Formation of superfluid liquid pocket in aerogel and its solidification by cooling
Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also o...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2013
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| Cite this: | Formation of superfluid liquid pocket in aerogel and its solidification by cooling / H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, Y. Okuda // Физика низких температур. — 2013. — Т. 39, № 9. — С. 1006–1011. — Бібліогр.: 34 назв. — англ. |
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| author | Matsuda, H. Ochi, A. Isozaki, R. Nomura, R. Okuda, Y. |
| author_facet | Matsuda, H. Ochi, A. Isozaki, R. Nomura, R. Okuda, Y. |
| citation_txt | Formation of superfluid liquid pocket in aerogel and its solidification by cooling / H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, Y. Okuda // Физика низких температур. — 2013. — Т. 39, № 9. — С. 1006–1011. — Бібліогр.: 34 назв. — англ. |
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| container_title | Физика низких температур |
| description | Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed.
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© H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, and Y. Okuda, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9, pp. 1006–1011
Formation of superfluid liquid pocket in aerogel
and its solidification by cooling
H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, and Y. Okuda
Department of Physics, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro, Tokyo 152-8551, Japan
E-mail: nomura.r.aa@m.titech.ac.jp
Received February 25, 2013
Formation of superfluid liquid pockets of
4
He surrounded by
4
He crystals were observed in an aerogel of 96%
porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-
ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a
smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport
process are discussed.
PACS: 64.70.D– Solid-liquid transitions;
67.80.bf Liquid-solid interfaces; growth kinetics;
67.25.D– Superfluid phase.
Keywords: superfluid
4
He, crystal growth, aerogel, supersolid.
1. Introduction
Properties of superfluid
4
He in porous materials have
been investigated extensively and variations in the static
properties, such as reduction in the superfluid transition
temperatures and elevation of the crystallization pressure
have been revealed [1–9]. However, not much is known
about the dynamical process of superfluid
4
He in porous
materials due to the lack of an appropriate method to tackle
the physics. Silica-aerogels are highly porous materials
whose pore size is on a nanometer scale while at the same
time being very transparent; we can thus investigate the
dynamics inside the material by visual observation. There
have been several reports on the imbibition process of
normal fluid and superfluid
4
He in aerogel by visualization
[10–12]; superfluid
4
He is imbibed in aerogel at a constant
rate while normal fluid
4
He is imbibed following the clas-
sical Washburn law. Anomalous two-step imbibition was
also found in highly porous aerogels [11]. These observa-
tions can be regarded as early trials for the nanofluidics in
both classical and quantum liquids.
Crystallization dynamics of superfluid
4
He has also
been investigated visually in aerogel [13,14]. A variable–
volume cell allowed us to make crystals at a constant tem-
perature and the entire crystallization process was observed
visually in the transparent aerogels. Crystallization of
4
He
in aerogels shows a dynamical phase transition at around
600 mK which is the result of the competition between
thermal fluctuation and spatial disorder: crystals grow via
creep at high temperatures and via avalanche at low tem-
peratures [13]. The creep and avalanche growth was clari-
fied as the thermal activation and macroscopic quantum
tunneling, respectively, from the crystallization rate and
nucleation probability measurements [14,15]. In the quan-
tum growth regime, the avalanche size distribution fol-
lowed a power law, demonstrating the self-organized criti-
cality at low temperatures where the quantum process
governs the dynamics [14,16].
In this paper, we report a formation of superfluid liquid
pockets surrounded by crystals in one particular aerogel. The
liquid pockets always appeared when the crystals were
grown in the high-temperature creep region and did not crys-
tallize further even with the application of higher pressure at
a constant temperature. With cooling, they were found to
crystallize below a particular temperature via avalanche.
Crystallization by cooling was also observed when crystals
occupied a smaller portion of the aerogel. Possible mechan-
ism for the crystallization by cooling is discussed. Some
results of this paper have been reported elsewhere [17].
