Presented by Thomas Lorenz 8 th International Workshop on the Physics - - PowerPoint PPT Presentation

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

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).

Daniel H. Kalantar - Lawrence Livermore National Laboratory 8th 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)

Presented by Thomas Lorenz

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

Strain rate Pressure Hopkinson bar Gas gun Lasers

Lasers access unique high pressure, high strain rate regime of material response to test the limits of theories and scaling laws

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

2 4 6

Position (mm) 0.1 0.01 1.0 2.0 4.0 6.0 8.0 Time (µs) Modulation amplitude (cm)

Barnes et al,

• J. Appl.
• Phys. 45,

727 (1974). Also Rayevsky and Lebedev

Modulations HE blow--off Al plate Al plate experiment Growth is reduced from fluid

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

Internal shield Laser beam Re-radiated x-rays Laser spots

Al foil CH(Br)

1 2 3 4 5 20 40 60 80 100

• 2

2 4 6 8 10 12 14

Laser power (TW) Drive temperature (T) Time (ns) Laser power Tr

Hohlraum M-band x-rays Metal foil package

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

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.5 1.0 1.5 2.0 5 10 15 20 Temperature (eV) Pressure (Mbar) Time (ns) T interface T melt P Pressure and temperature at the embedded interface Calculated internal energy trajectory Lindemann melt model

T T e

m m a a

• =

−

( )

− −

( )

2 1 2 1 3 η γ

η

/

2 4 6 8 10 1.0 1.2 1.4 1.6 1.8 2.0 Internal energy (kJ/g) Normalized density Hugoniot Isentrope Melt curve Internal energy

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 Y Y G P T G

• i

n

• =

+ +

( )

( )

( )

1 β ε ε , G G G G P G G T

• P
• T
• =

+       −       −

( )

      1 300

1 3

' '

/

η

5 10 15 5 10 15 20 25 Growth factor Time (ns) fluid strength model Predicted growth factors λ λ λ λ=20 µm + Al experiments Stable Stability curve (Nizovtsev and Rayevsky, 1991) 20 40 60 80 100 Wavelength (µm) Amplitude (µm) 0.6 0.4 0.2 Unstable η η λ λ

π λ π λ c D H H M

e e = −       −       −                

− −

1 0 86 1

2 3 2 3 2 2

. η ρ

D

Y g = 2

λ π ρ

M

G g = 4

Rayevsky Stability boundary formula

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

5 10 15 20 25 30 35 5 10 15 20 25

Growth factor Time (ns)

5 10 15 20 25 30 35 5 10 15 20 25

Growth factor Time (ns)

5 10 15 20 25 30 35 5 10 15 20 25

Growth factor Time (ns)

50 µm averages 20 µm averages 10 µm averages

Y=G/10 for t≥13 ns Equally weighted average Weighted average

Fluid SG Recovered strength

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

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

0.0 0.4 0.8 Modulation P/V (mm) Distance accelerated (mm) 5 10 15 20 Initial response Recovered strength

Rayevsky et al, IWPCTM, 1999.

Optical emission from shocked quartz Heating in localized regions of lattice

Brannon et al, SCCM 1983.

Shocked HE experiments show fluid-like response with saturation

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

Grain structure Fluid Cu foil Inclusions 2D simulation including grain structure t = 18 ns Grain boundaries

Simulations by G. Bazan, 2001

Ygrain = YSG Yboundary = 0

Al: t=21.5 ns

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

• Q. Johnson et al, 1970;
• J. S. Wark et al, 1989.

Compressed lattice Shocked Bragg Unshocked Bragg X-ray source Pressure source Shift of diffraction signal Unshocked Laue Shocked Laue Probing orthogonal lattice planes provides information

• n the transition to plasticity

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

Shot 2 (28102216) Streaked Laue 2.0 5.0 8.0 Time (ns) 0.88 0.92 0.96 1.00 1.04

5 10 15 20 0.80 0.85 0.90 0.95 1.00 1.05 1.10 2 4 6 8 10 12 14 0.80 0.85 0.90 0.95 1.00 1.05 1.10

Si (400) Bragg Si (400) Laue

Lattice spacing d/d0

Lattice spacing d/d0

Diffraction signal (Exposure, arb. units)

0.88 0.92 0.96 1.00 1.04 Shot 1 (28102219) Streaked Bragg 2.0 5.0 8.0 Time (ns)

Normalized lattice spacing, d/d0 Normalized lattice spacing, d/d0 Diffraction signal (Exposure, arb. units)

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

Laue Bragg Laser drive X-ray source

Time Time Compressed Uncompressed Compressed Uncompressed

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.80 0.85 0.90 0.95 1.00 1.05 1.10 0.1 0.2 0.3 0.4 0.5 0.6 0.80 0.85 0.90 0.95 1.00 1.05 1.10

Lattice spacing d/do Lattice spacing d/do

Compressed Compressed

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

The timescale for plastic deformation in Si is much longer than for Cu based on Orowan’s equation

Orowan equation:

∆ε ∆t = N |b| v

Dislocation velocity (mm/s) 104 102 100 10-2 10-4 10-6

Introduction to Dislocations, Hull and Bacon (Fig. 3.12)

10-2 10-16 100 101 102 103 Shear stress (MPa) Cu Si 106 difference in velocity for Si, Cu

Silicon

∆

∆ ∆ ∆t >1 µs : dislocations do not move

—5% strain, dislocations separated by at least the Burger’s vector (3.8 Å) (diffraction linewidth indicates N < 1014 m-2) —Linear extrapolation of dislocation velocity in Si (0.1 mm/s)

