**Shock-Wave Loading of Pre-Compressed Samples**

Raymond Jeanloz,^1^ Peter M. Celliers,^2^ Gilbert W. Collins,^2^ John H.
Eggert,^2^ Kanani K. M. Lee,^3^ Paul Loubeyre^4^

^1^Department of Earth and Planetary Science and of Astronomy,
University of California, Berkeley, CA 94720; ^2^Lawrence Livermore
National Laboratory, Livermore, CA; ^3^New Mexico State University, Las
Cruces, NM; ^4^CEA, Bruyeres, France

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

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 pressures are much larger than the crushing strength of minerals
(up to about \~1-10 GPa, depending on strain rate, pressure and
temperature), so can be evaluated by disregarding strength and treating
the rock 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 average density
(ρ*~planet~*) and radius (*R~planet~*):

> *P~center~* \~ 7 TPa (ρ*~planet~*/ρ~Jupiter~)^2^
> (*R~planet~*/*R~Jupiter~*)^2^ (1)

Here the scaling factor is matched to Jupiter-like planets, and the
effects of compression and of differentiation (segregation of dense
materials toward the center of a planet) act to increase the central
pressure for larger or denser planets relative to (1). Consequently,
peak pressures in the 1-10 TPa range exist inside large planets, with
Earth's central pressure being 0.37 TPa and "super-giant" planets being
expected to have central pressures in the 10-100 TPa range.

Similarly, 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

*P~impact~* ≈ 1 TPa (*M~star~*/*M~Sun~*) (ρ*~planet~*/5.5 g cm^-3^)
(*R~orbit~*/1 AU) ^-1^ (2)

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 x
10^11^ m); also, the characteristic impact velocity (*u*~0~) is taken as
the average orbital velocity according to Kepler's law, *u*~0~ =
2π*R~orbit~*/*T~orbit~* with *T~orbit~* being the orbital period. Thus,
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.

While recognizing that materials have been characterized at such
conditions through specialized experiments (e.g., shock-wave
measurements to the 10 TPa range in the proximity of underground nuclear
explosion tests) (*1, 2*), 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 0.1-1 TPa range (*3*). 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 (*4*)

∆*E* ≈ -- *P* ∆*V* \~ 10^5^ J per mole of atoms (3)

with volume changes (∆*V*) being approximately 20% of the 5 cm^3^
typical molar volume of condensed matter (here we consider a mole of
atoms, or gram-formula weight, which is 3.5, 5 and 6 cm^3^ for diamond,
MgO and water, respectively, at ambient conditions). The work of
compression thus corresponds to typical bonding energies (\~1 eV = 96 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 fluids or crystals at zero
pressure (and low temperature) to become metals by \~10^11^ Pa (*4, 5*).

![](media/image1.jpeg){width="3.7694444444444444in"
height="1.3194444444444444in"}![](media/image2.jpeg){width="1.8298611111111112in"
height="1.3125in"}

**Fig. 1.** Schematic of diamond-anvil cell (*left*), showing both a
cross-section (blue arrow indicates direction of incoming, shock-wave
generating laser beams) and a pulled-apart view, and photograph
(*right*) of a diamond cell as a laser-induced shock is being generated
during an experiment at the Omega laser facility (University of
Rochester).

In the present article, we briefly describe laboratory techniques that
have recently been developed for studying materials to the 10-100 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 AU (*6*), (1)-(2) imply a strong
motivation for characterizing materials up to the 100 TPa (1 Gbar)
level. In order to reach such conditions, we combine static and dynamic
techniques for compressing samples: specifically, propagating a shock
wave through a sample that has been pre-compressed in a diamond-anvil
cell (Fig. 1). By starting with a material that is already at high
(static) pressures, one not only reaches much higher pressures upon
shock compression, but also 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, one can tune the
final pressure-density-temperature (*P*--ρ--*T*) state that is achieved.

**Experimental Approach**

Diamond-cell samples are necessarily small, \~100-500 µm diameter by
5-50 µm 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 \~ cm diameter by mm
thickness). Instead, a laser-generated shock-wave is better suited to
the dimensions of the diamond cell, with a well-defined shock front of
about 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 (a thin coating of an absorbing
medium is generally deposited on that diamond surface). The outermost
diamond is thereby vaporized, launching a high-amplitude pressure wave
into the anvil due to a combination of the rapid thermal expansion of
the heated diamond 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
(∂*K~S~*/∂*P* \> 0 for the adiabatic bulk modulus *K~S~*). As a result,
a shock-front is created inside the anvil and propagates toward the
sample (*7, 8*).