2. Experimental setups
Silica-aerogel is a transparent porous material with a highly
open structure which consists of nanometer scale silica par-
ticles [18–22]. It has been used to investigate the disorder
effects on condensed phases of He [3,9,11,13,14, 22–26]. A
silica-aerogel sample of 96% porosity was grown in situ in a
flat glass tube by Panasonic Corporation. The tube is shown
in Fig. 1 and had an inner space 1 mm deep, 8 mm wide
and 10 mm high. There was no gap between the inner wall
Formation of superfluid liquid pocket in aerogel
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9 1007
of the tube and the aerogel. The bottom of the tube was
glued on a glass plate and the aerogel had contact with
outer space only through the upper aperture.
The blocked capillary method was usually adopted to
study crystallization of
4
He in porous material in earlier
works. This temperature sweep method, however, made it
difficult to study the details of the crystallization dynam-
ics as a function of temperature. Instead, we decided to
use a variable-volume cell which allows us to grow crys-
tals in aerogel at a constant temperature. It has succeeded
in revealing the temperature effect on the crystallization
dynamics [13,14,27,28]. The variable-volume cell was
composed of two chambers, a high-pressure chamber (A)
and a low-pressure chamber (B). The aerogel was in-
stalled in chamber A. Part of both chambers was made of
phosphor bronze bellows connected by a rigid copper rod.
The volume of chamber A was able to be controlled by
the low-pressure liquid in chamber B due to a larger cross
section of the bellows for chamber B. Pressure of cham-
ber A was measured by a capacitive pressure gauge.
Chamber A has optical windows and its interior was ob-
servable from outside the cryostat. The cell was installed
in a dilution refrigerator with optical access. The initial
condensation of
4
He gas was finished above the critical
point temperature to avoid damage due to shrinkage of
the aerogel caused by the gas–liquid interface [29,30].
Detailed description of the sample cell was given in pub-
lications [13,14,27,28].
3. Results
3.1. Liquid pocket formation and its crystallization
by cooling
The initial condition of the experiment was such that
4
He bulk crystals and superfluid liquid coexisted in the
space outside of the aerogel at the bulk crystallization pres-
sure; only the superfluid liquid existed in the aerogel at this
moment due to the elevated crystallization pressure in the
aerogel. Next, we started pressurizing chamber B conti-
nuously at a fixed rate in the high-temperature creep re-
gion. The outer bulk crystals grew with the compression of
chamber A and finally filled the space outside of the aero-
gel. Thereafter, the pressure in chamber A increased above
the bulk crystallization pressure with the compression of
bulk crystals.
For this aerogel, the first crystal nucleated at a particu-
lar point in the aerogel about 3 mm below the aperture at a
pressure typically 2 bar above the bulk crystallization pres-
sure as in Fig. 2(b). The crystal–superfluid interface in the
aerogel expanded smoothly as in Figs. 2(c)–(e) because it
was in the creep region at the high temperature. It was
found in this aerogel that the crystallization eventually
stopped and liquid pockets remained even if the compres-
sion of the chamber continued: two small superfluid pock-
ets surrounded by crystals were left over in the aerogel as
indicated by two arrows in Fig. 2(f). In other aerogels of
the same porosity and of 98 and 99.5% porosities reported
in our previous publications, crystallization always contin-
ued until the crystals completely filled the aerogel.
A pressure–temperature trace of this process is shown in
Fig. 3. The crosses labeled by 2(a) and 2(f) indicate the
points at which Figs. 2(a) and 2(f) were photograghed,
respectively. An overpressure of about 40 mbar was ap-
plied in this run but the leftover liquid pockets did not
crystallize.
The liquid pockets were reproducibly observed for this
aerogel whenever the crystals were grown in the creep re-
gion. They did not crystallize even with an application of
100 mbar overpressure for 20 min. The size of the liquid
pockets changed from time to time and tended to be small-
er at faster crystallizations. The larger pocket on the left
part of the aerogel in Fig. 2(f) was always formed but its
size was only about half that at faster crystallization. The
smaller pocket on the right sometimes was not formed.
