Ortho–para conversion in the solid hydrogens at high pressures
At low pressures the ortho–para conversion in H₂ and D₂ is a slow process governed by the magnetic dipole interaction of nuclear magnetic moments, phonons being the main energy sink. As the pressure is raised to a few GPa and the Debye temperature increases substantially, the conversion energy finds...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2003
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| Cite this: | Ortho–para conversion in the solid hydrogens at high pressures / M.A. Strzhemechny, R.J. Hemley // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 941-946. — Бібліогр.: 30 назв. — англ. |
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| author | Strzhemechny, M.A. Hemley, R.J. |
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| citation_txt | Ortho–para conversion in the solid hydrogens at high pressures / M.A. Strzhemechny, R.J. Hemley // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 941-946. — Бібліогр.: 30 назв. — англ. |
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| description | At low pressures the ortho–para conversion in H₂ and D₂ is a slow process governed by the magnetic dipole interaction of nuclear magnetic moments, phonons being the main energy sink. As the pressure is raised to a few GPa and the Debye temperature increases substantially, the conversion energy finds itself in an area where phonon states are depleted and conversion slows down. The recent Raman and NMR experiments showed that the conversion rate in H₂ after an initial slowdown predicted by theory increases immensely. As for solid D₂, conversion rates have apparently not yet been directly measured under pressure. In order to explain the anomaly observed in H₂, we have suggested a new conversion mechanism, in which the basic conversion-producing interaction only initiates conversion whereas the energy is removed by rotational excitations via the stronger electric quadrupole-quadrupole interaction. Estimated conversion rates are in good qualitative agreement with available experimental observations. Here we extend the theory to solid D₂ taking into account the differences between H₂ and D₂ in the molecular and solid-state parameters. The new libron-mediated channel is predicted to result for D₂ in conversion rates under pressure that are by an order of magnitude larger than at P = 0.
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Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 941–946
Ortho–para conversion in the solid hydrogens at high
pressures
M.A. Strzhemechny1,2 and R.J. Hemley2
1B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
2Geophysical Laboratory and Center for High-Pressure Research, Carnegie Institution of Washington
5251 Broad Branch Road NW, Washington DC 20015, USA
E-mail: strzhemechny@ilt.kharkov.ua
At low pressures the ortho–para conversion in H2 and D2 is a slow process governed by the mag-
netic dipole interaction of nuclear magnetic moments, phonons being the main energy sink. As the
pressure is raised to a few GPa and the Debye temperature increases substantially, the conversion
energy finds itself in an area where phonon states are depleted and conversion slows down. The re-
cent Raman and NMR experiments showed that the conversion rate in H2 after an initial slowdown
predicted by theory increases immensely. As for solid D2, conversion rates have apparently not yet
been directly measured under pressure. In order to explain the anomaly observed in H2, we have
suggested a new conversion mechanism, in which the basic conversion-producing interaction only
initiates conversion whereas the energy is removed by rotational excitations via the stronger elec-
tric quadrupole-quadrupole interaction. Estimated conversion rates are in good qualitative agree-
ment with available experimental observations. Here we extend the theory to solid D2 taking into
account the differences between H2 and D2 in the molecular and solid-state parameters. The new
libron-mediated channel is predicted to result for D2 in conversion rates under pressure that are by
an order of magnitude larger than at P � 0.
PACS: 61.10.–i, 61.66.–f, 65.70.+y
1. Introduction
The requirements of quantum mechanics for a ho-
monuclear hydrogen species (H2, D2, T2) rigidly link
the rotational momentum J and the total nuclear spin
I of the molecule [1]. The states with even I values
have even J values and vice versa. The states with the
parity of the largest possible I value are called ortho
while the states with the other parity are para. Thus,
in H2 the states with I � 1 (and, hence, odd J) are
para; in D2 the states with I � 2 (and, hence, with
I � 0 too and with even J) are ortho while those with
I � 1 (and odd J) are para. Since the energy difference
between the J � 1 and J � 0 rotational levels is about
170 K for H2 and 85 K for D2, only these two states
are actually occupied in the solid phase at low temper-
atures. Transitions between states of different parity
(J or I), termed ortho-para conversion, are strictly
forbidden in a single molecule. The presence of mag-
netic fields produced by other molecules results in ob-
servable conversion rates. At low pressures and low
temperatures the conversion process has a low proba-
bility, especially in solid deuterium (for conversion
rates in H2 and D2 at ambient pressure see Ref. 2).
