The pressure effect on the recombination and relaxation of hydrogen atoms in solid hydrogen

Article abstract of DOI:10.1016/S0009-2614(00)00201-3

We have studied experimentally for the first time the properties of hydrogen atoms in solid hydrogen under pressure. The recombination rate constant has activation-type temperature dependence in the pressure range from 0 to 22 MPa. The activation energy increases linearly with external pressure E_a=(2.4 P+106 K), as should be expected in the case of a tunneling vacancy mechanism in atom diffusion. Strong pressure effects on the linewidth of the ESR signal and on the spin-lattice relaxation time T₁ were explained by the competition between the local ortho-para conversion process around the H atom and the pressure-dependent diffusion.

Full text of DOI:10.1016/S0009-2614(00)00201-3

24 March 2000
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Chemical Physics Letters 319 2000 535–541
www.elsevier.nlrlocatercplett
The pressure effect on the recombination and relaxation of
hydrogen atoms in solid hydrogen
a
a,c
Valeri Shevtsov a,b, Takayuki Kumada a,), Yasuyuki Aratono , Tetsuo Miyazaki
a
Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan
Russia Research Center ‘‘KurchatoÕ Institute’’, Moscow 123182, Russian Federation
b
c
Nagoya UniÕersity, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Received 9 February 2000
Abstract
We have studied experimentally for the first time the properties of hydrogen atoms in solid hydrogen under pressure. The
recombination rate constant has activation-type temperature dependence in the pressure range from 0 to 22 MPa. The
Ž
.
activation energy increases linearly with external pressure Eas 2.4 Pq106 K , as should be expected in the case of a
tunneling vacancy mechanism in atom diffusion. Strong pressure effects on the linewidth of the ESR signal and on the
spin–lattice relaxation time T1 were explained by the competition between the local ortho–para conversion process around
the H atom and the pressure-dependent diffusion. q 2000 Elsevier Science B.V. All rights reserved.
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1. Introduction
atoms 1,2 and molecules 3,4 and the tunneling
chemical reactions with H and D atoms participating
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The hydrogen atom in solid molecular hydrogen
is an example of a quantum impurity in a quantum
crystal. Since the H atom and H2 molecule are the
lightest stable species in the universe with relatively
weak interaction between them, the amplitudes of
zero-point motion of both atoms and molecules are
comparable with the lattice period of the crystal.
This causes a substantial contribution of the quantum
effects to both static and dynamic properties of this
system. The most interesting manifestations of these
effects are the finite mobility at very low tempera-
tures due to the quantum tunneling diffusion of both
5,6 . Charged impurities in para-hydrogen-like
y
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electron bubbles 7 and H2 anions 8 also reveal
essentially quantum properties.
The quantum diffusion of H atoms in solid H2
results in the recombination reaction HqH ™ H2.
This is a second-order process in the atomic concen-
tration C:
dCrdtsy2 K T C2 ,
Ž .
1
Ž .
Ž .
where K T is the temperature-dependent recom-
bination rate constant. If the diffusion is homoge-
neous then the relation between K and the diffusion
coefficient D of H atoms is given by Ks4paD,
where a is the intermolecular distance in solid hy-
)
Corresponding author. Fax: q81-29-282-5927; e-mail:
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drogen taken as the effective reaction radius 9 .
kumada@popsvr.tokai.jaeri.go.jp
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
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PII: S0009-2614 00 00201-3

