Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment
The paper reports preliminary results on the kinetics of the molecular spin conversion in solid methane (CH₄) and deuterated methane (CD₄), obtained through thermal conductivity measurements in the temperature range 2–10 K.
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| Дата: | 2007 |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Назва видання: | Физика низких температур |
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| Цитувати: | Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment / E. Pisarska, P. Stachowiak, A. Jeźowski // Физика низких температур. — 2007. — Т. 33, № 6-7. — С. 768-771. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1217862017-06-17T03:03:15Z Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment Pisarska, E. Stachowiak, P.. Jeźowski, A. Classical Cryocrystals The paper reports preliminary results on the kinetics of the molecular spin conversion in solid methane (CH₄) and deuterated methane (CD₄), obtained through thermal conductivity measurements in the temperature range 2–10 K. 2007 Article Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment / E. Pisarska, P. Stachowiak, A. Jeźowski // Физика низких температур. — 2007. — Т. 33, № 6-7. — С. 768-771. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 63.20.–e; 66.70.+f http://dspace.nbuv.gov.ua/handle/123456789/121786 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| topic |
Classical Cryocrystals Classical Cryocrystals |
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Classical Cryocrystals Classical Cryocrystals Pisarska, E. Stachowiak, P.. Jeźowski, A. Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment Физика низких температур |
| description |
The paper reports preliminary results on the kinetics of the molecular spin conversion in solid methane
(CH₄) and deuterated methane (CD₄), obtained through thermal conductivity measurements in the
temperature range 2–10 K. |
| format |
Article |
| author |
Pisarska, E. Stachowiak, P.. Jeźowski, A. |
| author_facet |
Pisarska, E. Stachowiak, P.. Jeźowski, A. |
| author_sort |
Pisarska, E. |
| title |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment |
| title_short |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment |
| title_full |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment |
| title_fullStr |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment |
| title_full_unstemmed |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment |
| title_sort |
observation of relaxation of molecular spins in ch₄ and cd₄ crystals in thermal conductivity experiment |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2007 |
| topic_facet |
Classical Cryocrystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121786 |
| citation_txt |
Observation of relaxation of molecular spins in CH₄ and CD₄ crystals in thermal conductivity experiment / E. Pisarska, P. Stachowiak, A. Jeźowski // Физика низких температур. — 2007. — Т. 33, № 6-7. — С. 768-771. — Бібліогр.: 18 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT pisarskae observationofrelaxationofmolecularspinsinch4andcd4crystalsinthermalconductivityexperiment AT stachowiakp observationofrelaxationofmolecularspinsinch4andcd4crystalsinthermalconductivityexperiment AT jezowskia observationofrelaxationofmolecularspinsinch4andcd4crystalsinthermalconductivityexperiment |
| first_indexed |
2025-07-08T20:31:16Z |
| last_indexed |
2025-07-08T20:31:16Z |
| _version_ |
1837112154392625152 |
| fulltext |
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7, p. 768–771
Observation of relaxation of molecular spins in CH4
and CD4 crystals in thermal conductivity experiment
Elwira Pisarska, Piotr Stachowiak, and Andrzej Je�owski
Institute for Low Temperatures and Structure Research, Polish Academy of Sciences
PN 1410, 50-950 Wroc³aw, Poland
E-mail: e.pisarska@int.pan.wroc.pl
Received November 7, 2006.
The paper reports preliminary results on the kinetics of the molecular spin conversion in solid methane
(CH4) and deuterated methane (CD 4), obtained through thermal conductivity measurements in the
temperature range 2–10 K.
PACS: 63.20.–e Phonons in crystal lattices;
66.70.+f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves.
Keywords: organic compounds, nuclear spin conversion rate, thermal conductivity, phonons.
Introduction
Methane (CH4) is a hydrocarbon molecule that con-
sists of a single carbon atom (placed at the center) bonded
to four hydrogen atoms (at the tetrahedron). This simplest
hydrocarbon is a solid at 90.66 K at equilibrium vapor
pressure, and displays unchanged crystallographic struc-
ture down to 20.4 K. In this structure, called phase I, the
tetrahedral molecules are orientationally disordered, per-
forming rotations which do not show any long-range cor-
relation. The temperature 20.4 K is the temperature of
phase transition to phase II, which structure is illustrated
in Fig. 1. There are eight sublattices: six orientationally
ordered moleculas, occupy sites of dihedral symmetry
(D d2 ) performing collective librations, and two orienta-
tionally disordered moleculas, rotating almost freely, oc-
cupy sites of octahedral symmetry (Oh ) where the octu-
pole fields, due to neighboring molecules influence,
cancel exactly. Solid CH4 undergoes one phase transi-
tions, whereas the deuterated methane exhibits one more
transition. The deuterated methane solidifies at equilib-
rium vapor pressure at 89.78 K and exists in the phase
identical to phase I of CH4, down to temperature 27.0 K.
