4He Interface Research Articles

Bound state of a 3He atom at the interface of crystal and superfluid 4He

The bound state of a 3He atom at the interface between coexisting crystalline and superfluid phases of 4He is studied theoretically by means of first principle Quantum Monte Carlo simulations. We consider both the case of a solid/superfluid 4He interface, as well as that of a few solid layers of 4He forming on an attractive substrate. It is observed that the 3He bound state is sharply localized in a well-defined, quasi-2D layer of 4He in the region intermediate between the solid and the liquid. The layer in which the 3He atom resides displays an intriguing interplay of atomic localization and quantum-mechanical exchanges; is not necessarily the first “non-solid” layer, as suggested in previous studies, and it is affected by the attractive strength of the substrate.

Resonant surface scattering and dislocation flutter explain Kapitza resistance at a solid/solid 4He interface

In this report we investigate the Kapitza resistance RK at an interface between a classical solid and a 4He quantum crystal, as a function of temperature. We provide a premise for RK based on a combination of two separate mechanisms which occur simultaneously. Owing to the fact that the phonon wavelengths in solid 4He and in the superfluid are of the same order of magnitude, we infer that one mechanism is due to resonant scattering of phonons by nanoscale surface roughness as predicted by Adamenko and Fuks1 for solid/superfluid interfaces. The other mechanism involves the interaction of thermal phonons with mobile vibrating dislocations within solid 4He. The present analysis demonstrates the plausibility of these two mechanisms in solving the long outstanding problem of the Kapitza resistance anomaly of solid 4He in contact with copper for temperatures ranging from 0.4 to 2 K.

Asymmetry in melting and growth relaxation of 4He crystals in superfluid after manipulation by acoustic radiation pressure

The relaxation dynamics of the crystal–superfluid interface of 4He after deformation induced by acoustic radiation pressure was investigated for various crystal orientations. The melting relaxation after growth was approximately 10 times slower than the growth relaxation after melting for vicinal surfaces and facets, while both relaxation times were consistent with each other for rough surfaces. The asymmetry in the time constant between the melting and growth of vicinal surfaces and facets can be qualitatively explained as the effect of superflow induced by local rapid interface motion, such as a quick rounding of facet edges of the 4He crystal. Rough surfaces move more isotropically and no significant local rapid interface motion is induced; therefore, their relaxation is likely to be symmetric with a minimal effect of superflow. While the growth relaxation was simply back to the initial shape in a single stage, the melting relaxation was much more complex with multiple stages and the exhibition of various anomalous shapes depending on temperature. Anomalous shapes such as needle-like shapes during melting have a larger curvature and higher energy and thus should have disappeared more quickly than the growth shape with a smaller curvature, but they were considerably stable and disappeared slowly. This counter-intuitive asymmetry suggests the significant role of superflow in the relaxation process.

Fluctuating Surfaces of Growing 4He Crystals in Aerogel

Crystal-superfluid interface of 4He in aerogel was shown to advance smoothly in a high temperature creep growth region above 0.6 K. In this report, we focused on the shape of the growing interface in the region and attempted to analyze the roughness of interfaces. The growth of rough interfaces is very common in nature and is known to often follow a scaling law; roughness usually increases with time and saturates in the later stage. We measured the roughness w(t) defined as the standard deviation of the interface height as a function of time t. It was found that w(t) in 98 % porosity aerogel initially increased with t and decreased after a particular time in the later stage. The abrupt reduction of roughness in the end of crystallization is unusual if it is intrinsic in the crystallization in aerogel.