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V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
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Previously 1 , the recombination of H in solid H2
and the ESR line width are quite different, they were
shown to depend on diffusion and, consequently, on
pressure.
was studied at zero pressure in the temperature
range from 1.35 to 5.9 K. Two distinct types of H
atom diffusion were found. At T-4 K the diffusion
proceeds, most probably, via successive repetition of
the tunneling exchange reactions HqH2 ™ H2 qH.
The rate was shown to be determined by one-phonon
interactions with lattice vibrations, resulting in linear
dependence on temperature. At T)4.5 K the activa-
tion-type diffusion prevails, which, however, is as-
sumed to be controlled by the tunneling Õacancy
2. Experimental
The general scheme of the experimental setup is
shown in Fig. 1. Solid hydrogen was prepared by
slow crystallization from the liquid phase in a quartz
sample cell with i.d. 3 mm, which was cooled by a
commercial continuous flow cryostat.
The high-pressure system includes hydrogen and
helium high-pressure cylinders, a pressure meter and
a simple cryogenic ‘pressure multiplier’. The latter
enables to double the pressure supplied by the high-
pressure cylinder by changing the temperature of the
‘multiplier’ cylinder between 77 and 370 K. Pres-
sures lower than 14 MPa were stabilized by an
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mechanism 10 . According to this mechanism the
diffusion of H atom occurs by tunneling to the
nearby vacant position in the lattice. Although the
tunneling itself should not depend on temperature,
the diffusion coefficient reveals an activation tem-
perature dependence since it is proportional to the
relative concentration of vacancies, which is equal to
E0 qPÕ
cÕ sexp y
,
2
Ž .
ž
/
T
where E0 is the energy required to remove the
hydrogen molecule from the H2 crystal, P is the
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external pressure and Õ is the vacancy volume 11 .
The main argument for the tunneling vacancy mech-
anism was the coincidence of the low-temperature
activation energies obtained for the diffusion of vari-
ous species in solid hydrogen: 103"5 K for H
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atoms 1 , 91"8 K for HD molecules 12 , and
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96"8 K for o-H2 molecules 13 . Single activation
energy despite different masses and, consequently,
different zero-point energies of these particles, can
be easily explained by the tunneling vacancy model
as the vacancy formation energy E0 f100 K, which
is independent of the type of the tunneling particle.
Besides, this value is rather close to the value E0 s
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112 K calculated by Ebner and Sung 10 .
The experiments to be presented here add pres-
sure as another coordinate to the studies of H atoms
Ž .
in solid H2. Thus, according to Eq. 2 the linear
pressure dependence of the activation energy of the
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.
recombination rate constant, K T, P would be di-
rect evidence for the vacancies involved in the diffu-
sion process. That was the primary aim of this study.
Also the pressure effect on the relaxation character-
istics of H atoms was studied. Although the mecha-
nisms which determine the spin–lattice relaxation
Fig. 1. The experimental setup.

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V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
537
ordinary pressure reducing valve with accuracy bet-
ter than "1%. Pressures in the range from 14 to 30
MPa were stabilized by regulation of the temperature
other hand, an unavoidable feature of the continuous
flow cryostat used at T)4.2 K is the temperature
gradient along the flow direction, which depends on
several factors, the flow rate F being the most
important of them. Thus we carried out separate
calibration measurements of the sample temperature
using a Ge resistance thermometer immersed into the
solid hydrogen just in the sample region. Its tempera-
ture was measured as a function of the temperature
of the other two thermometers and the flow rate of
in the ‘pressure multiplier’ system using
computer-controlled heater.
a
Usually the solid hydrogen sample is pressurized
by helium gas and annealed at the temperature close
to the melting point at a given pressure in order to
assure the uniform pressure distribution along the
sample. Special test experiments were made with
high pressure achieved using hydrogen gas at Ps13
MPa and they give the same results as those using
helium as pressure transmitting medium. Thus, de-
spite the finite solubility of helium in liquid hydro-
gen at high pressures, we believe that neither helium
atoms dissolve in the solid hydrogen nor, at least,
they penetrate into the atomic region on the time
scale of the experiment.
the cold He gas through the cryostat, T s
s
Ž
.
f T1, T2 , F . If the presence of the calibrating Ge
resistor does not change substantially the tempera-
ture distribution in the cryostat one may use the
obtained calibration to determine the sample temper-
ature in the real experiment. The comparison of our
measurements of the temperature dependence of the
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.
ESR line width of H atoms at Ps0 see Fig. 4
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The JEOL TE-200 X-band ESR spectrometer was
used to detect and investigate H atoms in solid H2.
Hydrogen atoms were produced in situ by white
with previous studies 14 enabled us to introduce a
small correction term to the calibration obtained,
making the temperature measurements more accu-
rate.
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X-ray 50 keV in maximum irradiation through the
window in the microwave cavity of the ESR spec-
trometer. The height of the irradiated region was
determined to be 8.5 mm, resulting in a sample
volume of 0.06 cm3. Irradiation time was ;5 h at
Tf4.8 K. The maximum atomic concentration ob-
tained is of the order of 0.1 ppm. Certain difficulties
in ESR measurements appeared due to strong spuri-
ous ESR signals from irradiated quartz parts of the
cryostat. Fortunately, they were relatively stable dur-
ing the measurements and could be obtained by
subsequent subtraction after the H atoms in the
sample have totally recombined at the temperatures
close to the melting point at a given pressure. The
absolute amounts of H atoms were measured by
comparison with a secondary reference sample of
Mn2q in MgO, which was pre-calibrated using the
reference sample made of TEMPO solution in benzol
having the same size and positioned in the same
place as the hydrogen sample.
Ž
All the experimental parameters temperatures,
.
pressure, flow rate were monitored by a personal
computer using self-made software. Besides, the
computer controlled the digital temperature stabilizer
Scientific Instrument DTC 9650 and kept the pres-
sure constant if the ‘pressure multiplier’ was used.
The typical experimental procedure was as fol-
lows. Every sample was studied at a fixed pressure,
since any pressure change requires a long relaxation
time to provide uniform pressure distribution along
the sample. Note, that annealing at high tempera-
tures is impossible after irradiation, since it in-
evitably results in complete recombination of H
atoms. After the irradiation was finished the temper-
ature of the sample was cycled in a stepwise mode
between 4.4 K and the ‘measurement’ temperatures
Tm as shown in Fig. 2b. The recombination of H
atoms can be observed from the evolution of the
intensities of the ESR spectra which are obtained at
TsTm. However, at high Tm it was practically
impossible to acquire the ESR signal of H atoms,
since the its amplitude decreases with increasing
temperature not only because the magnetization is
proportional to 1rTm but also due to strong tempera-
ture-induced line broadening as shown in Fig. 4. In
that case the recombination rate was estimated from
Ž
.
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.
Unfortunately, the temperature of the sample in
the present setup cannot be monitored directly during
the ESR measurement, because the introduction of
any thermometer with attached conducting wires into
the sample region results in deterioration of the
Q-value of the ESR cavity. The nearest thermometer
is ;2.5 cm lower than the sample region. On the

