Volume 32, Issue 2, 01 February 1961

Clustering in an Alpha Iron‐Molybdenum Solid Solution
View Description Hide DescriptionClustering in alpha iron‐molybdenum alloys begins with the formation and growth of dislocation rings from supersaturated vacancies. The rings form on {100} planes and reach a maximum diameter of ∼800 A. Segregation of molybdenum to these rings starts just after their formation. Molybdenum‐rich zones grow inside the rings until a disk is formed. After very long periods of aging, particles of the bcc η solid solution form from the clusters at aging temperatures below 500°C.

Likelihood Detection of Small Signals in Stationary Noise
View Description Hide DescriptionAn approximation to the likelihood ratio which may be used in detecting a small signal in stationary noise is derived. The result contains only low‐order moments of the signal and only stationary properties of the noise; hence it is applicable without change of form to any sufficiently long observation period. In the Gaussian case, with the signal also stationary and both signal and noise power spectra continuous, the result represents passage through a linear Eckart filter, followed by square law detection and equal‐weight smoothing.

On the Macroscopic Analysis of the Conducting Electromechanical Solid with Application to Cylinders Subjected to Axial Electric Fields
View Description Hide DescriptionIn the present work, the ambient to melting phase of the problem has been examined from the standpoint of intercoupled electrical, thermal, and mechanical effects in order to establish the foundations for a theoretical solution, and to establish the intervals over which the solution is valid. Thermoelectric and electromagnetic effects were considered relative to their influence on the distribution of temperature and electric field within the conductor. Body forces resulting from the electromagnetic field were also considered and the corresponding stresses worked out.
The principal analytic result obtained is that for the nonlinear problem resulting from electrothermal coupling through temperature‐dependent electrical conductivity. General solutions have been obtained for conditions of no heat loss at the boundary, radiation at the boundary (Newton's law of cooling), and the boundary fixed at the initial temperature.
Various examples of engineering interest have been worked out and the results are compared with solutions obtained assuming constant electrical conductivity.
It has been found that significant electromechanical body forces may be present under certain circumstances and it is shown that these body forces may play an important part in the breakup of wires subjected to large, suddenly applied fields.

Phenomenological Elastomechanical Behavior of Rubbers over Wide Ranges of Strain
View Description Hide DescriptionRelationships have been developed which permit a relatively good description of the elastomechanical behavior of natural rubbers over the full range of deformations. These relationships were obtained by development of a general relationship set forth by Mooney. A stress function was obtained from which principal stresses may be evaluated for any given set of compatible strains. This theory was tested by applying it to experimental results of Treloar. It is demonstrated that by the insertion of relatively simple ``exponential type'' functions, a very good fit was obtained over the whole range of Treloar's data. In this form, the properties of natural rubber can be described by three parameters, A, B, and β. It has been found (to be demonstrated in a later paper) that there are unique relationships between A and β, B and β, and between β and rubberhardness for a range of natural rubbers from pure gum vulcanizates to the hardest of commercial natural rubbers.

Thermionic and Photoelectric Emission from Magnesium Oxide
View Description Hide DescriptionMeasurements of the thermionic emission as a function of temperature and the photoelectric yield as a function of the photon energy in the range from 2.5 ev to 11.5 ev have been made on magnesium oxide in the form of thin films, powders, and single crystals. The thermionic emission measurements indicate that the position of the Fermi energy in most samples of MgO is controlled primarily by the electrons in a donor level located approximately 3.4 ev below the vacuum level. Measurements of the enhancement of the photoelectric yield in the impurity sensitive region gives evidence for impurity levels slightly greater than 2.4 ev and 5 ev below the bottom of the conduction band. A sharp rise in yield at 7.5 ev in active samples coincides with the optical absorption edge associated with exciton formation. Heating the samples in oxygen greatly reduces the rise at 7.5 ev but has little effect on the yield at energies greater than 10 ev. From this it is concluded that the energy difference from the top of the filled band to the vacuum level is less than 10 ev.

Tunneling Through Thin Insulating Layers
View Description Hide DescriptionThe resistance of thin aluminum‐oxide films has been measured as a function of the voltage across the film and of the film thickness as calculated from its capacitance. All films showed ohmic behavior at low voltages, and exponential rise of current at higher voltages, in qualitative agreement with R. Holm's theoretical calculations for tunneling through thin vacuum layers. However, the resistance was several orders of magnitude lower than either the bulk value for Al_{2}O_{3} or the calculated value for tunneling through vacuum. By making use of an effective mass in the oxide equal to about of the electron mass, the calculated values for tunneling can be brought into line with the experimental results.

