Isochoric thermal conductivity of solid nitrogen
The isochoric thermal conductivity of solid nitrogen has been investigated on four samples of different densities in the temperature interval from 20 K to the onset of melting. In α-N₂ the isochoric thermal conductivity exhibits a dependence weaker than Λ1/T; in β-N₂ it increases slightly with...
Збережено в:
| Опубліковано в: : | Физика низких температур |
|---|---|
| Дата: | 2005 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2005
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/121462 |
| 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: | Isochoric thermal conductivity of solid nitrogen / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2005. — Т. 31, № 5. — С. 553-557. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-121462 |
|---|---|
| record_format |
dspace |
| spelling |
Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. 2017-06-14T11:49:38Z 2017-06-14T11:49:38Z 2005 Isochoric thermal conductivity of solid nitrogen / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2005. — Т. 31, № 5. — С. 553-557. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 66.70.+f, 63.20.Ls https://nasplib.isofts.kiev.ua/handle/123456789/121462 The isochoric thermal conductivity of solid nitrogen has been investigated on four samples of different densities in the temperature interval from 20 K to the onset of melting. In α-N₂ the isochoric thermal conductivity exhibits a dependence weaker than Λ1/T; in β-N₂ it increases slightly with temperature. The experimental results are discussed within a model in which the heat is transported by low-frequency phonons or by «diffusive» modes above the mobility edge. The growth of the thermal conductivity in β-N₂ is attributed to the decreasing «rotational» component of the total thermal resistance, which occurs as the rotational correlations between the neighboring molecules become weaker. This study was supported by the Ukrainian Ministry of Education and Science, Project (7/286-2001 «Novel quantum and unharmonic effects in mixtures of cryocrystals». en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Физические свойства криокристаллов Isochoric thermal conductivity of solid nitrogen Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Isochoric thermal conductivity of solid nitrogen |
| spellingShingle |
Isochoric thermal conductivity of solid nitrogen Konstantinov, V.A. Manzhelii, V.G. Revyakin, V.P. Sagan, V.V. Физические свойства криокристаллов |
| title_short |
Isochoric thermal conductivity of solid nitrogen |
| title_full |
Isochoric thermal conductivity of solid nitrogen |
| title_fullStr |
Isochoric thermal conductivity of solid nitrogen |
| title_full_unstemmed |
Isochoric thermal conductivity of solid nitrogen |
| title_sort |
isochoric thermal conductivity of solid nitrogen |
| 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. |
| topic |
Физические свойства криокристаллов |
| topic_facet |
Физические свойства криокристаллов |
| publishDate |
2005 |
| language |
English |
| container_title |
Физика низких температур |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
The isochoric thermal conductivity of solid nitrogen has been investigated on four samples of
different densities in the temperature interval from 20 K to the onset of melting. In α-N₂ the
isochoric thermal conductivity exhibits a dependence weaker than Λ1/T; in β-N₂ it increases
slightly with temperature. The experimental results are discussed within a model in which the heat
is transported by low-frequency phonons or by «diffusive» modes above the mobility edge. The
growth of the thermal conductivity in β-N₂ is attributed to the decreasing «rotational» component
of the total thermal resistance, which occurs as the rotational correlations between the neighboring
molecules become weaker.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121462 |
| citation_txt |
Isochoric thermal conductivity of solid nitrogen / V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, V.V. Sagan // Физика низких температур. — 2005. — Т. 31, № 5. — С. 553-557. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT konstantinovva isochoricthermalconductivityofsolidnitrogen AT manzheliivg isochoricthermalconductivityofsolidnitrogen AT revyakinvp isochoricthermalconductivityofsolidnitrogen AT saganvv isochoricthermalconductivityofsolidnitrogen |
| first_indexed |
2025-11-25T21:07:28Z |
| last_indexed |
2025-11-25T21:07:28Z |
| _version_ |
1850550812288221184 |
| fulltext |
Fizika Nizkikh Temperatur, 2005, v. 31, No. 5, p. 553–557
Isochoric thermal conductivity of solid nitrogen
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 July 8, 2004
The isochoric thermal conductivity of solid nitrogen has been investigated on four samples of
different densities in the temperature interval from 20 K to the onset of melting. In �-N2 the
isochoric thermal conductivity exhibits a dependence weaker than ��1/T; in �-N2 it increases
slightly with temperature. The experimental results are discussed within a model in which the heat
is transported by low-frequency phonons or by «diffusive» modes above the mobility edge. The
growth of the thermal conductivity in �-N2 is attributed to the decreasing «rotational» component
of the total thermal resistance, which occurs as the rotational correlations between the neighbor-
ing molecules become weaker.
