The Phase of Submonolayer 4He Films Near Monolayer Completion

We study the state of ⁴He films physisorbed to general Lennard–Jones type substrates at coverages near monolayer completion as a function of the range C₃ and well-depth D of the substrate-helium potential. By examining the liquid-state energetics as well as the coverage dependence of the third sound speed and roton energies in the two-parameter space (C₃,D), we can estimate the position of the boundary between those strongly interacting substrates wherein the ⁴He film essentially forms a quasi two-dimensional solid prior to second layer formation and weaker interacting substrates for which the ⁴He film remains mobile and superfluid. Our approach utilizes a combination of information from both variational calculations and also correlated basis function theory to examine in detail the excitation structure in the monolayer liquid as a function of film coverage and substrate potential.      

4He on weakly attractive substrates: Structure,stability, and wetting behavior

Using a microscopic variational approach we examine the structure and the excitation spectrum of layered⁴He liquids absorbed to alkali metal and graphite substrates. We find that the alkali metal substrates produce a less pronounced layering structure than the shorter-range graphite/solid helium potential. For the excitations, three features are in common to the substrates: First, for coverages of a monolayer or more, a surface mode is present. Second, a bulk mode which gains strength as the coverage is increased, is identifiable for films with sufficiently high coverage. Finally, a two-dimensional mode that propagates within the first layer is observed for the more attractive substrates. We also present results that we obtain by using the nonlocal density functional theory. We document the reliability and shortcomings of this approach by making a detailed comparison of experimental, Monte Carlo, and variational theory results for the structure, energetics, and excitations. We also give a brief discussion on the wetting properties of helium on alkali metal and graphite/solid helium substrates.     

He4 on copper: Some effects of preadsorbed noble-gas layers

We have made adsorption measurements of He⁴ on a copper sponge preplated with a series of noble-gas layers. The behavior of the isosteric heat of adsorption and the partial molar entropy of submonolayer He⁴ on these substrates is presented and discussed. The general behavior is of a rapid decrease in the average entropy of the helium as helium coverage is increased, on all substrates. Changing the substrate seems only to change scaling factors in the behavior of the helium film.Work supported in part by a Frederick Gardner Cottrell Grant-In-Aid from the Research Corporation, New York.Alfred P. Sloan Research Fellow.     

Trapping of two-dimensional electrons in substrate potentials

We report preliminary measurements of high (ripplon-limited) electron mobility on helium films supported by a hydrogen-coated glass substrate. From the smooth dependence of the mobility as a function of helium film thickness we deduce that no polaron transition occurs on films thicker than 500 Å at T>1 K. On poorer quality substrates we observe a rapid drop in the mobility at a substrate-dependent critical film thickness. We interpret these drops as due to localization in variations in the substrate potential.     

Superconducting properties of ion beam modified YBCO microbridges

We prepared ion beam modified microbridges based on thin sputtered or laser ablated YBCO films on SrTiO₃ substrates. The microbridges with a width of 10 μm were irradiated through slits in a 700 nm thick double layer resist mask. In our experiments we used O⁺ ions with an ion energy of 30 keV or 100 keV varying the dose between 10¹³ ions·cm⁻² and 10¹⁴ ions·cm⁻². We investigated the influence of film thickness and slit width on the superconducting properties of these junctions. We show the temperature dependence of the junctions properties on microwave radiation or external magnetic fields.     

Structural Studies of Nanocrystalline Nitrogen–Helium Solids by Raman Spectroscopy

Structural and thermal properties of nanocrystalline nitrogen–helium solids are studied by Raman spectroscopy at temperature range 1.8–41 K. The N₂ vibrational line possesses spectral structure very similar to what is observed in bulk solid nitrogen, indicating ordered structure inside the nanocrystallites. The spectral observations show that the structure of the solid is dependent on the N₂ content in the gas mixture used for sample preparation. Evidence for disordered nitrogen on the surfaces and interfaces of nanocrystallites can be extracted from the Raman spectra of the most diluted samples. Removing superfluid helium from the sample and annealing at 21 K did not affect the structure of the solid, whereas higher annealing temperatures yielded strong increase of density as evidenced by the up to ∼10-fold increase of Raman signal. The α-solid—β -solid transition, evidenced by a ∼0.8 cm⁻¹ shift in the peak position, was seen in the collapsed nitrogen samples approximately at the same temperature as in a solid nitrogen film.     

