Heat transfer in solid halogenated methanes: trifluoromethane
The isochoric thermal conductivity of solid trifluoromethane was investigated for three samples of different densities in the interval from 75 K to the onset of melting. The isochoric thermal conductivity first decreases with increasing temperature, passes through a minimum at T ~ 100 K, and then st...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Heat transfer in solid halogenated methanes: trifluoromethane / V.A. Konstantinov, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2009. — Т. 35, № 4. — С. 376-379. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1171102017-05-20T03:03:46Z Heat transfer in solid halogenated methanes: trifluoromethane Konstantinov, V.A. Revyakin, V.P. Sagan, V.V 7th International Conference on Cryocrystals and Quantum Crystals The isochoric thermal conductivity of solid trifluoromethane was investigated for three samples of different densities in the interval from 75 K to the onset of melting. The isochoric thermal conductivity first decreases with increasing temperature, passes through a minimum at T ~ 100 K, and then starts to increase slowly. The results obtained are compared with the thermal conductivities of other freons of methane series. The correlation between the temperature dependence of isochoric thermal conductivity and the character of the rotational molecular motion is discussed. 2009 Article Heat transfer in solid halogenated methanes: trifluoromethane / V.A. Konstantinov, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2009. — Т. 35, № 4. — С. 376-379. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 66.70.–f, 63.20.Kk http://dspace.nbuv.gov.ua/handle/123456789/117110 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 |
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7th International Conference on Cryocrystals and Quantum Crystals 7th International Conference on Cryocrystals and Quantum Crystals Konstantinov, V.A. Revyakin, V.P. Sagan, V.V Heat transfer in solid halogenated methanes: trifluoromethane Физика низких температур |
| description |
The isochoric thermal conductivity of solid trifluoromethane was investigated for three samples of different densities in the interval from 75 K to the onset of melting. The isochoric thermal conductivity first decreases with increasing temperature, passes through a minimum at T ~ 100 K, and then starts to increase slowly. The results obtained are compared with the thermal conductivities of other freons of methane series. The correlation between the temperature dependence of isochoric thermal conductivity and the character of the rotational molecular motion is discussed. |
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Article |
| author |
Konstantinov, V.A. Revyakin, V.P. Sagan, V.V |
| author_facet |
Konstantinov, V.A. Revyakin, V.P. Sagan, V.V |
| author_sort |
Konstantinov, V.A. |
| title |
Heat transfer in solid halogenated methanes: trifluoromethane |
| title_short |
Heat transfer in solid halogenated methanes: trifluoromethane |
| title_full |
Heat transfer in solid halogenated methanes: trifluoromethane |
| title_fullStr |
Heat transfer in solid halogenated methanes: trifluoromethane |
| title_full_unstemmed |
Heat transfer in solid halogenated methanes: trifluoromethane |
| title_sort |
heat transfer in solid halogenated methanes: trifluoromethane |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2009 |
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7th International Conference on Cryocrystals and Quantum Crystals |
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http://dspace.nbuv.gov.ua/handle/123456789/117110 |
| citation_txt |
Heat transfer in solid halogenated methanes:
trifluoromethane / V.A. Konstantinov, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2009. — Т. 35, № 4. — С. 376-379. — Бібліогр.: 18 назв. — англ. |
| series |
Физика низких температур |
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AT konstantinovva heattransferinsolidhalogenatedmethanestrifluoromethane AT revyakinvp heattransferinsolidhalogenatedmethanestrifluoromethane AT saganvv heattransferinsolidhalogenatedmethanestrifluoromethane |
| first_indexed |
2025-07-08T11:39:58Z |
| last_indexed |
2025-07-08T11:39:58Z |
| _version_ |
1837078727396163584 |
| fulltext |
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4, p. 376–379
Heat transfer in solid halogenated methanes:
trifluoromethane
V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: konstantinov@ilt.kharkov.ua
Received January 4, 2009
The isochoric thermal conductivity of solid trifluoromethane was investigated for three samples of dif-
ferent densities in the interval from 75 K to the onset of melting. The isochoric thermal conductivity first de-
creases with increasing temperature, passes through a minimum at T ~ 100 K, and then starts to increase
slowly. The results obtained are compared with the thermal conductivities of other freons of methane series.
The correlation between the temperature dependence of isochoric thermal conductivity and the character of
the rotational molecular motion is discussed.
PACS: 66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves;
63.20.Kk Phonon interactions with other quasiparticles.
Keywords: thermal conductivity, phonons, phonon-rotation coupling, diffusive modes.
