1. Introduction

Interest in the metallization of hydrogen dates from

1935 when Wigner and Huntington[1] predicted that at

sufficiently high density �at temperature T = 0 K solid

H2 would dissociate into solid H. Both electrons are lo-

calized on the H2 molecule and so the molecular solid is

an insulator. At sufficiently high density the PdV com-

pressive energy of the monatomic solid is less than that

of molecular solid, which drives the dissociative transi-

tion from the molecular to the monatomic phase. Solid H

has one electron per band and is a metal. Thus, this phase

transition is accompanied by an insulator-metal transition

(IMT). In 1935 Wigner and Huntington estimated the

pressure corresponding to the density of this IMT to be

about 25 GPa (0.25 Mbar). The quantum physics in their

calculation had then only recently been developed and

their calculation was a test of the new quantum theory.

However, this IMT is yet to be observed experimentally

up to pressures approaching 400 GPa near 0 K.

Theoretical predictions of metallization below 400 GPa

have been proven incorrect by experiments in diamond

anvil cells (DACs). The facts that this IMT of element

Z = 1 has neither been observed experimentally nor cor-

rectly predicted theoretically pose as challenging a prob-

lem as ever encountered in condensed matter physics.

Pressures above 300 GPa have been achieved in

H2 in a DAC, but still higher pressure is required. Based

on history, it will be some time before the IMT of H2

driven by pressure alone will be observed experimen-

tally. However, the addition of thermal energy might

drive this transition. The free energy has a term - TS,

where S is entropy. Dissociation at sufficiently high T in-

creases entropy and minimizes free energy. However, to

produce a metal, T should be small relative to the Fermi

temperature TF of condensed H (T/TF � 1). Thus far, it

has not been possible to heat H2 in a DAC because hy-

drogen rapidly diffuses out of its sample holder. Some

other method is needed.

2. Dynamic adiabatic compression with a two-stage

gun

Compressions by a single shock wave, multiple

shock waves, and along an isentrope are adiabatic be-

cause they occur in a time small compared to times re-

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328

Department of Physics, Harvard University, Cambridge MA 02138, U.S.A.Electronic address: nellis@physics.harvard.edu

特集 衝撃超高圧力研究の新展開

Discovery of Metallic Fluid Hydrogen at 140 GPa andTen-fold Compressed Liquid Density

W.J. Nellis

This paper is the history of the discovery of metallic, fluid hydrogen at 3000 K achieved with a two-stage light-gas gun(2SG) at the Lawrence Livermore National Laboratory (LLNL). The temperature is low in that the electrons are highlydegenerate and the experimental lifetime is long in that the fluid is in thermal equilibrium. The necessary technologyand experimental data were developed over a period of twenty-five years without realizing the end result would be me-tallic fluid hydrogen. The requirements for success were physical intuition, creative thinking concerning experimentsto be performed and how to interpret results, persistence, a willingness to take risks, and luck. Knowing where to lookis not luck, but the cooperation of nature is required to make any discovery. The biggest impediment was the fundingsystem, which discourages risk.[two-stage gun, dense hydrogen, semiconductor-metal transition, dynamic compression]

quired for significant thermal transport and mass diffu-

sion out of the sample. They are also slow compared to

atomic collision times, so that dynamically compressed

material is in thermal equilibrium. In fact, temperature is

tunable between relatively high temperatures achieved

by a single shock on the Hugoniot and relatively low

temperatures on the isentrope. Tuning is done by choice

of the relative amounts of shock and isentropic heating.

This technique is most effective in the case of a com-

pressible low-density material, such as liquid H2, con-

tained between two high-density incompressible anvils.

Pressures up to ~100 GPa, densities up to 12-fold of

liquid-H2 density, and temperatures up to several

1000 K were achieved by impact of a 20-g projectile ac-

celerated to as much as 7 km/s with a 2SG at LLNL

(Fig. 1). Single-shock Hugoniot equation-of-state data

are obtained by measuring impact velocity, the velocity

of the shock wave induced in the target sample, and con-

serving mass, momentum, and internal energy via the

Hugoniot equations. The kinetic energy of 20 g traveling

7 km/s is 0.5 MJ, comparable to that of the 1012 protons

and antiprotons accelerated close to the speed of light at

the Fermilab. The 2SG uses the same energy of a projec-

tile to study novel states of condensed matter, as

Fermilab uses to study novel states of sub-nuclear mat-

ter.

