Volume 25, Issue 3, 01 March 1954

The Period and Amplitude of the Van Der Pol Limit Cycle
View Description Hide DescriptionThe amplitude and period of the limit cycle of the Van Der Pol equation, ÿ+y=vẏ(1−y ^{2}), are found for all values of v by joining graphically the results of solutions about v=0 and v=∞.

Response of a Pulsed Geiger Tube
View Description Hide DescriptionFor the purpose of extending the usefulness of a Geiger counter to higher radiation intensities, it has been suggested that the voltage applied to its electrodes be a periodically repeated pulse rather than the usual dc. If the duration of the pulse is of the order of the spread time of the discharge in the tube, the output current vs radiation intensity relation will differ from the usual linear one, largely because the resulting current surge may not reach its maximum before the end of the applied pulse. This relation will therefore depend, among other factors, on the not fully understood mechanism by which the discharge spreads. Using probability considerations, we here calculate this relation as a function of the response of the tube under ordinary operation. If the discharge spreads rapidly (e.g., exponentially) initially, an approximate general relationship not involving the detailed spread mechanism may be established. The response to be expected in two types of tubes is discussed in detail, using models for the spread mechanism which are mathematically simplified though probably physically adequate.

Potential Distribution and Prevention of a Space‐Charge‐Induced Minimum Between a Plane Secondary Electron Emitter and Parallel Control Grid
View Description Hide DescriptionFormulas are developed which define the profile of the electrostatic potential distribution in the semi‐infinite, space‐charge‐filled region between a plane emitter of secondary electrons and a parallel retarding‐field control grid. The calculation assumes a known secondary‐electron energy distribution and a cosine angular distribution. In practical application, the formulas must be evaluated numerically or graphically since the energy distribution cannot be expressed analytically except over limited regions. A method of determining the critical spacing between electrodes which will prevent formation of a space‐charge‐induced minimum in the potential distribution between the emitter and control grid is presented.

Methods of Processing Silver‐Magnesium Secondary Emitters for Electron Tubes
View Description Hide DescriptionIn order to prepare a good secondary electron emitting surface from a silver‐magnesium alloy, it was found that baking in dry oxygen would not form the desired surface as originally believed, whereas baking in the presence of water vapor did yield a good secondary emitter. Subsequent experiments showed that, because of the rapid diffusion of oxygen through heated silver, the magnesium in the alloy was oxidized in situ without diffusing to the surface to form the required magnesium oxide layer. With water vapor as an oxidizing medium, the diffusion rate of magnesium through the silver greatly exceeded that of the water vapor, and a satisfactory surface layer was formed. A new technique was then devised in which an original water‐vapor process formed the desired surface, followed by an oxygen process to oxidize the remanent magnesium throughout the volume of the alloy. With the new technique, good secondary emitters are possible which will withstand severe overheating without the evaporation of magnesium found with earlier techniques.

Symmetry as a Factor in Finite Difference Approximations
View Description Hide DescriptionThe effect of symmetry of the solutions to the finite difference diffusion equation upon the stability criterion is discussed. A simple example is included to illustrate the discussion.

Approximations in Linear Viscoelasticity Theory: Delta Function Approximations
View Description Hide DescriptionThe relationships between certain approximations that have been proposed recently in connection with the linear viscoelastic behavior of noncrosslinked amorphous polymers are discussed. The approximations reviewed here are applicable with slight modifications to other types of linear response, for example, dielectric behavior.

RLC Canonic Forms
View Description Hide DescriptionFoster's reactance theorem synthesizes the class of lossless networks in a so‐called canonic form. This idea is here generalized in order to show that there is a distinct class of RLC networks possessing a canonic form. It will be shown that when an RLC driving‐point impedance or admittance possesses a canonic form, its poles and zeros must alternate on each and every ``separate part'' of an algebraic curve (c) of a special nature located in the left half of the frequency plane s=σ+jω, belonging to one of the following two families: .A corollary of this theorem, in the case (c) is a straight line or circle, symmetrically placed with respect to the real axis, unifies the three known cases of LC networks, RL‐RC networks, and networks with slight dissipation.
Analysis and synthesis of RLC networks possessing a canonic form is introduced in the light of a more general approach to the problem based on the class consideration. The problem of the driving‐point impedances which contain mutual coupling in their Brune configuration has been clarified by outlining their generating functions and their network structure. (The latter part is omitted here and shall be presented in another article.)

