Showing papers on "Mean free path published in 1987"

A simple formula for diffusion calculations involving wall reflection and low density

Abstract: Diffusion theory is often employed to calculate the effects of wall destruction on the local concentration of an active species immersed in a scattering gas. In many situations the spatial dependence of the concentration is given to a good approximation by the fundamental diffusion mode, and the local loss frequency can be calculated using the container’s fundamental mode diffusion length Λ. The additional assumption that the density of the active species may be taken to be zero at the container boundaries gives a value of Λ=Λ0 which depends only on the container dimensions, but use of Λ0 can be seriously in error if the diffusion mean free path λm is comparable to the dimensions, or if the particle reflection coefficient R becomes of significance. An improved boundary condition may be written simply in terms of the linear extrapolation length λ, whose inverse is the logarithmic gradient of the particle density at the boundary. The equation λ=2(1+R)λm/3(1−R) allows the representation of the full range of ...

Cosmic-ray propagation in the Galaxy and in the heliosphere - the path-length distribution at low energy

Abstract: The energy dependence of the path-length distribution of cosmic rays at low energies, below relativistic velocities, is studied, and its implications for models of cosmic-ray confinement and propagation in the Galaxy and Galactic halo, including the effects of a possible Galactic wind, are studied. It is found that the mean free path in Galactic propagation must be fully energy-dependent, with the mean of an exponential path-length distribution increasing with increasing energy below 1 GeV per nucleon and decreasing with increasing energy above 1 GeV per nucleon. This indicates that, at low energies, diffusion is not the controlling process. The path-length distribution is not purely exponential but is depleted in short path lengths at low energies. This depletion is energy-dependent, being largest at low energies and decreasing with increasing energy.

Observation of weak localization of light in a finite slab: Anisotropy effects and light path classification.

Abstract: We report on the dependence of enhanced backscattering of light in a random medium on sample thickness, mean free path, and size of scattering centers. Introduction of a new difference technique allows for independent observation of contributions from long and short light paths in a suspension of polystyrene spheres. A new anisotropy effect, which has been found to be most prominent for the smallest particles studied, could be classified as a lower-order multiple-scattering phenomenon.

Ballistic electron transport in thin silicon dioxide films.

Abstract: Electron transport in thin (3.8--5.8-nm) silicon dioxide films has been investigated with use of the carrier-separation and vacuum-emission techniques. For the thinner films and smaller voltages, ballistic transport is inferred not only indirectly from the oscillations of the current-voltage characteristics (as originally reported by Lewicki and Maserjian) but also directly from the average energy measured via the carrier-separation technique and from the observation of the ballistic peak (about 0.15 eV wide) in the vacuum-emission experiments. In thicker films and/or at higher bias voltages, the transition from the ballistic to the steady-state regime is observed. Phonon replicas for the 0.153- and 0.063-eV longitudinal optical phonons have been observed in this transient situation. The experimental results have been compared to Monte Carlo simulations. Best agreement has been obtained by using a value of 0.7${m}_{0}$ for the polaron mass. The average mean free path of about 1 nm resulting from the simulation is in good agreement with Lewicki and Maserjian's experimental data.

New method to study the proximity effect at the normal-metal-superconductor interface.

Abstract: The excess current of a point contact on a Ag-Pb bilayer has been measured for several thicknesses of the Ag film. The excess current is due to Andreev reflection and contains information about the position dependence of the superconducting order parameter near the interface. If the Ag film is very thin, the excess current is that of a normal-metal--superconductor point contact, though slightly changed because of the depression of the order parameter at the surface of the bilayer. For larger thicknesses, the combination of the proximity effect and the limited mean free path of the electrons yields very different current-voltage characteristics.

