Showing papers on "Mean free path published in 1970"
TL;DR: In this paper, the surface roughness of thin metal films has been used to predict the thickness dependence of resistivity and its temperature coefficient of metal films, and the ratio of the roughness to the mean free path, h/λ, is introduced as a convenient parameter.
Abstract: The thickness dependence of resistivity and its temperature coefficient of thin metal films has been studied. A theory is proposed to include, the surface roughness in determining the film resistivity, in addition to the reduced mean free path to conduction electrons. The ratio of the roughness to the mean free path, h/λ, is introduced as a convenient parameter. The thickness dependence of the resistivity predicted by the present theory agrees with the well known Fuchs-Sondheimer theory if h/λ=0. If h/λ>0, the discrepancy between the two theories increases with the decrease in film thickness. Satisfactory agreement between the theoretical and experimental results can be obtained by adjusting the value of h/λ.
227 citations
TL;DR: In this paper, a bakable ultrahigh vacuum system has been constructed to sample the particle flux incident on the substrate of a planar diode sputtering system, where a beam of particles from the discharge is extracted into a long mean free path environment where it passes through a 90° deflection electrostatic analyzer into a quadrupole residual gas analyzer.
Abstract: A bakable ultrahigh vacuum system has been constructed to sample the particle flux incident on the substrate of a planar diode sputtering system. A beam of particles from the discharge is extracted into a long mean free path environment where it passes through a 90° deflection electrostatic analyzer into a quadrupole residual gas analyzer. The mass spectra of positive ions incident on a substrate during dc sputtering of copper and aluminum bronze are shown and the influence of hydrogen contamination is illustrated. The energy distribution of the Ar+ ions is presented for several values of the substrate bias.
118 citations
TL;DR: In this paper, the transition from continuum to molecular behaviour of gases is explored using a modified mean free path and relative intermolecular and boundary collisions are calculated and it is proposed that, by assuming the transport process to be partially continuum and partially molecular, according to such frequencies, there results a plausible account for some of the observed anomalies in gas flow characteristics in the transition regime.
Abstract: Comparison is made between the electrical and thermal conductivities of solids and the transport properties of gases, with special reference to boundary limiting effects. The transition from continuum to molecular behaviour of gases is explored using a modified mean free path. Relative intermolecular and boundary collisions are calculated and it is proposed that, by assuming the transport process to be partially continuum and partially molecular, according to such frequencies, there results a plausible account for some of the observed `anomalies' in gas flow characteristics in the transition regime.
101 citations
TL;DR: In this article, the mean free path for elastic scattering and for plasmon production was determined from beam attenuation measurements on films of various thicknesses, and the authors showed that elastic scattering can be achieved using a beam attenuator.
Abstract: : The mean free path for elastic scattering and for plasmon production was determined from beam attenuation measurements on films of various thicknesses. (Author)
54 citations
TL;DR: Minerals radiative thermal conductivity at high temperatures from IR measurement of absorption coefficient and refractive index was analyzed in this paper, showing that the absorption coefficient is positively correlated with the refractive indices.
Abstract: Minerals radiative thermal conductivity at high temperatures from IR measurement of absorption coefficient and refractive index
38 citations
TL;DR: In this article, the effect of Griffith flaws on the strength of glass-tungsten composites was investigated for small sizes of Griffith faults, and the results were in good agreement with those calculated by Fullman's equation.
Abstract: The effect of the limitation of Griffith flaws, introduced in an abraded surface of glass, on the strength of glass-tungsten composites was investigated for small sizes of Griffith flaws. Hasselman and Fulrath's proposed fracture theory for this type of system extended to small flaw sizes. The use of tungsten spheres with two particle sizes or a wide distribution about one average size as the dispersed phase in a glass matrix decreased the average mean free path in the matrix more than could be achieved with a single particle size dispersion. Average mean free paths determined experimentally by statistical techniques were in good agreement with those calculated by Fullman's equation. This technique was successfully used when the dispersed phase had two particle sizes or a wide particle size distribution. The strong effect of internal stresses caused by a mismatch of thermal expansion of the phases in reducing the strength of a composite was demonstrated.
35 citations
25 citations
TL;DR: In this article, the tip angle between the magnetic field H and the sample surface, at a fixed value of H, was used to infer an electronic mean free path at a constant temperature and also to study its temperature dependence.
Abstract: Radio-frequency size effect measurements have been made on parallel plate polycrystal and single-crystal samples of potassium in the temperature range 1.9-4.2 degrees K and at frequencies from 1 to 4 MHz. The r.f. size effect signal which arises from electrons near the elliptic limiting point on the Fermi surface was observed by sweeping the tip angle between the magnetic field H and the sample surface, at a fixed value of H. The variation in amplitude of these signals with H was used to infer an electronic mean free path at a fixed temperature, and also to study its temperature dependence.
