Pathways to metallic hydrogen
The traditional pathway that researchers have used in the goal of producing atomic metallic hydrogen is to compress samples with megabar pressures at low temperature. A number of phases have been observed in solid hydrogen and its isotopes, but all are in the insulating phase. The results of experim...
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irk-123456789-1171282017-05-21T03:03:20Z Pathways to metallic hydrogen Silvera, Isaac F. Deemyad, Shanti 7th International Conference on Cryocrystals and Quantum Crystals The traditional pathway that researchers have used in the goal of producing atomic metallic hydrogen is to compress samples with megabar pressures at low temperature. A number of phases have been observed in solid hydrogen and its isotopes, but all are in the insulating phase. The results of experiment and theory for this pathway are reviewed. In recent years a new pathway has become the focus of this challenge of producing metallic hydrogen, namely a path along the melting line. It has been predicted that the hydrogen melt line will have a peak and with increasing pressure the melt line may descend to zero Kelvin so that high pressure metallic hydrogen may be a quantum liquid. Even at lower pressures hydrogen may melt from a molecular solid to an atomic liquid. Earlier attempts to observe the peak in the melting line were thwarted by diffusion of hydrogen into the pressure cell components and other problems. In the second part of this paper we present a detailed description of our recent successful demonstration of a peak in the melting line of hydrogen. 2009 Article Pathways to metallic hydrogen / Isaac F. Silvera, Shanti Deemyad // Физика низких температур. — 2009. — Т. 35, № 4. — С. 413-422. — Бібліогр.: 65 назв. — англ. 0132-6414 PACS: 62.50.–p, 64.60.Ej, 67.63.–r http://dspace.nbuv.gov.ua/handle/123456789/117128 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals Silvera, Isaac F. Deemyad, Shanti Pathways to metallic hydrogen Физика низких температур |
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The traditional pathway that researchers have used in the goal of producing atomic metallic hydrogen is to compress samples with megabar pressures at low temperature. A number of phases have been observed in solid hydrogen and its isotopes, but all are in the insulating phase. The results of experiment and theory for this pathway are reviewed. In recent years a new pathway has become the focus of this challenge of producing metallic hydrogen, namely a path along the melting line. It has been predicted that the hydrogen melt line will have a peak and with increasing pressure the melt line may descend to zero Kelvin so that high pressure metallic hydrogen may be a quantum liquid. Even at lower pressures hydrogen may melt from a molecular solid to an atomic liquid. Earlier attempts to observe the peak in the melting line were thwarted by diffusion of hydrogen into the pressure cell components and other problems. In the second part of this paper we present a detailed description of our recent successful demonstration of a peak in the melting line of hydrogen. |
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Silvera, Isaac F. Deemyad, Shanti |
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Silvera, Isaac F. |
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Pathways to metallic hydrogen |
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Pathways to metallic hydrogen |
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Pathways to metallic hydrogen |
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Pathways to metallic hydrogen |
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Pathways to metallic hydrogen |
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pathways to metallic hydrogen |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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7th International Conference on Cryocrystals and Quantum Crystals |
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Pathways to metallic hydrogen / Isaac F. Silvera, Shanti Deemyad // Физика низких температур. — 2009. — Т. 35, № 4. — С. 413-422. — Бібліогр.: 65 назв. — англ. |
| series |
Физика низких температур |
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AT silveraisaacf pathwaystometallichydrogen AT deemyadshanti pathwaystometallichydrogen |
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2025-07-08T11:41:42Z |
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2025-07-08T11:41:42Z |
| _version_ |
1837078837196750848 |
| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4, p. 413–422
Pathways to metallic hydrogen
Isaac F. Silvera and Shanti Deemyad
Harvard University, Cambridge, MA 02138, USA
E-mail: silvera@physics.physics.edu
Received December 12, 2008
The traditional pathway that researchers have used in the goal of producing atomic metallic hydrogen
is to compress samples with megabar pressures at low temperature. A number of phases have been observed
in solid hydrogen and its isotopes, but all are in the insulating phase. The results of experiment and theory
for this pathway are reviewed. In recent years a new pathway has become the focus of this challenge of pro-
ducing metallic hydrogen, namely a path along the melting line. It has been predicted that the hydrogen melt
line will have a peak and with increasing pressure the melt line may descend to zero Kelvin so that high pres-
sure metallic hydrogen may be a quantum liquid. Even at lower pressures hydrogen may melt from a molecu-
lar solid to an atomic liquid. Earlier attempts to observe the peak in the melting line were thwarted by diffu-
sion of hydrogen into the pressure cell components and other problems. In the second part of this paper we
present a detailed description of our recent successful demonstration of a peak in the melting line of hydro-
gen.
