On the formation mechanism of impurity-helium solids: evidence for extensive clustering
Optical emission studies on a discharged nitrogen-helium gas jet injected into superfluid helium near 1.5 K are described. The analysis of atomic (a-group) and molecular Vegard-Kaplan transitions clearly indicates that the emitting species are embedded in the nitrogen clusters. The formation of the...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1288602018-01-15T03:03:57Z On the formation mechanism of impurity-helium solids: evidence for extensive clustering Popov, E.A. Eloranta, J. Ahokas, J. Kunttu, H. 3-й Международный семинар по физике низких температур в условиях микрогравитации Optical emission studies on a discharged nitrogen-helium gas jet injected into superfluid helium near 1.5 K are described. The analysis of atomic (a-group) and molecular Vegard-Kaplan transitions clearly indicates that the emitting species are embedded in the nitrogen clusters. The formation of the clusters is most efficient in the crater formed on the liquid surface. The model calculations based on the classical bubble model and density functional theory suggest that under the experimental conditions only clusters consisting of more than 1000 molecules have a kinetic energy sufficient for the stable cavity formation inside liquid helium. The results obtained suggest that the formation of impurity-helium solids is a consequence of extensive clustering in the gas jet. 2003 Article On the formation mechanism of impurity-helium solids: evidence for extensive clustering / E.A. Popov, J. Eloranta, J. Ahokas, H. Kunttu // Физика низких температур. — 2003. — Т. 29, № 6. — С. 684-689. — Бібліогр.: 24 назв. — англ. 0132-6414 PACS: 67.80.-s, 61.46.+w http://dspace.nbuv.gov.ua/handle/123456789/128860 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации |
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3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации Popov, E.A. Eloranta, J. Ahokas, J. Kunttu, H. On the formation mechanism of impurity-helium solids: evidence for extensive clustering Физика низких температур |
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Optical emission studies on a discharged nitrogen-helium gas jet injected into superfluid helium near 1.5 K are described. The analysis of atomic (a-group) and molecular Vegard-Kaplan transitions clearly indicates that the emitting species are embedded in the nitrogen clusters. The formation of the clusters is most efficient in the crater formed on the liquid surface. The model calculations based on the classical bubble model and density functional theory suggest that under the experimental conditions only clusters consisting of more than 1000 molecules have a kinetic energy sufficient for the stable cavity formation inside liquid helium. The results obtained suggest that the formation of impurity-helium solids is a consequence of extensive clustering in the gas jet. |
| format |
Article |
| author |
Popov, E.A. Eloranta, J. Ahokas, J. Kunttu, H. |
| author_facet |
Popov, E.A. Eloranta, J. Ahokas, J. Kunttu, H. |
| author_sort |
Popov, E.A. |
| title |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering |
| title_short |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering |
| title_full |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering |
| title_fullStr |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering |
| title_full_unstemmed |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering |
| title_sort |
on the formation mechanism of impurity-helium solids: evidence for extensive clustering |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2003 |
| topic_facet |
3-й Международный семинар по физике низких температур в условиях микрогравитации |
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http://dspace.nbuv.gov.ua/handle/123456789/128860 |
| citation_txt |
On the formation mechanism of impurity-helium solids: evidence for extensive clustering / E.A. Popov, J. Eloranta, J. Ahokas, H. Kunttu // Физика низких температур. — 2003. — Т. 29, № 6. — С. 684-689. — Бібліогр.: 24 назв. — англ. |
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Физика низких температур |
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2025-07-09T10:06:18Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6, p. 684–689
On the formation mechanism of impurity–helium solids:
evidence for extensive clustering
E.A. Popov1,2, J. Eloranta,1 J. Ahokas1, and H. Kunttu1
1Department of Chemistry, University of Jyväskylä, P.O.Box 35, FIN-40014, Finland
E-mail: Henrik.Kunttu@jyu.fi
2Institute of Energy Problems of Chemical Physics, Russian Academy of Sciences
Chernogolovka, Moscow Region 142432, Russia
Received December 19, 2002
Optical emission studies on a discharged nitrogen—helium gas jet injected into superfluid he-
lium near 1.5 K are described. The analysis of atomic (�-group) and molecular Vegard—Kaplan
transitions clearly indicates that the emitting species are embedded in the nitrogen clusters. The
formation of the clusters is most efficient in the crater formed on the liquid surface. The model cal-
culations based on the classical bubble model and density functional theory suggest that under the
experimental conditions only clusters consisting of more than 1000 molecules have a kinetic energy
sufficient for the stable cavity formation inside liquid helium. The results obtained suggest that
the formation of impurity—helium solids is a consequence of extensive clustering in the gas jet.
