Non-isothermal physical and chemical processes in superfluid helium
Metal atoms and small clusters introduced into superfluid helium (He II) concentrate there in quantized vortices to form (by further coagulation) the thin nanowires. The nanowires’ thickness and structure are well predicted by a double-staged mechanism. On the first stage the coagulation of cold par...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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Gordon, E.B. Kulish, M.I. Karabulin, A.V. Matyushenko, V.I. 2021-01-31T11:32:40Z 2021-01-31T11:32:40Z 2017 Non-isothermal physical and chemical processes in superfluid helium / E.B. Gordon, M.I. Kulish, A.V. Karabulin, V.I. Matyushenko // Физика низких температур. — 2017. — Т. 43, № 9. — С. 1354-1362. — Бібліогр.: 36 назв. — англ. 0132-6414 PACS: 67.40.Pm, 67.40.Vs https://nasplib.isofts.kiev.ua/handle/123456789/175178 Metal atoms and small clusters introduced into superfluid helium (He II) concentrate there in quantized vortices to form (by further coagulation) the thin nanowires. The nanowires’ thickness and structure are well predicted by a double-staged mechanism. On the first stage the coagulation of cold particles in the vortex cores leads to melting of their fusion product, which acquires a spherical shape due to surface tension. Then (second stage) provided these particles reach a certain size they do not possess sufficient energy to melt and eventually coalesce into the nano-wires. Nevertheless the assumption of melting for such refractory metal as tungsten, especially in He II, which possesses an extremely high thermal conductivity, induces natural skepticism. That is why we decided to register directly the visible thermal emission accompanying metals coagulation in He II. The brightness temperatures of this radiation for the tungsten, molybdenum, and platinum coagulation were found to be noticeably higher than even the metals’ melting temperatures. The region of He II that contained suspended metal particles expanded with the velocity of 50 m/s, being close to the Landau velocity, but coagulation took place even more quickly, so that the whole process of nanowire growth is completed at distances about 1.5 mm from the place of metal injection into He II. High rate of coagulation of guest metal particles as well as huge local overheating are associated with them concentrating in quantized vortex cores. The same process should take place not only for metals but for any atoms, molecules and small clusters embedded into He II. The authors are grateful to E. V. Dyatlova, A. S. Gordienko, and M. E. Stepanov for participating in the experiments. This work was financially supported by Russian Science Foundation (Grant No. 14-13-00574). en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкоразмерные и неупорядоченные системы Non-isothermal physical and chemical processes in superfluid helium Article published earlier |
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Non-isothermal physical and chemical processes in superfluid helium |
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Non-isothermal physical and chemical processes in superfluid helium Gordon, E.B. Kulish, M.I. Karabulin, A.V. Matyushenko, V.I. Низкоразмерные и неупорядоченные системы |
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Non-isothermal physical and chemical processes in superfluid helium |
| title_full |
Non-isothermal physical and chemical processes in superfluid helium |
| title_fullStr |
Non-isothermal physical and chemical processes in superfluid helium |
| title_full_unstemmed |
Non-isothermal physical and chemical processes in superfluid helium |
| title_sort |
non-isothermal physical and chemical processes in superfluid helium |
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Gordon, E.B. Kulish, M.I. Karabulin, A.V. Matyushenko, V.I. |
| author_facet |
Gordon, E.B. Kulish, M.I. Karabulin, A.V. Matyushenko, V.I. |
| topic |
Низкоразмерные и неупорядоченные системы |
| topic_facet |
Низкоразмерные и неупорядоченные системы |
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2017 |
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English |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
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Metal atoms and small clusters introduced into superfluid helium (He II) concentrate there in quantized vortices to form (by further coagulation) the thin nanowires. The nanowires’ thickness and structure are well predicted by a double-staged mechanism. On the first stage the coagulation of cold particles in the vortex cores leads to melting of their fusion product, which acquires a spherical shape due to surface tension. Then (second stage) provided these particles reach a certain size they do not possess sufficient energy to melt and eventually coalesce into the nano-wires. Nevertheless the assumption of melting for such refractory metal as tungsten, especially in He II, which possesses an extremely high thermal conductivity, induces natural skepticism. That is why we decided to register directly the visible thermal emission accompanying metals coagulation in He II. The brightness temperatures of this radiation for the tungsten, molybdenum, and platinum coagulation were found to be noticeably higher than even the metals’ melting temperatures. The region of He II that contained suspended metal particles expanded with the velocity of 50 m/s, being close to the Landau velocity, but coagulation took place even more quickly, so that the whole process of nanowire growth is completed at distances about 1.5 mm from the place of metal injection into He II. High rate of coagulation of guest metal particles as well as huge local overheating are associated with them concentrating in quantized vortex cores. The same process should take place not only for metals but for any atoms, molecules and small clusters embedded into He II.