PACS: 66.70.+f, 63.20.Ls
Introduction
The thermal conductivity of simple molecular crys-
tals is determined by both translational and orien-
tational motion of molecules in the lattice sites. This
motion can be either oscillatory or rotational depend-
ing on the relation between the noncentral force and
the rotational kinetic energy. Except for rare cases
(quantum crystals), the motion of molecules at rather
low temperatures is inherently oscillatory: the mo-
lecules execute orientational vibrations about equi-
librium directions. As the temperature rises, the
root-mean-square (rms) amplitudes of the librations
increase and the molecules can jump over some accessi-
ble orientations. This may lead to a phase transition be-
cause the long-range orientation order dissappears. By
choosing crystals with different parameters of molecu-
lar interaction and varying the temperature, it is possi-
ble to change the degree of the orientational order and
investigate the effect of the molecule rotation upon the
thermal conductivity.
Owing to their rather simple and largely similar
physical properties [1,2], the N2-type crystals (N2,
CO, N2O è CO2) consisting of linear molecules come
as suitable objects for such studies. In these crystals
the noncentral part of the molecular interaction is de-
termined mostly by the quadrupole force. At low tem-
peratures and pressures, these crystals have a cubic
lattice with four molecules per unit cell. The axes of
the molecules are along the body diagonals of cube. In
N2 and CO2 having equivalent diagonal directions the
crystal symmetry is Pa3, for the noncentrosymmetrical
molecules CO and N2O the crystal symmetry is P213.
In CO2 and N2O the noncentral interaction is very
strong and the long-range orientational order can per-
sist up to their melting temperatures. In N2 and CO
the barriers impeding the rotation of the molecules are
an order of magnitude lower; as a result, orientational
disordering phase transitions occur at 35.7 and 68.13 K,
respectively. In the high-temperature phases, the N2
and CO molecules occupy the sites of the hcp lattice
of the spatial group P63/mmc.
For a correct comparison with theory, thermal con-
ductivity must be measured at constant density, which
excludes the thermal expansion effect. Such investiga-
tions were made on CO2 and N2O in [3]. Significant
deviations from the dependence ��1/T were ob-
served at T � �D. It was shown that these departures
occurred when the thermal conductivity was approach-
ing its lower limit. The concept of the lower limit of
thermal conductivity [4] is based on the following: the
mean free paths of the oscillatory modes participating in
heat transfer are essentially limited, and the site-to-site
heat transport proceeds as a diffusive process.
The goal of this study was to investigate the
isochoric thermal conductivity of solid nitrogen in
both orientationally ordered and orientationally disor-
dered phases. Earlier, the thermal conductivity of ni-
© V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, and V.V. Sagan, 2005
trogen was investigated only under saturated vapour
pressure [5–7].
Experimental technique
Constant-volume investigations are possible for
molecular solids having a comparatively low thermal
pressure coefficient (dP/dT)V. Using a high-pressure
cell, it is possible to grow a solid sample of sufficient
density. In subsequent experiments it can be cooled
with practically unchanged volume, while the pres-
sure in the cell decreases slowly. In samples of mode-
rate densities the pressure drops to zero at a certain
characteristic temperature Ò0 and the isochoric condi-
tion is then broken; on further cooling, the sample can
separate from the walls of the cell. In the case of a
fixed volume, melting occurs in a certain temperature
interval and its onset shifts towards higher tempera-
tures as density of samples increases. This is seen, for
example, in the V–T phase diagram of solid N2 [2] in
Fig. 1. The deviations from the constant volume
caused by the thermal and elastic deformation of the
measuring cell were usually no more than 0.3% and
could be taken into account.
The investigation was made using a steady-state
technique in a coaxial-geometry setup. The measuring
beryllium bronze cell was 160 mm long with the inner
diameter 17.6 mm. The maximum permissible pressure
in it was 800 MPa. The inner measuring cylinder was
10.2 mm in diameter. Temperature sensors (platinum
resistance thermometers) were placed in special chan-
nels of the inner and outer cylinders to keep them un-
affected by high pressure. In the process of growing
the temperature gradient over the measuring cell was
1–2 K/ñm. The pressure in the inflow capillary was
varied within 50–200 ÌÐà to grow samples of differ-
ent densities. When the growth was completed, the
capillary was blocked by freezing it with liquid hydro-
gen, and the samples were annealed at premelting
temperatures for one to two hours to remove density
gradients. After measurement the samples were evapo-
rated into a thin-walled vessel and their masses were
measured by weighing. The molar volumes of the sam-
ples were estimated from the known volume of the
measuring cell and the sample masses. The total (dom-
inant) systematic error of measurement was no more
than 4% for the thermal conductivity and 0.2% for the
volume. The purity of N2 was no worse than 99.97%.
