Index of content:
Volume 22, Issue 4, 01 April 1951

Study of Precipitates of C and N in Iron with an Electron Microscope
View Description Hide DescriptionBy the use of the electron microscope it has been possible to study the precipitates of C and N in α‐iron. The physical shapes of the precipitates have been determined in each case as well as the fineness of dispersion The results of the investigation confirm the conclusions drawn from internal friction measurements made on these alloys and reported earlier.

Theory of D_{o} for Atomic Diffusion in Metals
View Description Hide DescriptionThe theory of the entropy of activation ΔS previously given for interstitial diffusion in metals is herein extended to self‐ and to chemical diffusion. It is concluded that this entropy of activation will always be positive; and it is shown that in the case of self‐diffusion and of chemical diffusion at very low concentrations, the better the empirical ΔS the better does it correlate with the theoretical positive ΔS. The large negative apparent ΔS frequently found for chemical diffusion at higher concentrations must be attributed either to inaccuracies in experiments or to the presence of short circuiting diffusion paths. It is predicted that the presently reported negative values of ΔS will become positive when very small concentrations are used in large grain size specimens.

On the Scattering of Plane Waves by Soft Obstacles. I. Spherical Obstacles
View Description Hide DescriptionAn approximate theory is developed for the scattering of plane waves by spherical obstacles with the propertym = λ_{0}/λ_{1}<1.5, where λ_{1} and λ_{0} are, respectively, the wavelengths of a plane wave in the scatteringmaterial and in the surrounding medium. In the exact theory the scattered field is found to be an infinite series of legendre polynomials whose coefficients are complicated combinations of Bessel functions. By making an approximation in the nth coefficient that is valid when either m‐1«1 or 2πa/λ_{0}»n (a = sphere diameter) it is possible to sum the series and obtain analytical closed form expressions for the total scattering cross section of the sphere and the intensity of the scatteredwave as a function of angle. These approximate expressions are compared in the optical case with the results obtained numerically by the Bureau of Standards Computing Laboratory. As an example of their accuracy and range, it is found that when m<1.1 the relative error in the approximate total scattering cross section is less than 5 percent for scatterers of any size; when 1.1<m<1.5, the relative error is less than 5 percent if 2πa(m‐1)/λ_{0}<6 and less than 25 percent for any size sphere.

Separation of Variables in Electromagnetic Theory
View Description Hide DescriptionSeparability conditions are obtained for the partial differential equations of electromagnetic theory. Wave guide and antenna problems are expressed in terms of the vector Helmholtz equation, and solutions are indicated by use of the simple method of separation of variables without recourse to Green's functions. It is shown that complete separation occurs only in rectangular coordinates, but that separation of the equation for one component of the vector field occurs in two coordinate systems. With cylindrical or rotational symmetry, separation is possible in eight coordinate systems.

Diffraction Errors in an Optical Measurement at Radio Wavelengths
View Description Hide DescriptionThe errors arising in the measurement of antenna patterns by means of a lens are examined. The effect of the lens aperture is separated from the effect of lens aberrations and only the effect of the aperture is discussed. Theoretical solution of the problem is obtained for a uniformly illuminated aperture and for short electromagnetic horns. The theory is found to be in agreement with experimental measurements. The phenomenon of mutilation due to the aperture is examined with the help of both computed results and experimental measurements. The systematic errors due to mutilation have been found and have been shown as precision limits. An extrapolation of the data suggests that a lens forty wavelengths wide can be used for the precision measurement of the patterns of antennas ten to twenty wavelengths wide. The technique is entering its range of usefulness at a wavelength of 3.2 cm and should increase in value as the wavelength is decreased.

Effect of Hydrostatic Pressure in an Electron Beam on the Operation of Traveling‐Wave Devices
View Description Hide DescriptionSmall velocity spreads in an electron beam appear to cause a decrease in gain and noise figure of a traveling‐wave tube. The actual decrease depends on a quantity μ, which can be interpreted physically as a measure of the ratio of the coupling of the electrons to each other via the hydrostaticpressure to the coupling of the electrons to the external wave guide circuit. Thus, physically, the effect of the velocity spread is to introduce further interactions among the electrons, in which the external circuit does not take part. This interaction may be thought of as a hydrostaticpressure similar to that in a liquid or gas.