PACS: 62.50.–p High-pressure effects in solids and liquids;
64.60.Ej Studies/theory of phase transitions of specific substances;
67.63.–r Hydrogen and isotopes.
Keywords: metallic atomic phase, high pressure, melting line of hydrogen.
1. Introduction
One of the great challenges of condensed matter phys-
ics is the experimental production of metallic hydrogen in
the laboratory. In 1935 Wigner and Huntington [1] pre-
dicted that at a pressure of 25 GPa (100 GPa = 1 Mbar)
solid molecular hydrogen would dissociate into an atomic
metallic solid. Modern measurements have extended
pressures by over an order of magnitude higher than the
original prediction and find that hydrogen remains in a
non-metallic phase. There is little doubt that at suffi-
ciently high density it will become a metal. The predic-
tion of metallization at 25 GPa was early in the develop-
ment of quantum mechanics in condensed matter. Modern
calculations now predict much higher pressures for the in-
sulator-to-metal (IM) transition, but still remain chal-
lenged in accuracy due to the large zero-point energy
which is important at both low and high pressures and is
not included as a first principles part of many approaches
such as modern density functional theory.
In 1968 Ashcroft [2] predicted that atomic metallic hy-
drogen may be a high-Tc (possibly room temperature) su-
perconductor, based on a BCS model. Although there
were early efforts to produce metallic hydrogen with
large presses, little progress was made until the late 1980s
when the development of the diamond anvil cell (DAC)
eventually enabled megabar pressures. In 1975 Ramaker
et al. [3] predicted that molecular hydrogen might be-
come metallic before dissociating, and much later Rich-
ardson and Ashcroft [4] predicted that this molecular
metal might be a very high temperature superconductor,
based on a non-conventional superconductivity model.
Recently, Cudazzo et al. [5] have carried out a first princi-
ples calculation of the electron–phonon interaction and
report high-Tc based on a BCS theory. They find very
high Tc’s, increasing with pressure, above about 450 GPa.
Early on, a number of theoretical groups became in-
tensely interested in the high-density properties of hydro-
gen. Brovman et al. [6] predicted that when the pressure
on atomic metallic hydrogen was released the atomic
phase might be stabilized against the molecular phase by
a 1 eV potential barrier, similar to the metastability of dia-
mond relative to graphite. They found that metastable
atomic hydrogen could even be a liquid, based on the
large zero-point motion and weak interaction potentials.
McDonald and Burgess [7] found that dense atomic hy-
drogen might not have a crystalline state. The question of
© Isaac F. Silvera and Shanti Deemyad, 2009
metastability at ambient pressure was considered by
Salpeter [8] and remains an open question. At the present
time a large number of modern calculations, reviewed
elsewhere [9], have predictions that the transition to the
metallic atomic phase might occur at multi-megabar pres-
sures. Modern theoretical techniques have been ex-
tremely successful in predicting the properties of heavier
more strongly interacting atomic and molecular solids as
a function of density. However, hydrogen is very light and
the intermolecular interactions are weak, resulting in
large zero-point motion and energy. Interestingly, there is
zero-point motion for the molecular centers and a
zero-point motion hidden in the internal vibration of the
molecule. As pressure is increased the large zero-point
motion of the molecular centers decreases, but at higher
pressures the internal zero-point energy of the internal
motion is «liberated» to the lattice as electronic densities
redistribute and modify the many-body effective inter-
molecular interactions, so that zero-point energy remains
important. Density functional techniques cannot handle
this motion and energy and do not predict correct gaps.
Molecular dynamics is generally useful for classical mo-
tions, but not for hydrogen at low temperatures. Quantum
Monte Carlo can handle the quantum aspects, but does not
predict gaps [10].
The extension of the predicted transition pressure to
higher pressures than that of Wigner and Huntington has
been strongly influenced by experimental observations.
St�dele and Martin [11] used a modified density func-
tional approach with exact exchange calculations to pre-
dict accurate gaps, resulting in stability of insulating mo-
lecular hydrogen against the metallic phase to 400 GPa or
greater. Experimentally, Narayana et al. [12] reported that
hydrogen remains molecular and transparent to 342 GPa,
while Loubeyre et al. [13] reported that hydrogen turns
opaque in the visible by a pressure of 320 GPa (but
non-metallic) due to a closing energy gap. An explanation
for this apparent contradiction will be given in the next
section [14].
2. Historical developments
2.1. The metal–insulator transition
We start by discussing the highest pressure results just
mentioned, that a lower pressure sample turns black while
a higher-pressure sample remains transparent. Silvera
[14] proposed that these seemingly contradictory reports
may be explained by problems with the high-pressure
ruby scale. Narayana et al. used the x-ray EOS of tung-
sten to determine the pressure, while Loubeyre et al. used
an extrapolation of the ruby scale, which was only cali-
brated to 80 GPa by Mao, Xu, and Bell [15].
