Volume 37, Issue 1, 01 January 1966

Magnetic Field Distribution in a Type II Superconductor
View Description Hide DescriptionDirect measurements of the magnetic field distribution in the gap between half‐ellipsoids of niobium in plastically deformed and annealed states were made using a bismuth thin‐film magnetoresistance probe. An empirical equation of the form r−r _{0}=C _{0} B+C _{1} (e^{C2B} −1) for the field distribution in the deformed sample was found. For the annealed sample, a surface discontinuity of the field was observed, which is a boundary condition for the equilibrium magnetization. Flux jumping was observed when the field was not increased slowly. The distribution in the annealed specimen had reproducible irregularities.

Superconductivity of a Composite of Fine Niobium Wires in Copper
View Description Hide DescriptionComposites consisting of fine Nb filaments in a copper matrix were fabricated, and the following superconductingpropertiesmeasured: the critical temperature, critical transverse magnetic field as a function of temperature, critical current density at 4.2°K as a function of transverse magnetic field, and magnetization at 4.2°K. The reduction in Nb filament size was checked by optical and electron micrography. Filament diameters ranged down to 100 Å. As the diameter decreased, T_{c}, H_{c} (T), and J_{c} all decreased. This behavior was attributed to the proximity effects of the copper matrix on the Nb. The results are closely comparable to those of investigations of superimposed thin films. It is therefore not expected that high critical fields can be attained by composites involving a type II superconductor in a matrix of a nonsuperconductor.

Stress Field Near a Dislocation Slip Plane in an Orthotropic Medium
View Description Hide DescriptionThe elastic stress field in the vicinity of a dislocation slip plane in an infinite orthotropic medium subjected to uniform shear at infinity is determined using a formulation in integral equations. It is assumed that a slip plane is different from a traction‐free surface crack in that it has uniform shear on its surface and remains closed under the applied stress field. However, the use of these mixed boundary conditions under the restrictions of plane stress in linear elasticity is found to give the same stress distribution as that for a shear crack. Although a shear crack under an applied uniform shear opens up into an ellipse, the opening per unit length is shown to be so small that for most engineering applications it can be considered closed and the equivalence of a shear crack and a slip plane is established. It is pointed out that this correspondence is not valid between a shear crack in a thick elastic plate and a slip plane in an infinite elastic medium. Results for an isotropic body are given as a limiting case of an orthotropic body.

Further Considerations on a Theory of Superlinearity in CdS and Related Materials
View Description Hide DescriptionA theory of superlinearity by Cardon and Bube is extended by considering the effect of a high density of shallow traps, either discrete or with a quasiexponential distribution. New conditions for the breakpoints of superlinearity are introduced. These new conditions allow the explanation of several features of superlinearity in sintered layers, including the ``anomalous'' observation of lifetime decrease above the superlinear region, as described in investigations on CdSe by Stupp. A possible relationship between such trap distributions and an apparent decrease in sensitizing center hole ionization energy in highly impure single crystals of CdS is suggested. A summary of all the basic superlinearity conditions is given, with principal emphasis on the physics of the involved mechanisms.

Determination of Electron Trapping Parameters
View Description Hide DescriptionA detailed investigation of different methods for determining electron trap parameters has been made on crystals of CdS‐CdSe. The principal techniques involved are decay of photoconductivity and thermally stimulated conductivity (TSC). Direct evidence of a quasicontinuous trap distribution with total density of 5×10^{15} cm^{−3}, trap depth range of 0.1–0.7 eV, and capture cross sections of the order of 10^{−16} cm^{2} is obtained, for which correct values of the parameters can be calculated from Fermi‐level analysis of either decay or TSC data. In the same crystals a discrete trap level with density of 2×10^{14} cm^{−3}, depth of 0.73 eV, and apparent cross section of 10^{−14} cm^{2} is also found. In spite of the large value of cross section derived from the freeing of trapped electrons, these traps exactly obey monomolecular kinetics. A temperature threshold at 180°K is found, below which it is not possible to fill these traps. Examination of a number of possibilities favors the proposal that these traps are characterized by a Coulomb‐repulsive barrier.

