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Showing papers on "Mean free path published in 1968"


Journal ArticleDOI
Kazumi Maki1
TL;DR: In this article, the fluctuation of the order parameter in a superconductor in the temperature slightly above the transition temperature is studied in the framework of the current microscopic theory, and it is shown that the elec- trical resistivity, the nuclear spin lattice relaxation time and the ultrasonic attenuation co-efficient decrease like 1-ai1li- 1I2 and 1-a'i1li − 1I3 in the classical and in the critical region. respectively, where 1l= (TITe) -1 and a and a' are constants of
Abstract: The fluctuation of the order parameter in a superconductor in the temperature slightly above the transition temperature is studied in the framework of the current microscopic theory. It is convenient to divide the temperature region where the fluctuation of the order parameter becomes important into two regions; the classical and the' critical region. In the classical region the spatial correlation of the fluctuation is of the Ornstein-Zernike type, while in the critical region it depends on the relative distance like r-3/2. We show that the elec­ trical resistivity, the nuclear spin lattice relaxation time and the ultrasonic attenuation co­ efficient decrease like 1-ai1li- 1I2 and 1-a'i1li- 1I3 in the classical and in the critical region . respectively, where 1l= (TITe) -1 and a and a' are constants of the order (Telp.) 1/2 (lPo)-3/2 and (Tel p.) 1/3 (lpo) -1 respectively. Here p. is the chemical potential, l is the electronic mean free path and Po is the fermi momentum. It is also shown that the thermal conductivity has no singular term at the transition temperature.

255 citations


Journal ArticleDOI
TL;DR: In this article, the electrical conductivity of continuous thin metal films with very smooth surfaces is treated using Fuchs' model with Fuchs parameter p near 1, and it is shown that the surface scattering can be treated to a good approximation by a mean free path method.

119 citations


Journal ArticleDOI
TL;DR: In this paper, free path distributions and collision rates for systems of hard-sphere and square-well molecules are computed and compared to simple models, and mean free paths for solids and dense fluids are found to be within 2% of those predicted by dividing the kinetic-theory mean free path by the relative probability of two molecules in contact.
Abstract: Free‐path distributions and collision rates for systems of hard‐sphere and square‐well molecules are computed and compared to simple models. Mean free paths for solids and dense fluids are found to be within 2% of those predicted by dividing the kinetic‐theory mean free path by the relative probability of two molecules in contact. These mean free paths are much smaller than a mean intermolecular spacing or even the diameter of a free volume. For hard‐sphere and hard‐disk fluids, free‐path distributions are found to be monotone decreasing, nearly exponential, and when scaled by the mean free path, nearly density independent for all fluid densities. This density independence precludes any essential difference in transport mechanisms between dilute and dense fluids based on independent free paths. Scaled free‐path distributions for hard‐sphere and hard‐disk solids are found to agree with those of their fluid counterparts except for long free paths where the smaller free‐path distribution for solids reflects their increased molecular localization. The free‐volume theory and its simple extensions are shown to be qualitatively inconsistent with the shape of observed free‐path distributions in solids. For fluids of square‐well molecules, the rate of hard‐core collisions is found to be insensitive to the presence of the square well, and so is the free‐path distribution as well as selected values of the pair‐distribution function. These features are in good agreement with the van der Waals hypothesis, which neglects soft collisions. For dense liquids, hard‐core collisions are in the majority, invalidating the hypothesis that soft‐core collisions cause a Brownian motion between successive hard‐core collisions.

106 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured the electrical resistivity at 4.2°K and the mean free path at 2.5 µm in an ion-pumped ultrahigh-vacuum (UHV) system and in a conventional oil-pump UHV system on unheated glass substrates.
Abstract: Measurements of the electrical resistivity at 296° and 4.2°K in aluminum films, evaporated both in an ion‐pumped ultrahigh‐vacuum system and in conventional oil‐pumped systems onto unheated glass substrates, are presented and used to calculate the intrinsic mean free path and intrinsic electrical resistivity at 4.2°K. It is shown that the UHV films are characterized by a maximum mean free path of the order of 1 μ and by smaller residual resistances than other films. While the mean free path so obtained is still several orders of magnitude smaller than the published value for high‐purity foils of bulk aluminum, it is nevertheless not small enough to appreciably influence the resistivity at 296°K which is measured to be ≈60% higher than the bulk value. This discrepancy, which may be due to structural effects, emphasizes the view that the sample artifact of adding the bulk thermal resistivity to a residual resistivity can be misleading in the case of thin films, even when surface scattering is accounted for.

