Coagulation of Metals in Superfluid and Normal Liquid Helium

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Coagulation of Metals in Superfluid and Normal Liquid Helium Eugene B. Gordon, Alexander Vladimirovich Karabulin, Mikhail I. Kulish, Vladimir Igorevich Matyushenko, and Maxim E. Stepanov J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08645 • Publication Date (Web): 17 Nov 2017 Downloaded from http://pubs.acs.org on November 21, 2017

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The Journal of Physical Chemistry

Coagulation of Metals in Superfluid and Normal Liquid Helium Eugene B. Gordon*1, Alexander V. Karabulin2, Mikhail I. Kulish1, Vladimir I. Matyushenko3, Maxim E. Stepanov1. 1

Institute of Problems of Chemical Physics RAS, 1 Semenov avenue, 142432, Chernogolovka,

Moscow Region, Russia. 2

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 31

Kashirskoe highway, 115409, Moscow, Russia. 3

The Branch of Talrose Institute for Energy Problems of Chemical Physics RAS, 1/10 Semenov

avenue, 142432, Chernogolovka, Moscow Region, Russia. Corresponding Author * E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

The thermal emission study in this work has shown that coagulation of metals in liquid helium is accompanied by enormous local overheating of several thousand degrees. Direct experiments demonstrated, for the first time, that condensation of metals in superfluid helium occurs via the specific mechanism which is substantially faster than that in normal liquid helium. It has been stated that coagulation of metals in superfluid helium indeed occurs in two stages - a "hot" one of nanoparticles coalescence with the formation of molten nanospheres and the subsequent stage of their sticking together into nanowires. It turned out that if a laser ablation of metal targets immersed in superfluid helium was used for introducing a metal into liquid, the formation of nanowires occurs at distances of only about one millimeter from the laser focus. This leads to the presence of a considerable number of spherical inclusions in nanowires grown in such a way.


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INTRODUCTION On the basis of results on molecular hydrogen embedding into superfluid helium the possibility of existence of specific mechanism for any guest particles coagulation in superfluid helium (He II) based on their concentrating in a core of quantized vortices was postulated.1 Indeed, a probability of mutual collisions for the particles trapped in the vortex should be much higher than that for their random “walk” in the bulk liquid helium due to collinearity of their velocities. In addition, since attraction of the particles to the vortex core is conditioned by Bernoulli forces, the particles enlargement during the process of condensation leads to an increase in the particlevortex attraction, and therefore, to an extension of their lifetime in the trapped state.2 Therefore, gradually this type of coagulation should become prevalent, and that is why the main product of condensation are not spherical particles as usual, but long thin filaments. It was then proposed3 to use this effect for production of thin metallic nanowires. This proposal was soon realized,4,5 in both cases a metal was introduced into superfluid helium by laser ablation of metallic targets immersed in He II. Another experimental approach has been later realized by atoms introduction from gas target into the droplets of superfluid helium.6 Analyzing the structure and thicknesses of nanowires grown in superfluid helium we came to the conclusion that the nanowires pass during their formation through the stage of coalescence of molten nanoclusters.7 The idea about metal melting in superfluid helium seems, at first glance, paradoxical due to record high thermal conductivity of He II. However the high rate of heat exchange in He II is provided by laminar motion of the normal component and after heat flux exceeds some threshold value this mechanism is not longer valid due to turbulence development, and liquid helium becomes oppositely the perfect heat insulator.8


