Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature
Experimental studies of the effect of methane condensation temperature on the value of the refractive index and density of the resulting thin films are reported. The main unit of the installation is a high-vacuum chamber, which routinely operates at 10⁻⁸ - 10⁻⁶ Torr. Measurements using a two-beam He...
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irk-123456789-1295082018-01-20T03:04:38Z Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature Drobyshev, A. Aldiyarov, A. Sokolov, D. Shinbayeva, A. Физические свойства криокристаллов Experimental studies of the effect of methane condensation temperature on the value of the refractive index and density of the resulting thin films are reported. The main unit of the installation is a high-vacuum chamber, which routinely operates at 10⁻⁸ - 10⁻⁶ Torr. Measurements using a two-beam He–Ne laser interferometer in the vicinity of the methane phase transition temperature T = 20.4 K in the range of 14–32 K were carried out. It has been shown that in the vicinity of T = 20 K the temperature dependence of the refractive index undergoes an abrupt decrease with decreasing temperature. It is assumed that this gap is the result of the phase transition from the orientational disordered phase (α-phase) to the partially ordered phase (β-phase) of solid methane. The calculations of the polarizability of the methane molecules in the solid phase at two values of the deposition temperature T = 16 K and T = 30 K were performed using the Lorentz–Lorenz equation. 2017 Article Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature / A. Drobyshev, A. Aldiyarov, D. Sokolov, A. Shinbayeva // Физика низких температур. — 2017. — Т. 43, № 6. — С. 909-913. — Бібліогр.: 37 назв. — англ. 0132-6414 PACS: 61.50.–f, 78.30.–j, 68.35.Rh http://dspace.nbuv.gov.ua/handle/123456789/129508 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Физические свойства криокристаллов Физические свойства криокристаллов |
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Физические свойства криокристаллов Физические свойства криокристаллов Drobyshev, A. Aldiyarov, A. Sokolov, D. Shinbayeva, A. Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature Физика низких температур |
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Experimental studies of the effect of methane condensation temperature on the value of the refractive index and density of the resulting thin films are reported. The main unit of the installation is a high-vacuum chamber, which routinely operates at 10⁻⁸ - 10⁻⁶ Torr. Measurements using a two-beam He–Ne laser interferometer in the vicinity of the methane phase transition temperature T = 20.4 K in the range of 14–32 K were carried out. It has been shown that in the vicinity of T = 20 K the temperature dependence of the refractive index undergoes an abrupt decrease with decreasing temperature. It is assumed that this gap is the result of the phase transition from the orientational disordered phase (α-phase) to the partially ordered phase (β-phase) of solid methane. The calculations of the polarizability of the methane molecules in the solid phase at two values of the deposition temperature T = 16 K and T = 30 K were performed using the Lorentz–Lorenz equation. |
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Drobyshev, A. Aldiyarov, A. Sokolov, D. Shinbayeva, A. |
| author_facet |
Drobyshev, A. Aldiyarov, A. Sokolov, D. Shinbayeva, A. |
| author_sort |
Drobyshev, A. |
| title |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
| title_short |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
| title_full |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
| title_fullStr |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
| title_full_unstemmed |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
| title_sort |
refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2017 |
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Физические свойства криокристаллов |
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| citation_txt |
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α–β-transition temperature / A. Drobyshev, A. Aldiyarov, D. Sokolov, A. Shinbayeva // Физика низких температур. — 2017. — Т. 43, № 6. — С. 909-913. — Бібліогр.: 37 назв. — англ. |
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Физика низких температур |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6, pp. 909–913
Refractive indices and density of cryovacuum-deposited
thin films of methane in the vicinity
of the α–β-transition temperature
A. Drobyshev, A. Aldiyarov, D. Sokolov, and A. Shinbayeva
Kazakh National University Almaty 050071, Kazakhstan
E-mail: Andrei.Drobyshev@kaznu.kz
Received July 28, 2016, revised September 22, 2016, published online April 25, 2017
Experimental studies of the effect of methane condensation temperature on the value of the refractive index
and density of the resulting thin films are reported. The main unit of the installation is a high-vacuum chamber,
which routinely operates at 10–8–10–6 Torr. Measurements using a two-beam He–Ne laser interferometer in the
vicinity of the methane phase transition temperature T = 20.4 K in the range of 14–32 K were carried out. It has
been shown that in the vicinity of T = 20 K the temperature dependence of the refractive index undergoes an ab-
rupt decrease with decreasing temperature. It is assumed that this gap is the result of the phase transition from
the orientational disordered phase (α-phase) to the partially ordered phase (β-phase) of solid methane. The calcu-
lations of the polarizability of the methane molecules in the solid phase at two values of the deposition tempera-
ture T = 16 K and T = 30 K were performed using the Lorentz–Lorenz equation.