PACS: 67.80.–s, 61.46.+w
1. Introduction
The experimental approach for stabilization of
atoms by injection of impurity—helium (Im—He) gas
jet into superfluid helium (He II) was first developed
by Gordon, Mezhov-Deglin, and Pugachev in 1974
[1]. The advantages of this approach are related to ef-
ficient pre-cooling of the gas jet prior to its immersion
into He II, high degree of dispersion of impurity parti-
cles, and efficient thermal dissipation by He II. Con-
sequently, stabilization of reactive atoms (N, H, D)
with exceedingly high densities has been achieved as
indicated by optical emission and Electron Paramag-
netic Resonance (EPR) measurements [2,3]. Since its
discovery, the original approach has been subject to
active development, and currently semitransparent
gel-like substances with He/Im ratios of 12–60 and
thermal stability up to 6–8 K are routinely grown. Al-
though their interior is filled with liquid He, these
macroscopic condensates are historically called impu-
rity—helium solids (IHS) [1–9]. An interesting ex-
tension to the cited series of investigations is provided
by a recent work by Mezhov-Deglin and Kokotin on
the helium—water condensate [10].
Studies on thermal properties of IHS have shown
that in presence of � 0.5% mole fraction of impurity
(N2, Kr) in the condensate completely suppresses the
convection flow of liquid He filling the condensate
[6,9]. It was supposed therefore, that IHS comprise a
porous network structure and thus resemble highly po-
rous aerogels filled with liquid He. More recently,
strong support for this hypothesis has been provided
by a series of structural studies by the Lee group at
Cornell University. Based on the complementary use
of ultrasound and x-ray diffraction techniques it has
been shown that Im—He solids are, indeed, me-
soporous with characteristic impurity cluster size near
6 nm, average impurity density � 1020 cm–3, and wide
pore distribution ranging from 8 to 860 nm [11–13].
Although the physical characteristics of Im—He
solids have been rather extensively studied for years,
their formation mechanism and structure are not un-
derstood on the molecular scale.
The model suggested by Gordon and Shestakov as-
cribed the formation of metastable Im—He conden-
sates to a Im—He solid phase (IHSP) consisting of
«sticking-together» Van der Waals impurity—helium
clusters, Im(He)n, i.e., a bare impurity atom or mole-
cule surrounded by solid layers of He atoms in a
© E.A. Popov, J. Eloranta, J. Ahokas, and H. Kunttu, 2003
superlattice-like arrangement [4,14]. This is, of co-
urse, a very hypothetical model, which for example
neglects entirely the role of impurity clusters in for-
mation of these solids.
The present study aims at providing new insights
into our understanding of Im—He condensates, and in
particular their formation mechanism. Instead of in-
terrogating the solids themselves, we concentrate in
processes taking place in the Im—He gas jet from the
discharge zone to its final immersion into He II. Here
the following issues are addressed: (i) the extent of
cluster formation in the gas jet, (ii) interaction of im-
purity particles (bare atoms or molecules, small clus-
ters) with liquid helium surface, and (iii) factors con-
trolling their probability to penetrate into bulk liquid
helium in the experimental conditions. In what fol-
lows we describe our spectroscopic observations in ni-
trogen-helium gas jets and present results from model
calculations of solvation of nitrogen species in He II.
2. Experimental methods
The experimental setup used in the present study
consists of a liquid He bath cryostat fitted with a set
of quartz windows (Fig. 1). The inner diameter of the
He bath is 120 mm, and it accumulates 7 L of liquid
He, which allows operation for more than 12 h. By
pumping the helium reservoir with a one-stage me-
chanical pump (20 L/s) the lowest accessible temper-
ature is near 1.4 K. The vapor pressure of He inside
the cryostat was measured with an absolute pressure
transducer (MKS Instruments, Baratron model 622).