|
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/175178 |
| citation_txt |
Non-isothermal physical and chemical processes in superfluid helium / E.B. Gordon, M.I. Kulish, A.V. Karabulin, V.I. Matyushenko // Физика низких температур. — 2017. — Т. 43, № 9. — С. 1354-1362. — Бібліогр.: 36 назв. — англ. |
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2025-11-24T21:53:29Z |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9, pp. 1354–1362
Non-isothermal physical and chemical processes
in superfluid helium
E.B. Gordon and M.I. Kulish
Institute of Problems of Chemical Physics RAS
Akad. Semenov Ave., Chernogolovka, Moscow region 142432, Russia
E-mail: Gordon@ficp.ac.ru
A.V. Karabulin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
31 Kashirskoe Shosse, Moscow 115409, Russia
V.I. Matyushenko
The Branch of Talrose Institute for Energy Problems of Chemical Physics RAS
1 Akad. Semenov Ave., Chernogolovka, Moscow region 142432, Russia
Received December 9, 2016, published online July 25, 2017
Metal atoms and small clusters introduced into superfluid helium (He II) concentrate there in quantized vortices
to form (by further coagulation) the thin nanowires. The nanowires’ thickness and structure are well predicted by a
double-staged mechanism. On the first stage the coagulation of cold particles in the vortex cores leads to melting of
their fusion product, which acquires a spherical shape due to surface tension. Then (second stage) provided these
particles reach a certain size they do not possess sufficient energy to melt and eventually coalesce into the nano-
wires. Nevertheless the assumption of melting for such refractory metal as tungsten, especially in He II, which pos-
sesses an extremely high thermal conductivity, induces natural skepticism. That is why we decided to register di-
rectly the visible thermal emission accompanying metals coagulation in He II. The brightness temperatures of this
radiation for the tungsten, molybdenum, and platinum coagulation were found to be noticeably higher than even the
metals’ melting temperatures. The region of He II that contained suspended metal particles expanded with the ve-
locity of 50 m/s, being close to the Landau velocity, but coagulation took place even more quickly, so that the whole
process of nanowire growth is completed at distances about 1.5 mm from the place of metal injection into He II.
High rate of coagulation of guest metal particles as well as huge local overheating are associated with them concen-
trating in quantized vortex cores. The same process should take place not only for metals but for any atoms, mole-
cules and small clusters embedded into He II.
PACS: 67.40.Pm Transport processes, second and other sounds, and thermal counterflow; Kapitza resistance;
67.40.Vs Vortices and turbulence.
Keywords: superfluid helium, coagulation, vortices, heat transfer, radiation cooling.
1. Introduction
Until recently it was believed that superfluid helium
(He II) is the simplest homogeneous low-temperature me-
dium for guest particles suspended inside it. It means that
the motion of these particles in He II should have a charac-
ter of simple diffusion, and any physical and chemical pro-
cesses between them should be strictly isothermal [1,2].
Indeed, such a quantum fluid as liquid helium can be re-
garded as a continuous medium with spatially averaged
characteristics; and in its superfluid state the helium pos-
sesses the record high, quantum thermal conductivity,
which should eliminate any local overheating [3].
Thus all researchers embedded the guest particles into
superfluid helium considered the processes inside He II as
strictly isothermal [4–6]. This opinion have been also
shared by all the authors, introducing impurity particles
into small droplets of superfluid helium [2,7–9].
However, in reality He II is proved to be extremely
complex and specific template for the physical and chemi-
© E.B. Gordon, M.I. Kulish, A.V. Karabulin, and V.I. Matyushenko, 2017
Non-isothermal physical and chemical processes in superfluid helium
cal processes of guest particles. First, it was found [10] that
these particles tend to concentrate in the cores of quantized
vortices always existing in He II. These vortices are practi-
cally one-dimensional objects with a diameter of about 1 Å
and a length up to many centimeters [10]. It had recently
become clear that due to the collinearity of velocities for
particles captured in vortex cores the probability of their
collisions there and of subsequent chemical and physical
processes is much higher in the vortices than in the bulk
[11]. Moreover, the elongation of particles during their
coagulation leads to increase of time that the resulting clus-
ter spends in the vortex, and hence, to increase of their
local concentration there [11]. This previously unknown
rapid process of spatially inhomogeneous condensation
should thus produce long thin filaments [12]. The results of
experiments with different metals and alloys introduced to
bulk He II support this conclusion [13,14]. (As was shown
recently, the same behavior demonstrate the metals cap-
tured inside large enough superfluid helium droplets)
[15,16]. However, it was expected that due to high thermal
conductivity of He II the atoms or small clusters will pack
tightly, forming either monoatomic chains or nanowires
with loose fractal structure. Anyway, the nanowires grown
in our experiments fortunately were dense, with almost
crystalline packing and «large» diameters of a few na-
nometers, being close to optimal for many chemical and
physical applications [17–19]. Such a behavior was associ-
ated with the existence of the limiting heat flux above
which the strong turbulence develops in He II. This turbu-
lence disrupts the laminar motion of the normal compo-
nent, which is responsible for the high heat transfer rate.
