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
SIMULTANEOUS VISAR AND TXD MEASUREMENTS ON SHOCKS
IN BERYLLIUM CRYSTALS
D. C. Swift, D. L. Paisley, G. A. Kyrala and A. Hauer
Los Alamos National Laboratory* NM 87545, USA
Shock waves were induced in single crystals of beryllium, by direct illumination using the TRIDENT laser
at Los Alamos. The velocity history at the surface was measured using a line-imaging VISAR, and transient
X-ray diffraction (TXD) records were obtained with a plasma backlighter and X-ray streak cameras. At
lower pressures, the VISAR records exhibited an elastic precursor followed by a plastic wave and spall. At
higher pressure, the velocity records showed a two-wave structure suggesting a phase change, then at the
highest pressure a single broad wave suggesting a shock directly into the high pressure phase. The rocking
curves of the crystals were typically about 2 degrees wide, so analysis of the TXD records is complicated by
the relatively large amount of blurring. However, the Bragg record of the shocked 0002 peak clearly indicates
a smaller lattice parameter at higher pressure. In the shots where polymorphism seemed to appear in the
VISAR record, additional lines appeared in the Bragg record, and new lines also appeared within the field
of view of the Laue camera. These results are consistent with a new quantum mechanical equation of state
for beryllium, which suggests that the hexagonal to body-centered cubic transition occurs at ~40 GPa on
the principal Hugoniot.
INTRODUCTION
Beryllium capsules axe among the designs being developed to contain the fuel for inertiallyconfined fusion (ICF). It is important to understand the properties of beryllium to underwrite
capsule designs, such as specifications for the
grain size so that the capsule implosion meets
symmetry and uniformity requirements.
The relevant properties of beryllium include
its strength as a function of orientation, melt,
and solid-solid phase transformations. Beryllium
adopts the hexagonal (hex) structure at STP, but
transforms to body-centered cubic (bcc) on heating.(i) Gas gun experiments have provided data
at slower deformation rates.(2)
We have performed a series of experiments using the Trident laser at Los Alamos to investigate the dynamic response of beryllium, and compared these with quantum mechanical equations
of state incorporating polymorphism.
"This work was performed under the auspices of the U.S.
Department of Energy under contract # W-7405-ENG-36.
EXPERIMENTAL METHOD
Shock waves were induced in foils and single
crystals of beryllium by direct illumination with
a beam from the Trident laser.(3) The pulse duration was 1.0 to 3.6ns over a spot 4mm in diameter. The spatially averaged intensity history
of the drive beam was measured using a photodiode. The shock conditions in the sample were
measured using a line-imaging VISAR recording
on a pair of optical streak cameras(4) and - for
the single crystal samples - transient X-ray
diffraction recorded on time-integrating film and
on X-ray streak cameras. (Fig. 1.)
The X-rays were generated by focusing a second Trident beam at full energy in the green
(-200 to 250 J) tightly (~100jum spot) onto a
manganese foil 6^m thick. The resulting hot
plasma emitted predominantly helium-like line
radiation, of wavelength 2.755 A. The wavelength
was verified with a transmission spectrometer.
The single crystal samples were 30 to 40jum
thick, and cut with the drive and VISAR sur1192
vacuum chamber
(view from above)
X-ray streak cameras
The line VISAR imaged 3 mm of the free surface across the center of the sample.
X-ray
backlighter
beam
FIGURE 1. Schematic of experimental set-up.
faces parallel to the 0001 planes. The samples
were cut from a single crystal boule made by
zone refining. The boule dates from the 1960s,
and only a little remains from the neck. As a
result, there was a considerable distribution of
orientations within each sample, thought to be
in the form of low-angle grain boundaries, giving
crystal rocking curves (distribution of scattered
intensity about the nominal Bragg angle) about
2° wide.
The TXD records were interpreted in terms
of lattice compression by deconvolving them using the rocking curve for the appropriate crystal
as the kernel. One objective of this program is
to identify melt on the Hugoniot from the TXD
signal. It is likely that the hex/bcc phase transition takes place before melt occurs, so an additional challenge is to follow Bragg reflections in
the bcc phase. It is not known whether the bcc
phase would always form in the same orientation
with respect to the hex, and hence whether the
position of a bcc reflections can be predicted in
advance, allowing experiments to be performed
with a limited TXD field of view.
The Bragg angle for the unshocked beryllium
was 46.7°. In each experiment, the sample was
oriented so that the unshocked reflection would
enter the 'Bragg' (south) camera, leaving space in
the field of view for the reflection from shocked
material. The position of the cLaue' (north) camera was constrained by the design of the target
chamber, and it was not possible to position the
target so that an unshocked Laue line would appear in the field of view.
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EXPERIMENTAL RESULTS
We performed experiments on four single crystals of beryllium. No attempt was made to recover shocked samples, to avoid compromising the
dynamic diagnostics.
In one shot (12196) the sample was not
shocked, to verify that a TXD signal could be obtained. Shielding was added to protect the sample from the X-ray source; the sample was recovered and subsequently re-used with a shock wave.
Time-integrated and time-resolved TXD records
were obtained. The profile of the 0002 Bragg reflection matched the rocking curve measured for
that sample extremely well, so in these experiments the width of the TXD lines was dominated
by the rocking curve and not by the spectrum of
the X-ray source.
