diamond anvil cells in 2006 reach 10- to 100-TPa (0.1–1 Gbar) pressure range with laser induced shock waves: Rich Murray 2011.01.17

[Rich Murray-2]

Diamond anvil cells in 2006 reach 10- to 100-TPa (0.1–1 Gbar) pressure
range with laser induced shock waves: Rich Murray 2011.01.17

http://www.pnas.org/content/104/22/9172.full

free full text

Achieving high-density states through shock-wave loading of
precompressed samples
Raymond Jeanloz * , † , ‡,
Peter M. Celliers § ,
Gilbert W. Collins § ,
Jon H. Eggert § ,
Kanani K. M. Lee ¶ ,
R. Stewart McWilliams *,
Stéphanie Brygoo ‖ , and
Paul Loubeyre ‖
+ Author Affiliations

Departments of *Earth and Planetary Science and
†Astronomy, University of California, Berkeley, CA 94720;
§Lawrence Livermore National Laboratory, Livermore, CA 94550;
¶Department of Physics, New Mexico State University, Las Cruces, NM 88003; and
‖Commissariat à l'Energie Atomique, 91680 Bruyères-le-Châtel, France
Edited by Ho-kwang Mao, Carnegie Institution of Washington,
Washington, DC, and accepted March 7, 2007 (received for review
September 19, 2006)

Abstract

Materials can be experimentally characterized to terapascal pressures
by sending a laser-induced shock wave through a sample that is
precompressed inside a diamond-anvil cell.
This combination of static and dynamic compression methods has been
experimentally demonstrated and ultimately provides access to the 10-
to 100-TPa (0.1–1 Gbar) pressure range that is relevant to planetary
science, testing first-principles theories of condensed matter, and
experimentally studying a new regime of chemical bonding.

high pressure planetary interiors diamond–anvil cell Hugoniot laser shock

In nature, and specifically when considering planets, high pressures
are clearly evident in two contexts: the conditions occurring deep
inside large planetary bodies and the transient stresses caused by
hypervelocity impact among planetary materials.
In both cases, typical peak stresses are much larger than the crushing
strength of minerals (up to ≈1–10 GPa, depending on material, strain
rate, pressure, and temperature), so pressures can be evaluated by
disregarding strength and treating the rock, metal, or ice as a fluid.

Ignoring the effects of compression, the central (hydrostatic)
pressure of a planet is therefore expected to scale roughly as the
square of the planet's bulk density (ρ planet, assumed constant
throughout the planet) and radius (R planet ):

Here, the scaling factor is adjusted to match the central pressure of
Jupiter-like planets (RJupiter and ρ Jupiter are the radius and bulk
density of Jupiter, respectively), and the effects of compression and
differentiation (segregation of dense materials toward the center of a
planet) act to increase the central pressure for larger, denser, more
compressed, or more differentiated planets relative to Eq. 1 .
Consequently, peak pressures in the 1- to 10-TPa range exist inside
large planets, with Earth's central pressure being 0.37 TPa and
“supergiant” planets expected to have central pressures in the 10- to
100-TPa range.

In addition to static considerations, impact (the key process
associated with growth of planets and the initial heating that drives
the geological evolution of planets) is also expected to generate TPa
pressures. Impedance-matching considerations described below can be
combined with Kepler's third law to deduce that peak impact pressures
for planetary objects orbiting a star of mass M star at an orbital
distance R orbit are of the order

Scaling here is to the mass of the Sun, and the average density and
orbit of Earth, the latter being in astronomical units (1 AU = 1.496 ×
1011 m); also, the characteristic impact velocity (u 0) is taken as
the average orbital velocity according to Kepler's law, u 0 = 2πR
orbit /T orbit with T orbit being the orbital period, and Eq. 2
assumes a symmetric hypervelocity impact.