For the objects larger than micron this effect is known, the
threshold heat flow being about 3 W/cm2 [20]. For very
small objects the concentration of vortices is too small to
disturb the flow laminarity [21]. In this case, the maximal
heat transfer rate W will be determined as the product of
the normal component density, the temperature, and the
laminar flow velocity restricted by the velocity of second
sound in He II, i.e.,
W = nnvskBT, (1)
where nn(T) is the normal component density, vs =
= 2·103 cm/s is the velocity of the second sound, and kB is
the Boltzmann constant.
The temperatures of typical experiments on impurity
particles introduction in He II are T = 1.6–2.0 K, thus the
density of the normal component is about 20–50% of the
total liquid helium density, nn = (0.4–1.0)·1022 cm–3.
Therefore, the limiting heat flow should be as large as
103 W/cm2 for small particles. For particles of mesoscopic
size the heat flow limit is still unknown, but it should be
compared with the heat removal rate required, for example,
to prevent melting of the merging product of two metal
balls of 1 nm diameter each (the clusters of such size are
the “bricks” for nanowire growth in the vortex core [17]).
This rate estimates as 105 W/cm2 [17]. We believe that
even for nanometer metal clusters the limiting heat flow
will be also significantly lower than that the above enor-
mously high estimate. (At the same time, in clusters con-
sisting of a few atoms the total energy released during co-
agulation is not sufficient to form a helium gas cavity
insulating heat transfer to the liquid; this problem requires
a special consideration which goes beyond the scope of
this paper).
Under the above assumptions, the scenario of events
taking place presumably above the limiting heat flow is
more or less clear: just after the act of coagulation the
He II around the merged particles converts to normal He I;
it then evaporates to form the sheath filled with low-
density helium gas, which reliably insulates the hot core.
The experimental results support our claim, that the co-
agulation of metal nanoclusters in He II is accompanied by
their fusion. Indeed, the dense packing of atoms in the nan-
owires with “large” (in comparison with vortex core’s thick-
ness) diameters, and the presence of metallic spheres with
the perfect shape and atomically smooth surface in the prod-
ucts had been observed [17]. Our model of nanowire for-
mation in He II, which is based on the assumption of adia-
batic regime of the coagulation process that leads to cluster
melting [17], had been confirmed in several independent
studies [22–24]. Nevertheless, we decided primarily to per-
form a systematic comparison of the diameters of nanowires
grown in a low temperature experiments from various met-
als with those predicted for them by the model [17].
However, by itself, the claim that, for example, tung-
sten, with its highest melting temperature among all me-
tals, can melt inside the liquid, which cooled down to prac-
tically zero absolute temperature and also possesses a
record-high thermal conductivity, cannot but cause a cer-
tain skepticism from any researcher. Therefore, we have
set as a major goal of this work to obtain direct experi-
mental evidence that metal clusters heat up during their
coagulation in He II to high, equal to several thousand de-
grees temperature.
The logic of our experimental study was as follows.
According to our model the nanowires are formed by fus-
ing of the spherical clusters with diameters of at least
1 nm. In such clusters the metallic binding already exists
[25] and taking into account the high temperatures of clus-
ters the density of free electrons in them must be very high.
This means that the intensity of thermal electromagnetic
emission should be close for such clusters to that defined
by the Planck formula. Liquid helium is optically trans-
parent, and the temperature of the cryostat walls is very
low, so that the corresponding thermal radiation is in prin-
ciple detectable experimentally.
It should be emphasized that the process of nanowires
growth in quantized vortices of superfluid helium consists
of several non-isothermal stages and which cannot be
characterized by a single temperature. Indeed, according to
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9 1355
E.B. Gordon, M.I. Kulish, A.V. Karabulin, and V.I. Matyushenko
our mechanism (see [17]), the first stage is the formation of
small clusters. At this stage the condensation process is not
obviously adiabatic and, moreover, the clusters are still not
metals and, hence, there are no free electrons in them. The
thermal radiation should be very weak and the first stage
should manifest itself as a delay of glowing. The second
stage starts when the clusters acquire metallic structure; the
clusters are very hot and intensively emit light. The subse-
quent coagulation diminishes the temperature of the molten
cluster and drops eventually its temperature down to melt-
ing point. Such clusters could not melt anymore under their
collision and they may only fuse together, resulting in na-
nowire fragments extended along the vortex core. Those
fragments then will attach to each other and so on; this
stage may be characterized as the third one. Thus, the in-
tense thermal emission is possible only during the second,
“bright”, stage, and during this stage the clusters of differ-
ent sizes possess different temperatures. Thus, one cannot
speak about a real temperature of this stage, but only judge
how the effective temperature is close to the melting point
of the metal. The main goal of our study was not in accu-
rate measurements of the temperature, but rather in an-
swering the question, how strong is the local overheating;
is it a few or few thousand K? Accordingly, the character-
istic coagulation time that we will determine is only the
duration of the bright stage.