The sample itself is pre-compressed inside a metal gasket, either
directly (e.g., if it is a fluid) or else within a pressure-transmitting
fluid (Fig. 2). Current methods allow samples to be pre-compressed up to
no more than \~1-10 GPa, because the diamond anvil from which the
shock-front enters needs to be thin, no more than about 100-400 µm thick
(*9, 10*). This amounts to little more than a microscope-slide cover
slip, albeit made of diamond. As discussed below, this limitation arises
from the short duration of laser pulses available at present-day
facilities.

![](media/image3.jpeg){width="2.7194444444444446in" height="2.1in"}

**Fig. 2.** Schematic cross-section of diamond anvils and sample, with
the drive-laser that creates the shock wave entering from below (as
described in the text, current laser systems require the anvil on the
shock-entry side to be thin). The sample is indicated, along with a
stepped shock-wave calibrant, and diagnostics described in the text
(VISAR and pyrometry) record the dynamic compression of the sample
through the second anvil.

Two types of calibrants are included in the gasket hole, along with the
sample: one or more small (\~1-10 µm) chips of ruby, and a shock-wave
standard. The ruby is used to measure the pressure of the pre-compressed
sample (*P*~1~), using the ruby-fluorescence method (*11*), from which
the density of the sample (ρ~1~) is determined prior to shock
compression (the equation of state of the sample must therefore be known
at the pressures of the pre-compression). The shock-wave standard
typically consists of a metal plate, stepped so as to have at least two
well-determined thicknesses. The metal must be a shock-wave standard,
(i.e., well-determined relationship between shock and particle
velocities, *U~S~* and *u~p~*). Aluminum, platinum and tungsten are
examples of shock-wave standards, and a measurement of the shock
velocity (the shock-wave transit-times across the different,
well-calibrated thicknesses of the standard) then yields the particle
velocity of the shock-front entering into the sample (*12*).

Upon exiting the first diamond anvil, the shock front traverses the
sample chamber (including both sample and calibrants) and then transits
through the second (back) diamond anvil. At this point, there is no
concern if the shock-wave decays, so the back anvil can be of typical
thickness for high-pressure experiments (\~ 2.5 mm); it serves as a
window, containing and allowing the sample to be characterized during
shock-compression. Both anvils as well as the sample (and calibrants)
are normally vaporized during an experiment, although the cell that
contains the anvils is re-useable. With shock velocities of order \~ 10
km/s = 10 µm/ns, the entire experiment is completed within a few
nanoseconds.

![](media/image4.jpeg){width="4.829861111111111in"
height="2.9319444444444445in"}

**Fig. 3.** VISAR record (*left*) from a laser-shock experiment through
a pre-compressed sample (*13*), showing velocity fringes as a function
of time (horizontal axis) obtained from an electronic streak camera
imaging light reflected off the stepped-Al shock standard (\~ 300 µm
width across the sample area). Schematically (*right*), VISAR operates
by splitting the laser light reflected off a sample (including the
stepped shock standard within the sample area) with a beam splitter, and
recombining the two images at the detector after one of them has been
sent through a delay line (e.g., a fiber-optic loop, indicated on the
upper path). Thus, the detector records superimposed images that show
the sample at two different time intervals; the resulting fringes
indicate displacements (in multiples of a wavelength), so for a given
delay-line time difference these represent velocities of the reflecting
interfaces.

A set of forward- and backward-travelling stress waves (shock or
rarefaction) is in general created at each interface between diamond,
calibrant and sample, so a complete temporal record is needed of the
various waves that traverse the sample. This is usually accomplished by
velocity interferometry, VISAR (*14*), that provides a record of the
shock and material (particle) velocities inside the sample chamber (Fig.
3). If the initial thickness of the (pre-compressed) sample is known, a
measurement of the shock-wave transit time determines the shock
velocity.