The temperature was measured with a silicon diode
sensor and Lake Shore 330 temperature controller.
A cryogenic discharge source, an optical cell and
temperature sensors were placed inside the cryostat
with an insertion allowing mutually independent op-
eration of the instrumentation. This design of the in-
sertion allows adjustment of the separation between
the discharge tube orifice and the He surface in the
sample cell in the range of 2–20 cm. The electrodeless
discharge was excited by an inductive coil, coaxially
installed around a liquid nitrogen cooled quartz dis-
charge tube 2 cm from the nozzle. The output of a
home made pulse generator, operating near 40 MHz,
was coupled to the coil, thus providing a RF discharge
with a power 10–70 W, and pulse duration ranging
from 1 �s up to continuous operation.
Nitrogen and helium gases of 99.99(9)% nominal
purity were premixed in a stainless steel cylinder. A
mechanical membrane regulator was used to provide
constant gas flow with accuracy better than 5% for a
typical gas flow rate of 5�1019 particles/s upon pres-
sure drop in the gas cylinder from 5 bar to 0.2 bar. The
optical measurement cell consists of a 40 mm diameter
quartz funnel attached to a standard quartz 10�10 mm
optical cuvette. Constant level of He II in the sample
cell was maintained by a fountain pump, which sup-
plied superfluid helium from the bottom of the
cryostat.
The experiments were performed by passing a mix-
ture of molecular nitrogen, diluted to 0.3–3% by he-
lium gas, through the discharge zone. The discharged
gas then escapes through a 0.8 mm diameter nozzle,
and propagates through the dense cold helium gas,
forming an intensively illuminated jet. The jet pro-
ceeds to the surface of He II producing a visually ob-
servable crater. Special attention was paid for selec-
tive collection of emission from three distinct
observation zones, namely the gas jet, the crater, and
bulk He II. For this purpose in some experiments the
quartz funnel was blocked with a black painted Pyrex
cover in order to allow collection of light solely from
bulk He II.
The collected light was focused onto the entrance
slit of a 0.3 m spectrograph (Acton), equipped with
2400, 600, 600 lines/mm gratings, blazed at 240, 300,
500 nm, respectively. The spectra were recorded with
a thermoelectrically cooled Charge-Coupled-Device
(CCD) camera (Princeton Instrument) attached to
the spectrograph. Depending on the grating, the spec-
tral bandwidth on the detector was 30, 120, or 120
nm, respectively. For more selective collection of light
On the formation mechanism of impurity—helium solids: evidence for extensive clustering
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 685
He II
1
5
4
3
2
6
7
6
Fig. 1. Experimental setup for injection of Im—He mix-
tures into superfluid helium: cryogenic discharge source
(1); quartz tube (2); liquid nitrogen cooled inductance
coil (3); nozzle (4), fountain pump (5); temperature sen-
sors (6); He II level gauge (7).
from different parts of the jet or bulk He II, a
high-grade UV quartz optical fiber bundle was used.
3. Experimental results
3.1. Characteristics of the jet
After passing the RF discharge zone, the nitro-
gen-helium gas mixture propagates in dense cold he-
lium gas (density 3�1019 atoms per cm3, T = 1.7 K) in a
laminar mode, forming a well-collimated jet (Fig. 2).
The peripheral part of the jet is rather cold, but its
core is relatively hot and less luminescent. We have
measured the velocity of the jet at T = 77 K and at
cryostat pressure of 5 mbar. The measurement was per-
formed by adjusting the discharge to 200 �s pulse and
500 Hz repetition rate. Under these conditions emis-
sion was monitored at 5 cm distance from the dis-
charge tube orifice with a photomultiplier tube fitted
with a horizontal 1.5 mm slit. From the observed
phase shift with respect to the pulse train, the flow ve-
locity was estimated to be v = 70 m/s.
While hitting the He II surface the jet stops and
produces a well defined crater. The crater is the most
intensively emitting region due to effective collisional
processes, which in turn promote aggregation of impu-
rities, and recombination of nitrogen atoms. The in-
tensity of the emission decreases dramatically in the
bulk He II, even at distances few mm beneath the
crater. Upon increasing the distance between the nozzle
and the He II surface to 10 cm or more, we observed a
transition from laminar (upper part) to purely turbu-
lent flow (lower part), which is visually characterized
by shaggy shape of the lower part of the jet.
