Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases
The isochoric thermal conductivities of solid (CO₂)₀,₉₀₅Kr₀,₀₉₅ and (CO2)₁₋xXex(x = 0.052 and 0.097) solution of different densities was investigated in the temperature interval from 150 K to the onset of melting. An unusual effect of point defects on the thermal conductivity has been detected. I...
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| Zitieren: | Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2006. — Т. 32, № 11. — С. 1414–1416. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-1208902017-06-14T03:05:14Z Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. Cryocrystals The isochoric thermal conductivities of solid (CO₂)₀,₉₀₅Kr₀,₀₉₅ and (CO2)₁₋xXex(x = 0.052 and 0.097) solution of different densities was investigated in the temperature interval from 150 K to the onset of melting. An unusual effect of point defects on the thermal conductivity has been detected. In pure CO₂ at T >150 K the isochoric thermal conductivity decreases smoothly with increasing temperature. In contrast, the thermal conductivity of solid CO₂/Kr and CO₂/Xe solutions first decreases passing through a minimum at 200–210 K and then starts to increase with temperature up to the onset of melting. This behavior of the isochoric thermal conductivity is attributed to the rotation of the CO₂ molecules which gains more freedom as the spherically symmetrical inert gas atoms dissolve in CO₂. 2006 Article Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2006. — Т. 32, № 11. — С. 1414–1416. — Бібліогр.: 9 назв. — англ. 0132-6414 PACS: 66.70.+f, 63.20.Ls http://dspace.nbuv.gov.ua/handle/123456789/120890 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 |
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Cryocrystals Cryocrystals |
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Cryocrystals Cryocrystals Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases Физика низких температур |
| description |
The isochoric thermal conductivities of solid (CO₂)₀,₉₀₅Kr₀,₀₉₅ and (CO2)₁₋xXex(x = 0.052 and
0.097) solution of different densities was investigated in the temperature interval from 150 K to
the onset of melting. An unusual effect of point defects on the thermal conductivity has been detected.
In pure CO₂ at T >150 K the isochoric thermal conductivity decreases smoothly with increasing
temperature. In contrast, the thermal conductivity of solid CO₂/Kr and CO₂/Xe solutions
first decreases passing through a minimum at 200–210 K and then starts to increase with
temperature up to the onset of melting. This behavior of the isochoric thermal conductivity is attributed
to the rotation of the CO₂ molecules which gains more freedom as the spherically symmetrical
inert gas atoms dissolve in CO₂. |
| format |
Article |
| author |
Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. |
| author_facet |
Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. |
| author_sort |
Konstantinov, V.A. |
| title |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases |
| title_short |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases |
| title_full |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases |
| title_fullStr |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases |
| title_full_unstemmed |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases |
| title_sort |
extraordinary temperature dependence of isochoric thermal conductivity of crystalline co₂ doped with inert gases |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2006 |
| topic_facet |
Cryocrystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120890 |
| citation_txt |
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO₂ doped with inert gases / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2006. — Т. 32, № 11. — С. 1414–1416. — Бібліогр.: 9 назв. — англ. |
| series |
Физика низких температур |
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AT konstantinovva extraordinarytemperaturedependenceofisochoricthermalconductivityofcrystallineco2dopedwithinertgases AT manzheliivg extraordinarytemperaturedependenceofisochoricthermalconductivityofcrystallineco2dopedwithinertgases AT revyakinvp extraordinarytemperaturedependenceofisochoricthermalconductivityofcrystallineco2dopedwithinertgases AT saganvv extraordinarytemperaturedependenceofisochoricthermalconductivityofcrystallineco2dopedwithinertgases |
| first_indexed |
2025-07-08T18:49:25Z |
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2025-07-08T18:49:25Z |
| _version_ |
1837105745599922176 |
| fulltext |
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11, p. 1414–1416
Extraordinary temperature dependence of isochoric
thermal conductivity of crystalline CO2 doped with
inert gases
V.A. Konstantinov, V.G. Manzhelii, 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 June 22, 2006
The isochoric thermal conductivities of solid (CO2)0.905Kr0.095 and (CO2)1–xXex(x = 0.052 and
0.097) solution of different densities was investigated in the temperature interval from 150 K to
the onset of melting. An unusual effect of point defects on the thermal conductivity has been de-
tected. In pure CO2 at T >150 K the isochoric thermal conductivity decreases smoothly with in-
creasing temperature. In contrast, the thermal conductivity of solid CO2/Kr and CO2/Xe solu-
tions first decreases passing through a minimum at 200–210 K and then starts to increase with
temperature up to the onset of melting. This behavior of the isochoric thermal conductivity is at-
tributed to the rotation of the CO2 molecules which gains more freedom as the spherically symmet-
rical inert gas atoms dissolve in CO2.
PACS: 66.70.+f, 63.20.Ls
Keywords: isochoric thermal conductivity, point defects, solid CO2, rotational correlation.
