In recent years a powerful experimental
tool has been added to the arsenal
at the disposal of the materials scientist
investigating materials response
at extreme regimes of strain rates, temperatures,
and pressures: laser compression.
This technique has been applied
successfully to mono-, poly-, and
nanocrystalline metals and the results
have been compared with predictions
from analytical models and molecular
dynamics simulations. Special flash
x-ray radiography and flash x-ray diffraction,
combined with laser shock
propagation, are yielding the strength
of metals at strain rates on the order of
107–108 s–1 and resolving details of the
kinetics of phase transitions. A puzzling
result is that experiments, analysis, and
simulations predict dislocation densities
that are off by orders of magnitude.
Other surprises undoubtedly await us
as we explore even higher pressure/
strain rate/temperature regimes enabled
by the National Ignition Facility.
Ever since the discovery of lasers in
the 1950s their interactions with materials
have been explored. Laser welding,
cutting, surface treatment, and
heat treatment of metals are well established
technologies which are highly
successful. By far the most important
application of lasers is in optical storage
devices. The power of lasers ranges
from less than 1 mW (for a common laser
pointer) to 700 TW—the combined
energy of 192 laser beams focused on a minute 2–3 mm diameter target at
the National Ignition Facility at Lawrence
Livermore National Laboratory
(LLNL) in Livermore, California.1 It
was realized early that lasers can also
produce shock waves in materials. As
early as 1963, Askaryon and Morez2
demonstrated that shock pulses could
be generated in metals from laser-pulseinduced
vaporization at the surface.
The use of surfaces covered by a lasertransparent
overlay was introduced by
Anderholm;3 this enabled the confinement
of the vapor products, resulting in
an increase of the peak pressure of the
shock launched into the metal. Shock
amplitudes as high or higher than
those generated by explosives or planar
impact devices could be generated with
a fundamental difference: the duration of the shock pulse was in the nanosecond
range. In the 1980s Clauer et al.4 used these laser-induced shock pulses
to modify the structure of engineering
alloys, increasing their strength and fatigue
The recent National Research Council
report titled “Frontiers in High Energy
Density Physics: The X-Games of
Contemporary Science” presents the
immense challenges facing science as
the extreme regimes of pressure, strain
rate, and temperature are explored.5 The schematic diagram shown in Figure
1 is a Weertman-Ashby plot for titanium
in which the temperature and
strain rate are plotted. The conventional
(i.e., known) and extreme (unknown)
deformation rate regimes are marked.
The bottom part of the plot (below
106 s–1) is the well-characterized region
in which deformation takes place by
dislocations, twinning, or diffusional
processes. The different regimes have
been extensively studied and are part
of the body of knowledge of materials
science and engineering.
regimes of pressure, temperature,
and strain rates that comprise
the top portion of the plot can only be
accessed through very special methods.
Although the fi rst fundamental
investigation, by C.S. Smith,6 was carried
out approximately 60 years ago,
this remains a frontier area. For strain
rates from 106 to 1010 s–1, deformation
mechanisms are less well understood
and conventional deformation mechanisms
are not applicable. An additional
complexity is introduced by nanostructured
metals, in which the mechanisms
of plastic deformation are significantly
different. Compression by high-power
lasers is one of the methods through
which we can access these extreme regimes.
Laser-induced shock waves can be
launched by several techniques; Figure
2 shows two more traditional and
two novel methods to illustrate the experimental
choices. Figure 2a shows
the direct incidence of laser energy
on the surface of the metal. The energy
deposited onto the metal surface
causes it to vaporize. The vapor pressure
creates a pressure pulse into the
metal specimen. Alternatively, lasers
can be used to accelerate a foil onto
the target, generating a shock wave of
square shape in this manner (Figure
2b). The difference in the duration of
the pulse between lasers and gas gun
or explosively driven flyer plates is on
the order of 100 or more. To access
very high pressure regimes of material
deformation and lattice dynamics, it is
desirable to increase the pressure to as
high a level as possible without melting
the target. A slower compression rate,
called quasi-isentropic compression,
presents a definite advantage over the
sharp shock compression, with a strain
rate at the front that is orders of magnitude
compression can be accomplished by
using a reservoir, shown in Figure 2c.
This acts as a ‘pillow’ that softens the
blow of the laser.7–9 A fourth method uses the Hohlraum effect (Figure 2d).
This is a German word that means
‘hollow cavity.’ It is the principle of
energy deposition of the National Ignition
Facility and will be described in a
later section. In essence, it enables the
generation of x-rays which illuminate
the target in a more uniform manner.
The lasers converge into the Hohlraum
and deposit their energy on the internal
walls, heating them up until they glow
in the soft x-ray spectral regime, creating
a mini-radiation chamber which
then launches a shock into the sample
being studied. These x-rays are the primary
source of energy deposition onto
The lasers used to produce shock
waves are high-amplitude pulses that
have a tailored shape. The laser source
with sufficient energy to launch these
single pulses is usually a glass laser.