Subsequent shots (12198, 12199, 12202 and
12206) were performed with increasing intensity
in the drive beam. (Fig. 2.)
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FIGURE 2. Drive intensity history for single crystal
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The line VISAR records showed no spatial
variation in the velocity history. The records in
the higher energy shots were quite noisy because
the plasma / hot electron shield was omitted to
make TXD alignment more accurate. There was
no evidence that the sample was preheated before the arrival of the shock wave. The records
from the lower intensity shots showed a precursor at ~lkm/s followed by a second wave. It
seems likely that this is an elastic precursor followed by a plastic wave. There was evidence of
spall and ringing after the maximum velocity was
reached. The records from the higher intensity
shots showed evidence of a multiple wave structure with a stronger precursor. (Fig.
3.)
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FIGURE 3. Line VISAR records.
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The magnitude of the elastic precursor was
considerably larger than one would expect from
models calibrated to /zs-scale experiments. This
probably reflects rate-dependent or orientationdependent contributions to the strength.
The Bragg TXD records showed a peak from
the unshocked material, and also one or more
peaks corresponding to compressed material. Because of the wide rocking curves, the noise was
quite large on the time-resolved records, so we
have concentrated so far on analyzing the timeintegrated results (static films and time-average
of the streak records). These will be used to guide
a Bayesian analysis of the time-resolved signals.
The records could be reproduced quite accurately
by fitting a set of discrete lines (each contributing
a distribution given by the rocking curve) at
different deviations to the unshocked Bragg peak.
The weaker lines seem to be statistically significant. The principal compressed peak deviated
more from the unshocked peak at higher intensities. (Fig.
4.)
In the Bragg records, additional lines appeared at the highest intensities. In the same
experiments, noisy lines appeared in the Laue
records, one line remaining roughly constant and
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FIGURE 5. TXD records (north camera).
Rocking curve for each crystal is shown for comparison.
the other moving (Fig.
5). Beryllium has a phase
transformation from the hexagonal to the bodycentered cubic (bcc)
structure: it is possible that
these additional lines are from the bcc.
If so, it
seems likely (albeit from only one comparison)
that the bcc forms in the same orientation with
respect to the hex, and thus that the position of a
bcc line can be predicted hi advance. The angles
were used to calculate lattice spacings, assuming
the orientation of the planes (Figs 6 and 7).
COMPARISON WITH THEORY
A two phase equation of state was calculated using ab initio quantum mechanics.(5) The
equation of state matched the hex/bcc boundary
1194
mation pressure deduced from the ab initio equation of state is consistent with the experiments.
unshocked (0002) -——
CONCLUSIONS
Shock waves were induced in samples of beryllium by irradiation with the Trident laser, and
measured using line-imaging VISAR-and transient X-ray diffraction (TXD). No undesirable hydrodynamic effects of a laser drive, such as preheat, were observed, though some problems were
encountered with plasma or hot electrons reducing the VISAR signal level. It was possible to
intensity
12206
12203
12202
12201 shot
12200
12199
c'(A)
1.6 12198
analyze the TXD records, even though the rocking curve of the samples was relatively large at
2°, giving broad diffraction lines.
At the lower drive intensities, the VISAR
records exhibited an elastic precursor followed by
a plastic wave, with evidence of spall and ringing
behind. At the higher drive intensities, there was
some sign of a two-wave structure tentatively
identified with the hex/bcc phase transition.
The TXD records showed the 0002 Bragg line
moving with drive intensity. At the higher drive
intensities, additional lines appeared in the Bragg
and Laue records, again suggesting a phase transition. The location of the lines was reasonably
reproducible between shots, indicating that the
bcc structure formed at the same orientation to
the hex in each experiment.
FIGURE 6. Lattice parameters deduced from south
camera records.
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ACKNOWLEDGEMENTS
We would like to acknowledge the contributions of Dan Thoma and Jason Cooley for preparing the crystal samples, Bob Springer for measuring the rockin curves, Roger Kopp for performing
LASNEX calculations, and the staff of Trident for
their help in performing the experiments.
FIGURE 7. Lattice parameters deduced from north
camera records.
observed at low pressures quite well. The principal Hugoniot was predicted to cross the hex/bcc
boundary at ~40 GPa.
Radiation hydrodynamics simulations were
performed using the measured drive profiles but
with a simpler equation of state for beryllium.
Velocity histories and density profiles were extracted from the simulations. The velocity histories were similar to the VISAR records but were
not in good agreement. This could be the result of using an inaccurate equation of state, or
because of uncertainties in the models used for
transport properties.
Assuming the extra Bragg and Laue lines indicate the occurrence of bcc material, the transfor-
REFERENCES
1. Young, D.A., "Phase diagrams of the elements," University of California (1991).
2. S P Marsh (Ed), "LASL Shock Hugoniot Data", University of California (1980).
3. Paisley, D.L., Swift, D.C., Johnson, R.P., Kopp, R.A.
and Kyrala, G.A., this conference.
4. Forsman, A.C. and Kyrala, G.A., Phys. Rev. E vol.
63, 056402 (2001).
5. Swift, D.C. and Ackland, G.J., First principles equations of state for simulations of shock waves, submitted to Phys. Rev. B (2001).
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