3.2. Emission spectra
The main monitored emissions were the atomic N
(2D–4S) transition (�-group, green afterglow), as
well as the Vegard—Kaplan A u X g
3 1� �� � � after-
glow in blue and UV range) system of molecular ni-
trogen. Both of these transitions are forbidden in the
gas phase and thus serve as sensitive probes for various
processes related to the formation of impurity clusters
and IHS.
686 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
E.A. Popov, J. Eloranta, J. Ahokas, and H. Kunttu
1
4
5
6
3
2
7
Fig. 2. A photograph of nitrogen-helium jet penetrating
into bulk He II. A schematic view of the optical cell is
also shown: the core of the jet (1); peripheral part of the
jet (2); crater (3); black painted Pyrex funnel (4); quartz
funnel (5); quartz cuvette (6); light collection zones (7).
Dotted arrows show the circulation of liquid He.
Wavelength, nm
In
te
n
si
ty
, a
rb
. u
n
its
240 280 320 360
a
b
c
0–10
0–9
0–8
0–70–6
0–5
0–4
0–3
Fig. 3. A section of the Vegard—Kaplan emission band of
molecular nitrogen collected from the gas jet (a), bulk
He II (b), and upon explosion of the nitrogen—helium
solid (c). The numbers refer to the quantum labels
( ) � v v . The stick spectra show the line positions in the
gas phase (black columns, Ref. 17), and in solid nitrogen
matrix (gray columns, Ref. 18).
A section of the the Vegard—Kaplan band of N2 is
presented in Fig. 3. The spectra are almost identical,
regardless of the location of the emitter (gas jet,
crater, bulk), and are characterized by linewidths of
� 1 nm , and a consistent red shift of � 360 cm–1 from
the corresponding gas phase lines. As described in the
experimental section, special attention was paid to
eliminate stray light from other parts of the cryostat.
Although spectroscopy of IHS is outside the scope of
this report, a spectrum obtained from explosion of a
helium-nitrogen condensate is provided for reference.
Apart from the broad, so far unassigned background
features, this spectrum clearly resembles the others.
These observations would strongly suggest that radia-
tive recombination of nitrogen atoms, leading to
Vegard—Kaplan band, occurs in very similar environ-
ments in all detection zones.
The strongly forbidden green �-group emission of
atomic nitrogen was detected even in the gas jet, far
from the liquid helium surface. The �-group emission,
collected near the crater was very intense and the
spectrum contained three peaks, centered at 521 and
522, and 523 nm (see Fig. 4). This observation pro-
vides additional support for the assignment that, in-
stead of monitoring transitions of more or less isolated
gas phase species, the spectra are strongly affected by
formation of clusters in the gas jet before it enters in
He II. No significant changes in the �-group emission
was observed when signal was collected from bulk
He II. Increasing the N2/He ratio of the gas mixture
from 0.3 to 3%, caused the shift of the �-group emis-
sion towards the 523 nm in the gas phase. We per-
formed spectroscopic studies on other atomic and mo-
lecular transitions such as N(2P–2D), the first
positive system (B A3 3
�� ) of N2, O(1S–1D), the
Herzberg I bands (A–X) of O2, as well as the �, �, and
bands of NO. These data, which will be published
separately, are consistent with the present obser-
vations.
4. Discussion
In the present study we concentrate on the
Vegard—Kaplan (V—K) emission system in the UV
region mainly for two reasons: (i) previous spectro-
scopic measurements in IHS were restricted to the vis-
ible range [5] and (ii) we expected to observe recom-
bination of atomic nitrogen in bulk He II and in
nitrogen—helium solid by monitoring radiative decay
of the metastable A3� state of the N2 molecule (triplet
exciton in the case of IHS). Detection of the V—K
emission in the gas phase is a rather challenging task
and would necessitate very high purity gases, espe-
cially free of any oxygen-containing impurities. More-
over, the discharge needs to be operated under special
conditions [15,16]. Quite surprisingly, we observed
rather intense V—K emission from the gas jet even in
the presence of oxygen impurities. Equally demonstra-
tive is the observation that the V—K lines are
red-shifted with respect to their pure gas phase coun-
terparts [17]. This would, indeed, strongly suggest
that the emission originates from recombination of at-
oms embedded in impurity particles. The V—K emis-
sion was studied in solid nitrogen matrix by Coletti
and Bonnot [18]. They observed rather intense emis-
sion at 20 K with a lifetime of the order of � 1 ms.
