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Volume 23, Issue 8, 01 August 1952

X‐Ray Diffraction by Face‐Centered Cubic Crystals with Deformation Faults
View Description Hide DescriptionIn view of the recent interest in the introduction of stacking faults in crystals during plastic deformation, the x‐ray diffraction effects have been calculated for face‐centered cubic crystals with deformation faults (as distinct from growth faults, the expressions for which are given in an appendix for comparison). Explicit expressions are derived for the reciprocal lattice intensity distribution, and it is shown how the intensity of faulting can be determined from measurements on the breadths of the reciprocal lattice streaks or the displacements of their peaks. It is then shown how these effects will be revealed in the x‐ray powder pattern and some practical aspects are discussed.

Some Limitations on the Maximum Frequency of Coherent Oscillations
View Description Hide DescriptionElectron beamoscillators are placed in one of two groups depending on whether or not they employ resonant energy‐extractors. A natural upper frequency limit exists for the group which does. This limit depends chiefly on the ac beam current density and the noise level in the resonant structure. For practical values of these parameters, the maximum frequency is below the range of visible light.

A Mathematical Analysis of a Dielectric Amplifier
View Description Hide DescriptionThis paper presents a mathematical analysis of the fundamental circuit on which the operation of dielectric amplifiers depends. The analysis is based on the assumption that the effective hysteresis curve of the amplifier's dielectric material may be represented by a hyperbolic sine function. The case of resistive load is analyzed and expressions for the steady‐state input and output currents are calculated. From a consideration of the transient response of the amplifier, an estimate of its time constant is obtained.

The Emission of Radiation from Diatomic Gases. IV. Emissivity Calculations for CO and HCl for Nonoverlapping Rotational Lines as a Function of Temperature and Optical Density
View Description Hide DescriptionSimplified expressions have been developed for the engineering emissivity of uniformly distributed diatomic gases for nonoverlapping rotational lines with a resonance contour. Unfortunately the rotational half‐widths for spectral lines arising from transitions between excited vibrational energy levels are generally not known. For this reason it was necessary to make the assumption that the rotational half‐widths for transitions of the form n→n+v, v=1 or 2, are identical. The theoretical analysis is, however, sufficiently general to be useful without modification when accurate data concerning the dependence of line‐width on vibrational excitation become available. Explicit expressions have been obtained for the contributions to the total emissivity associated with individual vibration‐rotation bands.
Representative emissivity calculations have been carried out for CO and HCl. Comparison of the calculated emissivities of CO with experimental data shows only fair agreement, suggesting either that the assumed description of rotational half‐widths is inadequate or else that the empirical emissivity data are not reliable at elevated temperatures.

Time‐Temperature Dependence of Linear Viscoelastic Behavior
View Description Hide DescriptionThe question is treated whether in the study of linear visco‐elastic behavior of a material change of temperature is completely equivalent to a shift of the logarithmic time scale or not. If it is, the material is termed ``thermo‐rheologically simple'' (class A).
It is shown that, by plotting the results of a similar rheological experiment (for instance, a creep experiment) performed at different temperatures and comparing the curves obtained, one can decide whether the materials considered belongs to class A or not, by seeing whether the curves can be made to fit by shifting them along the axis of logarithmic time. Once the material has been decided to behave thermo‐rheologically simple, one can plot the function describing the time‐shift as function of the temperature.
Some examples of thermo‐rheologically simple materials are quoted from the literature.
The micro‐rheological conditions for thermo‐rheologically simple behavior are discussed. It turns out that this behavior implies that in similar deformations at different temperatures always the same sequence of molecular events follows, whereas in materials not belonging to class A, not only the speed, but also the sequence of molecular processes changes when the temperature of the experiment changes. This implies, that materials of class A cannot from a heat treatment assume a special structure which could not be obtained by one temperature, whereas for materials of class B a heat treatment can indeed result in a special structure. It is reasonable to expect that thermo‐rheologically simple materials will be found only among polymers containing no crystallites and no pronounced polar groups.