Renormalization-group calculation of the superfluid/normal-fluid interface of liquid4He in gravity nearTλ

The superfluid/normal-fluid interface of liquid 4He is investigated in gravity on earth where a small heat current Q flows vertically upward or downward. We present a local space- and time-dependent renormalization-group (RG) calculation based on model F which describes the dynamic critical effects for temperatures T near the superfluid transition T_lambda. The model-F equations are rewritten in a dimensionless renormalized form and solved numerically as partial differential equations. Perturbative corrections are included for the spatially inhomogeneous system within a self-consistent one-loop approximation. The RG flow parameter is determined locally as a function of space and time by a constraint equation which is solved by a Newton iteration. As a result we obtain the temperature profile of the interface. Furthermore we calculate the average order parameter <psi>, the correlation length xi, the specific heat C_Q and the thermal resistivity rho_T where we observe a rounding of the critical singularity by the gravity and the heat current. We compare the thermal resistivity with an experiment and find good qualitative agreement. Moreover we discuss our previous approach for larger heat currents and the self-organized critical state and show that our theory agrees with recent experiments in this latter regime.

Instability of a Crystal 4He Facet in the Field of Gravity

We analyze here the analog of the Rayleigh instability in the field of gravity for the superfluid–crystal 4He interface provided that the heavier 4He crystal phase occupies the space over the lighter superfluid phase. We find that the conditions and onset of the gravitational instability are different in kind above and below the roughening transition temperature when the crystal 4He surface is in the rough or in the smooth faceted state, respectively. In the rough state of the surface the gravitational instability is fully analogous to the classical case of the fluid–fluid interface. In contrast, in the case of the crystal faceted surface the onset of the gravitational instability is associated with surmounting some potential barrier. The potential barrier results from nonzero magnitude of the facet step energy. The size and the tilting angle of the crystal facet are also important parameters for developing the instability. The initial stage of the instability can be described as a generation of crystallization waves at the superfluid–crystal interface. In particular, we discuss the experiments (Demaria et al. in J. Low Temp. Phys. 89:385, 1992; Tsymbalenko in Fiz. Nizk. Temp. 21:162, 1995; Tsymbalenko in Low Temp. Phys. 21:120, 1995) which may concern the gravitational instability of the superfluid-crystal 4He interface.

Hydrodynamic Instability During Non-uniform Growth of a Helium Crystal

The Rayleigh-Taylor instability (Taylor in Proc. R. Soc. Lond. Ser. A 201:192, 1950) is an instability of the interface which can be realized when the lighter fluid is propelling the heavier one. We analyze an analog of the hydrodynamic Rayleigh-Taylor instability for the superfluid-solid 4He interface under non-uniform growth rate of the solid phase. The development of the interface instability starts with an accelerated interface growth rate and provided that the magnitude of interface acceleration exceeds some critical value independent of the surface stiffness. The plane and spherical shapes of the liquid-solid interface are considered. For the Richtmyer-Meshkov (Meshkov in Izv. Akad. Nauk SSSR 5:151, 1969) limiting case of an impulsively accelerated interface, the onset of instability does not depend on the sign of the interface acceleration. The investigation of the surface instability can explain the features observed in the experiment (Chavanne et al. in Phys. Rev. Lett. 86:5506–5509, 2001) where the crystal 4He nucleation is triggered by focusing an ultrasonic wave of the large amplitude. The onset and development of the instability are expected at the surface of helium crystals in the course of their abnormal fast growth under large magnitudes of overpressures (Tsymbalenko in J. Low Temp. Phys. 138:795, 2005).

Rayleigh-Taylor instability of crystallization waves at the superfluid-solidH4einterface

At the superfluid-solid 4He interface there exist crystallization waves having much in common with gravitational-capillary waves at the interface between two normal fluids. The Rayleigh-Taylor instability is an instability of the interface which can be realized when the lighter fluid is propelling the heavier one. We investigate here the analogs of the Rayleigh-Taylor instability for the superfluid-solid 4He interface. In the case of a uniformly accelerated interface the instability occurs only for a growing solid phase when the magnitude of the acceleration exceeds some critical value independent of the surface stiffness. For the Richtmyer-Meshkov limiting case of an impulsively accelerated interface, the onset of instability does not depend on the sign of the interface acceleration. In both cases the effect of crystallization wave damping is the reduction in the perturbation growth rate of the Taylor unstable interface.

