Showing papers on "Mean free path published in 1969"

Rarefied Gas Dynamics

Abstract: Rarefied gas dynamics is concerned with flows at such low density that the molecular mean free path is not negligible. Under these conditions, the gas no longer behaves as a continuum. Important modifications in aerodynamic and heat transfer characteristics occur which are ascribable to the basic molecular structure of the gas.

Gamma Response of Semi‐insulating Material in the Presence of Trapping and Detrapping

Abstract: The photoelectric and Compton response to γ rays for a detector made from semi‐insulating material (i.e., a monocrystalline semiconductor containing trapping centers) was calculated for the case of charge transport by one type of carrier (electron or hole), and also for the case of two‐carrier transport (electron and hole) with each carrier having the same mean free path. Approximate expressions were then derived for the observable γ‐ray efficiency of the detector as a function of material parameters for CdTe crystals used in the fabrication of surface barrier detectors; this efficiency is dependent upon temperature and electric field intensity for specified values of the carrier mobility‐trapping time product and the threshold used in the recording of spectra. Spectra and values for efficiency were determined at room temperature for γ rays at energy values from 0.393 to 1.33 MeV, and also as a function of temperature over the range 24° to 68°C for γ rays from a 60Co source. The observations show behavior...

The Transport Equation in the Case of Coulomb Interactions

Abstract: A transport equation is derived for a system consisting of charged particles taking their interactions into account The order of magnitude of the mean free path of the particles in such a system is determined The rate at which the temperatures of the ions and electrons in the plasma become equal is evaluated

Semiconductor device with superlattice region

Abstract: The semiconductor device has two highly N-type end portions to which ohmic contacts are made, and a central portion which has a one dimensional spatial periodic variation, in its band-edge energy. This spatial periodic variation, or superlattice, is produced by doping or alloying to form a plurality of successive layers having alternating band-edge energies. The period of the spatial variation is less than the carrier mean free path, and is such as to form in momentum space a plurality of periodic minizones which are much smaller than the Brillouin zones. The device exhibits a bulk negative resistance and is used in oscillator and bistable circuits.

Slow-wave structures utilizing superconducting thin-film transmission lines.

Abstract: Slow‐wave propagation of electromagnetic waves in transmission lines formed of thin‐film superconductors has been studied theoretically and experimentally. Previous theoretical analyses have been extended to include nonlocal theories. Strong dependence of phase velocity is found on film thickness and interfilm spacing when these become less than a few penetration depths. Velocity is also modified by coherence length, mean free path, nature of reflection of electrons at the film surfaces, and by temperature and magnetic field. Experimental measurements were made to verify the dependence on thickness, spacing, and temperature by means of a resonance technique. Agreement with theory was excellent in the case of temperature. Data taken for varying thickness and spacing verified the general trend of theoretical predictions. They indicate a nonlocal behavior with some specular reflection, but scatter of the data taken for different films prevents precise comparison of theory and experiment. Estimates of bulk penetration depths were made for indium, λIn = 648±130 A. For tantalum a rough estimate could be made of λTa = 580 A. Data were consistent with the estimate of coherence length for indium of ξ0 ≈ 3000 A. Velocity was found to be independent of frequency in the range 50–500 MHz, while losses increased as the square. Pulse measurements indicated that delays of several microseconds and storage of several thousand pulses on a single line are feasible.

Superconducting Metals in Porous Glass as Granular Superconductors

Abstract: The critical fields of superconductors in porous glass are found to have the same temperature dependence as the critical field of a homogeneous dirty alloy. An effective mean free path for electrons in the normal state can be deduced; it is proportional to the pore diameter but is much smaller. This is most easily explained if the superconductor consists of grains separated by tunneling barriers, for this gives a mean free path equal to the grain size multiplied by an average of the transmission coefficient of the barriers. This model can also give a plausible explanation of the large change in critical field produced by chemical treatment of the glass before impregnation with metal. Parmenter's theory of granular superconductors shows that vortices can exist in such materials, and the critical current should be determined by vortex pinning. The measured critical current for indium in porous glass is less than that calculated from a Parmenter formula which assumes that the fields in the sample are uniform.