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In general, the process of nanowires formation was supposed to satisfy the following scenario.7 At the first “hot” stage a heat released as the result of condensation of metal atoms or nanoclusters in He II appears to be sufficient to evaporate the liquid helium surrounding. This envelope filled with rarified gas (because of a low He II saturated vapor pressure) serves as a good heat insulator. The process of metal condensation runs almost adiabatically and, as it occurs in a rarefied gas, the condensation of small cold metal clusters results in melting a clusterproduct due to the energy release caused by decreasing of total reagents surface. Naturally, the molten cluster acquires then dense structure and spherical shape due to surface tension. At the same time, the cluster-product is likely to leave parent vortex in order to be repeatedly caught by the core of another vortex. Concentration of clusters, as a rule, is small enough, so that during the time between successive collisions the clusters cool down to low temperatures. As clusters grow, the temperature attainable by their condensation gradually decreases, and, beginning from a certain critical size determined by thermophysical characteristics of the metal,7 it becomes close to its melting point. Starting from this size, the total melting becomes energetically impossible, and such clusters can only stick to each other in the core of the vortex forming the nanowire. Some authors who studied the formation of nanowires in cold helium droplets adopt this scenario.9-11 However, the above reasoning is based on the behavior established only for sufficiently large objects. Validity of the approach for nanoscale objects should be proved, both theoretically and experimentally. In theory, serious progress has been recently made. In Ref. 12 it was shown that the whole interaction of impurity particles with a vortex can be described as the Bernoulli force, and it also was found that the binding energy of a small sphere with the vortex is proportional to the sphere’s radius. We have observed experimentally the visible emission during the coagulation of W, Mo, and Pt13. The intensities of


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this emission being resolved in space and in time have proved that the glow originates from the bulk of superfluid helium and it arises later than the signals from both scattered laser light and plasma in laser focus. A serious support for its interpretation as thermal emission was the absence of visible emission in experiments with low-melting indium, in case of which the plasma emits not worse than in the cases of other metals, whereas the high temperatures could not develop during coagulation simply from energy considerations.

EXPERIMENTAL In this work by using the optical method developed in Ref. 13 the coagulation of metals in liquid helium was quantitatively studied. The low temperature experimental setup and the optical system for the observation of visible emission that accompanied the metal coagulation in liquid helium were already described elsewhere.7,13 The setup was assembled on the base of liquid helium optical cryostat provided with helium vapor pumping. The pumping performed by the tandem of two powerful pumps (models D.V.P. Vacuum Technology s.p.a LC.305 and Robuschi RBS_85/AV-V) allowed pumping down to 0.8 mbar as well as holding the pressure value on a required level with an accuracy of 0.1 mbar. The pressure was measured by a digital vacuum meter Thyracont VD85. The optical system is shown in Figure 1a. Laser ablation of metallic targets (tungsten, molybdenum and platinum) was used to embed atoms and small clusters of corresponding metals into liquid helium. The solid state diode-pumped Nd:LSB laser (wavelength 1.064 µm, pulse energy 0.1 mJ, pulse duration 0.4 ns and pulse repetition rate up to 4000 Hz) was applied.14 In this study the repetition rate of laser pulses was chosen to be 50 Hz to avoid rapid target burnout and to guarantee independence of coagulation processes on successive laser


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pulses. The laser beam was focused by a long-focus lens on the surface of the target immersed in liquid helium to form 100 micron-sized spot. A well-discernible gas bubble filled with plasma appeared in the spot during the irradiation. The thermal emission that accompanied coagulation in HeII was detected via sapphire windows by Hamamatsu photosensor module (PMT) with a gate function H11526-01. It was sensitive only in visible range. Gate function turn-on delay of 280 ns was sufficient to avoid the impact of fast processes such as laser beam scattering, plasmon excitation, etc.15

Figure 1. (a) Brief scheme of the experiment. (b) To the determination of temperature accompanied a coagulation of metals inside liquid helium. The curve corresponds to Planck formula for the emission of a black-body with T = 3900 K, that close to the melting point of


