Average Mean Free Path Research Articles

Electron mean free path of tungsten and the electrical resistivity of epitaxial (110) tungsten films

This work describes a study of the classical electrical resistivity size effect in tungsten. The important length scale for this size effect is the isotropic average electron mean free path (EMFP), which was determined to be 19.1 nm for W at 293 K by employing density functional theory. To explore the size effect experimentally, (110) oriented epitaxial W films with thicknesses ranging from 9.8 to 299.7 nm were prepared by sputter deposition onto ($11\overline{2}0$) Al${}_{2}$O${}_{3}$ substrates at 520 \ifmmode^\circ\else\textdegree\fi{}C followed by postdeposition annealing in Ar-4$%$H${}_{2}$ at 850 \ifmmode^\circ\else\textdegree\fi{}C. Film resistivities were measured at room temperature and at liquid He temperature. The Fuchs-Sondheimer (FS) surface scattering model with a low specularity parameter ($p$ $=$ 0.11) was shown to provide a good description of the film resistivity as a function of film thickness. Further, it is shown that an upper bound to the EMFP cannot be established by fitting resistivity data to the FS model, whereas a lower bound can be assessed.

IONIZATION NEAR ZONES ASSOCIATED WITH QUASARS ATz∼ 6

We analyze the size evolution of HII regions around 27 quasars between z=5.7 to 6.4 ('quasar near-zones' or NZ). We include more sources than previous studies, and we use more accurate redshifts for the host galaxies, with 8 CO molecular line redshifts and 9 MgII redshifts. We confirm the trend for an increase in NZ size with decreasing redshift, with the luminosity normalized proper size evolving as: R_{NZ,corrected} = (7.4 \pm 0.3) - (8.0 \pm 1.1) \times (z-6) Mpc. While derivation of the absolute neutral fraction remains difficult with this technique, the evolution of the NZ sizes suggests a decrease in the neutral fraction of intergalactic hydrogen by a factor ~ 9.4 from z=6.4 to 5.7, in its simplest interpretation. Alternatively, recent numerical simulations suggest that this rapid increase in near-zone size from z=6.4 to 5.7 is due to the rapid increase in the background photo-ionization rate at the end of the percolation or overlap phase, when the average mean free path of ionizing photons increases dramatically. In either case, the results are consistent with the idea that z ~ 6 to 7 corresponds to the tail end of cosmic reionization. The scatter in the normalized NZ sizes is larger than expected simply from measurement errors, and likely reflects intrinsic differences in the quasars or their environments. We find that the near-zone sizes increase with quasar UV luminosity, as expected for photo-ionization dominated by quasar radiation.

Localization length in two-dimensional disordered systems: effects of evanescentmodes

We study the influence of evanescent modes on the scaling behavior of therenormalized localization length (RLL) in 2D disordered systems, using theδ-function potential strip model and the multichain tight-binding Anderson model. In theweak disorder regime we have evaluated the RLL for large numbers of modesM. It is shown that RLL shrinks with increasingM which indicates that the electron states will remain localized in an infinitely wide systemfor an arbitrarily small disorder, in agreement with existing theories. In the thermodynamiclimit () for the two models, we obtain the localization length in an infinitely large system. Weshow that the presence of evanescent modes enhances the RLL with respect to the valueobtained when evanescent modes are absent. We also derive an exact relationshipbetween the localization length and its corresponding average mean free path for anM-channel system for the case where propagating as well as evanescent channels arepresent.

Dust settling in magnetorotationally driven turbulent discs - I. Numerical methods and evidence for a vigorous streaming instability

