Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite
The effective thermal conductivity of samples of cryocrystal nanocomposite obtained from argon and SiO2 nanopowder was determined in the temperature interval 2–35 K using the steady-state method. The thermal conductivity of crystalline argon with nanoparticles of amorphous silica oxide embedded in...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1285082018-01-11T03:02:39Z Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite Nikonkov, R.V. Stachowiak, P. Jeżowski, A. Krivchikov, A.I. Наноструктуры при низких температурах The effective thermal conductivity of samples of cryocrystal nanocomposite obtained from argon and SiO2 nanopowder was determined in the temperature interval 2–35 K using the steady-state method. The thermal conductivity of crystalline argon with nanoparticles of amorphous silica oxide embedded in its structure shows a weak dependence on particle linear dimension in the interval 5–42 nm. The temperature dependence of the thermal conductivity of the nanocomposites can be well approximated by taking into account only the two mechanisms of heat carrier scattering: phonon-phonon interaction in U-processes and scattering of phonons by dislocations. 2016 Article Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite / R.V. Nikonkov, P. Stachowiak, A. Jeżowski, and A.I. Krivchikov // Физика низких температур. — 2016. — Т. 42, № 4. — С. 403–406 . — Бібліогр.: 31 назв. — англ. 0132-6414 PACS: 65.60 +a, 66.70.–f, 63.20.–e http://dspace.nbuv.gov.ua/handle/123456789/128508 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Наноструктуры при низких температурах Наноструктуры при низких температурах |
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Наноструктуры при низких температурах Наноструктуры при низких температурах Nikonkov, R.V. Stachowiak, P. Jeżowski, A. Krivchikov, A.I. Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite Физика низких температур |
| description |
The effective thermal conductivity of samples of cryocrystal nanocomposite obtained from argon and SiO2
nanopowder was determined in the temperature interval 2–35 K using the steady-state method. The thermal conductivity
of crystalline argon with nanoparticles of amorphous silica oxide embedded in its structure shows a weak dependence
on particle linear dimension in the interval 5–42 nm. The temperature dependence of the thermal conductivity
of the nanocomposites can be well approximated by taking into account only the two mechanisms of heat
carrier scattering: phonon-phonon interaction in U-processes and scattering of phonons by dislocations. |
| format |
Article |
| author |
Nikonkov, R.V. Stachowiak, P. Jeżowski, A. Krivchikov, A.I. |
| author_facet |
Nikonkov, R.V. Stachowiak, P. Jeżowski, A. Krivchikov, A.I. |
| author_sort |
Nikonkov, R.V. |
| title |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite |
| title_short |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite |
| title_full |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite |
| title_fullStr |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite |
| title_full_unstemmed |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite |
| title_sort |
thermal conductivity of argon–sio₂ cryocrystal nanocomposite |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| topic_facet |
Наноструктуры при низких температурах |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128508 |
| citation_txt |
Thermal conductivity of argon–SiO₂ cryocrystal nanocomposite / R.V. Nikonkov, P. Stachowiak, A. Jeżowski, and A.I. Krivchikov // Физика низких температур. — 2016. — Т. 42, № 4. — С. 403–406 . — Бібліогр.: 31 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT nikonkovrv thermalconductivityofargonsio2cryocrystalnanocomposite AT stachowiakp thermalconductivityofargonsio2cryocrystalnanocomposite AT jezowskia thermalconductivityofargonsio2cryocrystalnanocomposite AT krivchikovai thermalconductivityofargonsio2cryocrystalnanocomposite |
| first_indexed |
2025-07-09T09:13:35Z |
| last_indexed |
2025-07-09T09:13:35Z |
| _version_ |
1837160115855163392 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4, pp. 403–406
Thermal conductivity of argon–SiO2 cryocrystal
nanocomposite
R.V. Nikonkov, P. Stachowiak, and A. Jeżowski
Institute for Low Temperature and Structure Research, Polish Academy of Sciences, PN 1410, 50-950 Wroclaw, Poland
E-mail: P.Stachowiak@int.pan.wroc.pl
A.I. Krivchikov
B. Verkin Institute for Low Temperature Physics and Engineering of NAS Ukraine
47 Prospekt Nauky, Kharkiv 61103, Ukraine
Received December 19, 2015, published online February 24, 2016
The effective thermal conductivity of samples of cryocrystal nanocomposite obtained from argon and SiO2
nanopowder was determined in the temperature interval 2–35 K using the steady-state method. The thermal conduc-
tivity of crystalline argon with nanoparticles of amorphous silica oxide embedded in its structure shows a weak de-
pendence on particle linear dimension in the interval 5–42 nm. The temperature dependence of the thermal conduc-
tivity of the nanocomposites can be well approximated by taking into account only the two mechanisms of heat
carrier scattering: phonon-phonon interaction in U-processes and scattering of phonons by dislocations.
