The thermal diffusivity of molecular cryocrystals
Low-temperature thermal diffusivity of molecular cryocrystals (O₂, N₂, CO, N₂O and CO₂) has been investigated and some anomalies were found. The thermal diffusivity of these crystals vary by more than 4–6 orders of the magnitude in the temperature range from 1 K up to their triple points. The therm...
Збережено в:
| Дата: | 2019 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2019
|
| Назва видання: | Физика низких температур |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/176085 |
| 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: | The thermal diffusivity of molecular cryocrystals / V.V. Sumarokov, A. Jeżowski, P. Stachowiak, Y.A. Freiman // Физика низких температур. — 2019. — Т. 45, № 3. — С. 391-394. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-176085 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1760852021-02-05T01:27:09Z The thermal diffusivity of molecular cryocrystals Sumarokov, V.V. Jeżowski, A. Stachowiak, P. Freiman, Y.A. Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Low-temperature thermal diffusivity of molecular cryocrystals (O₂, N₂, CO, N₂O and CO₂) has been investigated and some anomalies were found. The thermal diffusivity of these crystals vary by more than 4–6 orders of the magnitude in the temperature range from 1 K up to their triple points. The thermal diffusivity displays jumps at the phase transition points. It has been found that the thermal diffusivity of solid oxygen is nonmonotonic. Below 4 K, the temperature dependence shows a plateau which is due to the fact that both the heat capacity and the thermal conductivity have the cubic temperature dependence in this temperature range. For the cryocrystals of the nitrogen group, a similar plateau is shifted to lower temperatures. The temperature dependence of the equalization time for these crystals is studied. Досліджено низькотемпературну температуропровідність молекулярних кріокристалів (O₂, N₂, CO, N₂O і CO₂). Температуропровідність цих кристалів змінюється більш ніж на 4–6 порядків в області температур від 1 К до їх потрійних точок. В області фазових перетворень спостерігаються стрибки температуропровідності. Виявлено, що температуропровідність твердого кисню є немонотонною. Нижче 4 К на температурній залежності спостерігається плато, яке обумовлено тим, що як теплоємність, так і теплопровідність в цьому температурному діапазоні мають кубічну температурну залежність. Для кріокристалів азотної групи подібне плато зміщується в бік більш низьких температур. Вивчено температурну залежність часів вирівнювання температури для цих кристалів. Исследована низкотемпературная температуропроводность молекулярных криокристаллов (O₂, N₂, CO, N₂O и CO₂). Температуропроводность этих кристаллов изменяется более чем на 4–6 порядков в области температур от 1 К до их тройных точек. В области фазовых переходов наблюдаются скачки температуропроводности. Обнаружено, что температуропроводность твердого кислорода является немонотонной. Ниже 4 К на температурной зависимости наблюдается плато, обусловленное тем, что как теплоемкость, так и теплопроводность в этом температурном диапазоне имеют кубическую температурную зависимость. Для криокристаллов азотной группы подобное плато смещается в сторону более низких температур. Изучена температурная зависимость времен выравнивания температуры для этих кристаллов. 2019 Article The thermal diffusivity of molecular cryocrystals / V.V. Sumarokov, A. Jeżowski, P. Stachowiak, Y.A. Freiman // Физика низких температур. — 2019. — Т. 45, № 3. — С. 391-394. — Бібліогр.: 13 назв. — англ. 0132-6414 http://dspace.nbuv.gov.ua/handle/123456789/176085 en Физика низких температур 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 |
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) |
| spellingShingle |
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) Sumarokov, V.V. Jeżowski, A. Stachowiak, P. Freiman, Y.A. The thermal diffusivity of molecular cryocrystals Физика низких температур |
| description |
Low-temperature thermal diffusivity of molecular cryocrystals (O₂, N₂, CO, N₂O and CO₂) has been investigated and some anomalies were found. The thermal diffusivity of these crystals vary by more than 4–6 orders of
the magnitude in the temperature range from 1 K up to their triple points. The thermal diffusivity displays jumps
at the phase transition points. It has been found that the thermal diffusivity of solid oxygen is nonmonotonic. Below 4 K, the temperature dependence shows a plateau which is due to the fact that both the heat capacity and the