Surface impact ionization in silicon devices

Abstract: In the past, carrier ionization rates in the silicon bulk have been measured and reported extensively. We present experiments and accurate electric field calculations for deriving the surface impact ionization rate of electrons. It is given by \alpha_{n}(surface) = 2.45 \cdot 10^{6} \cdot \exp(-1.92.10^{6}/E) [cm-1] Due to the lower mean free path at the surface, this ionization rate is much smaller then the well known bulk values and falls-off more steeply for low electric fields. The consequences for the simulation of MOS substrate currents will be shown.

Size and temperature effects on the Seebeck coefficient of thin bismuth films

Abstract: The electrical resistivity and the Seebeck coefficient of thermally evaporated thin bismuth films of thicknesses from 300 to 1900 A\r{} have been measured in the temperature range 300--470 K. The latter is negative and its magnitude is found to increase initially with increasing temperature, reach a maximum, and then decrease with a further rise in temperature. The temperature at which the Seebeck coefficient is maximum is found to be thickness dependent, decreasing with increasing thickness. The observed dependence is explained by considering that the Fermi energy is temperature dependent. Bismuth films show a negative temperature coefficient of resistivity. The thickness dependence of the electrical resistivity and the Seebeck coefficient of simultaneously prepared films are analyzed using the newer effective mean-free-path model. From the analysis, important material constants like the mean free path, the electron concentration, and the effective mass of electrons have been evaluated.

Direct simulation of high-vorticity gas flows

Abstract: The computational limitations associated with the molecular dynamics (MD) method and the direct simulation Monte Carlo (DSMC) method are reviewed in the context of the computation of dilute gas flows with high vorticity. It is concluded that the MD method is generally limited to the dense gas case in which the molecular diameter is one‐tenth or more of the mean free path. It is shown that the cell size in DSMC calculations should be small in comparison with the mean free path, and that this may be facilitated by a new subcell procedure for the selection of collision partners.

Breakdown of the Debye theory of bulk ion recombination

Abstract: We have investigated how the rate of diffusion‐controlled bulk recombination between electrons and positive ions is influenced by the mean free path of electrons. By use of the Monte Carlo method previously developed we have calculated the rate constant as a function of the mean free path. For mean free paths negligibly short compared with the Onsager length, the rate constant increases linearly with increasing mean free path, in agreement with the Debye theory of bulk ion recombination. However, as the mean free path further increases, the rate constant goes through a maximum and then decreases. The present result quantitatively explains recent experimental data on electron–ion recombination rate constants in liquid methane in which the mean free path of electrons is comparable with the Onsager length.

Mean-free-path concept in polycrystalline metals.

Abstract: A crude analysis of the observed thickness dependence of the conductivity in fine-grained metals shows a very weak connection with the resistivity caused by grain-boundary scattering. An ``effective intrinsic mean free path'' for the whole polycrystal, as introduced in the well-known theory of Mayadas and Shatzkes, cannot explain the observed size effect. It is impossible to define a mean free path for the whole polycrystal, especially if the resistivity is governed by grain-boundary scattering.

Long Mean Free Path Coherent Transport in Doped Polyacetylene

Abstract: A modified technique has been used to synthesize stretch oriented polyacetylene with fewer sp3 defects than in material prepared by other methods. The higher quality material exhibits substantially higher electrical conductivity. The data indicate a long electronic mean free path consistent with coherent metallic transport.

Energy transport and evaporation of weakly interacting particles in the Sun

Abstract: The transport of energy and the evaporation rate of conjectured weakly interacting massive particles in the Sun are calculated by simulating their Brownian motion in a model of the Sun. This is an efficient method for the numerical solution of the Boltzmann equation for these particles as a function of their mass and mean free path l. For values of l comparable to or larger than the radius of the Sun we discuss a new approach to the solution of this equation, while for small values of l we apply the Chapman-Enskog expansion to first order to obtain the luminosity function.

