^{1}, Muhammet Mammetkuliyev

^{1}and Jussi Eloranta

^{1,a)}

### Abstract

Laser ablation of copper and silver targets immersed in bulk normal and superfluid 4He was studied through time-resolved shadowgraph photography. In normal fluid, only a sub-millimeter cavitation bubble is created and immediate formation of metal clusters is observed within a few hundred microseconds. The metal clusters remain spatially tightly focused up to 15 ms, and it is proposed that this observation may find applications in particle image velocimetry. In superfluid helium, the cavitation bubble formation process is distinctly different from the normal fluid. Due to the high thermal conductivity and an apparent lag in the breakdown of superfluidity, about 20% of the laser pulse energy was transferred directly into the liquid and a large gas bubble, up to several millimeters depending on laser pulse energy, is created. The internal temperature of the gas bubble is estimated to exceed 9 K and the following bubble cool down period therefore includes two separate phase transitions: gas–normal liquid and normal liquid–superfluid. The last stage of the cool down process was assigned to the superfluid lambda transition where a sudden formation of large metal clusters is observed. This is attributed to high vorticity created in the volume where the gas bubble previously resided. As shown by theoretical bosonic density functional theory calculations, quantized vortices can trap atoms and dimers efficiently, exhibiting static binding energies up to 22 K. This, combined with hydrodynamic Bernoulli attraction, yields total binding energies as high as 35 K. For larger clusters, the static binding energy increases as a function of the volume occupied in the liquid to minimize the surface tension energy. For heliophobic species an energy barrier develops as a function of the cluster size, whereas heliophilics show barrierless entry into vortices. The present theoretical and experimental observations are used to rationalize the previously reported metal nanowire assembly in both superfluid bulk liquid helium and helium droplets, both of which share the common element of a rapid passage through the lambda point. The origin of vorticity is tentatively assigned to the Zurek-Kibble mechanism. Implications of the large gas bubble formation by laser ablation to previous experiments aimed at implanting atomic and dimeric species in bulk superfluid helium are also discussed, and it is proposed that the developed visualization method should be used as a diagnostic tool in such experiments to avoid measurements in dense gaseous environments.

Financial support from the National Science Foundation grant CHE-0949057 and the Interdisciplinary Research Institute for the Sciences (IRIS) is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENTAL

III. THEORETICAL MODEL

IV. RESULTS

V. DISCUSSION

### Key Topics

- Liquid helium
- 91.0
- Superfluids
- 71.0
- Rotating flows
- 66.0
- Laser ablation
- 53.0
- Liquid metals
- 40.0

##### B01D5/00

## Figures

Schematic overview of the experimental setup.

Schematic overview of the experimental setup.

Time-resolved shadowgraph images of laser ablation of Cu target in (a) normal liquid helium (2.3 K) and (b) superfluid helium (1.6 K). Laser pulse energy was 5 mJ/pulse. The metal cluster populations are highlighted by red circles. The times at which the snapshots were taken are indicated in each frame. The ablation target is located on the right and shown in black.

Time-resolved shadowgraph images of laser ablation of Cu target in (a) normal liquid helium (2.3 K) and (b) superfluid helium (1.6 K). Laser pulse energy was 5 mJ/pulse. The metal cluster populations are highlighted by red circles. The times at which the snapshots were taken are indicated in each frame. The ablation target is located on the right and shown in black.

Time-resolved shadowgraph images of laser ablation of sterling silver surface in superfluid helium at 1.7 K. The stack of ablation targets is on the left and appears in black. The target in the middle of the stack is ablated with 1 mJ/pulse laser pulse energy.

Time-resolved shadowgraph images of laser ablation of sterling silver surface in superfluid helium at 1.7 K. The stack of ablation targets is on the left and appears in black. The target in the middle of the stack is ablated with 1 mJ/pulse laser pulse energy.

Static binding energies of selected impurities to a ground state vortex line. R represents the impurity-vortex core distance and E the total energy of the system.