While recognizing that materials have been characterized at such
conditions through specialized experiments (e.g., shock-wave
measurements to the 10- to 100-TPa range in the proximity of
underground nuclear explosions and from impact of a foil driven by
hohlraum-emitted x-rays) (1–3), laboratory experiments tend to achieve
significantly lower pressures. As with planetary phenomena, both
static (diamond-anvil cell) and dynamic (shock-wave) methods are
available for studying macroscopic samples at high pressures, but
these are normally limited to the 0.1- to 1-TPa range (4). Still,
these pressures are of fundamental interest because the
internal-energy change associated with compression to the 0.1-TPa (1
Mbar) level is roughly (5)

with volume changes (ΔV) being ≈20% of the 5-cm3 typical molar volume
of terrestrial-planet matter (here we consider a mole of atoms, or
gram-formula weight, which is 3.5, 5, and 6 cm3 for diamond, MgO, and
water, respectively, at ambient conditions). The work of compression
thus corresponds to bonding energies (≈1 eV = 97 kJ per mole,
characteristic of the outer, bonding electrons of atoms), meaning that
the chemical bond is profoundly changed by pressures of 0.1 TPa. This
expectation has been verified through numerous experiments showing
that the chemical properties of matter are significantly altered under
pressure: for instance, hydrogen, oxygen, and the “noble gas” xenon
transform from insulating, transparent gas, fluids, or crystals at low
pressure to become metals by ≈0.1 TPa (5, 6).

In this article, we briefly describe laboratory techniques that have
recently been developed for studying materials to the 10- to 100-TPa
range of relevance to planetary science. In particular, as most
planets now known are supergiants of several (≈1.5–8) Jupiter masses
orbiting stars at distances of a fraction of 1 astronomical unit (7),
Eqs. 1 and 2 imply a strong motivation for characterizing materials up
to the 100-TPa (1 Gbar) level. To reach such conditions, we combine
static and dynamic techniques for compressing samples: specifically,
propagating a shock wave through a sample that has been precompressed
in a diamond-anvil cell (Fig. 1). By starting with a material that is
already at high (static) pressures, one reaches higher compressions
than could be obtained by driving a shock directly into an
uncompressed sample.

Moreover, by varying the initial density (pressure) of the sample, and
also by pulse-shaping the shock-wave entering the sample, one can tune
the final pressure-density-temperature (P–ρ–T) state that is achieved
upon dynamic loading. This tuning is particularly relevant to
planetary applications, because the average temperature profile
through the convective interior of a planet is isentropic, rather than
following a shock-compression curve (Hugoniot). Precompression thus
allows one to significantly reduce the heating that tends to dominate
the highest-pressure dynamic experiments, which is important for
better characterizing the interatomic forces under compression.

Experimental Approach

Diamond-cell samples are necessarily small, ≈100–500 μm in diameter by
5–50 μm in thickness, as it is the small area of the diamond tip
(culet) that allows high pressures to be achieved. Shock compression
of such small samples is not well suited to experiments involving
mechanical impact, for example, by a projectile launched from a
light-gas gun (which currently sets the state of the art for
high-quality shock-wave measurements, but involves sample dimensions
of centimeter diameter by millimeter thickness). Instead, a
laser-generated shock wave is better suited to the dimensions of the
diamond cell, with a well defined shock front of ≈200–500 μm diameter
being readily achieved at presently available facilities.

Several laser beams are typically focused onto the outer surface of
one of the diamond anvils, so as to generate an intense pulse of light
that is absorbed at the diamond surface (thin layers of
laser-absorbing plastic and x-ray-absorbing Au usually are deposited
on that diamond surface) (Fig. 2). The outermost diamond is thereby
vaporized, launching a high-amplitude pressure wave into the anvil
caused by a combination of the rapid thermal pressure generated in the
diamond (resulting from heating at nearly constant volume) and
linear-momentum balance (“rocket effect”) relative to the diamond
vapor that expands outward, back toward the incoming laser beams. Such
a high-amplitude wave has the property of being self-steepening for a
material with a normal equation of state (∂Ks /∂P > 0 for the
adiabatic bulk modulus Ks ). As a result,  As a result, a shock front
is created inside the anvil and propagates toward the sample (8,
9)....

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