PACS: 61.50.–f Structure of bulk crystals;
78.30.–j Infrared and Raman spectra;
68.35.Rh Phase transitions and critical phenomena.
Keywords: methane; thin films, refractive index; density; substrate; phase transition.
1. Introduction
Solid methane has for nearly a century attracted the at-
tention of researchers, and this interest continues unabated
to the present, for strong and diverse reasons. The starting
point of this long history of research was the discovery by
Clusius (1929) [1] of the anomalous behavior of the heat
capacity of methane at temperature T = 20.4 K. In 1959
James and Keenan [2] demonstrated theoretically that this
anomaly may be explained as the phase transition from the
high-temperature orientationally disordered phase of me-
thane (α-phase) to the partially ordered phase at a tempera-
ture below Tc = 20.4 K (β-phase). Later it was discovered
[3–5] that the β-phase is the intermediate state of solid me-
thane towards the full orientation ordering phase (γ-phase).
The observed peculiarities in the properties of solid me-
thane, both structural and other (i.e., optical, thermal, me-
chanical) are largely due to the nuclear spin relaxation pro-
cesses and their influence on the rotational and transl-
ational subsystems of the methane crystal lattice. Study of
these processes has been carried out either directly using
structural methods [6,7] and the method of nuclear magnet-
ic resonance [8–10], or indirectly, by examining the impact
of conversion processes on the macroscopic characteristics
of solid methane. This most clearly affects the vibrational
spectra of methane in the range of translational and
librational vibrations [11,12], as well as the thermophysical
properties of methane, such as heat capacity [13,14], ther-
mal conductivity [15], and density [16,17].
This article presents results of the studies of the influ-
ence of deposition temperature of methane on the refrac-
tive index and density values of the resulting thin films. In
contrast to a rather large number of studies of equilibrium
solid methane samples [6,16–18], here we demonstrate
results obtained directly in the course of low-temperature
deposition of the samples, which for this reason were es-
sentially in a non-equilibrium state. Measurements were
carried out in the vicinity of the phase transition tempera-
ture T = 20.4 K in the range of 14–32 K.
The transition from the orientationally disordered α-phase
to the partially ordered β-phase and back changes the condi-
tions of interaction between the external electromagnetic
field and methane molecules, so as to change the contribution
of the rotational subsystem to the process. This should affect
the value of the refractive index, and the temperature de-
© A. Drobyshev, A. Aldiyarov, D. Sokolov, and A. Shinbayeva, 2017
A. Drobyshev, A. Aldiyarov, D. Sokolov, and A. Shinbayeva
pendence of this index must undergo a jump in the vicinity
of the transformation temperature. In addition, we keep in
mind the fact that the mechanism of spin-nuclear conversion
in the solid phase of methane are not yet fully understood
[19,20]. Therefore, a study of the optical and thermal prop-
erties of solid methane in non-equilibrium states may con-
tribute to this understanding.
2. Experimental setup
The main unit of the experimental setup is a high-va-
cuum chamber which routinely operates at 10–8–10–6 Torr
(described in detail elsewhere [21]). This pressure was
obtained by continuous evacuation with a turbomolecular
pump Turbo-V-301 backed with a dry scroll vacuum pump
SH-110. Pressure measurement was conducted using a
converter FRG-700 with a AGC-100 controller.