A Plasma Instability Induced by Electron‐Hole Generation in Impact Ionization
View Description Hide DescriptionExistence of a new kind of plasma densityinstability, caused by the dependence of the plasmageneration rate on the electric field, is predicted, and lower frequency oscillations believed due to it have been observed experimentally. The observed oscillations, induced by shunting the plasma with an external capacitance, are damped and of frequency 2∼10 Mc/sec in n‐InSb at 77°K. The electron‐hole generation rate has been calculated from the observations and is found to vary approximately as the eighth power of the electric field, with values from about 10^{6} to 10^{8} sec^{−1} for electric fields between 2.3 and 4.0×10^{4} V/m. When a small external transverse magnetic field was applied, the generation rate increased, but obeyed the identical relationship as a function of electric field as observed in zero magnetic field. Evaluation of the threshold conditions for instability indicates that the microwave radiation observed from an impact‐ionization plasma in InSb can be the result of this density instability.

Theory of a Microwave Plasma Instability due to Transverse Breakdown
View Description Hide DescriptionA theory describing a plasma instability in solids occurring in the microwave frequency region is presented. Oscillations of the uniform‐mode magnetoplasma resonance type are excited because of the dependence of the electron‐hole generation rate on the strong Hall electric field. The generation rate necessary for the instability to grow in InSb at 77°K is larger than 9×10^{9} sec^{−1}, in a transverse magnetic field of 8400 G. The existence of the magnetoplasma resonance in a bar‐shaped crystal of n‐InSb has been confirmed experimentally. The theory explains in qualitative fashion many features of the microwave radiation from InSb observed by Suzuki.

Thermal Conductivities of MgO, Al_{2}O_{3}, and ZrO_{2} Powders to 850°C. I. Experimental
View Description Hide DescriptionThermal conductivities were measured for extensively characterized magnesia, alumina, and zirconia powders.Thermal conductivities of the powders in dry air at atmospheric pressure were determined at volume fractions solid varying from 0.49 to 0.70 as a function of temperature from about 100° to about 850°C. Particle‐size distribution, chemical composition, x‐ray diffraction pattern, weight loss on heating, pore‐free density, and surface area of each powder were measured. Thermal conductivities were determined by a steady‐state method employing radial heat flow in a hollow cylinder and by an unsteady‐state method based on the model of heating a cylinder of a perfect conductor surrounded by an infinite amount of the material whose thermal conductivity is being measured.
The thermal conductivities of the powders increased with increasing volume fraction solid. The influence of gas conductivity was greater than that of the solid on the thermal conductivity of the powers. The thermal conductivity for each powder measured increased at a decreasing rate with increasing temperature, following an approximately quadratic temperature dependence. Thermal conductivity was increased by the presence of a sorbed water film as well as by mechanical pressure on the particles.

Thermal Conductivities of MgO, Al_{2}O_{3}, and ZrO_{2} Powders to 850°C. II. Theoretical
View Description Hide DescriptionA theoretical expression is presented to relate the effective thermal conductivity of statistically describable two‐phase systems to the conductivities of the pure phases, the volume concentrations of the phases, and a shape factor. Auxiliary equations to relate bulk gas conductivity and small interparticle distance and to predict a radiationheat transfer contribution to effective thermal conductivity are also presented. The shape factor is a property of the discontinuous phase and is related to the two‐phase system only through the volume balance of the phases. In the derivation of the expression no assumptions are made concerning particle shape, size, or spatial arrangement. However, the derivation is based on a simplified model in that the isotherms in the model are assumed to be planes perpendicular to the heat flow. In exact solutions of the heat flow equation, no assumptions are made regarding the heat flow or temperature pattern. On the other hand, exact solutions have been carried out only for simple shapes in fixed arrangements that seem to fall short of describing actual powder‐gas systems.

Hot‐Electron Transfer through Thin‐Film Al–Al_{2}O_{3} Triodes
View Description Hide DescriptionTriode devices, consisting of Al–Al_{2}O_{3}–Al–Al_{2}O_{3}–Al films, were used to inject hot electrons into an oxide film. Transmission ratios were measured as a function of collection‐oxide thickness, collection bias, and injection at 77° and 300°K. These data were compared with a model for hot‐electron penetration in which electron‐electron interactions in the metal were invoked, with a mean free path l_{e} ∝ (ε−ε_{ f })^{−2}; once‐scattered electrons were included in the collected fraction. Assuming an energy loss of 0.1 eV per interaction in the oxide (from optical absorption data), the comparison of the model and the experimental data yielded a mean free path between these interactions of approximately 12 Å. The predicted transmission ratios agreed quite well with the experimental data.

