CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
EXPERIMENTAL STUDY OF HIGHLY COMPRESSED IRON USING
LASER DRIVEN SHOCKS
A. Benuzzi-Mounaix1, G. Huser1, M. Koenig1, B. Faral1, N. Grandjouan1, D. Batani2,
E. Henry1'2, M. Tomasini2, B. Marchet3, T. Hall4, M. Boustie5, Th. De Resseguier5,
M. Hallouin5, F. Guyot6
1
Laboratoirepour VUtilisation des Lasers Intenses (LULI), Unite Mixte n° 7605 CNRS - CEA - Ecole
Polytechnique - Universite Pierre et Marie Curie, 91128 Palaiseau, FRANCE
2
Dipartimento di Fisica, Universita degli Studi di Milano - Bicocca and INF M, Via Emanueli 15, 20126 Milano
ITALY
3
Commissariat a I'Energie Atomique, Centre DAM/Ile-de-France, BP 12, 91680 Bruyeres-le-Chdtel, FRANCE
4
Department of Physics, University of Essex, CO4 3SQ, UK
5
Laboratoire de Combustion et de Detonique, UPR n° 9028 CNRS, ENSMA, site du Futuroscope, BP 109,
86960 Futuroscope Cedex, France
6
IPG, Laboratoire de MINERALOGIE-CRISTALLOGRAPHIE, Universite Paris-Jussieu
Tour 16 Case 115, 4 place Jussieu, 75252 PARIS CEDEX 05, France
Abstract. Experiments with lasers have recently provided important improvements in our knowledge
of highly compressed matter (in particular, Equation Of State). We present recent results on iron
which are relevant to planetary physics. We measured the free surface velocity of the compressed iron
by using a VISAR diagnostic, and the shock velocity through step targets on the same shot. An
absolute EOS is then deduced for pressures 1-7 Mbar. The experiments have been performed at the
LULI laboratory of the Ecole Polytechnique.
INTRODUCTION
shock and fluid velocities on a same shot using selfemission diagnostic and a VISAR, as previously
used in recent laser experiments [2]. These
experiments have been carried out at the
Laboratoire pour 1'Utilisation des Lasers Intenses
(LULI) of the Ecole Polytechnique.
Iron is the most abundant component of the
Earth's interior. Its Equation Of State (EOS) in the
high pressure range (P > 100 GPa) has important
implications in describing the Earth's core [1];
indeed, knowledge of its properties enables to
estimate the quantity of stocked heat which is
fundamental for the modeling of the convection
processus in the mantle.
In this paper, we describe the first laser shock
experiment dedicated to the absolute EOS
measurement in the 1-7 Mbar range. We measured
EXPERIMENTAL SET UP
Experiments have been performed using three of
the six available beams of the LULI Nd-glass laser
(converted at X = 0.527 um, with a maximum total
energy E2(0 ~ 100 J) focused on a same focal spot.
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To determine rear surface velocity V (from
which we deduced the fluid velocity U, as
explained below) and the shock velocity D on the
same laser shot, we used stepped targets and a
probe beam at A, = 0.532 Jim coupled with two
VISAR interferometers with different sensitivities.
Since expected velocities V were of the order of 321 km/s, we chose VISARs with 3 mm and 15 mm
etalons, giving a sensitivity of 16.68 and 3.39 km/(s
fringe) respectively. From the fringe pattern
moving, we measured the free surface velocity V as
a function of time applying Doppler effect formula
[2]. The rear surface velocity is related to the fluid
velocity by [5]:
The laser temporal profile was a square with a rise
time of 120 ps giving a full width at half maximum
(FWHM) of 720 ps. Each beam had a 90 mm
diameter and was focused with a 500 mm lens. To
eliminate large scale spatial modulations of
intensity and to obtain a flat intensity profile in the
focal spot [3], we used phase zone plates (PZP) [4].
Characteristics of our optical system (lens+PZP)
were such that our focal spot had a 500 jum FWHM,
with a - 250 jim diameter flat region at the center.
Spatially averaged intensities between
810 12 W/cm 2 and 6 1013 W/cm2 were obtained,
depending on the number of drive beams.
The diagnostics we used in this experiment are
presented on Figure 1.
The self-emission diagnostic was based on a
streak camera recording the emitted light from the
rear surface of the target. Since iron is a material
that heats up very little when compressed by a
shockwave (for pressures of 1- 8 Mbar, temperature
are of 2000 - 25000 K), we expected to have a
signal on this particular diagnostic only at maximal
laser intensity. The aim of the self emission
measurements was to test the reliability of this
diagnostic to infer the temperature. We supposed
that rear side emission had a blackbody spectrum
and we calibrated the whole optical bench using an
etalon lamp (OL 455 from Optronic Lab, Inc.). The
streak camera was then calibrated with a short laser
pulse to establish a relation between the energy
deposited on the slit of the streak and the number of
counts given by the CCD.
v = u-
—
dP)s
0)
where Urw is the velocity of the release wave
coming back into compressed iron, after the shock
breaks out. In the limit of a weak shock wave
(1 -po/p «1), one has V «2U. We calculated V
by using (1) and the equation of state given by
SESAME tables. The deviation from the velocity
doubling rule is displayed in figure 2. The
discrepancy is less than 3% for pressures up to
~ 3 Mbar and than 10 % in the range 4-7 Mbar.
Lenses + PZP
VISAR#2
Streak
VISAR#1
Streak
FIGURE 2: Computed values of V (by eq (1)) compared with
the approximation V = 2U
To measure the shock velocity D on the same
shot, we used stepped targets. Targets were made
of an iron foil whose thickness has been
determined by hydrodynamic simulations. This was
FIGURE 1 : Experimental set up
84
Laio et al. [6] (Fig. 4). Error bars in the low
pressure region are mainly generated from the
uncertainty on fringe moving measurement.