Copper substrate covered with planar silver film was
used. This substrate with a diameter of 60 mm was put in
thermal contact with a closed-cycle helium Gifford-
McMahon refrigerator and placed inside a vacuum cham-
ber. The double-stage cooling system cooled the substrate
to 14 K. A resistor heater was connected to the end of the
second stage and, with the collaborative work of the re-
frigerator and heater, the temperature could be varied
from 14–200 K. The temperature was monitored by a TS
670-1.4 silicon diode connected to a М335/20 tempera-
ture controller, which kept the temperature constant to
within 0.5 K.
In this study we used methane gas produced by IHSAN
TECHNOGAZ with purity of 99.99%.The gas was injected
from a vessel of known volume V through a needle valve.
By measuring the change in the pressure in this calibrated
volume, we could determine the amount of the gas that was
introduced into the chamber:
PVm
RT
∆ µ
= ,
where m is masse of the introduced methane, kg; ΔP is pres-
sure difference, Pa, in calibrated volume V·m3, before and
after gas injection; μ is masse of methane molecule, mol; R is
universal gas constant, J/K·mol; T is gas temperature, K.
Thanks to special protective screens, all of the injected
gas was deposited on the substrate, when the vacuum
chamber was closed. The thickness d of the deposited film
and its refractive index n were measured using two inter-
ference patterns (Fig. 1), generated by two He–Ne lasers
and P25a-SS-0-100 photomultiplier tubes. So the density ρ
of condensed film of methane could be determine as:
m
Sd
ρ = ,
where S is surface area of the condensation, m2; d is thick-
ness of the condensed film, m.
The interference curves for each laser beam during the
deposition of methane at the temperature Tc = 16 K and
gas pressure Pc = 1.2·10–4 Torr are shown in Fig. 1. The
upper curve corresponds to the angle of incidence of 0°;
the lower curve was obtained at an angle of incidence of
45°. Measurements were performed at a frequency of
100 Hz, which makes it possible to determine the period of
oscillation to within ± 0.05 s.
So in this article we present the results of the experi-
mental studies of the refractive index and the density of
thin films of methane, deposited on the metal substrate in
the range of 14–32 K. The pressure of deposition was Pc =
= 1.2·10–4 Torr. The thickness of samples was d = 1.5 μm.
The main sources of error were related to the measurement
of the interference period and random error (0,3%). Thus,
the total error in the measured values of the refractive indi-
ces amounts to no more than 0.6%.
3. Results and discussion
Before discussing the results, we note once again, that
the data shown in Fig. 2 and 3 were obtained at the fixed
temperature of the film deposition, and that each data point
corresponds to a newly prepared film.
Figure 2 shows the results of our measurements of the re-
fractive index of methane compared to those of other authors.
It is evident that our results are in good agreement with the
other authors' data, apart from [24,26]. For example, in [17]
at T = 30 K and equilibrium pressure the refractive index of
methane was measured to be n = 1.333, whereas in [22] for
the same conditions the value of n = 1.329 was obtained. In
[23] the value of n = 1.323 was calculated for the temperature
T = 20 K. A value of n = 1.350 obtained for T = 20 K by ap-
proximation of high-temperature data in [24] appears some-
what overstated.
As seen in Fig. 2, our dataset has a distinct gap in the
vicinity of the phase transition temperature T = 20.4 K. In
our opinion this is due to the fact that each of these da-
tasets is related to different phase states of a thin film of
Fig. 1. Interference curves for each laser beam during the deposi-
tion of methane at the substrate temperature Tc = 16 K and gas
pressure Pc = 1.2·10–4 Torr. The upper curve corresponds to the
angle of incidence of 0°, the lower curve was obtained at an angle
of incidence of 45°.
