Showing papers on "Mean free path published in 1988"
TL;DR: In this paper, the mean free path l in air is presented for temperatures 15, 20, 23 and 25°C for both dry air and moist air at relative humidities of 50 and 100%, at atmospheric pressure (1.01325 × 105 Pa) and at pressure 1 × 105 PA.
346 citations
TL;DR: In this article, the resistivity of nearly solid-density Al was measured as a function of temperature over 4 orders of magnitudes above ambient by observing the self-reflection of an intense, 0.5 psec, 308-nm light pulse incident on a planar Al target.
Abstract: The resistivity of nearly solid-density Al was measured as a function of temperature over 4 orders of magnitudfe above ambient by observing the self-reflection of an intense, 0.5 psec, 308-nm light pulse incident on a planar Al target. As an increasing function of electron temperature, the resistivity is observed initially to increase, reach a maximum which is relatively constant over an extended temperature range, and then decrease at the highest temperatures. The broad maximum is interpreted as "resistivity saturation," a condition in which the mean free path of the conduction electrons reaches a minimum value as a function of temperature, regardless of the extent of any further disorder in the material.
308 citations
TL;DR: In the case of high molecular weight and relatively few sp3 defects, even relatively weak interchain coupling is sufficient to avoid one-dimensional localization; this leads to coherent transport with a mean free path that is limited by either the mean separation between chain imperfections or by phonon scattering.
246 citations
TL;DR: The confinement of electrons in small dimensions can lead to a discretization of energy levels and an out-of-plane conductivity that shows nonanalytic behavior in the approach to the classical limit is found.
Abstract: The confinement of electrons in small dimensions can lead to a discretization of energy levels. The associated quantum size effects in turn lead to an out-of-plane conductivity that shows nonanalytic behavior in the approach to the classical limit. The principal size dependence of the conductivity is \ensuremath{\sim}1/d for a film of thickness d; however, there is also a correction term that has an essential singularity in the small parameter l/d, where l is the mean free path in a bulk sample. Surface roughness in the film is introduced by establishing two physical length scales. Variations in d on length scales shorter than l are treated quantum mechanically by a suitable coordinate transformation. On the other hand, large-scale fluctuations which might reflect the presence of grains are incorporated classically by segmenting the film into independent units of length l. Impurity effects have also been included and in fact crossover behavior in the conductivity is found from a surface-dominated to an impurity-dominated regime. The transport coefficients---conductivity and thermopower---are found to show oscillations as a function of d with a period of half the Fermi wavelength.
215 citations
TL;DR: In this article, a detailed experimental study of coherent backscattering of light from aqueous suspensions of polystyrene microspheres is presented, focusing on the effects of particle size, of absorption due to added dye and of light polarization on the shape and height of the backscatter cone.
Abstract: A detailed experimental study of coherent backscattering of light from aqueous suspensions of polystyrene microspheres is presented. Emphasis is on the effects of particle size, of absorption due to added dye and of light polarization on the shape and height of the backscattering cone. For parallel polarization of incident and scattered beams, the scalar diffusion theory, parametrized by the transport mean free path l*, agrees well with our data up to surprizingly large scattering angles (ql * ~ 1) and quantitatively accounts for the rounding of the cones due to absorption. No deviations from the usual Gaussian statistics of scattered fields is observed up to λ/l* ∼ 0.1.
195 citations
TL;DR: In this paper, a multiple scattering model for seismic wave propagation in random heterogeneous media is proposed to separate the scattering effect and the absorption based on the measured energy density distribution curves.
Abstract: In order to separate the scattering effect from intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In paper I (Wu, 1985), radiative transfer theory is applied to seismic wave propagation and the energy density distribution (or the average intensity) in space for a point source is formulated in the frequency domain. It is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves. In this paper, the data from digital recordings in the Hindu Kush region are used as an example of application of the theory. We also discuss two approximate solutions of coda envelope in the time domain: the single scattering approximation and the diffusion approximation and discuss the relation with the frequency domain solution. We point out that in only two cases can the apparent attenuation be expressed as an exponential decay form. One is the dark medium case, i.e., when B o ≫ 0.5, where B o = ŋ s /(ŋ s + ŋ a ) is the seismic albedo, ŋ s is the scattering coefficient, ŋ a is the absorption coefficient. In this case the absorption is dominant, the apparent attenuation b can be approximated by the coherent wave attenuation b = ŋ s +ŋ a The other case is the diffuse scattering regime, i.e., when B o ≫ 0.5 (bright medium) and R≫ L s ,t ≫ τs, where R and t are the propagation distance and lapse time, L s and τ s are the scattering lengths (mean free path) and scattering time (mean free time), respectively. However, in this case the envelope decays with a rate close to the intrinsic attenuation, while the intensity decreases with distance with a coefficient b≈d 0 (ŋ a +ŋ s ) ≈ d s ŋ s where d o d s are the diffusion multipliers (0 1).