PACS: 65.60 +a Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.;
66.70.–f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves;
63.20.–e Phonons in crystal lattices.
Keywords: thermal conductivity, cryocrystals, nanocomposites, phonon-phonon processes, dislocation scattering.
Introduction
Not very long ago a new chapter in technology has been
crack opened. It seems that the bulk materials using nano-
and microparticles due to their particular thermal proper-
ties are going to play an important role in many future ap-
plications [1–4]. Along with the advent of the new materi-
als, new basic problems and questions regarding the
thermal transport mechanisms in bulk solids containing
numerous nanoparticles in their crystalline matrices have
emerged. Many thermal conduction mechanisms of the
new materials were negligible or just absent from the clas-
sical ones. Therefore, the analysis of phonon transfer in
crystals containing nanoparticles requires a new approach.
For example, when we consider a phonon of a wave vector
q, which encounters on its pathway a nanoparticle of linear
dimensions R, it gets scattered. The result of the scattering
depends on the so called size parameter ,χ which is de-
fined as Rχ = q . When the size parameter is small
(χ 1)<< , the scattering rule obeys Rayleigh law, i.e., the
scattering probability varies as frequency to the fourth
power. At the other limit, where the size parameter reaches
big numbers ( 1)χ >> the scattering probability is inde-
pendent of frequency of the phonon and the phonon scat-
tering cross section depends on the path length through
which the phonon travels across the nanoparticle and the
associated phase lag [5]. Thus, the size of the nanoparticle
becomes a very important factor for scattering cross sec-
tion in this regime. In the Rayleigh scattering regime, the
scattering cross section depends both on the difference of
masses of the nanoparticle and the host crystal and on the
difference of the force constancies acting in the two con-
stituencies [5]. In the case of polydispersion of nanoparti-
cles, when the size of nanoparticles deviates from its mean
value, the scattering cross section based on mean diameter
increases with increasing standard deviation of the linear
dimension of the nanoparticles [5]. The considerations
sketched above do not exhaust the complexity of problems
related to the thermal energy transfer in the discussed
nanostructured objects. They can be helpful for the analy-
sis of thermal transport processes in case of the nanoparti-
cles being far from each other. The term “far from each
other” is considered here with respect to the wavelength of
the phonons. Therefore, if the ratio of distance between the
nanoparticles and the wavelength is much large than 1,
© R.V. Nikonkov, P. Stachowiak, A. Jeżowski, and A.I. Krivchikov, 2016
R.V. Nikonkov, P. Stachowiak, A. Jeżowski, and A.I. Krivchikov
then independent phonon scattering (the scattering by one
nanoparticle without reference to the others) is a good ap-
proach. However, if the ratio σ of the interparticle distance
d and the phonon wavelength 2 /π q is close to 1, for cor-
rect description of the thermal processes multiple and de-
pendent phonon scatterings have to be taken into account.