There is no delayed fluorescence in a metal, and the
plasmon excitation by a laser lasts for a time much shorter
than a nanosecond [26]. The only source of parasitic light
in the microsecond time range is the radiation of plasma
excited in the focal spot of the laser. Its contribution must
be determined in special experiments.
2. Experimental
Our method for nanowires production in superfluid he-
lium has been described in sufficient detail elsewhere [13].
The experimental setup was assembled on the basis of an
optical liquid helium cryostat; the temperature was lowered
by pumping the liquid helium vapor down to a pressure of
700 Pa, which corresponds to a temperature of 1.55 K. The
atoms and small clusters of metal were introduced into
superfluid helium bulk by laser ablation from the surface
of submerged in He II targets made of corresponding met-
als. The pulse-repetition solid state diode-pumped Nd:LSB
laser used for ablation had the following characteristics:
wavelength λ = 1.064 µm, pulse energy E = 0.1 mJ, pulse
duration τ = 0.4 ns, and repetition rate f = 0–4000 Hz. Irra-
diation was carried out through sapphire windows of the
cryostat, the laser beam was focused on the target surface
to a spot of 50–100 µm in size. The metal particles were
captured on the cores of quantized vortices nucleated in the
laser focus and then condensate there to form thin nano-
wires. These nanowires joined together, forming a 3D
nanoweb, and fell down to the surface of the standart TEM
grids, placed at the cell bottom. Upon warming to room
temperature the grids were examined using an electron
microscope JEM-2100 (JEOL company).
The design of the apparatus for optical measurements is
clear from Fig. 1. Hamamatsu photosensor H11526-110-NN
module based on photomultiplier (PMT) equipped with gate
function was used to register emission [27]. The sensitive
diameter of the photocathode was 8 mm and its spectral sen-
sitivity is shown in [27]. Tektronix TDS 7054 oscilloscope
and the custom made gate signal generator also were used.
In integral experiments the photocathode of the photo-
sensor module was placed at 95 mm from the laser focus
spot on the surface of metallic targets. In spatially resolved
experiments the photo camera objective of 75 mm focal
length was arranged so that it provided a double magnifica-
tion of the image in the vicinity of the laser spot. The
PMT, equipped with a 1 mm width slit, could be moved
within the plane of this image along the line parallel to
laser beam axis. Thus, 0.5 mm spatial resolution was
achieved in the time-of-flight measurements.
The gate of PMT was preset using the gate generator at
“OFF” ~50 μs before a laser pulse. The signal to set the gate
“ON” came simultaneously with the laser pulse from the
laser “TRIGGER OUT” and due to the internal delays both
in gate generator and photosensor module the PMT was
Fig. 1. (Color online) The scheme and photo of the experimental
setup for optical measurements.
1356 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9
Non-isothermal physical and chemical processes in superfluid helium
turned on 180 ns after the laser pulse. In thus way we man-
aged to avoid saturation of the PMT by the large laser signal.
To improve the signal-to-noise ratio, each oscilloscope
trace was averaged 128 times. The repetition rates of laser
and oscilloscope trigger pulses were 50 Hz. Laser pulses
started at zero time of every oscilloscope record.
3. The comparison of diameters of nanowires grown
from different metals with the predictions
of the model [17]
The morphology of the samples from different metals
was quite similar. They represented nanowebs with cell
sides of 50-300 nm. The diameter of individual nanowires
was practically the same along the whole web, but its value
clearly depended on the kind of the metal. It changed from
7-8 nm for fusible indium to 2 nm for refractory tungsten.
A simple formula based on thermodynamic and geometric
considerations was derived [17]
( )max
b
p m
Q
R a
C T Q
= ⋅
+
, (2)
where Qb is the evaporation heat of the metal; a is the
thickness of the monolayer (a ≈ 0.4 nm); Qm is the heat of
melting, and Cp is the heat capacity of solid metal.
In this paper we compared the diameters of all na-
nowires grown in our studies [17,28–31] with those pre-
dicted as in Eq. (2). It can be seen in Fig. 2, that despite the
simplicity of the approach, there is an almost quantitative
agreement with all experimental data.
The nanowires made of different metals had, generally
speaking, different structure: some of them were single
crystals, others were polycrystals or amorphous. However,
prior to electron microscope analysis the nanowires were
heated up to room temperature and experienced contact
with air. Therefore, what structures they had in superfluid
helium is unknown. Thin nanowires have proved to pos-
sess the low temperature stability [29,30]. In particular,
silver nanowires the structure of which was carefully stu-
died [23], when heated to room temperature even changed
their topology, breaking up into separate nanoparticles. For
us it is important that all nanowires shown in Fig. 2 had
close packing, which together with their diameters obeying
Eq. (2) constitute the evidence they grew via the stage of
molten protoclusters.