The main conversion-promoting mechanism both in
H2 and D2 is the magnetic dipole interaction H ss be-
tween nonzero nuclear spins of two J � 1 molecules,
one of which goes from J � 1 to J � 0 state, dissipating
the energy into one or two phonons.
With the advent of the modern diamond anvil cell
techniques, pressure has become an instrument that is
able to drastically change the interplay between dif-
ferent energies in many physical phenomena, one of
which is conversion in the hydrogens. The conversion
rate in solid H2 slightly increases with pressure,
reaches a maximum, then goes down (as predicted by
the low-pressure conversion theory [3,4]). But as the
pressure is raised above ; 2.5 GPa the conversion rate
unexpectedly curves up (see Fig. 1), reaching values
by a few orders of magnitude exceeding those ob-
served at moderate pressures (see detailed discussion
and the relevant references in Ref. 5). This conversion
enhancement in pressurized H2 was first studied in
sufficient detail by Raman scattering [6] and then by
© M.A. Strzhemechny and R.J. Hemley, 2003
NMR [7]; indirectly it has been corroborated by
Raman scattering in the Ar(H2)2 stoichiometric com-
pound [8].
Three factors control the conversion process. One is
the interaction that initiates a conversion act. The sec-
ond one is the agent that carries away the conversion
energy Ec released during this act. And the third one
is the pathway the energy goes from the kinetic rota-
tional form to that determined by the energy sink ex-
citations. The shape of the density of phonon states
does not suffer crucial changes [9] under pressure; the
width of the phonon energy distribution expands very
fast with compression; the energy Ec (to be dissipated
into phonons) decreases with compression. Due to the
combination of these facts, already at relatively mod-
erate pressures, Ec finds itself in an energy domain
where the density of phonon states is extremely low,
rendering the conversion less and less probable. There-
fore, given everything else untouched, phonons cannot
be the agent for an efficient conversion energy re-
moval at high pressures. It is clear that one has to look
for an other type(s) of excitation. The most obvious
candidate can be the rotational excitations. Quite sim-
ple considerations [10] show that pressure-related
changes in the rotational spectrum of mixed ortho–para
H2 crystals open up a possibility to dissipate the con-
version energy into the rotational energy bath. Below
we discuss the new conversion mechanism in some de-
tail.
At low pressures, the conversion mechanisms in
solid D2 are known [11]. The ambient-condition con-
version rates are known to high accuracy at low tem-
peratures in the solid (cf. Ref. 2) and the calculated
conversion constants [11,12] are in good agreement
with experiment. Although a certain conversion en-
hancement in pressurized D2 was reported by Cui et
al. [13], no systematic conversion rate measurements
have apparently been made in D2 at elevated pres-
sures. The authors know only of one Raman scattering
measurement that can give an estimate of the conver-
sion rate K in solid D2 at a pressure of 17 Gpa [14].
The corresponding evaluation, using the known rela-
tionship [15] modified for D2, and assuming an ex-
ponential variation of the J � 1 fraction in time (see
subsequently sections), gives K ; 8 10 3� � h�1, which
is substantially faster than at zero pressure (K �
� � � �5 6 10 4 1. h ) [16]. The main aim of this work is to
show that considerations similar to those for dense H2
are applicable for the conversion in D2 at high pres-
sures and that a conversion acceleration should be ex-
pected at sufficiently high pressures. The theoretical
predictions for conversion rates in solid D2 at high
pressures should stimulate further experimental study.
In the next Section we analyze the deuterium mo-
lecular parameters and the interactions relevant to the
issue of conversion in solid D2 at high densities (com-
paring them with those in solid H2) with an eye for
the most efficient mechanisms to be operative at high
pressures. We then present (Sec. 3) the current under-
standing of the reasons behind the pressure-related
conversion acceleration in H2. Section 4 deals with a
qualitative evaluation of the conversion rates in solid
D2 at high pressures for a few of the most promising
mechanisms.
