Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration
The results of measurements of the thermal conductivity of pure and carbon-monoxide-doped nitrogen crystals, for samples containing up to 0.7% of CO molecules, in the temperature range 1.2–26 K are presented. From the preliminary analysis it results that the interaction of phonons with admixture mol...
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| Zitieren: | Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration / P. Stachowiak, V.V. Sumarokov, J. Mucha, A. Jeżowski // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 989-991. — Бібліогр.: 7 назв. — англ. |
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Stachowiak, P. Sumarokov, V.V. Mucha, J. Jeżowski, A. 2018-01-14T12:58:09Z 2018-01-14T12:58:09Z 2003 Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration / P. Stachowiak, V.V. Sumarokov, J. Mucha, A. Jeżowski // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 989-991. — Бібліогр.: 7 назв. — англ. 0132-6414 PACS: 66.70.+f, 67.80.Gb https://nasplib.isofts.kiev.ua/handle/123456789/128920 The results of measurements of the thermal conductivity of pure and carbon-monoxide-doped nitrogen crystals, for samples containing up to 0.7% of CO molecules, in the temperature range 1.2–26 K are presented. From the preliminary analysis it results that the interaction of phonons with admixture molecule featuring the same mass, as the host molecule, is relatively weak and depends weakly on the admixture concentration within investigated range of carbon monoxide in nitrogen crystal. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Physics in Quantum Crystals Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration Article published earlier |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration Stachowiak, P. Sumarokov, V.V. Mucha, J. Jeżowski, A. Physics in Quantum Crystals |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration |
| title_full |
Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration |
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excess thermal resistivity in n₂–co solid solution at low carbon monoxide concentration |
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Stachowiak, P. Sumarokov, V.V. Mucha, J. Jeżowski, A. |
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Stachowiak, P. Sumarokov, V.V. Mucha, J. Jeżowski, A. |
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Physics in Quantum Crystals |
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Physics in Quantum Crystals |
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2003 |
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English |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
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The results of measurements of the thermal conductivity of pure and carbon-monoxide-doped nitrogen crystals, for samples containing up to 0.7% of CO molecules, in the temperature range 1.2–26 K are presented. From the preliminary analysis it results that the interaction of phonons with admixture molecule featuring the same mass, as the host molecule, is relatively weak and depends weakly on the admixture concentration within investigated range of carbon monoxide in nitrogen crystal.
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/128920 |
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Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration / P. Stachowiak, V.V. Sumarokov, J. Mucha, A. Jeżowski // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 989-991. — Бібліогр.: 7 назв. — англ. |
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2025-11-27T01:32:07Z |
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2025-11-27T01:32:07Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 989–991
Excess thermal resistivity in N2–CO solid solution at low
carbon monoxide concentration
P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Je¿owski
Institute for Low Temperatures and Structure Research, Polish Academy of Sciences
P.O. Box 1410, Wroclaw 50-950, Poland
E-mail: p_stach@int.pan.wroc.pl
The results of measurements of the thermal conductivity of pure and carbon-monoxide-doped
nitrogen crystals, for samples containing up to 0.7% of CO molecules, in the temperature range
1.2–26 K are presented. From the preliminary analysis it results that the interaction of phonons
with admixture molecule featuring the same mass, as the host molecule, is relatively weak and de-
pends weakly on the admixture concentration within investigated range of carbon monoxide in ni-
trogen crystal.
PACS: 66.70.+f, 67.80.Gb
Introduction
Crystals of nitrogen and carbon monoxide belong
to the same group of the simplest molecular solids.
Both of them have at low temperatures a crystallo-
graphic structure featuring cubic symmetry with four
molecules in an elementary cell, with molecules axes
oriented along spatial diagonals of the cubic cell. A
displacement of mass center relative to interaction
center of CO molecule causes that the CO crystal be-
longs to P213 space group, while N2 — to Pa3 [1].
