Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures
The temperature dependence of the linear thermal expansion coefficient α(T) has been investigated in the temperature range of 2.5 to 23 K for two different CH4–C60 solutions in which CH4 molecules occupied 24 and 50% of the octahedral interstitial sites of the C60 lattice. In both cases, α(T) exhibi...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Cite this: | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures / A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, G.E. Gadd, S. Moricca, D. Cassidy, B. Sundqvist // Физика низких температур. — 2007. — Т. 33, № 12. — С.1401-1405. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859993307614019584 |
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| author | Dolbin, A.V. Esel’son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Gadd, G.E. Moricca, S. Cassidy, D. Sundqvist, B. |
| author_facet | Dolbin, A.V. Esel’son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Gadd, G.E. Moricca, S. Cassidy, D. Sundqvist, B. |
| citation_txt | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures / A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, G.E. Gadd, S. Moricca, D. Cassidy, B. Sundqvist // Физика низких температур. — 2007. — Т. 33, № 12. — С.1401-1405. — Бібліогр.: 16 назв. — англ. |
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| description | The temperature dependence of the linear thermal expansion coefficient α(T) has been investigated in the temperature range of 2.5 to 23 K for two different CH4–C60 solutions in which CH4 molecules occupied 24 and 50% of the octahedral interstitial sites of the C60 lattice. In both cases, α(T) exhibits hysteresis, suggesting the existence of two types of orientational glass associated with these solutions. The temperature of the first-order phase transition between these two glasses was estimated and the behavior of these two glasses compared. The characteristic times of thermalization τ1, reorientation of the C60 molecules τ2, and of the phase transformation between the glasses τ', have been estimated for these solutions. Both the temperature dependence of α(T) and the characteristic thermalization time τ1are found to have features near the phase transition temperature and an explanation has been put forward to explain these observed features.
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| first_indexed | 2025-12-07T16:33:08Z |
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Fizika Nizkikh Temperatur, 2007, v. 33, No. 12, p. 1401–1405
Specific features of thermal expansion and
polyamorphism in CH4–C60 solutions at low temperatures
A.V. Dolbin1, V.B. Esel’son1, V.G. Gavrilko1, V.G. Manzhelii1, N.A. Vinnikov1,
G.E. Gadd2, S. Moricca2, D. Cassidy2, and B. Sundqvist3
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: dolbin@ilt.kharkov.ua
2
Australian Nuclear Science & Technology Organisation, NSW 2234, Australia
3
Department of Physics, Umea University, SE - 901 87 Umea, Sweden
Received July 11, 2007
The temperature dependence of the linear thermal expansion coefficient �(T) has been investigated in
the temperature range of 2.5 to 23 K for two different CH4–C60 solutions in which CH4 molecules occupied
24 and 50% of the octahedral interstitial sites of the C60 lattice. In both cases, �(T) exhibits hysteresis, sug-
gesting the existence of two types of orientational glass associated with these solutions. The temperature of
the first-order phase transition between these two glasses was estimated and the behavior of these two
glasses compared. The characteristic times of thermalization �1, reorientation of the C60 molecules �2, and
of the phase transformation between the glasses ��, have been estimated for these solutions. Both the temper-
ature dependence of �(T) and the characteristic thermalization time �1 are found to have features near the
phase transition temperature and an explanation has been put forward to explain these observed features.
PACS: 74.70.Wz Fullerenes and related materials.
Keywords:thermal expansion, orientational glass, polyamorphism.
Introduction
At temperatures below 90 K, fullerite C60 changes into
the state of an orientational glass [1]. Investigations of the
thermal expansion of such orientational glasses based on
C60 and at the same time being saturated with atomic and
diatomic gases [2–5], has revealed interesting features in
their low-temperature behavior, amongst these being the
first-order phase transition at around liquid helium temper-
atures — the so-called phenomenon of polyamorphism [3].
These investigations of the coexisting orientational glasses
concentrated primarily on the distinctions between the two
glasses, such as the characteristic times of system
thermalization and reorientation of the C60 molecules but
as well as these, the temperature of the phase transition as
well as the characteristic time for phase interconversion
between the glasses, was also studied.
