Showing papers on "Mean free path published in 1976"

Saturation of the high-temperature normal-state electrical resistivity of superconductors

Abstract: The high temperature, normal state resistivity of strong coupled superconducting transition metal compounds and other materials with high resistivities saturates at a value corresponding to an electron mean free path of order the interatomic spacing. This accounts for the nonlinear temperature dependence of the resistivity observed in these compounds at high temperature.

Compton scattering opacities in a partially degenerate electron plasma at high temperatures

Abstract: We solve the integral equation for the Compton scattering mean free path, in a partially degenerate electron gas at high temperature, where this process dominates the photon transport. We avoid two approximations which were made in previous calculations and correct an error in the literature. Finally we give an expression for the Rosseland mean opacity. (AIP)

Electrical resistivity, TCR and thermoelectric power of annealed thin copper films

Abstract: The electrical resistivity, temperature coefficient of resistance (TCR) and thermoelectric power are measured on systematically annealed copper films formed by the vacuum evaporation method. From the measured quantities the scattering coefficient and the bulk mean free path of the conduction electrons are calculated. The electron mean free path is found to be 410+or-100 AA. The energy dependence of mean free path U and the energy dependence of Fermi surface area V are calculated from the thermoelectric power measurements as a function of thickness. Both U and V are found to be negative and thickness-dependent.

Thermal properties of dilute (La, Ce) Al2 alloys

Abstract: We report on measurements of the specific heat and transport properties (resistivity, heat conductivity and thermopower) of dilute (La1−x Ce x )Al2 alloys withx≦0.04 between 0.3 and 10 K. The specific heat experiments were extended to a magnetic field of 47 kOe; the transport measurements were performed on single crystals. For Ce concentrations less than 0.5 a/o Kondo type single impurity behavior was observed for all quantities under investigation. A mean Kondo temperature $$\bar T_K = (0.36 \pm 0.06) K$$ was obtained from the “S=1/2 exchange model” using our own data taken in the normal as well as in the superconducting state and data from the literature. Whereas neither the mean free path nor interimpurity correlations were significantly reflected in the specific heat, they obscured the transport properties above 0.5 a/o. The influence of crystal field excitation and band structure effects on the experimental results is also discussed.

Use of generalized orthogonal polynomial solutions of Boltzmann’s equation in certain aeronomy problems: Auroral ion velocity distributions

Abstract: We present a method of solution of Boltzmann's equation that is valid for conditions where the species velocity distribution function departs significantly from a Maxwellian. This method should be particularly useful for problems in aeronomy and space physics where there are large or rapidly varying forces acting on a neutral or ionized gas or for problems dealing with highly rarefied gases where the mean free path for collisions is comparable to or greater than the characteristic scale length of the problem. The method of solution, which was first introduced by Mintzer, corresponds to expanding the species distribution function in a generalized orthogonal polynomial series with an arbitrary weight factor. The specific form of the weight factor depends on the details of the problem. The method is illustrated by calculating auroral ion velocity distributions for a relaxation collision model, and the results are compared with the velocity distributions obtained from an exact solution to Boltzmann's equation.

Experimental study of diffusion charging of aerosols

Abstract: The electrical charging of aerosol particles by unipolar gaseous ions was studied theoretically and experimentally. The primary objective of the study was to make precise determinations of the aerosol particle charge under various conditions of charging and to compare the experimental results with those predicted by theory. Experiments were performed using monodisperse oleic acid aerosols generated by a vibrating orifice generator, monodisperse NaCl and DOP (di-octyl phthalate) aerosols generated by an electrostatic classification method, and sulfuric acid aerosols generated by the photo-chemical conversion of gaseous SO/sub 2/ in the smog chamber. The experiments covered a particle size range of 0.0075 ..mu..m to 5.04 ..mu..m diameter. The corresponding range in Knudsen number (Kn = lambda/sub i//a, lambda/sub i/ = mean free path of ions, a = particle radius) was from 0.0056 to 3.86. The charging parameter, n/sub 0/t, was varied between 2.56 x 10/sup 6/ to 5.1 x 10/sup 7/ ion-s/cc, where n/sub 0/ is the concentration of ions and t is the charging time. Comparisons of the results with available aerosol charging theories indicate that there is reasonable agreement between the theory and experiment in the continuum regime (Kn > 1) and the transition regimes (Kn approx. or equal to 1), where the ion mean free path is no longer small in comparison with particle size, there is considerable discrepancy between the experimental data and available charging theories. A semi-empirical equation was developed which agrees well with the experimental data over the entire range of particle size and charging parameters covered in the experiments. Theoretical results are presented showing the distribution of charges on the particles as a function of particle size and the charging parameter n/sub 0/t. 70 figures, 24 tables, 112 references. (auth)« less

Cross-field energy transport by plasma waves

Abstract: Energy transport across a magnetic field by plasma and ion waves is shown to be an important process even in thermal equilibrium, because their propagation is uninhibited by the magnetic field and their long mean free path.