A Resonant Cavity Study of Semiconductors
View Description Hide DescriptionA solution of Maxwell's equations is obtained in a resonant cavity with a center post of arbitrary electrical properties. The solution gives the dielectric coefficient and the conductivity of the center post in terms of the natural frequency and Q of the cavity. The theory is of particular use in the study of semiconductors where perturbation theories are of little value. It is shown that a transition from a cylindrical mode to a coaxial mode occurs as the conductivity of the center post is varied. This transition occurs for a relatively small change in conductivity. The present results are compared with those of perturbation theory, and it is shown that the latter are valid over a greater range than the conditions imposed in their derivation indicate.

16 Percent Aluminum‐Iron Alloy Cold Rolled in the Order‐Disorder Temperature Range
View Description Hide DescriptionThe methods of fabricating 16 percent Al‐Fe from cast slab to thin‐gauge sheet are described in some detail. The melting, casting, homogenizing, hot rolling, and cold rolling at 575°C and room temperature are described. Particular attention is focused upon the 575°C cold rolling from the standpoint of the possible beneficial effects derived from an ordering reaction which occurs in this alloy. The technique of cold reduction from 0.007 in. to 0.0005 in. at room temperature is discussed.
Magnetic data on a limited number of heat‐treated laminated cores are given. Useful physical properties, other than magnetic, of previous limited interest because of the inability to fabricate the alloy into ductile strong thin sheets, are discussed. These properties include excellent oxidationresistance at high temperatures, good wet‐corrosion resistance to certain chemical solutions, and high electrical resistivity.

Diode Theory in the Light of Hole Injection
View Description Hide DescriptionClassical diode theory, as applied to metalpoint contacts made to an n‐type semiconductor, is adequate only for small forward voltages at which, under certain conditions, hole current may be negligible. The shape of the theoretically predicted diodecharacteristic is not affected by the hole injection process at low voltages, no matter what the composition of the current. However, for voltages in excess of a certain value, dependent only on the resistivity of the material (on the order of 0.1 volt for 5 ohm‐centimeter germanium), the spreading resistance is comparable to the barrier resistance, and it is the hole injection process which accounts for continued rectification. The extent to which the spreading resistance is decreased by hole injection depends on the ratio, γ, of hole current to total current. The present paper includes a theory of the effect of this ratio on the diodecharacteristic at higher forward voltages. A method of measuring γ from V‐I characteristics alone is indicated.

Boundary Disturbances in High‐Explosive Shock Tubes
View Description Hide DescriptionHigh‐velocity disturbances are observed to propagate along the walls of a high‐explosive operated shock tube in advance of the plane shock. Experiments are presented which determine the dependence of the geometry, energy, and velocity of the disturbance on such variables as the gas contained in the shock tube, the shock strength, and the roughness and composition of the supporting boundary. A model is constructed to explain the flow within the disturbance. Arguments are presented which show the disturbance to result from radiation originating in the luminous plane shock.

Arcing at Electrical Contacts on Closure. Part IV. Activation of Contacts by Organic Vapor
View Description Hide DescriptionThe activation of electrical contacts by decomposition products from organic vapors depends upon an adequate surface layer of adsorbed molecules. In earlier work minimum vapor pressures were given for activation by a number of organic compounds. From new experiments reported here the time available for adsorption between successive arcs is equally important, so that the minimum vapor pressure for activation to occur is inversely proportional to the time available for adsorption, or directly proportional to the rate of operation. The effective contact area and the energy are important also and, although quantitative data have not been obtained, it is reasonable to guess that these variables are connected by a relation not far from p/n=KE/A, where n is the minimum rate for activation to occur for the pressure p on the effective contact area A with the available energyE. Quantitative experiments have been made only upon the activation of palladium contacts by vapor of the organic compound known as fluorene, and only the proportionality between p and n has been established.

Use of Restricted Variational Principles for the Solution of Differential Equations
View Description Hide DescriptionA technique is given by which nonlinear differential equations may be solved approximately, using variational principles for which certain restrictions are made. Ordinary first‐ and second‐order equations are discussed in detail. The method is extended to encompass partial differential equations and applied to the Boltzmann transport equation.

Apparent Density of Thin Evaporated Films
View Description Hide DescriptionMeasurements of the apparent densities of copper and silverfilms formed by evaporation are described. The interpretation of the results and the manifestations of low apparant densities in physical experiments are discussed.

Noise in Semiconductors: Spectrum of a Two‐Parameter Random Signal
View Description Hide DescriptionWith intended application to the theory of current noise in semiconductors, the spectrum is calculated of a random signal which may be in one of two states (YES‐NO: random telegraph signal), where the mean lives σ and τ of the two states may be different. The form of the spectrum is the same as for the case with equal lives, the single parameter τ for that (classical) case now being replaced by 2[(1/σ)+(1/τ)]^{−1}; i.e., the rates of transition are additive.