However, when the crystals were grown in the same way
in the low-temperature avalanche region, crystallization
was completed to fill the aerogel and no liquid pocket was
formed.
We stopped the supply of liquid
4
He to chamber B and
the compression of the chamber A when the liquid pockets
were formed. Immediately we cooled the system shown by
the trace in Fig. 3. An enlarged image of the larger liquid
pocket is shown in Fig. 4. During this cooling, the measured
pressure of chamber A was nearly constant. At 390 mK, the
liquid pockets began to crystallize via avalanche at the cross
4(a) in Fig. 3 whose image is shown in Fig. 4(a). It is not
possible to see from Fig. 4 if it is via avalanche but this is
obviously confirmed from the video clip. The crystallization
continued with cooling as in Figs. 4(b)–(e). At 190 mK or at
the cross 4(f) in Fig. 3, the whole portion of the liquid pocket
crystallized as shown in Fig. 4(f). As the avalanche growth
took place below 600 mK when the crystals were grown in
Fig. 1. (Color online) Flat glass tube to be filled with aerogel. Inner
space of the tube is 1 mm deep, 8 mm wide and 10 mm high.
H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, and Y. Okuda
1008 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9
aerogel at a constant temperature, the liquid pockets grew via
avalanche with the cooling below 390 mK.
3.2. Crystallization by cooling in a partly filled case
After finding the crystallization of the liquid pocket, we
decided to see what would happen by cooling when the
crystallization was stopped before the formation of the
liquid pocket in the same aerogel sample. The crystalliza-
tion images and the pressure–temperature trace of this
process are shown in Figs. 5 and 6. We first pressurized
chamber B continuously at a fixed rate to grow crystals in
the aerogel in the high-temperature creep region as shown
in Figs. 5(a) and 5(b), and stopped the crystallization when
the crystals occupied a smaller portion, about one third of
the aerogel as in Fig. 5(c). We photograghed Figs. 5(b) and
5(c) at the crosses indicated by (b) and (c) in Fig. 6. Con-
trary to the liquid pocket case, the bulk crystals still have
contact with superfluid liquid in the aerogel. We waited at
the constant temperature for about 750 s and the pressure
dropped by about 30 mbar during this period; after that we
cooled down the system. At 474 mK the partially filled
Fig. 2. (Color online) Crystallization image of 4He via creep in a 96% porosity aerogel in a flat glass tube at 850 mK. Two superfluid
liquid pockets were left unfrozen as indicated by arrows in (f). Time is indicated in each frame. The profile of the crystal–liquid inter-
face is drawn and highlighted to aid clear viewing.
Fig. 3. (Color online) Temperature–pressure trace during the
crystallization in Figs. 2 and 4. The crosses labeled by 2(a), 2(f),
4(a) and 4(f) are the points at which the photos of Figs. 2(a) and
2(f) and Figs. 4(a) and 4(f) were taken.
Formation of superfluid liquid pocket in aerogel
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9 1009
crystals began to grow via avalanche as in Fig. 5(d) and
continued to grow with further cooling as in Fig. 5(e). The
crystallization temperature in the partially filled case was
higher than that of the liquid pocket case. The crystalliza-
tion by cooling did not fill the aerogel but eventually
stopped as in Fig. 5(f). In Figs. 5(d)–(f), the profile of each
avalanche is drawn for clarity. The crosses labeled by (d),
(e) and (f) in Fig. 6 were the point at which Figs. 5(d)–(f)
were photograghed.
