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Volume 28, Issue 6, 01 June 1957

Low‐Temperature Reactor Irradiation Effects in Metals
View Description Hide DescriptionThe effects of structural and chemical defects on the low‐temperature (30–50°K) annealing peak in low‐temperature reactor‐irradiated aluminum and copper were studied. From the fact that the density of reactor‐induced defects did not affect the annealing kinetics, it was possible to conclude that the low‐temperature annealing process was of the first order without a unique activation energy. The fact fact that both oversized and undersized atoms could suppress this annealing peak led to the conclusion that the radiation‐induced defects were more complicated than simple point defects. The suggestion is made that a defect similar to a crowdion must be created by low‐temperature neutron irradiation. This data also supports to some degree the viewpoint that a radiation‐induced defect, possibly a crowdion, has sufficient knock‐on energy to migrate several hundred atomic distances. The experiments also contain evidence which rule out all forms of vacancy‐interstitial annihilation.

Nonlaminar Flow in Cylindrical Electron Beams
View Description Hide DescriptionExperimental measurements on the transverse velocity distribution in cylindrically symmetric electron beams emergent from magnetically shielded cathodes are reported. For strong magnetic fields the transverse velocity distribution at the beam center has been found to be composed of discrete classes. These results are explained on the basis of a beam model with nonlaminar flow in which thermal velocities and space charge are neglected. The mechanism depends on the periodic passage of electrons through or very near the beam axis and the fact that the wavelength of this periodicity is a decreasing function of the distance between the point of entry into the magnetic field and the axis.
When the space charge and magnetic forces are comparable, no discrete transverse velocity distribution was observed. It is shown, however, that the beam should still be in the same type of nonlaminar flow as above.

Low‐Temperature Deformation of Copper Single Crystals
View Description Hide DescriptionSingle crystals of copper were deformed at 4.2°K and 77.3°K. At 4.2°K, after a large strain produced by normal slip, jerky flow (discontinuous slip) occurs. From the study of reactor irradiated crystals, it was deduced that a packet of 30 slip lines, each containing 10^{4}dislocations, was released to form each jerk of the discontinuous flow. For samples of certain orientation the region of discontinuous flow was followed by a region of deformation twinning. The fact that deformation twinning was taking place was verified by x‐ray methods. The twinning elements were determined to be the (111) plane and the [112] direction. At 77.3°K, discontinuous slip was not observed. In a limited range of orientations, twinning has been observed at 77.3°K. The effects of reactor irradiations on discontinuous slip and on twinning were also studied and it was determined that the occurrence of twinning was unaffected by the irradiations.

Correction for the Finite Magnetic Modulation Amplitude in Paramagnetic and Nuclear Magnetic Resonance Lines
View Description Hide DescriptionA general method of correcting for the finite magnetic modulation amplitude in line shape analyses of paramagnetic or nuclear magnetic resonance lines is described. The method consists of determining the proper ``folding'' function for the detection system. Once this has been determined, the numerical ``unfolding'' procedure of A. R. Stokes can be used to compute the true line shape from the observed shape of an arbitrary experimental line.

Glow‐Arc Transition in Current‐Stabilized Electrical Discharges
View Description Hide DescriptionThe purpose of this investigation was to measure the limits with regard to currents and time duration of the glow and arc modes for the low current discharge at atmospheric pressure. In addition, some indications were obtained as to the conditions at the cathode which lead to such transitions. Accurate measurements in the normally unstable transition region were made possible through the use of a current stabilized power supply, together with special instrumentation for determining the magnitude and duration of the arc or glow voltage for periods as short as 0.02 microsecond.
It is shown that glow‐arc transitions can occur for currents as low as 0.002 amp and for currents at least as high as 1.0 amp in the atmospheric pressure argon discharge. The duration of the arc mode at low currents is usually less than 5 microseconds. These low current transitions occur only when an oxide film is present on the cathode and are caused by the action of high fields created by positive ions across the bulk of the thin oxide films.

Waves on the Surface of a Crystal
View Description Hide DescriptionSurface waves in crystals are investigated for surface orientations and directions of propagation which preclude waves of plane strain. These waves are of importance in the study of very high frequency vibrations of certain crystal plates. It is shown that, in the AT cut of quartz, one and only one surface wave can propagate along the digonal axis. By reduction to the case of orthorhombic symmetry, it is shown that the surface wave is the result of coupling between a surface wave of plane strain and either a face‐shear mode or a transverse thickness‐shear mode. The former combination is associated with flexural and the latter with extensional vibrations of AT plates. Computation of the wave velocity requires the simultaneous solution of algebraic equations of the third and fifth degrees as opposed to a single cubic equation in the case of waves of plane strain.