Radiation Damage Effects on Order‐Disorder in Nickel‐Manganese Alloys
View Description Hide DescriptionEffects of fast neutron irradiation in a nuclear reactor on order‐disorder in a series of nickel‐manganese alloys ranging from 16.5 to 31.9 atomic percent manganese have been studied by resistivity and magnetic induction measurements. Attainment of an ``irradiated state'' differing from either cold work or thermal disordering is suggested by comparison of exposure results on initially cold work disordered and initially thermally disordered Ni_{3}Mn. In a region from 16.5 to approximately 22 percent manganese, thermally disordered alloys are markedly affected by irradiation. These effects also appear to be superposed on the disordering produced by irradiation of initially ordered alloys.
From theoretical exponential dependence on period of irradiation, fast neutron disordering of Ni_{3}Mn is determined by relating the Bragg and Williams order parameter quadratically with resistivity and linearly with magnetic induction. This leads to an estimate of 5000 for the ratio of the number of atomic replacements to primary collisions with neutrons of energy in excess of 0.5 Mev.

Experimental Study of Low‐Frequency Effects on the Dynamic Modulus of a Buna‐N Rubber
View Description Hide DescriptionThe linear dynamic Young's modulus of a vulcanized Buna‐N gum rubber is measured at frequencies of 0.05, 0.10, and 1.00 cps, in the temperature range −22°C to 30°C, by a method in which a small differential sinusoidal elongation is superimposed on a 5 percent static elongation. The width of the dispersion range on the temperature scale (the range in which the logarithm of the modulus increases steeply with decreasing temperature) is only about 10°C, as contrasted with widths as great as 25°C found in previous measurements on a similar compound at frequencies of several kilocycles. The modulus‐temperature plot shifts upward by only about 4°C per decade of frequency increase in the present range, as contrasted with about 10°C per decade in the previous measurements at higher frequencies. It is concluded that this elastomer cannot be described properly by means of the ``method of reduced variables,'' in which the dynamic properties are ascribed to mechanisms having identical temperature dependence, and that the low‐temperature behavior is governed by mechanisms distinct from those effective in the audio‐frequency range at room temperature.

Estimation of Correlation Coefficients from Scatter Diagrams
View Description Hide DescriptionTheoretical relations between statistical scatter diagrams of two random variables and their joint probability density functions are used to derive a simple method of estimating correlation coefficients. The cases considered are those of variables with Gaussian and Rayleigh distributions. Theoretical curves and experimental scatter diagrams are given for each case. Some factors which may influence the accuracy of the proposed method are discussed, and it is concluded that the errors in estimating correlation coefficient will be of the order ±0.1.

Fast Time Analysis of Intermittent Point‐to‐Plane Corona in Air. II. The Positive Pre‐Onset Streamer Corona
View Description Hide DescriptionAnalysis has been made of pre‐onset streamers in room air at 760 mm with fast oscilloscope using both photomultiplier and electrical registration. The shape of the photon pulse observed by W. N. English is confirmed, and is interpreted. Current and luminosity roughly parallel each other in the streamer. Tip velocities ranged from 6×10^{7} cm/sec to 2×10^{7} cm/sec being highest near the point. The luminosity is constant over the path except at the very beginning and at the end of the path suggesting that ionization is also constant. The net number of positive ions left behind per cm length of streamer in consequence of the electron flow into the point is constant, and has been measured to be about 8×10^{9} ions per cm in general agreement with earlier work. Lateral deflection of the ends of streamer tracks by space charge left behind from previous streamers was directly observed.

Diffusion of Gold into Copper
View Description Hide DescriptionRadioactive tracer techniques have been utilized to measure the rate of diffusion of gold into polycrystal‐line copper over the temperature range from 1000° to 375°C. These experiments have yielded the values Q=44 900±1300 cal/mole and D _{0}=0.10±0.06 cm^{2}/sec for the volume diffusion process in the temperature range from 1000°C to 750°C. Diffusion measurements at 550°C and 375°C indicated that the measured rates at these temperatures had been enhanced by grain‐boundary diffusion. Considerable attention was directed toward the variation of the diffusion coefficient with (1) the purity of the copper, (2) the grain size of the copper, (3) the thickness of the plating, and (4) the time of anneal. Variations of these parameters showed no significant effect on the diffusion coefficient, with the exception of the time of anneal. The measured diffusion rate at 1000°C was observed to decrease with increasing time of anneal.