910 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6
Refractive indices and density of cryovacuum-deposited thin films of methane in the vicinity of the α-β-transition temperature
methane. The data in the temperature range 16–19 K re-
lates to partially orientational ordered β-phase of methane,
while the temperature interval 20.4–30 K corresponds to
the α-state with hindered rotating molecule of methane in
the crystal lattice sites. Thus it can be concluded that the
accompanying partial orientational ordering of the methane
molecules upon the α–β-transition [2] results in a substan-
tial and abrupt decrease of the refractive index of the sam-
ples in the vicinity of the phase transition temperature.
As can be seen from Fig. 2, most of the values for n
[17,22,23,26–28] are in satisfactory agreement with our
data, except for [24]. Possible causes for this deviation are
given in [17].
With regard to the reduction of the refractive index with
decreasing temperature, common for both phases, this be-
havior is also characteristic of some other cryofilms. For
example, for carbon dioxide [29] the refractive index de-
creases from n = 1.35 for the deposition temperature of T =
= 77 K to n = 1.22 for T = 10 K. Under the same condi-
tions, the refractive index of ammonia [30] decreases from
n = 1.41 to n = 1.37. The similar behavior was earlier ob-
served in our previous works in the studies of cryovacuum
films of carbon dioxide and water [31,32], the results being
in good agreement with other data [29,30].
Simultaneously with the measurement of the refractive
indices of methane films, their densities were determined
depending on the deposition temperature. These data are
shown in Fig. 3. The error in measurement of density ρ
does not exceed 4–5% and is determined mainly as the
error in measurement of the residual pressure of methane
gas in the calibration volume, and the random error.
Comparison of our data with the results of other authors
allows us to draw the following conclusions. First, there is a
significant difference in the densities of the equilibrium
samples [6,17,18] and those obtained directly (as here) dur-
ing cryodeposition [27]. In particular, in [6] the lattice pa-
rameters of solid methane are investigated using x-ray dif-
fraction in the vicinity of the α–β-transition (T = 20.4 K).
The samples were deposited from the gas phase on a sub-
strate at a temperature of T = 5 K and further annealed for
2 hours at a temperature of 35–40 K. The lattice parameters
of a defect-free polycrystalline sample of methane were
measured at progressively lower temperatures. In the vicini-
ty of the phase transition temperature T = 20,4 K, an abrupt
increase in the density of methane was clearly observed [6].
Analysis of the results of our measurements of the den-
sity of methane leads to the following conclusions. As can
be seen, the density of the methane films remains practical-
ly constant with decreasing deposition temperature. A mi-
nor decrease in the density values is slightly higher than
the measurement error. Our results are in excellent agree-
ment with the other data [27] obtained in the same manner.
The data in [24,26] clearly deviate from the majority of the
results. For the data obtained in [24], deviation of the re-
sults from those obtained by other authors is characteristic,
including the values of the refractive index.
A slight decrease in the density of methane with decreas-
ing deposition temperature may be due to the increasing
porosity of the samples. This agrees with the data for other
cryodeposited gases [29,30], for which the density of
cryofilms is typically reduced as a result of reduction in the
deposition temperature. As such, for carbon dioxide, the
change in the deposition temperature from 77 to 20 K leads
to a drop in the cryofilms density from ρ = 1670 kg/m3 (at
77 K) to ρ = 1080 kg/m3 (at 20 K). With respect to the den-
sity in the vicinity of the phase transition temperature, it
should be noted that the error of our measurements of me-
thane density (about 4–5%) does not allow us to identify the
phase transition from the α- to β-phase.
Available data for the coefficients of refraction and
density of methane produced during the same experiment
allowed us to determine the polarizability of the methane
molecules in the solid phase. These calculations were per-
formed using the Lorentz–Lorenz equation by analogy to
Fig. 2. Plots of refractive index of methane against deposition
temperature. Fig. 3. Relationship between the density of methane cryofilms
and their deposition temperature.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6 911
A. Drobyshev, A. Aldiyarov, D. Sokolov, and A. Shinbayeva
the calculations of polarizability of carbon dioxide carried
out in [29]:
2 2[( 1)/( 2)]3 / An n M 4 Nα = − − πρ ,
where: α is polarizability volume, m3, M is molar mass,
М = 16.04 kg/kmol; NA is Avogadro’s number, NA =
= 6.022·1026 1/kmol; n is refractive index for λ = 632.8
nm; ρ is density of solid methane, kg/m3.