4. Choice of objects
Our goal was to register in an optical range the thermal
radiation that accompany the coagulation of metallic parti-
cles introduced into superfluid helium by laser ablation
from targets of the corresponding metal immersed in He II.
Table 1. Characteristics of the metals studied. Tmelt and Cp are tabulated values for bulk materials [35]. Tad is the adiabatic tempera-
ture of the 1 nm diameter cluster formed by fusion of two cold smaller clusters. Dclust is the diameter of the cluster formed by merging
of two cold identical spherical clusters, which has a temperature T = Tmelt, λmax(Tmelt) and λmax(Tad) — wavelengths, corresponding to
maximal black-body emission for T = Tmelt and T = Tad, correspondingly.
Metal (ato-
mic number)
Tmelt,
K
λmax(Tmelt),
μm
*Tad,
K
λmax(Tad),
μm
Heat capaci-
ty, Cp,
J/(mol·K)
Latent heat of
fusion Q0,
kJ/mol
Full heat of melting
Q = Q0 + CpTmelt, kJ/mol
*Dclust,
nm
In (49) 430 6.44 1900 1.53 26.7 3.24 11.5 4.78
Pt (78) 2041 1.42 3280 0.88 25.9 27.8 52.8 1.97
Mo (42) 2890 1.0 4200 0.69 28 23.93 80.9 1.89
W (74) 3695 0.78 6690 0.43 24.3 35.2 89.8 1.98
Comment: Values marked with * were obtained using the Eq. (5) of Ref. 17.
Fig. 2. (Color online) Comparison of the experimental nanowire
diameters (dexp) with predictions of Eq. (2). The data for of nano-
wires made of W, Mo, Pt and InPb alloy are reproduced from
Refs. 31–33.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9 1357
E.B. Gordon, M.I. Kulish, A.V. Karabulin, and V.I. Matyushenko
We wanted to prove that the metal clusters produced by
condensation heated up to temperatures of several thou-
sand degrees. That is why we used the photomultiplier
sensitive only in visible. The choice of such metals as indi-
um, molybdenum, platinum and tungsten as the objects of
study was dictated by the goal of study; their thermal prop-
erties are listed in Table 1.
We were guided by the following considerations. Ac-
cording to our scenario, we considered most probable [17]
that a nanowire starts to grow when the heat released during
two metal clusters fusion becomes insufficient to melt the
cluster produced by coagulation. Therefore, at this stage the
temperature of clusters should be equal to their melting tem-
perature, which should be lower than the melting point of
the bulk metal (Tmelt). However, for our cluster sizes, the
difference is only 10–15% [34] and for a time we will ne-
glect the difference between these two temperatures. As
shown in Table 1, the maximum of black-body radiation at
Tmelt for refractory tungsten is close to the red boundary of
the PMT sensitivity, so in this case the emission is easy to be
registered. In contrast, the maximum black-body radiation at
Tmelt for fusible indium is far beyond the sensitivity range of
the PMT, and thus, there is no hope to register an emission
during the indium coagulation. Even for molybdenum and
especially platinum, which have intermediate melting tem-
peratures, the thermal radiation should be attenuated under
registration by orders of magnitude.
However, in the early stages of coagulation the temper-
ature of molten clusters should be much higher than Tmelt.
The temperatures calculated for the adiabatic merging of
two spherical clusters with a diameter of 1 nm (which for
all metals was less than the diameter of protoclusters) are
shown in Table 1. For such clusters the temperatures are
really high, so that in the cases of Mo and Pt one could
hope to register the thermal radiation during the early stag-
es of coalescence. In the case of indium, in order to have a
temperature of 3000 K the clusters had to consist only of a
few atoms, and that is too little to display the metal bind-
ing: thus, their emissivity should be very low.
Under this logic if the effective temperature of metallic
clusters is close to the melting temperature of the respec-
tive metal, the large thermal emission signal would be de-
tected only for tungsten. But if the effective temperature of
nanoclusters turns out to be significantly higher than Tmelt
the emission for molybdenum and even for platinum would
be detectable as well.
5. Optical experiments
Accordingly to the existing understanding of ablation in
liquids [36], a gas bubble filled with plasma in laser focus
on the surface of target has the characteristic size of a few
tenths of mm; the plasma decay products (primarily, atoms
and small metal clusters) enter the liquid through the bub-
ble surface. The metal nanoparticles in He II have enough
time to cool down before their mutual collisions; otherwise
the main products of coagulation would have been micron-
size spheres with atomically smooth surface [17]. Ablation
efficiencies for all metals under study, as measured via the
volume of the crater formed due to laser action, are compa-
rable and can be estimated as 1010–1011 atoms per pulse
with energy 0.1 mJ.