The samples were liquid H2 at 20 K, 25 mm in di-

ameter, and 0.5 mm thick, contained between two 2-mm-

thick anvils of c-cut single-crystal Al2O3. The dynami-

cally compressed samples were 0.05 mm thick. Four

高圧力の科学と技術 Vol. 17, No. 4 (2007)

329

Fig. 1. Photograph of two-stage light-gas gun. Length ofgun is 20 m.

Fig. 2. Photograph of holder of liquid-H2 sample. Outer di-ameter of holder is 12.5 cm. Liquid-H2 coolant was trans-ferred down to Cu connector with 900 bend at bottom of stain-less-steel fill tube. On top of holder are vent line for H2 gasthat evaporates from coolant and inlet to condense H2 or D2

gas into liquid sample at 20 K. Above holder (not shown) was0.5-liter reservoir of liquid-H2 that kept 0.l liter of coolant insample holder filled until gun was fired. Stainless steel coax-ial cables 0.5 mm in diameter were used to measure voltageand allow electrical current to flow. Cryogenic assembly waswrapped with -100 layers of aluminized mylar for thermal in-sulation in evacuated target chamber (10-4 to 10-3 torr) of gasgun. This increased lifetime of coolant, giving more time inwhich to fire gun. No one is in gun-room when gun is fired.

Fig. 3. Schematic of experiment to measure electrical con-ductivity of dynamically compressed liquid H2. For highervalues of conductivity a shunt resistor (not shown) was placedin parallel with conductivity cell. In this way current is flow-ing in shunt resistor prior to induced conduction in hydrogen.This permits current to branch in minimum time (ns).

electrodes 0.75 mm in diameter were used to measure

electrical conductivity. These dimensions are sufficiently

large to enable ns time resolution with the ~100 ns ex-

perimental lifetime. Since the sample holder does not ex-

perience static pressures, its materials were chosen for

their known physical properties at ambient pressure.

Since material strength is not needed to confine the sam-

ple, construction materials were weak and a 100-GPa

shock wave destroys the sample holder in each experi-

ment. Thus, each experimental data point required as-

sembly of its own cryogenic sample holder. A sample

holder is shown in Fig. 2. A schematic of a sample

holder is illustrated in Fig. 3. Effects on thermodynamic

states achieved in hydrogen by single, multiple, and iso-

thermal (0 K) compression are illustrated in Fig. 4.

The projectile launched by the 2SG is a metal-

impactor plate hot-pressed into a plastic sabot. The gun

is driven by up to 5 kg of gunpowder, which compresses

60 g of H2 gas, the light gas in the gun. The 60 g of H2,

if mixed with oxygen, has an explosive energy equiva-

lent of 2 kg of TNT. The liquid-H2 coolant in the sample

holder has an explosive energy content of another 2 kg of

TNT. Care was taken to ensure that H2 does not mix with

O2, and that if they did mix there is insufficient energy

present to spark a reaction. The velocity of the projectile

on impact with the target determines the pressure

achieved. Projectile velocity was measured in free flight

by X-radiography using two pulses with 0.05 �sec

widths. Spatial centers of the pulses were separated by

300 mm.

To perform the experiments discussed below, start-

ing in 1976 I collaborated with A.C. Mitchell, without

whom these experiments would not have been per-

formed. In 1991 S.T. Weir joined us to measure electri-

cal conductivities of quasi-isentropically compressed

fluid hydrogen, the experiments that discovered the

semiconductor-metal transition at 140 GPa. Several tech-

nicians built and installed sample holders in the target

chamber of the 2SG, assisted in the measurements, and

maintained and fired the 2SG. The hydrogen

conductivities were reported previously[2, 3] and dy-

namic compression and its various scientific aspects

have been reviewed[4].

3. The History

In 1976 I joined the Dynamic Compression Group

in H Division. As a graduate student I had measured

electrical and thermal properties of rare-earth metals

from 4 to 300 K using liquid He, H2, and N2 as coolants.