145 citations
TL;DR: In this paper, the excitation and decay of surface plasmons at a silver-air interface using a time-resolved optical technique was studied and a momentum lifetime of 48 fs (13 \ensuremath{\mu}m) was found.
Abstract: We have studied the excitation and decay of surface plasmons at a silver-air interface using a time-resolved optical technique. Monitoring the surface-plasmon propagation enabled us to measure the dephasing of surface plasmons via their mean free path and a momentum lifetime of 48 fs (13 \ensuremath{\mu}m) was found. After a very rapid plasmon decay the energy is transferred into a strain wave and an increase in the temperature of the silver film. We have observed the acoustic phonons, associated with the strain, bouncing up and down the silver film and the heat diffusion on a picosecond time scale.
97 citations
TL;DR: It is proved here that the recently observed universal conductance fluctuations in normal metals at very low temperatures are a rigorous consequence of that diffusion equation, in the regime in which L \ensuremath{\gg} (mean free path) and N\ensure Math{gg}1.
Abstract: Recently, a macroscopic theory of N-channel disordered condeuctors showed that the statistical distribution of the transfer matrix for a system of length L evolves with L according to a diffusion equation in N dimensions. It is proved here that the recently observed universal conductance fluctuations in normal metals at very low temperatures are a rigorous consequence of that diffusion equation, in the regime in which L\ensuremath{\gg} (mean free path) and N\ensuremath{\gg}1. The value found for the fluctuation coincides with the one obtained from elaborate microscopic calculations.
72 citations
TL;DR: In this paper, the authors investigated how the dynamics of geminate recombination between a positive ion and an electron depends upon the mean free path of the electron for scattering by the solvent.
Abstract: We investigate how the dynamics of geminate recombination between a positive ion and an electron depends upon the mean free path of the electron for scattering by the solvent. We calculate the escape probability of geminate recombination as a function of the electron mean free path, by use of the Monte Carlo method we previously developed. When the mean free path is negligibly short compared with the Onsager length, the calculated escape probability agrees with the Onsager result. However, it increases with increasing mean free path and becomes much higher than the Onsager result, for long mean free paths. We also study how the effect of an applied electric field on the escape probability is influenced by the length of the electron mean free path. Our theory quantitatively explains recent experimental data on free ion yields in liquids such as methane, argon, and tetramethylsilane, which sustain high electron mobilities or equivalently long electron mean free paths.
67 citations
TL;DR: In this paper, the growth rates of modes and associated behavior in a Fermi liquid unstable to density fluctuations are studied by using Landau theory, and the hydrodynamic and collosionless limits are bridged by treating the collision integral in the relaxation-time approximation.
51 citations
TL;DR: In this article, the authors explored the interaction of microwaves with superconductors via extensive measurements of the surface resistance and reactance Xs at 10 GHz of superconducting Sn.
Abstract: The interaction of microwaves with superconductors was explored via extensive measurements of the surface resistance Rs and reactance Xs at 10 GHz of superconducting Sn. The measurements were carried out as functions of thickness d and temperature T for Sn films ranging in thickness from 190 A to bulk. By varying the thickness with accompanied variation of mean free path, we were able to examine the wave‐vector dependence of the microwave‐superconductor interaction. An analysis, based on the Bardeen–Cooper–Schrieffer electrodynamical kernel, was developed for calculating Rs and Xs as functions of d, T, and frequency. Details of the measurement techniques and analysis are presented. Experiment and theory agree excellently, with no adjustable parameters. For films with d<800 A we find that the electrodynamics is local because of impurity scattering, while for thicker films nonlocal effects are important. The results imply that superconducting films with microwave response that agrees with theoretical expect...
TL;DR: In this article, a Monte Carlo simulation over a wide range of mean free paths, ratios of plasma to gyroradius, and radial electric fields is performed to compute the transport coefficients and confinement times in stellarators.