Crystalline carbon monoxide forms homogeneous
solutions with nitrogen at any concentration and the
molecules mutually replace one another in the lattice
sites [2]. Solid solution of N2 with CO is a unique sys-
tem for thermal conductivity investigation due to
equality of masses of nitrogen and carbon monoxide
molecules. In the previous thermal conductivity ad-
mixture-effect investigations the guest atom (or mole-
cule) possessed the mass different than that of the host
one, see, e.g., Refs. 3, 4. Therefore, the observed and
analyzed effect was regarded as an «isotopic» phenom-
enon — phonons in the investigated crystals were
«scattered by the mass difference». In CO:N2 crystals
the situation is different. With the absence of the mass
defect one can observe phonon scattering on different
force constants and related to them deformation of the
lattice around the admixture molecule. In the case of
nitrogen crystals doped with carbon monoxide, the de-
formation of the lattice is even stronger due to above-
mentioned displacement of the mass and interaction
centers of the admixture CO molecule.
The purpose of the experiment which preliminary
results are being presented here is the investigation of
phonon scattering on difference in force constants of
interaction between molecules forming the crystal and
related to that lattice deformation around foreign mo-
lecule embedded in the crystal.
Experimental
To investigate the same-mass-impurity effect in so-
lidified nitrogen, the measurements of dependence of
the thermal conductivity coefficient on temperature
�( )T for several samples containing intentionally in-
troduced carbon monoxide molecules, at different con-
centrations, have been carried out. The measurements
have been conducted in a home-designed 4He setup,
described in Ref. 5. They were performed with
steady-state flow method in the temperature range
1.2–26 K. The samples were grown and measured in a
glass ampoule of an inner diameter 6.7 mm and a
length 67 mm. Two calibrated germanium thermome-
ters were attached (spaced 37 mm apart) to the am-
poule serving the purpose of determination of the
value and the gradient of temperature. The nuclei of
the crystal were obtained from the liquid phase, the
main part being grown directly from gaseous phase.
The growth rate of the crystal, of about 1 mm/h, was
assured by the drift of temperature of the ampoule
base (about –0.3 K/h). When the crystal fully filled
the ampoule, the sample was annealed for 12 h with
the gradient of temperature amounting 0.4 K/cm,
© P. Stachowiak, V.V. Sumarokov, J. Mucha and A. Jezowski, 2003
slightly below the triple point of the mixture of gases
used to obtain the sample. Then the sample was cooled
to the temperature of liquid helium, the cooling rate
for both � and � phases being 1 K/h. Passing the re-
gion of phase transition was realized for a time period
of 16 h, while the gradient of temperature, about
0.3 K/cm caused the phase interface to move with a
velocity of about 0.5 cm/h. The samples cooled down
to liquid-helium temperature appeared to be transpar-
ent, without notable cracks and voids.
The gases used in the experiment had natural isotope
composition with impurities not exceeding 0.003%,
mostly oxygen. The random error of the thermal con-
ductivity measurements did not exceed 7%. The system-
atic error, which resulted mostly from inaccuracy of the
geometry specification, did not exceed 5%.
Results and discussion
The results of the measurements — the thermal
conductivity coefficient dependence on temperature
for pure nitrogen crystal and for samples of N2 con-
taining 0.2, 0.25, 0.3, 0.5 and 0.7% CO — have been
depicted in Fig. 1. The dependences display their be-
havior typical for a dielectric crystal: initially the
thermal conductivity increases with increasing tem-
perature, then after reaching a maximum value, de-
creases exponentially. The samples containing addi-
tional phonon scattering centers — carbon monoxide
admixture molecules — show at low temperatures
thermal conductivity lower than that of pure nitrogen,
following the expectation. For temperatures above the
maxima, where phonon-phonon scattering in U-pro-
cesses begin to dominate the thermal conductivity, the
data points of all samples tend to the same curve.
For preliminary analysis of the data, the reduced
excess thermal resistivity �W � dependence on con-
centration c of the admixture CO molecules has been
created:
�W c c /c T
� � �
�� �( ) [ ( ) ]� �dopped pure const
1 1 .
In the formula, �pure and �dopped( )c stand for thermal
conductivity coefficients at a fixed temperature for the
pure nitrogen crystal and the N2:CO sample, respec-
tively. The �W c�( ) obtained by smoothing the data,
for the temperature 2.5 K has been shown in Fig. 2.