Energy gap, transition temperature and electron-electron interaction of the weak coupling superconductors tin and indium as a function of the mean free path of the electrons

Abstract: The energy gap and the transition temperature of the weak coupling superconductors tin and indium are measured as a function of the mean free path of the electrons. Both of them increase with decreasing mean free path. The ratioα=2Δ 0/kTc increases proportionally to the reciprocal mean free path from 3.6 to 4.0 for tin and from 3.6 to 3.95 for indium. A theoretical consideration is presented showing that the electron-electron interaction is increased in dirty superconductors. Without any fit we find from the theoretical calculation an increase inNV for indium ofδNV=5 · 10−10 m/l tr and for tinδNV=2 · 10−10 m/l tr (ltr is the transport mean free path of the electrons). The experiments give an increase inNV for indium ofδNV=4.2 · 10−10 m/ltr and for tinδNV=1.7 · 10−10 m/l tr. The agreement is surprisingly good.

Charge transport in non-crystalline semiconductors

Abstract: A description is given of the theory of the transport properties of electrons in non-crystalline solids and liquids. Two different mechanisms by which an electron can move are distinguished. One is that familiar in crystalline semiconductors and metals, in which the mobility is not thermally activated and a mean free path can be defined. The other is thermally activated hopping which occurs particularly in impurity conduction, and in which the electron jumps from one localised state to another with the emission or absorption of phonons. When the electron states are localised, the conductivity tends to zero with the temperature, even though the density of states is everywhere finite. Some experimental work is described which distinguishes the two types of charge transport and shows what happens at the transition between them. This includes impurity conduction in compensated semiconductors and conduction in cerium sulphide containing a high concentration of vacancies. The model established by this work is applied to chalcogenide glasses and to amorphous germanium. It is shown also that it provides a satisfactory explanation for the behaviour of threshold switches making use of a conducting glass as the heart of the device.

Axially Symmetric Expansion of a Monatomic Gas from an Orifice into a Vacuum

Abstract: The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas‐vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.

Acoustoelectric amplification in InSb

Abstract: It was demonstrated by Kikuchi that two modes of acoustoelectric domain oscillation occuirn InSb in a transverse magnetic field. Using lithium niohate transducers on an acoustic amplifier, we have measured linear acoustic gain as a function of electric and magnetic field and frequency. At high magnetic fields (B ≥ 3000 gauss) the results arein good agreement with White's theory. However, at low magnetic fields, the wavelength of the sound waves is lesst han the mean free path of the electrons, and the macroscopic theories break down. We have extended a microscopic theory of magnetacoustic interactions, duet o Spector, to include electron drift. We find excellent agreement between theory and experiment over the whole range of magnetic field. Moreover, the results account very clearly for the two modes of acoustic domain formation.

The electrical properties of dislocations in silicon—II: The effects on conductivity

Abstract: Conductivity measurements were made on both n -type and p -type silicon which contained parallel arrays of edge dislocations. The dislocation densities were of the order of 10 6 -10 7 per cm 2 and were introduced by plastic deformation at 750°. Measurements parallel and perpendicular to the array show that the conductivity is highly anisotropic, indicating that space charge cylinders surround the dislocation in both material types. These results imply that the dislocation has an acceptor state which is active in n -type material and a donor state which is active in p -type material. In n -type material, the data are consistent with the cylindrical void model of Read if the model is modified to include scattering by the space charge cylinder. For the current parallel to the dislocation this modification results in the electrons within one mean free path of the space charge cylinder having a mobility reduced by 50 per cent at low temperatures and by 80 per cent at high temperatures. In p -type material the data cannot be as easily explained. The data are, however, qualitatively in agreement with the donor band model suggested earlier, if it is assumed that the density of donor states decreases with increasing electron energy.

Quantum and classical size effects in the thermoelectric power of thin bismuth films

Abstract: Anomalous behaviour of the thermoelectric power of thin Bi films has been observed and the results are consistent with those anticipated, based on both quantum and classical size effects in scattering. Mayer's theory relating thermoelectric power to film thickness can be applied to the present results provided that the bulk conduction electron mean free path is used for calculations of the thermoelectric power of thick specimens and that the conduction electron de Broglie wavelength is used for thin specimens.

The condensation coefficient of liquid helium ii.

Abstract: The condensation coefficient (defined as the fraction of gas atoms striking the liquid-vapour interface which cross it to form part of the liquid) has been measured for liquid helium II from 1° K to the λ point, and was found to be not less than 090 and probably unity. The measurements, made by reflecting second sound pulses from the surface, are not in agreement with the macroscopic theories of Osborne and of Chernikova; the former theory gives agreement with experiment when modified to take account of conditions in the vapour a fraction of a mean free path above the surface. The problem of providing a microscopic interpretation of these results is briefly discussed.