We have calculated polarizability α at two values of the
deposition temperature T = 16 K and T = 30 K, correspond-
ing to samples in two different states of the rotational subsys-
tem of the crystal lattice of methane. For T = 16 K, we used
the measured values of density of ρ = 510 kg/m3 and refrac-
tive index of n = 1.275. The corresponding value of pola-
rizability was α16K = (2.15 ± 0.08)·10–30 m3. For T = 30 K
we used the values of density of ρ =5 20 kg/m3 and refractive
index of n = 1.340; the value of polarizability was calculated
to be α30K = (2.60 ± 0.08)·10–30 m3.Thus, the calculated rela-
tive change in polarizability of methane in this temperature
range is α16K/α30K = 0.83.
4. Conclusions
In recent years, laboratory studies of cryodeposited gas-
es including methane have been actively ongoing as part of
astrophysical investigations [25–28]. These studies are
similar to our research in terms of problem formulation,
conditions and methods of measurements. They rightly
take into account the importance of simultaneous meas-
urement of refractive index and density of cryofilms in the
same experiment, because the values of both of these pa-
rameters depend on the conditions of cryodeposition. Re-
sults presented here are in good agreement with the publi-
cations cited above and can also be interesting and useful
from the point of astrophysics. The purpose of our research
was a more detailed study of temperature dependence of
the refractive index and density of cryofilms solid me-
thane, for which, as noted earlier [2–5], at T = 20.4 K the
transition from the orientational disordered phase (α-phase)
to the partially ordered phase (β-phase) occurs. It is as-
sumed that this transition must influence the refractive
indices of solid methane. As seen in Fig. 2, in the vicinity
of T = 20 K, the temperature dependence of refractive in-
dex undergoes an abrupt decrease with decreasing tem-
perature, which confirms this assumption.
As for the density of methane cryofilms, our results are
in good agreement with the data of authors working on a
similar procedure [25,27]. The absence of peculiarities in
temperature dependence of density in the neighborhood of
T = 20 K may be due to the lack of the necessary experi-
mental precision. Moreover, the increasing sample porosity
with decreasing temperature of deposition can compensate
for the effect observed in [6]. Thus, we assume that the
increase in the density of the crystal due to the decrease of
the lattice parameter with temperature decreasing is com-
pensated by increasing of samples porosity degree.
We have calculated the polarizability α at two deposition
temperatures of T = 16 K and T = 30 K, corresponding to
samples in two different states of rotational subsystem of
crystal lattice of methane. The calculated relative change in
polarizability of methane in this temperature range is
α16K/α30K = 0.83. We can assume that observed change in
polarizability is the result of transition of a part of the free
rotators to an orientationally ordered state. Since the main
contribution to methane polarizability brings the rotational
subsystem, the decrease in the number of rotators should
lead to a decrease of polarizability. In addition the change of
polarizability may also be due to the fact [33,34], that the
polarizability is proportional to the size of molecule, and that
it depends on the rovibrational state, which varies substan-
tially as a result of α–β-transition [26,35–37]. The decreas-
ing of polarizability, calculated by us, is in good agreement
with the results of Costantino and Daniels [23], which pre-
sents data on the temperature dependence of dielectric con-
stant of solid methane, the value of which is directly related
to polarizability.
This research was supported by the Ministry of Educa-
tion and Science of the Republic of Kazakhstan, Grant
N 3118/GF4-15. Thanks to PhD Tokmoldin Nurlan for
discussions during the course of the work and useful com-
ments on this manuscript.
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6 913
http://link.springer.com/journal/10909
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1. Introduction
2. Experimental setup
3. Results and discussion
4. Conclusions
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