Abstract: Neoclassical transport coefficients and confinement times in stellarators of general geometry and tokamaks with and without ripple are computed by Monte Carlo simulation over wide ranges of mean free paths, ratios of plasma to gyroradius, and radial electric fields. The results for monoenergetic particles can be represented by simple formulas using a transport coefficient normalized to the tokamak plateau value and a mean free path normalized to half the connection length. Transport coefficients obtained with monoenergetic particles subjected to pitch angle scattering and energy relaxation are convoluted with a Maxwellian energy distribution. The results are compared with theory and simulations using a particle distribution subjected to pitch angle as well as energy scattering. The overall agreement is good. Transport coefficients with Maxwellian energy distributions for l=2 stellarators and for various other stellarator configurations are shown. Particle transport coefficients, as well as energy transport coefficients, for these configurations are computed for ions (deuterons) as well as for electrons. Estimates of particle and energy confinement times are also obtained.
TL;DR: In this article, a scaling relation between the multiple scattering intensity at arbitrary phase shift and the multiple-scattering intensity in the diffraction or small-phase-shift regime was derived.
Abstract: Beam broadening is discussed in the context of the standard formalism for multiple small-angle scattering, in which coherent single-particle scattering is incoherently, or stochastically, compounded by a random system of spherical particles in a uniform matrix. Bethe's analysis of scattering when sample thickness greatly exceeds the scattering mean free path is combined with the dynamical analysis of single-particle scattering to obtain a new scaling relation between the multiple-scattering intensity at arbitrary phase shift and the multiple-scattering intensity in the diffraction or small-phase-shift regime. A formula is derived for the curvature of the scattering at Q = 0 which expresses this scaling and which can be used in particle size determinations. It is shown that strong multiple scattering, as in very thick samples, tends to render beam broadening insensitive to the cross over from diffractive to refractive single-particle scattering.
TL;DR: A simple modified Ruderman-Kittel-Kasuya-Yosida mechanism for semiconductors is proposed in which carriers from two valence bands located in different regions of the Brillouin zone contribute and a finite mean free path is implemented.
Abstract: The influence of the concentration of charge carriers on the ferromagnetic phase transition of the semimagnetic semiconductor Pb1-x-ySnyMnxTe for various compositions is reported. A critical density of carriers above which a ferromagnetic transition can take place, is observed. A simple modified Ruderman-Kittel-Kasuya-Yosida mechanism for semiconductors is proposed in which carriers from two valence bands located in different regions of the Brillouin zone contribute and a finite mean free path is implemented. An excellent quantitative agreement with the data is obtained.
TL;DR: In this paper, it was shown experimentally that in the forward direction the length scale of quasiballistic photons dominates the dynamic intensity-intensity correlation function of light multiply scattered from randomly diffusing spheres.
Abstract: We find experimentally that in the forward direction the length scale of quasiballistic photons dominates the dynamic intensity-intensity correlation function of light multiply scattered from randomly diffusing spheres. This implies a breakdown of the photon-diffusion approximation, which is characterized by a single length, the transport mean free path. We suggest why this breakdown occurs, introduce phenomenologically a dynamic correlation length as an additional length scale, and with this extension reconcile the theory with experiment.
TL;DR: In this article, a more complete quasi-linear result for the pitch-angle diffusion coefficient of particles in a uniform magnetic field with superposed parallel and antiparallel propagating transverse Alfven waves yields finite and wellbehaved expressions for the mean free path of a solar particle.
Abstract: The discrepancy between the observed particle's mean free path against scattering {lambda}{sub fit} as derived from applying time-dependent spatial diffusion models to solar particle events and the theoretical value {lambda}{sub t} from quasi-linear theory can be resolved. A more complete quasi-linear result for the pitch-angle diffusion coefficient of particles in a uniform magnetic field with superposed parallel and antiparallel propagating transverse Alfven waves yields finite and well-behaved expressions for the mean free path {lambda}{sub t} even for rather large values of the spectral index q of the assumed power law spectrum of the power spectrum of magnetic irregularities. It is shown that values of q between 2.1 and 2.2 lead to remarkable good agreement of {lambda}{sub t} with the observed variation of {lambda}{sub fit} from solar cosmic ray events.
TL;DR: In this article, the potential distribution in a plasma sheath is determined by solving Poisson's equation self-consistently using a kinetic theory nonlocal ion transport model for charge transfer collisions.