Universal Gravity Turn Trajectories
View Description Hide DescriptionOne of the simplest trajectory programs for the powered flight of a missile through the atmosphere is the ``gravity turn,'' which results from simply keeping the propulsive thrust always parallel to the vector velocity. However, even for a ``point mass'' missile, in a uniform gravitational field with constant thrust and no aerodynamic forces, the differential equations for the motion are nonlinear and require numerical integration. To avoid the necessity of doing this computation anew for each missile preliminary design, a method has been found for integrating the equations for the singular case of zero initial velocity. When expressed in terms of appropriate dimensionless variables, the resulting solutions are ``universal'' in the sense that they constitute a good approximation to any gravity turn with a small, nearly vertical, initial velocity. The solutions depend upon two parameters, the initial thrust to weight ratio η and a parameter k which corresponds to the initial ``kick angle'' of nonsingular gravity turns.

Effect of Neutron Interaction on Criticality. II
View Description Hide DescriptionA method for calculating the criticality conditions for spatially disconnected fissile regions based on the multiplication constant k is presented. To illustrate the method, the case of two interacting infinite water‐tamped fissile slabs containing solutions of pure U^{235} in water is considered.

Scattering by an Inhomogeneous Solid. II. The Correlation Function and Its Application
View Description Hide DescriptionExperiments on the angular intensity distribution of x‐rays scattered by porous materials (hole structures) in the range of small angles are described. It is shown that the scattering can be characterized by an exponential correlation function in the case of a distribution of holes of random shape and size in solid; a theoretical derivation of the exponential function is given for this case. When the correlation function is an exponential, the rule holds that the reciprocal square root of the scattered intensity is a linear function of the square of the scattering angle. The specific surface of the material is determined by the slope of this straight line. Specific surfaces of a number of compositions are calculated from their experimental correlation functions and compared to surfaces based on adsorption measurements.

Relation of Radio Measurements to the Spectrum of Tropospheric Dielectric Fluctuations
View Description Hide DescriptionThe size spectrum of isotropic fluctuations in the troposphere'sdielectric constant is related to quantities measured by radio means. Two classes of experiments are analyzed: (1) line‐of‐sight phase and amplitude instability and (2) refractometermeasurements of dielectric fluctuations. This analysis is independent of models for the dielectric fluctuations and provides a system from which the spectrum can be estimated from experimental data. The measured quantities are expressed as weighted integrals of the spectrum, many of which may be inverted to give the spectrum directly in terms of the data. Aerial smoothing by the receivers and finite data sample effects are studied, in addition to the basic propagation mechanisms.

Small Signal Power Theorem for Electron Beams
View Description Hide DescriptionAn analysis is presented of a filament beam in arbitrary dc electric and magnetic fields. The trajectory of the filament beam in the absence of ac fields may thus follow an arbitrary curve. It is shown that the electromagnetic power delivered by the filament beam is, within the assumptions of small signal theory, balanced by a decrease in the beam of a quantity, the ``generalized ac power'' in the beam. This ac power involves products of the small signal beam‐excitation amplitudes.
The ac power theorem for a filament beam can be extended to a thick beam. This is done to find the small signal ac power theorem for a two‐dimensional rectilinear beam of finite thickness. The power theorem presented here is applicable to M‐type and E‐type traveling‐wave devices. Applications to the noise theory and signal analysis of electron beams are indicated.

Minimum Saturating Fields for Ferromagnetic Crystals
View Description Hide DescriptionThe conditions for magnetic saturation are investigated analytically for a very thin ferromagnetic single‐crystal disk or spheroid of cubic crystalline symmetry and positive magnetic anisotropy constant K _{1}, whose axis of revolution is perpendicular to a {100} or {110} plane. Contrary to some previous work, it is found that an external field ranging in magnitude from NI_{s} to NI_{s} +2K _{1}/I_{s} (where NI_{s} is the demagnetizing field) is sufficient for saturation in any direction in either of these planes. Above this field, the crystal behaves as a single magnetic domain. The applicability of the calculated minimum saturating fields to torque measurements is discussed.

Magnetostriction of Aluminum‐Iron Single Crystals in the Region of 6 to 30 Atomic Percent Aluminum
View Description Hide DescriptionThe spontaneous saturationmagnetostriction and the forced magnetostriction were measured on slowly cooled single crystals of the ferromagnetic aluminum‐iron alloys in the composition range from 6 to 30 atomic percent aluminum. The value of the first constant of spontaneous saturationmagnetostriction at 6 atomic percent aluminum is similar to that at 6 atomic percent silicon in iron. At compositions containing larger amounts of aluminum, the first constant becomes very large; however, near 30% aluminum the constant drops and approaches zero. The second constant of spontaneous saturation magnetrostriction is negative below 17% aluminum, reaches a maximum near Fe_{3}Al, and drops near 30% aluminum.
Values of the isotropic forced‐magnetostriction constant below 25 atomic percent aluminum were found to be slightly higher than that for iron but less than that for siliconiron. Above 25% aluminum the isotropic constant became very large. The anisotropic forced‐magnetostriction constants were the largest for the single crystal having 29.6% aluminum; a good fit of the experimental data to the calculated curve was found for this alloy.