In the early 1970s, there was very little federal support

for basic research in the U.S. When the opportunity arose

to do condensed-matter research at high pressures at

LLNL, I took it. Given the complexity of gas-gun experi-

ments, I teamed with A.C. Mitchell who had extensive

experience making fast measurements and knowledge of

the shock-compression literature.

In those days “dynamic compression” meant shock

compression, that is, compression by a single shock

wave (Hugoniot). My first measurements were Hugoniot

curves of fluids in Jupiter, Saturn, Uranus, and Neptune.

These planets accreted from nebular gases of H2, He,

CH4 , NH3 , and H2 O. The slow accretion process is

isentropic starting from extremely low densities. Shock

compression of liquids causes temperature to rise quickly

with shock pressure. At some high pressure and tempera-

ture the isentrope from low density gas crosses the

Hugoniot of the liquid. These shock-compressed fluids

are semiconductors near the Hugoniot and highly degen-

erate metallic fluids at higher densities along isentropes

starting from points on the Hugoniot. When the initial

funding from outside LLNL to study planetary liquids

disappeared in 1978, I obtained funding within LLNL by

高圧力の科学と技術 Vol. 17, No. 4 (2007)

330

Fig. 4. Illustration of how calculated pressure and densityachieved by dynamic compression of liquid H2 are tuned byvarying time over which pressure is applied. Single shocks(Hugoniot) produce high thermal and total pressures and rela-tively low compressions (long-dashed curves). Multipleshocks produced by reverberation achieve substantially lowertemperatures and thermal pressures and substantially highercompressions (solid curves), relatively close to 0-K isotherm(short-dashed curve)[3].

pointing out that we were studying reaction products of

detonated explosives: H2, N2, CO, O2, CO2, NH3, H2O,

hydrocarbons, and mixtures. Planetary fluids and prod-

ucts of reacted explosives are essentially the same mo-

lecular fluids at comparable pressures and temperatures.

Previously, many experiments on liquids had been

performed using shock waves generated by planar sys-

tems driven by high explosives. Our gas-gun experi-

ments would reach twice the pressures achieved

previously. Since very little Hugoniot data on cryogenic

liquids had been measured with a 2SG, I wanted to do

study many liquids. For this reason I designed cryogenic

sample holders to contain liquid-H2 coolant, with the

flexibility to readily adapt them for other cryogenic-

liquid coolants or for the flow of cold N2 gas. In this

way, we studied liquid H2/D2, He, N2, CO, O2, Ar, CH4,

Xe, CO2, and NH3. We also studied H2O, hydrocarbons,

and synthetic Uranus, a mixture of water, ammonia, and

isopropanol representative of the interiors of Uranus and

Neptune. However, because temperature increases rap-

idly with single-shock pressure, at sufficiently high pres-

sures materials get so hot that they reach a limiting or

maximum shock compression of only four-fold (4 times

initial density), insufficient to reach a degenerate (metal-

lic) state in hydrogen. We also developed techniques to

measure electrical conductivity under single shock by in-

serting electrodes into the liquid and we determined

gray-body temperature from the spectral dependence of

thermal emission from the shock front. For many liquids

we measured states reached by a second shock starting

from the first-shock state. These are called double-shock

states. For liquid hydrogen, a maximum compression of

about six-fold can be achieved with two shocks, again

not sufficient to reach a degenerate phase. The states

reached with one or two shocks cause multi-atomic mo-

lecular liquids to dissociate and react chemically. These

fluids are semiconducting.

In those days relatively little Hugoniot equation-of-

state data was available for solids used in shock experi-

ments at the pressures achieved by the 2SG. The

Hugoniot is required in the data analysis for any solid

that affects the state reached in the liquid sample. Such

solids are called standards and are used as impactor

plates, metal walls containing liquid samples, and anvils

used to achieve doubly or multiply shocked states.

Because of the rapid propagation of errors in the analysis

of shock data, it is not acceptable to extrapolate data ob-

tained at lower pressures. For this reason we measured

the Hugoniots of Al, Cu, Ta, Pt, and Al2O3 up to 200 GPa

and higher.