Electron transport studies of Ni33Zr67-based metallic glasses containing H, B, Al and Si

Abstract: The electrical resistivity has been measured on Ni33Zr67Hx (0

High Energy Electron Transport in Hydrocarbons

Abstract: High energy electrons play an important role in triggering the damage process in polymeric dielectrics, causing ageing or initiating avalanche breakdown In order to investigate the transport properties of these high energy electrons, first paraffin is used as the model material for polyethylene, and the interfacial photoemission technique, the method to inject electrons into it The results are compared with those measured using polyethylene sample The mean free path of the photoelectrons deduced from the energy distribution curves was found to be in the order necessary for electron multiplication, thus indicating the possibility of the occurrence of avalanche breakdown The possible energy loss process of the high energy electrons injected into hydrocarbons is also discussed

Resistivity and spontaneous anisotropy of resistivity in amorphous FexSi1-x films

Abstract: Amorphous FexSi1-x films have been obtained by triode sputtering. The samples are ferromagnetic, with T x (the crystallization temperature) and T c (the Curie temperature) both above 77 K within the composition range 0˙5 ≤ x ≤ 0˙77. The resistivity, ρ, and the spontaneous anisotropy of resistivity, (δρ/ρ) = (ρ|| - ρ|)/⊥, have been measured between 77 and 800 K (ρ|| and ρ⊥ are the resistivities with the saturation magnetization, Ms, parallel and perpendicular to the current direction, respectively). The behaviour of the resistivity shows strong evidence for a very short mean free path, and the temperature coefficient of the resistivity, α = (l/ρ)(dρ/dT), follows the Mooij correlation. A short mean free path, may preclude magnetic scattering effects in the isotropic resistivity. The spontaneous anisotropy of resistivity, however, shows an anisotropic contribution from magnetic scattering, having a clear dependence on Ms 2, independent of composition and temperature. This behaviour deviates from lin...

Critical path length for the similarity of elastic multiple scattering processes

Abstract: Multiple scattering processes characterized by or scaled to equal transport mean free path λtr are expected to give similar results (e.g., approximately equal particle distributions in space) at sufficiently large path lengths. By means of the Monte Carlo method, it is shown that the spatial and angular distributions generated by different elastic scattering processes with equal λtr clearly converge to similarity with increasing path length. The critical path length required for evident similarity is of order of magnitude such that the processes are at least plural. For scattering geometries where the effect of single large angle scattering is appreciable, the validity of this plural scattering condition may be restricted to suitably chosen scattering cross sections. Applications to electron penetration through matter are briefly discussed.

Proximity-effect-induced superconductivity at millikelvin temperatures

Abstract: A systematic study is reported of the proximity effect in superconductivity of thick Cu layers (4≤d n≤105 µm) in contact with Nb or Nb-Ti (46≤D s≤1041 µm) from measurements of the ac susceptibility and of the thermal conductivity. The induced superconducting properties of Cu are studied as a function of temperature (7 mK≤T≤1 K), field (0.4 mG≤H≤ 10 G), and electronic mean free path (0.2≤l≤14 µm). The Meissner screening length in Cu increases faster than the coherence length with decreasing temperature and eventually saturates, making the Cu fully superconducting. In this case, superconductivity can be destroyed sharply at a breakdown fieldH b; the transition atH b is hysteretic. The data are in agreement with numerical solutions of the de Gennes/Ginzburg-Landau theory, as demonstrated by the dependence of the Meissner screening length and of the breakdown field on temperature, field, and electronic mean free path. The data indicate that observation of a reduction in thermal conductivity requires a substantially larger induced pair potential than is necessary even for total field shielding. The concentration of Cooper pairs in Cu in contact to Nb is larger than in Cu in contact to Nb-Ti, even for Nb-Ti/Cu samples with a larger electron mean free path in the Cu part. No measurable superconducting field screening could be induced in the investigated temperature range in Pd (26≤d n≤72 µm) in contact to Nb/Cu or to Nb (D s≈5d n). This is explained by the fact that the coherence length is at least an order of magnitude smaller in Pd than in Cu. Evaporating a layer of Fe on Cu in the Nb/Cu samples results in a strong depression of the proximity effect.