21 citations
TL;DR: In this article, the energy gap and the transition temperature of strong-coupling superconductors were measured as functions of the mean free paths of the electrons, and the experimental results confirm the theoretical prediction that the attractive electron-electron interaction in disordered superconductions is increased.
Abstract: The energy gaps and the transition temperatures of the strong-coupling superconductors lead and mercury are measured as functions of the mean free paths of the electrons. The energy gap of lead increases with decreasing mean free path; the transition temperature is found to be constant. The energy gap of mercury runs through a maximum value with decreasing mean free path whereas the transition temperature decreases. The energy gap of pure mercury is extrapolated to the value 1.58 meV and yields the ratio 2Δ0/kTc=4.4. The experimental results confirm the theoretical prediction that the attractive electron-electron interaction in disordered superconductors is increased. But in addition, the strong-coupling effect appears to become more important in disordered superconductors. A comparison with similar experiments for weak-coupling superconductors is made.
21 citations
TL;DR: In this article, it was suggested that the carrier mobility of semiconducting glasses is considerably larger than the Hall-mobility because of potential perturbations due to a large density of charged defects and because of the ambipolar character of the conductivity.
Abstract: It is suggested that the carrier mobility of semiconducting glasses is considerably larger than the Hall-mobility because of potential perturbations due to a large density of charged defects and because of the ambipolar character of the conductivity. These potential perturbations force the main carrier transport to occur farther inside the bands at a distance E from the band edges, which is essentially given by the height of potential saddles between Coulomb-repulsive defects E ⋍ 0.2 eV for N rep. ⋍ 10 19 cm −3 ) , explaining the larger slope of the semiconductivity. The mean free path of carriers is estimated to be of the order of 100 A in agreement with the large pre-exponential factor of the semiconductivity. The Seebeck-effect—Hall-effect anomaly and the p-type semiconductivity can be explained due to the difference in effective masses of holes and electrons in simple bands.
20 citations
IBM1
TL;DR: In this article, the mean free path of hot electrons in Y has been determined as ∼ 10A at 7 eV above ther Fermi level EF using a new photoemission method.
TL;DR: A flow field survey has been made of the shock layer development on a flat plate, at M = 6, from just upstream of the leading edge to downstream of the merged layer as discussed by the authors.
Abstract: A flow field survey has been made of the shock layer development on a flat plate, at M = 6, from just upstream of the leading edge to downstream of the merged layer. The electron beam fluorescence technique has been used to measure density profiles from which a comprehensive description of the flow field is constructed. Close to the leading edge the flow is near free molecular and can be described in terms of two effective mean free paths, as proposed by Hamel and Cooper. The results suggest that continuum flow is not established for a distance approximately four times the mean free path for the collision of a free stream molecule with a body molecule. An upstream disturbance occurs a few free stream static mean free paths ahead of the leading edge, although this was aerodynamically sharp.
TL;DR: In this article, it was shown that the Ziman theory is applicable to liquid metals and most amorphous metal films, giving a conductivity equal to Se2L/12π3ħ, where S is the Fermi surface area and L the mean free path.
Abstract: It is frequently stated that amorphous semiconductors have, in contrast to crystals, a value of the conductivity which is relatively insensitive to composition. This is explained by assuming that each atom in a glass has as many nearest neighbours as the number of bonds it can from (Ge, 4; As, 3; Te, 2), so that there are no free electrons available to carry a current. The validity of this concept will be examined; it is not true for some amorphous films (Mg-Bi) which are not strongly bonded. Also some glasses, when heated above the softening point, seem to change their coordination numbers and become metallic.The theoretical models necessary to describe these results are outlined. In liquid metals and most amorphous metal films, the Ziman theory should be applicable, giving a conductivity equal to Se2L/12π3ħ, where S is the Fermi surface area and L the mean free path. When this is about 3000 Ω–1 cm–1, L is comparable with the distance between atoms and it cannot be smaller. For materials such as liquid Te for which the conductivity is lower, a “pseudogap” affects the conductivity. The lowest possible metallic conductivity is about 200 Ω–1 cm–1. For materials (liquids or non-crystalline solids) with lower conductivity, the current is due either to electrons excited to the “mobility shoulder” or to hopping conduction of the kind familiar in impurity conduction. A real gap (as contrasted with a pseudogap) must exist in transparent materials, and can be understood in terms of the tight-binding approximation.