73 citations


Journal ArticleDOI
TL;DR: In this article, the effects of the mean free path on the spin susceptibility of almost ferromagnetic metals were investigated and the low-temperature specific heat contribution of the spin fluctuations was calculated.
Abstract: We investigate the effects of the mean free path on the spin susceptibility of almost ferromagnetic metals. Using these results, we calculate the low-temperature specific-heat contribution of the spin fluctuations. While the term linear in temperature $T$ is unaffected by the mean free path, we find that the ${T}^{3} \mathrm{ln} T$ contribution is rapidly modified by impurities, in contrast to the phonon case.

71 citations


Journal ArticleDOI
TL;DR: In this article, the heat conduction and density distributions for rarefied gases at rest contained between two unequally heated parallel plates were determined for argon and nitrogen in the transition regime where the ratio of plate spacing to free path was between 1 and 20.
Abstract: The heat conduction and density distributions were experimentally determined for rarefied gases at rest contained between two unequally heated parallel plates Both argon and nitrogen were used as test gases Particular attention was focused on obtaining measurements in the transition regime where the ratio of plate spacing to mean free path was between 1 and 20 The gas density distribution was measured by observing the luminescence produced by a high‐energy electron beam traversed between the plates The experimental results for argon were compared with the analytical results of Wang Chang and Uhlenbeck, Gross and Ziering, and Lees In computing these results the thermal accommodation coefficient measured in the free‐molecule regime was used with the assumption that its value remained constant over the entire pressure range The average agreement between the heat conduction data and the results of the four‐moment methods of Lees and Gross‐Ziering was about 2%, while the measured density profiles agreed with the results of these analyses within 3% Both the heat conduction and density distribution data differ by ∼10‐20% from the results of Gross‐Ziering's eight‐moment method

56 citations


Journal ArticleDOI
TL;DR: In this paper, the distributions of electron energy loss from fima of evaporated carbon, have been studied for a range of film thicknesses from 165 to 835 A and electron energies from 23 to 70 key.
Abstract: The distributions of electron energy loss (range 10–100 ev) from fima of evaporated carbon, have been studied for a range of film thicknesses from 165 to 835 A and a range of electron energies from 23 to 70 key. It is shown that these distributions may be fitted, and hence predicted, within a deviation of a few per cent, for energy losses less than about 200 ev and the mean free path λ for inelastic electron scattering is determined for each electron energy. These values of λ are in good agreement with the experimental values of Brunger and Menz (1965) and with theoretical values evaluated using the Bohm—Pines plasma oscillation theory.

53 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of the temperature dependence of the free exciton diffusion coefficient is given, and the methods of calculating the capture probability of an exciton by impurity traps are discussed in terms of the exciton mean free path, capture radius of an impurity molecule, and average separation of two impurity molecules.
Abstract: A theoretical analysis of the temperature dependence of the free exciton diffusion coefficient is given. The methods of calculating the capture probability of an exciton by impurity traps are discussed in terms of the exciton mean free path, capture radius of an impurity molecule, and average separation of two impurity molecules. A comparison of the theory with the experiment is made. [Russian Text Ignored]

31 citations


Journal ArticleDOI
TL;DR: In this paper, the structure of an ionizing shock front in a monatomic gas is described and the ionization rates for either of these processes is controlled by the rate of excitation from the ground state to the first excited level.
Abstract: The structure of an ionizing shock front in a monatomic gas is described. Both atom‐atom and electron‐atom collisional ionization are considered. The ionization rates for either of these processes is assumed to be controlled by the rate of excitation from the ground state to the first excited level. In the front part of the shock, called the atom‐atom shock, atom collisional dissipative mechanisms (viscosity and thermal conductivity) determine the shock structure. A bimodal Mott‐Smith velocity distribution function is assumed for the atoms in this region, which has a thickness of the order of the atom‐atom viscosity mean free path. In the rear part of the shock front, called the relaxation zone, the collisional ionization processes determine the structure. For this region, which has a thickness proportional to the electron‐atom ionization mean free path, Maxwellian velocity distributions are assumed for the electrons, ions, and atoms. It was found that for Mach numbers of 30 or more the atom‐atom shock is...