Stacking Fault Energy in 4He Crystals

Recently observed non-classical rotational inertial (NCRI) in solid 4He is most probably related to defects which appear during the sample preparation. We have measured the energy of the stacking fault (SF) in an hcp 4He crystal at 0.2 K. The SF creates a groove with a dihedral angle of 155±5° on the crystal surface in a quasi-equilibrium with the liquid. The obtained value for the SF energy is (0.07±0.02) mJ/m2, which is ∼0.4 of the surface tension of the liquid–solid interface of 4He. Our findings suggest that the phenomenon of burst-like creation of new atomic layers might be accompanied by the creation of SFs.

Faraday instability of crystallization waves in 4He

Periodic modulation of the gravity acceleration makes a flat surface of a fluid unstable and standing waves are parametrically excited on the surface. This phenomenon is called Faraday instability. Since a crystal-superfluid interface of 4He at low temperatures is very mobile and behaves like a fluid surface, Saarloos and Weeks predicted that Faraday instability of the crystallization waves exists in 4He and that the threshold excitation for the instability depends on the crystal growth coefficient. We successfully observed the Faraday instability of the crystal-liquid interface at 160 mK. Faraday waves were parametrically generated at one half of the driving frequency 90 Hz. Amplitude of the Faraday wave becomes smaller at higher temperature due to decrease of the crystal growth coefficient and disappears above 200 mK.

Instability of the Solid-Liquid Interface of 4He during a Large Transformation

We report an instability of 4He crystal surface during a large modification of its shape observed by schlieren photography. 4He crystal was nucleated on an ultrasound transducer which was placed in the upper part of the sample cell facing the bottom. The crystal was grown on the transducer and the lowest part of it eventually touched the bottom of the cell. Almost immediately, the crystal started to change shape very quickly to adjust itself to the new boundary condition. During this large deformation, the hexagonal shape of the crystal surrounded by facets became unstable and the surface became corrugated. The corrugation pattern during the deformation was observed by a high-speed camera. The results were compared with Kelvin-Helmholtz type instability which Uwaha and Nozieres predicted.

Quantum Fingering of the Inverted Liquid-Crystal 4He Interface in the Field of Gravity

The simplest example of fingering occurs when a heavier liquid occupies the half-space above a lighter one. The fingers of the heavier liquid driven by gravity grow down, displacing the lighter liquid upward. The fingering of the superfluid phase into the 4He crystal facet below its roughening transition temperature can provide us an example of macroscopic quantum nucleation phenomena. Due to cusp-like singularity in the surface tension as a function of the facet orientation the crystal facet has a relative stability and its fingering is accompanied by overcoming some critical nucleation barrier. The barrier height is proportional to the square of the facet step energy and depends on a ratio of the facet size to the capillary length. At sufficiently low temperatures the thermal activation mechanism for the interface fingering is replaced with the quantum one associated with the penetration through the nucleation barrier.

Superfluid-Normal Interface of 4He Near a Wall

We observed a profile of nonequilibrium superfluid-normal (SN) interface of 4He near a vertical wall. A glass, brass or copper wall was used. The SN interface was produced by cooling liquid 4He in a bath from the bottom, where liquid 4He was pumped through a flow impedance in order to cool down the liquid. Superfluid (Normal fluid) occupied the lower (upper) part of the bath. The SN interface was visualized by three methods: simple visualization, shadowgraphy and schlieren method. The interface touched a vertical glass wall at almost 90°. A large hollow was observed near a brass wall which had intermediate thermal conductivity. Downward flow was observed on a copper wall due to the very good thermal conductivity of the wall. Various types of interface profile were observed depending on the thermal conductivity of the wall used.