In this paper, we have used the riemann code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas at specific radial locations in a vertically stratified protostellar accretion disc. The disc was modelled to have the density and temperature of a minimum mass solar nebula, and shearing box simulations at radii of 0.3 and 10 au are reported here. The disc was driven to a fully developed turbulence via the magnetorotational instability (MRI). The simulations span three gas scaleheights about the disc's midplane. We find that the inclusion of standard dust-to-gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution of the dust of all sizes reached a Gaussian profile within two scaleheights of the disc's midplane. The vertical scaleheights of these Gaussian profiles are shown to be proportional to the reciprocal of the square root of the dust radius when large spherical dust grains are considered. This result is consistent with theoretical expectation. The largest two families of dust in one of our simulations show a strong tendency to settle to the midplane of the accretion disc. The large dust tends to organize itself into elongated clumps of high density. The dynamics of these clumps is shown to be consistent with a streaming instability. The streaming instability is seen to be very vigorous and persistent once it forms. Each stream of high-density dust displays a reduced rms velocity dispersion. The velocity directions within the streams are also aligned relative to the mean shear, providing further evidence that we are witnessing a streaming instability. The densest clumpings of large dust are shown to form where the streams intersect. We have also shown that the mean free path and collision time for dust that participates in the streaming instability are reduced by almost two orders of magnitude relative to the average mean free paths and collision times. The rms velocities between the grains also need to fall below a minimum threshold in order for the grains to stick and we show that a small amount of the large dust in our 10 au simulation should have a propensity for grain coalescence. The results of our simulations are likely to be useful for those who model spectral energy distributions of protostellar discs and also for those who model dust coagulation and growth.

Mean free path in disordered multichannel tight-binding wires

Transport in a disordered tight-binding wire involves a collection of different mean free paths resulting from the distinct fermi points, which correspond to the various scattering channels of the wire. The generalization of Thouless' relation between the mean free path and the localization length $\xi$ permits to define an average channel mean free path,$\bar\ell$, such that $\xi\sim N\bar\ell$ in an $N$-channel system. The averaged mean free path $\bar\ell$ is expressed exactly in terms of the total reflection coefficient of the wire and compared with the mean free path defined in the maximum entropy approach.

Suppressed reflectivity due to spin-controlled localization in a magnetic semiconductor

The narrow gap semiconductor FeSi owes its strong paramagnetism to electron-correlation effects. Partial Co substitution for Fe produces a spin-polarized doped semiconductor. The spin-polarization causes suppression of the metallic reflectivity and increased scattering of charge carriers, in contrast to what happens in other magnetic semiconductors, where magnetic order reduces the scattering. The loss of metallicity continues progressively even into the fully polarized state, and entails as much as a 25% reduction in average mean-free path. We attribute the observed effect to a deepening of the potential wells presented by the randomly distributed Co atoms to the majority spin carriers. This mechanism inverts the sequence of steps for dealing with disorder and interactions from that in the classic Al'tshuler Aronov approach - where disorder amplifies the Coulomb interaction between carriers - in that here, the Coulomb interaction leads to spin polarization which in turn amplifies the disorder-induced scattering.

The transport of galactic and jovian cosmic ray electrons in the heliosphere

An overview is given on what we know about the cosmic ray diffusion process from the modelling of low-energy (MeV) electron transport in the heliosphere. For energies below ∼300 MeV, these electrons give a direct indication of the average mean free paths because they do not experience large adiabatic energy changes and their modulation is largely unaffected by global gradient and curvature drifts. Apart from galactic cosmic ray electrons, the jovian magnetosphere at ∼5 AU in the ecliptic plane is also a relatively strong source of MeV electrons, with energies up to ∼30 MeV. Therefore, when modelling the transport of these particles in the inner heliosphere, a three-dimensional treatment is essential. By comparing these models to observations from the Ulysses, Pioneer and Voyager missions, important conclusions can be made on e.g., the relative contributions of the galactic and jovian electrons to the total electron intensity, the magnitude of the parallel and perpendicular transport coefficients, and the time dependant treatment thereof.

A simple model for dislocation behavior, strain and strain rate hardening evolution in deforming aluminum alloys

In this work, modeling of the stress–strain behavior is carried out using a simple dislocation model. This model uses three variables to characterize the dislocation population: The average forest and mobile dislocation densities, ρf and ρm, and the average dislocation mean free path L. However, it is shown that within reasonable assumptions, only two of these variables are independent. The mathematical form derived from this dislocation-based model was applied to experimental stress–strain data determined at room temperature for pure aluminum, 3003-O, 2008-T4, 6022-T4, 5182-O and 5032-T4 aluminum alloy sheets. The evolution of the state variables was calculated for these materials from a single stress–strain curve. The average dislocation mean free paths at a strain of 0.5 were compared with TEM observations of dislocation cell sizes or inter-dislocation spacing for specimens deformed equal biaxially with the hydraulic bulge test. A very good agreement was obtained between predictions and experiments.