Abstract: Plasma sheaths are often assumed to be collision free; however, high‐voltage cathode sheaths are typically thicker than the mean free path for charge transfer collisions at pressures encountered in glow discharge processing equipment (greater than 10 mTorr) In this paper, the potential distribution in a plasma sheath is determined by solving Poisson’s equation self‐consistently using a kinetic theory nonlocal ion transport model for charge transfer collisions The relationship between the potential distribution, ion flux, and thickness of a plasma sheath is presented for arbitrary values of the sheath thickness relative to the mean free path for charge transfer The results may be used to estimate the ion flux from measurements of the sheath thickness and potential drop across the sheath Ion energy distribution functions and a one‐parameter approximation to the numerically determined potential distribution are also presented These results apply to rf discharges in a time‐averaged sense when the ion she
TL;DR: In this article, a two-dimensional tight-binding wideband model and a narrow-band model were proposed for the high-temperature superconductor YBa 2 Cu 3 O 7−δ in its normal state.
Abstract: The high-temperature superconductor YBa 2 Cu 3 O 7−δ in its normal state, shows unusual dependence of its transport properties on the oxygen deficiency parameter δ and on temperature: for δ ≈ 0 both the resistivity and the Hall number rise linearly with temperature, while the thermoelectric power is very small. In order to interpret this unusual combination of properties we propose two alternative models, a two-dimensional tight-binding wide-band model, and a narrow-band model. In the first case we assume scattering by a fully excited boson field, with a mean free path Λ ∝ 1/ T . In the second model we assume a band composed of two parts, where the upper smaller part does not contribute to transport (as would result from the existence of a mobility edge), and Λ is independent of temperature. The calculated results are compared with experiments.
TL;DR: In this article, a local field method is described for determining the microscopic potential, the electrical resistivity, and the electromigration driving force on an impurity in a metallic microstructure.
Abstract: A local-field method is described for determining the microscopic potential, the electrical resistivity, and the electromigration driving force on an impurity in a metallic microstructure. The method is an extension of Landauer's picture of residual-resistivity dipoles to microstructures, with greater emphasis placed upon the details of the quantum-mechanical scattering process. Using a microscopic, surface-impurity model for surface roughness, we apply the method to a metallic thin film. When the film thickness is smaller than the mean free path, the surface resistivity is found to have oscillatory behavior as a function of film thickness. The form of the oscillations depends upon multiple scattering between the surface impurity and the film surfaces. In thicker films, the Fuchs-Sondheimer result is recovered. The local potential set up by impurity scattering is dipolar in the near- and far-field regions. However, unlike the case of residual-resistivity dipoles in bulk, the effective dipole strength is generally different in the two regions. It is found that the residual-resistivity dipole field decays less rapidly with distance in a thin film than in bulk, thus resulting in a larger voltage drop across an impurity in a thin film. This field enhancement is expected in low-dimensional systems.
TL;DR: In this article, the authors used the shape of the pitch angle diffusion coefficient, the absolute value of the mean free path λ, and the rigidity dependence of λ(R) for the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun.
Abstract: In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(μ), the absolute value of the mean free path λ, and the rigidity dependence of the mean free path λ(R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the ‘layer model’ in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D(μ) and λ based on the trajectory simulation for 100 MeV protons (‘field’ approach) are compared with results obtained from solar proton data (‘particle’ approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (‘QLT’ approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the ‘field’ and ‘particle’ approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the ‘field’ and ‘QLT’ approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfven-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.
TL;DR: In this paper, the Hartree-Fock approximation and first Born approximation were used for the calculation of inelastic mean free paths of electrons in solids, and the results for the application of the method to the six solid media amorphous carbon, silicon, germanium, Al2O3, SiO2, and GeO2; are presented.
TL;DR: In this paper, the electronic structure of semiconductor compounds GaAs, InAs, and InP and alloys Ga 0.5In0.5As, Ga0.7Al0.3As and GaInAs alloys, obtained in the coherent potential approximation, is used to calculate the group velocity and velocity relaxation time limited by longitudinal optical phonons, alloy disorder, and ionized impurities as a function of electron energy.
Abstract: The electronic structure of semiconductor compounds GaAs, InAs, and InP and alloys Ga0.5In0.5As, Ga0.7Al0.3As, and InP0.5As0.5, obtained in the coherent potential approximation, is used to calculate the group velocity and velocity relaxation time limited by longitudinal optical phonons, alloy disorder, and ionized impurities as a function of electron energy at 300 K. The nonparabolic nature of the band structure is found to severely limit the electron mean free path. With the types of interactions considered to date, the presence of L valleys does not limit the mean free path of electrons moving in the 〈100〉 direction. At 1018‐cm−3 doping, electron‐electron interactions reduce the mean free path by only 15% to 20%. InAs and GaInAs alloys offer advantages over all the other materials for devices with base widths greater than 500 A; however, for thinner devices, ∼100 A, no material is appreciably better than GaAs, the III‐V compound currently under best control. The ballistic device‐related properties of se...