To distinguish the thermal emission of hot metal
nanoclusters in the bulk of He II from the signal registered
by PMT it was necessary first of all, to get rid of the scat-
tered laser radiation that could saturate the photomultiplier
dynodes by electrons for a long time. The laser pulse dura-
tion was 400 ps and the geometric dimensions of the cell
could not provide a scattered light delay of more than 1000
ps. It means that the delay of PMT high voltage switch-on
of 180 ns allowed us to reliably avoid the effect.
In order to remove the contribution of parasite light
from plasma in the laser focus we examined separately the
intensity and duration of the gas plasma glow. To do this,
the cryostat at the room temperature was filled with helium
gas of atmospheric pressure, and the emission of the focal
spot followed laser pulses was registered at 45° angle to
the plane of the target.
As Fig. 3 shows, the most intensive were plasma glows
for indium and tungsten; for molybdenum the intensity was
three times lower. This is quite natural, since the intensity
of the metal plasma emission depends mainly on the densi-
ty of energy levels, the probabilities of optical transitions
between them, the electron temperature, etc., but in no way
it depends on the metal melting temperature. Besides, in all
cases the duration of plasma emission did not exceed 1 μs.
The glow that accompanies the condensation of a metal
in superfluid helium was registered in the plane parallel to
the target. Therefore, the contribution of the emission from
the gas bubble near the focal spot was significantly sup-
pressed. Furthermore, as follows from Fig. 3, the glow of the
Fig. 3. (Color online) Emission signals from the focal spot for
indium, tungsten, and molybdenum. The measurements were
performed at 45° relative to the plane of the target in helium gas
at room temperature and atmospheric pressure.
1358 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9
Non-isothermal physical and chemical processes in superfluid helium
plasma gas could not be present in the signal at times longer
than 0.5 μs. The dependence of the light intensity in the liq-
uid superfluid helium induced by laser ablation of metal
targets is shown in Fig. 4. It is seen that for indium, for
which the laser plasma radiation had the same intensity as
the tungsten plasma, the emission from the bulk liquid heli-
um is practically absent. This is consistent with our expecta-
tions: the estimate made using the spectral PMT sensitivity
shows that the intensity of radiation accompanying the indi-
um coagulation should be at least four orders of magnitude
lower than that in the case of tungsten. At the same time it
served as proof of the weak contribution of the plasma emis-
sion from the focal spot to observed signals.
As expected, the emission for tungsten was the highest.
However, the emissions for molybdenum and platinum
were only a few times less than for refractory tungsten. It
is evident that the effective temperatures are even higher
than the melting temperature of the respecting metal.
A very important and hard-to-predict feature of the
emission from bulk He II is its temporal behavior. It was
suggested [6] that the coagulation of impurity particles in
the cores of quantized vortices is much faster than in the
bulk of superfluid helium, but it was unclear until now,
what are the characteristic times of metal coagulation in
quantized vortices for typical conditions of experiment. On
the basis of the observed experimentally independence of
nanowires morphology of the laser pulses repetition rate
(up to 4 kHz), it was suggested that the whole process of
nanowires formation in our experiments takes less than
250 µs [32]. The results of the present study allow us to
provide a more definite answer for the question.
As can be seen in Fig. 4, the duration of the “bright”
stage of the process, though depending on the type of metal
investigated was always much shorter than the above esti-
mate and never exceeded 20 µs. Of course, according to
our scenario [9] the “bright” stage of molten spherical clus-
ters growth should be followed by a “dark” stage of their
sticking together into nanowires without melting. Howev-
er, due to the acceleration of the process of metal conden-
sation in quantized vortices with the increase of condensate
size, the “dark” stage of the process which corresponds to
coalescence of spherical protoclusters, should proceed
faster than the “bright” stage of spherical molten cluster
growth. On the other hand, as it will be shown below, the
whole process of condensation proceeds at the distance
less than 1.5 mm from the laser spot, so the geometric fac-
tor in collection of the light by the PMT will have no effect
on the time profile of the observed signal. However, there
are other factors that can change the signal profile, in par-
ticular, the metal nanoparticles expansion inside He II, as
well as the cooling of hot clusters which may change the
spectral composition of the emission.
In order to reveal the role of those factors in the emis-
sion, we carried out special experiments. The influence of
the metal expansion in superfluid helium on the shape of
radiation signals was studied using spatially resolved tech-
niques, namely by moving the photomultiplier equipped
with a vertical optical slit 1 mm wide along the doubly
magnified image of the coagulation area created by the
objective (see Fig. 1). The signals were recorded at the
following positions of the optical slit: (i) at the laser spot
image, (ii) at a distance of 1.25 and (iii) at a distance of
2.5 mm from it.
From Fig. 5 it is clear, that the expansion of the region of
superfluid helium filled with suspended metal is very fast. Its
velocities for both W and Mo are close to the Landau veloci-
ty (50 m/s) which is the maximal velocity for motion of any
guest particles in He II without friction. It is worthwhile to
note that the rectangles in Fig. 5 represent the times corre-
sponding to the motion with the Landau velocity in the direc-
tion perpendicular to the target surface — for the propagation
at some angle to the normal the time of metal appearance at a
given distance from the target plane should be longer.