4. Discussion
Due to the density difference between liquid and crystal,
the mass transfer process has to be involved when crystals
grow at constant pressure. From the observation that the
crystals without any contact with outer bulk crystals grew
far away from the aperture in the aerogel, it was concluded
that the outer crystals were melted by the application of
stress,
4
He atoms entered the aerogel in the superfluid state
and recrystallized in the aerogel: the mass transport in aero-
gel is through the superfluid flow and the possibility of the
forced invasion of the outer crystals via plastic deformation
was excluded as the mass transport mechanism [14]. There-
fore, the crystallization should stop and liquid pockets
should be left if a supply path of the superfluid is blocked by
crystals in aerogel. Although the liquid pocket formation has
been observed only in one aerogel reported in this paper, it
offers another support for the assumed mass transport me-
chanism of crystallization in aerogel. In this aerogel, the
initial nucleation point of the crystal happened to be closer
to the upper opening than in other aerogels and it is reasona-
ble that the supply pass was blocked. This may be the reason
that the liquid pocket was observed only in this aerogel. In
the avalanche region, a gap may exist between the crystals
formed by the avalanche and act as the superfluid supply
path for the crystallization to the end. In the other aerogels
reported in the previous publications, the initial nucleation
point was close to the bottom and away from the upper
opening, and the crystal tended to grow from the bottom; the
Fig. 4. (Color online) Enlarged image of crystallization of a superfluid liquid pocket in aerogel by cooling. Time is indicated in each frame.
H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, and Y. Okuda
1010 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9
supply pass was not blocked and the crystallization was
completed to the end.
The bulk crystallization pressure is nearly temperature
independent at low temperatures and thus the driving force
for the crystallization of
4
He is the overpressure from this
bulk crystallization pressure [31,32]. What is the driving
force for the crystallization by cooling in aerogel? In this
aerogel the crystallization pressure at which the first crys-
tal appears in aerogel was (27.2 0.2) bar and no signifi-
cant temperature dependence was observed in this highly
porous material as in bulk. Therefore, the driving force for
the crystallization in aerogel would also be the overpres-
sure. This means that crystallization via cooling in aerogel
is very anomalous because no additional driving force is
gained by cooling.
Once the crystals undergo the supersolid transition,
mass transport through them should become possible
[33,34]. Therefore, one possible explanation for the crys-
tallization by cooling could be related to the supersolid
transition. The outer bulk crystals were stressed by bellows
and were possibly sustaining a density gradient by elastici-
ty; they would have a larger chemical potential than in
aerogel. When the bulk crystals became supersolid below a
transition temperature, mass transport through them should
take place to equilibrate the system. In the partially filled
case,
4
He atoms carried through the bulk crystals would be
able to enter the aerogel as a superfluid liquid since the
bulk crystals had direct contact with the superfluid liquid
in it. Thereafter,
4
He atoms would be transferred through
the aerogel and eventually recrystallize in the aerogel. Su-
persolidity of the bulk crystal would explain the crystalli-
zation by cooling in the partially filled case.
Fig. 5. (Color online) Crystallization image of 4He in a 96% porosity aerogel in a flat glass tube. The crystals were grown at constant tem-
perature as in (a), (b), and (c). Thereafter, the system was cooled down and the crystals began to grow via avalanche as in (d), (e), and (f).
Time is indicated in each frame.
Fig. 6. (Color online) Temperature–pressure trace during the
crystallization in Fig 5. The crosses labeled by (b)–(f) are the
points at which the photos of Figs. 5(b)–(f) were taken.
Formation of superfluid liquid pocket in aerogel
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 9 1011
In the liquid pocket case, however, supersolidity of the
bulk crystals could not induce the crystallization; bulk
crystal had no contact with the liquid pocket and the flow
pass was blocked by the crystals in the aerogel. Crystals in
the aerogel also needed to undergo the supersolid transition
to carry the mass for the crystallization. The crystallization
of the liquid pocket started at lower temperature than that
of the partially filled case and this may be because the su-
persolid transition temperature was lower in the aerogel
than in the bulk.
