A study on diffusion of H atoms in solid parahydrogen
Diffusion of hydrogen atoms in solid parahydrogen was investigated using high-resolution infrared spectroscopy. Hydrogen atoms were produced as by-products of a photoinduced reaction of nitric oxides embedded in solid parahydrogen. The diffusion of the hydrogen atoms is mainly terminated by the reac...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2003
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| Cite this: | A study on diffusion of H atoms in solid parahydrogen / Mizuho Fushitani Takamasa Momose // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 985-988. — Бібліогр.: 22 назв. — англ. |
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| citation_txt | A study on diffusion of H atoms in solid parahydrogen / Mizuho Fushitani Takamasa Momose // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 985-988. — Бібліогр.: 22 назв. — англ. |
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| description | Diffusion of hydrogen atoms in solid parahydrogen was investigated using high-resolution infrared spectroscopy. Hydrogen atoms were produced as by-products of a photoinduced reaction of nitric oxides embedded in solid parahydrogen. The diffusion of the hydrogen atoms is mainly terminated by the reaction of H + NO → HNO. The diffusion rate determined from the increase of the intensity of rotation-vibration transitions of HNO molecules was found to be two orders of magnitude larger than that determined by the self-recombination reaction of H + H → H₂ in pure parahydrogen crystals.
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Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 985–988
A study on diffusion of H atoms in solid parahydrogen
Mizuho Fushitani* and Takamasa Momose
Division of Chemistry, Graduate School of Science, Kyoto University,Kyoto 606-8502, Japan
E-mail: momose@kuchem.kyoto-u.ac.jp
Diffusion of hydrogen atoms in solid parahydrogen was investigated using high-resolution in-
frared spectroscopy. Hydrogen atoms were produced as by-products of a photoinduced reaction of
nitric oxides embedded in solid parahydrogen. The diffusion of the hydrogen atoms is mainly ter-
minated by the reaction of H + NO � HNO. The diffusion rate determined from the increase of the
intensity of rotation-vibration transitions of HNO molecules was found to be two orders of magni-
tude larger than that determined by the self-recombination reaction of H + H � H2 in pure
parahydrogen crystals.
PACS: 33.20.Ea, 67.80.Mg, 82.30.Cf
Introduction
Diffusion of hydrogen atoms in solid hydrogen has
attracted much attention as an object of research
[1–9], because the diffusion is believed to proceed
through the exchange reaction between an H atom and
a hydrogen molecule,
H + H2 � H2 + H, (1)
via quantum tunneling [1,2]. Since the activation en-
ergy of the reaction (1) in solid hydrogen is about
103 K [3], quantum tunneling is the only possible
mechanism at liquid He temperatures for the diffusion
of H atoms to take place through this reaction (1).
The diffusion of H atoms in solid parahydrogen
produced by x-ray or �-ray irradiation has been exten-
sively studied using ESR spectroscopy. The diffusion
of H atoms is terminated by the self-recombination re-
action,
H + H � H2, (2)
and thus the decay of the ESR signal of H atoms has
been well described by second order kinetics [3–5],
d
dt
kt
t
[ ]
[ ]
H
HH H� �
2, (3)
where [H]t is the concentration of H atoms at time t.
Since the diffusion rate of H atoms in solid hydrogen
is much slower than the recombination rate of the re-
action (2), the rate constant kH–H in Eq. (3) has
been considered to be the diffusion rate of the reac-
tion (1). It was found that the rate kH–H depends not
only on temperature [3,6] and pressure [5], but also
on the concentration of impurities such as orthohy-
drogen [1,4] and deuterium molecules [2,7]. The con-
centration dependence has been explained by the lo-
cal distortion of the lattice due to the difference in
the interactions between H�H2 and H impurity [4].
The local distortion induced by the different interac-
tions leads to a decrease of the quantum diffusion rate
due to the difference of energy between the initial
and final states [4]. Since the interaction between a
hydrogen atom and the isotopic impurity such as D2
and HD is stronger than the interaction between a
hydrogen atom and an orthohydrogen molecule, the
existence of these isotopic impurities makes the diffu-
sion rate slower than that wherein only orthohyd-
rogen impurities are present [2,7].