Copper

∆

∆ ∆ ∆t < 10 ps : dislocations do move

—5% strain, dislocations separated by at least the Berger’s vector (2.5 Å) —Velocity of dislocations calculated to be 400 m/s in MD simulations

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

The time scale for plastic deformation in Si is much longer than for Cu, due to its high Peierls barrier and activation energy

t t aB b

run

= = σ

Cu Si

• For σ

σ σ σ < YP: thermal activation regime, and

• For σ

σ σ σ > YP: phonon drag regime, Assume that σ σ σ σ = 3 GPa, and kT = 0.05 eV: For Si: YP = 0.07G0(1+AP/η η η η1/3) > 0.07G0 giving YP > 0.07 (63.7 GPa) = 4.5 GPa, ∆ ∆ ∆ ∆F = 0.2Gb3 = 0.2 (63.7GPa) (3.83 A)3 = 4.5 eV So σ σ σ σ < YP, and kT << ∆ ∆ ∆ ∆F: thermal activ. regime Assume ν ν ν νattempt = ν ν ν νDebye/100 = 1011 s-1 , So 1/twait = (1011 s-1) exp[-(4.5/.05) (1- 3/4.5)2] Giving twait > ~150 ns, meaning slow For Cu: YP = (6.3 x 10-3)G0(1+AP/η η η η1/3) = 0.42 GPa So σ σ σ σ > YP, meaning phonon drag regime Assume B = 10-10 MPa.s, and a/b < 103, So trun < (103) (10-10 MPa.s)/(3 GPa) = 30 ps: fast

t t F kT Y

wait attempt P

= = − −               1 1

2

ν σ exp ∆

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

A new wide-angle film detector is used to record many more lattice planes

X-rays diffracted from orthogonal lattice planes are recorded with 2 x-

ray streak cameras

A segmented film assembly records x-rays diffracted over a π

π π π-solid angle from many more lattice planes

Backlighter Crystal Plane Shock Drive Static film

90 60 30

θ

180 150 120 90 60 30

φ

( 0 0 2 ) ( 1-1 3 ) ( -3 1 3 ) ( -2-2 2 ) ( 3-1 1 ) ( -1 1 1 ) ( 1-1 1 ) ( 4 0 2 ) ( 3-1 3 ) ( 0 0 4 ) ( -1-1 3 ) ( 2 0 4 ) ( 2 2 2 ) ( 3 1 3 ) ( 1 1 3 ) ( -1 1 3 ) ( -1-1 1 ) ( -3-1 1 ) ( 1 1 1 ) ( -3-1 3 ) ( -4 0 2 ) ( 2-2 2 ) ( -2-2 2 ) ( -2 0 4 )

120 60 30 90 150 180 30 60 90

Calculated diffraction pattern from static Cu Polar angle, Θ Θ Θ Θ (°) Azimuthal angle, ø (°)

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

Detailed response of the lattice is better understood by recording diffraction from other lattice planes

Large angle detector has been fielded on Si shock experiments Shift of many different lines is observed; details are being studied

30 60 90

• 90
• 60
• 30

30 60 90 Polar angle, Θ Θ Θ Θ (°) Azimuthal angle, ø (°) Bragg data recorded on 3 film planes is mapped to spherical coordinates

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

• 3. VISAR wave profiles and sample recovery

Al-6061 wave profile measurements show elastic-plastic response with

spall on release

Fitting the shock breakout wave profile provides best-fit strength

parameters

VISAR beam LiF Al-6061 (195 µm thick) Shock drive LiF window Free surface Time (ns)

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 20 25 30 35 40 45

_ Particle speed (µm/ns)

Particle speed (µm/ns)

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

VISAR wave profiles provide information on the strength parameters for the shocked metal

The wave profile is sensitive to the constitutive model parameters for the

metal foil

Best-fit wave profile provides model parameters:

— Shear modulus G=320 kbar (276) — Bulk modulus K=794 kbar (742) — Yield strength Y=4.27 kbar (2.9)

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 25 30 35 40

Best fit G=276 K=722 Y=2.9

Particle speed (µm/ns) Time (ns)

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 25 30 35 40

Particle speed (µm/ns) Time (ns)

• 0.2

0.0 0.2 0.4 0.6 0.8 1.0 25 30 35 40

Particle speed (µm/ns) Time (ns)

Data – free surface Data LiF Best fit Data – free surface Data LiF Nominal

Best fit Nominal Variations

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

Transmission electron and optical microscope analysis shows residual structure that depends

• n the drive conditions

Shocked samples are recovered in a low density foam-filled tube Preliminary tests done at OMEGA; shock pressure is ~400 kbar, decays

to ~25 kbar at the rear surface

Side Back 1 mm Drive Beam 50 mg/cm3 foam Cu sample

Residual etch features Spall 200 µm Voids

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

TEM analysis of recovered Cu shows the residual microstructure

Residual microstructure of recovered single crystal Cu samples Higher pressures show twinning

0.5 µm Unshocked 40 J, Cu 130 kbar 205 J, Cu 400 kbar 320 J, CH/Cu 1.4 Mbar

Dislocations Micro-twins Twinning

100 nm

Dan Kalantar - IWPCTM 2001 Lawrence Livermore National Laboratory

Summary

Solid state hydrodynamic instability

— RT instability in Al to infer Y(P) — There is possible imprinting due to the initial grain structure

In situ dynamic x-ray diffraction

— Time-resolved diffraction relates the lattice behavior to the macroscopic response of Si and Cu under shock loading — Si responds uniaxially, Cu deforms plastically

Shock/recovery experiments

— Residual deformation structure in Cu depends on the shock pressure