Static binding energies of selected impurities to a ground state vortex line. R represents the impurity-vortex core distance and E the total energy of the system.

Static binding energies of large heliophobic impurities to a ground state vortex line. R represents the impurity-vortex core distance and E the total energy of the system. The R s values correspond to the exponentially repulsive potential shifts as specified in Eq. (2) with the corresponding approximate barycenter radii given in parentheses.

Static binding energies of large heliophobic impurities to a ground state vortex line. R represents the impurity-vortex core distance and E the total energy of the system. The R s values correspond to the exponentially repulsive potential shifts as specified in Eq. (2) with the corresponding approximate barycenter radii given in parentheses.

Liquid density contours from DFT calculations for two Ag atoms trapped at the center of a vortex line. The coordinate for Ag-Ag recombination is indicated along the vortex line core. The minimum energy is reached when Ag resides at the center of the vortex line. The relevant length scales are indicated through the vortex core and the impurity bubble diameters. The contour value was set just above the bulk liquid density at 0 K (0.021836 Å−3 32 ) to highlight the vortex line and Ag solvation shell structures.

Liquid density contours from DFT calculations for two Ag atoms trapped at the center of a vortex line. The coordinate for Ag-Ag recombination is indicated along the vortex line core. The minimum energy is reached when Ag resides at the center of the vortex line. The relevant length scales are indicated through the vortex core and the impurity bubble diameters. The contour value was set just above the bulk liquid density at 0 K (0.021836 Å−3 32 ) to highlight the vortex line and Ag solvation shell structures.

Plot of the calculated static impurity-vortex line binding energies (E Im-Vortex) as a function of the impurity solvation cavity barycenter radius (R). The open circles represent the DFT calculation results and the continuous red line corresponds to Eq. (4) with R′ = 1.35 Å. R s values represent the radial shifts in the purely exponential potential (see Eq. (2) ), which were used to approximate the behavior of larger metal clusters.

Plot of the calculated static impurity-vortex line binding energies (E Im-Vortex) as a function of the impurity solvation cavity barycenter radius (R). The open circles represent the DFT calculation results and the continuous red line corresponds to Eq. (4) with R′ = 1.35 Å. R s values represent the radial shifts in the purely exponential potential (see Eq. (2) ), which were used to approximate the behavior of larger metal clusters.

Plot of the calculated static impurity-vortex line repulsive barrier heights (E r ) as a function of the impurity solvation cavity barycenter radius (R). The open circles represent the results from the DFT calculations and the continuous red line corresponds to a least squares fit of Eq. (5) to the DFT data. R s denotes the radial shift in the purely exponential potential (see Eq. (2) ), which was used to mimic the behavior of large heliophobic clusters.

Plot of the calculated static impurity-vortex line repulsive barrier heights (E r ) as a function of the impurity solvation cavity barycenter radius (R). The open circles represent the results from the DFT calculations and the continuous red line corresponds to a least squares fit of Eq. (5) to the DFT data. R s denotes the radial shift in the purely exponential potential (see Eq. (2) ), which was used to mimic the behavior of large heliophobic clusters.

## Tables

Overview of the pair potentials applied in the DFT calculations where L indicates linear geometry, T the perpendicular approach, and S spherically averaged potential (i.e., (L + 2T)/3). R m denotes the potential minimum, E m the potential energy at the minimum, A 0, …,A 5 are potential parameters given in atomic units (a.u.) according to Eq. (2) with R s = 0, and R V gives the minimum distance where the parametrization is still valid.

Overview of the pair potentials applied in the DFT calculations where L indicates linear geometry, T the perpendicular approach, and S spherically averaged potential (i.e., (L + 2T)/3). R m denotes the potential minimum, E m the potential energy at the minimum, A 0, …,A 5 are potential parameters given in atomic units (a.u.) according to Eq. (2) with R s = 0, and R V gives the minimum distance where the parametrization is still valid.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content