The prediction of permeability for an epoxy/E‐glass composite using optical coherence tomographic images

AbstractKnowledge of the permeability tensor in liquid composite molding is important for process optimization. Unfortunately, experimental determination of permeability is difficult and time consuming. Numerical calculation of permeability from a model reinforcement can circumvent experimentation. However, permeability predictions often rely on a model reinforcement that does not accurately mimic the actual microstructure. A rapid, nondestructive technique called optical coherence tomography (OCT) can image the microstructure of a composite in minutes. Actual microstructural information can be then used to improve the accuracy of the model and therefore the predicted permeability. Additionally, the influence on fiber volume fraction and microstructural variability on permeability can be systematically studied.In this work, binary images were generated from the low contrast OCT data through image de‐noising, contrast enhancement and feature recognition. The resulting data were input to a lattice‐Boltzmann model for permeability prediction. The influence of the fiber volume fraction, tow surface area, average mean free channel path, and variable microstructure are discussed in terms of their individual and synergistic effects on permeability. The calculated axial and transverse permeabilities from the images show very good agreement with the experimental values.

Mechanical behaviour of alloys containing stable or evolving heterogeneous arrangements of particles

The effect of second phase particles on the deformation behaviour of a particle strengthened (e.g. oxide dispersion strengthened) alloy was studied. Instead of dealing with average characteristics of dislocation glide (such as the average mean free path), a particular distribution of particles in the glide plane was considered. A homogenisation technique based on the Delaunay triangulation was used that is considered to be a better representation of local particle arrangement than the Voronoi tessellation proposed previously. A softening effect of particle clustering was found. The method was also applied to a population of particles whose density decreases during plastic deformation due to Ostwald ripening.

Average absorption coefficients and mean free paths of radiation of the continuous spectrum in the region of multiple and total ionization

Consideration is given to problems of averaging absorption coefficients of atoms and multiply charged ions with passage to the region of total ionization. It is shown that correct allowance for ionization of hydrogen-like ions makes it possible to pass automatically to coefficients of absorption in the continuous spectrum. A comparison is made with detailed calculations of mean free paths for a number of elements.

Characterization of substructure resistance in asymmetric gas separation membranes

Gas permeation through a typical state-of-the-art membrane can be described by defining three morphological features: namely skin thickness, skin integrity, and substructure resistance. Traditional gas permeation measurements tend to characterize skin thickness and skin integrity, but not substructure resistance. This presents a serious obstacle to the optimization of advanced hollow fiber membranes, since as skin thicknesses are reduced, substructure resistance becomes an increasingly significant contribution to the overall permeation rate. This paper illustrates how substructure resistance can affect permeation properties and demonstrates a new technique for characterizing this frequently important morphological feature. The technique involves applying a constant transmembrane pressure while varying the average gas pressure within the membrane. Thus, the mean free path of gas molecules permeating through the substructure can be altered while maintaining a constant driving force for permeation. Such experiments characterize the magnitude of the substructure resistance, as well as provide insight into the governing transport mechanism. These constant driving force/variable pressure permeation measurements can estimate the average pressure or mean free path at the transition where substructure resistance becomes negligible. This can then be used to compare the morphological features of different membranes. This technique is demonstrated on well-defined coated ceramic membranes, asymmetric polymeric flat sheet membranes, and asymmetric polymeric hollow fiber membranes.

