Low-temperature thermal conductivity of solid carbon dioxide
Preliminary results of the thermal conductivity measurements performed in the temperature range 1.5-35 K on pure carbon dioxide are presented. The data below 25 K have been obtained for the first time. The thermal conductivity coefficient reaches very high value, of about 700 W/(m×K), unusual for si...
Збережено в:
| Дата: | 2003 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2003
|
| Назва видання: | Физика низких температур |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/128853 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Low-temperature thermal conductivity of solid carbon dioxide / V.V. Sumarokov, P. Stachowiak, A. Jezowski // Физика низких температур. — 2003. — Т. 29, № 5. — С. 603-605. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-128853 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1288532025-02-10T01:45:50Z Low-temperature thermal conductivity of solid carbon dioxide Sumarokov, V.V. Stachowiak, P. Jezowski, A. Динамика кристаллической решетки Preliminary results of the thermal conductivity measurements performed in the temperature range 1.5-35 K on pure carbon dioxide are presented. The data below 25 K have been obtained for the first time. The thermal conductivity coefficient reaches very high value, of about 700 W/(m×K), unusual for simple molecular crystal. Straightforward analysis applied to the data indicates the case of large-grained sample. 2003 Article Low-temperature thermal conductivity of solid carbon dioxide / V.V. Sumarokov, P. Stachowiak, A. Jezowski // Физика низких температур. — 2003. — Т. 29, № 5. — С. 603-605. — Бібліогр.: 9 назв. — англ. 0132-6414 PACS: 66.70.+f https://nasplib.isofts.kiev.ua/handle/123456789/128853 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Динамика кристаллической решетки Динамика кристаллической решетки |
| spellingShingle |
Динамика кристаллической решетки Динамика кристаллической решетки Sumarokov, V.V. Stachowiak, P. Jezowski, A. Low-temperature thermal conductivity of solid carbon dioxide Физика низких температур |
| description |
Preliminary results of the thermal conductivity measurements performed in the temperature range 1.5-35 K on pure carbon dioxide are presented. The data below 25 K have been obtained for the first time. The thermal conductivity coefficient reaches very high value, of about 700 W/(m×K), unusual for simple molecular crystal. Straightforward analysis applied to the data indicates the case of large-grained sample. |
| format |
Article |
| author |
Sumarokov, V.V. Stachowiak, P. Jezowski, A. |
| author_facet |
Sumarokov, V.V. Stachowiak, P. Jezowski, A. |
| author_sort |
Sumarokov, V.V. |
| title |
Low-temperature thermal conductivity of solid carbon dioxide |
| title_short |
Low-temperature thermal conductivity of solid carbon dioxide |
| title_full |
Low-temperature thermal conductivity of solid carbon dioxide |
| title_fullStr |
Low-temperature thermal conductivity of solid carbon dioxide |
| title_full_unstemmed |
Low-temperature thermal conductivity of solid carbon dioxide |
| title_sort |
low-temperature thermal conductivity of solid carbon dioxide |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
Динамика кристаллической решетки |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/128853 |
| citation_txt |
Low-temperature thermal conductivity of solid carbon dioxide / V.V. Sumarokov, P. Stachowiak, A. Jezowski // Физика низких температур. — 2003. — Т. 29, № 5. — С. 603-605. — Бібліогр.: 9 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT sumarokovvv lowtemperaturethermalconductivityofsolidcarbondioxide AT stachowiakp lowtemperaturethermalconductivityofsolidcarbondioxide AT jezowskia lowtemperaturethermalconductivityofsolidcarbondioxide |
| first_indexed |
2025-12-02T13:42:13Z |
| last_indexed |
2025-12-02T13:42:13Z |
| _version_ |
1850404171642044416 |
| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 5, p. 603–605
Low-temperature thermal conductivity of solid carbon
dioxide
V.V. Sumarokov, P. Stachowiak, and A. Je¿owski
Institute for Low Temperatures and Structure Research of the Polish Academy of Sciences
P.O. Box 1410, 50-950 Wroc³aw, Poland
E-mail: p_stach@int.pan.wroc.pl
Received May 4, 2003
Preliminary results of the thermal conductivity measurements performed in the temperature
range 1.5–35 K on pure carbon dioxide are presented. The data below 25 K have been obtained
for the first time. The thermal conductivity coefficient reaches very high value, of about
700 W/(m�K), unusual for simple molecular crystal. Straightforward analysis applied to the data
indicates the case of large-grained sample.