In order to determine whether the supersolidity is the case
for the crystallization by cooling or different physics are tak-
ing place, more systematic measurements must be conducted;
it will be informative to investigate the crystallization tem-
perature by changing the overpressure after the formation of
the liquid pocket or by changing the filling ratio of crystals in
the aerogel. These measurements are in progress and hope-
fully will be reported in a future publication.
5. Summary
Making use of a variable-volume cell, crystals were
grown in an 96% porosity aerogel at constant temperature
in the creep growth region and it was found that some parts
of the aerogel were left unfrozen as superfluid liquid pock-
ets. The liquid pockets did not crystallize even if further
pressure were applied to the system. This is because the
superfluid path in the aerogel was blocked by crystals re-
sulting in the cease of a mass supply for the crystallization.
By cooling, however, the liquid pocket began to crystallize
via avalanche below a particular temperature. This crystal-
lization by cooling was also observed for crystals which
partially filled the aerogel. The crystallization in the par-
tially filled case began at higher temperature than in the
liquid pocket. Possible scenario for the crystallization by
cooling is the supersolidity of the crystals but further re-
search is needed to come to a definite conclusion.
This study was supported in part by the Global Center
of Excellence Program at Tokyo Tech. “Nanoscience and
Quantum Physics Project”, a Grant-in-Aid for Scientific
Research (B) (Grant No. 21340095) from the Ministry of
Education, Culture, Sports, Science and Technology of
Japan and by a “Ground-based Research Announcement
for Space Utilization” promoted by JAXA.
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|
| id | nasplib_isofts_kiev_ua-123456789-118749 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-11-27T20:02:54Z |
| publishDate | 2013 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Matsuda, H. Ochi, A. Isozaki, R. Nomura, R. Okuda, Y. 2017-05-31T06:29:23Z 2017-05-31T06:29:23Z 2013 Formation of superfluid liquid pocket in aerogel and its solidification by cooling / H. Matsuda, A. Ochi, R. Isozaki, R. Nomura, Y. Okuda // Физика низких температур. — 2013. — Т. 39, № 9. — С. 1006–1011. — Бібліогр.: 34 назв. — англ. 0132-6414 PACS: 64.70.D–, 67.80.bf, 67.25.D– https://nasplib.isofts.kiev.ua/handle/123456789/118749 Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed. This study was supported in part by the Global Center of Excellence Program at Tokyo Tech. “Nanoscience and Quantum Physics Project”, a Grant-in-Aid for Scientific Research (B) (Grant No. 21340095) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by a “Ground-based Research Announcement for Space Utilization” promoted by JAXA. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Сверхтекучесть в низкоразмерных системах и в условиях ограниченной геометрии Formation of superfluid liquid pocket in aerogel and its solidification by cooling Article published earlier |
| spellingShingle | Formation of superfluid liquid pocket in aerogel and its solidification by cooling Matsuda, H. Ochi, A. Isozaki, R. Nomura, R. Okuda, Y. Сверхтекучесть в низкоразмерных системах и в условиях ограниченной геометрии |
| title | Formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| title_full | Formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| title_fullStr | Formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| title_full_unstemmed | Formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| title_short | Formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| title_sort | formation of superfluid liquid pocket in aerogel and its solidification by cooling |
| topic | Сверхтекучесть в низкоразмерных системах и в условиях ограниченной геометрии |
| topic_facet | Сверхтекучесть в низкоразмерных системах и в условиях ограниченной геометрии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118749 |
| work_keys_str_mv | AT matsudah formationofsuperfluidliquidpocketinaerogelanditssolidificationbycooling AT ochia formationofsuperfluidliquidpocketinaerogelanditssolidificationbycooling AT isozakir formationofsuperfluidliquidpocketinaerogelanditssolidificationbycooling AT nomurar formationofsuperfluidliquidpocketinaerogelanditssolidificationbycooling AT okuday formationofsuperfluidliquidpocketinaerogelanditssolidificationbycooling |