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tungsten. The normalized transmittances of interference filters centered at 0.40, 0.45, and 0.65 µm are also given. Special experiments were performed to justify the attribution of observed visible emission to the thermal radiation of metal nanoclusters during their coagulation in liquid helium.13 It was shown as a result that the whole emission, registered at times longer than 1 µs, occurs from the volume of liquid helium with a thickness of about 1.5 mm. The emission signal was sufficiently intense, and therefore the photomultiplier was applied in proportional mode with a bandwidth of up to 500 MHz, which determined by the bandwidth of the recording oscilloscope, and the repetition rate of laser pulses was 50 Hz. PMT signal was recorded by a digital oscilloscope Tektronix TDS 7054 in 128-fold averaging regime for improving signal-to-noise ratio. It was supposed that nanowires are forming from hot spherical clusters of nanometer size. These clusters contained high density of free electrons and should demonstrate black-body emission obeyed Planсk formula at least in visible and at microsecond times.16 Hereupon, the following procedure was used for measuring temperature of thermal emission that accompanying coagulation.17 Temporal dependences of both the thermal emission intensity E and calibration source (blackbody with known temperature Т0) emission intensity E0 were recorded by using two interferential filters with central wavelengths λ1 (intensities E(λ1) and E0(λ1)) and λ2 (E(λ2) and E0(λ2)). In this case, with additional assumption of emissivity independence on wavelength, the temperature T obeys the formula:

( ) ( )

= + ln ( ) : ( ) ∗ ∗ ( )

(1)

where and h are the Boltzmann and Planсk constants, respectively, is the speed of light. Filters with central wavelengths of 0.4, 0.45 or 0.65 µm and full-width-at-half of 0.01 µm were used. As it demonstrated in Fig. 1b, filters were chosen on the grounds of maximal sensitivity to


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temperature for the blackbody with tungsten melting temperature. Stabilized Tungsten Light Source SLS201L(/M) with known brightness temperature T0 = 2796 K was used as blackbody reference.

RESULTS AND DISCUSSION Typical kinetics of integral-over-spectrum optical emission accompanying the metal coagulation of different metals in superfluid helium is shown in Fig.2.

Figure 2. The pulses of visible emission accompanying coagulation of tungsten, molybdenum and platinum in superfluid helium (T = 1.2 K, P = 0.8 mbar). In inset, the front parts of the pulses are shown in more detail (the voltage on the PMT cathode was switched on with a delay of 280 ns). The metal nanoparticles are known not to luminesce. For very small metal nanoparticles heated by their coagulation, the thermal radiation should also be low-intensive, both because they still have few free electrons and because the energy released during coagulation is still insufficient to form a gas envelop isolated heat transfer. And only for the coagulation of nanometric clusters, the thermal radiation can become close to the black-body emission. We associate this effect with the existence of a maximum on the radiation pulse observed during platinum coagulation (see


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Fig.2). For molybdenum, and especially for tungsten, the specific energy released during coagulation is much higher; therefore, the maximum of the emission for them should occur at shorter times and, apparently, is overlapped with the radiation of the plasma at the laser focus. In general, the process of coagulation in liquid helium should be quite similar both in its normal (He I) and superfluid states. In normal helium, of course, the vortices are absent, and the coagulation process will be controlled by diffusion. But the very act of coagulation should not be different from that in He II, moreover the formation of gas bubble in He I does not even require the overcoming critical value of heat flow, since He I already conducts heat poorly. Meanwhile, in normal helium it is easy to investigate the effect of external pressure on the ablation and coagulation, whereas in superfluid helium the saturated vapor pressure does not exceed 40 mbar. Experiments have shown that the intensity of emission accompanying the coagulation in normal liquid helium is maximal at the highest pressure Рsvp and decrease strongly with pressure lowering (experimental results for platinum are shown in Figure 3). However, under further pumping of helium vapor just after liquid helium transition to its superfluid state the intensity of emission abruptly increases. Moreover, as it seen from Fig. 3, the characters of signal decay is also different, this evidences that the mechanism of metal coagulation in He II is different than that in He I. The temporal dependences contain information about both the coagulation kinetics and emitters’ temperature change in time.