It was found that the temperature of the first-order
phase transition for O2–C60 and N2–C60 glasses occured
in the temperature interval of 4.5–6 K, agreeing well with
theoretical estimates (T � 10 K) [3,6]. Polyamorphism
manifests itself as a hysteresis of the thermal expansion of
the fullerite saturated with gases. The co-existence of two
orientational glasses for a Xe–C60 solution has also been
found to be supported by x-ray phase analysis [7].
In the solutions investigated, it has been found that the
thermal expansion of the more stable glass phase (phase I)
at the relatively lower temperatures of the experiment,
consisted of both positive and negative contributions.
The characteristic time of the positive contribution �1
which describes thermalization (the processes of tempe-
rature equalization over the sample) was little dependent
on either the temperature, or the type or concentration of
the dissolved gas. Put in another way, the thermal conduc-
tivity of the solutions is mainly determined by the C60 ma-
trix, and its structure as an orientational glass. The charac-
teristic time of the negative contribution �2, exceeds �1 in
all measurement runs. The authors believe that �2 describes
the process of reorientation of the C60 molecules and will
be essentially dependent on the type of dissolved gas.
© A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, N.A.Vinnikov, G.E. Gadd, S. Moricca, D. Cassidy, and B. Sundqvist, 2007
The thermal expansion of the phase more stable at rela-
tively high temperatures (phase II) had no negative con-
tribution. The times �1 (thermalization) of phases I and II
were practically identical, which suggests that their ther-
mal conductivities are very close. It is important that the
thermalization times �1 had no noticeable features near
the phase transition temperature.
The change from the two-phase glass state to the sin-
gle–phase glass condition was stimulated by thermal
cycling of the system in a narrow temperature interval
(�T ~ 2 K). The characteristic time �� of the transition was
taken as a characteristic time of the phase transformation.
It exceeds both the times of thermalization �1 as well as
that of reorientation of the matrix molecules �2, in all
measurement events.
The features of C60 glasses have been interpreted theo-
retically in [3,6]. Some models with mechanisms have
been proposed [8,9] to explain the reorientation of the
classical C60 molecules at low temperatures. The thermo-
dynamics of the processes in C60 glasses was also
considered in [6].
The aim of these recent studies was to investigate the
effect of an impurity consisting of tetrahedral molecules
(CH4) upon the properties and interconversion kinetics of
orientational C60 glasses. To carry this out, CH4–C60 so-
lutions were prepared with molar CH4 concentrations of
both 24 and 50%.
The choice of CH4 as an impurity was also motivated
for the following reasons. Firstly, the effect of admixed
tetrahedral symmetric molecules upon the thermal expan-
sion of fullerite had so far until these studies, not been in-
vestigated. Secondly, it is naturally to be expected that
molecular symmetry would play a vital role in determin-
ing the interaction between the impurity and host C60
molecules and hence the properties of the solid C60 ma-
trix. Also in the case of CH4, this interaction would be
maximized on account of that the effective diameter of the
CH4 molecule is comparable in size to the octahedral
voids, which the dissolved molecules occupy in the crys-
tal lattice of fullerites [10–12]. It is therefore expected
that the CH4 impurity would deform the C60 lattice con-
siderably, affecting not only the lattice parameter, but also
the glass phase transition temperature, as well as other
properties of fullerite matrix.
Measurement technique and samples
The C60 sample (cylinder 10 mm in diameter and
5,27 mm high) with 24 mol.% CH4 was prepared and ana-
lyzed as follows. Prior to saturation with CH4, the sample
was kept under the condition of dynamic evacuation
(1�10–3 mm Hg, T = 300–400�C, t = 10 days) to remove
gas impurities. The pure C60 sample desaturated by this
procedure was placed into the measuring cell of the
dilatometer. The cell was then filled with CH4 at room
temperature to the pressure 760 mm Hg. The sample re-
mained under this condition for 69 days. Owing to this
doping procedure, the CH4 molecules occupied about
24% of the octahedral voids in the C60 lattice.
The composition and concentration of the gasses dis-
solved in the C60 sample were determined using a low-
temperature vacuum desorption gas analyzer (for design
and operation details see [13]). The results of the analysis
of the gas desorbed after the dilatometric measurements
as a result of stepwise heating of the CH4–C60 samples to
300�C are shown in Fig. 1 and the overall composition is
summarized in the Table. It is seen that most of the CH4
was desorbed by a temperature of 100�C.