Results and discussion
The isochoric thermal conductivity of solid N2 was
investigated on four samples of different densities in
the temperature interval from 20 K to the onset of
melting. The experimental thermal cunductivities are
shown in Fig. 2 with solid lines for smoothed values
and a dashed line for measurement under saturated va-
por pressure [2, 5–7]. Under the same P, T conditions,
the discrepancy between our and literature data was
no more than 5%. The molar volumes Vm, tempera-
tures T0 (onset of V = const condition) and Tm (onset
of sample melting) are shown in Table 1. This infor-
mation is also available in Fig. 1.
Table 1. Molar volumes Vm, temperatures T0 (onset of
V = const condition) and temperatures Tm (onset of
melting).
Sample No Vm, ñm3/mole T0, K Tm, K
1 27.36 24 102
2 27.68 33 96
3 27.98 36 92
4 28.76 48 80
In �-N2 the temperature dependence of the iso-
choric thermal conductivity is weaker than ��1/T
and in similar to that observed for CO2 and N2O [3].
The thermal conductivity is practically constant im-
mediately before the ��� transition. Earlier, the ther-
mal conductivity was observed to grow in orienta-
tionally disordered phases of some molecular crystals
[8]. The Bridgman coefficients g / V T�
( ln ln )�
calculated from the experimental results are 6.0 � 0.8
for �-N2 at T = 35 K and 4.3 � 0.5 for �-N2 at T = 60 K.
The orientational motion of the molecules in �-N2
manifests itself as large-angle librations (immediately
before the ��� transition the rms libration ampli-
tudes �
2�1/2 exceed 30�) attended with hopping
over a limited set of equivalent orientations related by
the group symmetry elements [1]. The frequency of
reorientations approaches 10–11 s–1 near the ���
trànsition [9]. The analysis of heat capacity data sug-
554 Fizika Nizkikh Temperatur, 2005, v. 31, No. 5
V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, and V.V. Sagan
0 20 40 60 80 100 120
27
28
29
30
31
� �+ Tm
T0
L� + L
N2
4
3
2
1
��
3
m
T, K
V
,ñ
m
/ì
o
le
Fig. 1. V–T phase diagram of solid N2 according to [1,2]:
molar volumes (----); arrows show the onset of V = const
condition and melting.
gests that practically free precession of the molecules
is observed in �-N2 after the phase transition, which is
accompanied by axial vibration through an angle �
with respect to the hexagonal axis of the cell [1]. In
the �-phase of N2 the frequency of reorientations varies
from 9.5�1011 s–1 immediately after ��� transition to
5.5�1012 s–1 before melting [9]. This exceed considerably
the Debye frequency 1.5�1012 s–1. No distinct libration
modes were detected in �-N2 in inelastic neutron scat-
tering experiments, and even the observed translational
acoustic phonons were broadened considerably due to
the translation-orientation interaction, excluding the
case of the smallest wave vectors [10].
Remembering that the orientational motion of the
molecules in �-N2 is essentially librational in charac-
ter, the thermal conductivity can be calculated within
a model in which the heat is transferred by low-fre-
quency phonons or «diffusive» modes above the mo-
bility edge. Earlier, the model was used to calculate
the thermal conductivity of CO2 and N2O [11].
Let us describe the thermal conductivity as:
�
�
�
( ) ( )
( )
T nk v
T
l x
x
dxB
D
x
x
/TD
�
�
�
��
�
�
��
�3
1
3 4
2
0
e
e
, (1)
wherå �D = v(h/kB) (6�2n)1/3, n is the number of
atoms (molecules) per unit volume, v is the polariza-
tion-averaged sound velocity, l(x) is the phonon mean
free path. At T � �D the mean free path is mainly de-
termined by the umklapp processes l(x) = lu, wherå:
l
CTu �
�2
, C = (12�3/�2) n–1/3 (�2 k
B
/mv2). (2)
Here � is the phonon wavelenth, � is the Grüneisen
constant, m is the atomic (molecular) mass, C is the
numerical coefficient. In the first approximation, the
translation-orientation interaction in molecular crys-
tals leads to extra scattering which can be taken into
account through simple renormalization of the coeffi-
cient C [12]. Remembering that the smallest phonon
mean free path is about half the wavelength: l(x) =
= ��/2, wherå � � 1, the «diffusivity» edge �* can
be found as:
�
�* �
CT
2
, (3)
which corresponds to the effective temperature �* =
= 2hv/�kBCT. (It is assumed that �* � �D, other-
wise �* = �D.) Below, the term «diffusive» is applied
to the modes whose mean free paths reached the
smallest values [11]. The integral of thermal conduc-
tivity is subdivided into two parts describing the con-
tributions to the thermal conductivity from the
low-frequency phonons and the «diffusive» modes:
� = �ph + �dif, (4)
�
�
�
ph
e
e
( ) ( )
( )
*
T nk v
T
l x
x
dxB
D
x
x
/T
�
�
�
��
�
�
��
�
! �3
1
3 4
2
0
!