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Figure 3. Kinetics of visible thermal emission initiated by Platinum embedding into He I and He II at different pressures (and temperatures) (1 - 680 mbar (3.80 K), 2 - 345 mbar (3.25 K), 3 - 65 mbar (2.30 K), and 4 - 2 mbar (1.35 K) – the last in He II). The temporal dependences of temperature determined by formula (1) for tungsten, molybdenum and platinum are shown in Figure 4. They fit our scenario:13 at short times where the clusters are small the temperatures are very high, but when the clusters begin to form nanowires these temperatures gradually decrease to practically constant value correlated with the melting point of metals, equal to 3700 K, 2900 K, and 2040 K for W, Mo and Pt, correspondingly. Comparison of the data of Figures 2 and 4 shows that the temperature drop to a value close to Tmelt for a given metal occurs already when the signal intensity is still high enough and its value does not change until the signal decreases to the level of noise.


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Figure 4. The calculated by the formula (1) temporal dependences of temperature developed in the course of coagulation in He II (T = 1.2 K, P = 0.8 mbar) of (a) - tungsten, (b) - molybdenum and (c) – platinum. The noise is grown at large times because the emission intensity drops down with time.


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The hot stage that corresponded to the period of growth of spherical clusters lasts about 10 µs. In superfluid helium during the second stage, that of nanowires production, the filaments grow aligned along the vortex core. In places of filament junction the temperature is close to the melting point. The number of such junctions decreases while nanowires are growing and therefore intensity of the glow decreases, but the temperature remains constant. Fig. 5 shows the temporal behavior of the temperature of tungsten clusters during their coagulation in normal liquid helium at pressure of its saturated vapor of about 70 mbar (T = 2.3 K) which was determined in the same way as data of Fig.4. It demonstrates that not only the intensity of emission, but also the characteristic temperature of clusters in normal helium behave in a very different way than that in superfluid helium: for some time the temperature of the clusters remains close to Tmelt, but long before the signal intensity drops to the noise level it resumes its fall.

Figure 5. The calculated by the formula (1) temporal dependence of temperature developed in the course of tungsten coagulation in normal helium (T = 4.2 K, P = 1 bar). The difference may be as well explained in the framework of the scenario proposed.7,13 Indeed in normal liquid helium the temperature achieved during the first stage of coagulation (which now takes place in the bulk) is very high too. In this case as well, when the temperature becomes


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close to the melting point of the metal, complete melting of the coagulation product becomes impossible, and the clusters simply begin to fuse together forming clots, as in ordinary coagulation. As the clots are growing large their structure has become loose, respectively the specific energy released during melting and the local temperature developing during condensation both gradually fall. In addition, the adherent optically dense clusters partially shield the hot spots of their mutual contacts. This is the reason of final temperature diminishing in normal helium. In order to explain the dependence of the thermal emission outgoing from liquid helium bulk on its saturated vapor pressure, that presented in Fig. 3, one should keep in mind that all embedded into liquid helium atoms and clusters of metal are passing through the small area (≈10-1mm2) of a gas plasma filled bubble formed in the laser focus.18 We can already estimate the depth of metal penetration into helium, because we know that the "hot" stage, which determines the local structure of condensation products, lasts less than 10 microseconds. Metal particles embedded into superfluid helium are rapidly decelerated to the Landau velocity (50 m/s), whereupon they move laminarly with very small losses,19 passing the distance of 0.5 mm in 10 µs. This conclusion agrees with the spatially-resolved measurements of the intensity of the thermal radiation accompanying the coagulation of metals in superfluid helium13. In normal He the metal particles should rapidly cool down to thermal velocities and move further diffusively and, therefore, slowly. The estimate gives the distance x ≈ (Dt)1/2 = (10-4 cm2/s·10-5 s)1/2 = 3·10-5 cm, where D is the diffusion coefficient of nanometer-sized particles, which could not exceed the coefficient for diffusion of 3Не in 4Не that determined in Ref. 20. This means that in normal helium the coagulation of metal particles occurs at much smaller depth, just near the surface and metal concentration inside the liquid is inversely proportional to the bubble area. Because the