The pressure (*P*~H~), density (ρ~H~) and internal energy change (*E*~H~
-- *E*~1~) of the sample during shock compression is then determined by
the Hugoniot relations that describe conservation of mass, linear
momentum and energy (*V* = 1/ρ is specific volume) (*7*):

> ρ~1~*U~S~* = ρ~H~ (*U~S~* -- *u~p~*) (4)
>
> *P*~H~ -- *P*~1~ = ρ~1~ *U~S~* *u~p~* (5)
>
> *E*~H~ -- *E*~1~ = (1/2) (*P*~H~ + *P*~1~) (*V*~1~ *--* *V*~H~) (6)

Here, subscripts H and 1 indicate the shock-compressed (Hugoniot) state
and the initial, unshocked (in the present case, statically
pre-compressed) state, respectively; *U~S~* is the velocity of the shock
front (assumed to be steady), and *u~p~* is the particle velocity to
which the material is accelerated upon shock loading (without loss of
generality, the material is taken as having *u~p~* = 0 prior to shock
compression). These relations describe a one-dimensional compression
such that, for unit cross-section, *U~S~* and ρ~1~*U~S~* define a volume
and corresponding mass of unshocked material that is engulfed by the
shock front in unit time. That mass is compressed to a volume *U~S~* --
*u~p~* having a density ρ~H~; the volume change (per unit cross section
and mass engulfed by the shock front in unit time) is thus given by --
*u~p~* in (4). The pressure change across the shock front is the force
per unit cross section, or the mass ρ~1~*U~S~* times the acceleration
*u~p~* in (5). Finally, (6) states that half the -- *P*∆*V*
compressional energy change is lost in accelerating the material to the
velocity *u~p~* on shock loading (the internal energy is expressed in
J/kg = m^2^ s^-2^ here).

It is empirically found that the shock-wave velocity scales linearly
with particle velocity for a wide variety of materials over a moderate
range of compressions (*7, 12, 15, 16*):

> *U~S~* = *c* + *s u~p~* (7)

Therefore, the Hugoniot pressure (5) scales as \~ *u~p~*^2^ and the
energy change (6) deposited into unit volume of the sample scales as \~
*u~p~*^3^. For a laser-produced shock wave, assuming the energy
deposited into the sample is proportional to the laser intensity *I*,
one consequently expects the shock pressure to scale roughly as

> *P* \~ *I* ^2/3^ (8)

In reality, laser-induced shock pressures appear to rise less rapidly
than (8), the exponent being closer to 0.6 than 0.7, no doubt due to
inefficiencies in laser-target coupling that can become worse as *I*
increases (*17, 18*) and to *U~S~* ultimately increasing sub-linearly
with *u~p~* (deviations from (7) typically involve a negative
contribution quadratic in *u~p~* (e.g., *2*)).

Although reasonable for understanding the conditions achieved by
laser-driven shock waves, (8) is inadequate for determining the
properties -- notably, the equation of state -- of a sample at high
pressures. Instead, one applies the fact that conservation of mass and
momentum require that both the particle velocity and pressure be
constant across each interface traversed by the shock wave(s) (*7, 15*).
Measuring the shock velocity, hence pressure, density and particle
velocity in the stepped shock-wave standard (blue point in Fig. 4),
determines the magnitude of the stress wave entering the sample itself.
The material velocity and pressure of the sample and standard are
brought to the common values *u~p~* and *P*~H~ across the interface (red
point in Fig. 4): the pressure in the standard decreases or increases,
respectively, depending on whether it is less or more compressible than
the sample (Fig. 4 illustrates the former case, with the pressure drop
in the standard indicated by the curved blue arrow; in detail, a
correction is made in order to account for the fact that the
decompression follows an isentrope rather than the Hugoniot).

![](media/image5.pct)

**Fig. 4.** Impedance matching solution for the Hugoniot pressure
(*P*~H~) and particle velocity (*u~p~*) in the sample, as determined
from the shock velocity *U~S~* measured across the sample that by (5)
defines the slope of the red line (*P*~1~ is ignored here). The
intersection with the equation of state of the standard (blue curve),
reflected about the pressure--particle velocity state achieved in the
standard (blue point), defines the common state (red point) behind the
forward- and backward-travelling waves in the sample and standard. In a
mechanical-impact experiment, *u*~0~ would correspond to the impact
velocity of the standard into the sample.

**Conditions Achieved**

In order to evaluate the conditions generated in laser-shock experiments
on pre-compressed samples, we calculate the Hugoniot equation of state
by way of the Mie--Grüneisen approach that takes the sample pressure
(Hugoniot pressure *P~H~* achieved on shock loading) as arising from two
terms, compression along a reference path to the final volume (*V*) plus
thermal pressure at that (constant) volume (*15, 16*):

> *P*~H~ (*V*) = *P*~S~(*V*) + (γ/*V*) \[*E*~H~(*V*) -- *E*~S~(*V*)\]
> (9)

Here, the reference path is an isentrope (indicated by subscript *S*),
and the Grüneisen parameter γ = *V*(∂*P*/∂*E*)*~V~* depends on volume
but is dimensionless and assumed not to depend on temperature.