"
#
$
$
, (5)
�
�
�
�
dif
e
e
( )
(
*
T nk v
T vh
k xT
x
B
D
/T
/T
B
x
x
D
�
�
�
��
�
�
��
�3
2
3 4
�
1 2)
dx
�
!
!
!
"
#
$
$
$
.
(6)
The results were computer-fitted by the least-square
technique to the smoothed thermal conductivity values
Isochoric thermal conductivity of solid nitrogen
Fizika Nizkikh Temperatur, 2005, v. 31, No. 5 555
20 40 60 80 100
0
1
2
3
4
N2
�min
�dif
�ph
�V
T, K
�
, m
W
/ñ
m
�
Fig. 3. Fitting to smoothed values of experimental ther-
mal conductivity and contributions to thermal conductivity
from low-frequency phonons �ph and «diffusive» modes
�dif calculated according to (5),(6); the lower limit of lat-
tice heat conduetivity �min obtained as an asymptote of the
dependence �V(T) (---).
20 40 60 80 100
2
3
4
5
4
3
2
1
N
2
T , K
�
, m
W
/ñ
m
�
Fig. 2. Isochoric thermal conductivity of four solid N2 sam-
ples of different densities (see Table 1): smoothed values
(%), measurement under saturated vapor pressure according
to [2, 5–7] (---), the arrows indicate the onset of melting.
for sample in the � phaså using n = 2.21�1022 cm–3 and
v = 1.17�103 m/s [2] and varying the parameters C
and �. The best agreement with experiment was ob-
tained with C = 3.0�10–9 cm/K and � = 1.8. Corres-
pondingly, C = 0.9�10–9 cm/K and � = 2.7 for CO2
and C = 1.5�10–9 cm/K and � = 2.3 for N2O [11]. The
fitting to smoothed experimental thermal conductivi-
ties and the contributions from the low-frequency
phonons �ph and the «diffusive» modes �dif (calcu-
lated by Eqs. (5),(6)) are shown in Fig. 3.
It is seen that the «diffusive» behavior of the oscil-
latory modes appears above 20 K, and immediately be-
fore the ��� transition nearly half of the heat is
transported by the «diffusive» modes. The curves �ph
and �dif calculated for the � phase of N2 were extrapo-
lated to the region of the existence of the � phase. The
change from one structure to another may cause a
jump of the partial contributions to the thermal con-
ductivity but it will not be too large because a major
part of the heat is transported by the «diffusive»
modes and they are only slightly sensitive to the struc-
ture of the crystal. The lower limit of thermal conduc-
tivity �&min (Fig. 3, broken line) was calculated as-
suming that all the modes were «diffusive»:
& � �
�
�
�
�
�
�
�
��
�
�
��
�
�min
( )
3
6 1
1 3
2 3
2 3
2
�
� /
/
B
D
x
x
n k v
T x
d
e
e
x
D/T
0
�
� .
(7)
Note that �&min is again independent of structure and
determined only by the crystal density and hence the
Debye temperature were invariant for the constant vol-
ume. The lower limit of thermal conductivity �&min fit-
ted as an asymptote of the dependence �V (T) is � = 1.8
times higher than the value calculated according to
Cahill and Pohl [4]. The discrepancy can partly be ac-
counted for by the imperfection of the model. Neverthe-
less, there is a certain correlation between � and the
number of the degrees of freedom (three translational
and z rotational degrees) of molecules: � � (3+z)/3
[11]. Cahill and Pohl considered amorphous substances
and strongly disordered crystals consisting of atoms
having no rotational degrees of freedom.
The discussion of the lower limit of thermal con-
ductivity of molecular crystals brings up the inevita-
ble question: should the site-to-site transport of the
rotational energy of the molecules be taken into ac-
count? The above correlation suggests the positive an-
swer. In this context, the heat transfer in molecular
crystals, solid nitrogen in particular, can be inter-
preted as follows. At low temperatures, when the
phonon and libron branches are well separated, the
phonons forming the heat flow are scattered by both
phonons and librons [12]. As a result, the thermal re-
sistance increases in comparison with the situation,
e. g., in inert gases [3]. As the temperature rises, the
phonon-libron interaction enhances and the mixed
translation-orientation modes start to transport the
heat. The heat transfer increases and extra scattering
evolves due to the strong anharmonicity of the
librational vibrations. Finally, under a very strong
scattering when the heat is transported directly from
molecule to molecule (Einstein model), both the rota-
tional and translational energies should equally be
taken into account.