One of the problems of the venerable so-called quasi-
hydrostatic 80 GPa calibration was that the pressurization
medium, argon, is not quasi-hydrostatic at high pressure;
only helium and hydrogen remain relatively soft at high
pressure. Thus, to obtain an improved calibration helium
should be used as the pressurization medium. A new scale
based on calibration of ruby in helium, extending to
150 GPa and latest equations-of-state of metals used for
the reference pressure was developed by Chijioke et al.
[16,17]; this scale differed substantially from the earlier
scale at the highest pressures of the calibration. To the ex-
tent that this scale can be extrapolated to the 300 GPa re-
gion, the pressure of Loubeyre et al. would be as much as
50–60 GPa higher [14], removing the contradiction.
It is now believed that hydrogen will become atomic in
the 400–600 GPa region. The darkening of hydrogen and
extrapolations by Loubeyre et al. [13], as well as later
work by Baer et al. [18], along with a number of calcula-
tions tend to support such a belief. In Fig. 1 we show a
possible phase diagram for hydrogen. There are three ex-
perimentally studied regions at lower pressures: the low-
est pressure phase which has an HCP structure, the BSP,
and the A-phases (to be discussed ahead); the high-tem-
perature reverberating shock wave experiments of Weir et
al. [19], who found a conducting liquid phase believed to
be metallic and atomic; and the melting line to about
800 K by Datchi et al. [20] and Gregoryanz et al. [21].
An understanding of the melting line may be key to un-
derstanding the very high pressure properties of hydrogen
and much of this paper will be focused on recent develop-
ments. Diatschenko et al. [22] first studied the melting
line to 373 K and 7.7 GPa and could fit their results to a
modified Simon equation. Datchi et al. and Gregoryanz et
al. found that the experimental melting lines were better
fit with a theoretical Kechin melting curve [23], rather
than a traditional Simon curve. The Kechin form has a
peak in the melting line. Scandolo [24] calculated, using
density functional theory, that at high pressure the melt-
414 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
Isaac F. Silvera and Shanti Deemyad
1000
500
T
,
K
100 200 300 400 500
P, GPa
semiconducting
fluid
metallic fluid
melting line
molecular
metallic
atomic
metallic
molecular insulator
HCPBSP A
Fig. 1. Phase diagram of hydrogen including known low pres-
sure phases (solid lines) in the insulating solid (HCP, BSP,
and A) and possible metallic phase lines.
ing curve might have a negative slope. This was followed
by an extensive ab initio molecular dynamics two-phase
(liquid–solid) high-temperature melting line calculation
by Bonev et al. [25], shown in Fig. 2. A number of re-
markable results were found: the theoretical melting line
indeed has a peak; the peak is below 1000 K; and in the
region above the melting line there is a dissociative tran-
sition from diatomic to monatomic hydrogen (diamond
marker line). Bonev et al., using density functional theory
found this line to be a first order phase transitions
whereas Delaney et al. [26] using quantum Monte Carlo
techniques find a continuous degree of dissociation in
fluid hydrogen with increasing density. Thus, the nature
of dissociation of hydrogen at high pressure and tempera-
ture is an important experimental challenge.
In a quantum solid such as helium, as pressure (den-
sity) is increased the particles at lattice sites become more
localized and behave more classically. This is because
with compression the effective mean field potential that a
lattice particle sits in stiffens up and becomes more har-
monic. In hydrogen at very high pressure it is believed
that the unusual behavior of becoming more quantum (the
ratio of zero-point energy to intermolecular interaction
energy increases at high pressures) is due to a softening of
the effective pair potentials with increasing compression.
Not only are the molecules more weakly bound, but also
the atom–atom bonding weakens [27]. This is supported
by earlier calculations of the interactions in dense hydro-
gen as a function of density [28,29]. The behavior of the
melting line in the region of calculation leads to some in-
triguing extrapolations (not yet confirmed by theory).
First, (Fig. 2) the «diamond» line will intersect the melt-
ing line, so that for higher pressures solid molecular hy-
drogen would melt to atomic hydrogen. Second, the melt-
ing line extrapolates down to T � 0 K, implying that hy-
drogen might be an atomic metallic liquid at very high
pressure. A phase diagram based on these extrapolations
is shown in Fig. 3. The calculation of the melting line by
Bonev et al., valid for higher temperatures, did not in-
clude zero-point energy contributions so that the melting
line calculations could not easily be extended to lower
temperatures. More recently Attaccalite and Sorella [30]
have introduced a novel ab initio MD calculation in
which the approximation maintains validity at lower tem-
peratures. Their work supports the extrapolation. This
implies that there could be a pressure window where the
metallic hydrogen is liquid at T � 0 K. At still higher
pressures the atoms would localize into a solid.