While our original intent had been to compress liq-

uid H2 quasi-isentropically with a reverberating shock

wave, we first wanted to gain experience with the com-

plex experimental system by doing single-shock and

double-shock experiments on molecular reaction prod-

ucts of detonated explosives. These are easier to do than

H2. We almost spent too much time doing this before

moving on to multiply shocked states. We investigated

singly and doubly shocked states until 1990, one reason

for which was they involved little risk. However, the

Cold War ended in 1989 and we were at a defense labo-

ratory.

In 1990 Art Mitchell and I measured electrical

conductivities of liquid H2 on the Hugoniot between 10

and 20 GPa, the first time the electrical conductivity of

condensed hydrogen had been measured at any pressure.

At the same time, at our small two-stage gun Sam Weir

was shock-compacting powders of high-temperature

superconducting oxides with a shock reverberating in the

powder between Cu anvils. We decided to combine ele-

ments of both experiments; i.e., to measure the electrical

conductivity of liquid H2 as it was compressed by a

shock reverberating between two Al2O3 anvils. Computer

simulations showed that a compression of about 10-fold

would be achieved with about ~10 shocks. Because the

pressure achieved by multiple shock compression is

equal to the first shock pressure in one of the anvils, in-

dependent of the equation of state of the liquid, we could

determine pressure in the liquid by measurement of

impactor velocity. By using electrically insulating Al2O3

anvils, we could achieve a pressure of 200 GPa in dense

fluid hydrogen, ten times higher than achieved by a sin-

gle shock, and measure its electrical conductivity with

electrodes (Fig. 3). All we had to do was replace the

5 mm-thick liquid H2 layer in the single-shock experi-

ments with a composite specimen consisting of a 2 mm-

thick Al2O3 crystal, followed by a 0.5 mm-thick layer of

liquid H2, followed by a second Al2O3 crystal.

Conventional wisdom said that one should search

for metallic hydrogen near 0 K, as Wigner and

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331

Huntington had said in 1935. Since by the early 1990s

metallic hydrogen near 0 K had yet to be observed ex-

perimentally, something else needed to be tried in addi-

tion to compressing H2 in a DAC. We could make dense

hydrogen at 200 GPa at a temperature that was less than

that achieved by a single shock at 20 GPa and we knew

how to measure electrical conductivity in the process.

Suddenly it became obvious that we should try to find

metallic hydrogen; i.e., to take the risk. Since the

required pressure at 0 K predicted at the time was

300 GPa, it was quite possible that we would not find it.

But what would we find at these conditions that essen-

tially had not before been studied? It was important that

the experiments be done and we set out to do them.

In the early 1990s we no longer had funding in our

group to do hydrogen experiments. So in 1991 Sam Weir

and I wrote a proposal and submitted it to the Laboratory

Directed Research and Development Program (LDRD).

Sam was a postdoctoral researcher nearing the end of his

appointment. The main goal of LDRD was to provide

postdoctoral researchers with projects that would lead to

a career at LLNL. The proposal should also study an

“interesting” scientific problem. Because individual

reviewers have varying biases as to the definition of

“interesting”, the scientific importance of a proposed

study is not necessarily obvious to the deciders. From

1985 to 1990 I tried yearly and unsuccessfully to get an

LDRD grant on a variety of topics.

Sam was the only young person at LLNL at that

time who knew how to measure electrical conductivities

of shock-compressed matter. So the main point of our

proposal was to give Sam the opportunity to carry his ex-

pertise into a career position. The reviewers understood

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332

Fig. 5. Electrical conductivities of Cs (open inverted trian-gles) and Rb (open squares)[7], oxygen (solid triangles)[5],nitrogen (solid circles)[6] and hydrogen (solid diamonds)[3]versus a*/D-1/3, where a* is effective Bohr radius of electronsin atom that form conduction band in fluid and D is numberdensity of atoms. D1/3a* is ratio of effective atom size to dis-tance between atoms[6].