Table 1. The composition of the gas mixture (molar fractions
nmol) desorbed from the C60 sample with 24 mol.% CH4.
Gas impurity nmol
CH4 0.93
O2+N2 0.06
CO2 0.01
The methods of preparation and analysis of the C60
sample with 50 mol. % CH4 are described elsewhere [14].
The thermal expansion of the CH4–C60 solutions was
investigated using a low temperature capacitance
dilatometer (for details of the dilatometer design and
measuring technique see [15]). Immediately before the
dilatometric investigation, the measuring cell with the
CH4–C60 sample was cooled slowly down to 70 K. At this
temperature the CH4 that remained unabsorbed by the
sample was removed from the cell. The further cooling
and the subsequent investigations were performed under
a vacuum of no worse than 1�10–5 mm Hg. The thermal
expansion was measured after a four-hour exposure of the
CH4–C60 sample to the temperature of liquid helium.
1402 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
A.V. Dolbin et al.
0
2
4
6
8
10
12
14
20 100 200 300
T, C
n
,
%
1.1
0.1 1.4
0.2
0.3
CO2
CH4
O + N2 2
9.2
11.7
1.3
Fig. 1. The composition of the gas mixture (percentage of oc-
tahedral void occupancy) desorbed from the C60 sample with
24 mol.% CH4.
Measurement results. Discussion
The temperature dependences of the linear thermal ex-
pansion coefficient (LTEC), �(T) taken from the C60 sam-
ples with 24 mol. % CH4 and 50 mol. % CH4, are shown
in Fig. 2. The dependences were obtained by averaging
the results of several series of experiments.
It is seen that on heating (curves 1, 2) and subsequent
cooling (curves 3, 4) the LTEC has a hysteresis at T > 4 K
(24 mol. % CH4) and T > 3.5 K (50 mol. % CH4). This
hysteresis points to the first-order phase transition be-
tween the orientational glasses. Below either of these re-
spective temperatures, the measured values of �(T) for
heating for and cooling of the respective solutions, are
practically identical. On heating, the thermal expansion
of the CH4–C60 samples consisted of both positive and
negative components with different characteristic times,
�1 and �2, respectively. These components were separated
using the method described in [2,3]. The temperature de-
pendence of the positive and negative contributions to the
LTEC for the samples with 24 mol. % CH4 and 50 mol. %
CH4 are shown in Fig. 3. In contrast to heating, the ther-
mal expansion measured on cooling the samples down
from the highest temperature of the experiment showed
only a positive contribution (curves 3 and 4 in Fig. 2).
The first-order phase transition of the orientational
glasses formed in the O2–C60 and N2–C60 systems occurs
in the temperature interval 4.5–6 K [4,5] (see the Intro-
duction). This was evident from the unstable behavior of
the thermal expansion in this region. On heating the
CH4–C60 samples, �(T) showed a distinct maximum at
4–5.5 K (Fig. 2) and the measured values were rather
poorly reproducible. No such signs of these first-order
phase transition have been observed in other C60 — based
orientational glasses prior to above reported ones.
Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1403
5 10 15 20
0
0.2
0.4
0.6
0.8
1.0
T, K
2
4,5
1
3
2 3 4 5 6 7 8
0
0.1
0.2
1
T, K
3
4,5
2
�
(T
),
1
0
,
K
–
5
–
1
�
(T
),
1
0
,
K
–
5
–
1
a
b
Fig. 2. Temperature dependences of linear thermal expansion
coefficient for 24 mol. % CH4–C60 and 50 mol. % CH4–C60
samples in the intervals 2.5–23 K (a) and 2.5–8 K (b): 1 – heat-
ing (50 mol. % CH4); 2 – heating (24 mol. % CH4); 3 – cooling
(50 mol. % CH4); 4 – cooling (24 mol. % CH4); 5 – pure C60
(dotted curve).