Concerning the temperature measurement, we
obtained an emission signal only for shocks of 7-8
Mbar. By taking into account that the resolution of
this diagnostic is about 50 ps, the measured
emission is that of the expanding plasma radiating
layer. We present the experimental result on the
plane (U,T) compared to Hugoniot and isentrope
given by SESAME tables (figure 5).
done in order to ensure the best shock steadiness
obtainable with the LULI laser. For our laser
conditions, the total thickness ranged from 12 to
18 |im. The step thickness was 2.9 ^im. Steps were
obtained by ionic etching, ensuring nominal density
in the targets. The shock velocity was deduced by
measuring the time it takes the shock to cross the
step (see figure 3).
1 ns
400
FIGURE 3 : Experimental VISAR image. Fringe shift
measurement gives a rear side velocity of 10.8±0.2 km/s and
transit time in the steps is 245±45 ps, yielding a shock velocity
ofll.8±0.5km/s.
FIGURE 4 : Experimental points on iron's principal Hugoniot,
Molecular Dynamics calculated points by Laio et al., and
SESAME Equation Of State curve.
RESULTS
From VISAR diagnostic (see figure 3), we were
able to check the steadiness of the shock by looking
at the rear surface velocity variation into the step.
We experimentally found a variation < 4 % which
is in good agreement with hydrodynamic simulation
predictions. Such result has been taken into account
for error bar determination.
To obtain a series of points on the principal
Hugoniot, we used laser intensities ranging from
1013 W/cm2 to 6 1013 W/cm2. Generated pressures
were then ranging froml to 7 Mbar.
As can be seen in figure 4, principal Hugoniot
measurement was achievable with a good precision
(±10%) up to 2-3 Mbar. The large uncertainty (±
25%), at higher laser intensity (for pressures > 4
Mbar), is mainly due to velocity doubling rule
which is not well satisfied. The measurement of D
and V allows us to get points on the Hugoniot in
the (P, p) plane by using Hugoniot-Rankine
relations. Experimental points show good
agreement with the Los Alamos SESAME
Equation Of State model and with points obtained
by an ab initio molecular dynamics calculation by
FIGURE 5 Experimental brightness temperature of the rear side
expanding plasma compared with SESAME tables
Our experimental point underestimates the real
temperature. First of all, the measured temperature
is a brightness temperature: it is possible that the
blackbody emission hypothesis is not well satisfied
and the opacities play an important role. An other
crucial point of this type of measurements is the
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streak camera absolute calibration: our emission
signal is quite weak and we could be out of the
streak camera's linear response range.
The VISAR diagnostic gives us access to relative
reflectivity as a function of time (i.e. reflectivity is
normalized to 1 before shock breakout).
Experimental results (fig. 6) show two regimes: (a)
for strong shocks (P = 4-7 Mbar), reflectivity
decreases after the shock breakout;
(b) for "weak" shocks (P = 1-3 Mbar), the
reflectivity increases after the shock breakout.
' 1.2
whether it is in solid (y phase) or liquid phase. The
questions to be answered are: could the reflectivity
of the liquid iron be greater than the reflectivity of
solid iron in standard conditions? Or could the
reflectivity of the solid y phase be greater than the
reflectivity of the solid aphase? A last possible
explanation would be that this increasing of
reflectivity is due to some impurities on the surface
target before the shot: after the shock breakout the
surface could be "cleaned" by the heating. We have
to point out that the target surface was previously
polished and was a priori of good quality. In any
case an experimental confirmation and reflectivity
ab initio calculations are necessary to conclude.
CONCLUSIONS
Reliable results for the absolute measurement of
iron EOS in the range 0.5-7 Mbar were obtained for
the first time with a medium sized high power laser.
Nevertheless, there are still important issues that
need to be worked on: e. g. the isentropic release
needs to be characterized in order to get a better
measurement of fluid velocity.
Reflectivity measurement is an available
diagnostic to put in evidence phase transitions, but
ab initio calculation are needed to interpret
experimental results.
0.2
0
0
. . . . I . . . . I . . . . I . . . . I . . . . I ..
0.5
1
1.5
2
2.5
3.5
Time (ns)
Reflectivity
1.5
ACKNOWLEDGEMENTS
The authors would like to thank Ph. Moreau
(LULI) for his important contribution to the success
of the experiment.
0.5
-
1
0
1
2
3
4
REFERENCES
5
FIGURE 6: Reflectivity measurement as function of time. Up:
case of strong shocks. Down: case of "weak" shocks.
1. Anderson, W., and Ahrens, T., J.Geophys. Res.,
99 (B3), 4273 (1994).
2. Celliers, P., et al., Appl. Phys. Lett., 73, 1320
(1998).
3. Koenig, M, et al., Phys. Rev.E 50, 3314 (1994).
4. Bett, T.H., et al., Appl Opt., 34, 4025 (1995).
5. Zel'dovich, Ya, B., and Raizer, Yu. P., Physics of
Shock Waves and High Temperature
Hydrodynamic Phenomena, Academic Press,
New York, (1967).
6. A. Laio et al, Science, 287, 1027 (2000).
7. A. Benuzzi et al. Phys. Plasmas, 5, 2410 (1998).
Case (a) is well reproduced by calculations
based on hydrodynamic rear side description given
by MULTI code and on reflectivity calculation as in
Benuzzi et al [7]. The result of case (b) is quite
surprising and we have not managed to explain it
yet. Assuming adiabatic expansion, we expect the
rear side of the target to be in the region of iron
diagram phase around the melting point at P = 0.
Indeed the rear side physical conditions are T «
0.14 eV, p ~ 7 g/cm3, P = 0. So we cannot decide
86