TL;DR: In this paper, the authors report the results of two types of experiments on the thermo-electric coefficients of GaAs-Ga1-xAlxAs heterojunctions and show that the phonon mean free path in the GaAs substrate is increased by polishing the rear surface.
Abstract: The authors report the results of two types of experiments on the thermo-electric coefficients of GaAs-Ga1-xAlxAs heterojunctions. In the first set of experiments, the density and mobility of a two-dimensional electron gas has been varied over a wide range by illumination. The zero-field thermopower is reduced by the increased carrier density but the oscillation amplitude at any particular field is insensitive to it. In the second set of experiments they have increased the phonon mean free path in the GaAs substrate by polishing the rear surface. This results in an increase in magnitude of the thermo-electric coefficients which is consistent with phonon drag effects.
TL;DR: In this article, a new method for determining the inelastic mean free path was applied to the ordered polycrystalline AlNi alloy and the results obtained agree well with the literature data.
Abstract: A new method for determining the inelastic mean free path was applied to the ordered polycrystalline AlNi alloy. The results obtained agree well with the literature data.
TL;DR: In the low temperature region (less than 50 K), the resistivity π of the quasi-crystalline Al-Mn and Al-V alloys increases rapidly with decreasing temperature T and is proportional to −log T or T −a on the higher temperature side and to −T 1/2 on the lower side.
TL;DR: In this paper, exact formulae for various integrals of the Compton scattering cross-section are derived for various integral functions, including the interaction kernel, energy exchange rate, and transport mean free path.
Abstract: Exact formulae are derived for various integrals of the Compton scattering cross-section. The interaction kernel is integrated over outgoing photon frequency and direction, and over a relativistic Maxwellian distribution for the electrons. The total Compton cross-section, the energy exchange rate, and the transport mean free path are thereby expressed in terms of single integrals of analytic functions. In addition, these integrals produce simple analytic expressions in the limiting cases of either small or large frequency or electron temperature. A numerical method based on Gaussian quadrature is used to compute the transport mean free path. A comparison with previously published results is presented.
TL;DR: In this article, the effects of realistic band structures on the group velocities and mean free paths due to scattering by longitudinal optical phonons, ionized impurities, alloy disorder, and other electrons on limiting ballistic transport in GaAs, InAs and InAsP alloys were studied.
Abstract: We studied the effects of realistic band structures on the group velocities and mean free paths due to scattering by longitudinal optical phonons, ionized impurities, alloy disorder, and other electrons on limiting ballistic transport in GaAs, InAs, InP, GaInAs, GaAlAs, and InAsP alloys. The upper cutoff frequency and fraction of ballistic electrons transporting through devices made from these materials are calculated. For thick devices (≥500 A), GaInAs alloys have distinct advantages. However, for thin devices (≊100 A), the cutoff frequencies range around 15 THz, and none of the materials have an appreciably higher ballistic fraction than GaAs.
TL;DR: In this paper, the evolution of the electron acoustic signal has been measured for Be− and Si−doped GaAs and Ga0.28Al0.19In0.53As layers with doping levels from1017 to 1020 at. cm−3.
Abstract: The evolution of the electron acoustic signal has been measured for Be‐ and Si‐doped GaAs and Ga0.28Al0.19In0.53As layers with doping levels from1017 to 1020 at. cm−3. The samples have also been analyzed by cathodoluminescence spectroscopy for near‐band‐edge transition and deep level emission. The results are explained by the reduction of the mean free path of phonons, giving rise to a lattice thermal conductivity decrease. Meanwhile, the electronic part of the thermal conductivity of these compounds is found to be nearly negligible.
TL;DR: In this paper, the scattering of conduction electrons at grain boundaries in polycrystalline copper, molybdenum, and iron was studied and linear functions of the specific electrical resistance versus concentration of grain boundaries were determined.
Abstract: The scattering of conduction electrons at grain boundaries in polycrystalline copper, molybdenum, and iron is studied. Linear functions of the specific electrical resistance versus concentration of grain boundaries are determined. Coefficients of conduction electron scattering kGB at grain boundaries as well as the specific electrical resistance of a single crystal are also determined for these metals. Additionally, the mean free path, lo, and the reflection coefficient, R, for conduction electrons are assessed from the internal size effect in the temperature range from 80 to 300 K.