In this paper, we report on our recent study of the
diffusion of H atoms in solid parahydrogen. Hydrogen
atoms were produced as by-products of the photolysis
of NO molecules in solid parahydrogen. We found
that the diffusion is terminated mainly by the reaction
between an H atom and an NO molecule,
H + NO � HNO. (4)
Since the reaction (4) must be a diffusion-controlled
reaction, the diffusion rate of H atoms in solid para-
hydrogen is obtained from the temporal change of the
intensity of rotation-vibration transitions of HNO.
© Mizuho Fushitani and Takamasa Momose, 2003
* Present address: Institut für Experimentalphysik, Freie Universität Berlin, Germany
Experiments
Parahydrogen crystals containing small amounts of
NO molecules were prepared employing the same
method described in Ref. 10. Briefly, pure parahydro-
gen gas prepared through low-temperature catalysis
with ferric oxides was premixed with 10 ppm NO
gases at room temperature. Nitric oxides (Sumitomo
Seika, 99.999 %) were used without further purifica-
tion. The premixed gas was introduced into a sample
cell kept at 8.4 K to grow a transparent parahydrogen
crystal. The cell was made of copper, whose ends were
sealed with BaF2 optical windows for infrared spec-
troscopy.
An ArF excimer laser (193 nm, 2 mJ/pulse, 40 Hz)
was used for the photolysis of NO in solid para-
hydrogen. Spectral measurements were carried out at
5.2 K using a Fourier-transform infrared (FTIR) spec-
trometer (Bruker IFS 120HR) combined with a liquid
N2 cooled MCT detector and a globar source. The
globar light was turned on during the whole experi-
ment.
Results of photolysis
Figure 1 shows FTIR spectra in the spectral regions of
3800–3710, 2720–2680, 1890–1860 and 990–950 cm–1
before UV irradiation (a), just after the UV (193 nm)
irradiation for 20 minutes (b), and 155 minutes after
the UV irradiation (c). After the UV irradiation, the
sample was constantly kept at 5.2 K in darkness, ex-
cept for the weak light of the globar source of the
FTIR spectrometer. The peaks in the region of
1890–1860 cm–1 are assigned to the rotation-vibration
transitions of NO molecules isolated in solid para-
hydrogen. The corresponding absorption in the Ar ma-
trix has been observed at 1873 cm–1 [11]. After the
193-nm irradiation, the absorption of NO decreased
while new absorption appeared in the spectral regions
of 3800–3710, 2720–2680 and 990–950 cm–1, as
seen in Fig. 1,b. The peaks at 3787.1, 3765.5 and
3719.9 cm–1 in the region of 3800–3710 cm–1 are as-
signed to the R(1), R(0), P(1) transitions, respec-
tively, of the �3 asymmetric vibration of H2O mole-
cules isolated in solid parahydrogen [12,13]. The
spectrum at 990–950 cm–1 is identical to that of the �2
bending vibrational transition of NH3 molecules iso-
lated in solid parahydrogen that we have observed
previously [14]. The spectral change from Fig. 1,a to
Fig. 1,b clearly indicates that H2O and NH3 molecules
were produced by the 193-nm excitation of NO mole-
cules in solid parahydrogen.
It should be noted that one photon of 193-nm radia-
tion is not enough to dissociate an NO molecule into N
and O atoms in the gas phase, since the dissociation
energy of NO molecules (6.50 eV) [15] is slightly
higher than the photon energy of 193 nm (= 6.42 eV).
In condensed phases, however, formation of N(4S)
atoms by 193-nm photolysis of NO molecules has been
observed in solid Ar [16] and in solid hydrogen [17],
although the mechanism of the photodissociation of
NO molecules in the condensed phases is yet to be ex-
plained clearly. In any case, we surmise that NH3 mo-
lecules in the present system must be produced by the
986 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Mizuho Fushitani and Takamasa Momose
H O HNO NO NH
R(1) R(0) P(1)
2 3
3800 3760 3720 2720 2700 2680 1880 1860 980 960
a
b
c
�10
Wavenumber, cm
–1
Fig. 1. FTIR spectra of H2O, HNO, NO and NH3 in solid parahydrogen at 5.2 K: before UV irradiation (a); just after
UV (193 nm) irradiation for 20 min (b); after 155 min in the dark (c).
reaction between the photodissociated N atoms and
hydrogen molecules as follows:
NO + h� (193 nm) � N + O, (5)
N + 2H2 � NH3 + H . (6)
As for the O atoms produced in the reaction (5), they
immediately reacted with hydrogen molecules to form
H2O via the OH radical thus:
O + H2 � OH + H, (7)
OH + H2 � (H3O) � H2O + H. (8)
The formation mechanism of H2O molecules will be
discussed in a separate paper in more detail [18]. In
any case, it is important to know here that H atoms
were produced as by-products of the above reactions.