2. Molecular parameters and interactions
In Table we compile the values of the quantities
that are relevant to the conversion in H2 and D2.
Table
The molecular and nuclear parameters of the deuterium
and hydrogen molecules; �n � � �505038 36 10 24. ( ) erg/Gs is
the nuclear magneton; Q unit for quadrupole moment times
electron charge is 13449 10 26. � � CGSE
Property (units) D2 H2
� (in �n) 0.8574073 [17] 2.79245(2) [18]
�rot / J (in �n) 0.44288(52) [19] 0.88291(7)* [20]
QN ( )10 27 2� �cm 2.738(16) [22] —
Q (Q units) 0.48529 [23] 0.47702 [23]
E J( ) ( )� �1 1cm 59.7804 [24] 118.495 [25]
E J( ) ( )� �2 1cm 179.065 [24] 354.39 [25]
* Consistency of the relationship �rot( )J � 2 ; 2 1�rot( )J � was
shown by Ramsey [21].
942 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
M.A. Strzhemechny and R.J. Hemley
1 2 3 4 5 6 7
0
100
200
300
C
o
n
ve
rs
io
n
ra
te
,
%
/
h
� = � /�0
100% Pa3
75% hcp
Hemley et al. (1998)
Pravica and Silvera (1998)
Fig. 1. Measured conversion rates in H2 versus density.
The points are from [6] (solid circles) and [7] (empty
squares). Rate data for low and moderate pressures are not
shown. The curves are semi-quantitative evaluations [10]
for 100% and 75% ortho fractions.
There are three basic interactions that can change
the parity of the total nuclear spin of a D2 or H2 mole-
cule that is supposed to convert [11]:
(A) Interaction of the magnetic nuclear moment of
the chosen molecule with the nonzero nuclear spin of a
neighbor molecule.
(B) Interaction of the same chosen nuclear mag-
netic moment with the effective magnetic moment of
the J � 1 state of a proper neighbor.
(C) Interaction of the nuclear electrical quadru-
pole moment of the chosen molecule (nonzero for
I � 1) with the electric field gradient due to the
quadrupole moment of the J � 1 rotational state of a
proper neighbor.
Interaction (A) is operative not only when the con-
version-promoting neighbor has I � 1, i.e., is in the
J � 1 state (case A1) but also when I � 2, i.e., when
the promoter is in a state with J � 0 (case A2). The
former interaction (A1) is a direct analog of the corre-
sponding interaction in H2, whereas the latter (A2) is
inherent only in D2. Both terms can be written in the
same form
H ss { R� � � �
�
��4 6 2
1
2 2
3�
� �
� � �� ��( } (
,
S S C n )) .
(1)
Here � is the nuclear magnetic moment of the deuteron
(proton); R R w w n�� �� ��� � �
� �0 2( )( ) ;d/ R
R0 is the radius vector between the two molecular
centers; � and � refer to the respective deuterons
(protons) respectively in the primed and un-primed
molecules; S� is the nuclear spin operator of deuteron
(proton) � ; d is the interatomic distance in the mole-
cule; w and w are the unit vectors along the respec-
tive molecular axes; { }NA B� and ( )A BM M� denote
respectively direct and scalar products [26] of two ir-
reducible tensors (in the latter case, of the same
rank).
Interaction (B) is another direct analog of the re-
spective interaction in solid H2 with the difference
that the effective value of � rot in D2 is appreciably
larger than in H2 (see Table).
Interaction (C) can be represented by the follow-
ing Hamiltonian
H q Ne QQ� �3 70 2
� � � �({ ) )} ))
i
i i i• RC S C w C n2 2 4 4
5( ( ( . (2)
Here Q is the quadrupole moment of the deuterium
molecule in the J � 1 state; QN is the nuclear quadru-
pole moment of the deuteron; R ni i iR� is the dis-
tance between deuton i in the chosen molecule and
the center of the conversion-promoting para neighbor;
other notation as in Eq. (1).
Since the orientational interactions play an impor-
tant role at high pressures, the above two Hamil-
tonians should be complemented by the electric quad-
rupole-quadrupole (EQQ) interaction energy
H EQQ eQ� �
35
2
2( )
� �� �({ ( ) ( )} • ( ))
ij
i j ij ijRC w C w C n2 2 4 4
5
(3)
where i and j numerate lattice sites occupied by J � 1
molecules.