Here the multiple phonon scattering means that a scattered
wave from one nanoparticle is incident on another particle
to be scattered again while the dependent scattering is far-
field interference of waves scattered by the different nano-
particles due to phase difference, which is ignored in the
independent scattering regime. When 1σ ≈ , the multiple
elastic scattering due to nanoparticles modifies the original
crystalline matrix phonons velocity, density of states and
their equilibrium intensity while the dependent scattering
results in change of original cross section for phonon scat-
tering by the nanoparticles. In this indirect way the multi-
ple and dependent processes influence the crystal thermal
conductivity [6]. In a real crystal — with nanoparticles
embedded in its structure — the abovementioned condition
1σ ≈ may be fulfilled when the volume density of the na-
noparticles is either high enough or at low temperatures.
As for the former, for a given volume fraction, the
interparticle distance is smaller for smaller linear dimen-
sions of the nanoparticles.
The effect of nanoparticles on the thermal conductivity
of nanocomposites was quantitatively confirmed by nu-
merous experiments [7–10]. Here we report our prelimi-
nary results of investigations of thermal conductivity of
argon crystals containing in their volume silica nanoparti-
cles of different linear dimensions. We have chosen the
crystal because of its simplicity, both in terms of the crys-
tallographic structure and interatomic interactions. As with
other rare gas solids, it is bound by van der Waals forces
and has an fcc structure in the whole range of temperatures
and pressures.
The argon crystal is also the best experimentally known
noble gas one. The first measurements of its thermal con-
ductivity were made in the 1950’s by White and Woods
[11]. Up to now, a number of measurements have been
made by other experimentators, both at constant volume
and at equilibrium vapor pressure, in various temperature
intervals, see e.g. [12–14].
Experiment
In our experiment the thermal conductivity of cryocrystal
nanocomposites was determined by steady-state heat flow
method in the temperature range from 2.2 to 35 K. The meth-
odology of the measurement and its technical aspect have
been described in details in our previous paper [15].
The thermal conductivity cell was made from glass tube
of an inner diameter of 6 mm, a wall thickness of 1 mm
and a length of 50 mm. To the ends of the tube two caps
made of copper were fixed with epoxy. The cell was
equipped with two germanium resistance thermometers
spaced 10 mm from each other. The lower one was mount-
ed 10 mm above the bottom of the ampoule. To the top cap
an electric gradient heater was attached. Through the cap a
thin-wall stainless steel capillary ran. The capillary allowed
to pump out the cell or fill it with argon gas and thermal
exchange gas of helium. During the experiment the bottom
cap rested in a copper base of controlled temperature.
For obtaining the nanocomposite samples, argon gas of
99.999% purity produced by Messer Group GmbH and
amorphous silica oxide nanoparticles of linear dimension
of about 5 nm, 15 nm and 42 nm were used. The SiO2 5 and
42 nm nanoparticle powders were synthesized in the Insti-
tute for Low Temperatures and Structure Research PAS,
Wrocław, Poland by combustion method while the one of
15 nm was obtained from Sigma-Aldrich Ltd. The 15 nm
nanoparticles showed higher dispersion than those ob-
tained in the ILTSR PAS. The size of the particles was
determined by Brunauer–Emmett–Teller method. The sur-
face area of the powders were 533.6, 143.2 and 64.1 m2/g
for 5, 15 and 42 nm nanoparticles, respectively.
The powder of an amount of 0.15 g was placed inside
the cell after the bottom cap was fixed to the glass tube.
Then the upper cap was also glued and the assembled cell
was installed in the cryostat. The nanopowder volume den-
sity in the cell was 7%. The cell prepared in the way de-
scribed above was placed in the measuring chamber of the
cryostat. At the beginning of the experiment the tempera-
ture of the cell was lowered to a little bit above the triple
point temperature of argon and argon gas was let to the
cell, whereupon the condensation to its liquid phase began.