TL;DR: In this paper, a rarefied gas over an infinite plane wall is considered on the basis of a relaxation model of the Boltzmann equation and the solution is obtained in the form: Hilbert solution and boundary layer term which is appreciable only in a thin layer adjacent to the boundary.
Abstract: Flow of a rarefied gas over an infinite plane wall is considered on the basis of a relaxation model of the Boltzmann equation The solution is obtained in the form: Hilbert solution and boundary layer term which is appreciable only in a thin layer (with thickness of order of the mean free path) adjacent to the boundary The Hilbert part dominates in the region away from the boundary By using these results the asymptotic behavior (for small mean free path) of plane compressible Couette flow is investigated
TL;DR: In this article, the effects of sample purity on the excess conductivity of Al films were measured and it was shown that excess conductivities were strongly dependent on the electronic mean free path in contrast with the theory of Aslamazov and Larkin.
TL;DR: In this article, the authors reported the singlet-singlet excitation spectrum of triplet exciton phosphorescence for pure single crystals of hexachlorobenzene and compared with the direct absorption spectrum.
Abstract: The singlet-singlet excitation spectrum of triplet exciton phosphorescence for pure single crystals of hexachlorobenzene is reported and compared with the direct absorption spectrum. The observed antibatic behaviour is explained by a mechanism of diffusive random walk of the triplet exciton with surface quenching. No singlet exciton dominated rate processes were detected. The measured diffusion coefficient Dc*c* perpendicular to the ab plane was 2.4 × 10−5cm2sec−l. The diffusion coefficient for charge carriers was measured to be 10−2 cm2 sec−1. The mobilities of these charge carriers were μ+ = 1.2 cm2 V−l sec−l and μ− = 0.96 cm2 V−1 sec−l. The temperature dependence of Dc*c* was studied. There was no evidence for long-range trap-to-trap migration of the exciton. Above 115 °K no temperature dependence of the mean free path was observed. From the measured spectral band width of the polarized absorption spectrum the mean exciton scattering time was calculated as 2.4 × 10−14 sec. The combined coulomb...
TL;DR: In this paper, the radiofrequency size effect (RFSE) was investigated on a hollow box of which a part of the upper side was a pure metal sheet of tin and the experiments were conducted on a single-input single-out (SISO) channel.
Abstract: Transmission experiments on the radio-frequency size effect (RFSE) are described, from which the temperature-dependent part of the mean free path as well as its absolute value are determined. A comparison is given with the results of Gantmakher and Sharvin on the limiting point-size effect and on the parallel RFSE. The experiments were done on a hollow box of which a part of the upper side was a pure metal sheet of tin.
TL;DR: In this article, the authors solved the ambipolar diffusion problem when charged particles inertia and heating of positive ions together with the ion mobility variation in the radial electrostatic field are taken into consideration.
Abstract: The ambipolar diffusion problem is solved when charged particles inertia and heating of positive ions together with the ion mobility variation in the radial electrostatic field are taken into consideration For both constant mean free time and constant mean free path situations approximate formulae are found for the variation of drift velocity of ions and radial potential close to the wall when the collisionless sheath is assumed It is shown that the plasma column can be subdivided into three regions in the radial direction: the region of ambipolar diffusion, the transition region where the ion inertia predominates and the collisionless sheath at the wall The influence of this structure on the mass spectrometric sampling technique of a positive column is also noted
TL;DR: In this paper, Avogadro's number number number density of neutrals number density density of the charged particles particle, pressure collisional cross-section for neutral molecules ze, total charge per particle particle particle mass-mean radius absolute temperature spherical volume of the disturbance drift velocity charged particle velocity neutral gas velocity number of charges per particle mass density of particle attachment energy dielectric constant for free space efficiency efficiency for viscous generator efficiency for the limit where the charges carry most of the energy characteristic radius of a disturbance mean free path of gas molecules ion mobility neutral gas viscosity
TL;DR: In this paper, the problem of determining the crystal thickness at which the kinematical theory can be used in electron diffraction is discussed by calculating distribution functions over the number of scattering events from the N beam dynamical theory.
Abstract: The problem of determining the crystal thickness at which the kinematical theory can be used in electron diffraction is discussed by calculating distribution functions over the number of scattering events from the N beam dynamical theory. We consider coronene (C24H12) as representing a model for a biological crystal having a rather large unit cell and a large number of excited beams in the Laue case. For a thick crystal a symmetrical Poisson distribution is obtained, and this leads to a mean free path for elastic scattering of 83 A for coronene at 100 kV. In the limiting case of one unit-cell dimension of thickness at 100 kV, it is found that the kinematical theory should be a good approximation, the multiple scattering error being 5%. The possibility of decreasing multiple elastic scattering errors by raising the accelerating voltage is considered, and when Fujiwara's relativistic corrections are taken into account the improvement above 500 kV is predicted to be negligible.