The macroscopic equations for the J � 1 fraction x
are different for the two hydrogen isotopes under consi-
deration. In H2, both operating conversion-promoting
interactions result in a second-order reaction equation
dx
dt
Kx� 2 for hydrogen (4)
where the conversion parameter K can depend on
compression and, generally, on x. At low pressures, K
is virtually a constant K0 and Eq. (4) has the solu-
tion (x0 being the ortho fraction at t � 0): 1 0/x K t� .
In D2, both J � 1 and J � 0 contribute to the conver-
sion probability as promoters, so that the respective
equation for the J � 1 fraction is
dx
dt
kx k x x� � � �2 1( ) for deuterium
At zero pressure the values of k and k are very close so
that, effectively, Eq. (5) yields an exponential decay
dependence x t kt( ) exp( )� � .
3. Conversion in solid H2 at high pressure
We briefly summarize the main causes that lead to
the dramatic conversion acceleration in solid H2 at
high pressures. As shown above, phonons cease to be
efficient as conversion energy sink at comparatively
moderate pressures. The main idea for a consistent ex-
planation of the pressure-related conversion enhance-
ment was to consider orientational (rotational) de-
grees of freedom. There are a few problems to be
solved for a successful implementation of that idea: (i)
the particular conversion channel (energy path, type
of conversion act, sink excitations); (ii) the shape of
the rotational energy spectrum in such a highly ran-
dom system as an orientationally disordered ortho-
para mixture; and (iii) the compression-induced varia-
tion of the said spectrum.
The path mainly responsible for this acceleration
[10] is as follows (Fig. 2). The Hamiltonian H ss
starts conversion, producing a non-equilibrium inter-
mediate state, from which the system goes to equilib-
rium through the stronger EQQ interaction and emits
Ortho–para conversion in the solid hydrogens at high pressures
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 943
a rotational excitation. This path becomes efficient
only at a sufficiently high pressure [5].
Proceeding from the available experimental evi-
dence we argue [5,27] that, given a large enough J � 1
concentration, the rotational spectrum of a mixed
crystal basically resembles that of an orientationally
ordered state: a low-energy maximum containing local
ground states and a maximum at higher energies that
corresponds to local but collectivized excited rota-
tional states.
Evolution of the rotational spectrum with compres-
sion is schematically represented in Fig. 3. Because of
the normalization employed the plot is valid both for
H2 or D2. Though being directly applicable to a 100%
J � 1 orientationally ordered solid, the reasoning of
the preceding paragraph makes the plot qualitatively
valid for sufficiently high J � 1 concentrations even in
the disordered state. A very important feature is the
pressure-related decrease in the conversion energy due
to the growing strength of the negative molecu-
lar-field offset.
Calculation of the conversion rate at high pressure
is impossible in analytical form; using semi-quantita-
tive evaluations [10], we obtained results (the curves
in Fig. 1) that are consistent with the experimental
findings. It was later shown [5] that other channels,
though bringing about considerable changes (mostly
at moderate pressures), do not contribute appreciably
to the pressure-related conversion enhancement. The
new theory predicts a few effects, some of which find
confirmation in the available experimental results.
Unlike at low pressures, the conversion rate K should
be a strong function of the running J � 1 fraction x.
Analysis of the x versus time curves [5,6] for suffi-
ciently high pressures shows (Fig. 4) that, indeed, the
conversion rate considerably decreases in time (or
with decreasing J � 1 fraction).