Scattering of long-wavelength phonons by point defects in cubic lattices

Abstract: The phase-shift method in solid state scattering theory is applied to the study of the scattering of long-wavelength phonons by point defects in the cubic lattice model of Montroll and Potts. Expressions for the mean free path and Debye temperature are derived for a solid containing a small concentration of point defects.

D.C. Electric Conductivity in Films of Aluminum Fine Particles Prepared by Evaporation in Helium Gas

Abstract: It was reported in a previous paper that aluminum granular films prepared by means of gas evaporation in helium showed enhanced superconductivity. In the present experiment, a temperature dependence of D. C. electrical resistivities of these films is measured by means of a four contact method. It is found that absolute values of the resistance depend on the film thickness but the most of the films show temperature independent resistivity. These features are interpreted in terms of electronic mean free path and the particle size of the films.

Evidence of anisotropic mean free path as furnished by galvanomagnetic measurements

Abstract: If in the Boltzmann equation, written with an ansiotropic relaxation time,τ(k), a suitable substitution of variables is carried out, it is found that Kohler's rule is valid as long as the quotient of the mean free path,l(k), and an average relaxation time\(\overline{\overline \tau } \) remains constant. Deviations from Kohler's rule in the case of comparing field and temperature dependence of the galvanomagnetic effects for different metals and varying crystal orientation lead to the conclusion that the anisotropy of the relaxation time changes with temperature.

Weak interaction of photons and neutrino-electron scattering

Abstract: The neutrino-electron scattering has been discussed according to the photon-neutrino weak-coupling theory. The results are then compared with those obtained in the current-current coupling theory. The rate for neutrino-electron scattering has also been discussed for nondegenerate and degenerate gases. Astrophysical applications are then made by evaluating the ratio of the neutrino mean free path to the stellar radius. It is shown that, according to the photon-neutrino weak coupling, the neutrino mean free path exceeds the stellar radius for massive stars, white dwarfs and neutron stars. This result is significant in the sense that according to the current-current coupling theory, the ratio of the neutrino mean free path to the stellar radius for neutron stars can be much less than unity, though for other types of stars the neutrino mean free path exceeds the stellar radius. Finally, some remarks are made about the experiment attempted by Reines and Kropp to detect solar neutrinos using knock-on electrons produced in the neutrino-electron scattering.

Near-surface electron temperature of weakly ionized plasma according to kinetic theory.

Abstract: Properties of electrons near absorbing and emitting surfaces are studied for weakly ionized plasmas by analyzing the Boltzmann equation governing the electrons. For simplicity, it is assumed that the electric field intensity is given a priori. It is shown that there exists a “nonequilibrium absorption layer,” near the surface, wherein the kinetic distribution of electrons is completely out of equilibrium for all values of the mean free path, when the surface is highly absorbent with small or no electron emission. This layer is responsible for the large electron temperature jump at the surface, and it governs the electron temperature profile through the continuum as well as the rarefied plasmas. From the analysis it is found that the simple surface boundary condition for the continuum electron energy equation previously employed by the present author is correct when there is no surface emission. A similar simple surface boundary condition is deduced for surfaces with given finite emission rates.

Dynamic Critical Fluctuation of Superconductivity Order Parameter above the Transition Point

Abstract: Dynamic correlation function of fluctuation field in a dirty superconductor is investigated above the transition point. . It is determined self-consistently in the critical range of temperature where the mean field theory breaks down and interactions among fluctuation modes must be taken into account. Correlation function is of diffusional type with a diffusion constant which becomes singular as (T/Tc-1)1-(4Id) where dis dimensionality. The inverse correlation lengtb is proportional to (T/T(!-1)2Id and is independent of mean free path of electron. , Electrical conductivity of a bulk system in the critical range contains a term which in­ creases like (T/Tc-l) -1/3 and which is independent of mean free path. However in a case of a film system a problem arises.

The drag of a cylinder in the transition region

Abstract: The equation for the drag of a cylinder the size of which is comparable with the mean free path of the gas molecules is derived under the assumptions of diffuse reflection and full accommodation and with the use of the concept of the “molecular layer.” The thickness of the “molecular layer” was determined from the asymptotic reduction of the derived equation to the corresponding equation in the range of small Knudsen numbers. The derived equation is analyzed and checked against the experimental data.