On Stability of Linear Varying‐Parameter Systems
View Description Hide DescriptionA linear varying‐parameter system is defined to be stable if and only if every bounded input produces a bounded output. It is shown that a necessary and sufficient condition for stability is that the impulsive response of the system W(t, τ) should be integrable (considered as a function τ) for all t. From this result and the fact that the system function H(s; t) is the laplace transform of W(t, τ), it is deduced that a necessary condition for stability of a linear varying‐parameter system is that the system function H(s; t) should be analytic and bounded in the right half and on the imaginary axis of the s‐plane for all t. This result represents a generalization of the familiar frequency domain criterion which is commonly used in connection with fixed systems. The generalized criterion is applied to the investigation of stability of a variable feedback system.

The Effect of a Grounded Slab on the Radiation from a Line Source
View Description Hide DescriptionA theoretical investigation, based upon the method of fourier transforms, is made of the effect of a grounded dielectric slab on the radiation from a line source. It is shown that the principal part of the electric field above the dielectric slab can be found either by evaluating the resultant contour integral, using the saddle‐point method of integration, or by evaluating the integral containing the tangential H‐field along the interface. The radiation pattern of the principal field is found to be identical with the resultant field of a direct ray and a reflected ray that can be obtained by a simple consideration of geometrical optics. The condition of the existence of propagating modes in the dielectric slab has been discussed in detail. When the slab is thick enough to support a propagating mode, in addition to the space wave, a surface wave will appear in the neighborhood of the interface. The latter attenuates rapidly as the point of observation is moved away from the interface. The deformation of the path of integration corresponding to different angles of observation has been displayed graphically both in the original h‐plane and the transformed τ‐plane.

Formulas for the Determination of Residual Stress in Wires by the Layer Removal Method
View Description Hide DescriptionThe distribution of residual axial stress in a beam or wire of circular cross section is derived as a function of the moment required to straighten the wire after removal of successive layers of material. Application of the formulas involves two graphical differentiations and integrations of experimental curves.

Directional Distribution of 1040‐Kev Radiation from a High Voltage X‐Ray Tube
View Description Hide DescriptionThe distribution of the 1040‐kev x‐rays emitted in various directions by a high voltage x‐ray tube has been measured by means of an indium resonance detector.

Lattice Distortion Spectrum of Evaporated Gold
View Description Hide DescriptionGold was deposited in various pressures of nitrogen from 0.001μ to 110μ at low temperatures. The electrical resistance of the goldfilm was observed to decrease as it warmed, enabling the distribution of lattice distortions to be computed as a function of decay energy. The distortion spectrum from 70·10^{−14} to 130·10^{−14} erg was found to consist of three peaks—one at 80·10^{−14}, one at 100·10^{−14}, and one at 120·10^{−14} erg. The relative number of distortions for a particular decay energy was found to decrease as the nitrogen pressure increased. The final resistivities of the goldfilms were shown to be dependent on the film thickness over the range 40A to 420A in a manner which agreed with theory and gave a value of 970A for the mean free path of the conduction electrons.

High Temperature Structure and Thermal Expansion of Some Metals as Determined by X‐Ray Diffraction Data. I. Platinum, Tantalum, Niobium, and Molybdenum
View Description Hide DescriptionThe crystal structure and thermal expansion of platinum,tantalum,niobium, and molybdenum have been determined between 1100° and 2500°K. These metals were found to undergo a uniform thermal expansion over the temperature range of this investigation and to undergo no structural change. The permanent elongation of tantalum wires, produced by annealing at temperatures between 2473° and 2773°K, appears to be caused by reorientation of crystal grains in the specimen and to preferred direction of crystal growth during annealing, rather than to a change in crystal structure.
Quadratic equations have been developed for the thermal expansion of platinum,tantalum,niobium, and molybdenum. These equations are represented, respectively, by and .
Values of the expansion coefficient α were computed for each of the metals by differentiating the above equations. Our values were compared with those obtained from the Grueneisen theory and indicate that the theory provides a reasonably satisfactory means of extrapolating thermal expansion data obtained at low and moderate temperatures.