Similarly as CH4, solid deuterated methane exhibits a
phase transition to the eight-sublattice partially orient-
ationally ordered state at 27.0 K. Upon further cooling,
the crystal undergoes a phase transition, at 22.1 K, to
phase III with a complete long-range orientational order.
Methane and deuterated methane molecules in their
ground electronic and vibrational state may be classified
into three distinct spin species, according to the represen-
tation of the tetrahedral group (A, T, or E) to which their
orientational wave functions belong. Each spin species is
© Elwira Pisarska, Piotr Stachowiak, and Andrzej Je�owski, 2007
Fig. 1. The structure of CH4 in phase II. Tetrahedra represent
the 75% of molecules which are orientationally ordered in the
structure. The circle shows a CH4 molecule at the site where
molecular fields cancel for symmetry reason, which enables al-
most free rotation of the molecule.
associated with a unique value of the total nuclear-spin
quantum number I (in case of methane: A with I � 2, T
with I �1, and E with I � 0, and in case of deuterated meth-
ane: A with I � 4, T with I � 2, and E with I � 0) and has
distinct molecule ground-state energy. The energy levels
assigned to molecules on the disordered (Oh ) and ordered
(D d2 ) sublattice in phase II of solid CH4 are shown in
Fig. 2.
The occupancy of each state is a function of tempera-
ture; after a change of the temperature at slowly reaches
its equilibrium value due to the slow process of spin con-
version. Several experiments have shown that this con-
version occurs between nuclear spin symmetry species in
solid methane (CH4) [4–15]. At the same time, there are
few reports where the conversion in solid deuterated me-
thane (CD4) was observed [17,18]. In these measure-
ments, the nuclear spin conversion was detected in CD4
molecules embedded in krypton matrix.
In this paper, the results of study of conversion rate in
the solid CD4 and CH4 at temperatures 2–10 K by using
the thermal conductivity technique are presented.
Experimental detail
The crystals were grown from CH4 and CD4 of high
chemical purity. The concentration of foreign chemical
admixtures did not exceed 5 ppm for CH4, and 10 ppm for
CD4. The O2 concentration was 0.00007%, for both CH4
and CD4. The experiments (crystal growth, thermal treat-
ment and measurement) were performed in a cylindrical
glass ampoule with an inner diameter of 4.2 mm and
length of 36 mm. The samples were solidified from the
gas phase directly at a rate of 1.5 mm/h. At the beginning
of the growth process the ampoule was kept at a tempera-
ture just below the triple point (with some temperature
gradient applied). Next, the gas was admitted to the am-
poule and lowering of the temperature of the bottom of
ampoule began. During sample growth the gas pressure
was maintained at 10 kPa. After growing, the sample was
slowly (at a rate of 1 K/h) cooled down to the desired tem-
perature. The temperature gradient along the crystal and
the temperature of the sample were determined by two
germanium thermometers separated by 12 mm. The error
of measurement of the thermal conductivity was be-
low 1%.
We have measured the conversion rate by observing
changes of thermal conductivity in time, in the tempera-
ture interval 2–10 K. First, the samples were kept at a con-
stant temperature between 10 and 16 K for a few hours. In
the second step, they were further cooled down to the de-
sired final temperature (the temperature of the sample
was rapidly lowered after switching off the heater). Then,
the thermal conductivity coefficient was recorded every
3 min. The time taken to determine a single thermal con-
ductivity value was 5–10 h and it depended mainly on the
final temperature (the lower temperature the longer mea-
surements) and the isotope (the measurement time for
CD4 samples was considerably longer than for CH4). The
time dependence of the thermal conductivity of an exem-
plary sample is given in Fig. 3. The thermal conductivity
(�) increases continuously, and this change can be ap-
proximated by a sum of two exponential terms. The solid
line in Fig. 3 is the fit of our data by the function
� � � �� � � � �0 1 2A t A tT Cexp [ / ] exp [ / ] , (1)
where �T �14 min is the time necessary to achieve the
temperature 1.4 K — starting from 10 K — after switch-
ing off the heater (this exponent would be observed in any
Observation of relaxation of molecular spins in CH4 and CD4 crystals in thermal conductivity experiment
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7 769
0
10
20
30
40
50
60
70 66.5 E
60.7 A, T
41.5 T
30.0 E, T
34.6 E, T
12.7 T 12.7 T
0. A0. A
NSNS
ba
0
1
2
3
70
72
74
76
78
80
82
A
T
T
T
T
E
L
ib
ra
ti
on
s
2.8 E
2.51 E
1.9 T
1.66 T
0. A0. A0. A
1.70 T
LC TheoryTheory
E
ne
rg
y,
K
E
ne
rg
y,
K
T
un
ne
li
ng
le
ve
ls
Fig. 2. Low-lying energy levels for different spin modifica-
tions of CH4 molecules: a — orientationally ordered molecu-
les, b — orientationally disordered molecules. Theory — the
theoretical values from [1], NS — obtained from neutron scat-
tering measurements [2], LC — from paramagnetic level-cross-
ing experiment [3].