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538
V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
Ž .
in accordance with Eq. 2 . The parameters obtained
are
K s 9"5 =10y13 cm3 sy1
,
Ž
.
0
E0 s106"4 K ,
Õs2.4"0.1 KrMPa.
3a
Ž
.
The insert in Fig. 3 shows the pressure depen-
dence of the ‘individual’ activation energies Ea ob-
tained from the fit of the experimental points by the
Ž .
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.
simple Arrhenius expression K T sK0 exp EarT .
The pressure-independent pre-exponent K0 was cho-
Ž .
sen here and in Eq. 3 , since the ‘individual’ pre-ex-
ponents Kp reveal no specific pressure dependence
but show rather large scatter around K0 because of
the relatively narrow temperature interval consid-
ered.
Note, that our data at zero pressure are in a good
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agreement with earlier experiments 1,2 at Ps0,
which are represented by the hatched area in the
main Fig. 3 and by the open circle in the insert.
Fig. 2. The typical evolution of pressure and temperature during
Ž .
Ž .
the recombination measurements:
a
external pressure; and
b
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.
sample temperature solid line , and the concentration of H atoms
Ž
.
closed circles .
the ESR spectra measured at Ts4.4 K before and
after the temperature step TsTm and from the dura-
tion of the step.
3. Results and discussions
We observed several strong pressure effects on
the diffusion-related features of the H atoms.
3.1. The pressure effect on the recombination rate
The recombination rate constant strongly de-
creases with increase of pressure as shown in Fig. 3.
For example, at Ts8 K the decrease was about 3
orders of magnitude with pressure increasing from 0
Ž .
to 22 MPa. The temperature dependence of K T
becomes stronger at higher pressure, indicating that
there also is a pressure-induced increase of the acti-
vation energy. Different symbols in Fig. 3 represent
the data obtained on eight samples at different exter-
nal pressures. The solid lines correspond to the fit of
the experimental data by the relation
Fig. 3. The temperature dependence of the recombination rate
constant at various pressures: v, 0 MPa; ', 10.0 MPa; l, 12.0
MPa; %, 13.0 MPa; ), 14.0 MPa; and B, 22.0 MPa. Solid lines
Ž .
represent the results of the fit by Eq. 3 for Ps0, 10, 13 and 22
MPa, respectively. Hatched stripes show the results of previous
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measurements 1 at Ps0. The insert shows the pressure depen-
E0 qPÕ
K T, P sK exp y
3
Ž .
Ž
.
dence of the activation energy for the recombination rate constant
0
T
Ž
.
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closed circles . The open circle represents the result of Ref. 1 .