However, the comparison of delayed signal 2 with inte-
grated signal 4 shows that at a distance of 1.25 mm from
the focal spot the emission is already quite weak and at a
distance of 2.5 mm it disappears completely (see signal 3).
This means that the “hot” stage of coagulation is even
shorter than the time needed for the metal to expand and
Fig. 4. (Color online) The temporal behavior of the visible emis-
sion in bulk He II as induced by laser ablation of In, Mo, Pt and
W targets (a). Ditto at a better time resolution (b).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9 1359
E.B. Gordon, M.I. Kulish, A.V. Karabulin, and V.I. Matyushenko
the whole process of metal condensation in superfluid he-
lium occurs in vicinity of the place of ablation.
Methodologically, it is a very important result. It shows
that the intensity of the laser ablation, which we used for
nanowires synthesis, leads to an initial concentration of the
metal embedded into the He II so high that the whole coagu-
lation process in the vortices occurs very close to the surface
of gas bubble existed in laser focus. This, of course, does not
promote formation of high-quality and long nanowires.
The emission spectra were not studied in our experi-
ments. Yet, in order to reveal how strong are the temporal
changes of the radiation spectra we used the broadband
glass filters, “blue” SZS20 and “red” KS10 (their transmis-
sion spectra together with the spectral sensitivity of PMT
photocathode are shown in Fig. 6). Taking into account the
spectral efficiency of the cathode, one can consider that the
first filter spans the 380–450 nm spectral range while the
second one registers the radiation in the 600-650 nm re-
gion. Figure 6(a) shows the time dependence of the intensi-
ty of the emission induced by tungsten coalescence as regi-
stered using the “blue” (1) and “red” (2) filters. Both am-
plitudes are of close, but since the energy width of the
“red” filter is four times smaller than that of the “blue” one
and the PMT efficiency in the “red” is four times lower
than in the “blue”, we conclude that over 90% of the ener-
gy is concentrated in the red wing of the emission spec-
trum. This is consistent with our approximation of tungsten
protoclusters as blackbody with a temperature below
4000 K. The comparison of curves 1 and 2 shows clearly
that at short times the blue part of the spectrum is more
intensive than later. This is obvious evidence that the emit-
ter cools down during the emission, yet, as it follows from
our estimates, this effect is rather small.
But if so, the characteristic times of radiation signals
presented in Fig. 4 reflect mainly the kinetics of metal
clusters coagulation in superfluid helium. To estimate the
rate of such coagulation it makes sense first of all to use a
simplified representation of the coagulation as a simple
bimolecular coalescence of two identical clusters which
can be described by the kinetic equation:
2dn kn
dt
= − (3)
giving the hyperbolic temporal dependence of the reagent
concentration
Fig. 5. (Color online) Spatial distribution of the thermal emission of
tungsten (a) and molybdenum (b) in superfluid helium. The curves
corresponded to three distances from laser focus: 0 (1), 1.25 (2),
and 2.5 mm (3). The rectangles mark the moment of arrival at ob-
servation point 1.25 mm of the flat front moving with Landau ve-
locity, VL = 50 m/s. Curves 4 are the integrated emission signals as
registered for the similar conditions without optical slit.
Fig. 6. (Color online) The thermal emission accompanying the
tungsten coagulation as registered through the “blue” (1) and
“red” (2) filters (a); transmission spectra through “blue” (1) and
“red” (2) filters; the normalized spectral sensitivity of the PMT
cathode presented in Figure as well (green curve) (b).
1360 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9
Non-isothermal physical and chemical processes in superfluid helium
0
01
n
n C
kn t
= +
+
(4)
The coefficient C is responsible for the background due
to scattered light of the room illumination. As seen in Fig. 7,
for all metals emission intensity decrease fits well the hy-
perbolic dependence characteristic for the recombination.
For molybdenum and especially for platinum there are
some deviations at short times. We expected such effects
as a manifestation of the fact that very small clusters that
appear at the first stage of coagulation have a non-metallic
binding. In this case they do not contain free electrons and
their thermal emission should be much weaker than it fol-
lows from the Planck formula for the blackbody.
The coefficients corresponding to the extrapolations
shown in Fig. 7 have the following meanings: n0 is the
initial concentration of the atoms, and k0 is basically the
rate constant of the bimolecular reaction of two clusters
sticking together. Since the reagents captured at the vortex
can move only along the its core the reaction should be
considered as one-dimensional and the rate constant for
different metals should represent the ratio of the velocities
of their motion inside the vortex. From Fig. 7 it follows
that the “rate constant” ratios kMo (42) : kW (74) : kPt (78) =
= 4.9 : 3.7 : 2.3 (atomic weights are in brackets) do not
contradict this interpretation: the lighter the atom, the fast-
er its motion along the core of the vortex.