Mathematical foundations of the immersed finite element method

In this paper, we propose an immersed solid system (ISS) method to efficiently treat the fluid–structure interaction (FSI) problems. Augmenting a fluid in the moving solid domain, we introduce a volumetric force to obtain the correct dynamics for both the fluid and the structure. We further define an Euler–Lagrange mapping to describe the motion of the immersed solid. A weak formulation (WF) is then constructed and shown to be equivalent to both the FSI and the ISS under certain regularity assumptions. The weak formulation (WF) may be computed numerically by an implicit algorithm with the finite element method, and the streamline upwind/Petrov–Galerkin method. Compared with the successful immersed boundary method (IBM) by Peskin and co-workers (J Comput Phys 160:705–719, 2000; Acta Numerica 11:479–517, 2002; SIAM J Sci Stat Comput 13(6):1361–1376, 1992) the ISS method applies to more general geometries with non-uniform grids and avoids the inaccuracy in approximating the Dirac delta function     

On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction

Partitioned Newton type solution strategies for the strongly coupled system of equations arising in the computational modelling of fluid–solid interaction require the evaluation of various coupling terms. An essential part of all ALE type solution strategies is the fluid mesh motion. In this paper, we investigate the effect of the terms which couple the fluid flow with the fluid mesh motion on the convergence behaviour of the overall solution procedure. We show that the computational efficiency of the simulation of many fluid–solid interaction processes, including fluid flow through flexible pipes, can be increased significantly if some of these coupling terms are calculated exactly.     

Transmission of Phonons with Anomalous Dispersion through the Interface of Two Continuous Media

We solve the problem of phonon transmission through the interface between a quantum fluid with anomalous dispersion and a solid, for arbitrary angles of incidence. The Wiener–Hopf method is applied to solve the equations of the quantum fluid in the half-space, and in particular the solution is obtained for the dispersion relation of a Bose–Einstein condensate (BEC) and of superfluid helium at small wave vectors. It is shown that the solutions are running waves deformed near the border by specific surface standing waves. Boundary conditions are used to derive the transmission and reflection coefficients for the phonons, incident on either side of the interface, as a function of the incidence angles and the phonon frequencies. The deformation of wave packets passing through the interface is described both far from and near to the critical incidence angles.     

Measurements of Third Sound Attenuation at T=1.35 K

The results of measurements of ordinary third sound attenuation at T=1.35 K are reported. The attenuation is measured by using a continuous wave technique for frequencies up to 40 kHz. We find that for helium film thicknesses in the regime 5.09≤d≤9.90 layers the attenuation of third sound increases both with frequency and film thickness. We discuss our results in the context of previous work in this area.     

Interpolation functions in the immersed boundary and finite element methods

In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured at the fluid–solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence test is thoroughly conducted for the independent fluid and solid meshes in a fluid–structure interaction system. The required mesh size ratio between the fluid and solid domains is obtained.     

Characterization of spray deposited CoWO<Subscript>4</Subscript> thin films for photovoltaic electrochemical studies

Preparation of Cobalt tungstate (CoWO₄) thin film by spray pyrolysis with ammonical solution as a precursor is presented. The phase and surface morphology characterizations have been carried out by XRD and SEM analysis. The study of optical absorption spectrum in the wavelength range 350 – 850 nm shows direct as well as indirect optical transitions in the thin film material. The d. c. electrical conductivity measurements in the temperature range 310–500 K indicate semiconducting behavior of the thin film. The thin films deposited on fluorine doped tin oxide (FTO) coated conducting glass substrates were used as a photoanode in photovoltaic electrochemical (PVEC) cell with configuration: CoWO₄ | Ce⁴⁺, Ce³⁺ | Pt; 0.1 M in 0.1 N H₂SO₄. The PVEC characterization reveals the fill factor and power conversion efficiency to be 0.36 and 0.62%, respectively. The flat band potential is found to be −0.18 V (SCE).     

