless HE drive used to compress and accelerate a plate with pre- imposed modulations � Pre-imposed modulations grow by the Rayleigh-Taylor instability � The growth is reduced from classical (fluid) due to material strength Al plate experiment Growth is reduced from fluid 1.0 Modulation amplitude (cm) Barnes et al , Modulations J. Appl. Phys. 45, 727 (1974). 0.1 Al plate Also Rayevsky and Lebedev HE blow--off 0.01 2.0 4.0 6.0 8.0 0 2 4 6 Position (mm) Time (µs) Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
1. Solid state RT instability experiment � An internally shielded hohlraum is used to shock compress an Al-6061 metal foil at high pressure � Internal shields block hard x-rays from preheating package � A shaped laser pulse generates a series of gentle shocks for nearly isentropic compression Hohlraum Internal shield M-band x-rays Drive temperature (T) 100 Laser power (TW) 5 Laser Laser power beam 80 T r 4 60 3 40 2 20 1 Re-radiated 0 0 x-rays Metal foil package -2 0 2 4 6 8 10 12 14 Laser spots Time (ns) CH(Br) Al foil Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Detailed simulations predict that the Al foil remains solid throughout the experiment � The Al remains below the melt curve � The foil trajectory is nearly isentropic to 1.8 Mbar 2 a 1 2 a 1 3 / T T e ( ) ( γ − − ) − η o Lindemann melt model = η m m o Pressure and temperature at the Calculated internal energy embedded interface trajectory 10 0.6 2.0 Internal energy (kJ/g) P Pressure (Mbar) 0.5 Temperature (eV) 8 Hugoniot 1.5 0.4 6 Melt curve T melt 0.3 1.0 Isentrope 4 0.2 0.5 2 0.1 Internal energy T interface 0.0 0 0.0 1.0 1.2 1.4 1.6 1.8 2.0 0 5 10 15 20 Time (ns) Normalized density Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Simulations of the instability growth demonstrate sensitivity to the strength of the Al � Growth rates with strength are expected to be reduced from classical (fluid) Steinberg-Guinan constitutive model Rayevsky Stability boundary formula 2 G P T , 2 2 H 2 H n ( ) π π Y Y 1 − − − λ ( ( ) ) = + β ε + ε 3 3 1 0 86 . e 1 e o i λ λ G η = η − − c D o λ M G ' P G ' + − = 4 G = 2 Y P T G G 1 T 300 π = ( − ) o 1 3 / G G η λ D M η g g o o ρ ρ Stability curve (Nizovtsev and Rayevsky, 1991) Predicted growth factors λ λ =20 µm λ λ 15 0.6 + Al experiments Amplitude (µm) Growth factor 10 0.4 fluid 5 0.2 Unstable Stable strength model 0 0 0 5 10 15 20 25 0 20 40 60 80 100 Wavelength (µm) Time (ns) Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
The RT growth is nearly fluid at early times, but it is suppressed at later times � Experiments were conducted with 10, 20 and 50 µm wavelengths � Modeling was done assuming the following: — Fluid — Nominal Steinberg-Guinan — Fluid until 13 ns, then S-G with theoretical maximum Y=G/10 35 35 35 50 µm averages 20 µm averages 10 µm averages 30 30 30 Fluid 25 25 25 Recovered strength Growth factor Growth factor Growth factor Equally Y=G/10 for t ≥ 13 ns weighted 20 20 20 average 15 15 15 Weighted average 10 10 10 5 5 5 SG 0 0 0 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Time (ns) Time (ns) Time (ns) Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
The RT growth is nearly fluid at early times, but it is suppressed at later times; suggestive of model from Grady/Asay and data by Rayevsky and Lebedev � High pressure strain causes localized heating and softening in shear bands; bulk Al flows as fluid due to localized deformation � As heat conducts into the bulk material, the metal regains bulk solid strength and continued growth is inhibited Optical emission from shocked quartz Shocked HE experiments show fluid-like response with saturation Modulation P/V (mm) Recovered strength 0.8 Heating in localized regions of 0.4 lattice Initial response 0.0 0 5 10 15 20 Distance accelerated (mm) Brannon et al , SCCM 1983. Rayevsky et al , IWPCTM, 1999. Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
The late time images show features that may be due to hydrodynamic imprinting of the grain structure � The spatial scale of the late-time modulation is similar to initial grain structure � 2D simulations incorporating the grain boundaries start to show effects at t=18 ns, 3D simulation has been started 2D simulation including Al: t=21.5 ns grain structure Fluid Cu foil Grain t = 18 ns boundaries Inclusions Grain Y grain = Y SG Y boundary = 0 structure Simulations by G. Bazan, 2001 Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
2. Dynamic x-ray diffraction � In situ x-ray diffraction probes the long range lattice order under shock compression � Shock pressure generated using a hohlraum x-ray drive or by direct laser irradiation � Time-resolution with x-ray streak cameras provides information on dynamic lattice response Shift of diffraction signal Shocked Bragg X-ray source Unshocked Bragg Probing orthogonal lattice planes provides information Compressed lattice on the transition to plasticity Shocked Laue Q. Johnson et al , 1970; Pressure source Unshocked Laue J. S. Wark et al , 1989. Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Simultaneous measurements of orthogonal planes indicates Si responds uniaxially on a ns time scale � 40 µm thick Si shocked along (100) axis � P=115-135 kbar; HEL=84 kbar Streaked Bragg Streaked Laue 1.04 1.04 Normalized lattice Normalized lattice spacing, d/d 0 spacing, d/d 0 1.00 1.00 0.96 0.96 0.92 0.92 Shot 2 (28102216) Shot 1 (28102219) 0.88 0.88 2.0 5.0 8.0 2.0 5.0 8.0 Time (ns) Time (ns) 20 14 (Exposure, arb. units) (Exposure, arb. units) Diffraction signal Diffraction signal Si (400) Bragg 12 Si (400) Laue 15 10 10 8 6 5 4 2 0 0.80 0.85 0.90 0.95 1.00 1.05 1.10 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Lattice spacing d/d 0 Lattice spacing d/d 0 Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
Cu undergoes a transition to 3D lattice compression at high pressure � 8 µm single crystal Cu shocked along (100) axis � P = 180 kbar; HEL ~ 2 kbar Compressed Compressed Laser drive Uncompressed Uncompressed Time Time Bragg Laue 0.6 1.6 1.4 0.5 1.2 0.4 1 Compressed 0.3 0.8 X-ray source 0.6 Compressed 0.2 0.4 0.1 0.2 0 0 0.80 0.85 0.90 0.95 1.00 1.05 1.10 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Lattice spacing d/d o Lattice spacing d/d o Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory
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