Low-field magnetoresistance in metals

Abstract: Low-field magnetoresistance and Hall coefficient are calculated in the anisotropic-relaxation-time approximation. Simple results are obtained for Fermi-surface models which can be composed of spherical, cylindrical, and planar surfaces. Influences of the Fermi-surface geometry and the scattering anisotropy on the low-field magnetoresistance are discussed. With small modifications the method is applied to polyvalent metals with nearly-free-electron Fermi-surfaces. Simultaneous magnetoresistance and Hall-coefficient measurements combined with a three-group model calculation for the electronic mean free path are suggested as a means to determine the anisotropy of the electronic scattering in nearly-free-electron-like polyvalent metals. In an Appendix the results are extended to the longitudinal magnetoresistance.

Anisotropic size effects in semiconductors and semimetals

Abstract: Large differences between the characteristic times of various electronic relaxation processes (momentum relaxation, energy relaxation, intervalley relaxation, electron-hole recombination) make it possible to divide carriers into groups between which relaxation is relatively slow. Each of the "long" relaxation times can be matched by a characteristic diffusion length which is much greater than the usual mean free path. Transport coefficients of such groups are generally anisotropic even in cubic crystals and the anisotropy varies from group to group (this anisotropy may be natural or it may be induced by pressure, magnetic field, etc.). Therefore, the passage of a current produces nonequilibrium carrier densities in such groups. The density gradients are oriented at right-angles to the current and they decay over distances of the order of the diffusion length. The effects associated with the formation of nonequilibrium carriers and the influence of their diffusion on the transport coefficients are referred to in the paper as the anisotropic size effects. The paper reviews experimental and theoretical investigations of various manifestations of such effects. An analysis is made of the size dependences of the electrical conductivity and magnetoresistance manifested in "thick" samples (thickness of the order of the diffusion length). Other topics considered include nonlinearity of the electrical conductivity in relatively weak fields, redistribution of carriers in "strong" fields (accompanied by giant changes in the total number of carriers and by formation of domains, depletion layers, and accumulation layers), influence of the anisotropic size effects on the skin effect (which changes the surface impedance of semimetals by an order of magnitude), and electromagnetic excitation of sound in semimetals.

Double-probe theory for a continuum low-density plasma

Abstract: A theoretical treatment is given for the double-probe method in an electron/positive-ion plasma having mean free path

Hall effect in thin films of gold-silver alloys

Abstract: Measurements on Hall constant and magnetoresistance of thin films (350 A-800 A) of Ag-Au alloys with concentrations up to 20% gold have been made. An effective relaxation time is deduced from the variation of the Hall coefficient with the concentration which is found to be proportional to the mean free path of the electrons. The mean free path of the film decreases by about a factor of 3 from the bulk value for silver on the addition of gold to silver. The results are consistent with those of other workers who have used different methods and also indicate that the relaxation time is anisotropic in thin films of alloy. Size effects have also been discussed.

Monte Carlo studies of hot‐electron energy distribution in thin insulating films. I. Constant mean free path and a one‐dimensional simulation

Abstract: The hot‐electron energy distribution produced in a high electric field F across a thin insulating film is studied by Monte Carlo calculations on a digital computer. The dominant electron collisions are assumed to be those with the lattice, producing single optical‐phonon emissions of energy eph. The mean free path λ is taken as a constant independent of energy, and both isotropic and anisotropic scattering are studied. A scaling law for the average electron energy Eave,ss in the steady‐state distribution, previously found analytically for isotropic scattering, namely, Eave,ss=k (Fλ)2e/ph, is found to hold also for anisotropic scattering, k being a numerical constant determined by the detailed nature of the scattering law. Forward scattering produces larger values of k, backward scattering smaller values. No matter how strongly peaked the forward scattering, short of exact (ϑ=0) forward scattering, there is a finite steady‐state distribution. An analogous scaling law is found for the development distance D...