PACS: 66.70.+f
Solid carbon dioxide belongs to the group of simple
molecular crystals formed from linear molecules (N2,
CO, CO2 and N2O belong to the same group). At
equilibrium vapor pressure CO2 crystal has unchanged
fcc structure in the whole range of its existence [1,2].
In the solid phase the axes of O–C–O molecules,
whose carbon atoms are located in the sites of the lat-
tice, are oriented along space diagonals of the cubic
elementary cell (Pa3 space group).
Thermal, optical and other properties of solid CO2
have been studied over a wide range of temperature
and pressure, see, e.g., [1,2] and references therein.
However, the thermal conductivity at equilibrium va-
por pressure was investigated only for temperatures
above 27 K [3]. Extension of investigation of the ther-
mal conductivity of solid CO2 towards lower tempera-
tures is of interest by itself. Besides that, a comparison
with the results obtained earlier for other simple mo-
lecular crystals would provide new information con-
cerning various internal processes in the crystals.
This work presents preliminary results of measure-
ments of the thermal conductivity of solid carbon di-
oxide in the temperature range 1.5–36 K.
Experimental
The crystal of CO2 was grown, thermally treated
and measured in the home-designed liquid He experi-
mental setup, described fully in [4].
The central part of the setup is a cylindrical glass
ampoule which, during the experiment, contains the
sample under investigation. The ampoule, of length of
36 mm, has inner diameter of 4.2 mm and the wall
thickness of 1 mm. Two germanium resistance ther-
mometers are attached to the wall of the ampoule by
means of thin cooper rings and heat-conducting glue.
During measurements the thermometers serve the pur-
pose of temperature and temperature gradient deter-
mination. The distance between the thermometers is
12 mm and the lower thermometer is positioned
� 9 mm from the bottom of the ampoule.
The CO2 crystal was obtained from gas of natural
isotopic composition and of 99.999% chemical purity;
the purity of the gas was checked by means of a mass
spectrometer. The sample of solid CO2 was grown
from gaseous phase, starting at the bottom of the am-
poule, with the following conditions of condensation:
the temperature � 173.3 K, the pressure � 14 kPa, the
growth rate � 1.5 mm/h. During the sample growth
the temperature gradient of � 2.2 K/cm along the am-
poule was maintained. When the crystal fully filled
the ampoule, the growth process of the sample was
terminated and the temperature gradient was reduced
to about 1.1 K/cm. Next, the sample was cooled. The
cooling rate of the sample was about 0.1 K/h in the
temperature range 173–100 K, � 0.2 K/h in the range
100–70 K and � 0.5 K/h below 70 K. At liquid he-
lium temperatures the sample was transparent without
any visible defects or voids. When the sample was at
© V.V. Sumarokov, P. Stachowiak, and A. Je¿owski, 2003
the temperature of � 4.2 K, before the measurements
start, gaseous helium at pressure of � 1 kPa was ad-
mitted to the ampoule to improve thermal contact of
the sample with the two thermometers and the gradi-
ent heater. Measurements of the thermal conductivity
of CO2 were performed by steady state flow method.
The experimental error did not exceed 10%.
Other detail of the experiment has been described
in Refs. 4–6.
Results and discussion
The results of the measurements of the thermal con-
ductivity coefficient dependence on temperature for
solid CO2 in the temperature range 1.5–36 K have
been depicted in Fig. 1. In the figure earlier high-tem-
perature carbon dioxide data of Koloskova et al. [3]
have also been included.
In terms of quality, the dependence of the thermal
conductivity on temperature, �(T), obtained in the
experiment is typical for a dielectric crystal, see, e.g.,
[1,2]. Initially, in the lowest temperatures, the ther-
mal conductivity increases with increasing tempera-
ture, then at temperature around 5 K the coefficient
attains its maximum value. For temperatures corre-
sponding those above the maximum, the thermal con-
ductivity initially quickly decreases, following the ex-
ponential decay, and then the decrease becomes
weaker. The maximum value of the thermal conduc-
tivity coefficient � of 720 W/(m�K) should be no-
ticed. This value is much greater than any of those for
other (so-far investigated) simple molecular crystals
[5–8], except the solid para-hydrogen [7] — for com-
parison also the data obtained earlier for crystals of
pure nitrogen [5], nitrous oxide [7] and para-hydro-
gen [8] have been depicted in Fig. 1.