Vertical profile of effective turbidity reconstructed from broadening of incoherent body-wave pulses-II.Application to Kamchatka data

SUMMARY The vertical profile of eVective turbidity under Kamchatka is reconstructed from observations of distance-dependent broadening of the inchoherent pulse of highfrequency body waves from small earthquakes, by means of a new approach and data processing scheme developed in Paper I. The key ‘eVective turbidity’ parameter, g e ,u sed is an immediate generalization of the common isotropic turbidity/scattering coeYcient g. Measurements of 200‐600 onset-to-peak delays for P and S waves for five Kamchatka stations are used for interpretation. The estimates based on these data correspond to the 2‐4 Hz frequency band. The inversion of data is performed in terms of the parameters of two generic vertical eVective turbidity structures: a piecewise-constant profile (PCP) and truncated-inverse-power-law profile (TPLP), both used in several variants. The variants of the inversions give consistent results, but also reveal rather limited resolution, not permitting the recovery of detailed profiles or a comparison of results among individual stations. The inversions indicate that the values of eVective turbidity decay from the surface down: within the depth interval h=0‐50 km, the decay is gradual; at greater depths it is much steeper, roughly following the inverse cube law. The estimates of average eVective mean free path l e =1/g e are very close for P and S waves: 50‐60 km (±20 per cent) for the 0‐20 km layer; 250‐300 km (±30 per cent) for the 20‐80 km layer; and at h>60‐80 km, l e #100(h/40)’2‐4 for both P and S waves. The value of both the P- and the S-wave optical thickness (total scattering loss) of the upper 200 km is about 0.75 (±25 per cent), and the lithosphericscattering contribution to t* P is estimated as 0.2 s at 1 Hz. The expected S-wave scattering loss agrees reasonably with the standard regional amplitude attenuation curve, probably reflecting the secondary role of intrinsic loss at 3 Hz. The S-wave scattering Q in the lithosphere of Kamchatka is estimated for f =1 Hz as 125, 205 and 255 for hypocentral distances of shallow events of 30, 100 and 300 km, respectively.

Non-equilibrium Electron Dynamics Phenomena in Scaled Sub-100 nm Gate Length Metal Semiconductor Field Effect Transistors: Gate-fringing, Velocity Overshoot, and Short-channel Tunneling

Ultrashort channel GaAs metal semiconductor field effect transistors were fabricated with gate lengths ranging from 30 nm to 105 nm, by electron beam lithography, in order to examine the scaling characteristics of transconductance. For gate lengths in sub-100 nanometer range, where gradual channel approximation is no longer valid, it was observed that the transconductance varies with a variety of small-dimension-related, nonequilibrium electron dynamics phenomena such as gate-fringing effect, electron velocity overshoot, and short-channel tunneling. Short-channel tunneling was suggested experimentally for the first time to explain the degradation of transistor performance, overriding an enhancement due to electron velocity overshoot for a gate length smaller than the average inelastic mean free path of an electron.

Decay length of the pressure dependent deposition rate for magnetron sputtering

The pressure dependence of the deposition rate for magnetron sputter deposition of various elemental semiconductors and metals was investigated by x-ray measurements on sputtered films and quartz monitor measurements. It was found that for all elements investigated the dependence of the rate Φ on pressure-distance (pd) is well described by Φ=Φ0(1−e−cpd)/cpd. The value of c equals the inverse characteristic pressure-distance product (pd)0, which is the characteristics of the exponential decay of rate with pressure for low pressures. The experimental data of (pd)0 vary from 4.6 Pa cm for aluminum to 120 Pa cm for tungsten. It is shown that (pd)0 depend on both material specific properties and process parameters. The material specific properties are mainly the atomic mass and diameter, and the surface binding energy. The process parameters target voltage and power density act via the increase of the mean free path and the reduction of gas density, respectively, on (pd)0. As a first approximation, the characteristic pressure-distance product for argon as sputtering gas is proportional to the product of target atomic mass, average atomic energy and thermal mean free path.

Hall Effect and Thermoelectric Power in Multilayers Prepared on Microstructured Substrate

We report the first measurement of Hall effect and thermoelectric power ( S ) in multilayers prepared on a V-groove microstructured substrate for current-at-an-angle-to-plane (CAP) geometry to extract the contribution from the current-perpendicular-to-plane (CPP) geometry. In the field dependence of extraordinary Hall resistivity (ρ H M ), we found a clear difference between CAP and current-in-plane (CIP) geometries. In contrast, ρ H M values at saturation field are almost the same despite the large difference in the resistivity (ρ) between the two geometries. From the comparison of the results for two samples with different layer thicknesses, the ratio of the average mean free path of conduction electrons to the layer thickness was found to play an essential role in the scaling relations between ρ H M ( S ) and ρ.