The Oscillations of Magnetic Suspensions
View Description Hide DescriptionThe oscillations of a magnetic suspension between two equal poles are formulated in terms of a nonlinear ordinary differential equation of the second order that may be integrated in terms of elliptic integrals of the second kind. The case of unequal poles is treated by an analogous procedure involving a Legendre reduction. The further refinement of viscous damping is treated by numerical integration, and the relaxation times are found by exponential extrapolation.

Analysis of Synchronous Conditions in the Cylindrical Magnetron Space Charge
View Description Hide DescriptionIn the multianode cylindrical magnetron there exist favored phase velocities of the electromagnetic wave around the interaction space between anode and cathode. These velocities are characteristic of the resonant system attached to the anode segments. In the oscillating magnetron the electronic space charge within the interaction space is presumed to maintain sychronism with one of these velocities. Certain of the conditions of synchronism which can be discussed analytically are treated in this paper. The results, although based on restrictive assumptions, can be used in the interpretation of magnetron operation and in predicting regions of efficient behavior.

The Deformation of Gold Wire at High Temperature
View Description Hide DescriptionGold wires were subjected to small tensile stresses at high temperatures and the strain‐time relationships were determined. These creep curves were similar to those generally obtained for metals at lower temperatures, except that the minimum creep rate was proportional to the applied stress; i.e., the flow was viscous. This coefficient of viscosity was determined as well as its variation with temperature. The surface energy of solid gold was also determined. Theories that have been presented to explain the viscous behavior of metals are briefly discussed.

Amplification of the Traveling Wave Tube
View Description Hide DescriptionA method is presented for solving the equation which determines the modes of a helix with an electron beam [Chu and Jackson, Proc. Inst. Radio Engrs. 36, 853 (1948)]. The essential idea is to consider the modes as a perturbation of the modes produced by the cold helix. From the solution of the equation, the dependence of the amplification factor of the tube upon the geometrical parameters and the operating conditions is explicitly determined. The solution shows also that the tube will not amplify for too large values of the dc electron beam current.

Interfacial Free Energy of Coherent Twin Boundaries in Copper
View Description Hide DescriptionThe ratio of the interfacial free energy of coherent twin boundaries to the average grain boundaryfree energy in copper has been measured by means of the dihedral angles formed at the intersections of twin boundaries and grain boundaries with each other and with a copper/lead vapor interface. The mean value found for the ratio is 0.035±0.006.

Crystallography and Interfacial Free Energy of Noncoherent Twin Boundaries in Copper
View Description Hide DescriptionThe crystallography and interfacial free energy of noncoherent twin boundaries in copper have been investigated. It is found that the noncoherent twin boundary is approximately parallel to a {113} plane of one crystal and to a {335} plane of the other. The ratio of the interfacial free energy of noncoherent twin boundaries to the average grain boundaryfree energy in copper is found to be 0.80±0.015. Two measurements by a second method confirm the magnitude of this value.

Leak Location by Radioactive Gases in Buried Pipes
View Description Hide DescriptionThis paper describes basic considerations and experiments on leak location by means of radioactive tracer gases in underground pipes. C‐14 labelled carbon monoxide and radon were used as tracers. The principles of the method are described. Suitable techniques for preparing and detecting the tracer gas have been worked out. Calculations on the spreading of a column of tracer gas in a pipe follow. Leak location on two small scale installations was carried out experimentally.

Diffraction Pattern of Microwaves Near Rods
View Description Hide DescriptionThe diffraction patterns of electromagnetic waves in the neighborhood of rods a half‐wave long have been calculated from rigorous electromagnetic theory and checked with 8‐cm microwaves. This was the one case in which the patterns could be calculated at short distances from the diffracting objects without undue difficulty. The agreement of measurements and exact theory was sufficient to suggest that microwave measurements within a few wavelengths of diffracting objects will be a fruitful approach to diffraction problems. Heretofore most calculations of diffraction patterns at large distances have been based on blind assumptions as to the distribution of intensity near the diffracting apertures and objects.