It is believed that point defects cause extra phonon
scattering reducing the thermal conductivity �, but
the sign of the dependence �(T) in the high-tempera-
ture region usually remains invariant [1]. The term
«point defects» is commonly used in reference to iso-
lated impurity atoms, molecules and vacancies. Ear-
lier, such unusual behavior of the isochoric thermal
conductivity was observed in solid CO2 doped with
Xe [2]. In pure CO2 the isochoric thermal conductiv-
ity decreases with rising temperature exhibiting a de-
pendence weaker than �V � 1/T [3]. As the Xe con-
centration in CO2 increases from 0.25 to 2%, the
thermal conductivity magnitude decreases by 30–40%
and becomes temperature-independent. The explana-
tions of this behavior can be based on the concept of
the «lower limit of the thermal conductivity» [4] as-
suming a «diffusive» mode of site-to-site heat transfer.
The thermal conductivity of the sample grown from a
dense gas phase with 9.1% Xe was observed to increase
with temperature but the reason for this behavior is
still obscure. The isochoric thermal conductivity was
usually investigated in a rather narrow interval near
the melting point (190–230 K) and could not provide
information about its behavior at lower temperatures.
It was however important to know whether the de-
crease in the thermal conductivity with temperature
lowering was continuous and thus demonstrated the
behavior typical of glasses or the thermal conductivity
could start increasing like in crystals.
Later on, an increase in the high-temperature ther-
mal conductivity at rising temperature was found in
orientationally disordered phases of some molecular
crystals [5,6]. This occurs because the phonon scatter-
ing at collective rotational excitations grows weaker
as the rotational correlations between the neighboring
molecules attenuate. The same can be true for the
anomalous behavior of the thermal conductivity in the
solid CO2/Xe solution. The gain a deeper insight into
the effect, it was necessary to extend considerably the
temperature interval of isochoric thermal conductivity
measurement and to increase the pressure in the mea-
suring cell. The investigation was made in a coaxial-ge-
ometry setup using a steady-state method [7]. The
measuring beryllium bronze cell was 160 mm long,
© V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, and V.V. Sagan, 2006
with an inner diameter of 17.6 mm. The maximum per-
missible pressure in it was 800 MPa. The inner mea-
suring cylinder was 10.2 mm in diameter. Temperature
sensors (platinum resistance thermometers) were
placed in special channels of the inner and outer cylin-
ders to keep them unaffected by high pressure. A set of
protecting cylinders was used to reduce the axial heat
flows. During the growth process the temperature gra-
dient along the measuring cell was about 3 K/cm.
The pressure in the inflow capillary was varied in the
interval 40–140 MPa to grow samples of different
densities. According to electron diffraction data [8,9],
the highest solubility of Kr and Xe in CO2 in the sam-
ples evaporated from the gas phase onto a coolable
substrate was no more than 30 and 5 mol.%, respec-
tively. The solubility can be different in bulk samples
grown from a dense gas phase. To keep the gas mixture
in the inflow capillarity from accumulating the com-
ponent that was being pushed out, several acts of
short-duration depressurization by 30–40% were per-
formed during the growth process with subsequent
restoration of pressure. The pressure was produced
with a thermocompressor whose working volume was
an order of magnitude larger than that of the measur-
ing cell (200 cm3 and 28.5 cm3, respectively). This ex-
cluded large variations of the component concentra-
tions in the gas phase and inhibited a concentration
gradient in the solution. When the growth was com-
pleted, the inflow capillary was blocked by freezing it
with liquid nitrogen, and the samples were annealed
at T = 205–210 K for 1.5–2 h to remove density gradi-
ents. The total (dominant) error of measurement was
no more than 4%. The initial purity of the gases was
no worse than 99.9%.
The isochoric thermal conductivities of solid
(CO2)0.905Kr0.095 and (CO2)1–xXex solutions (x =
= 0.052 and 0.097) of different densities were investi-
gated in the temperature interval from 150 K to the
onset of melting. (The concentrations are indicated for
the initial gas mixture used to grow samples; they
were preassigned when the components became dis-
placed.) The isochoric thermal conductivity of the
solid (CO2)0.905Kr0.095 solution is shown in Fig. 1 for
the samples grown at P = 40, 90 and 140 MPa. The
temperature intervals are specified between the ar-
rows. The lower boundary of the interval is the tem-
perature at which the sample either separates from the
walls of the cell or becomes discontinuous. In this case
the «effective» thermal conductivity reaches a plateau
or decreases (not seen in the figure). The region of
high-temperature measurement is limited by the onset
of melting. Here the thermal conductivity also de-
creases usually a little [7].
It is clearly seen that the thermal conductivity of
two samples first decreases with increasing tempera-
ture, passes through a minimum at 200–210 K and then
increases up to the onset of melting. This behavior is
less pronounced in the CO2/Kr solution grown under
the lowest pressure (40 MPa), because it most closely
approaches a free sample.