Direct observation of the hot-electron distribution in GaAs/AlGaAs heterostructures

We have directly observed the electric-field-driven hot-electron distribution in high-mobility GaAs/AlGaAs heterostructures by detecting the grating-induced far-infrared Smith-Purcell emission. In samples with very low concentration the distribution develops a non-thermal shape at low electric fields due to the dominance of LO phonon emission. For the first time the average mean free path of the hot electrons is determined by studying the emission signal as a function of the grating period length.

A study of the propagation of solar energetic protons in the inner heliosphere

Eight solar energetic proton events observed in the inner heliosphere on the spacecraft Helios 1 or 2 are studied. Particle pitch angle diffusion coefficients and mean free paths are derived from a power spectral analysis of the turbulence of the magnetic field during the time of the events. Quasi‐linear theory of wave‐particle interaction is applied strictly throughout in combination with the slab model of fluctuations. Several points receive special attention: (1) the large difference in scattering conditions from one event to the other, which requires an individual analysis of each event; (2) the selection of the exact stretch of magnetic field data to be analyzed and the influence of this choice on the result; (3) the exclusion of data periods that contain discontinuities and other nonoscillatory structures; and (4) short‐scale variations of the overall field fluctuation level, which can be considerable. As a consequence, the mean free paths of the particles are derived from time series of the varying momentary power density spectra as an appropriate average of the scattering conditions (as an average mean free path). These results from the magnetic field spectra are then compared with results of fits of propagation models to the particle time‐intensity and time‐anisotropy profiles observed at the same time. Of eight such comparisons, half of the cases exhibit for the first time an approximate agreement between the results of the two approaches, particle analysis and magnetic field analysis. The others, however, still show the discrepancy that is cited in the literature. Among the events with good agreement are the two extreme cases in the whole Helios data set, the event of April 11, 1978, Helios 2, with a mean free path from quasi‐linear theory of 0.01 AU, and the events of June 7, 1980, Helios 1, with a mean free path from quasi‐linear theory of about 0.8 AU at a rigidity of 0.1 GV. This shows not only that quasi‐linear theory in a wave and slab model framework is indeed capable of producing correct results under certain conditions if an appropriate case‐by‐case analysis is conducted, but also that these cases can encompass a wide range of turbulence strengths. Several possibilities for the source of the discrepancy that remains for the other cases, which the theory and the assumptions applied in this work obviously do not explain, are discussed. However, at the present time no definite solution to the problem is obvious.

Imaging small particles with secondary electrons

High resolution secondary electron microscopy (HRSEM) in dedicated scanning transmission electron microscopy (STEM) instruments has proved very useful for characterizing supported catalysts. In order to understand the contrast mechanisms of HRSEM images of small particles, clean samples and UHV environments are needed since the emission of secondary electrons (SEs) can be significantly influenced by contamination on the particle surface. In this paper we report results on imaging small metal particles by HRSEM in a UHV STEM instrument. In addition, we show that with computer assistance digitized HRSEM images of small metal particles can be used to estimate the average inelastic mean free path and the mean escape depth of the collected SEs.The Vacuum Generators UHV STEM HB-501S, codenamed MIDAS (a Microscope for Imaging, Diffraction and Analysis of Surfaces), was used for these experiments. Detailed descriptions of the MIDAS system have been published previously. The collection efficiency of SEs approaches 100% through the use of magnetic ‘parallelizers’ situated inside the objective pole pieces.

Interpretation of Damage to Mammalian Cells, E.Coli and Bacteriophages by Incorporated Radionuclides for Prolonged Irradiation

Abstract Previous analysis of published survival data for Auger electron and beta emitting nuclides incorporated into mammalian cells have been extended to include E. coli and bacteriophages. A unified scheme for the expression of damage is explored in terms of the localised secondary charged particle fluence of electrons, their average mean free path for ionisation and the number of DNA segments at risk in the target.