The laser energy used in current
experimental facilities varies from
10 J/mm2 to 1 kJ/mm2 with durations
that typically vary between 1 and 10
ns. On NIF, the energies can go much
higher. Figure 3 shows a typical laserinduced
pressure wave propagating in
a sample of vanadium. The pressure
decays rapidly as the pulse travels and
dissipates. It can be seen that after
propagating 0.25 mm the amplitude
of the pulse is a small fraction of the
This rapid decay of the
pulse presents an advantage in ‘freezing
in’ the structural changes introduced
by the pulse, since it acts as a
self-quenching mechanism. In gas gun
and explosive experiments the postshock
temperature of the samples can
rise easily to levels where recovery
and recrystallization occur, destroying
the effects that we want to study. The
lateral dimensions of the laser beam
are small in comparison with gas gun
and explosive experiments—a few
mm versus 100–300 mm. However,
these dimensions are sufficient to extract
specimens for characterization by
transmission electron microscopy.
LASERS AND MOLECULAR
Lasers and molecular dynamics simulations
are well suited for each other,
since they both occur at high strain
rates (~108 s–1). This is even more accentuated
if nanocrystalline metals are investigated because the size of
grains that can be modeled in molecular
dynamics is in the nanometer range.
Thus, the comparison of structures
characterized by transmission electron
microscopy (TEM) from laser recovery
experiments with molecular dynamics
(MD) simulations is a fertile ground for
An illustration of this is shown in
Figure 4a, which is a schematic of a
propagating shock front and partial
dislocation loops generated and growing
behind it. The shock stress is often in the regime in which dislocations can
be homogeneously generated (pressure
> shear modulus/10). Thus, a dense
network of dislocations is developed.
These can be perfect dislocations, leading
to the formation of cellular structures,
or partial dislocations, leading
to stacking faults, as those observed
in Figure 4b.
The formation of these
defects can be modeled by molecular
dynamics, and the results are shown
in Figure 5.10 A section through the
simulation box in Figure 5a shows the parallel lines which are stacking faults.
The formation of these stacking faults
through the generation and expansion
of partial dislocation loops is shown in
Figure 5b. The density of these loops
increases behind the shock front. The
formation of these loops is complex,
with schematic pictures already advanced
early on, as shown in Figure
5c.11 We note that the leading edge of
partial loops can develop velocities
close to the bulk sound velocity, at this
high stress and when not pulled back
by a trailing partial dislocation.
The dramatic picture of Figure 6
shows both dislocation nucleation at
a pre-existing dislocation loop and the
homogeneous dislocation nucleation
front for a ramped shock propagating
through a copper specimen.12 Approximately
350 million atoms were
used in the simulation. Only the atoms
disturbed from their original face-centered
cubic (f.c.c.) lattice position are
imaged. The broad view of the front
shows, in a section, the intense dislocation
activity generated by the propagation
of the shock front at pressures
beyond the homogeneous nucleation
limit, producing mostly partial loops
with only the leading partial produced.
The close view shows, in perspective,
how dislocation loops are nucleated at
a pre-existing defect. These are partial
dislocations, the leading partial being
followed by the trailing, which recomposes
the perfect f.c.c. structure. This
explains the ‘hole’ in the core of the
loops imaged in the right-hand side of
Figure 6. These dramatic representations
can lead to quantified predictions
of dislocation densities.
The plot shown in Figure 7 presents
the shock strength (related to the maximum
stress) as a function of the plasticity
(related to the dislocation density).
This is the so-called Holian–Lomdahl
plot.13 As expected, the plasticity increases
with the shock strength, since
dislocation density is directly related
to the pressure. The results from simulations
by Cao et al.14 for copper and
Jarmakani et al.10 for nickel are shown
in the top of Figure 7, together with the
analytical predictions from the homogeneous
dislocation model. The comparison
of these computed dislocation
densities with experimentally measured
(through TEM) densities and with an analytical homogeneous dislocation
theory provided a puzzling surprise:
the predictions from molecular dynamics
(MD) and theory are orders of magnitude
higher than the experimentally
Although results by
Murr15 are shown, extensive TEM work
by other groups confirm these low (in
comparison with MD and theoretical
predictions) dislocation densities (expressed
as plasticity in Figure 7; see
caption for relationship between the
two) (e.g., Bourne et al.16). Murr and
Kuhlmann–Wilsdorf17 had predicted
an empirical relationship of the form
between the pressure, P, and dislocation
density, π, based on experimental
measurements of dislocation cell sizes:
π α P1/2. Figure 7 shows that the experimental
results, in the bottom of the
plot, follow the same trend as the MD
simulations and theory, but are lower
by orders of magnitude. This difference
is not yet completely understood,
but three effects play a role, separately
- The strain rate at the shock front in
MD simulations is extremely high.
The shock wave propagates into an
ideal lattice devoid of dislocations.
Thus, the deviatoric stress is integrally
accommodated by homogeneous
dislocation loop generation.