5 10 15 20
–0.2
0
0.2
0.4
0.6
0.8
1.0
T, K
5
1
2
3
4
2 3 4 5 6 7 8
–0.1
0
0.1
0.2
T, K
5
1
2
3
4
�
(T
),
1
0
,
K
–
5
–
1
�
(T
),
1
0
,
K
–
5
–
1
a
b
Fig. 3. Temperature dependence of the positive and negative
contributions to the linear thermal expansion coefficient, with
heating , for 50 mol% and 24 mol%, CH4–C60 solutions: T =
= 2.5–23 K (a), T = 2.5–8 K (b): 1 – positive contribution
(50 mol % CH4); 2 – positive contribution (24 mol. % CH4);
3 – negative contribution (50 mol. % CH4); 4 – negative con-
tribution (24 mol. % CH4); 5 – pure C60 (dotted line).
Note that the above feature exists only for the positive
contribution to the thermal expansion (Fig. 3). It is there-
fore reasonable to expect that the temperature depend-
ence of the characteristic time �1 of the positive contribu-
tion to thermal expansion also will have a feature in this
temperature region. This assumption is indeed supported
by the analysis of the T dependence of �1(T) and �2(T).
Since the positive component characterizes thermali-
zation of the sample [2,3], its characteristic time �1 in-
creases drastically near the temperature of the orien-
tational phase transition because the formation of the new
phase consumes heat and thus prolongs the time for tem-
perature equalization over the sample volume (Fig. 4).
There is another interesting feature that was not regis-
tered in previously studied C60 solutions, namely that the
�1 of the 50 mol. % CH4–C60 sample far exceeds �1 of
pure C60. It is natural to assume that the high-concentra-
tion CH4 can deform the C60 lattice significantly produc-
ing micro cracking in the sample, which in turn can in-
crease the thermal resistance of the sample and hence the
thermalization time �1. Note that the thermal expansion of
a cubic-symmetry sample is isotropic and indifferent to
micro cracking in the sample.
In contrast to the above, the characteristic time �2, of
the negative component of the LTEC is found to be weakly
dependent on temperature (see Fig. 5), which is consis-
tent with the theoretical conclusions reached in [3]. In this
study, we observed for the first time a strong dependence
of �2 on the concentration of the gas dissolved in C60.
To investigate the relative stability of the orientational
CH4–C60 glasses at different temperatures T, we mea-
sured the time dependence of the thermal expansion coef-
ficient of the CH4–C60 samples in the process of thermal
cycling in a narrow interval T ± �T, where �T is no more
than 2 K. The details of the technique are described previ-
ously [2,3]. The thermal cycling in the interval 5.5–23 K
shifted the LTEC values from curves 1 and 2 to curves 3
and 4, respectively (Fig. 2), which suggests a higher sta-
bility of the «high-temperature» phase II, over this ther-
mal cycling interval.
We have also estimated the characteristic time �� of the
phase transition between the two orientational CH4–C60
glasses. The technique of estimation has previously been
described in [2,3]. The obtained temperature dependence
of the characteristic time ��, of phase transition, for both
CH4–C60 solutions, are shown in Fig. 6. The ��-values are
found to be little dependent on the CH4 concentration.
1404 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
A.V. Dolbin et al.
5 10 15 20 25
0
50
100
150
T, K
�
1
,s
Fig. 4. Characteristic time �1 of positive contributions to the ther-
mal expansion of CH4–C60 samples with 50 mol. % CH4 (x),
24 mol. % CH4 (�� and pure C60 (�).
2 4 6 8 10 12 14 16 18 20 22 24
0
1000
2000
3000
4000
5000
6000
7000
T, K
�
�,
s
Fig. 6. Temperature dependences of the characteristic time �� of
phase transition in orientational CH4–C60, N2–C60 and O2–C60
glasses [4,5]. I–II phase transition: 50 mol. % CH4–C60 (�),
24 mol. % CH4–C60 (�), 100 mol. % N2–C60 (�), 80 mol. %
O2–C60 (�).
5 10 15 20 25
1100
T, K
20
55
150
400
7
�
2
,
s
Fig. 5. Characteristic time �2 of negative contributions to ther-
mal expansion of C60 samples with 50 mol. % CH4 (�) and
24 mol. % CH4 (�).
For comparison, Fig. 6 illustrates the corresponding de-
pendence as measured for the N2–C60 and O2–C60 solu-
tions, which have linear impurity molecules [4,5].