New Measurements of Wetting by Helium Mixtures

We have measured the contact angle of the 3He–4He interface on a sapphire window in the temperature range from 50 to 845 mK. Contrary to what had been found by Ueno et al. in two successive experiments, we have found complete wetting by the 4He-rich phase. Our new results have two consequences: first, we suspect that there were some artefacts in the experiments by Ueno et al. Secondly, we now believe that the critical Casimir forces are dominated by the van der Waals force in this experimental situation.

Nucleation of 4He Crystal at Melting Pressure by Acoustic Waves

When an acoustic wave pulse of several msec was applied to superfluid 4He at melting pressure, 4He crystal was nucleated on the transducer and rapidly disappeared after the pulse. We measured thresholds of the acoustic wave power which induced a nucleation in the temperature range between 0.09 K and 1 K. The treshold of the nucleation exhibited no temperature dependence below 0.3 K. The nucleation was not induced above 0.6 K even if the injected acoustic pulse was strong. 0.6 K is close to the inversion temperature at which the direction of the force by acoustic wave was inverted on the solid-liquid interface of 4He [Phys. Rev. Lett. 90, 075301 (2003)]. Our observation indicates that the effect of acoustic radiation pressure contributes to the heterogeneous nucleation by acoustic waves.

Optical Imaging of Helium Interfaces

This review describes the development work done in the Low Temperature Laboratory (LTL) at the Helsinki University of Technology which has yielded high-resolution interferometric measurements on various helium interfaces at ultra low temperatures. The optical project was started in the end of 1980s and the free surface of superfluid 3He was seen for the first time ever in 1991. Additionally to the liquid/vapor interface of 3He, also the liquid/solid interface of both 4He and 3He has been the object of investigations. In the course of these studies several important experimental results have been obtained like the discoveries of a new surface state and two new growth mechanisms with 4He crystals, or the observation of a multitude of different facets on 3He crystals. The most significant findings from all these measurements are presented together with the corresponding background information and the details of the experimental setup. At the end of the review we also indicate the plans for new measurements with a faster CCD camera we hope to realize in the near future.

Anisotropy effect on the flow-induced instability of the solid-superfluid interface

At the solid-superfluid interface of 4 He a Kelvin–Helmholtz type instability is expected to occur with a tangential flow. Nonlinear effect in the instability is studied with a perturbation expansion. For an isotropic interface the amplitude of the destabilized crystallization wave grows without limit, which suggests a chaotic motion. With a strong crystal anisotropy and for the surface orientation of minimum stiffness, the amplitude has a stable fixed point and a corrugated interface may be stabilized. Increasing further the anisotropy changes the type of the bifurcation from subcritical to supercritical.

Interferometric studies of interfaces at milliKelvin temperatures

A brief review of our recent work on interfaces in quantum systems at millikelvin temperatures is presented. In this paper, we concentrate on high-resolution interferometry on superfluid/solid interface in4He. Our results show a novel surface transition at small inclination angles off the c-axis, slow facet growth which cannot be assigned to the regular screw-dislocation-mediated mechanism, and fast spiral growth moderated by step localization.

Quantum theory of solid-liquid coexistence and interface in4He

We present new results of a Monte Carlo simulation of the solid-liquid coexistence and interface in4He atT=0. Calculations are based on a Local Density Shadow wave function, which provides an equation of state and a density range of coexistence in good agreement with the experimental data. Results concerning the {111} interface will be shown. They include accurate estimates of the interfacial energy and width, the mobility of the particles and the amount of change in the ordering of the particles through the interface. Direct analyses of the configurations will also be given.

Dimples due to dislocations at the superfluid/solid interface of4He

On vicinal planes the surface stiffness is quite anisotropic and a crystal defect, terminating at the interface, is predicted to produce a 10...50 nm deep dimple with macroscopic lateral extent (up to a few mm). We have searched for such depressions using high resolution interferometry. Sometimes our measured interferograms of the super fluid/solid interface display unexpectedly large dimples. The volume and shape of the observed objects suggest that these dimples are caused by bundles of about 10 dislocations.