thermal conductivity have the cubic temperature dependence in this temperature range. For the cryocrystals of
the nitrogen group, a similar plateau is shifted to lower temperatures. The temperature dependence of the equalization time for these crystals is studied. |
| format |
Article |
| author |
Sumarokov, V.V. Jeżowski, A. Stachowiak, P. Freiman, Y.A. |
| author_facet |
Sumarokov, V.V. Jeżowski, A. Stachowiak, P. Freiman, Y.A. |
| author_sort |
Sumarokov, V.V. |
| title |
The thermal diffusivity of molecular cryocrystals |
| title_short |
The thermal diffusivity of molecular cryocrystals |
| title_full |
The thermal diffusivity of molecular cryocrystals |
| title_fullStr |
The thermal diffusivity of molecular cryocrystals |
| title_full_unstemmed |
The thermal diffusivity of molecular cryocrystals |
| title_sort |
thermal diffusivity of molecular cryocrystals |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2019 |
| topic_facet |
Спеціальний випуск. “Proceedings of 12th International Conference on Cryocrystals and Quantum Crystals (CC-2018)” (Wrocław, Poland, August 26–31, 2018) |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/176085 |
| citation_txt |
The thermal diffusivity of molecular cryocrystals / V.V. Sumarokov, A. Jeżowski, P. Stachowiak, Y.A. Freiman // Физика низких температур. — 2019. — Т. 45, № 3. — С. 391-394. — Бібліогр.: 13 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT sumarokovvv thethermaldiffusivityofmolecularcryocrystals AT jezowskia thethermaldiffusivityofmolecularcryocrystals AT stachowiakp thethermaldiffusivityofmolecularcryocrystals AT freimanya thethermaldiffusivityofmolecularcryocrystals AT sumarokovvv thermaldiffusivityofmolecularcryocrystals AT jezowskia thermaldiffusivityofmolecularcryocrystals AT stachowiakp thermaldiffusivityofmolecularcryocrystals AT freimanya thermaldiffusivityofmolecularcryocrystals |
| first_indexed |
2025-07-15T13:42:23Z |
| last_indexed |
2025-07-15T13:42:23Z |
| _version_ |
1837720607466192896 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3, pp. 391–394
The thermal diffusivity of molecular cryocrystals
V.V. Sumarokov1, A. Jeżowski2, P. Stachowiak2, and Yu.A. Freiman1
1B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine,
47 Nauky Ave., Kharkov 61103, Ukraine
E-mail: sumarokov@ilt.kharkov.ua
2W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences,
P.O. Box 1410, 50-950 Wrocław, Poland
Received November 12, 2018
Low-temperature thermal diffusivity of molecular cryocrystals (O2, N2, CO, N2O and CO2) has been investi-
gated and some anomalies were found. The thermal diffusivity of these crystals vary by more than 4–6 orders of
the magnitude in the temperature range from 1 K up to their triple points. The thermal diffusivity displays jumps
at the phase transition points. It has been found that the thermal diffusivity of solid oxygen is nonmonotonic. Be-
low 4 K, the temperature dependence shows a plateau which is due to the fact that both the heat capacity and the
thermal conductivity have the cubic temperature dependence in this temperature range. For the cryocrystals of
the nitrogen group, a similar plateau is shifted to lower temperatures. The temperature dependence of the equali-
zation time for these crystals is studied.
Keywords: thermal diffusivity, thermal conductivity, specific heat, density, molecular cryocrystals.
Thermal properties are important characteristics of sub-
stances. The heat capacity, thermal conductivity, and ther-
mal diffusivity describe the rates of change in internal en-
ergy, heat propagation, and temperature changes in thermal
processes in a substance. The first two properties are exa-
mined when the substance is in thermal equilibrium. In
non-equilibrium thermal processes, the rate of temperature
equalization over the substance is characterized by the
thermal diffusivity [1]. Information on this property is im-
portant for cryogenic technology, in planning of low-
temperature experiments, in space research, etc. Here we
present the temperature dependence of the thermal diffu-
sivity of simple molecular cryocrystals: nitrogen (N2), car-
bon monoxide (CO), nitrous oxide (N2O), carbon dioxide
(CO2) and oxygen (O2) at low temperatures.
Heat propagation in a substance in the absence of inter-
nal heat sources is described by the equation of thermal
conductivity [2]
( ) ,T a T T∂
= ∆
∂τ
( )( )
( ) ( )
k Ta T
T C T
=
ρ
,
where T is the temperature, τ is the time, a is the thermal
diffusivity coefficient, ∆ is the Laplace operator, k is the
thermal conductivity coefficient, ρ is the density and C is
the specific heat.