It is interesting to note that in contrast to the N2–C60
and O2–C60 solutions [4,5], the dependence ��(T) of the
orientational CH4–C60 glasses for both solutions, exhibit
no maxima (see Fig. 6). This behavior of the temperature
dependence of the characteristic phase transition time
��(T) for CH4–C60, may be determined by the rotational
dynamics of the CH4 impurity in the octahedral voids of
the crystal lattice of fullerite [16].
Conclusions
The first-order phase transition was observed in the
solutions formed by dissolving CH4 in orientationally
disordered C60 at liquid helium temperatures. The ther-
mal expansion of one of the coexisting orientational
CH4–C60 glasses (phase I) was found to contain a nega-
tive contribution. Earlier, similar results were obtained on
C60 saturated with He, Kr, Xe, H2, D2, N2, O2 [2–5].
It is first observed that the temperature dependence of
the positive component of the thermal expansion and the
characteristic time �1 of phase I have maxima which are
interpreted as indications of the first-order phase transi-
tion between the orientational glasses. The significant de-
formation of the C60 lattice by the dissolved CH4 is also
evident from the concentration dependence of this char-
acteristic thermalization time �1 for the CH4–C60 sample.
In contrast to the N2–C60 and O2–C60 solutions [4,5],
the characteristic phase transformation time �� in the
CH4–C60 solutions decreases monotonously with increas-
ing temperature.
The coexisting glasses formed in gas-fullerite solu-
tions differ in the orientation of the C60 molecules. It is
therefore reasonable to expect a certain correlation be-
tween the characteristic time �2 of reorientation of C60
molecules and the characteristic time �� of the mutual
glass phase transition. However, this sort of correlation
was not found in previous investigations [2–5]. There is
no evidence of such correlation for CH4–C60 either (see
Figs. 5, 6). The absence of �2 – �� correlation agrees with
the speculations reached in the theoretical studies [6,8,9].
The authors assume that the characteristic time �2 de-
scribes only the reorientation of the C60 molecules dis-
posed between the domains, whereas the C60 molecules
disposed inside the domains have a certain invariant ori-
entation. The characteristic times of the phase transition
�� describe the changes in the orientation of the C60 mole-
cules inside the domains. Thus, �2 and �� are associated
with processes that are not connected directly.
We wish to thank Prof. A.S. Bakai for valuable discussion.
The authors are indebted to the Science and Technol-
ogy Center in Ukraine (Project Uzb-116J) for support.
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Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1405
|
| id | nasplib_isofts_kiev_ua-123456789-7775 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T16:33:08Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Dolbin, A.V. Esel’son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Gadd, G.E. Moricca, S. Cassidy, D. Sundqvist, B. 2010-04-12T13:16:20Z 2010-04-12T13:16:20Z 2007 Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures / A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, G.E. Gadd, S. Moricca, D. Cassidy, B. Sundqvist // Физика низких температур. — 2007. — Т. 33, № 12. — С.1401-1405. — Бібліогр.: 16 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/7775 The temperature dependence of the linear thermal expansion coefficient α(T) has been investigated in the temperature range of 2.5 to 23 K for two different CH4–C60 solutions in which CH4 molecules occupied 24 and 50% of the octahedral interstitial sites of the C60 lattice. In both cases, α(T) exhibits hysteresis, suggesting the existence of two types of orientational glass associated with these solutions. The temperature of the first-order phase transition between these two glasses was estimated and the behavior of these two glasses compared. The characteristic times of thermalization τ1, reorientation of the C60 molecules τ2, and of the phase transformation between the glasses τ', have been estimated for these solutions. Both the temperature dependence of α(T) and the characteristic thermalization time τ1are found to have features near the phase transition temperature and an explanation has been put forward to explain these observed features. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Динамика кристаллической решетки Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures Article published earlier |
| spellingShingle | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures Dolbin, A.V. Esel’son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Gadd, G.E. Moricca, S. Cassidy, D. Sundqvist, B. Динамика кристаллической решетки |
| title | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures |
| title_full | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures |
| title_fullStr | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures |
| title_full_unstemmed | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures |
| title_short | Specific features of thermal expansion and polyamorphism in CH4–C60 solutions at low temperatures |
| title_sort | specific features of thermal expansion and polyamorphism in ch4–c60 solutions at low temperatures |
| topic | Динамика кристаллической решетки |
| topic_facet | Динамика кристаллической решетки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/7775 |
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