Introduction
The solid freons of the methane series consisting of tet-
rahedral molecules are convenient objects to investigate the
correlation between the rotational motion of molecules and
the behavior of thermal conductivity. Methane (CH4) and
carbon tetrahalogenides (CF4, CCl4, CBr4, CJ4) form
high-temperature «plastic» or orientationally-disordered
phases in which the rotational motion of molecules is similar
to their motion in the liquid state [1,2]. In crystals consisting
of lower-symmetry molecules such as chloroform (CHCl3),
methylene chloride (CH2Cl2) or dichlorodifluoromethane
(CCl2F2) the forces of the noncentral interaction of mole-
cules are much stronger and the long-range order usually
persists in them up to the melting temperature. The relative
simplicity of the freon molecules allows adequate interpre-
tation of experimental results.
The orientational motion in molecular crystals can be
either vibrational or rotational depending on the tempera-
ture and the relationship between the noncentral forces
and the kinetic energy of rotation. At low temperatures
the motion of molecules in molecular crystals is, with rare
exception (quantum crystals), of oscillatory character: at
Ò � 0 molecules perform zero orientational vibrations
about the equilibrium directions. As the temperature
rises, the r.m.s. amplitudes of librations increase and the
molecules can hop over the accessible orientations. This
disturbs the long-range order and can provoke a phase
transition. The degree of orientational order can be varied
by changing the temperature and selecting crystals with
different parameters of the molecular interaction, which
permits us to investigate the influence of the rotational
motion of molecules upon the thermal properties of the
crystal, including its thermal conductivity.
It is best to measure thermal conductivity at a fixed
density, which excludes the effect of thermal expansion
and ensures a more adequate comparison with theory.
This is particularly important at high temperatures when
the thermal expansion coefficients are large. Previously,
we investigated the isochoric thermal conductivity of
CH4 [3], CCl4 [4], CHCl3 and CH2Cl2 [5], CF2Cl2 and
CHF2Cl [6]. The regularities of the heat transport in sim-
ple molecular crystals (including the methane-series
freons) depending on the rotational degrees of freedom of
molecules at the Debye and higher temperatures (T � QD)
can be generalized as follows. Because of the strong
translational-orientational (TO) coupling in the orienta-
tionally-ordered phases [7], molecular librations contrib-
ute considerably to the thermal resistance W = 1/� of the
crystal. As a result, the isochoric thermal conductivity ap-
proaches its lower limit and deviates significantly from
the dependence � � 1/T (CHCl3, CH2Cl2, and CF2Cl2).
The concept of the lower limit of thermal conductivity
© V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan, 2009
implies that �min can be achieved if the heat transport is
realized through thermal energy diffusion between the
neighboring quantum-mechanical oscillators whose life-
time is about half the oscillation period [8]. On a
weakly-retarded rotation, the translational-orientational
component of the total thermal resistance decreases ow-
ing to weakening of TO coupling and the isochoric ther-
mal conductivity can grow with temperature. We ob-
served this effect in methane and carbon tetrachloride
[3,4]. A weak growth of thermal conductivity was also
found in the high-temperature phase of solid chlorodi-
fluoromethane (CHF2Cl) [6]. This behavior is not entirely
clear for the lack of full information about the character of
the rotational motion of the molecules in solid CHF2Cl.
According to calorimetric data [9], solid CHF2Cl experi-
ences a �-type phase transition at 59 K and melts at 115,7 K
with an entropy jump �Sf/R = 4,25 (R is gas constant).
Note that a crystal is defined as plastic if it obeys the
Timmerman criterion: the melting entropy of phase I must
be below 2,5 R. Calculation of the Debye temperature of
CHF2Cl from calorimetric data gives (70 � 5) K. The
crystal structure of CHF2Cl was investigated at 10 and 70
K by the neutron scattering method [10]. The low-temper-
ature phase is monoclinic; it has the spatial symmetry
P112/n (C h2
4 ) and eight molecules in the cell. The
high-temperature phase is tetragonal with the spatial sym-
metry P42/n (C h2
4 ) and it also has eight molecules in the
cell. A shifting-type phase transition occurs at 59 K and
has little effect on the position and orientation of the mol-
ecules. The object of this study was trifluoromethane
(CHF3). The molecule rotation at the lattice sites of CHF3
was investigated previously by the NMR technique
[11,12].
Experimental
Constant volume investigations are possible for mo-
lecular solids having a comparatively high compressibil-
ity coefficient. Using a high pressure cell, it is possible to
grow a sample of sufficient density which in subsequent
experiments can be cooled with practically unchanged
volume. For samples of moderate densities the pressure
drops during cooling to zero at a certain characteristic
temperature T0 and the isochoric condition is then broken.
On further cooling, the sample can separate from the
walls of the cell or its continuity can be disturbed. In the
case of a fixed volume melting occurs in a certain temper-
ature interval, and its onset shifts towards higher tempera-
tures as the density of the samples increases.