Experiments on the Self-Organized Critical State of 4He

When a heat flux Q is applied downward through a sample of ⁴He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity-induced gradient in T _λ . All the helium in the sample is then at the same reduced temperature and the helium is said to be in the Self-Organized Critical (SOC) state. We have made the first measurements of the ⁴He SOC state specific heat, C _{∇ T} (T(Q)). There is no measurable difference between C _{∇ T} and the static zero-gravity ⁴He specific heat for temperatures between 650 and 250 nK below T _λ . Closer to T _λ , the specific heat is depressed and reaches a maximum value at 50 nK below T _λ . This depression is similar to that predicted theoretically as reported by R. Haussmann (Phys. Rev. B 60, 12349, 1999). Contrary to the expectations of theory, however, we see another depression far below T _λ . In addition, over the heat flux range of 30 nW/cm² to 13 μW/cm², we have made improved measurements of the speed of a recently discovered propagating thermal mode, which travels only upstream against the nominal heat flux of the SOC state. We are able to accurately predict the speed of this wave by treating the helium of SOC state as a traditional fluid with a temperature dependent thermal conductivity.     

Ellipsometric Study of Superfluid Onset in Thin Liquid 4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed ⁴He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed ⁴He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a ⁴He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.     

Nonlinear Transport of Wigner Solid on Superfluid 3He–A

Electrons trapped on the surface of liquid helium form the Wigner solid accompanied with the periodic surface deformation (dimple lattice). Because of the soft surface, the Wigner solid shows unique nonlinear transport properties. Here we present the results of the nonlinear transport measurements of the Wigner solid on the superfluid ³He A phase at temperatures down to 200 μK in a magnetic field of 0.363 Tesla. The transition from linear to nonlinear behavior is observed as increasing the driving voltage. This behavior is very similar to those previously observed in the B phase and normal phase, and attributable to the deformation of the dimple shape caused by the strong damping of liquid ³He.     

Planar Hall effect of indium antimonide thin film on silicon and nickel–zinc ferrite substrates

We have investigated Hall and planar Hall (PH) effect of indium antimonide (InSb) films thermally evaporated on two different substrates including Si and soft magnetic Ni–Zn ferrite. Polycrystalline InSb film with an average grain size of 1.2 μm shows substantial electron mobility of 6,700 cm²/Vs for Si and 5,680 cm²/Vs for Ni–Zn ferrite substrates respectively. Four-point bridge type Hall bar of InSb was fabricated using photolithography followed by chemical wet etch. An abrupt change in PH deviated from a normal PH curve was found on a ferrite substrate within a low field range of −50 to 50 Oe while no change happens on the Si substrate. Sharp PH curve immediately returns to the ordinary PH curve when applied field goes over −50 to 50 Oe without leaving any hysteresis of resistance. This is mainly attributed to the presence of the Bloch wall of Ni–Zn ferrite underneath InSb Hall bar. Intragranular domain wall movement is believed to be a prime source of the anomalous PH behavior in the low field range. The linear field dependence of PH in a resolution of 10 mΩ/Oe is sensitive high enough to be used as low-field magnetic sensors.     

Three-dimensional Schwoebel–Ehrlich barrier

It is well known that the Schwoebel–Ehrlich barrier affects, and even dictates, surface microstructure evolution – such as the transition of growth modes from layer-by-layer to island growth. The conventional Schwoebel–Ehrlich barrier refers to the case when an adatom diffuses down an island of one monolayer. During thin film deposition, an adatom often needs to diffuse down an island of multiple layers. For the latter, we demonstrate and calculate the corresponding Schwoebel–Ehrlich barrier – which we call three-dimensional Schwoebel–Ehrlich barrier. Our calculations show that the three-dimensional Schwoebel–Ehrlich barrier can be large even if its conventional counterpart is small – as in aluminum. We further propose and demonstrate a possible process of engineering surface faceting and film texture, by modifying the three-dimensional Schwoebel–Ehrlich barrier. This revised version was published online in June 2006 with corrections to the Cover Date.     

Three-dimensional modal analysis of an idealized human head including fluid–structure interaction effects

A three-dimensional analytical and numerical method is presented in this article for the analysis of the acoustic fluid–structure interaction systems including, but not limited to, the brain, cerebro-spinal fluid (CSF), and skull. The model considers a three-dimensional acoustic fluid medium interacting with two solid domains. This article deals with the analytical and numerical computation of eigenproperties for an idealized human head model including fluid–structure interaction phenomena. We determine in the present work the natural frequencies and the modes shapes of the system of the brain, cerebro-spinal fluid (CSF), and skull. Two models are presented in this study: an elastic skull model and a rigid model. In the analysis, a potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a solid problem. A finite element method analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effects of the fluid thickness and compressibility on the natural frequencies are also investigated.