In real experiments, the strain rate
at the front is lower and there is an
existing network of dislocations,
which can accommodate some of
the stresses through motion.
- Molecular dynamics simulations
(marked Release-Jarmakani) show
a dramatic decrease in dislocation
density upon unloading. This is
shown in Figure 8. A fraction of
these loops can shrink upon unloading
if no cross-slip has taken
place since the deviatoric stresses
are removed. When this occurs,
the dislocation density decreases.
The dislocation configurations at
the peak stress and after unloading
are shown in Figure 8. The green
regions are stacking faults. This
decrease in dislocation density
corresponds to a decrease in plasticity.
The results for calculations
at three maximum pressure levels
are plotted in Figure 7. The arrow
in the plot represents the drop in
plasticity due to unloading (also
called ‘release’ in shock jargon).
- Thermal recovery: even the release
simulations shown in Figure 7 only
last a fraction of a nanosecond.
However, thermal effects lasting
up to microseconds might lead to
dislocation rearrangement and reactions
that would likely decrease
the net dislocation density. Such
effects could be partly explored by
dislocation dynamics simulations or other physically based plasticity
models informed by experiments
and atomistic simulations.
This and many other issues are not
yet resolved, and laser experiments
combined with molecular dynamics
simulations and physically based models
will shed light on the deformation
mechanisms in these extreme regimes.
Of particular importance are flash x-ray
diffraction experiments which can
probe the shocked state and infer the
defect structure during the laser compression
process. These experiments
are currently being carried out by Wark
and coworkers at Oxford University,
U.K.,19,20 using the Vulcan Laser facility,
and by Hawreliak et al.,21 and
Milathianaki and McNaney et al.22 at
LLNL using the Omega and Janus facility.
Another new technique is to use
flash x-ray radiography to observe the
rate of material deformation driven
by buoyancy-type hydrodynamic instabilities.
This new experimental
technique allows material strength to
be inferred at very high pressures and
strain rates.23,24 This technique will be
developed on the NIF laser, where samples in the solid state can be studied at
extraordinary pressures, P > 103 GPa,
approaching those found, for example,
at the centers of the giant planets.7,25
LIVERMORE NATIONAL LABORATORY IGNITION FACILITY
The experimental facilities of Omega
(Laboratory for Laser Energetics, University
of Rochester, New York), Jupiter
(LLNL), Trident (Los Alamos National
Laboratory), and Vulcan (U.K.)
enable unique materials experiments.
These facilities have been and are being
successfully used to explore the
extreme material regimes not accessible
by other shock wave means such
as explosive detonation and gas gun
impact. The National Ignition Facility
at LLNL will provide a much higher
energy deposition capability. As we
embark on the NIF era, it is imperative
to understand the basic physics of plastic
deformation of advanced materials
in the extreme regimes created under
these conditions. The National Ignition
Facility Program at LLNL is designed
- Energy: demonstrate fusion ignition
and energy gain—the first
step toward limitless fusion power
- National security: understand the
complex underlying physics of nuclear
weapons, ensuring the safety
and reliability of the country’s
- Basic science: NIF experiments
can create immense pressures
and temperatures similar to those
in planetary interiors, stars, and
supernovae, shedding light on astrophysical
science and nuclear physics.26
The National Ignition Facility is
massive, with 192 high-power laser
beams designed to be fired simultaneously
and focused on a capsule. Figure
9 shows an overall view of the facility,
which occupies an area equivalent
to approximately four football fields.
These 192 laser beams converge onto a
chamber having approximate diameter
of 10m (Figure 10). Precise timing of
the beams has to be ensured to within
~50 ps. These beams enter a hollow
cylinder, the Hohlraum, interact with
the walls and generate the intense xrays
that illuminate the capsule (Figure
11). Direct incidence of the laser beams
onto the hollow capsule is less uniform
and can create instabilities in the compression
process. The capsule, which
contains the fusion material (a solid
deuterium layer with 80 μm thickness),
is compressed from its initial diameter
of 2 mm to approximately 0.5 mm.
At that point fusion burn should take
place, generating more energy than the
combined energy of the laser beams.
Laser-induced shocks and isentropic
compression are new and powerful research
tools to investigate the behavior
of materials under extreme conditions.
The processes of plastic deformation,
fracture, and fragmentation under
these conditions are still poorly known.
Many questions remain to be explored
using the powerful experimental capabilities,
instrumentation and diagnostic
tools, computational and analytical
techniques, and advanced characterization
We thank Drs. BY Cao, H. Jarmakani,
and Mr. C.T. Wei for help in experiments
and simulations. Research
funded by the University of California
Offi ce of the President, ILSA, and Lawrence
Livermore National Laboratory
under Laboratory Directed Research
and Development Program grant 09-SI-010.
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M.A. Meyers is at the University of California, San
Diego; B.A. Remington and B. Maddox are with Lawrence Livermore
National Lab.; and E.M. Bringa is with
the Universidad Nacional de Cuyo, Argentina. Dr.
Meyers can be reached at firstname.lastname@example.org.