The change of the sign of the dependence �(T) is
rather unusual: earlier only a general decrease in the
thermal conductivity of the lattice was observed after
introducing an impurity [1]. The temperature of the
�V(T) minimum is practically independent of the
sample density, which is additional evidence that the
effect has nothing to do with the premelting condi-
tion. The smoothed isobaric (P = 0) and isochoric (for
the sample with Vm = 27.1 cm3/mol) thermal con-
ductivities of pure CO2 [3] and the isochoric thermal
conductivity of the solid (CO2)0.905Kr0.095 and
(CO2)1–xXex (x = 0.052 and 0.097) grown at P =
= 140 MPa are shown in Fig. 2. The temperature de-
pendence of the isobaric thermal conductivity of pure
CO2 is close to 1/T. The isochoric curve deviates con-
siderably from this dependence because the thermal
conductivity approaches its «lower limit» [3]. The
thermal conductivity of three solutions are very close
in magnitude and exhibit similar temperature depen-
dences. The slight distinctions in the thermal conduc-
tivity of the (CO2)1–xXex solutions at x = 0.052 and
0.097 may be attributed to the smaller (less than
9.7%) solubility of Xe in CO2 [9].
As mentioned above, the isochoric thermal conduc-
tivity increasing with temperature is typical of some
molecular crystals with high symmetry of molecules
[5,6]. (For comparison, see the isochoric thermal con-
ductivity SF6 of the sample with Vm = 58.25 cm3/mol
at the figure bottom.) According to electron diffrac-
tion data [8,9], Kr or Xe dissolved in CO2 loosen the
crystal lattice and reduce the contribution of the
anisotropic component to the binding energy of the
Extraordinary temperature dependence of isochoric thermal conductivity of crystalline CO2
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1415
160 180 200 220 240
1.5
2.0
2.5
3.0
CO
2
+ 9.5% Kr
T, K
�
, m
W
/(
cm
K
)
Fig. 1. Isochoric thermal conductivity of solid
(CO2)0.905Kr0.095 solution for samples grown from a dense
gas phase at P, MPa: 40 (�), 90 (�) and 140 (�).
molecular crystal. Unfortunately, the structure of
condensed films was investigated only up to 46 K in
CO2/Kr and 60 K in CO2/Xe. The results of our
study suggest that the rotational motion of the CO2
molecules in these solutions is to a great extent free at
premelting temperatures.
As was shown in our previous studies, the consider-
able freedom of the rotational motion of the molecules
in molecular crystals leads to an increase in the
isochoric thermal conductivity [5,6]. This occurs be-
cause the phonon scattering at collective rotational
excitations becomes weaker as the rotational correla-
tions of the neighboring molecules attenuate. The ex-
traordinary behavior of the isochoric thermal conduc-
tivity of solid CO2 doped with inert gases prompts the
conclusions about intensive reorientational motion of
the molecules in these solid solutions at premelting
temperatures.
This study was supported by the Ukrainian Minis-
try of Education and Science, Project �7/286-2001
«Novel quantum and anharmonic effects in mixtures
of cryocrystals».
1. R. Berman, Thermal Conduction in Solids, Oxford,
Clarendon Press (1976).
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Fiz. Nizk. Temp. 14, 749 (1988) [Sov. J. Low Temp.
Phys. 14, 412 (1988].
3. V.A. Konstantinov, V.G. Manzhelii, S.A. Smirnov, and
A.M. Tolkachev, Fiz. Nizk. Temp. 14, 189 (1988)
[Sov. J. Low Temp. Phys. 14, 104 (1988)].
4. D.G. Cahill, S.K. Watson, and R.O. Pohl, Phys. Rev.
B46, 6131 (1992).
5. V.A. Konstantinov and V.G. Manzhelii, in: Die Kunst
of Phonons, T. Paskiewizc, and T. Rapsewizc (eds.),
New York, London: Plenum Press (1994), p. 321.
6. O.I. Purskii, N.N. Zholonko, and V.A. Konstantinov,
Fiz. Nizk. Temp. 29, 1021 (2003) [Low Temp. Phys.
29, 749 (2003)].
7. V.A. Konstantinov, S.A. Smirnov, and V.P. Revyakin,
Instr. Exp. Tech. 42, 133 (1999).
8. S.J. Kovalenko and A.A. Solodovnik, Fiz. Nizk. Temp.
18, 749 (1992) [Low Temp. Phys. 18, 626 (1992)].
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Temp. 19, 336 (1993) [Low Temp. Phys. 19, 238
(1993)].
1416 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, and V.V. Sagan
100 150 200 250 300
2
4
6
SF6
pure CO2
�P
�V
CO2 + 9.7% Xe
CO2 + 9.5% Kr
CO2+ 5.2% Xe
T, K
�
, m
W
/(
cm
K
)
Fig. 2. Smoothed isobaric (P = 0) and isochoric (Vm =
= 27.1 cm3/mol) thermal conductivities of pure CO2 and
the isochoric thermal conductivity of solid CO2/Kr and
CO2/Xe solutions grown at P = 140 MPa. For compari-
son the isochoric thermal conductivity SF6 of the sample
with Vm = 58.25 cm3/mol is shown at the bottom.
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