Viscosity of vortices in pure superconductors

Abstract: The vortex viscosity at low temperatures was obtained for pure superconductors with electron mean free path l satisfying the conditions vT/sup -1/<

Temperature dependence of hole mobilities in Te thin films

Abstract: Results are given of measurements of the temperature dependence of electrical conductivity, Hall constant, and Hall mobility of holes in Te thin films. Two series of samples with different thicknesses, prepared at two condensation rates, 1.21 and 8.60 nm/s, are measured. The temperature courses of bulk values of the hole mobility which satisfy the conception concerning the scattering of holes by barriers on grain boundaries, where the mean distance of these barriers is larger than the mean free path of holes in crystallites, are obtained by evaluating the results according to Petritz' model. It appears that the barrier height is dependent on film density. [Russian Text Ignored]

Source emission and photoelectron production in a seeded CO2 laser mixture

Abstract: Measurements of spark source emission, transmission, and photoionization spectra in a CO2 laser mixture seeded with a low‐ionization‐threshold additive are presented. The results show a photoelectron density enhancement in excess of 3 orders of magnitude contained within a narrow transmission band at 1200 A. Enhancement is also observed at wavelengths between 1700 and 2100 A. The long‐wavelength effect, characterized by an increased photon mean free path, may identify a two‐step photoionization process.

Coherent multiple production in proton-nucleus collisions at 200 and 300 GeV/c

Abstract: Two stacks of nuclear emulsion were exposed to 205- and 303-GeV/c proton beams. By following the beam protons, inelastic events induced by proton-nucleus collisions are obtained. Then the mean free path for coherent production and its energy dependence are studied. Finally, a feature of the target--mass-number dependence of the cross section for the inelastic proton-nucleus collision is shown. (AIP)

Magnetic field dependence of the microwave surface resistance of pure niobium

Abstract: The microwave surface resistance of pure niobium has been measured in magnetic fields up toH c3 . The surface resistance in the mixed state state was found to depend strongly on the mean free path, in contrast to the earlier theory of Caroli and Maki but in agreement with the recent theoretical work of Cerdeira, Houghton, and Maki. Neglect in the theory of the surface solution for the order parameter limits the value of making comparisons with our results except in the orientation where the steady magnetic field is perpendicular to the surface. In this orientation we have found the slope of the curve of surface resistance plotted against flux density to be proportional to mean free path, as predicted by the recent theory. The theory has been developed only for absolute zero, and so in order to make comparisons we have extrapolated an empirical scaling procedure that reduces data at different temperatures to a single curve. Estimates of the constant of proportionality in the mean-free-path dependence are limited in accuracy by the present uncertainty in the values of κ 2 (T). Although both the earlier and recent theories purport to deal with the anisotropy of the surface resistance when the direction of the steady magnetic field is varied with respect to the wave vector of the electromagnetic field but is kept perpendicular to the microwave current, neither includes the large shielding effects produced by the vortex-free layer that can exist at the real surface and persist up toH c3 . Agreement with the mean free path dependence predicted by the recent theory could not be achieved by incorporating measurements aboveH c2 into a simple layer model to adjust the measured values of the surface resistance with the steady field parallel to the surface. However, the discrepancy between the predicted and measured anisotropies was reduced by this procedure. Other aspects of our experimental results that fall outside the range of validity of the recent theory are compared with general features established by earlier experimental and theoretical work on impure type II superconductors. In particular, the anisotropy of the surface resistance in fields just belowH c3 was found to be temperature independent, as predicted by Thompson and confirmed by Monceau and Waysand. The observed magnetic hysteresis effects in the mixed state are discussed in relation to the nascent vortex model and to the existence of an oxygen-rich surface layer.

Numerical modeling of suprathermal electron transport in laser-produced plasmas. Report number 36

Abstract: Supra-thermal electrons can radically alter the dynamics of imploding laser fusion targets by preheating the target material, by transforming energy to a rapid ion blowoff or, due to mean free path effects, decoupling the core from the corona. In order to correctly simulate the dynamics of a laser driven target, it is necessary to develop an accurate physical and computational model of these electrons. The difficulties inherent in this problem can be appreciated by noting that the supra-thermal velocities can vary by over an order of magnitude while the density of the background thermal electron fluid through which they propagate can vary by over four orders of magnitude. Since the supra-thermal mean free-path is proportional to v{sup 4}/n{sub e}, there can be an eight order of magnitude variation in this scaling parameter. Since the transport of supra-thermal electrons must be followed in both the diffusive and free streaming limits, neither flux limited diffusion models nor truncated moment methods are adequate. A three component model of transport of supra-thermal electrons is developed here to satisfy all requirements discussed in this paper.