In �-N2 the isochoric thermal conductivity in-
creases slightly with temperature. The absolute value
of thermal conductivity is only 10–12% higher than its
lower limit �&min . This means that in �-N2 most of the
heat is transported by the «diffusive» modes. The con-
cept of the «lower limit» of thermal conductivity pos-
tulates its «saturation» rather than its growth. The in-
crease in the isochoric thermal conductivity with
temperature was observed earlier in orientationally
disordered phases of some molecular crystals [8]. This
effect can be due to the «rotational» component of the
total thermal resistance, which decreases as the rota-
tional correlation’s between the neighboring mole-
cules become weaker.
The dependence of the thermal conductivity on the
molar volume can also be interpreted within this
model. The Bridgman coefficient g / V T�
( ln ln )�
is the weighted mean with respect to the phonons and
«diffusive» modes whose volume dependences are con-
siderably different [11]:
g g g� '
�
�
�
�
ph
ph
dif
dif . (8)
Equation (8) describes the general tendency of the
Bridgman coefficient to decrease as more of heat is being
transported by «diffusive» modes. The calculation using
the procedure [11] and the mean Gruneisen coefficient �
= 2.2 for nitrogen [1,2] gives g = 5.2 at T = 35 K and 3.4
at T = 60 K, which is in reasonable agreement with the
experimental values.
Conclusions
The isochoric thermal conductivity of solid N2 has
been investigated on four samples of different densi-
ties in the temperature interval from 20 K to the onset
of melting. In �-N2 the isochoric thermal conductivity
varies following a dependence weaker than ��1/T; in
�-N2 it increases slightly with temperature. It is
shown that the experimental results can be explained
within a model in which the heat is transported by
low-frequency phonons and by «diffusive» modes
above the boundary of mobility. In �-N2 most of the
556 Fizika Nizkikh Temperatur, 2005, v. 31, No. 5
V.A. Konstantinov, V.G. Manzhelii, V.P. Revyakin, and V.V. Sagan
heat transported by the «diffusive» modes. The weak
growth of the thermal conductivity in �-N2 can be at-
tributed to the decrease in the «rotational» component
of the total thermal resistance due to the relaxing rota-
tional correlations between the neighboring molecules.
This study was supported by the Ukrainian Minis-
try of Education and Science, Project (7/286-2001
«Novel quantum and unharmonic effects in mixtures
of cryocrystals».
1. Physics of Cryocrystals, V.G. Manzhelii and Yu.A.
Freiman (eds.), AIP, New York (1996).
2. V.G. Manzhelii, A.I. Prokhvatilov, V.G. Gavrilko,
and A.P. Isakina, Structure and Termodynamic
Properties of Cryocrystals, Begell House, inc., New
York, Walingford, U.K. (1999).
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. H.M. Roder, Cryogenics 2, 302 (1962).
6. L.A. Koloskova, I.N. Krupskii, V.G. Manzhelii, and
B.Ya. Gorodilov, Fiz. Tverd. Tela 15, 1913 (1973)
[Sov. Phys. Solid State 15, 1278 (1973)].
7. P. Stachoviak, V.V. Sumarokov, J. Mucha, and A.
Jezowski, Phys. Rev. B50, 543 (1994).
8. O.I. Purskii, N.N. Zholonko, and V.A. Konstantinov,
Fiz. Nizk. Temp. 29, 1021 (2003) [Low Temp. Phys.
29, 771 (2003)].
9. T.A. Scott, Phys. Lett. C27, 89 (1976).
10. B.M. Powell, G. Doling, and H.F. Nieman, J. Chem.
Phys. 79, 982 (1983).
11. V.A. Konstantinov, Fiz. Nizk. Temp. 29, 567 (2003)
[Low Temp. Phys. 29, 442 (2003)].
12. V.G. Manzhelii, V.B. Kokshenev, L.A. Koloskova,
and I.N. Krupskii, Fiz. Nizk. Temp. 1, 1302 (1975)
[Sov. J. Low Temp. Phys. 1, 624 (1975)].
Isochoric thermal conductivity of solid nitrogen
Fizika Nizkikh Temperatur, 2005, v. 31, No. 5 557
|