Similarly to our findings in the nitrogen—helium jet,
the V—K lines are red shifted from the gas phase by
350 cm–1 in solid nitrogen.
The atomic (2D5/2, 3/2—
4S3/2) transitions of ni-
trogen are strongly forbidden by spin and parity selec-
tion rules of electric dipole, and their observation is
ascribed mostly to electric quadruple. The 2D5/2 and
2D3/2 states lie 19224 cm–1 and 19233 cm–1 (2.38 eV)
above the 4S3/2 ground state, and their calculated
lifetimes are 44 h and 17 h, respectively [19]. Thus,
detection of pure atomic emission within the time of
flight of the jet should not be feasible at the con-
On the formation mechanism of impurity—helium solids: evidence for extensive clustering
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 687
Wavelength, nm
520
In
te
n
si
ty
, a
rb
. u
n
its
522 524 526
a
b
1+
2
5
4
3
1
a,b
0
Fig. 4. The effect of the gas mixture on the 2D–4S emission
of atomic nitrogen. N2/He = 1/400 (solid line), 1/100
(dotted line). A grating with 2400 groves/mm was used
(a). N2/He = 1/100 (dotted line), 1/30 (dashed line).
Grating with 600 groves/mm was used (b). The arrow indi-
cates the gas phase position of the transition (Ref. 19). The
stick spectrum represents observation in solid nitrogen ma-
trix (Ref. 24).
ditions of the present experiments. Therefore, some
process taking place in the gas jet is dramatically af-
fecting the transition probability, and consequently
decreasing the lifetime of the atomic transition. Ag-
gregation of nitrogen molecules around the emitter
would obviously be such a process. In fact, unlike in
the gas phase, in an irradiated nitrogen solid the green
atomic emission is the most prominent spectral feature
[20]. In solid nitrogen this emission consists of eight
main lines, the most intense being at 522 nm
(zero-phonon line) and 523–525 nm (phonon-induced
wing). Furthermore, the 2D–4S emission has a life
time of 40 s in solid nitrogen [21]. The similarity be-
tween our spectra and the one obtained in solid nitro-
gen is obvious already at the highest dilution, and gets
stronger at increased nitrogen content (see Fig. 5).
One important factor promoting nucleation and clus-
ter formation in the jet is related to its ability to switch
from laminar to turbulent mode upon lowering the tem-
perature. Let us consider the jet as an incompressible
flow through dense helium gas. Within this framework
the Reinolds number is defined by the straightforward
relation Re = vD/�. Here v is the velocity of the jet, D
is the diameter of the jet (pipe flow), and � is the kine-
matic viscosity (viscosity divided by density). Upon de-
creasing the temperature of the nitrogen—helium jet
from initial T = 80 K to T = 10 K (temperature few mm
above the He II surface), the kinematic viscosity of the
jet decreases by a factor of 25. In a pipe flow characterized
by v = 70 m/s, D = 0.005 m, � (80 K) = 1.8�10–3 m2/s,
� (10 K) = 6�10–5 m2/s, the jet should change from lami-
nar (Re = 210 at T = 80 K), to turbulent (Re = 5600 at T =
= 10 K). We observed indeed a shaggy front of the jet in
the vicinity of He II surface. Moreover, the shaggy front
was clearly seen even when the distance between He II
surface and the nozzle was more than 10 cm, and the jet
did not reach the surface. We assign this observation to the
onset of turbulent flow.