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V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
539
Ž
.
Thus, the obtained dependence K T, P indicates
that the recombination of H atoms in solid hydrogen
at T)5.5 K and 0-P-22 MPa is determined by
the diffusion, which includes thermally activated
processes. The linear pressure dependence of the
activation energy points out that the vacancies are
very likely involved in the diffusion of H atoms
at Ps0. Fig. 4 demonstrates that there is substantial
dependence of the linewidth on pressure as well.
This figure depicts the temperature dependencies of
the peak-to-peak width of the first derivative of the
low-field hyperfine component of the ESR absorp-
tion signals, which were obtained at zero pressure
and pressures of ;10 and ;13 MPa. The crosshairs
Ž .
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according to Eq. 2 . Finally, the strongest argument
represent the data of Ref. 14 at Ps0, which are
rather close to our data. One can see that the ESR
line clearly narrows with increasing pressure at a
given temperature. In addition, the temperature, at
which the line starts to broaden, becomes higher
when pressure increases.
in favor of the tunneling vacancy model is the
Ž
.
Ž .
vacancy volume obtained 3a , which is Õs3.4 2
=10y23 cm3. This value practically coincides with
n
y1 s
Ž
the elementary volume for hcp lattice of H2
3.8=10y23 cm3 at Ps0 and ny1 s3.5=10y23
3
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cm at Ps26 MPa 15 .
The linewidth of H atoms in solid hydrogen is
determined by the magnetic dipole interaction be-
tween the electron spin of a H atom and the nuclear
spins of neighboring o-H2 molecules, which in-
creases with the decrease of H–o-H2 distance. Thus,
one might expect the increase of the ESR line to
3.2. The pressure effect on the ESR linewidth of H
atoms
The ESR linewidth of H atoms in solid H2 was
found 14 to have strong dependence on temperature
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Fig. 4. The temperature dependence of the peak-to-peak ESR linewidth of hydrogen atoms in solid hydrogen at various external pressures:
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`, Ps0; I, Ps10–10.5 MPa; and e, Ps12–14 MPa. Crosshairs represent the results 12 obtained at Ps0. Solid lines are guides
for the eye.

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V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
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broaden with increasing density pressure . However,
the experiment gives just the opposite dependence.
The qualitative explanation for this discrepancy is
based on the fact that the effective distance Reff
between the H atom and o-H2 is substantially larger
than the nearest-neighbor distance a in solid hydro-
gen. This can be easily seen from the data presented
in Fig. 4. The absolute values of the linewidths are
much less than the estimate which can be calculated
on the basis of Van Vleck theory of the second
3.3. The pressure effect on the spin–lattice relax-
ation of H atoms
The longitudinal relaxation of H atoms was stud-
ied by pulsed ESR techniques. Special measures
were undertaken to remove the contribution from the
quartz background signal. The relaxation time T1
grows from 0.5 to 1.3 s with pressure increasing
from 0 to 22 MPa as shown in Fig. 5. The solid line
is a linear fit to the data points: T1 s0.5q3.4 P,
where T1 is measured in seconds, and P in MPa.
The spin–lattice relaxation mechanism for H
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moment of dipole interaction 16 . Since the H atom
takes the substitutional position in the hcp lattice
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17 , its linewidth in the case of a normal hydrogen
matrix containing 75% of o-H2 should be D Bpp s
atoms in solid H2 was proposed in Ref. 19 . It
Ž .
includes two stages, there is: 1 the relaxation of
254 mT.
Zeeman energy of the H atom to the quadrupole
The abnormally small linewidth was explained
energy of the o-H2 system in the solid hydrogen;
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x
Ž .
14,18 by the fast ortho-to-para conversion of the
and 2 relaxation of the energy from the quadrupole
neighboring o-H2 molecules in the first few coordi-
nation spheres of a hydrogen atom, which is cat-
alyzed by its electron magnetic moment. The cat-
alyzed conversion time of atom’s nearest neighbors
is about 5 orders of magnitude faster than the natural
selfconversion process in solid hydrogen and can be
system to the lattice vibrations. The last stage is the
fastest, since it is determined by strong electric
quadrupole interaction between o-H2 molecules.
Thus the total relaxation rate is limited by the first
stage, which is determined by the magnetic dipole
interaction between the electron spin of the H atom
and the small rotational magnetic moment of the
o-H2 molecule.
Therefore, everything that was mentioned in the
previous section about the effective dipole interac-
tion between electron and nuclear spin magnetic
moments can be applied to understand the pressure
effect on the spin–lattice relaxation of H atoms in
solid H2. The pressure-induced decrease of atom
diffusion at an almost constant local conversion rate
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roughly estimated as tcc f10 s 18 . Yet, it strongly
increases with distance as tcc A R12. This local cat-
alyzed conversion effectively decreases the dipole
interaction of the H atom and thus narrows the line.
However, the diffusion should obviously increase the
local o-H2 concentration and, therefore, broaden the
line. Thus, the linewidth is determined by the compe-
tition of two processes: the diffusion of H atoms and
the local ortho–para conversion around H atoms.
The pressure used in this study practically does
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not affect the conversion rate 15 . On the other
hand, the increase of pressure significantly slows
down the diffusion as it was shown above. Hence,
the pressure applied should enhance the local
ortho–para conversion of the neighboring H2
molecules, and narrow the ESR linewidth.
The line should begin to broaden substantially at
temperature Tb when the diffusion jump time be-
comes smaller than the local conversion time. This
qualitatively explains the experimental observation
that Tb increases with pressure increase, since the
same value of the diffusion rate can be obtained at
higher temperatures if the pressure rises.
Thus the pressure effect on the linewidth is in
qualitative agreement with the recombination data.
Fig. 5. The pressure dependence of the spin–lattice relaxation
time of H atoms.

