precision equation-of-state eos measurements using laser
TRANSCRIPT
M. A. BarriosUniversity of RochesterLaboratory for Laser Energetics
Omega Laser Facility Users’ Group Workshop
Rochester, NY29 April – 1 May 2009
Precision Equation-of-State (EOS) Measurements Using Laser-Driven Shock Waves On the OMEGA Laser
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Pre
ssu
re (
Mb
ar)
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00.9 1.4 1.9 2.4 3.42.9
Density (g/cc)
3.9
E17322b
• Theimpedance-matching(IM)techniquehasbeenusedfordecades toobtainEOSmeasurements,mainlyusingopaquestandards.
• Bothrandomandsystematicerrors,inherentinIM,mustbeaddressed.
• Transparentstandards(quartz) allow one to measure the shock velocity (Us)withinthestandard,reducingrandomerrors.
• Thishigh-precisiontechniquewasappliedtoCHandCH2.
Summary
Precision equation-of-state (EOS) measurements areobtainedusingquartzasastandard
Collaborators
D.E.FratanduonoT.R.Boehly
D. D. Meyerhofer
University of RochesterLaboratory for Laser Energetics
D.G.HicksP.M.Celliers
J. Eggert
Lawrence Livermore National Laboratory
Laser-drivenshocksareusedtostudymaterials at high pressure
E17067a
Themeasurementoftwovariablesisneeded to close these equations; e.g., Us = F(Up).
Rankine–Hugoniotequations
U U Us s p
s p
0 1
1 0 0
-t t=
P P- t= U U
_ i
Shocked
Den
sity
Unshocked
Laboratory frame position
p2, t2 p1, t1
Us
Up
EOS Measurements
Theparticlevelocityandpressureareconserved across a contact interface
E17323
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0302520151050
Pre
ssu
re (
Mb
)
Particle velocity, Up (nm/ns)
Initial state(from Us in standard)
U sU p
Releaseisentrope(known std.)P=t
0
Known standard Hugoniot
Usl UpP=t0
P
Up
x
Usl
SampleStandard
P
x
Us
SampleStandard
P
x
SampleStandard
Usl
Up
ImpedanceMatchUs = F(Up)
Needtominimizeexperimentalerrorandaddresssystematic errors for precision EOS measurements
E13920b
• Measurementaccuracydependsonknowledge ofstandard.
• MostIMstudiesquote onlyrandomerrors.
• Cannotpropagatesystematic errors using theoretical EOS.
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Pre
ssu
re (M
b)
Particle velocity, Up (nm/ns)
RandomErrors
SystematicErrors
RandomErrors
• Randomerrors
, ; u1 4 6 3 5 s0" \ #- - -- -t
dth h t
th t
dtd=^ ]h g
Athighpressuresinconsistenciesexistbetween EOSmodelsanddataforaluminum
E17070a
Systematic Errors
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6 8
Aluminum
Density (g/cm3)
Pre
ssu
re (
Mb
ar)
10 12
SESAME EOS
(Abs) Simonenko (1985)(Abs) Podurets (1994)(Abs) Knudson (2003)(Mo) Ragan (1982/4)(Mo) Glushak (1989)(SiO2) Al’shuler (1977)(Fe) Kormer (1962)(Fe) Trunin (1986)(Fe) Avorin (1987)(Fe) Trunin (1995)(??) Al’shuler (1974)(Abs & Ta) Mitchell (1981)
Experimental fit
Modified EOSSESAME 3718SESAME 3700Modified EOSLinear Us – Up fit
Higherprecisionisachievedusing atransparentstandard
E17324
RandomErrors
Sample
VISAR-1 shot 29425
Integratedvelocity
Instantaneousvelocities
AlSample
SampleSiO2
Al
Al
Al
VISAR-1 shot 52118
0 2 4 6ns
ns
200
nm 0
–200
500
nm 0
–500SiO2 pusher
Laser
Laser
Us
Sample
Us
Dx
Al
0 2–2 4Us is inferred from transit times
QuartzvalidityasastandardisestablishedthroughamplestudyofitsEOSandagreementwithpreviousresults
E17325
1 M.D.Knudsonet al., J. Appl. Phys. 97, 073514 (2005).2T.R.Boehlyet al., in Shock Compression of Conducted Matter–2007, Vol. 955, p 19–22.
D.G.Hickset al., Phys. Plasmas 12, 082702 (2005).
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Particle speed (nm/ns)
Sh
ock
sp
eed
(n
m/n
s)
50
Nuclear ~10 ns
Laser ~0.3 ns
GPa 140 450 945 1594
a-quartz EOS (Al as reference)
Gas gun explosive~100s of ns
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Particle speed (km/s)
Pre
ssu
re (
GP
a)
Releaseisentrope (±)
Directimpact
Direct measurement1IM with AL standard1
IM with SiO2 standard2
PrecisionEOSdatamoretightlyconstrain polystyrene (CH) EOS
E17792
10
9
8
7
6
5
4
3
2
Pre
ssu
re (
Mb
ar)
1
00.9 1.4 1.9 2.4 3.42.9
Density (g/cc)
3.9
SESAME 7590SESAME 7591SESAME 7592
Barrios (2008)Dudoland (1969)McQueen (1970)VanThiel (1980)Marsh (1980)
PrecisionEOSdatamoretightlyconstrain polystyrene (CH) EOSandpolypropylene(CH2) EOS
E17792
10
9
8
7
6
5
4
3
2
Pre
ssu
re (
Mb
ar)
1
00.9 1.4 1.9 2.4 3.42.9
Density (g/cc)
3.9
SESAME 7590SESAME 7591SESAME 7592SESAME 7171
Barrios (2008)Dudoland (1969)McQueen (1970)VanThiel (1980)Marsh (1980)
E17322b
• Theimpedance-matching(IM)techniquehasbeenusedfordecades toobtainEOSmeasurements,mainlyusingopaquestandards.
• Bothrandomandsystematicerrors,inherentinIM,mustbeaddressed.
• Transparentstandards(quartz) allow one to measure the shock velocity (Us)withinthestandard,reducingrandomerrors.
• Thishigh-precisiontechniquewasappliedtoCHandCH2.
Summary/Conclusions
Precision equation-of-state (EOS) measurements areobtainedusingquartzasastandard