Fig. 6. (a) Charge densities (4�r2�*�) of valence electrons of H, N, O, Rb, and Cs atoms versus radial distance r from nucleusof each atom. For comparison charge densities have been shifted radially so that maximum of each curve is at 1 bohr. (b) Curvesin (a) plotted on expanded scale[6].

the scientific importance and awarded us the grant. It

took the first-year to do the first experiment, which was

successful. Sam’s two-year postdoctoral position expired

in 1992 at the end of the first year of our LDRD-funded

proposal. I requested that LDRD renew us for the second

year to give me, his group leader, the best chance of get-

ting Sam promoted to a career position. LDRD awarded

us the second year of funding. Unfortunately, I was not

able to convince the H Division Leader to promote Sam.

So Sam moved to another division at LLNL; Art

Mitchell was already retired.

Fortunately, Art continued to work on this project in

retirement and Sam came over to our 2SG when we per-

formed shock reverberation experiments on hydrogen. It

took three years to complete ten experiments and a year

to analyze the data. In 1996 we published the first re-

sults. This work was published with trepidation because

we knew we had not thought of every possibility that

could explain our data. Nevertheless, we were confident

of our interpretation. Fortunately, no criticism emerged

that we could not answer. We then received funding for

postdoctoral researchers, Ricky Chau and Marina Bastea.

Our model to explain hydrogen did not depend on the

fact that the sample was hydrogen. We expected similar

results for liquid oxygen and nitrogen, as were

observed[5, 6]. Measured conductivities of fluid Cs and

Rb at similar conditions undergo the same semiconduc-

tor-metal transition[7]. Similar experiments on fluid hy-

drogen compressed by a reverberating shock driven by

high explosives yielded similar results[8].

It took until 2002 to demonstrate that fluid H, N, O,

Rb, and Cs all undergo the same Mott transition to mini-

mum metallic conductivity (Fig. 5)[4, 6]. The semicon-

ductor-metal transition occurs by overlap of quantum-

mechanical radial charge-density distributions on

adjacent atoms in each fluid (Fig. 6). Their metallic

conductivities are relatively low, about 2000/(ohm-cm),

because conductivity is dominated by disorder. The de-

generacy factor of metallic H is T/TF~0.01, essentially

that of solid Cs at room temperature. The density de-

pendence of the approach to minimum metallic conduc-

tivity is determined by the radial extent of the charge-

density distribution.

4. Risk

The technology needed to perform and interpret

these experiments existed before I started this project.

This project had significant funding for fifteen years

when we started searching for metallic hydrogen. The

obvious question then is “Why did it take so long?” At

LLNL one could get substantial funding with enough

“salesmanship. However, if the goal is not reached in

~3 years, most such projects are terminated. On the other

hand, if one kept a low profile by not requesting support

for a visible project, then one could work for a longer pe-

riod at a slower rate. I chose the “low-profile” route. The

difficulty with this is that one tends to become more con-

servative with time and does not want to risk failure be-

cause it might result in loss of funding that one does

have. We were successful because we were able to per-

sist in working on molecular liquids for twenty years.

We were fortunate because the reviewers of our proposal

awarded it to us. We were lucky because nature cooper-

ated in giving us what we were looking for.

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333

References

[1] E. Wigner, H.B. Huntington: J. Chem. Phys., 3, 764(1935).

[2] S.T. Weir, A.C. Mitchell, W.J. Nellis: Phys. Rev.Lett., 76, 1860 (1996).

[3] W.J. Nellis, S.T. Weir, A.C. Mitchell: Phys. Rev. B,59, 3434 (1999).

[4] W.J. Nellis: Rep. Prog. Phys., 69, 1479 (2006).[5] M. Bastea, A.C. Mitchell, W.J. Nellis: Phys. Rev.Lett., 86, 3108 (2001).

[6] R. Chau, A.C. Mitchell, R.W. Minich, W.J. Nellis:Phys. Rev. Lett., 90, 245501 (2003).

[7] F. Hensel, P. Edwards: Physics World, 4, 43 (1996).[8] V.E. Fortov, V.Ya. Ternovoi, M.V. Zhernokletov,M.A. Mochalov, A.L. Mikhailov, A.S. Filimonov, A.A.Pyalling, V.B. Mintsev, V.K. Gryaznov, I.L.Iosilevskii: JETP, 97, 259 (2003).

[Received April 20, 2007]© 2007日本高圧力学会