TL;DR: In this paper, the effect of Griffith flaws on the strength of glass-tungsten composites was investigated for small sizes of Griffith faults, and the results were in good agreement with those calculated by Fullman's equation.
TL;DR: In this paper, a magnetically reversible type-II superconductor with both a high Ginzburg-Landau parameter (κ g > 1) and with BCS coherence length > electronic mean free path was obtained.
TL;DR: In this paper, it is argued that the strong T 2 term, found in the bulk resistivity at low temperatures, is not a consequence of electron-electron collisions, but is caused by an averaging, over the entire Fermi surface, of temperature dependences which are different for different regions because of Umklapp scattering.
Abstract: The variation of electrical resistivity of thin rectangular, single crystal films of 99.9999% gallium has been investigated from 1.1° to 20°K, as a function of crystalline orientation, for thicknesses between 40 and 250 µ. As long as the ratio of the thickness to the average bulk mean free path ≪1, the ideal resistivity is proportional to a power which depends on the orientation of the film and which varies betweenT 3 andT 1.5 . It is argued that the strongT 2 term, found in the bulk resistivity at low temperatures, is not a consequence of electron-electron collisions, but is caused by an averaging, over the entire Fermi surface, of temperature dependences which are different for different regions because of Umklapp scattering. For the thinnest specimens size effects are appreciable up to 15°K, but there is both quantitative and qualitative disagreement between our results and the theoretical calculations of Fuchs, which are for an idealized metal. Attempts are made to show that a change in the nature of the bulk scattering mechanisms can be deduced by comparing our data with Fuch's predictions.
01 Jan 1970
TL;DR: In this article, NMR measurements of the spin-lattice relaxation time T1 have been carried out in niobium metal, in order to investigate the elementary excitation spectrum in the superconducting mixed state.
Abstract: Pulsed NMR measurements of the spin-lattice relaxation timeT1 have been carried out in niobium metal, in order to investigate the elementary excitation spectrum in the superconducting mixed state. The dependences ofT1 on temperature, external field, and mean free path were determined. The results below ∼5°K were in agreement with the theory of field-induced gapless superconductivity. The best fit was obtained with a scale factor 0.35±0.2, in agreement with recent ultrasonic attenuation results. Anomalously fast relaxation was observed above ∼5°K, which could not be interpreted in terms of the present theory of thermal vortex fluctuations.
TL;DR: In this article, the authors used the theory of Tinkham to estimate the electronic mean free path for thin metal films quenched at liquid He temperatures using the observed variation of the critical field.
TL;DR: In this article, the relation between particle loss and fluctuation level is studied, and a comparison of the plasma loss in stable and unstable regions is made, where wave diffusion is estimated from correlation measurements.
Abstract: The relation between particle loss and fluctuation level is studied. Stable discharges are found in hydrogen under conditions of long mean free path and high shear, and with gases of high mass under almost all conditions. A comparison is made of the plasma loss in stable and unstable regions. Wave diffusion is estimated from correlation measurements. Particle loss rate and fluctuation level are found to be essentially uncorrelated.
TL;DR: In this paper, a new measurement of the plasmon mean free path in aluminium based on a new experimental method is reported, which is the first measurement of this path in aluminum.
Abstract: The generalized Holstein‐Biberman transport theory developed in Part I is used to calculate the effect of reflecting walls in increasing the decay time of Doppler broadened resonance radiation in cylinders and slabs. The results are compared with the corresponding results obtained from the Cayless diffusion theory for optical thicknesses between about 20 and 3000. It is shown that the Cayless theory grossly underestimates the effect over the entire range, giving values for the fractional increase in decay time which are too small by about a factor of 3 at the smaller optical thicknesses, and too small by about a factor of 30 at the larger thicknesses. The discrepancy is shown to arise partly from the inaccurate boundary condition used in the Cayless theory and partly from the inapplicability of the mean free path concept to processes involving the transport of resonance radiation. The consequences for the behavior of low‐pressure mercury rare‐gas discharges are discussed, and it is estimated that wall reflectance must begin to have a significant effect on the characteristics of such discharges at reflectances as low as 20% rather than at the 50% reflectance predicted by the Cayless theory.
TL;DR: In this paper, the transition from continuous to rarefied flow for spherical and cylindrical gas sources for rigid and Maxwellian molecules is studied using the concept of the anisotropy of the mean free path length.
Abstract: Using the concept of the anisotropy of the mean free path length we study the transition from continuous to rarefied flow for spherical and cylindrical gas sources for rigid and Maxwellian molecules.