Potential Barrier Parameters in Thin‐Film Al–Al_{2}O_{3}‐Metal Diodes
View Description Hide DescriptionInternal photoelectric thresholds for collection of electrons through a thin Al_{2}O_{3} layer formed by anodization in an aqueous nonsolvent electrolyte were measured as a function of photon energy, applied bias, oxide thickness, temperature, and overlayer metal. These data were analyzed in terms of photoexcitation mechanisms and optical absorption calculations to determine the potential barrier profile presented by anodized Al_{2}O_{3} between metalfilms. The barrier profile was found to be given by the work function of the metal minus the electron affinity of the oxide, modified by the image effect for an electron between conductors and by the applied bias and the work function difference between the metals. For this agreement the electron affinity of the oxide was chosen to be approximately 2.0 eV and the high‐frequency dielectric constant was used. A slight asymmetry was observed for Al–Al_{2}O_{3}–Al devices, possibly resulting from the metal‐oxide transition regions. The potential barrier was found to increase with decreasing temperature, consistent with I‐V characteristics.

Linear Response Functions and the Phenomenological Equations of Internal Friction
View Description Hide DescriptionLinear response function analysis has been applied to the internal friction problem. With the use of the Kramers‐Kronig relations, the analysis takes on a very convenient form which is of particular usefulness for experimental analysis. The Fourier transform of the response function is related very simply to the phase lag and the modulus defect. The general formulation is applied to simple cases of relaxation and resonance. It is also applied to the space‐dependent vibrating dislocation model of Granato and Lücke, and the effects of higher modes are treated. It is shown that on the high‐frequency side of the damping peak, for low damping, the higher modes contribute an increase in the damping which has the same frequency dependence as the fundamental. For high damping, the situation is indeterminate on the far high‐frequency side, but for frequencies near the peak, the fundamental mode analysis of Granato and Lücke is unchanged.

Direct Measurement of the Nernst‐Ettingshausen Dimensionless Figure of Merit
View Description Hide DescriptionA method is given for obtaining the Nernst‐Ettingshausen dimensionless figure of merit, in a direct measurement, as the ratio of two voltages. A discussion of the method is given for experiments involving rectangular sample geometries and also for more general geometrical configurations. Both isotropic and anisotropic materials are considered. The method is based on measurements of the ratio of the adiabatic electrical resistance to the isothermal electrical resistance. The superposition of the voltage of the Peltier‐Seebeck effect is avoided by arranging for the completion of the experiments in a length of time which is short compared to the Peltier‐Seebeck time constant for the sample. The required equipment and circuitry are simple, being similar to a four‐probe resistivitymeasurement circuit with the voltage being determined by use of an oscilloscope.

Magnetohydrodynamic Flows in Closed Regions with Complete Symmetry about an Axis
View Description Hide DescriptionA formal perturbational technique was developed to obtain solutions for magnetohydrodynamic flow problems in closed regions with symmetric properties of flow and boundary conditions about an axis. The system of highly nonlinear partial differential equations, governing the problems of this class, was found to reduce to systems of simultaneous linear partial differential equations, thus creating a possibility of obtaining solutions by classical mathematical methods. The technique used was based on a well‐known power series type of perturbational expansion in terms of a small parameter, which in the limit was assumed to become the solution of the original system. The general technique was applied to the magnetohydrodynamic flow in a toroid under the influence of a uniform applied magnetic field along the direction of the main axis of the toroid. It was found that the secondary flow caused by the centrifugal body force on the fluid element due to the curvature created induced electromagnetic components and a pressure variation along the radial direction.
The solutions were carried out to include completely the second perturbational equations and the electromagnetic and flow fields were discussed for different values of characteristic parameters appearing in the solutions.

Dislocation Energies and the Concept of Line Tension
View Description Hide DescriptionThe concept of a dislocation line tension is discussed and explicit expressions for the total energy of various dislocation configurations in different orientations are given. Based on these energy calculations, it is found that for all cases of practical interest (bow‐out segment L≦10^{5} b) there is a significant (>25%) difference between the results as obtained from the simplest version of line tension encountered in the literature and the method of the present paper. The difference amounts to as much as a factor of two for a straight‐edge dislocation with L=10^{3} b.

Photolytic and Reduction Coloring of Na‐Compensated CaWO_{4}:Nd
View Description Hide DescriptionTwo sets of CaWO_{4}:Nd:Na crystals have been grown having Nd concentrations of 0.5 and 1.0 at.%, and various concentrations of Na. The photolytic coloring is somewhat enhanced by the presence of Na, whereas reduction coloring is made much more difficult by full compensation of the Nd with Na. The 2.9‐eV absorption for the extraordinary ray becomes more prominent with increasing Na content, in the case of reduction coloring. The atomic model applicable is discussed. Practical applications of these findings are also mentioned.