29 citations


Journal ArticleDOI
TL;DR: The mechanism which gives rise to the oscillatory structure in the quasiparticle density of states of superconducting films with spatially varying electron-electron interaction is discussed in this paper.
Abstract: The mechanism which gives rise to the oscillatory structure in the quasiparticle density of states of superconducting films with spatially varying electron-electron interaction is discussed It is shown that the Tomasch effect results from processes in which a quasiparticle is condensed into the sea of Cooper pairs, leaving behind a different but degenerate quasiparticle The tunneling density of states is obtained for a composite two-region superconductor The nature of the density-of-states structure depends strongly upon the ratio of the energy gaps of the two regions In the low-energy range, bound eigenstates characterized by the quantization of the difference of the momenta of the degenerate quasiparticles are found for infinite mean free path Explicit results are presented for the composite film systems In-Al and In-Pb for several values of the elctron mean free path

27 citations


Journal ArticleDOI
TL;DR: In this article, Monte Carlo calculations were performed to determine the scattering of hot electrons within these thin-film sandwiches, and a mean free path of 10 A was found, which can be explained by the high-frequency dielectric constant.
Abstract: Photomeasurements on Al–Al2O3–Au thin‐film sandwiches revealed a very asymmetric barrier shape, Φ1 and Φ2 being 1.8 and 4 eV, respectively. The image‐force lowering of the barrier can be explained by the high‐frequency dielectric constant. When photoemission measurements are performed only in the visible region, the Au electrode will not emit photoelectrons because of the large Φ2 value. The Al electrode, however, will emit photoelectrons if the Au electrode is sufficiently positively biased. The existence of only one source for photoelectrons facilitates the interpretation of photomeasurements. Monte Carlo calculations were performed to determine the scattering of hot electrons within these films. Electron‐optical phonon scattering was assumed and a mean free path of 10 A was found. The method to determine scattering by photoemission gives values on scattering within the image‐force region.

Journal ArticleDOI
L. Štourač, A. Vaško, I. Srb, C. Musil, F. Štrba 
TL;DR: In this paper, the thermal conductivity of amorphous semiconducting system Se-Ge in the temperature range of 100 to 300°K was measured and the Debye model was used for the analysis of the experimental values and the calculated mean free path of phonons was related to the size of the basic structure units of the selenium glass.
Abstract: The thermal conductivity of the amorphous semiconducting system Se-Ge in the temperature range of 100 to 300°K was measured. The Debye model was used for the analysis of the experimental values and the calculated mean free path of phonons was related to the size of the basic structure units of the selenium glass. The shift of the thermal conductivity of amorphous selenium doped with germanium was explained by means of the increase of the velocity of sound observed together with the occurrence of the covalent bond Se-Ge between the basic structure units of the studied amorphous system.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the effect of heat conduction through a rarefied gas contained between concentric cylinders and formulated coupled linear integral equations for perturbed temperature and density.
Abstract: Heat conduction through a rarefied gas contained between concentric cylinders is studied analytically. Emphasis is placed on the connection with the experimental determination of thermal accommodation coefficients by the low‐pressure method. The linearized BGK‐model equation is used, based on small relative temperature difference. Two coupled linear integral equations for the perturbed temperature and density are then formulated. An asymptotic analysis is carried out for the case of mean free path much greater than the inner but of the same order as the outer cylinder radius, which corresponds to typical operating conditions for experiments. The lowest‐order deviation of the heat flux from its free‐molecular value is of O[ln(Kn)/Kn], the same as that obtained by Knudsen iteration. Numerical calculations are performed to find this term. It is found that for a mean free path 20 or more times the inner cylinder radius the relative error introduced by using the free‐molecular value for the heat flux is less t...

Journal ArticleDOI
TL;DR: In this paper, the thermal conductivity of amorphous semiconducting As2Se3 is studied in the temperature range from 100 to 300°K and the influence of germanium and silver impurities is shown.
Abstract: The thermal conductivity of amorphous semiconducting As2Se3 is studied in the temperature range from 100 to 300°K and the influence of germanium and silver impurities is shown. The mean free path of phonons is determined and the observed change of the thermal conductivity is explained by the change of the velocity of sound in amorphous As2Se2 containing germanium.