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bubble size decreases with increasing of helium saturated vapor pressure, the density of the metal suspended in liquid helium increases, and as a result, the coagulation rate and the intensity of thermal radiation increases. This explains the growth of the integral irradiance with increasing of the normal liquid helium pressure Рsvp. Of course, the concentration of the metal inside of superfluid helium at the same ablation rates is much lower than in normal liquid, since both the bubble area is larger and the depth of penetration of metal particles into the liquid is much greater. The fact that the radiation intensity in superfluid helium is anyway much higher than in normal helium, especially at low pressures, is the first direct proof of the existence in He II of specific mechanism of coagulation, which is substantially faster than the usual diffusion-controlled mechanism. Since in He II the temperature and thus radiation spectrum are practically constant at times greater than 10 µs and the depth of metal expansion in He II is only a few mm for the first 80 µs, we can assume that the temporal dependence of the radiation reflects the rate of coagulation process. In accordance with that the kinetics in the time range of 10-80 µs really obeys the hyperbolic law, which is characteristic for coagulation reaction.13

CONCLUSIONS It is important that even in He II at our experimental conditions the coagulation of the metal occurs at very close distances from the plasma bubble. This is a major drawback of the method of nanowire synthesis based on ablation of metals in superfluid helium. Firstly, the area adjacent to the bubble is a region of hydrodynamic instabilities, which leads to distortions in the structure of nanowires and therefore to their relatively short length. Secondly, concentration of metal in the reaction region is so high that nanoclusters often collide with each other without being


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thermalized. That, according to our assumption,7,13 leads to the appearance of inclusions of spherical nanoclusters in nanowires. Besides the consumption of the ablated metal for inclusions production decreases the yield of nanowires. Understanding of this shortcoming has allowed us to create a new design, where spherical inclusions in nanowires are absent, and the length of individual nanowires in a nanoweb is significantly higher than in the original method.21 That will be especially important in the studies of different size effects, for example in superconductivity22 or in quantum phase shift.23 Finally the main conclusion of this study can be represented graphically as it done in Fig.6.

Figure 6. Temporal dependences of the temperature developed during tungsten coagulation in superfluid (T = 1.2 K, P = 0.8 mbar) (a) and normal (T = 4.2, P = 1000 mbar) (b) helium and their interpretation according to the model proposed. Different colors in Fig.6a correspond to different pairs of filters (blue curve - 400 and 650 nm, red curve - 450 and 650 nm). As it is seen, two different pairs of optical filters display close behavior confirming Planck character of the spectra. (a) Stage I – hot stage of spherical clusters growth, stage II – stage of nanowire growth; (b) Stage I – hot stage of spherical clusters growth, stage II – stage of clusters gluing together, stage III – stage of clusters sticking together in a clods.


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As it seen from Fig. 2 cooling of the clusters, i.e. the loss of their thermal energy never slows down. However starting from a certain time the color temperature ceases to fall. We explain this by the fact that during the nanowire formation only the points of whiskers welding together remain hot, because the temperature, naturally, should be close to the melting point of the metal because of latent heat of melting presence. We would like as well to stress that it was believed until recently that all processes of impurities coagulation in such a homogeneous and record-fast heat-conducting liquid as superfluid helium: (i) were controlled by diffusion and were therefore slow, and (ii) were strictly isothermal and therefore led to the formation of loose products. It is conclusively proved in this paper that at least for the coagulation of metals, both of these fundamental statements are completely wrong. First, a fast specific coagulation process realized in He II is not controlled by diffusion but caused by the concentration of impurities within the cores of quantized vortices; that’s why its products are predominately thin long nanowires. Secondly, in liquid helium, the coagulation process at its initial stages is not isothermal but oppositely leads to enormous local overheating, as a result of which coagulation products for all metals, including the most refractory tungsten, melt to form the dense-packing structures.