The internal energy along the isentrope, *E*~S~(*V*), is given by the
isentropic equation of state *P*~S~(*V*) because -- (∂*E*/*∂V*)*~S~* =
*P*. We specifically use the Eulerian finite-strain formulation for the
isentrope, motivated by the fact that the Cauchy stress (the trace of
which gives the pressure) is intrinsically a function of Eulerian strain
(*19*), and that the resulting equation of state is empirically found to
successfully match experimental measurements involving both finite and
infinitesimal compression (e.g., wave-velocity measurements) (*16, 20*).
That is, the internal energy change upon isentropic compression is
assumed well-described by a Taylor expansion in the Eulerian
finite-strain measure *f* = (1/2) \[(*V*/*V*~0~)^--2/3^ -- 1\] (defined
positive on compression)

∆*E~S~* = (9/2) *V*~0~ *K*~0*S*~ *f* ^2^ \[1 + (*K*~0*S*~*'* -- 4) *f* +
...\] (10)

*K* is the bulk modulus, subscript zero indicates zero-pressure
conditions and prime is for differentiation as a function of pressure.
The coefficients have been evaluated in (10) such that *P*~S~ and
∆*E~S~* both vanish as *f* goes to zero. The resulting *P--V* equation
of state (Birch--Murnaghan form) is

> *P~S~* = 3 *K*~0*S*~ *f* (1 + 2*f* )^5/2^ \[1 + (3/2)(*K*~0*S*~*'* --
> 4) *f* + ...\] (11)

Combining (9) with (6) yields

> *P*~H~ = {*P*~S~ + (γ/*V*~H~)\[(*P*~1~(*V*~1~ -- *V*~H~)/2
> +$\int_{V_{1}}^{V_{H}}P_{S}\text{dV}$\]} {1 -- (γ/*V*~H~) (*V*~1~ --
> *V*~H~)/2}^--1^ (12)

with *P*~1~ = *P*~1~(*V*~1~) being the pre-compression pressure at
volume *V*~1~, and *P*~H~ = *P*~H~(*V*~H~) and *P*~S~ = *P*~S~(*V*~H~)
are the Hugoniot and isentrope pressures at volume *V*~H~. Here, we
ignore the possibility of phase transformations in order to avoid
complicating the discussion, but such transformations (e.g.,
solid--solid, or melting) can be taken into account if the equation of
state and initial energy of the high pressure phase is known.
Consequently, applying (10) and (11) to (12), the Hugoniot pressure
normalized by the zero-pressure adiabatic bulk modulus is

> $\frac{P_{H}}{K_{0S}} = \left\{ A + B + C \right\}\left\{ 1 - \frac{g}{2}\left\lbrack \left( \frac{1 + 2f_{H}}{1 + 2f_{1}} \right)^{\frac{3}{2}} - 1 \right\rbrack \right\}^{- 1}$
> (13a)

*A* = 3 (1 + 2*f~H~*)^3/2^ *f~H~* {1 + \[2 + (3/2) (*K*~0*S*~*'* -- 4 --
γ)\] *f~H~*

> \+ 3 (*K*~0*S*~*'* -- 4) \[1 -- (γ/2)\] *f~H~* ^2^ + ...} (13b)

*B* = 9 (γ/2) (1 + 2*f~H~*)^3/2^ *f*~1~ ^2^ \[1 + (*K*~0*S*~*'* -- 4)
*f*~1~ + ...\] (13c)

*C* = 3 (γ/2) (1 + 2*f*~1~)^3/2^ *f*~1~ \[(1 + 2*f~H~*)^3/2^ -- (1 +
2*f*~1~)\] \[1 + (3/2) (*K*~0*S*~*'* -- 4) *f*~1~ + ...\] (13d)

Without pre-compression, the terms *B* and *C* vanish and the
denominator in (13a) is simplified.