Ultrasonic attenuation at 500 kHz in superconducting tin

Abstract: The temperature dependence of the longitudinal ultrasonic attenuation in single crystals of white tin has been measured by a resonance technique at a frequency of 500 kHz between 1 and 4.2 $^\circ$K, for propagation along (100) and (001). The resistance ratio of the samples varied from 800 to 30 000 and in all cases the electronic mean free path is smaller than the ultrasonic wavelength. No difference is found between propagation along (100) and (001) in the most heavily doped samples, in contrast to the suggestion of Kadanoff & Pippard, although in this case the normalized attenuation curve lies above the form found by Bardeen, Cooper & Schrieffer (B.C.S.). A systematic decrease of attenuation with increasing purity is found, so that in the most pure samples the curve lies well below the B.C.S. form. This effect is more marked for (001) propagation. A simple model is used to calculate the details of elastic scattering in the anisotropic superconductor, and it is shown that scattering across the Fermi surface can account for the lack of any orientational differences. The free path of the excitations is modified by the anisotropy : this brings the theory into very good agreement with the present results, and also increases the theoretical anisotropy of thermal conductivity in tin so as to agree with experiment. Phonon scattering across the Fermi surface is shown to account for the variation of attenuation with purity ; the anisotropy of this effect is consistent with the gap anisotropy.

Experimental Determination of Thermal Accommodation Coefficients

Abstract: The free molecule flow regime of rarefied gas dynamics and heat transfer is of considerable Interest In any situation dealing with a highly rarefied atmosphere. Free molecule flow occurs when the Knudsen number Kn, is greater than about 3 where Kn = λ/L is the ratio of the mean free path λ to the characteristic length of the system L [1,2]. In a free molecule flow situation collisions between gas molecules are negligible when compared with collisions between gas molecules and the solid surfaces. Hence, a molecule may be considered to travel from one wall to the other without suffering a collision in between.

A new method for studying surface scattering of electrons in thin metallic plates

Abstract: A determination of the surface scattering, mean free path, and bulk resistivity of electrons in a specimen requires three independent experiments. A new method is proposed making use of the measurement of the first and second terms in the expansion of a decaying eddy current in a thin plate. The decay rates have been calculated and tabulated using the free electron model and assuming an isotropic electron mean free path.

Collisionless Thermalization of Electrons in a Beam‐Plasma System

Abstract: Collisionless thermalization of a stream of energetic electrons injected into a plasma has been observed by means of an electron energy spectrometer. Accurate measurements of the energy distribution of the injected electrons have shown that a mean energy loss as well as an energy spread of the injected electrons occur when the distance traveled by these electrons through the plasma exceeds 10 to 15 e‐folding lengths of the fastest growing plasma wave mode. The effects of electron‐neutral collisional damping on collisionless thermalization have also been established. It has been shown that collisionless thermalization can be inhibited, if the electron collision mean free path is made small enough, or if the effective plasma thickness is kept smaller than about 20 plasma wavelengths for the injected electrons. These experimental results have been found to be consistent with the theory of double stream interaction between injected electrons and stationary plasma electrons.

Elastic Properties of Superconductors: Nb, V, and Ta

Abstract: The magnetic field dependence of Young's modulus of type-I and type-II superconductors is used to study the properties of the intermediate and mixed states. The density and separation of vortices in the mixed state are computed from the observed field dependence of the elasticity by use of a model which allows the vortex to expand. A residual stiffness associated with trapped flux is observed to decrease at lower temperatures as a result of reduced pinning forces acting on the vortices. The pinning forces appear to be associated with more than elastic coupling done to the imperfections. The largest total change in stiffness due to the superconducting transition is associated with the longest normal-electron mean free path. Shielding of the lattice initeractions in the superconductng state appears to be more effective the longer the coherence of the superconducting pairs between scatterings. Use of elastic measurements as a means of determining bulk characteristics of the superconductor is found to be quite accurate for materials with low acoustic losses. Anisotropies in the bulk critical fields of niobium are determined simultaneously with the magnetization.

Flows of a Weakly Ionized Gas between Parallel Cold Walls

Abstract: Ambipolar diffusion between parallel cold walls in the weakly ionized gas which flows in the direction parallel to walls is investigated theoretically. The whole region is divided into three ones: the linear, non-linear and sheath regions where the linear diffusion equations, the continuum equations contaning inertia terms and the collisionless equations are used respectively. Solutions are patched and the Bohm's criterion is used to match the nonlinear and sheath regions. The thickness of the non-linear region is O (α 1/4 ). The density of electrons and ions decreases to a fraction of O (α 1/2 ) at the sheath edge. And the potential drop between the center and the walls is \(O\left(-\frac{1}{2}\frac{kT_{e}}{e}\ln\alpha^{-1}\right)\). (α∼ l i 2 / L 2 , l i is the mean free path of ions and 2 L is the distance between walls).