ACKNOWLEDGEMENT This work was supported by the Program of basic research of the Presidium of the Russian Academy of Sciences №13 "Condensed matter and plasma at high energy densities".


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REFERENCES (1)

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Embedding into Superfluid Helium. JETP Letters 2007, 85, 581-584. (2)

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4He. J. Low Temp. Phys. 2009, 157, 429-475. (3)

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Superfluid Helium with Nanofilament Formation. Low Temp. Phys. 2009, 35, 209-213. (4)

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Formation by Gold Nano-Fragment Coalescence on Quantized Vortices in He II. EPL 2010, 90, 34002-p1-34002-p5. (5)

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Properties of Metallic Nanowires Obtained in Quantum Vortices of Superfluid Helium. Low Tepm. Phys. 2010, 36, 590-595. (6)

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Metallic Nanowires and Nanoclusters Formed in Superfluid Helium. JETP 2011, 112, 1061– 1070. (8)

Donnelly R.J. Quantized Vortices in Helium II; Cambridge University Press:

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(18) Yang G.W. Laser Ablation in Liquids: Applications in The Synthesis of Nanocrystals. Prog. Mater Sci. 2007, 52, 648-698. (19) Allum D.R.; McClintock P.V.E.; Phillips A. The Breakdown of Superfluidity in Liquid 4

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Figure 1. (a) Brief scheme of the experiment. (b) To the determination of temperature accompanied a coagulation of metals inside liquid helium. The curve corresponds to Planck formula for the emission of a black-body with T = 3900 K, that close to the melting point of tungsten. The normalized transmittances of interference filters centered at 0.40, 0.45, and 0.65 µm are also given. 82x133mm (300 x 300 DPI)



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Figure 2. The pulses of visible emission accompanying coagulation of tungsten, molybdenum and platinum in superfluid helium (T = 1.2 K, P = 0.8 mbar). In inset, the front parts of the pulses are shown in more detail (the voltage on the PMT cathode was switched on with a delay of 280 ns). 82x57mm (300 x 300 DPI)


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Figure 3. Kinetics of visible thermal emission initiated by Platinum embedding into He I and He II at different pressures (and temperatures) (1 680 mbar (3.80 K), 2 345 mbar (3.25 K), 3 65 mbar (2.30 K), and 4 2 mbar (1.35 K) – the last in He II). 82x82mm (300 x 300 DPI)



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Figure 4. The calculated by the formula (1) temporal dependences of temperature developed in the course of coagulation in He II (T = 1.2 K, P = 0.8 mbar) of (a) tungsten, (b) molybdenum and (c) – platinum. The noise is grown at large times because the emission intensity drops down with time. 82x173mm (300 x 300 DPI)


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Figure 5. The calculated by the formula (1) temporal dependence of temperature developed in the course of tungsten coagulation in normal helium (T = 4.2 K, P = 1 bar). 82x57mm (300 x 300 DPI)



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Figure 6. Temporal dependences of the temperature developed during tungsten coagulation in superfluid (T = 1.2 K, P = 0.8 mbar) (a) and normal (T = 4.2, P = 1000 mbar) (b) helium and their interpretation according to the model proposed. Different colors in Fig.6a correspond to different pairs of filters (blue curve - 400 and 650 nm, red curve - 450 and 650 nm). As it is seen, two different pairs of optical filters display close behavior confirming Planck character of the spectra. (a) Stage I – hot stage of spherical clusters growth, stage II – stage of nanowire growth; (b) Stage I – hot stage of spherical clusters growth, stage II – stage of clusters gluing together, stage III – stage of clusters sticking together in a clods. 165x79mm (300 x 300 DPI)


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TOC Graphic 254x254mm (100 x 100 DPI)


Coagulation of Metals in Superfluid and Normal Liquid Helium

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