Theory of LASER Oscillations in Fabry‐Perot Resonators
View Description Hide DescriptionThe Fabry‐Perot interferometer has been suggested for use as a high‐mode LASER (light amplification by stimulated emission of radiation) resonator. The oscillation condition for a Fabry‐Perot LASER is derived from an integral equation for the angular spectrum of the field. The kernel of the integral equation involves the scattering matrices of the end mirrors. This integral equation leads to a stationary expression. The use of physically reasonable trial spectra allows one to estimate the effect of ``walkoff,'' diffraction, reflector curvature, and reflector tilt in terms of an ``effective'' reflection coefficient for the infinite‐aperture Fabry‐Perot. Taking into account the effect of ``walkoff,'' an approximate necessary and sufficient condition for oscillation normal to the reflectors is derived.

Determination of Crystallite Size Distributions from X‐Ray Line Broadening
View Description Hide DescriptionThe broadening of an 00lpowder diffraction line caused by a distribution of sizes of crystallites is discussed. A function of the intensity, P(h _{3}) sin^{2}(πh _{3}), is derived. Its cosine transform gives the size distribution directly. The first term of a series expansion of this distribution function corresponds to the expression previously obtained by Warren and Averbach. In addition, this function gives less weight to the extremes of the diffraction line shape.

Energy Dependence of Radiation Damage in Tungsten
View Description Hide DescriptionThe rate of radiation damage in tungsten is shown experimentally to depend on the energy of the incident deuterons almost as 1/E. The small deviation from the 1/E dependence is in a direction opposite to that predicted by the hard sphere model for secondary defect production.

Etch Pits at Dislocations in Copper
View Description Hide DescriptionA possible mechanism for the development of etch pits at dislocations in copper by etching in solution is presented, and experiments are described which may substantiate this mechanism. Etchants which will develop pits at clean dislocations on the (111), (100), and (110) faces of copper are described. These etchants are capable of distinguishing between clean dislocations and dislocations with a ``Cottrell atmosphere'' in 99.999% copper. Clean edge and screw dislocations can also be differentiated with these etchants. Some observations concerning the relation of facet structure, developed by etching, to the dislocationstructure of the crystal are reported.

Sputtering of Vitreous Silica by 20‐ to 60‐kev Xe^{+} Ions
View Description Hide DescriptionExperimental values for the sputtering of quartz by xenon positive ions at flux densities of 2×10^{15} ions/cm^{2} sec in a vacuum of 10^{−5} mm Hg are found by measuring the volume of the sputteredcavity by means of interference fringe contours. The sputtering ratios are 0.706±0.061 at 20 kev, 0.85±0.13 at 30 kev, 1.78±0.13 at 40 kev, 1.74±0.12 at 50 kev, and 1.31±0.09 at 60 kev. The technique of volume measurement by interference fringe contours has an accuracy of ±2×10^{−8} cc and is estimated to have an ultimate accuracy of ±10^{−10} cc.

Influence of Tensor Conductivity on Current Distribution in a MHD Generator
View Description Hide DescriptionMagnetohydrodynamic generators may operate under conditions such that the product of electron cyclotron frequency and mean collision time is not small compared to unity. Accordingly the electrical conductivity is a tensor rather than a scalar quantity. The influence of tensor conductivity on the electrical current distribution has been investigated in two idealized situations, one pertaining to the entrance and exit regions of the generator and the other pertaining to the region near segmented electrodes. The calculations predict modifications of the internal impedance of the generator which can be described in terms of increases in the effective duct length and width.

Theoretical Bound on the Thermoelectric Figure of Merit from Irreversible Thermodynamics
View Description Hide DescriptionThe principles of irreversible thermodynamics have been used with an idealized model to independently derive Joffe's dimensionless ``figure of merit,'' Tα^{2}σ/(κ)_{ J2}=0, and a theoretical upper bound of infinity.

Ultrasonic Attenuation of Longitudinal Waves in Plastics
View Description Hide DescriptionHughes' pulse technique for measuring longitudinal velocities has been adapted and extended to measureattenuation of longitudinal waves in the frequency range from 250 to 1,000 kc. Data for attenuation in nepers per wavelength in six different plastics (Plexiglas, polystyrene, nylon 101, Formica XXN, polyethylene, and Teflon) are given for eight different frequencies ranging from 250 to 1000 kc. The results for Plexiglas and polystyrene are compared with results obtained previously by other methods. Attenuation in nepers per wavelength has been found to decrease when frequency increases for all plastics, except for Teflon, which shows a well‐defined peak at about 700 kc.