In order to focus on general scaling relations, rather than detailed
calculations for specific materials, we assume *K*~0*S*~*'* = 4
(second-order or Birch equation of state), γ/*V* = γ~0~/*V*~0~ =
constant and γ~0~ = 1.5 because these are typical values for condensed
matter (*K*~0*S*~*'* ≈ 3-6 and γ~0~ ≈ 1-2 in most instances) (*16*). In
addition, we treat the pre-compression as being isentropic rather than
isothermal, ignoring the percent-level difference between the isotherm
and isentrope pressure at volume *V*~1~. The results show that Gbar (100
TPa) pressures are expected for materials compressed \~ 10- to 20-fold
for the Hugoniot and isentrope (or isotherm), respectively (Fig. 5).
Detailed pressures would differ for different parameter values than
those assumed here (larger values of γ increase the Hugoniot pressure at
a given volume, and larger values of *K*~0*S*~*'* increase both the
adbiabat and Hugoniot pressure at a given volume). Also, more terms may
be needed in the finite-strain expansions (10), (11) and (13) at high
compressions; by the same token, a limitation of the linear *U~S~* --
*u~p~* relation (7) is evident from the figure (it can be shown that the
Hugoniot pressure becomes infinite for a compression ρ/ρ~0~ = *s*/(*s*
-- 1) = 5 for the value of *s* used here (*15*)).

![](media/image6.pct)

**Fig. 5.** Predicted pressure--density equations of state for condensed
matter, due to isentropic compression (Adiabat: heavy dark blue curve),
shock compression (Hugoniot: heavy red curve) and shock compression of
samples pre-compressed to initial densities of ρ/ρ~0~ = 1.1, 1.5, 2.0
and 3.0 (unlabelled thin red, green, turquoise and blue curves: see Fig.
6) assuming *K*~0*S*~*'* = 4 and γ~0~ = 1.5. Pressure and density are
normalized to the zero-pressure bulk modulus and density, respectively,
and the Mbar (100 GPa) and Gbar (100 TPa) pressure regimes are indicated
based on a typical value of *K*~0*S*~ = 10^11^ Pa (corresponding central
pressures for Earth, Jupiter and super-giant planets are indicated on
the right). The Hugoniot for the linear *U~S~*--*u~p~* relation (7) and
the density dependence of the electron--gas pressure, *P~EG~* \~ ρ^5/3^
(*8*) are shown by thin black and grey lines (because *c* in (7) is the
zero-pressure bulk sound velocity, (*K*~0*S*~/ρ~0~)^1/2^, its value is
absorbed in the pressure normalization used here; in accord with
*K*~0*S*~*'* = 4 for the finite-strain calculations, we set *s* = 5/4
(*16*)). Conditions near zero pressure are shown on a linear plot
(*inset*) to complement the log--log plot of the main figure.

The effect of pre-compression is to significantly decrease the thermal
pressure of the Hugoniot state, with much of the *P*--ρ regime between
the Hugoniot and adiabat (or isotherm) being accessible with as little
as 50 percent (1.5-fold) initial pre-compression (Fig. 5). Thus
pre-compression is closely analogous to the application of multiple
shocks, including in the fact that breaking a shock front into as few as
4 reverberations makes the compression nearly isentropic (*21*). As
compressible fluids, such as H~2~ and He of planetary interest, can be
subjected to relatively large pre-compressions, it is evident that the
high-pressure thermodynamic state can be effectively tuned over a broad
range of temperatures or internal energies (Fig. 6).

![](media/image7.pct)

**Fig. 6.** Internal energy as a function of pressure corresponding to
Fig. 5, showing the adiabat and the Hugoniots for initially uncompressed
and pre-compressed samples. Approximate dimensional values for the axes
are indicated assuming *V*~0~ \~ 5 cm per mol of atoms and *K*~0*S*~ =
10^11^ Pa; a typical pre-compressed sample size is about 400 µm diameter
by 10 µm thick, or roughly 300 nmol of atoms. Note that the pressure
dependence of the Hugoniot energy for the linear *U~S~* -- *u~p~*
relation (7) is similar to that derived from the Mie--Grüneisen analysis
(9), even though the analogous pressure--density equations of state
differ considerably (Fig. 5).

Megajoule-class lasers represent the state of the art in facilities
currently under development for laser-shock experiments (*22*). As these
consist of \~10^2^ beams, each delivering 1-10 kJ, Fig. 6 suggests that
energies corresponding to Gbar pressures should be deliverable to a
pre-compressed sample even if only a fraction of the beams can be used
with limited efficiency (e.g., ten 1 kJ beams coupled at 1 percent
efficiency to provide 100 J in the sample). As a result, Gbar pressures
relevant to large planetary interiors should become accessible in the
laboratory for the first time.