Visual observation during preparation of IHS
showed that some small particles penetrate into bulk
He II directly from the jet. However, most of the im-
purities tend to float on the surface and stick to the
walls of the quartz cell, growing on the walls, and fi-
nally sink down to the bottom. In the following we as-
sume that penetration of an impurity into liquid He
depends on the kinetic energy of the particle, which in
the present case is defined by the velocity of the prop-
agating jet. More precisely, the kinetic energy should
exceed the energy required for solvating the given spe-
cies. This energy can be estimated by the classical bub-
ble model:
E
b
(R
b
) = VN–He(Rb
) + 4�R2
b
�, (1)
where Rb is the bubble radius and � is surface tension
(�He = 3.6�10–4 J/m2). By neglecting all dissipative
processes, and the van der Waals attraction, one can
obtain a lower bound for the critical velocity required
for a species to penetrate into the liquid:
vcr > 4R
b
(��/m)1/2. (2)
In order to estimate the radius of the cavity produced
by a solvated cluster we need to evaluate the interac-
tion potential of the cluster in liquid helium. Here we
rely on the approximate N2–He Lennard-Jones (LJ)
potential with � = 18 cm–1 and R0 = 3.6 A [22]. By
assuming a perfect spherical cluster with N = 1000,
sharp edge, and � = 1 g/cm3 = 0.0217 molecules/ A3
we end up with a radius of 22.2 A. The effective in-
teraction potential can be formulated as:
� �V r r V r r d rLJeff N( ) ( ) ( )� � � �
2
3 . (3)
We computed solvation of impurity N(2D) and N(4S)
atoms as well as the (N2)1000 cluster in liquid helium
using density functional theory [23]. Figure 5 repre-
sents results of such calculation for a bare N atom and
a (N2)1000 cluster in a spherical cavity. We can now
estimate the critical velocities for a single atom (Rb =
= 4 Å) and the cluster (Rb = 22.2 Å). Substitution
into Eq.(1) yields vN > 400 m/s and vcl > 70 m/s
688 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
E.A. Popov, J. Eloranta, J. Ahokas, and H. Kunttu
5 10 15
–0.02
0
0.02
0.04
25 30 35
R, Å
–0.02
0
0.02
0.04
0.06
�
He
VN—He
�
He
Vcl—HeD
e
n
si
ty
, Å
–
3
E
n
e
rg
y,
cm
–
1
1
0
3
Fig. 5. The density profiles of liquid He near ground state
nitrogen atom (upper panel) and molecular nitrogen clus-
ter with n = 1000 (lower panel) are shown. The corre-
sponding pair potentials are also shown.
for the atom and the cluster, respectively. It should
be emphasized here that we neglect all other dis-
sipative processes such as creation of ripplons and
shock waves. Consequently, the real values should be
even greater. On the other hand, Van der Waals
binding should slightly favor solvation. Although our
theoretical treatment is relatively crude, it clearly
shows that under the experimental conditions, seed-
ing bare atoms into bulk helium is not feasible by a
slowly propagating gas jet.
5. Summary
We have described optical emission studies on dis-
charged nitrogen—helium gas mixtures under experi-
mental conditions in which IHS are typically pre-
pared. The analysis of the observed atomic (�-group)
and molecular Vegard–Kaplan transitions clearly in-
dicate that, instead of isolated atoms or molecules,
these emissions originate from nitrogen clusters or ma-
trix-like particles. The formation of clusters takes
place already in the discharge zone, and is most effi-
cient at the point where the gas jet hits the surface of
He II, and a well defined crater is formed. The en-
hancement of emission intensity at the lower part of
the jet is ascribed to change from laminar to turbulent
flow.
Penetration of chemical species into liquid He II is
discussed within the classical bubble model. The cal-
culated critical velocity, 400 m/s, needed for solva-
tion of a bare N atom clearly exceeds the measured ve-
locity of the jet, and only clusters consisting of at
least 1000 molecules may have sufficient kinetic en-
ergy to overcome the barrier for stable cavity forma-
tion in bulk He II. By combining the present experi-
mental findings and model calculations, we conclude
that formation of impurity clusters, i.e., building
blocks of IHS, occurs via extensive clustering in the
jet and, most efficiently, in the crater. Coalescence of
these nanosize clusters inside He II leads then to for-
mation of macroscopic condensates. Finally, deposi-
tion of impurity—helium jet into the liquid helium
through its surface could be utilized for efficient for-
mation of mass-selected neutral clusters and produc-
tion of amorphous materials. Aerogel-like IHS,
formed from Ne, Ar, Kr, and N2 impurities represent
one of such example.
Acknowledgements
We wish to thank David M. Lee and Vladimir
Khmelenko for fruitful discussions on impurity helium
solids. This work was supported by the Academy of
Finland.
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On the formation mechanism of impurity—helium solids: evidence for extensive clustering
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