Resonance Absorption of Neutrons by Thorium Cylinders
View Description Hide DescriptionThe integrated effective resonance neutron absorption cross section of thorium‐232 cylinders has been experimentally investigated by danger coefficient measurements in the Hanford Test Pile. The results were interpreted to yield the effective resonance integral as a function of the surface‐to‐mass ratio of the thorium cylinders. The experiments were extended to determine the Doppler coefficients resulting from heating the thorium in a constant neutronenergy spectrum in the reactor.
After correction for 1/vneutron absorption, the effective resonance integral can be approximated as a function of the surface‐to‐mass ratio by .The value assigned to the Doppler coefficient of the volume absorption of the effective resonance integral is .The results are compared to similar measurements on uranium.

Microwave Measurements of the Properties of a dc Hydrogen Discharge
View Description Hide DescriptionMicrowave measurements of the properties of thin cross‐sectional elements of a dc hydrogen discharge have been made. These measurements were accomplished by exposure of portions of the discharge in the gap between the cones of an S‐band re‐entrant cavity operating in the TM_{010} mode. The equipment and techniques for making the microwave measurements employing the re‐entrant cavity are described. Measurements in the positive column of a dc hydrogen discharge showed the following results: Electron density increases with increasing tube current and also with increasing gas pressure in the pressure range measured (2 to 8‐mm Hg). Electron collision frequency is approximately equal to 4.6×10^{9} multiplied by the gas pressure in mm Hg, and is independent of tube current. When measurements were made in the negative glow region, several anomalous effects including a negative frequency shift were observed. These have been explained qualitatively as being caused by plasma resonance phenomena. The fact that these plasma resonance phenomena were also observed at a frequency of 8550 Mc demonstrates that the electron density in portions of the negative glow is at least 300 times greater than the density in the positive column.

Potential and Capacity of Concentric Coaxial Capped Cylinders
View Description Hide DescriptionAn exact solution is obtained for the potential in the space between two finite concentric coaxial right circular capped cylinders; and from the potentials an exact solution of the capacity is found. A set of infinite equations is involved but detailed numerical calculations, made for nine different geometries, show that if the ratio of height of the outer cylinder to diameter of the inner cylinder is less than about unity only the first eight equations and the first eight unknowns in them need be considered for obtaining three figure accuracy of the capacity. The theory is correct when the inner cylinder shrinks to a disk and also when the radius of the outer cylinder goes to infinity. Thus the theory yields the capacity for a horizontal disk midway between infinite conducting planes. When the planes become infinitesimally close to the disk the problem becomes two‐dimensional, and the three‐dimensional capacity expression goes over to an expression obtained by a conformal transformation. A table of coefficients for 1st, 2nd, 3rd, 4th, 6th, and 8th order approximations is given for computing quantities of interest and to show the rapidity of convergence of results for the nine geometries considered. For one of the cases the equipotentials and lines of force are computed and diagrammed.

On the Width and Energy of Domain Walls in Small Multi‐Domain Particles
View Description Hide DescriptionA two‐domain ferromagnetic particle is considered. It is shown that the inclusion of the magnetostatic energy in the derivation of the wall characteristics yields values of these characteristics considerably different from those in bulk material.

Internal Friction in the Presence of a Static Stress
View Description Hide DescriptionThe internal friction of pure lead, copper, and aluminumsingle crystals was measured as a function of an externally applied static biasing stress. The low strain amplitude damping of copper and lead was found to be essentially unaffected by the presence of the static stress. Aluminum differs from lead and copper in that at room temperature, damping is independent of amplitude at low strain amplitudes (ε<10^{−6}). The damping in aluminum becomes strain‐amplitude dependent only at higher strain amplitudes. The presence of the static stress causes this amplitude dependence to shift to lower stress amplitudes by an amount comparable to the static stress applied.

Infrared Emission from High‐Frequency Discharges in CO_{2}
View Description Hide DescriptionThe infrared radiation at about 2.7 μ and 4.3 μ from the E type glow discharge in CO_{2}, powered by external electrodes at 10 Mc/sec, was examined with a lead telluride cell, a lead sulfide cell, and a radiation thermo‐couple through appropriate filters. The rf power was pulsed at 5–30 cps. The pressure dependence and power dependence of the emitted intensity, and the efficiency of energy conversion to the two infrared bands were measured. The fast photoconductive detectors indicated a radiation decay time of the order of several milli‐seconds after the pulse cutoff, and the decay half‐life was measured as a function of various discharge parameters, and also in the presence of Hg vapor and N_{2}O. It is concluded that the vibrational states are excited by a purely thermal process, with no significant enhancement due to collisions with slow electrons.
 LETTERS TO THE EDITOR


Low‐Temperature Measurements of the Young's Modulus and Internal Friction of Copper during Irradiation
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