Despite high maximum value of the thermal con-
ductivity, which can be regarded as an evidence for
good quality of the investigated carbon dioxide crystal
and high chemical purity of the sample, the depend-
ence �(T) in low temperatures is far from typical for
low-defect-content dielectric crystal. In the standard
case of a dielectric crystal with low density of point
defects and dislocations, the low-temperature thermal
conductivity is specified by scattering of phonons on
grain or sample boundaries, which (being independent
from the phonon frequency) give � � T3. In the case of
our CO2 sample the dependence is � � T1.7. This de-
pendence is close to that observed in case of prevailing
scattering of phonons on dislocation strain fields [9].
Assuming predominating in low temperatures scatter-
ing of phonons on dislocations in CO2 and using the
information on crystal structure obtained from analy-
sis of nitrogen thermal conductivity data [5] (where
boundary scattering dominated in low temperatures)
one can estimate the order of the grain size of the in-
vestigated carbon dioxide crystal, as follows. From
the thermal conductivity expression for a gas, � �
� 1 3 Cvl (where C stands for the specific heat of
phonon gas, v for the velocity of propagation of pho-
nons and l for the phonon mean free path — in this
particular case limited by the sample grains size) one
gets the grain size of the CO2 sample �10 mm. The
above result has been obtained by assuming specific
heat of N2 about ten times greater than that of CO2
[1], the same phonon propagation velocity in nitrogen
and in carbon dioxide [1], and by taking (from the ex-
periments) the ratio � �CO N2 2
/ � 100, and the nitro-
gen crystal grain size of the order of � 10–2 mm (from
Ref. 5). It means that in our experiment we dealt with
a large-grained sample, possibly with a single crystal.
High thermal conductivity in higher temperatures
may result from relatively low anharmonicity of CO2
molecule translational vibrations and, therefore, weak
phonon—phonon interaction.
More detailed analysis of the results of measure-
ments of the dependence of thermal conductivity on
temperature for solid carbon dioxide will be published
elsewhere.
604 Fizika Nizkikh Temperatur, 2003, v. 29, No. 5
V.V. Sumarokov, P. Stachowiak, and A. Je¿owski
1 10 100
�T1.7
– our results for CO2
– Koloskova et al.[3]
– Data for N2 [5]
– Data for N2
2
O [7]
– Data for p -H [8]
T, K
1
10
10
10
, W
/(
m
K
)
�
3
2
Fig. 1. Temperature dependence of thermal conductivity
coefficient of solid carbon dioxide. Earlier data for nitro-
gen, para-hydrogen and nitrous oxide crystals have also
been included.
1. Physics of Cryocrystals, Yu.A. Freiman and V.G.
Manzhelii (eds.), AIP, New York (1996).
2. V.G. Manzhelii, A.I. Prochvatilov, V.G. Gavrilko,
and A.I. Isakina, Structure and Thermodynamic Pro-
perties of Cryocrystals, Begell House, New York (1998).
3. L.A. Koloskova, I.N. Krupskii, V.G. Manzhelii, B.Ya.
Gorodilov, and Yu.G. Kravchenko, Fiz. Tverd. Tela
16, 3089 (1974) [Sov. Phys. Solid State 16, 1993
(1974)]; Fiz. Kondens. Sost., Institute for Low Tem-
perature Physics and Engeneering (Kharkov), USSR,
No. 31 (1974), p. 69.
4. A. Je¿owski and P. Stachowiak, Cryogenics 32, 601
(1992).
5. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Je-
¿owski, Phys. Rev. B50, 543 (1994).
6. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Je-
¿owski, J. Low Temp. Phys. 111, 379 (1998).
7. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Je-
¿owski, The Conference on Cryocrystals and Quatum
Crystals, Freising’2002, poster presentation.
8. O.A. Korolyuk, B.Ya. Gorodilov, A.I. Krivchikov,
and V.G. Manzhelii, Fiz. Nizk. Temp. 25, 944 (1999)
[Low Temp. Phys. 25, 708 (1999)].
9. R. Berman, Thermal Conduction in Solids, Clarendon,
Oxford (1976).
Low-temperature thermal conductivity of solid carbon dioxide
Fizika Nizkikh Temperatur, 2003, v. 29, No. 5 605
|