Effect of Coherent Radiation on the Stability of a Crossed‐Field Electron Beam
View Description Hide DescriptionIt has been suggested that a toroidal space vehicle might be raised to a very high positive potential relative to the surrounding space by causing a stable crossed field electron beam to circulate around its outer surface. In this arrangement the electric field exists only between the space vehicle and the electron beam; the magnetic field is imposed by coils within the space vehicle. For the case of very low electron density it has been shown that such a beam can be stabilized against the diocotron (slipping stream) instability by being made sufficiently thick. The stability against coherent radiative perturbations of such a thick beam is studied under the following simplifying assumptions: (a) the geometry is taken as infinite cylindrical; (b) the ratio of all frequencies in the problem to the electron cyclotron frequency is negligible; (c) no perturbation electric fields along the magnetic field lines; (d) on the basis of an analogy, but without direct proof, certain continuous spectra of real eigenvalues occurring in the problem are unimportant; (e) the electrons are cold, and (f) the outer boundary of the ``space vehicle,'' i.e., the cylinder, is perfectly conducting. It is concluded that if there is a gap between the inner edge of the beam and the cylinder, one unstable mode is present for each azimuthal mode number . It is interesting that this unstable mode represents a radiation directly into space without the assistance of either waveguides or antennas.

Noble Gas Plasma Produced by Fission Fragments
View Description Hide DescriptionThe generation of a plasma by fission‐fragment ionization of noble gases is reported. The experimental data consist of steady‐state current‐voltage (I‐V) characteristics obtained with ceramic‐metal ionization tubes which were operated in the high neutron flux region of a nuclear reactor. The observed dependence of I on V ^{½} for applied potentials <100 V is shown to be consistent with the theory that the predominant charge loss in the plasma is volume recombination of diatomic ions and electrons. The ion generation rate is calculated from the energy loss rate of the fission fragments in the gas and I‐Vcharacteristics for the noble gases are computed. These characteristics, which do not contain any adjustable parameters, are in agreement with the experimental data within±10%. Data are presented for neon, argon, xenon, and neon‐argon (Ar/Ne=10^{−3}) for gas pressures in the range 30 to 400 Torr. Typically, for a gas pressure of 240 Torr and a neutron flux of 10^{13} cm^{−2}·sec^{−1}, the computed values for ion generation rate and electron density in the pure gases were ≈5×10^{16} cm^{−3}·sec^{−1} and ≈3×10^{11} cm^{−3}, respectively. For the neon‐argon mixture, the electron density was estimated to be ≈7×10^{11} cm^{−3}. This higher density arises not only because of additional production of Ar^{+} ions via neon metastables encountering argon neutrals, but also because of a reduction in the formation rate of Ar_{2} ^{+} ions (followed promptly by dissociative recombination). The point is that Ar^{+}+Ar+Ne→Ar_{2} ^{+} is unlikely compared with Ne^{+}+2Ne→Ne_{2} ^{+}, for a small argon admixture.

Electronic Properties of Titanium Monoxide
View Description Hide DescriptionElectric, magnetic, and optical properties of the rocksalt form of titanium monoxide (TiO_{0.80} to TiO_{1.25}) have been studied. TiO is metallic, exhibiting weak paramagnetism.Properties of TiO‐phase samples are determined primarily by the relative concentration of titanium and oxygen atoms and to a lesser extent by sample preparation. The resistivity of TiO_{1} can be represented as the sum of an extremely large residual resistivity and a temperature‐dependent part having positive slope. Although off‐stoichiometric samples exhibit resistivity vs temperature variation not typical of metals, the entire phase can be characterized as metallic. Specular reflectance data suggest that the yellow color of TiO‐phase samples is due to a plasma edge relaxation in the yellow region of the visible spectrum.

Electron Emission from Aluminum after Quenching
View Description Hide DescriptionEmission of electrons (``Exo‐electrons'') from aluminum was observed by an openwindow Geiger‐Müller counter after quenching from temperatures between 300° and 450°C. Emission rates as a function of time at room temperature agreed well with data calculated on the basis of a model involving the diffusion of point defects toward the surface. The energy of formation for the process was determined and discussed in terms of point imperfections.