The achievement of accurate theoretical predictions of
the properties of hydrogen under pressure with regard to
metallization has in general been very challenging. Thus,
the first important test for this new pathway to metallic
hydrogen is to demonstrate that a peak exists in the melt-
ing curve. A peak has recently been experimentally dem-
onstrated by Deemyad and Silvera [31] and will be dis-
cussed in detail further in this paper.
The possibility of producing a (high-pressure) liquid
at T � 0 K, with mobile electrons and protons has led to
tantalizing predictions of two component superconduc-
tivity (electrons and protons) as well as superfluidity
in liquid metallic hydrogen [32]. Recently, it has been
shown that the Onsager–Feynman quantization as well
as the London Law in a magnetic field would be vio-
lated [33]. However, we emphasize that violation of On-
sager–Feynman quantization and the London law is for
multi-component superconductors.
Pathways to metallic hydrogen
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 415
1000
800
600
400
200
0 50 100 150 200 250
P, GPa
T
,
K
Fig. 2. The melting line of hydrogen predicted by Bonev et al.
showing experimental data at lower pressures and tempera-
tures. The line at high pressure and temperature with the dia-
mond symbol is the predicted first order liquid–liquid phase
transition from molecular to atomic hydrogen.
2500
2000
1500
1000
500
0 100 200 300 400
T
,
K
P, GPa
Metallic
liquid H
Metallic
liquid H
Metallic
liquid H
at T = 0 K
Semiconducting
liquid
Hugoniot of
fluid H2
Liquid H2 Liquid H
Solid
metallic H
Solid H2
Tmelt
TDiss
HCP
BSP
A
Hydrogen
at high pressure
and temperature
~~
Fig. 3. Phase diagram of hydrogen at high pressure showing
extrapolation of the melting line (below 700 K) to very high
pressure. The melting line of Bonev et al. was carried out
to 700 K. The recent work of Attaccalite and Sorella (filled
circle) confirms the extrapolation to 400 K.
The above predictions follow from some of the most
sophisticated analyzes yet. But, although the electrons
were treated quantum mechanically, nuclei were clas-
sically propagated in the molecular dynamics. Further-
more, the melting line depends on the structure of the
solid below the line. This has not been investigated and
could have some surprises [18]. Still another possibility is
that metallic hydrogen may be metastable so that once
produced at high pressure it could be quenched to ambient
pressure and remain in the metallic state. An experimental
production of metallic hydrogen is needed to resolve
these issues.
2.2. High pressure molecular phases
There are a number of high-pressure phases in the
solid hydrogens. However, it is important to first consider
the ortho–para states of the molecules, as the phase dia-
grams depend critically on the ortho–para concentra-
tions. The instantaneous intermolecular interaction be-
tween H 2 molecules is anisotropic; however, in the solid
the effective interaction depends on the rotational states
of the molecules. The rotational states are labelled by the
rotational quantum number J and its projection M. In the
low-pressure solids, J is a good quantum number; the
splitting between single-molecule rotational states is
BJ J( )�1 where B is the rotational constant (~59 cm–1 �
� 88 K, for hydrogen), whereas the anisotropic interac-
tions are a few degrees Kelvin. Since the rotational
splittings are hundreds of degrees at low temperature, in
equilibrium the J � 0 state is the single-molecule ground
state. The wave function for J � 0, the spherical harmonic
Y YJM ( , )� � � 00, is a constant so that the molecules are in
spherically symmetric states. As a result, for para hydro-
gen the expectation value for the anisotropic intermo-
lecular interactions is zero when the interactions are eval-
uated for the quantum states. The many-body ground state
of the solid is close-packed (HCP), like rare gas solids. As
pressure is increased, the instantaneous (non-quantum
expectation value) anisotropic interactions grow so that
the spherical harmonics become a poorer description of
the single-molecule states. At a critical pressure, the ad-
mixture of J states becomes so large that J is no longer a
good quantum number and the ground molecular states
become non-spherical. This breaks the symmetry of the
ground state as a quantum phase transition and the mole-
cules go into an orientationally ordered phase called the
broken symmetry phase (BSP). By contrast, solid J �1
molecules have p-like distributions and the solids are
orientationally ordered in the Pa3 structure at zero-pres-
sure and low temperature [34]. Thus, the ground state of
the solid depends on the ortho–para species. One of the
most important points is that for the homo-nuclear di-
atomic hydrogens, isolated ortho- and para molecules do
not thermalize with each other and behave as non-identi-
cal molecules.