It is seen in Fig. 1,c that the absorption of NO that
survived from the UV photolysis further decreased af-
ter the sample was kept in darkness at 5.2 K, while
new absorption appeared simultaneously in the spec-
tral regions of 2720–2680 cm–1. The new absorption
can be attributed to HNO molecules, as the H–N
stretching vibrational transition of HNO in solid Ar
was observed at 2717 cm–1 [11]. Thus, the spectral
change from Fig. 1,b to Fig. 1,c indicates that HNO
molecules were produced in darkness in the UV irradi-
ated solid parahydrogen.
The formation of HNO is not a result of the reac-
tion of H2 + NO � HNO + H, since the reaction is en-
dothermic by 239.6 kJ/mol (� 30000 K) [19] and
thus it does not proceed at low temperatures. In fact,
no trace of the formation of HNO molecules was ob-
served in crystals that were not irradiated and kept in
darkness for several hours after the crystal growth.
Thus, the production of HNO must be a result of the re-
action between an H atom produced by the reactions
(6)–(8) and an NO molecule surviving the UV photoly-
sis, as shown in reaction (4). The reaction (4) is known
to be exothermic to a degree of –196.3 kJ/mol [19].
Analysis
Since NO molecules are immobile in solid para-
hydrogen at 5 K, the reaction (4) must be a result of
the diffusion of H atoms in solid parahydrogen. A mi-
grated H atom that encountered an NO molecule
forms an HNO molecule through the reaction (4).
Since this reaction (4) proceeds without any barrier
[20], the rate of the formation of HNO corresponds to
the diffusion rate of H atoms in solid parahydrogen.
The rate of the formation of HNO must be de-
scribed in terms of second order kinetics thus:
d
dt
kt
t t
[ ]
[ ] [ ]
HNO
H NOH NO� � , (9)
where [X]t is the concentration of molecule X at time
t. The reaction rate kH–NO in Eq. (9) is considered to
be the diffusion rate of H atoms in solid hydrogen.
For convenience, we define the mole fraction of the
concentration of HNO molecules at time t as
c t t
t t
( )
[ ]
[ ] [ ]
�
�
HNO
HNO NO
. (10)
Integrating Eq. (9) with respect to time t, the solu-
tion of Eq. (9) in terms of the mole fraction is found
to be
c t
k t
k
( )
[ ] exp { ([ ] [ ] ) } [ ]
[ ] exp {
�
� ��
�
H NO H H
NO
H NO
H N
0 0 0 0
0 O NO H H([ ] [ ] ) } [ ]0 0 0� �t
,
(11)
where [X]0 is the initial concentration of molecule X.
The mole fraction c(t) can be obtained from the ob-
served integrated intensities of HNO and NO mole-
cules as
c t
I
I AI
t
t t
( ) ,�
�
HNO
HNO NO
(12)
where I[X]t is the integrated intensity of molecule X.
The constant A in Eq. (12) is the ratio of the transi-
tion intensity of the H–N stretching vibration of
HNO to that of the fundamental vibration of NO. In
the present study, we have estimated the constant A
from the condition that the sum of [HNO]t + [NO]t is
constant at any time.
Figure 2 shows the temporal behavior of the mole
fraction c(t) of HNO molecules after the photolysis.
The time when the UV laser was turned off was taken
A study on diffusion of H atoms in solid parahydrogen
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 987
0.2
0.1
0
0 50 100 150
c
t, min
Fig. 2. Time evolution of the mole fraction of HNO in
darkness. The solid curve represents the theoretical curve
fitted with Eq. (11).
as the initial time, that is t = 0. Although some HNO
molecules were produced during the photolysis, we ig-
nored them in Fig. 2; the initial mole fraction c(0)
was set to zero in Fig. 2. The solid curve in Fig. 2 rep-
resents the curve fitted with Eq. (11). The best fitted
parameters were kH–NO = 6.22·10–25 m3/(atom·min)
and [H]0 = 3.95·1021 atom/m3. Here, the initial con-
centration of NO was fixed to [NO]0 = 1.99·1022 mole-
cule/m3 which was calculated from the integrated in-
tensity of NO assuming that the transition intensity of
NO in solid parahydrogen is identical to the transition
intensity (4.38·10–20 m/molecule) of NO in the gas
phase [21]. The initial concentration of H atoms de-
termined by the fitting is in good agreement with the
calculated value of [H]0 = 2.26·1022 atom/m3, assum-
ing that [H]0 = [NH3]0 + 2[H2O]0 along with using
the transition intensity (2.55·10–19 m/molecule)
of the �2 bending mode of NH3 and the intensity
(8.27·10–20 m/molecule) of the �3 asymmetric mode
of H2O in the gas phase [21].