Because of the hyperbolic dependence on time there is
no concept of characteristic time for coagulation process
but, as shown in Fig. 7, under conditions of our experi-
ments the process lasts about 2 µs.
6. Conclusions
The entire body of data related to the production of nano-
wires by condensation of different metals inside superfluid
helium demonstrates, that the structure of nanowires (qualita-
tively) and their diameters (quantitatively) confirm the sce-
nario of metal coagulation in quantized vortices in He II as
proposed in Ref. 17. According to this scenario, during the
initial “hot” stage the small metal clusters, even if they were
previously cooled to low temperature, fuse to larger clusters
and simultaneously heat above their melting temperatures.
Only starting from the clusters with diameter exceeded its
limiting value, determined by thermo-chemical properties of
the metal, they stick together into nanowires.
According to this scenario, the nanoparticles heated
above their melting temperature should exist during the ini-
tial stages of metal condensation in He II. Provided they
grow up to nanometer size such clusters acquire metallic
binding and thus contain a lot of free electrons (especially
when they are heated up to high temperatures). For that rea-
son they should intensively emit photons in IR, and even in
visible spectrum. This radiation has been experimentally
detected in the bulk He II during the condensation of tung-
sten, molybdenum, and platinum. The spectral region of this
emission is the argument that it belongs to clusters heated up
to at least the metal melting point. At the same time, the
fusible indium, whose laser plasma emits in the visible not
less efficiently than other metals under study, does not
demonstrate any visible radiation during coagulation; this
confirms the thermal nature of the emission.
The surprising fact of refractory metal melting in He II
is the consequence of the specific character of heat transfer
in superfluid helium. He II possesses enormously high
thermal conductivity but only up to a rather low value of
heat flow. Above this limit the heat flow becomes sup-
pressed due to the development of turbulence. Superfluid
helium then converts to the normal fluid state, and then
evaporates to form a heat insulating envelope filled with
low-pressure helium gas.
The kinetics of thermal radiation decay, as registered in
our study and explained above is the first indication of
abnormally high rate of coagulation of impurities via their
one-dimensional motion towards each other along quan-
tized vortices. It turns out that with the actual metal con-
centrations created inside He II in our experiments, the
entire condensation process takes place very close to the
surface of the gas plasma bubble in the laser focus, the
turbulence being quite strong.
As shown in this study, the expansion of the metal inside
liquid helium is surprisingly fast, with the velocity close to
Landau velocity (despite the fact that at temperature of our
experiments, T = 1.7 K, the fraction of the normal, viscous
component is still rather high). But even this large rate is
insufficient to compete with process of coagulation.
The important conclusions of this work are.
The existence of huge local overheating is the result of
the unique properties of superfluid helium, and it is expected
not only for metals. Similar effects could be observable not
only in the bulk liquid helium, but also in cold helium drop-
lets [2,7–9,15,16]. If a liquid helium droplet contains guest
Fig. 7. (Color online) The approximation of the thermal emis-
sions temporary dependencies by the hyperbolic law for tungsten,
platinum and molybdenum. Solid curves are an experimental
results, open circles represent hyperbolic dependencies.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9 1361
E.B. Gordon, M.I. Kulish, A.V. Karabulin, and V.I. Matyushenko
atoms, molecules or, especially, clusters, the overheating
during their chemical or photochemical processes could
result in the appearance of gas cavity in the droplet. Indeed,
the high temperature of metal clusters in He II exists, as fol-
lows from our results, for a time of about 10–6 s, which is a
few orders of magnitude longer than the time of sound wave
propagation in liquid helium from the center of droplet to its
surface. Because of the zero pressure around a droplet the
gas cavity is expected to appreciably expand during that
time. Besides, existence of a radiative (without helium at-
oms evaporation) channel of cluster cooling can entail to
underestimation of the final droplet size.
And finally, the local overheating should occur not only
in the case of chemical reactions between the particles em-
bedded into He II, but also during coalescence of chemically
inert particles. Indeed Van der Waals forces are weaker than
chemical ones only by about 30 times. It means that in this
case local overheatings of 30–100 K, which is significant at
cryogenic temperatures, can be observed.
Thus, the existence of huge local overheatings kills any
promises of producing under the special conditions of super-
fluid helium any entity made of exotic chemical compounds.
However, it simultaneously guaranties a hope to use He II
for synthesizing unique nanomaterials, the exotic properties
and high possible cost of which justify application of expen-
sive and small-scale method of their production.
Acknowledgments
The authors are grateful to E.V. Dyatlova, A.S. Gordienko
and M.E. Stepanov for participating in the experiments.
This work was financially supported by Russian Sci-
ence Foundation (grant No. 14-13-00574).
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1362 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 9
1. Introduction
2. Experimental
3. The comparison of diameters of nanowires grown from different metals with the predictions of the model [17]
4. Choice of objects
5. Optical experiments
6. Conclusions
Acknowledgments
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