The ortho–para states are a result of the Pauli Prin-
ciple. Consider isolated hydrogen molecules: the wave
function must be antisymmetric under proton exchange.
Thus, the symmetric even-J rotational states are coupled
to the antisymmetric nuclear spin singlets, with I � 0, and
the odd-J states are coupled to the triplet I �1states. The
former are called para-hydrogen and the latter ortho-hy-
drogen. The nomenclature changes for deuterium (in
which the deuterons are spin�1bosons and the molecular
wavefunctions are symmetric under nucleon exchange).
The ground state with J � 0 is ortho-deuterium (even-J
combines with symmetric I � 0 2, nuclear states) and the
odd-rotational states combine with I �1spin states. Thus,
para-hydrogen and ortho-deuterium behave similarly. A
key point is that transitions between ortho and para (con-
version) are strongly forbidden for isolated molecules,
and the conversion rate is very slow in the interacting
low-pressure solid state. A zero-pressure solid can take
from days to weeks to come to the thermal equilibrium for
the occupation of the rotational states. Thus, it is possible
to produce and study almost pure ortho-hydrogen or
para-deuterium [35] that is out-of-equilibrium and me-
tastable. As pressure is increased, the ortho–para de-
scription remains valid, even though the single-molecule
states change. This was not always clear throughout the
community and it was thought that under pressure this
description was not valid [36]. This picture was clarified
theoretically by Silvera [37].
It is most interesting to study solids of the pure spe-
cies, and methods exist for producing high purity ortho or
para samples. It is clearly vital to know the ortho–para
concentration of a sample. In general, this is difficult to
measure in a DAC, but if the initial concentration and the
conversion rate are known, then one can determine the
state of the solid as a function of time. At elevated pres-
sures the conversion rates increase [38,39] so that con-
version to equilibrium may take hours rather than weeks.
Hydrogen converts much faster than deuterium, as the
conversion mechanism depends principally on the nu-
clear magnetic moment, which is much larger in hyd-
rogen.
In a DAC at high pressure and low temperature (less
than � 20 K) a pure ortho-hydrogen sample will down
convert to para-hydrogen, whereas a para-hydrogen
sample is stable. Thus, it is much easier to study the J � 0
species, maintaining the system at low temperature, with
short time excursions to higher temperatures. It is also
more interesting because of the BSP quantum phase tran-
sition. Most studies have been on para-hydrogen or
ortho-deuterium, and of course ortho–para mixtures, un-
fortunately usually with an undetermined concentration.
416 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
Isaac F. Silvera and Shanti Deemyad
At present there are three well-defined high-pressure
phases that have been experimentally observed in the
solid molecular hydrogens. An example of the phase dia-
gram for ortho-deuterium [40] is shown in Fig. 4; a simi-
lar diagram exists for para-hydrogen. The LP phase (low
pressure, sometimes called phase I) is an HCP solid; the
BSP (broken symmetry phase), first predicted by Raich
and Etters [41], exhibits orientational order of para-hy-
drogen and has been observed in D 2, H 2, and HD (at 28,
110, and 69 GPa, respectively, in the T � 0 limit [42–44]).
At higher pressures a transition to a new phase called the
A-phase (III) takes place. This phase was unexpected and
is believed to be a transition to a lower energy phase of
orientational order [45]. The A-phase occurs at around
150 GPa for hydrogen and deuterium [46,47]. This phase
was first reported to be metallic [48,49], but later it was
shown that it is molecular insulator [50–53]. No other
phases have yet been found at higher pressures in the
solid.
This background introduction is completed with a dis-
cussion of hydrogen deuteride. HD turns out to be a very
interesting, unusual solid for high-pressure studies. It
does not have the ortho–para designation, as the two nu-
clei in a molecule are not identical. As a consequence, the
transitions between even and odd J states are rapid and
the molecular states in the solid thermalize within milli-
seconds. This has a dramatic effect on the BSP phase line
which is reentrant, as seen in Fig. 5 [44,54], compared to
the monotonically increasing phase line of hydrogen or
deuterium. Silvera et al. [55] explained this by the ther-
mal population of the J �1 state. They proposed that for
each fixed concentration of J �1there is a different phase
line, as shown by the dashed lines in Fig. 5,a. As tempera-
ture is increased in HD and the J �1 states become occu-
pied, the phase line traverses from each of these fictitious
lines to another; as temperature is increased further, the
BSP phase disorders for entropic reasons, leading to the
reentrant behavior. Recently, Hetenyi et al. [56] have de-
veloped a molecular field model for quantum rotors
which reproduces most of the features of orientational
ordering.