The rate constant kH–NO in the reaction (4) is consid-
ered to be a diffusion rate of H atoms in the present sys-
tem. It should be noted that the rate of kH–NO =
= 6.22·10–25 m3/(atom·min) determined above is two
orders of magnitude larger than the rate kH–H =
= 5.0·10–27 m3/(atom·min) reported previously for
the rate of the self-recombination reaction (2) of H
atoms in solid parahydrogen [4]. If both kH–NO and
kH–H correspond to the diffusion rate of H atoms in
solid parahydrogen, the rate kH–NO must be one half
of the rate kH–H. The discrepancy between the experi-
mentally determined values of these two rates, how-
ever, is obvious.
Part of the reason for the discrepancy may be due to
the difference in the condition of the crystal, such as
the concentration of orthohydrogen molecules and/or
vacancies or defects. Another explanation could be
due to the difference in the interactions between H
and NO, and between the two H atoms. Since NO
molecules have a permanent electric dipole moment,
the attractive interaction between an H atom and an
NO molecule must be stronger than the interaction be-
tween two H atoms. By employing the classical inter-
molecular interaction theory [22], the interaction be-
tween H and NO is estimated to be roughly 200 times
stronger than the interaction between two H atoms.
The stronger interaction between an H atom and an
NO molecule may accelerate the diffusion of H atoms
in solid parahydrogen containing NO molecules com-
pared with the diffusion in a crystal without NO mole-
cules in it. In any case, the discrepancy is so obvious
that further experiments may be needed to understand
the rate obtained in this study.
This study was partially supported by Grant-in-Aid
for Scientific Research of the Ministry of Education,
Science, Culture, and Sports of Japan.
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988 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Mizuho Fushitani and Takamasa Momose
|
| id | nasplib_isofts_kiev_ua-123456789-128917 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-02T09:06:50Z |
| publishDate | 2003 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Mizuho Fushitani Takamasa Momose 2018-01-14T12:54:32Z 2018-01-14T12:54:32Z 2003 A study on diffusion of H atoms in solid parahydrogen / Mizuho Fushitani Takamasa Momose // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 985-988. — Бібліогр.: 22 назв. — англ. 0132-6414 PACS: 33.20.Ea, 67.80.Mg, 82.30.Cf https://nasplib.isofts.kiev.ua/handle/123456789/128917 Diffusion of hydrogen atoms in solid parahydrogen was investigated using high-resolution infrared spectroscopy. Hydrogen atoms were produced as by-products of a photoinduced reaction of nitric oxides embedded in solid parahydrogen. The diffusion of the hydrogen atoms is mainly terminated by the reaction of H + NO → HNO. The diffusion rate determined from the increase of the intensity of rotation-vibration transitions of HNO molecules was found to be two orders of magnitude larger than that determined by the self-recombination reaction of H + H → H₂ in pure parahydrogen crystals. This study was partially supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Culture, and Sports of Japan. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Physics in Quantum Crystals A study on diffusion of H atoms in solid parahydrogen Article published earlier |
| spellingShingle | A study on diffusion of H atoms in solid parahydrogen Mizuho Fushitani Takamasa Momose Physics in Quantum Crystals |
| title | A study on diffusion of H atoms in solid parahydrogen |
| title_full | A study on diffusion of H atoms in solid parahydrogen |
| title_fullStr | A study on diffusion of H atoms in solid parahydrogen |
| title_full_unstemmed | A study on diffusion of H atoms in solid parahydrogen |
| title_short | A study on diffusion of H atoms in solid parahydrogen |
| title_sort | study on diffusion of h atoms in solid parahydrogen |
| topic | Physics in Quantum Crystals |
| topic_facet | Physics in Quantum Crystals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/128917 |
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