The dependence of reduced excess thermal conduc-
tivity on impurity concentration can be interpreted in
the framework of the «most significant phonons» ap-
proximation. In this approximation one assumes that
for steady state flow, at any temperature there exists
such a frequency �∼ T that a group of phonons of fre-
quencies from the range ( ,� � � � − , +� � where
�� �/
1, carries the greatest part of the heat flux
being transported in the sample. In the most signifi-
cant phonons approximation, the contributions of
phonons scattered in separate mechanisms to the total
thermal resistivity W of a sample are additive. There-
fore, the excess thermal resistivity �W c�( ) depicted in
Fig. 2 can be regarded as the component related to the
scattering of phonons on CO molecules. From the Fig. 2
one can see that the excess resistance per one molecule of
the admixture hardly depends on carbon monoxide con-
centration. Only a slight tendency (however still within
the experiment error) for an increase of �W c�( ) is ob-
served. It could mean that for concentrations of car-
bon monoxide molecules in nitrogen crystal not ex-
ceeding 0.7% an interaction leading to weakening of
the phonon scattering on the carbon monoxide mole-
cules with increasing concentration of the admixture
is observed.
It also should be noticed that in N2:CO crystal the
excess thermal resistivity per unit concentration is a
small number when compared to that obtained for im-
purities featuring the mass different than that of host,
see, e.g., Ref. 6. This confirms results of earlier theo-
retical investigations which have shown that the scat-
990 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
P. Stachowiak, V.V. Sumarokov, J. Mucha, and A. Je¿owski
10
10
100
T, K
�
,
m
W
/c
m
K�
pure N
0.20 % CO in N2
2
0.25 % CO in N2
0.30 % CO in N2
0.50 % CO in N2
0.70 % CO in N2
1
Fig. 1. Thermal conductivity of pure and carbon-mon-
oxide-doped solid nitrogen vs temperature.
0
1
2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Concentration of CO molecules in N , %c 2
�
W
* ,
c
m
K
/m
W
�
Fig. 2. Admixture effect in N2–CO system at 2.5 K. Solid
line is a plot of function �W� = 1.07 + 0.398 c.
tering of phonons on point defects with different force
constants and deformations of the lattice around for-
eign impurities is less effective then the scattering re-
sulting from the difference between masses of host and
admixture [7]. This also explains earlier success of the
approach, in which foreign impurities in dielectric
crystals were regarded as pure isotopic admixtures,
e.g., Ref. 4.
Concluding, the thermal conductivity of pure and
carbon-monoxide-doped nitrogen crystals has been
measured for the samples containing 0.2, 0.25, 0.3, 0.5
and 0.7% of CO molecules, in the temperature range
1.2–26 K. The simple analysis has shown that the
scattering of phonons on admixture molecules possess-
ing the same mass as the host molecule is relatively
weak when compared with the scattering on a mole-
cule featuring different mass. It has also been found
that the interaction depends rather weakly on the ad-
mixture concentration within investigated range of
carbon monoxide in nitrogen crystal.
1. Physics of Cryocrystals, Yu.A. Freiman and V.G.
Manzhelii (eds.), AIP, New York (1996).
2. V.G. Manzhelii, A.I. Prokhvatilov, I.Ya. Minchina,
and L.D. Yantsevich, Handbook of Binary Solutions
of Cryocrystals, Begell House, New York (1996).
3. J.E. Clemans, Phys. Rev. B15, 1072 (1977).
4. F.C. Baumann and R.O. Pohl, Phys. Rev. 163, 843
(1967).
5. A. Je¿owski and P. Stachowiak, Cryogenics 32, 601
(1992).
6. Yu.A. Freiman, A. Je¿owski, P. Stachowiak, V.V.
Sumarokov, and J. Mucha, Fiz. Niz. Temp. 22, 194
(1996) [Low Temp. Phys. 22, 148 (1996)].
7. J.A. Krumhansl and J.A.D. Matthew, Phys. Rev. 140,
A1812 (1965).
Excess thermal resistivity in N2–CO solid solution at low carbon monoxide concentration
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 991
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