One of the key benefits of the high energy-density laser facilities is
not only that they deliver pulses having high power (\~ PW/cm^2^) over
the 0.5-1 mm width of the sample area, but also that they can do so for
the relatively long period of \~ 10-20 ns (versus the τ \~ 1-4 ns
effective pulse width of current facilities) (*22*). This is directly
relevant to our experiments, because the shock front is followed by a
rarefaction wave that develops at the end of the laser pulse (i.e., at
time τ) and catches up with the shock in a time interval ∆*t* from the
initiation of shock loading. The shock-wave thus travels a distance
*U~S~* ∆*t* before being attenuated. The rarefaction starts after the
interface has traveled a distance *u~p~*τ, and travels at approximately
the velocity *U~S~* + *u~p~* because the material is moving at velocity
*u~p~* and the local (high-pressure) sound velocity is about equal to
the shock velocity. Therefore, the catch-up distance is

> ∆*x* = *U~S~* ∆*t* ≈ (*U~S~* + *u~p~*)(∆*t* -- τ) + *u~p~*τ (14)

such that

∆*x* ≈ *U~S~*^2^ τ / *u~p~* \~ (10^2^ µm/ns) τ (15)

As a result, a 10-20 ns pulse width allows use of a \~ 1-2 mm thick
diamond on the entry side, typical of the anvils that are used in
static-compression experiments at Mbar pressures. Rather than being
limited to the 1-10 GPa pressures, as at present, pre-compressions into
the 100 GPa range should thus be possible in experiments at the largest
laser facilities under development. That is, samples already transformed
to a high-pressure (e.g., metallic) state could serve as starting
materials for experiments to the 10-100 TPa level.

![](media/image8.pct)

**Fig. 7.** VISAR records of shock-loaded H~2~O (pre-compressed to \~ 1
GPa) showing the transition from transparent behavior at *P* \~ 50 GPa
and *T* \< 3500 K (*left*: reflection of diamond-sample interface is
visible through the shock-compressed sample); to opaque at *P* \~ 100
GPa and 3500 \< *T* \< 9000 K (*center*); to reflecting at *P* \> 150
GPa and *T* \> 9000 K (*right*: reflection from shock front evident from
time-dependent fringes) (*13*).

**Initial Experiments and Future Potential**

Fig. 7 illustrates the potential of laser-shock experiments on
pre-compressed materials. Here, VISAR is used to characterize the
optical properties of the sample, as well as determining the Hugoniot
pressure and density. In addition, an estimate of the blackbody
temperature of the sample is obtained by optical pyrometry. The
experiments clearly show that H~2~O transforms from a transparent
dielectric at low pressures and temperatures to a metallic-like state
when taken to pressures and temperatures exceeding 150 GPa and 9000 K
(*13*). The profound change in outer, valence-electron states --
chemical bonding -- induced by high pressures and temperatures is
visibly evident.

That pressure and temperature can be separately tuned is crucial,
however, because either induces electronic changes in materials. Helium,
for instance, can be either thermally ionized or pressure-ionized, and
it is by varying the initial compression that one can experimentally
validate theoretical expectations of the conditions under which the
insulator--metal transition takes place (Fig. 8).

![](media/image9.pct)

**Fig. 8.** Predicted contours of electrical conductivity (thin grey
solid and dashed curves) for He as a function of pressure and
temperature, showing that metallic properties can be induced either by
high *P* or by high *T*. These influences can be separately documented
by varying the initial density of the sample: dashed contours from lower
left toward upper right, colored for low pre-compressions (1- to
3.5-fold initial compression) and black for 5- and 7-fold initial
compression. Conditions at which several experiments have been performed
are indicated by colored symbols, for which the electrical conductivity
can be inferred from optical absorption and reflectivity (see Fig. 7). A
model isentrope for Jupiter's interior is shown for comparison.

These results illustrating dramatic changes in chemical bonding at Mbar
(100 GPa) conditions reinforce the significance of being able to achieve
significantly higher pressures in the future (Fig. 6). Evidently,
compressional-energy changes can reach keV in the Gbar (100 TPa) regime,
comparable to energies of core-electron orbitals. Deep-electron levels
within the atom can therefore participate in chemical bonding, and an
entirely new type of chemistry becomes accessible in a (sub-nuclear)
regime that is as yet unexplored by experiments.

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