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V. SheÕtsoÕ et al.rChemical Physics Letters 319 2000 535–541
541
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2
A.S. Iskovskhih, A.Ya. Katunin, I.I. Lukashevich, V.V. Skl-
yarevskii, V.V. Suraev, V.V. Filippov, V.A. Shevtsov, Sov.
around the H atom causes the increase of the effec-
tive H–o-H2 distance, and results in growth of T1.
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Phys. JETP 64 1986 1085.
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3
L.I. Amstutz, J.R. Thompson, H. Meyer, Phys. Rev. Lett. 21
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1968 1175.
4. Conclusions
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4 V. Shevtsov, E. Ylinen, P. Malmi, M. Punkkinen, J. Low
Ž
.
Temp. Phys. to be published .
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Ž
.
5
T. Miyazaki, Radiat. Phys. Chem. 37 1991 635, and the
related papers on tunneling reactions cited therein.
The first experiments on H atoms in solid hydro-
gen, carried out at non-zero pressures, give important
results on the pressure effect on the high-temperature
diffusion properties of H atoms. The linear pressure
dependence of the diffusion activation energy and
the obtained effective volume of the vacancy in solid
H2 unambiguously gives an indication on the va-
cancy mechanism of the diffusion of hydrogen atoms.
Practically coincident activation energies for various
diffusion species in solid hydrogen infer that the
atom–vacancy exchange occurs, most probably, by
tunneling. The observed pressure effects on the ESR
linewidth and on the spin–lattice relaxation can be
explained by the competition between the local or-
tho–para conversion catalyzed by the H atom and its
pressure-dependent diffusion rate.
w x
6
A.V. Ivliev, A.S. Iskovskikh, A.Ya. Katunin, I.I. Lukashe-
vich, V.V. Sklyarevskii, V.V. Suraev, V.V. Filippov, N.I.
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.
Filippov, V.A. Shevtsov, JETP Lett. 38 1983 379.
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T. Kumada, S. Mori, J. Kumagai, Y. Aratono, T. Miyazaki,
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J. Phys. Chem. A 103 1999 8966.
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T. Kumada, N. Kitagawa, S. Mori, J. Kumagai, Y. Aratono,
T. Miyazaki, J. Low Temp. Phys. 114 1999 413.
J.C. Polanyi Ed. , Chemical Kinetics, University Park Press,
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16 J.H. Van Vleck, Phys. Rev. 74 1948 1168.
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17 T. Kumada, N. Kitagawa, T. Noda, J. Kumagai, Y. Aratono,
This work was supported by the JAERI foreign
researcher inviting program. One of the authors V.S.
appreciates the support also from RFBR grant No.
99-02-17357.
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