Monte Carlo studies of hot-electron energy distributions in thin insulating films. II. Energy-dependent mean free path and instability

Abstract: Monte Carlo calculations are used to study theoretically hot‐electron transport through a thin insulating film subjected to a high uniform electric field F. A constant energy‐independent mean free path λ leads to a stable steady‐state energy distribution for the electrons, characterized by an average steady‐state energy Eav,ss. Eav,ss depends on λ, F, and eph, the optical phonon energy associated with scattering of the hot electrons by the lattice. An energy‐dependent mean free path λ (E), which increases with increasing electron energy, can lead to energetic runaway of either a relatively small number of electrons in the distribution (quasistability or a bimodal distribution) or the entire distribution (instability). A graphical method has been developed to gain insight into this problem. The method rests on an analysis of the intersections of two curves plotted in the E‐λ plane, one curve being the plot of Eav,ss versus λ, where λ is the mean‐free‐path parameter taken to be constant (energy independent)...

Multigroup radiation cross sections of high temperature uranium plasmas

Abstract: Multigroup cross sections for thermal radiation in a uranium plasma at solid state density and temperatures in the KeV range are presented. Bound-free and free-free absorption is taken into account. Compton scattering is approximately described by the Thomson formula and by the Compton cross section for free electrons at rest. The results contain tables of one-group Rosseland means of the mean free path (valid in the optically thick limit) and of six-group Planck absorption and scattering cross sections (valid in the optically thin limit).

Inverse Mean Free Path, Stopping Power, CSDA Range, and Straggling in Silicon and Silicon Dioxide for Electrons of Energy < or = 10 keV.

Abstract: : The interaction of electrons with the solids Si and SiO2 is described based on a 'modified electron gas model' for the valence band electrons in Si, a model insulator theory for the valence band electrons in SiO2, and inner shell ionization derived from atomic, generalized oscillator strengths. Contributions to the inverse mean free path and stopping power from the various interaction processes are tabulated for electron energies from threshold ((approximately equal) 4 eV above Fermi level) to 10 keV for Si and from 10 eV to 10 keV for SiO2. Electron range in the continuous slowing-down approximation and straggling are tabulated for electron energies from 10 eV to 10 keV for both materials.

Resistivity anomalies for ferromagnetic metals at Curie points. II. Short-range magnetization fluctuations

Abstract: Using the itinerant model of magnetic moment in ferromagnetic metals, we have investigated the resistivity anomalies near the Curie temperatureT c . In this paper, the short-range magnetization fluctuations have been taken into account in calculating the spin correlation function in the paramagnetic region. The mean free path is considered to be comparable with the correlation length and to be temperature dependent nearT c . A critical exponent is introduced for the mean free path and its value is established to be not smaller than 1/2. The resistivity is found to be continuous throughT c . The temperature derivative of the resistivity is found to be divergent linearly and positively near and aboveT c . These results confirm the phase transition nature of the resistivity anomalies of the ferromagnetic metals nearT c and show that the short-range order must also exist in the itinerant model of the magnetic electrons.

Quasi-one-dimensional fluctuation contribution to ultrasonic attenuation in clean type-II superconductors above T c ( B )

Abstract: We have calculated the effect of fluctuations on the ultrasonic attenuation in a clean bulk type-II superconductor at temperatures above the transition temperature and in magnetic fields near the zero-temperature upper critical field, where the fluctuations are effectively one dimensional. The result is a decrease in the attenuation which should be observable experimentally. The effect increases with increasing mean free path.

The theory of the effect of anisotropic scattering by impurities on the electromagnetic response of superconductors

Abstract: The usual theory of scattering by non-magnetic impurities in superconductors is extended to cases where the scattering is not isotropic and the mean free path, l, is not very short. The starting point is the equation for the vertex function from which the electromagnetic response of the superconductor is derived. The anomalous limit, ql>>1 where q is a typical wavevector of the field, is studied in some detail and, in particular, the dependence of penetration depth on mean free path is derived. The results show that anisotropic scattering gives rise to measurable deviations from the theory of Mattis and Bardeen (1958).

Experimental results on scattering and absorption of phonons in dilute 3He-4He mixtures

Abstract: Measurements are presented on diffusive phonon signals in 3 He- 4 He mixtures. The results are described by an absorption and scattering parameter α, determined by the effective mean free path, and an absorption rate β, as functions of the molar 3 He concentration in the range X ⩽ 5 × 10 −3 , and of the temperature in the range 50 mK T

Inverse Mean Free Path, Stopping Power, CSDA Range, and Straggling in Ge and GaAs for Electrons of Energy Less Than or = 10 keV.

Abstract: : The interaction of electrons with the solids Ge and GaAs is described based on a model insulator theory for the valence band electrons and inner shell ionization derived from classical-binary-collision cross sections. Contributions to the inverse mean free path and stopping power from the various interaction processes are tabulated for electron energies from threshold (approximately 2 eV for Ge and approximately 2.5 eV for GaAs) to 10 keV. Electron range in the continuous slowing-down approximation and straggling are tabulated for electron energies from 10 eV to 10 keV for both materials.