The temperature dependence of the thermal diffusivity of
these substances were obtained using the experimental data
on the density, the heat capacity and the thermal conductivity
both our own [3–8] and literature data from Refs. 9–12. The
resulting temperature dependences of the heat capacity, den-
sity, thermal conductivity and thermal diffusivity for oxygen
crystal and for the N2-type solids are shown in Figs. 1–5.
The temperature dependence of the coefficient of thermal
diffusivity of solid oxygen is shown in Fig. 1. The tempera-
ture dependences of the density, heat capacity, and thermal
conductivity of solid oxygen [3,4,9–13] are also shown in
Fig. 1. The temperature dependence a(T) of solid oxygen is
nonmonotonic. In low-temperature α and β phases, the coef-
ficient a(T) decreases with increasing temperature. In γ
phase of crystalline oxygen, the thermal diffusivity increases
with temperature, which is mainly due to an unusual behav-
ior of the thermal conductivity — it increases with increas-
ing temperature. In the vicinity of the phase transitions,
jumps of the thermal diffusivity are observed. At γ–β phase
transition, the a(T) undergoes an upward jump of 125%.
With further decrease of the temperature in the β phase, the
thermal diffusivity increases by about 100% which is due to
the fact that the heat capacity in the β phase increases with
increasing temperature, whereas the thermal conductivity
and the density do not vary significantly with temperature.
At the temperature of β–α phase transition, the jump of a
exceeds 350%. With further decrease of the temperature, the
thermal diffusivity sharply increases and in the region of the
maximum of the heat conductivity the growth slows down,
where an inflection is observed and the curve attains a plat-
eau which is due to the fact that in this temperature range
© V.V. Sumarokov, A. Jeżowski, P. Stachowiak, and Yu.A. Freiman, 2019
V.V. Sumarokov, A. Jeżowski, P. Stachowiak, and Yu.A. Freiman
dependences on temperature, both of the heat capacity and
the thermal conductivity, vary according to a cubic law
while the density is almost independent of the temperature.
Figure 2 shows the temperature dependences of the co-
efficient of thermal diffusivity a(T) of solid nitrogen, as
well as the literature data on the temperature dependences
of the thermal conductivity [4,5], the density [9–13], and
the heat capacity [9–13]. The curve a(T) is monotonic,
although the dependence k(T) displays a sharp maximum.
The a(T) curve shows a jump at the temperature of α–β
phase transition. Unlike the case of oxygen, no plateau in
the area of liquid helium temperatures is observed.
The temperature dependences of the thermal diffusivity,
thermal conductivity [6], density [9–13], and heat capacity
[9–13] for solid carbon monoxide are presented in Fig. 3.
All curves are monotonous, except for the thermal conduc-
tion curve. In the given temperature range the value of the
thermal diffusivity of solid carbon monoxide varies by
4 orders of magnitude.
Figure 4 shows the temperature dependences of the
thermal diffusivity, thermal conductivity [7], density [9–13],
and heat capacity [9–13], of solid nitrous oxide. The curves
a(T), ρ(T), C(T) are monotonic. The value of a(T) varies
more than 5 orders below 60 K.
Figure 5 shows the temperature dependences of a(T), as
well as that of thermal conductivity [8], density [9–13], and
heat capacity [9–13] for solid carbon dioxide. The curves
a(T), ρ(T), C(T) are monotonous.
Figure 6 shows the thermal diffusivity curves for N2, CO,
N2O, CO2 and O2 cryocrystals. It was found that the thermal
diffusivity for simple molecular cryocrystals vary by more
than 4–6 orders of magnitude in the temperature range from
1 K up to their triple points. Contrary to the case of solid O2,
the curves а(Т) for solid N2, CO, N2O and CO2, do not dis-
play any plateau below 4 K. As mentioned above, the plat-
eau in the case of solid oxygen exists because in this tem-
perature range both the heat capacity and the thermal
conductivity have the same cubic dependence on temperature
Fig. 1. (Color online) Temperature dependences of the thermal
diffusivity a [cm2/s], the thermal conductivity k [mW/(cm·K)]
[3,4], the density ρ [g/cm3] [9–13] and the heat capacity C [J/(g·K)]
[9–13] for crystalline oxygen.
Fig. 2. (Color online) Temperature dependences of the thermal dif-
fusivity a [cm2/s], the thermal conductivity k [mW/(cm·K)] [4,5],
the density ρ [g/cm3] [9–13] and the heat capacity C [J/(g·K)] [9–13]
for solid nitrogen.