In the experimental work the phase line was deter-
mined by a shift in the Raman active vibron mode as the
phase line was crossed, as was done in hydrogen and deu-
terium. However, in HD the shift goes through zero at
about 100 GPa (the shift does not change sign in the
homonuclear species); the Raman lines rapidly broaden
so that it is difficult to follow the phase line to higher
pressures and the uncertainties become large. Recently,
Chijioke and Silvera [54] have extended the phase dia-
gram of HD to higher pressures, and determined the onset
of the A-phase (Fig. 5,b). They used infrared absorption,
as there are IR active vibrons in the BSP phase and none
in the LP phase, so the BSP–LP phase line could be ex-
Pathways to metallic hydrogen
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 417
200
150100
150
100
50
0
T
,
K
P, GPa
50 200
o-D , IR, run 12
o-D , IR, run 22
mixed crystal, Raman, Hemley et al.
mixed crystal, Raman, run2
mixed crystal, IR, run2
LP(I)
BSP (II)
D-A(III)
Phase Diagram
of Deuterium
Fig. 4. The high pressure phase diagram of ortho-deuterium
showing the LP, BSP and A-phases.
140
120
100
80
60
40
20
0 20 40 60 80 100 120
T
,
K
T
,
K
P, GPa
P, GPa
150
100
50
0
0
20 40 60 80 100 120 140 160 180
a
b
c = 2 ·10
–2
c = 1 ·10
–3
c = 1 ·10
–6
c = 0
HD
EQQ order, c=1
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HCP phase
BSP phase
A phase
HD IR phase lines
D2 phase line
HD Raman phase line [5]
Fig. 5. The phase diagram of HD: as determined by Raman
scattering (a); by IR spectroscopy (b). The symbols represent
P–T points where infrared spectra were recorded to determine
the phase diagram.
tended to higher pressures. The emergence of the A-phase
was detected by observation of a new IR active vibron.
HD has one more feature that distinguishes it from the
homonuclear diatomic hydrogens, and that is a permanent
electric dipole moment, resulting from the displacement
of the electronic charge from the nuclear charge. With a
permanent dipole moment, p, the rotational transitions are
IR active, which enabled Trefler and Gush [57] to spec-
troscopically determine its value to be 5.85·10–4 D.
3. The melting line of hydrogen
Over the past decades the pathway to metallic hydro-
gen that has been followed has been to compress solid hy-
drogen at low temperature to a sufficiently high density to
achieve metallization. In recent years the possibility of
a high temperature pathway along the melting line has
opened up. Although multi-megabar pressures can be
achieved in DACs, the temperature range for studying the
hydrogen melting line by continuous heating to elevated
temperatures has been limited by diffusion of hydrogen
into the gasket or diamonds, followed by embrittlement
and failure of the diamonds. Datchi et al. [20] extended
the range of the melting line to 526 K and 15 GPa. This
experiment was limited in temperature as hydrogen dif-
fused into the metallic gasket at high temperature and the
sample was lost. Gregoryanz et al. [21] extended these
measurements to around 800 K and 44 GPa using a ce-
ramic insert in their gasket that confined the hydrogen
long enough for measurements. Their extension of the
melting line terminated when they could no longer distin-
guish melting by a shift in the Raman active vibron when
crossing the melting line. At elevated temperatures the di-
amonds would embrittle due to hydrogen diffusion and
fail [58]. Both groups found a better fit of the melting line
to a Kechin curve that implied a peak in the melting line at
higher pressures.
Diffusion is a relatively slow and thermally activated
process; hydrogen does not significantly diffuse into dia-
mond at low temperature. In order to study the melting
line at higher temperatures the diffusion must be slowed
or inhibited. There are two conventional ways by which
samples are heated in diamond anvil cells: resistive heat-
ing, as was done by Datchi et al. [20] and Gregoryanz et
al. [21], and CW laser heating [59,60]. In the latter tech-
nique, a high power laser beam is focused on an absorber
in a DAC, as shown in Fig. 6. Laser power as high as 50 W
is used to achieve temperatures of thousands of degrees.
The diamonds also heat but insulation between the hot
sample absorber and the diamond surface prevents the di-
amond from burning or graphitizing. Both of these meth-
ods allow diffusion of hydrogen or helium into the dia-
mond and seriously limit the time that a sample of
hydrogen can be studied at high temperatures.