4. Conversion in solid D2 at high pressure
Turning now to the efficiency of various conversion
channels in solid deuterium at high pressures we can
make use of some of the formulas derived for the case
of H2 [5] by allowing for the differences in the molec-
ular parameters. All of the standard channels (i.e.,
944 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
M.A. Strzhemechny and R.J. Hemley
J
J
0
0
= 1
= 1
J0= 0J
J
0
0
= 0
= 0
phonon
or
libron
phonon
or
libron
V Q
H
H
ss
ss
Fig. 2. Vertices for direct (standard) pathway and a path-
way with intermediate state. For standard channels (upper
diagram), H ss starts conversion and produces sink excita-
tions. In channels with intermediate states, H ss only starts
conversion whereas excitations are created through the
stronger EQQ interaction. 2 4 6 8 10
R
excited J = 1
molecule
converting
J = 1 molecule
J = 2
roton
L
6
4
2
0
E
/
B
� / �
0
= �
5/3
Fig. 3. Energy scheme (applicable both for H2 and D2) for
conversion transitions involving J � 1 and J � 2 excitations
with varying EQQ interaction. The J � 2 roton (arrow R)
is too energetic to take up the conversion energy. The en-
ergy floor is the state in which the chosen molecule has
converted and all other J � 1 molecules are in their local
rotational ground states. During conversion the chosen
molecule starts from a state with the energy to be released
(solid down-pointing arrow). Another ortho molecule can
now be excited to the libron band (shaded region) to take
up the energy (shown as a broken up-pointing arrow L).
At a critical � value (large circle) the energy span of the
excited molecule is wide enough to accommodate the en-
tire conversion energy.
those without an intermediate state) are phonon-as-
sisted and are therefore inefficient at high pressures.
The idea of the intermediate state with subsequent
participation of the EQQ interaction is productive for
D2 as well. Without going into detailed calculations
for channels with intermediate state, which will be
published elsewhere, we give a quantitative descrip-
tion of what can be expected for conversion rates in
compressed D2. Interaction A1 (cf. Sec. 2) will yield
the same result as for H2 but only for the conversion
parameter k in Eq. (5), viz., (cf. [10])
k
E
gA
c
1
13 3
2 0�
�
�
�
/
[ ( )]
( ). (6)
Here � � �� / 0 is the crystal density ratio reduced to
the P � 0 value; Ec is the conversion energy as a func-
tion of � (see Fig. 3) and g0( )� is the density of rota-
tional (libron-like) states. The contribution due to in-
teraction A2, which goes to the conversion parameter
k , in analytical form is similar to Eq. (6). Interaction
B gives a contribution to k of the same form as in Eq.
(6). Finally, interaction C contributes also to k but,
originating from the energy with a different depend-
ence on the separation R [compare Eqs. (1) and (2)],
is different as a function of compression � :
k
E
gC
c
�
�
�
�
19 3
2 0
/
[ ( )]
( ). (7)
As mentioned above, at zero pressure the constants k
and k are virtually the same, that is, k kA B1
kC ; kA2. As the pressure is increased to the level
in which the channels with intermediate state become
efficient, this match will be lifted and the time de-
pendence of the J � 1 concentration will cease to be
exponential.
As it was explained above, Fig. 3 is plotted in re-
duced variables such that it is valid both for H2 and
D2. However, when replotting in absolute values
(J � 1 energies, pressures, compressions) it will look
different for the two isotopes. It should be also noted
that Fig. 3 is rigorously applicable only for pure J � 1
solids; lower x necessitate recalculation of, for exam-
ple, the position of the critical point (solid circle in
Fig. 3) where rotational excitations come into play.
The quantities we need for re-scaling to absolute val-
ues are the volume dependence of the Debye frequency
[28] and the equation of states (EOS). Fortunately, at
high pressures the equation of state for H2 and D2 are
almost the same [29], the differences are appreciable
only at rather low pressures. The corresponding esti-
mations give the following critical pressure values.
For pure para (J � 1) deuterium the indirect channel
will become efficient at a pressure of 1.5 GPa and
cease to operate around 4.8 GPa; for normal (33%
para) deuterium these two pressure values are 14 GPa
and 32 GPa. We note that the working range for nor-
mal D2 extends beyond the critical pressure (28 GPa)
[30], at which D2 transforms to the broken-symmetry
phase (BSP). This means that at these pressures the
amount of the admixed J � 2 state should be apprecia-
ble. As can be seen from Table, the effective magnetic
moment of this state is large enough to change notice-
ably the strength of the total conversion-initiating in-
teraction. This problem requires a special consi-
deration, preferably with the structure of the BSP
known.