Thermoelectric Behavior of p‐n Junctions
View Description Hide DescriptionEquations are derived, on the basis of an emission model, for the flow of carriers and electronic heat which occurs when a temperature drop as well as an applied potential exists across a p‐njunction. The application of the equations is discussed for small‐signal situations, where the Onsager relation is obeyed, as well as for large‐signal situations. In particular, the efficiency of p‐njunctions for thermoelectric conversion is compared with that of homogeneous semiconductors and thermionic diodes.

Analytical Solutions for Some Zone Melting Problems
View Description Hide DescriptionAnalytical solutions to the zone melting problem are obtained for any initial distribution of solute for the case of two geometries. One is the infinite straight bar and the other the re‐entrant annular ring. The former is particularly interesting because under certain conditions the semi‐infinite bar may be treated as infinite. The annular ring calculation provides, among other applications, a means of giving quantitative answers to questions arising in the zone leveling process.

Microwave Analog to the Scattering of Light by Nonspherical Particles
View Description Hide DescriptionA microwave technique has been developed for obtaining total cross sections and angular distributions for the scattering of electromagnetic radiation by nonspherical particles whose size is of the order of the wavelength. The scattering by spheroidal and cylindrical refracting particles has been measured for three orthogonal orientations of the symmetry axis. Comparison of the results with exact and approximate theoretical calculations for spheres, spheroids, and finite and infinite cylinders indicates the possibility of developing useful approximation methods. Some interesting effects have been noted, particularly a very large resonance in the scattering by finite cylinders. The results have been given preliminary application to the problem of the nature of the interstellar material which absorbs and polarizes starlight.

Iron Whisker Surface Rearrangements Resulting from the Hydrogen Reduction of Oxides and from Thermal Etching
View Description Hide DescriptionThe hydrogen reduction of high‐temperature oxidation products grown on ironwhiskers produces ironsurfaces whose topography depends on the orientation of the surface that was oxidized. The different topographies for {100} and {110} surfaces are shown, and the dependence is further illustrated on the polycrystallineironsurfaces which result from the heating of a single‐crystal α ironwhisker through its transformation temperature of 910°C. Rearranged surfaces covered with parallel striations and unusual dendritic surface structures are shown and discussed. Both the striations and dendrites are the result of thermal etching of a ``polycrystalline''ironwhisker at temperatures between 800°–1200°C.

Coupled Mode Theory of Electron‐Beam Parametric Amplification
View Description Hide DescriptionA theory of parametric amplification in a filamentary electron beam by transverse fields is developed in coupled mode form. Space charge effects are neglected. In addition to beam modes at the signal frequency, beam modes at frequencies ω_{ n }=ω+ω_{ p }, n=0, ±1, ±2…, where ω_{ p } is the pump frequency, are coupled together. A discussion of the general form of the equations is given and reveals the circumstances under which exponential gain or periodic energy transfer between various modes can occur. When applied to quadrupole electric pump fields, a description of the quadrupoleamplifiers of Adler, Wade, and Gordon is obtained. This theory is then used to evaluate the noise contribution from synchronous beam modes and higher cyclotron idler modes. Coupling by axially symmetric electric fields and by axially symmetric magnetic fields is discussed, and other amplification schemes suggested. The theory of coupling by axially symmetric fields can also be used to study lens effects on noise in the gun region.

Backward Waves in Longitudinally Magnetized Ferrite Rods
View Description Hide DescriptionA quasi‐static approximation (▿×H=0) is used to investigate the backward waves that propagate along a longitudinally magnetized ferrite rod. These waves propagate in the frequency range where the perme‐ability of the ferrite is negative, γH _{0}<ω<γH _{0}[1 + (M _{0}/μ_{0} H _{0})]^{½}, and can have a phase velocity much smaller than the velocity of light. The quasi‐static approximation is shown to be valid whenever the free‐space wavelength is greater than the circumference of the ferrite rod. Traveling‐wave interaction of a drifting electron stream with these backward waves is considered, and a start‐oscillation length of 1 in. at 4000 Mc is shown to be theoretically possible for a 600‐v, 0.4‐ma electron beam. Experimental verification of these waves is provided by measuring the phase velocity and signal strength along a longitudinally magnetized ferrite rod that completely fills a waveguide. Phase velocities as small as one one‐hundredth of the velocity of light are measured.