Volume 18, Issue 6, 01 June 1947

Crystal Pattern Synthesis by an Approximate Summation of Fourier Series
View Description Hide DescriptionA faithful representation of the locations of the peaks of electron density maps can be obtained rapidly by determining for each point in the projected unit cell the algebraic sum of the amplitudes of those reflections which are contributing either a maximum or a minimum at each point. Since maxima and minima do not, in general, fall at the specific points of the grid, an approximation must be introduced. Using the semi‐polar form of Fourier series, the approximate summation can be accomplished with the use of one hundred and fifty strips. The method was tested by determining the peak locations in the structure of diopside projected on 001. Potential applications of the approximate summation include rapid checking of the validity of assumed crystal structures.

Single Crystal Electron Diffraction by Micro‐Crystalline Materials
View Description Hide DescriptionIt is shown that the double lens probe‐type electron diffractioncamera described earlier is capable of producing useful electron diffraction patterns of single microscopic crystals in the size range 200–2000A; the formation of an opaque carbonaceous deposit, which occurs when an electron probe is focused on a specimen, is prevented in the diffraction camera by previously exposing the specimen chamber to an electron spray. A number of examples of two‐dimensional grating patterns and Kikuchi‐line patterns obtained from such crystals are shown. From either type of pattern it is possible to obtain accurate values for some of the lattice spacings, while from the Kikuchi‐line patterns it is possible to deduce accurately the orientation of the crystals relative to the electron beam. The results are shown to agree reasonably well with the predictions of the dynamical theory as presented by MacGillavry. It is concluded that a two‐dimensional grating pattern is to be expected from a crystal oriented with an important lattice vector approximately parallel to the electron beam independent of slight disorders or warping of the crystal. Kikuchi‐line patterns are to be expected for most other crystals which are not excessively thick or disordered. The theory also shows that both types of patterns may be obtained simultaneously.

Microsecond Measurement of the Phosphorescence of X‐Ray Fluorescent Screens
View Description Hide DescriptionMicrosecond square‐wave x‐ray pulses, repeated a thousand times a second, were obtained by operating an x‐ray tube directly from a radar pulser. The phosphorescent build‐up and decay of light emitted by fluorescent materials when irradiated by the x‐ray pulses was observed with a multiplier phototube connected to an oscilloscope. Oscillograms of CaWO_{4}(radiographic intensifying screen) and BaSO_{4} indicate simple exponential response, with decay to 1/eth intensity in 6 and 0.8 microseconds, respectively. MgWO_{4} and Patterson B (fluoroscopic) and D (photofluorographic) screens were found to complete their main response to microsecond excitation in 10 to 100 microseconds, but their decay is not exponential.

X‐Ray Diffraction Studies of Chrome‐Steel Slags
View Description Hide DescriptionX‐ray diffraction studies of the crystalline constituents in the acid open hearth chrome‐steel samples showed that chromium exists in these samples as a chrome‐iron spinel of the form, FeO·Cr_{2}O_{3}. Its density was 5.109 g/cc and its melting 2160°C. It crystallized in the face‐centered cubic structure with a _{0}=8.348A and Z=8.

Spherical Aberration of Compound Magnetic Lenses
View Description Hide DescriptionA reduction of the spherical aberration of strong electron lenses can be achieved by a strong lens as a virtual image former and by a transformation of the image in a real one by means of one or more weak lenses. Calculations are carried out for bell‐shaped magnetic fields of the axial field distribution,and numerical values of the achieved reduction of the aberration are given for different lens strength, magnification, and image distance of the compound system.

Physical Properties of Calcium Tungstate X‐Ray Screens
View Description Hide DescriptionThe absolute energy of the light from a fluorescent calcium tungstate x‐ray screen, its spectral distribution, and the efficiency of conversion from x‐rays to light have been determined. The absolute energy and its spectral distribution were obtained spectrographically by comparison with a standard tungsten filament lamp. Equations are given for determining the distribution of light in the diffusing screen material, and calculation of the light losses are made for varying screen thickness and x‐ray absorption. The data for energy distribution of the ingoing x‐rays were taken from measurements obtained in this laboratory by a new method to be published elsewhere. Allowance for scattering and secondary x‐radiation was made and a conversion efficiency of 5.0 percent was obtained for this calcium tungstate phosphor.