Since the zero-pressure conversion energy is less
than the deuterium Debye temperature, the principal
Ortho–para conversion in the solid hydrogens at high pressures
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 945
0.1 0.2 0.3 0.4 0.5
1.2
1.6
2.0
2.4
2.8
Run 15
J = 1 fraction
C
o
n
ve
rs
io
n
r
a
te
, a
rb
. u
n
its
/h
Fig. 4. The conversion rate K in H2 as a function of the
running J � 1 fraction for a pressure of 47.7 GPa, as recon-
structed from Raman scattering measurements [6]. The
drop in K is more than two-fold.
0 10 20 30 40
3
6
9
12
k
,
10
–
4
h–1
P, GPa
D
100% para
33% para (normal)
‘
2
Fig. 5. The conversion parameter k in D2 as a function of
pressure, as predicted in this report.
conversion mechanism at P � 0 is a one-phonon one
(which is not so in H2). Therefore, the phonon-medi-
ated conversion rate as a function of pressure will have
no distinct maximum at low pressures but will start to
decrease on initial compression and at a comparatively
low pressures (if the para fraction is high) will start
building up but to lower final values compared to H2.
A schematic representation of this dependence is
shown in Fig. 5.
Acknowledgments
This work was supported by the CRDF (grant
UP2-2445-KH-02) and NSF/DMR. The authors
thank A. F. Goncharov for providing his unpublished
results. M.A.S. also thanks Irina Legchenkova for
technical assistance.
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946 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
M.A. Strzhemechny and R.J. Hemley
|
| id | nasplib_isofts_kiev_ua-123456789-128907 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T18:00:14Z |
| publishDate | 2003 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Strzhemechny, M.A. Hemley, R.J. 2018-01-14T12:38:35Z 2018-01-14T12:38:35Z 2003 Ortho–para conversion in the solid hydrogens at high pressures / M.A. Strzhemechny, R.J. Hemley // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 941-946. — Бібліогр.: 30 назв. — англ. 0132-6414 PACS: 61.10.-i, 61.66.-f, 65.70.+y https://nasplib.isofts.kiev.ua/handle/123456789/128907 At low pressures the ortho–para conversion in H₂ and D₂ is a slow process governed by the magnetic dipole interaction of nuclear magnetic moments, phonons being the main energy sink. As the pressure is raised to a few GPa and the Debye temperature increases substantially, the conversion energy finds itself in an area where phonon states are depleted and conversion slows down. The recent Raman and NMR experiments showed that the conversion rate in H₂ after an initial slowdown predicted by theory increases immensely. As for solid D₂, conversion rates have apparently not yet been directly measured under pressure. In order to explain the anomaly observed in H₂, we have suggested a new conversion mechanism, in which the basic conversion-producing interaction only initiates conversion whereas the energy is removed by rotational excitations via the stronger electric quadrupole-quadrupole interaction. Estimated conversion rates are in good qualitative agreement with available experimental observations. Here we extend the theory to solid D₂ taking into account the differences between H₂ and D₂ in the molecular and solid-state parameters. The new libron-mediated channel is predicted to result for D₂ in conversion rates under pressure that are by an order of magnitude larger than at P = 0. This work was supported by the CRDF (grant UP2-2445-KH-02) and NSF/DMR. The authors thank A. F. Goncharov for providing his unpublished results. M.A.S. also thanks Irina Legchenkova for technical assistance. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур High-Pressure Studies Ortho–para conversion in the solid hydrogens at high pressures Article published earlier |
| spellingShingle | Ortho–para conversion in the solid hydrogens at high pressures Strzhemechny, M.A. Hemley, R.J. High-Pressure Studies |
| title | Ortho–para conversion in the solid hydrogens at high pressures |
| title_full | Ortho–para conversion in the solid hydrogens at high pressures |
| title_fullStr | Ortho–para conversion in the solid hydrogens at high pressures |
| title_full_unstemmed | Ortho–para conversion in the solid hydrogens at high pressures |
| title_short | Ortho–para conversion in the solid hydrogens at high pressures |
| title_sort | ortho–para conversion in the solid hydrogens at high pressures |
| topic | High-Pressure Studies |
| topic_facet | High-Pressure Studies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/128907 |
| work_keys_str_mv | AT strzhemechnyma orthoparaconversioninthesolidhydrogensathighpressures AT hemleyrj orthoparaconversioninthesolidhydrogensathighpressures |