During the condensation the temperature of the upper part
of the cell was kept a few Kelvins higher than the tempera-
ture of the bottom so that the liquid gradually filled the cell
from its bottom to the top. In this way we obtained an ar-
gon–SiO2 liquid nanocomposite. Finally, the temperature
of the bottom of the ampoule was slowly lowered — the
liquid solidified forming an argon–SiO2 cryocrystal
nanocomposite. Cooling rate during the crystal growth was
3 K/h. After crystallization the nanocomposite was cooled
down to the temperature of the thermal conductivity meas-
urement at the cooling rate of 6 K/h.
In the process of determination of the thermal conduc-
tivity two distorting factors were taken into account: 1. The
parasitic temperature gradient being a result of the heat
radiation due to the temperature mismatch of the LHe
thermal shield of the measuring cell and the sample and 2.
The heat transported by the cell glass wall. To determine
the first one, the measurements of the parasitic temperature
gradient was carried out at various temperatures for each of
the samples. As for the second one, the measurement of the
dependence of the thermal conductivity coefficient of emp-
ty cell was performed in a separate experiment.
The random error of the thermal conductivity measure-
ment in low temperatures did not exceed 1.5%, whereas
404 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4
Thermal conductivity of argon–SiO2 cryocrystal nanocomposite
above 20 K it increased to 3%, mostly due to effects con-
nected with spurious heat leaks. The systematic error did
not exceed 3%.
Results and discussion
Thermal conductivity ( )Tκ of the investigated
nanocomposites and pure solid argon [16] are both pre-
sented in Fig. 1. For all argon–SiO2 cryocrystal nanocom-
posites their thermal conductivity is lower than that of the
bulk polycrystal argon [16–20]. The dependence ( )Tκ
shows a behavior typical for polycrystaline atomic crystals.
With decreasing temperature the thermal conductivity ini-
tially increases according to the relationship ( ) TTκ ∝ then
it attains a maximum and finally decreases as T2. The be-
havior of 2( ) TTκ ∝ is specified by dominant scattering of
phonons by static strain fields surrounding dislocations
[19]. The thermal conductivity of Ar–15 nm SiO2 nano-
composite shows the smallest thermal conductivity. In the
temperatures below 6 K the dependence can be approxi-
mated by ( ) nTTκ ∝ , where n = 1.55. Here it should be not-
ed that the exponent n < 2 is, in some cases, the manifesta-
tion of a complex fractal structure of a substance [21–23].
For the preliminary analysis of the temperature depend-
ence of thermal conductivity coefficient of the investigated
samples we used a simple thermal conductivity model.
Assuming that the heat is conducted along parallel paths,
the thermal conductivity coefficient of components of a
medium is additive. It follows that the thermal conductivity
of two-component medium consisting of polycrystalline
argon and nano-SiO2 material can be approximated as a
weighted sum of the thermal conductivities of solid argon
Ar ( )Tκ and the nanoparticles of SiO2
2SiO ( )Tκ according
to the following expression [24]:
2Ar SiO( ) ( ) ( )T T Tκ = κ + κ . (1)
The value of thermal conductivity of the argon–SiO2
nanocomposite consists of the thermal conductivity
Ar ( )Tκ of solid argon which is a medium for SiO2 parti-
cles. The thermal conductivity Ar ( )Tκ is determined by
phonon transport of the heat [25–29]. The contribution of
thermal conductivity coefficient of SiO2 nanoparticle,
2SiO ( )Tκ , to the sum ( )Tκ is small — in Fig. 1 such low-
thermal conductivity
2SiO ( )Tκ obtained for the SiO2
nanopowder of 15 nm alone was depicted. The thermal con-
ductivity
2SiO ( )Tκ shows a dependence which is almost not
influenced by the size of SiO2 nanoparticles in the interval
from 5 up to 42 nm. In Fig. 1 the dependence
2SiO ( )Tκ for
15 nm nanopowder is shown. The data obtained for the nano-
particles of linear dimensions of 5 and 42 nm agree with the
shown ones within the experiment accuracy.