Velocity and absorption coefficient of ultrasonic waves in molten and glassy silicates and borates

Abstract: The velocity and absorption coefficient of longitudinal ultrasonic waves with 5 and 10 MHz in molten and glassy silicates and borates have been measured by means of the pulse-echo method in 300 to 1600 K. The silicate and borate were Na2O−SiO2, K2O−SiO2, PbO−SiO2, Na2O−B2O3, and PbO−B2O3. The velocity of sound decreased with increasing temperature and decreased rapidly near the transition temperature of glasses. The product of the one-third power of velocity of sound and the molar volume of the oxide melt was constant and independent of temperature. The absorption coefficient of ultrasonic waves in the oxide melts increased with an increase in viscosity. The absorption mechanisms of ultrasonic waves and the mean free path of phonons in the oxide melts were discussed.

Weak localisation of photons in a disordered two-dimensional medium

Abstract: The authors calculate the back-scattered intensity of light from a disordered two-dimensional medium which results from the weak localisation (time-reversed trajectories) of photons. They find that for theta > lambda / xi , the shape of the back-scattered peak is identical to that for a three-dimensional system with the same elastic mean free path, where xi is the two-dimensional optical localisation length. The triangular shape which was found for three dimensions is suppressed because all the solutions of Maxwell's equations for the electric field are localised for any degree of disorder.

Electron Transport Properties of Ag/Co Layered Metallic Films

Abstract: Measurements of resistance parallel to the layers have been made for sample periodicities A between 16 and 160A at temperatures of 4.2, 78, and 295K. A simple analysis, extending Fuch's theory to multiple layers and involving a single fitting parameter, fits the data well and indicates a transmission coefficient of an electron through an Ag/Co interface which is independent of A and which only changes slightly with temperature between 4.2 and 295K. Preliminary data on the resistivity perpendicular to the layers are given.

Photoelectron Mean Free Path in Langmuir–Blodgett Film Estimated from Angular Dependence of X-Ray Photoelectron Spectra

Abstract: The Langmuir–Blodgett (built-up) film of barium stearate was prepared and its angular dependence of X-ray photoelectron spectra was obtained A simple layer model was proposed to evaluate angular dependence of X-ray photoelectron spectra The electron mean free path of C1s photoelectron (kinetic energy of ca965 eV) was determined from comparison between experimental and calculated take-off angle dependences of intensity of C1s spectra

The Propagation of High-Frequency Phonons in Liquid4He

Abstract: For the propagation of high energy phonons in liquid 4He it is often more important to know whether they remain at a high energy ie ≥ 9 K, rather than knowing they stay at exactly the same energy. It is shown that the energy mean free path is much longer than the scattering mean free path. The flux of high energy phonons that can travel through 4 mm of liquid 4He is calculated as a function of temperature.

Mobility oscillations of electrons on thin He films

Abstract: Among the various probes for studying surfaces, free electrons probably play the most important role nowadays. More and more soph~sticated techniques have been developed to investigate the structure and the excitation of surfaces by low energy electron diffraction, electron energy loss spectroscopy, etc. These methods usually require luItra high vacuum conditions and are therefore suitable only for studying solid surfaces. For liqu~ds the vapor pressure in general is so high and hence the mean free path of the electrons so short that these techniques are not applicable. Here we discuss a method that although quite different from the conventional electron spectroscopies, also makes use of free (or rather quasl-free) electrons to obtain information about substrate surfaces via the interaction of the electrons with these substrates. This method relies on materials with a negative electron affinity and is therefore, in particular, suited for the quantum liquids and solids formed by helium hydrogen; it can be applied even under conditions where the mean free path of the electrons is relative1 y short. In the work presented here we have used the electrons to study thin liquid films of He covering solid substrates, mainly

Thermal Conductivity of Single-Crystal and Sintered RBa2Cu3O7 at low Temperatures

Abstract: The thermal conductivity k of micro-twinned single crystals of YBa2Cu3O7 and HoBa2Cu3O7 and a sintered sample of YBa2Cu3O7 has been measured for temperatures 0.03