To overcome this problem we have used the method of
pulsed laser heating to heat samples in DACs [61] and de-
veloped a method to determine the peak temperature of
the sample using CW detection. In this method a platinum
foil is embedded in the hydrogen sample acting as a laser
absorber; it is the foil that heats and warms the adjacent
hydrogen pressing on its surface. Two advantages exist
for pulsed laser heating of hydrogen to reduce hydrogen
diffusion into the confining elements. First, hydrogen
mainly diffuses during the hot pulse and this time is insuf-
ficient for important diffusive changes. Second, the gas-
ket and diamonds do not get very hot [62]. The latter can
be justified by the following argument. Although energy
is flowing from the absorber to the hydrogen to the dia-
monds, the thermal time constants of the components and
sample are very different. The metallic absorber is sub-
stantially smaller than the hydrogen sample and has a
short thermal time constant compared to that of the hydro-
gen. The surface of the absorber warms during the pulse;
the energy then diffuses into the absorber in several mi-
croseconds to a much lower temperature than the peak
temperature. The excess thermal energy from the absor-
ber flows into the hydrogen at an even lower temperature
and is conducted away into the high thermal conductivity
diamonds until the DAC reaches ambient temperature.
We use a Spectra Physics pulsed neodymium vanadate
laser operating at 1.064 �m. A pulse of width � 70 to
200 ns with an energy of a few milijoules (pulse power
can be up to of order ~30 kW) is more than sufficient to
heat the sample so that it is in local thermal equilibrium
(a few ps is sufficient for thermalization). The sample
heats and cools (in several laser pulse widths). With a low
pulse repetition rate, the average power of the laser is
418 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
Isaac F. Silvera and Shanti Deemyad
Fig. 6. Laser heating in the heart of a DAC showing a sample
in a gasket between two diamonds. The laser power heats a
«black» absorber (platinum) embedded in a sample along with
a grain of ruby for pressure determination. Temperature is de-
termined by collecting the thermal black-body radiation in a
spectrometer and fitting to the Planck function. Diamonds
must be insulated from the hot sample to prevent excessive
heating and burning.
only a few hundred miliwatts, so that the average temper-
ature remains low.
Accurate measurement of the peak temperature during
pulsed laser heating can be accomplished. Pulsed heating
was first reported by Basset and Weathers [63]; however,
they measured the thermal radiation emitted from the
sample throughout the heating and cooling period of the
sample, and when fitted to a Planck function this gives a
temperature lower than the peak temperature. The black-
body radiation energy flux at wavelength
is
F
T kT
hc
x
x
�
�
�
�
15
1
4
4
5
(e )
. (1)
This varies as T 5; � is the Stefan–Boltzmann constant,
x hc kT
/
, and the other symbols have their usual mean-
ing. Due to the strong temperature dependence most of
the radiation is emitted at the peak temperature, Tpeak.
This irradiance vs wavelength can be fitted reasonably
well to a blackbody curve to give an effective temperature
that can be a few hundred K lower than the peak tempera-
ture, depending on the magnitude of Tpeak. The correc-
tion can be calculated by convolving the blackbody curve
with the heating curve,
F F T t dt
�
�
�
0
[ ( )] , (2)
which is determined using the measured laser pulse shape
and the material properties. A correction table can be de-
veloped and the peak temperature can be determined [61].
Conventionally one measures the blackbody irradi-
ance as a function of wavelength in the visible with a
spectrometer and an integrating CCD photo detector. This
technique yields high precision for temperatures above
�1000 K. This procedure can be used for accurate mea-
surements in a DAC but the irradiance falls off rapidly
with decreasing temperature as shown in Fig. 7, and the
peak irradiance shifts into the infrared. Since the pre-
dicted temperatures for the melt line were below 1000 K
we developed an optical pyrometer for use in the IR using
narrow band IR filters [65] and a cooled InSb detector,
shown in Fig. 8.
A diamond anvil cell capable of achieving pressures in
the megabar range was cryogenically loaded with hydro-
gen. The cell was removed from the cryostat so that the
ambient temperature of the pressurized hydrogen was
room temperature. The absorber was a platinum foil sit-
ting on ruby chips to separate it from the diamond surface
by a layer of hydrogen so that the diamonds would not be
in direct contact with the heated absorber. The ruby chips
also served to measure the pressure by the wavelength
shift of the ruby fluorescence peak, using a recently im-
proved pressure scale [16]. The solid–liquid melting tem-
perature was measured in two ways. As shown in Fig. 8,
we use a video monitor to observe the absorber surface
when it is heated. The monitoring CCD camera responds
to the pulsed laser wavelength, so that we observe the sur-
face only when it is heated (the pulse repetition rate was
20 KHz). We monitor the laser speckle and this speckle
pattern starts to move when the hydrogen melts. The se-
cond method is to plot the temperature vs average laser
power, shown in Fig. 9. In the Fig. 9,a we show plateaus
used to determine the melting temperature; these plateaus
were found to agree with the visual observation of the
melting. Plateaus at the melting line are ubiquitous, and
there are various explanations in the literature. When the
laser power is increased and hydrogen melts, the incre-
mental pulsed laser power goes into the heat of melting
Pathways to metallic hydrogen
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 419
1 2 3 4 5
Wavelength, m�
300 K
700 K
1000 K
1300 K
Ir
ra
d
ia
n
ce
,
ar
b
.
u
n
it
s
10
5
10
4
10
3
10
2
10
1
10
0
10
–1
10
–2
10
–3
Fig. 7. Calculated black-body irradiance on an logarithmic
scale as a function of wavelength for several temperatures
shown in the legend.