Fig. 3. (Color online) Temperature dependences of the thermal
diffusivity a [cm2/s], the thermal conductivity k [mW/(cm·K)]
[6], the density ρ [g/cm3] [9–13] and the heat capacity C
[J/(g·K)] [9–13] for solid carbon monoxide.
392 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
The thermal diffusivity of molecular cryocrystals
while the density weakly depends on temperature. For the
crystals of the nitrogen group, the plateau should be shifted to
lower temperatures where the thermal conductivity as a func-
tion of temperature will obey the cubic dependence.
Let us consider the temperature dependences of the
equalization times for these cryocrystals. The ratio of tem-
perature to equalization time (τ) is proportional to the ratio
of temperature to the square of the characteristic crystal
size (R2): 2/ / ,T aT Rτ ∝ whence the equalization time
2 / .R aτ ∝
As an illustration, for the comparison purpose we calcu-
lated the temperature dependences of the equalization time
in solid oxygen and in crystals of the nitrogen group for
arbitrary taken the crystal size of 1 cm.
The obtained dependences were shown in semi-log scale
in Fig. 7. In the case of oxygen at low temperatures, the
equalization time is almost temperature independent. Above
liquid helium temperatures, the curve increases with tempe-
rature. At α–β phase transition, a jump of approximately
Fig. 4. (Color online) Temperature dependences of the thermal dif-
fusivity a [cm2/s], the thermal conductivity k [mW/(cm·K)] [7], the
density ρ [g/cm3] [9–13] and the heat capacity C [J/(g·K)] [9–13] for
nitrous oxide cryocrystal.
Fig. 5. (Color online) Temperature dependences of the thermal dif-
fusivity a [cm2/s], the thermal conductivity k [mW/(cm·K)] [8], the
density ρ [g/cm3] [9–13] and the heat capacity C [J/(g·K)] [9–13] for
solid carbon dioxide.
Fig. 6. (Color online) Temperature dependences of the thermal
diffusivity for cryocrystals CO2 (1), N2O (2), N2 (3), CO (4), O2 (5).
Fig. 7. (Color online) Temperature dependences of the equalization
times in cryocrystals N2 (1), CO (2), N2O (3), CO2 (4), O2 (5).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3 393
V.V. Sumarokov, A. Jeżowski, P. Stachowiak, and Yu.A. Freiman
370% is observed. In β phase of oxygen crystal the parame-
ter R2/a keeps increasing with temperature. During the β–γ
transition, the equalization time increases abruptly by more
than 120%. Finally, in the γ phase of solid oxygen the equal-
ization time decreases with increasing temperature.
The equalization time curves for the crystals of solid ni-
trogen group are monotonous, with the exception of the
vicinity of phase transitions. The range of change of equal-
ization times for the temperatures spanning from 1 K to the
triple points is more than 4–6 orders of magnitude.
In conclusion, the temperature dependences of the
thermal diffusivity of simple molecular cryocrystals O2,
N2, CO, N2O and CO2 have been analyzed. The thermal
diffusivity varies in the range of more than 4–6 orders of
magnitude in the temperature area from 1 K up to their
triple points, and in the phase transition regions displays
the jumps. In the case of solid oxygen, the temperature
dependence of the thermal diffusivity reveals a non-
monotonic character and goes to a plateau below 4 K. The
plateau for the cryocrystals of the nitrogen group is shifted
to lower temperatures. The thermal diffusivity decreases
with increasing temperature. However, in γ phase of solid
oxygen, the coefficient of thermal diffusivity increases
with temperature.
_______
1. V.P. Isachenko, V.A. Osipova, and A.S. Sukomel, Heat
Transfer, Energy, Moscow (1969) (in Russian).
2. L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 7,
Theory of Elasticity, Science, Moscow, Main editorial board
for physical and mathematical literature (1987) (in Russian).
3. A. Jeżowski, P. Stachowiak, V.V. Sumarokov, J. Mucha, and
Yu.A. Freiman, Phys. Rev. Lett. 71, 97 (1993).
4. Yu.A. Freiman, A. Jeżowski, P. Stachowiak, V.V.
Sumarokov, and J. Mucha, Fiz. Nizk. Temp. 22, 194 (1996)
[Low Temp. Phys. 22, 148 (1996)].
5. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Jeżowski,
Phys. Rev. B 50(1), 543 (1994).
6. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Jeżowski,
J. Low Temp. Phys. 111, 379 (1998).
7. P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Jeżowski,
Phys. Rev. B 67, 172102 (2003).
8. V.V. Sumarokov, P. Stachowiak, and A. Jeżowski, Fiz. Nizk.
Temp. 29, 603 (2003) [Low Temp. Phys. 29, 449 (2003)].
9. Cryocrystals, B.I. Verkin, A.F. Prikhotko (eds.), Kiev,
Naukova Dumka (1983) (in Russian).
10. Properties of the Condensed Phases of Hydrogen and Oxygen,
Handbook, B.I. Verkin et al. (eds.), Naukova Dumka, Kiev
(1984) (in Russian).
11. Handbook of Properties of Condensed Phases of Hydrogen
and Oxygen, B.I. Verkin (ed.), Hemisphere Publ. Corp., New
York (1990).
12. Physics of Cryocrystals, V.G. Manzhelii, Yu.A. Freiman,
M.L. Klein, and A.A. Maradudin (eds.), AIP (1997).
13. Structure and Thermodynamic Properties of Cryocrystals,
Handbook, V.G. Manzhelii, A.I. Prokhvatilov, V.G. Gavrilko,
and A.I. Isakina, Begell House, Inc. Publishers, New York,
Wallingford, UK (1998).
___________________________
Температуропровідність молекулярних
кріокристалів
В.В. Сумароков, A. Jeżowski, P. Stachowiak,
Ю.О. Фрейман
Досліджено низькотемпературну температуропровідність
молекулярних кріокристалів (O2, N2, CO, N2O і CO2).
Температуропровідність цих кристалів змінюється більш ніж
на 4–6 порядків в області температур від 1 К до їх потрійних
точок. В області фазових перетворень спостерігаються стриб-
ки температуропровідності. Виявлено, що температуро-
провідність твердого кисню є немонотонною. Нижче 4 К на
температурній залежності спостерігається плато, яке обумов-
лено тим, що як теплоємність, так і теплопровідність в цьому
температурному діапазоні мають кубічну температурну зале-
жність. Для кріокристалів азотної групи подібне плато зміщу-
ється в бік більш низьких температур. Вивчено температурну
залежність часів вирівнювання температури для цих кристалів.
Ключові слова: теплопровідність, температуропровідність,
питома теплоємність, густина, молекулярні кріокристали.
Температуропроводность молекулярных
криокристаллов
В.В. Сумароков, A. Jeżowski, P. Stachowiak,
Ю.А. Фрейман
Исследована низкотемпературная температуропроводность
молекулярных криокристаллов (O2, N2, CO, N2O и CO2). Тем-
пературопроводность этих кристаллов изменяется более чем
на 4–6 порядков в области температур от 1 К до их тройных
точек. В области фазовых переходов наблюдаются скачки тем-
пературопроводности. Обнаружено, что температуропровод-
ность твердого кислорода является немонотонной. Ниже 4 К на
температурной зависимости наблюдается плато, обусловленное
тем, что как теплоемкость, так и теплопроводность в этом тем-
пературном диапазоне имеют кубическую температурную за-
висимость. Для криокристаллов азотной группы подобное пла-
то смещается в сторону более низких температур. Изучена
температурная зависимость времен выравнивания температуры
для этих кристаллов.
Ключевые слова: теплопроводность, температуропроводность,
удельная теплоемкость, плотность, молекулярные криокри-
сталлы.
394 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 3
https://doi.org/10.1103/PhysRevLett.71.97
https://scholar.google.com.ua/citations?user=JYxY_kkAAAAJ&hl=ru&oi=sra
https://scholar.google.com.ua/citations?user=SaOPKA8AAAAJ&hl=ru&oi=sra
https://doi.org/10.1103/PhysRevB.50.543
https://scholar.google.com.ua/citations?user=JYxY_kkAAAAJ&hl=ru&oi=sra
https://scholar.google.com.ua/citations?user=SaOPKA8AAAAJ&hl=ru&oi=sra
https://doi.org/10.1023/A:1022291821092
https://scholar.google.com.ua/citations?user=JYxY_kkAAAAJ&hl=ru&oi=sra
https://scholar.google.com.ua/citations?user=SaOPKA8AAAAJ&hl=ru&oi=sra
https://doi.org/10.1103/PhysRevB.67.172102
https://doi:10.1063/1.1542510
|