Pressure and Oil Flow in Oil‐filled Cables at Load Variations
View Description Hide DescriptionThis paper presents a method for calculating pressure and oil flow in a section of an oil‐filled cable at load variations with due regard to both the hydraulic resistance of the oil canals and the elasticity of the sheath and the pressure armor, if any, and the compressibility of the oil. The present article restricts itself to cable sections terminated with oil reservoirs in which the pressure is constant; in a forthcoming paper this restriction will be dropped. Formulas are given for pressure, oil current, and amount of oil which flows through a cross section of the cable for an arbitrarily prescribed oil expansion per unit length. These formulas are applied to the following oil expansion functions: S _{0}·1, d/dt(N _{0}·1), e^{−t/T} ·1, and 1/√t·1, which represent the oil expansion or terms occurring in the series giving the oil expansion in some important cases. Generalized functions are plotted for the pressure at the midpoint, the oil current at the endpoints, and the amount of oil which passes the endpoints for the above mentioned oil expansion functions. Using these generalized functions, the calculation of pressure and oil flow, with the simplifying assumptions made here, is reduced to elementary operations. Numerical examples illustrate the use of the given formulas and curves.

The Electrostatic Field of a Point Charge Inside a Cylinder, in Connection with Wave Guide Theory
View Description Hide DescriptionIn this paper the field of a point charge inside a hollow, infinitely long circular cylinder is studied. The case of an axial point charge is treated in detail. Three different methods are developed. The first method shows how to calculate the induced charges at the surface of the cylinder without explicit knowledge of the potential itself. The surface charge‐density function is obtained as the solution of a Fourier‐type integral equation. Then the potential caused by these charges is calculated. The second method works in the opposite direction. Here the potential is obtained as solution of a boundary value problem, followed by the calculation of the corresponding charges at the surface of the cylinder.
The integral, obtained for the surface charge density, is transformed by contour integration. Although the resulting series is very useful for numerical purposes, a stronger method is necessary, in order to calculate the charge density just opposite the point source. Figure 1 shows the calculated values of the induced surface charge density. Several approximations for the charge‐density function are considered, in connection with recent work of Weber (cf. Table I).
The same is done for the field inside the cylinder. Various formulas are given which allow of numerical calculations. In Table II some calculated values of the potential are shown.
The third method is based on the theory of Fourier‐Bessel‐Dini series. The potential is developed in terms of discrete normal solutions of the potential equation in cylindrical coordinates. The coefficients in this development can be derived from the behavior of the potential in the immediate neighborhood of the primary source.
Furthermore, it is emphasized that the study of the above potential problem can serve as a guide in questions of wave propagation in hollow circular cylinders. In this connection the third method is shown to be extremely useful, as it enables us to calculate directly the fields in the far zone from that in the immediate neighborhood of the exciting source. This new method is demonstrated in case of acoustic waves inside a cylinder, caused by a harmonically vibrating point source.

The Elastic Constants of Materials Loaded with Non‐Rigid Fillers
View Description Hide DescriptionGeneral expressions are given for the modulus of rigidity, , and compressibility, k̄, of a medium of Lame's constants, λ_{1} and λ_{2}, loaded with a volume fraction, φ, of a filler of constants λ_{1}′ and λ_{2}′. To terms in the first power of φIf the ``filler'' is a gas at a pressure,p, in a nearly incompressible medium, these givewhere φ is the volume loading, p is the pressure within the spherical cavities in the deformed state. Barred symbols refer to the properties of the loaded material; unbarred, to the medium alone. Expressions for the displacements and stresses within the medium and the particles, neglecting interactions between particles, are also given.

Heat Transfer between a Fluid and a Porous Solid Generating Heat
View Description Hide DescriptionThe theory, due to Anzelius, of the transfer of heat between a fluid flowing with constant velocity through a porous solid is extended to include the case where the solid generates heat. Expressions are obtained for the temperatures of solid and fluid as functions of position and time, it being assumed that the heat source function is a linear function of the temperature of the solid with coefficients independent of position and time. The application of the theory to a description of the temperature in catalyticreactions is indicated.
 LETTERS TO THE EDITOR


Concerning Estimates of the Minimum Sparking Potential Based upon the Cathode Work Function
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Measurement of the Dynamic Stretch‐Modulus and Hysteresis of Tire Cords
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On the Analysis of Internal Flow Machinery
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Objective Aperture System for the Electron Microscope
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