Fig. 8. The optical layout used for measuring the spectral
irradiance in the infrared and for visually monitoring the melt-
ing of the hydrogen.
and as the power is increased the pool of melted hydrogen
increases, resulting in the plateau, without the rise in tem-
perature found in the single-phase solid. The heat of the
melted region flows into the solid region. Eventually, the
power input to the melt is faster than the heat can be car-
ried away and the temperature of the melt (and absorber)
again rises. This is shown in the Fig. 9,b. As this was the
our first high-temperature melting line measurement with
hydrogen, for most of the pressure points we were conser-
vative in going to very high temperature to avoid possible
increased diffusion, so in most runs we did not demon-
strate the temperature rise beyond the plateau.
Our experimental extension of the melting line is
shown in Fig. 10 and has a peak. Our lowest pressure
point overlaps the data of Gregoryanz et al. who me-
asured the temperature with a thermocouple. The data
exhibits a rather sharp peak at (64 7 4. � ) GPa and
(1055 20� ) K, and the data set cannot be fit with a Kechin
curve. The pressure was measured before and after heat-
ing. The pressure during the pulsed heating might be en-
hanced by 5–10% due to a thermal effect demonstrated by
a finite element analysis. The unexpectedly sharp struc-
ture of the melting line may imply some unanticipated be-
havior in the solid or the liquid.
This first observation of a peak and the extension of
the melting line to higher pressures was terminated for an
unusual reason. Generally high-pressure experiments ex-
tending into the megabar pressure region are ended by
failure of the diamond anvils. In our case, as pressure was
increased, the signal from the ruby chips utilized to mea-
sure the pressure became weaker. The ruby signal was ob-
served before and after heating cycles, and the second
measurement was always weaker. Eventually, as the pres-
sure approached 100 GPa we could no longer excite the
ruby fluorescence, and other techniques of measuring the
pressure were not successful [31]. Since we had observed
the long sought after peak in the melting line, we ended
the experiment. We suspected that the ruby fluorescence
might have been quenched by hydrogen diffusion into the
ruby chips which were embedded in the hydrogen and
heated during the laser pulsing as they were in contact
with the absorber. A few hours after ending the experi-
ment we started measuring the ruby signal from one of the
chips as a function of time. In Fig. 11 we show the inte-
grated intensity of the ruby fluorescence line as a function
420 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
Isaac F. Silvera and Shanti Deemyad
a
b
1000
950
900
850
800
750
700
1200
1000
800
T
,
K
T
,
K
460 470 480 490 500 510
Average Laser Power, mW
Laser Power, arb. units
P = 46.7 GPa
P = 75 GPa
P = 80.7 GPa
Melting Plateau
Fig. 9. Plots of the peak temperature vs average laser power
showing the rise in temperature and the plateaus when the
hydrogen melts, for two different pressures (a). A plot of the
plateau at 75 GPa showing the rise in temperature beyond
the plateau. The temperature was determined with 5 narrow
band filters (b). In this case a single filter was used, resulting
in larger uncertainties in the temperature.
1000
800
600
400
50 100 150 200
T
,
K
P, GPa
Our Data
Datchi et al.
Gregoryanz et al.
Bonev et al. Melt Line
Bonev et al. liq.-liq. transition
Fig. 10. The experimental melting line of hydrogen showing
our results along with earlier results at lower pressures. The
dashed curve is fit to the theoretical result of Bonev et al. fit to
a Kechin curve. The solid line is the calculated liquid–liquid
phase line for dissociation of hydrogen in the melt.
of time showing the recovery of the signal due, we as-
sume, to the out-diffusion of hydrogen. Overnight, the
ruby recovered its full signal, shown by the point at lon-
gest time. The frequency of the ruby R1 peak did not mea-
surably shift with time. Thus, we assume the same was
true under pressure, so that the ruby pressure scale could
be used with some confidence for determining the sample
pressure. In the future this problem can be easily over-
come by exciting ruby chips that are not in contact with
the absorber and heated.
The technique of pulsed laser heating of hydrogen at
high pressure has been demonstrated to overcome the
problems that limited earlier researchers from extending
the melting line to higher pressures and temperatures. It is
our intention to extend the melting line to higher pres-
sures in the megabar range by this new method. It may be
a new pathway to metallic hydrogen.
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