The investigation was made using a steady-state tech-
nique in a coaxial-geometry setup [13]. The measuring
beryllium bronze cell was 160 mm long with an inner
diameter of 17.6 mm. The maximum permissible pressure
in it was 600 MPa. The inner measuring cylinder was
10.2 mm in diameter. The temperature sensors (platinum
resistance thermometers) were placed in special channels
of the inner and outer cylinders and thus escaped
high-pressure effects. A system of protecting cylinders
was used to reduce the axial heat flows. During the
growth process the temperature gradient over the measur-
ing cell was 2–3 K/cm. The pressure in the inflow capil-
lary was varied within 50–150 MPa to grow samples of
different densities. When the growth was completed, the
capillary was blocked by freezing it with liquid hydrogen,
and the samples were annealed for one to two hours at
their premelting temperatures to remove the density gra-
dients. After measurements the samples were evaporated
into a thin-walled vessel and their masses were measure
by weighing. The molar volumes of the samples were
found from the known volume of the measuring cell and
the sample masses. The total dominant systematic error of
measurement was no more then 4% for the thermal con-
ductivity and 0.2% for the volume. The purity of CHF3
was no worse than 99.98%.
Results and discussion
The isochoric thermal conductivity of solid trifluo-
romethane was investigated on three samples of different
densities in the interval from 75 K to the onset of melting.
The experimental results are shown in Fig. 1 (solid lines
are smoothed thermal conductivity values; the dashed
line shows the thermal conductivity measured under satu-
rated vapor pressure). The molar volumes Vm, tempera-
tures T0 (onset of V = const condition) and Tm (onset of
sample melting) are shown in Table 1. The Bridgman coef-
ficients g V T� –( ln / ln ) � calculated from the experi-
mental results are 4.8 � 0.8 at T = 115 K. Isochoric thermal
Heat transfer in solid halogenated methanes: trifluoromethane
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 377
�
,
m
W
/c
m
K
70 80 90 100 110 120 130 140
1.5
2.0
2.5
3.0
3.5
CHF3
T, K
Fig. 1. The isochoric thermal conductivity of three solid CHF3
samples of different densities: Nos. 1 ���, 2 �
�, 3 (�� (see also
Table 1). Solid lines show smoothed values of isochoric ther-
mal conductivity. Dashed line and rhombus are for the thermal
conductivity of a free sample. Arrows mark the onset of the
experimental condition V = const and the onset of the sample
melting.
conductivity first decreases with increasing temperature,
passes through a minimum at Ò � 100 K, and then starts to
increase slowly up to the onset of melting.
Trifluoromethane CHF3 melts at Tm = 117.97 K, the
melting entropy being �Sf/R = 4.14 [14]. According to
heat capacity data [14], there are no phase transitions in
the interval 15–117 K. We estimated the Debye tempera-
ture (�D = 88 � 5 K) from the low-temperature part of
these data. The existence of only one crystalline modifi-
cation in the region 20–106 K is also supported by Raman
and IR spectral investigations [15]. This points to the ab-
sence of strong hydrogen bonds in CHF3. Neutron scat-
tering investigations of the crystallographic structure of
CHF3 at 4.2, 40 and 70 K [16] revealed only one crystal-
line phase of the spatial symmetry P21/c with four differ-
ently oriented molecules in the monoclinic cell.
Absorption line shapes of the NMR signal and the
spin-lattice relaxation times were investigated on the 1H
and 19F nuclei of CHF3 at T = 7–116 K [11] and 4.2–120
K [12], respectively. It is found that above T = 80 K the
second NMR moment decreases sharply from 11.5 G2
to 3.0 G2 immediately prior to melting, which suggests
enhancement of the molecule rotation about the three
fold axis. The activation energy of rotation and the
preexponential Arrhenius factors were calculated to be
17.0 kJ/mol and 1.0
10–16 s [11], and 18.0 kJ/mol and
(4.9–8.9)
10–17 s [12], respectively. In Fig. 2 these re-
sults are presented as a logarithmic function of frequency
of reorientations about the three fold axis versus the in-
verse temperature. The upper frequency of the lattice
modes which correspond to �D = 88 K is shown at the top
of Fig. 2. The data of the two studies are in good agree-
ment. At the melting temperature the reorientation fre-
quency is three orders of magnitude lower than the Debye
frequency, which is rather surprising. The growth of ther-
mal conductivity with temperature was observed previ-
ously in orientationally-disordered phases of methane
and carbon tetrahalogenides, in which the molecule rota-
tion is weakly hindered or almost free [1,2].