Since the contribution of nanoparticles to the resultant
thermal conductivity of the investigated nanocomposite is
negligible, in further analysis we focus exclusively on ar-
gon matrix phonons. Let us take into account only two
mechanisms of heat carrier scattering: phonon-phonon
interactions in U-processes and scattering of phonons by
dislocations. The influence of grain boundary scattering
is small in the thermal conductivity of the current sam-
ples [25]. Therefore, the dependence Ar ( )Tκ can be writ-
ten as a reciprocal of the sum of thermal resistance due to
phonon dislocation scattering and phonon-phonon scatter-
ing in U-processes with the following expression
Ar dis ph1/ ( ) 1/ ( ) 1/ ( )T T Tκ = κ + κ , (2)
where 1 /
ph ( ) eE Tk T AT −= describes the three-phonon
processes and 2
dis )(T BT=κ is the contribution of disloca-
tion scattering. We fitted equation (2) to all the data ob-
tained in the described here experiment. The solid lines
shown in Fig.1 are results of the fitting. As one can see
from the figure, the fittings describe the experimental data
well, both for pure argon and argon–SiO2 nanocomposites.
The best fit parameters A, B and E are given in Table 1.
Table 1. Value of the parameters A, B and Е of equation (2),
for which the experimentally obtained dependence of the thermal
conductivity of the investigated nanocomposites is best approxi-
mated.
Sample Three-phonon
U-processes
Dislocation
scattering
A, Wm–1 E, K В, Wm–1⋅K–3
Pure Ar 21 11.5 0.25
Ar–5 nm SiO2 21 8 0.07
Ar–15 nm SiO2 21 5 0.036
Ar–42 nm SiO2 20 7 0.06
Fig. 1. Thermal conductivity of: pure solid argon () [16], SiO2
nanoparticles of 15 nm linear dimension (), argon with SiO2
nanoparticles of linear dimentions 5 nm ( ) and 15 nm (). For
the clarity of the picture, the data obtained for solid argon–SiO2
nanoparticles of linear dimension of 42 nm were not shown.
Three solid lines are model approximation of temperature de-
pendence of the thermal conductivity of the solid argon and the
investigated nanocomposite samples.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4 405
R.V. Nikonkov, P. Stachowiak, A. Jeżowski, and A.I. Krivchikov
In the framework of the model described above, the re-
duction of the thermal conductivity of the investigated
nanocomposite is a result of an increase, in comparison to
the pure argon polycrystal, of intensity of phonon scatter-
ing by dislocations. This may be an effect of an increase of
the dislocation density in the nanocomposite, which in turn
may be a combined result of heterogeneous growth of pol-
ycrystalline argon with the nanoparticles being the crystal-
lization centers and the cooling process of the composite in
pre-melting temperature region, wherein solid argon shows
a large value of the coefficient of linear expansion [30,31]
A deviation from the dependence 2( )T Tκ ∝ for the
sample of argon–15 nm SiO2 at temperatures T < 6 K should
be noted. The deviation may be a result of contribution of
the thermal conductivity of nanopowder to the total ther-
mal conductivity. It can be observed due to low thermal
conductivity of the investigated sample.
Summary
The dependence of thermal conductivity coefficient on
temperature of Ar–SiO2 nanocomposites was experimen-
tally investigated in the temperature range 2–35 K by
steady-state heat flow method. The investigated samples
consisted of solid argon with SiO2 amorphous nanoparti-
cles embedded in the argon crystalline matrix. The fraction
of silica was 7% of the volume of the investigated samples.
It was found that the thermal conductivity of the Ar–SiO2
nanocomposites can be described by taking into account
merely two argon crystal phonon scattering mechanism:
phonon-phonon scattering in U-processes and scattering of
phonons by the crystal dislocations.
The authors want to thank Dr. Robert Pązik for provid-
ing SiO2 nanopowders.
This work was supported by the National Science Cen-
tre (Poland) grant nr. UMO-2013/08/M/ST3/00934.
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Introduction
Experiment
Results and discussion
Summary
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