0 50 100 150 200 250 300 350
0.050
0.052
0.054
0.056
0.058
0.060
0.062
0.064
0.066
CH ,4 T = 1.4 K
t, min
�
, W
/(
m
·K
)
Fig. 3. Dependence of thermal conductivity on time after stor-
ing the sample at 10 K and rapid change of the temperature to
1.4 K (CH4 sample). The solid line approximates the experi-
mental data.
solid), and the thermal conductivity change corresponds
to the spin conversion with the characteristic conversion
time �C � 79 min.
Results and discussion
The observed variations of the thermal conductivity in
time is a result of two independent physical phenomena:
the energy transfer to the phonon system, which accompa-
nies the change of occupation of spin states, and the
change of the influence of symmetry of the molecule
wave function (spin state) on interaction with phonons.
Both of these effects have the same relaxation time and
the data obtained give the resulting conversion rate.
The conversion rate found by times measured for CD4
and CH4 crystals is shown in Fig. 4. The points have been
obtained by fitting the collected data using Eq. (1). Our
conversion measurements are in good agreement with
results published earlier for CH4 samples (see Fig. 4)
[4–16]. The CD 4 results we have obtained for the first
time.
In Fig. 4 the solid lines show the temperature depend-
ence of the conversion rate � for CH 4 samples, follow-
ing [4]:
�
�
� � � � �
�
�
�
1
1 2 1
C
kA n E B
C
T
( ( )) exp ,
n
k T
k �
�
�
�
�
�
�
�
�
�
�
�
�
�
�
exp
�
�
1
1
,
where the temperature dependence is given by the Bose
factor of the phonons. The second term describes a ther-
mally activated process. These two curves describe two
characteristic rates: one associated with the conversion of
free rotators (the samples were kept at a temperature
above 4 K, where the occupation numbers of ordered mol-
ecules are near their high-temperature limit so the conver-
sion behavior is dominated by the free rotors) and the
other, with the conversion of ordered molecules (the sam-
ples were kept at a temperature below 2 K for a few days
to let ordered molecules convert, then the samples
were heated and the conversion rate measured). In case
the conversion behavior is dominated by free rotators,
the energy E1 of the 0 1� transition is 12.4 K (see Fig. 2)
and A � (0.91 � 0.27) h �1, B � (42.6 � 9.3) h–1, C �
= (19.3 � 2.7) K. For the ordered molecules E1 17� . K,
A � (0.024�0.003) h �1, B � �( )447 185 h �1, C � �(44
� 4 4) K .
All our samples were kept at high temperature and �
was measured after a rapid cool down. Therefore, the tem-
perature dependence of the transition rates of CH4 similar
to the dependence for free rotators was expected. For CD4
the temperature dependence of the conversion rate is si-
milar to that of the ordered one in the CH4. As noticed,
CH4 below 20.4 K in phase II has two sublattices differ-
ing in local symmetry. By choosing the initial and final
temperatures, the conversion processes of free rotators
and ordered molecules can be separated. In our experi-
ment, the data relate to conversion rates of free rotators.
In case of CD4 below 22.1 K the crystal undergoes the
phase transition to phase III with complete orientational
order. Therefore, regardless of the choice of the initial
and final temperatures, our data describe the conversion
rate of the ordered molecules of CD4.
Concluding, the conversion rate in solidified methane
and deuterated methane has been measured by observing
changes of the thermal conductivity in time in the tempe-
rature range 2–10 K. The CH4 samples, with regard to the
crystallographic phase (phase II) and the measurement
procedure, shows temperature dependence of the conver-
sion rate dominated by the «free rotators». In the case of
CD4 samples the temperature dependence of the conver-
sion rate shows that of «ordered molecules». This result is
independent of the measurement procedure and is due to
the fact that in the crystallographic phase (phase III) only
orientationally ordered molecules exist.
The authors are grateful to Dr. A.I. Krivchikov for
fruitful discussions. This work was supported by the Pol-
ish State Committee for Scientific Research.
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770 Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7
Elwira Pisarska, Piotr Stachowiak, and Andrzej Je�owski
0 0.2 0.4 0.6 0.8 1.0
–4
–2
0
2
4
6
free rotator
ordered molecules
0.1
1,0
3,0
10,0
50,0
150,0
T , K
1.522.5510
1/T , K
–1
�
,h
ln
[h
])
(�
Fig. 4. Comparison between several conversion measurements
(our data: CD4 (�), CD4–Kr (3% of Kr) (�), CH4 (�); data
for CH4 samples from: Grieger et al. [4] (�), Buchman et al.
[5] (�), Higinbotham et al. [6] (�), Lushington et al. [7] (�),
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Observation of relaxation of molecular spins in CH4 and CD4 crystals in thermal conductivity experiment
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 6/7 771
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