Journal ArticleDOI
TL;DR: Amplitude independent normal state attenuation of longitudinal ultrasound propagating in /001/ direction in single crystal PB at low temperatures at low temperature was reported in this article, showing that longitudinal ultrasound propagation propagates in /1/direction in /
Abstract: Amplitude independent normal state attenuation of longitudinal ultrasound propagating in /001/ direction in single crystal PB at low temperatures


Journal ArticleDOI
TL;DR: In this article, the electrical effects of a charged sphere immersed in weakly ionized gas of infinite extent are analyzed on the basis of kinetic theory, and approximate solutions are obtained by the application of a moment method in which velocity space is split based on exact orbit calculation, selfconsistent with the field.
Abstract: The electrical effects of a charged sphere immersed in weakly ionized gas of infinite extent are analyzed on the basis of kinetic theory. Approximate solutions are obtained by the application of a moment method in which velocity space is split on the basis of exact orbit calculation, self‐consistent with the field. The theory is shown to reproduce both the collisionless and the continuum results in the appropriate limits. Detailed analysis is performed asymptotically for small Debye length but arbitrary mean free path. For quantitative calculations a completely absorbing probe surface at a highly negative potential is chosen. Criteria for the collisionless or collision‐dominated sheath are obtained explicitly. The voltage‐current characteristics are presented in a form useful for direct prediction of electron number density in terms of measured voltage and current, provided the mean free path is known. If the mean free path is only estimated, the results can be used directly to check self‐consistency of that estimate.

Journal ArticleDOI
TL;DR: In this article, a method of calculating thermal conductivity near the surface of a metal is proposed, based on the kinetic theory of gases, which is applied to the problem of heat conduction in the surface region of metal exposed to blackbody radiation.
Abstract: A method of calculating thermal conductivity near the surface of a metal is proposed. Kinetic theory is used to show that the thermal conductivity decreases near the surface and becomes zero at the surface if there is no heat flow across the surface.Kinetic theory is also applied to the problem of heat conduction in the surface region of a metal exposed to blackbody radiation. The resultant temperature distribution is exponential. From a practical standpoint, a useful consequence of the theory is that the absorption depth for blackbody radiation should equal the mean free path of electrons in metals. In the layer of a metal which absorbs incident radiation, the electrons possess increments of energy from both absorbed radiation and thermal conduction. The fraction of the electron's energy lost per collision is taken from the kinetic theory of gases as a first approximation. Thus, thermal conduction is reduced by factors of 10‐5 to 10‐6 in the surface region of the metal. The factor is not needed for the conduction process in the bulk of the material because the energies entering and leaving an elemental layer are independent of each other, permitting random walk to equilibrate the energy. Application of the theory to the heating rate of a tantalum sample exposed to 1500 W/cm2 leads to results consistent with the experimental data available.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a temperature distribution model noting heat fluxes due to low electron density, large mean free path, turbulent heat transfer and high electron density in the magnetosphere.
Abstract: Magnetosphere temperature distribution model noting heat fluxes due to low electron density, large mean free path, turbulent heat transfer, etc

Journal ArticleDOI
U. Brandt1
TL;DR: In this paper, the density of states in bulk type-II superconductors is calculated for magnetic inductions B below H c 2 and all mean free paths, and the vertex corrections due to the impurities can be calculated by a ladder graph approximation.

Journal ArticleDOI
TL;DR: In this article, it was shown that the electron energy loss distributions observed in electron transmission (energy 23-70 kev) through Al films 435 A-1950 A may be fitted in the energy ranges from 5 to 55-100 ev within a deviation of a few per cent.
Abstract: It is shown that the electron energy loss distributions observed in electron transmission (energy 23–70 kev) through Al films 435 A–1950 A thick may be fitted in the energy ranges from 5 to 55–100 ev within a deviation of a few per cent. The fitting is made in terms of assumed electron energy loss distributions for the principal volume and surface losses which are centred, respectively, at about 15 ev and 7 ev. Consistent values of λi, the mean free path for single (volume) inelastic electron scattering into all angles, are evaluated for six electron energies in the given range. An attempt has been made to evaluate in detail the effects on the observed energy loss spectra of the energy loss distributions arising from surface and surface-volume electron interactions. The determined values of λi are in good agreement with the plasma oscillation theory.

Journal ArticleDOI
TL;DR: In this paper, the authors show that if the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz < 0 than with qz ≥ 0.
Abstract: If the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz > 0 than with qz < 0. The resulting difference between the Stokes and anti-Stokes Brillouin intensities is proportional to the mean free path of the phonon involved and to the temperature gradient. The effect should be observable by either neutron or photon scattering.