Table 2 gives a general information about the meth-
ane-series freons: melting temperatures Tm, phase transition
temperatures TI-II, structure and the number of molecules in
the unit cell z, melting entropy �Sf/R, Debye temperatures
�D, Bridgman coefficients g / V T� –( ln ln ) � , dipole
moments of molecules �. Included are also the data for
CBr4 (its thermal conductivity was measured in Ref. 17).
The isochoric thermal conductivity of orientationally-dis-
ordered phases in the methane-series freons increases
with temperature. (The exception is methane in where the
378 Fizika Nizkikh Temperatur, 2009, v. 35, No. 4
V.A. Konstantinov, V.P. Revyakin, and V.V. Sagan
Òàble 1. Ìîlar volumes Vm of the samples, temperatures T0 of the
onset of experimental condition V = const and temperatures Tm of
the onset of melting
Number of sample Vm, cm
3
/mole T0, K Tm, K
1 36.58 104 125
2 35.9 93 131
3 35.45 82 135
Òàble 2. Melting temperatures Tm, phase transition temperatures
TI-II, structure and the number of molecules per unit cell z, melting
entropy �Sf/R, Debye temperatures �D (the corresponding temper-
ature is given in brackets), Bridgman coefficients g, dipole mo-
ments of molecules �
Substance Tm, TI-II Structure z �Sf/R �D, K g �, D
(I)
CH4
(II)
90.6
20.5
Fm3m
–
P43m
4
32
1.24
96 (90 K)
141 (0 K)
8.8
0
(I)
CCl4
(II)
250.3
225.5
Fm3m
C2/c
4
32
1.21
92 (0 K)
6.0
6.5
0
(I)
CBr4
(II)
363
320
Fm3m
C2/c
4
32
1.3 62 (300 K)
3.8
3.4
0
(I)
CHF2Cl
(II)
115.7
59
P42/n
P112/n
8
8
4.25
70 (0 K)
4.5
1.41
CHCl3 210 Pnma 4 5.4 86
�
3.9 1.01
CH2Cl2 176 Pbcn 4 3.13 115
�
4.6 1.6
CF2Cl2 115 Fdd2 8 4.2 80
�
5.0 0.51
CHF3 118 P21/c 4 4.14 88
�
4.6 1.6
*Estimates obtained from IR and Raman spectra for the upper
boundary of the lattice modes.
6 7 8 9 10 11 12 13 14
4
6
8
10
12
14
2
1
Tm
10 , K/T
3
CHF3lo
g
�
Fig. 2. Frequency of reorientation jumps of molecules in crys-
talline CHF3 for to studies according to Refs. 11, 12.
thermal conductivity has a maximum and then starts to
decrease [3].) This is because the translational-orien-
tational component of the total thermal resistance de-
creases sharply as the rotation of the molecules becomes
weakly hindered. In some crystals with reorientation fre-
quencies up to 104 s–1 (CHCl3, CH2Cl2 and CF2Cl2)
the isochoric thermal conductivity approaches its lower
limit �min [5,6] and deviates significantly from the de-
pendence � � 1/T.
Apart from CHF3, a weak growth of isochoric thermal
conductivity with temperature was also observed in
CHF2Cl (I) [6]. However, in the latter case only the Raman
spectra were investigated at T = 20–80 K [18] and NMR
data are unavailable. The lattice modes exhibit distinct
peaks at T = 20 K and broad overlapping bands at T = 80 K,
which are more common for orientationally-disordered
crystals. At 20 K there were three split peaks in the inter-
val 30–50 ñm–1 (43–72 K) and three split peaks in the re-
gion 55–80 ñ–1 (79–115 K). They were presumably
assigned to the translational and librational modes, respec-
tively. The upper boundary of the translational modes
agrees well with the Debye frequency obtained from calo-
rimetric data. However, the analysis of the spectra of the
intramolecular modes at 80 K reveals no disordered struc-
ture. The observed picture might therefore be a result of
broadening and re-overlapping of the corresponding com-
ponents. We can expect intensive reorientational motion in
solid CHF2Cl at least about the C–Cl axis.
The weak growth of isochoric thermal conductivity
with temperature in solid CHF3 and CHF2Cl suggests that
the translational-orientational coupling becomes weaker
in these crystals at premelting temperatures owing to the
intensive molecule reorientations about the three fold
axes. It is rather surprising that in CHF3 the reorientation
frequency is much lower than the boundary Debye one.
This fact calls for further theoretical studies. At present
there is no general theory that could relate the behavior of
thermal conductivity to the character of the orientational
motion of molecules in molecular crystals.
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Heat transfer in solid halogenated methanes: trifluoromethane
Fizika Nizkikh Temperatur, 2009, v. 35, No. 4 379
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