Journal ArticleDOI
01 Jan 1968
TL;DR: In this paper, the zero bias tunneling conductance is investigated theoretically and shown to be a promising experimental tool for detecting first order phase transitions in high field superconductors. But it is difficult to obtain the exact zero bias conductance for arbitrary spin orbital mean free path.
Abstract: The zero bias tunneling conductance is investigated theoretically and shown to be a promising experimental tool for detecting first order phase transitions in high field superconductors. We calculate and evaluate numerically the zero bias tunneling conductance for arbitrary spin orbital mean free path. In doing the calculations we distinguish between thin films in a parallel field and highℵ-value materials in a perpendicular field. In the former case anomalous properties appear for sufficient long spin orbital mean free path. Finally we determine the minimum spin orbital mean free path which is compatible with a first order phase transition and show that it is much smaller than commonly believed.

Journal ArticleDOI
TL;DR: In this paper, measurements of the anisotropy of the electronic attenuation, the electron mean free path and the superconducting energy gap in cadmium are presented for the propagation of longitudinal ultrasound along the three principle crystallographic directions.


Journal ArticleDOI
TL;DR: In this article, the electronic contribution to the normal state ultrasonic attenuation of longitudinal waves propagating in aluminum has been measured over a wide range of ql, and the data can be fitted to the free electron theory with an isotropic mean free path close to that obtained from resistivity measurements.

Journal ArticleDOI
TL;DR: In this article, a new type of heat pulse detector based on the avalanche phenomenon in a doped semiconductor was proposed, which measured phonon mean free path as a function of magnetic field in MgO:Fe2+.
Abstract: By means of a new type of heat pulse detector based on the avalanche phenomenon in a doped semiconductor, phonon pulses as short in duration as 0.1 μsec have been studied in magnetic fields up to 30 kOe. Measurements of phonon mean free path as a function of magnetic field have been made in MgO:Fe2+. This detector should make it possible to determine the frequency spectrum of a heat pulse for the first time.

Journal ArticleDOI
TL;DR: In this paper, the mean free path of 50 kev-electrons for plasmon excitation was determined with an accuracy of about 20% from the integrated intensities, which is in good agreement with the theoretical value calculated from Ferrell's free electron model.
Abstract: Energy spectra of 50 kev-electrons scattered inelastically in thin Al foils of various thicknesses have been measured as a function of scattering angle. The measured angular distribution of electrons which have excited one or more volume plasmons is compared with theoretical calculations and good agreement is obtained. From the integrated intensities, the mean free path of 50 kev-electrons for plasmon excitation is determined with an accuracy of about 20%. The resulting value Λ=820 A is in good agreement with the theoretical value calculated fromFerrell's free electron model (Λ=760A).

Journal ArticleDOI
TL;DR: In this paper, the longitudinal magnetoresistance was measured along the direction of a pure single crystal of copper and the temperature dependence of the saturation ratio was given between 4 and 35 degrees.
Abstract: The longitudinal magnetoresistance was measured along the [100] direction of a pure single crystal of copper The temperature dependence of the saturation ratio, $\frac{\ensuremath{\rho}(B=\mathrm{sat})}{\ensuremath{\rho}(B=0)}$, is given between 4 and 35\ifmmode^\circ\else\textdegree\fi{}K A limit is placed on the diffusion approximation for small-angle electron scattering and it is suggested that the assumption of a relaxation time or of a mean free path parallel to the velocity is not valid for some types of impurity or low-temperature phonon scattering

Journal ArticleDOI
TL;DR: In this paper, thermal conductivity measurements on lanthanum cobalt nitrate in the temperature range 1-5 °K and in magnetic fields up to 20 kOe are described.
Abstract: Thermal conductivity measurements on lanthanum cobalt nitrate in the temperature range 1–5 °K and in magnetic fields up to 20 kOe are described. The data are analyzed in terms of a simple model in which phonons that are on speaking terms with the paramagnetic cobalt ions are completely removed from the heat flux; this allows one to calculate the mean free path of these phonons due to other processes. In crystals of low thermal conductivity the interacting phonons are not completely removed from the heat flux and the model, extended to include this, allows one to determine the strength of the spin–lattice interaction.