An Estimate of the Energies of the Positive Ions in a Negative Point‐to‐Plane Corona
View Description Hide DescriptionAn attempt has been made to measure the energies with which positive ions arrive at the cathode of a negative point‐to‐plane corona in N_{2}. A hairpin thermocouple was used as the point electrode. It was heated by the corona current, and its thermal emf was recorded by a galvanometer. After appropriate calibration, the potential across the Crookes darkspace was determined to be about 300 volts, and the average energy with which ions arrive at the corona point to be about 15 ev.

On the Theory of Antenna Beam Shaping
View Description Hide DescriptionThe diffraction pattern of an aperture with amplitude distribution A(x) and phase function ψ(x) is examined for two cases: (1) controlled variation of the amplitude distribution with known uniform phase; (2) controlled variation of phase with known amplitude distribution. For Case 1, it is shown that a symmetrically tapered amplitude distribution produces a diffraction pattern with reduced secondary lobes, while an asymmetric amplitude distribution produces a shaped pattern. Thus, antenna beam shaping may be achieved by controlled variation of amplitude distribution in an aperture in which there is uniform phase. For Case 2, it is shown that a specified beam shape may be approximated by controlled variation of phase in the aperture when the amplitude distribution is known. The method of calculation is an extension of the method originally formulated by Chu for calculating cylindrical reflectors to transform a given primary radiation pattern to a specified shaped pattern. A general formulation of Chu's method for an amplitude distribution on a curved surface is developed. The theoretical results are applied to the design of progressive‐phase antennas and experimental results given.

A Point Focusing X‐Ray Monochromator for the Study of Low Angle Diffraction
View Description Hide DescriptionA point focusing x‐ray monochromator was designed and constructed for low angle scattering studies. The anastigmatic point focus is achieved by means of two cylindrically bent quartz crystals whose focal circles are mutually perpendicular. The beam, emanating from the copper target of an x‐ray tube, is reflected in succession, first from the crystal defining the horizontal focal circle, and second from the crystal defining the vertical focal circle following which it comes to a monochromatic point focus of wavelength 1.537A (CuKα_{1}). The sample to be studied is placed between the second crystal and the point focus, and the scattered beam is detected by means of a photographic film placed at the point focus, at right angles to the undeviated beam, the latter being suppressed by means of an absorber, or allowed to pass through a hole in the film.
Mathematical analysis, in which a ray was traced through the two‐crystal system, revealed correctly the shape and size of the point focus, and the possibility of reducing the latter in size by stopping down the beam emerging from the target.

Latex Particle Size Determination Using Diffraction Peaks Obtained with the Point Focusing X‐Ray Monochromator
View Description Hide DescriptionWe describe the results of experiments we have made, using the point focusing monochromator as the primary tool, to determine the particle size of latex spheres. The suitability of the instrument for this particular study is described and the experimental data obtained are tabulated, these data coming from our experiments with three physically distinct samples of Dow latex. We attempt to make a critical interpretation of the data by considering separately several possible space arrangements which the latex spheres might assume when the water, which is initially the suspending fluid, is evaporated. Corrections for the finite size and shape of the ``point'' focus are described. The absence of a significant difference in the mean particle sizes of the three samples considered is established.
The data from all three samples is combined to yield a mean particle diameter under an external pressure of one atmosphere of 2687.5A with a statistical standard deviation of 1.2A and a fixed (systematic) error estimated to be not more than ±7A.

Anelasticity of Zinc
View Description Hide DescriptionAnelastic properties of zincsingle crystal of high purity (99.996 percent) have been studied, using bars vibrating transversely at audio frequencies in free‐free modes. Internal friction, effective elasticity, and shape of resonance curve were determined against the strain amplitude. When the driving force exceeds a critical value, the internal friction increases, its maximum‐amplitude‐frequency decreases, and its resonance curve becomes asymmetrical. Furthermore, under this condition a discontinuous phenomenon, which is supposed to be closely correlated with slips occurring in the crystal, has been found. This discontinuous phenomenon was recorded under different stresses.

The Decay and Recovery of the Pulsed Emission of Oxide‐Coated Cathodes
View Description Hide DescriptionThe decay and recovery of the pulsed emission of cathodes consisting of BaO on nickel are studied. The emission of the cathodes is measured in diodes of cylindrical geometry having water‐cooled copperanodes spaced 0.019 inch from the cathode.
Most of the diodes show a decay of anode current when first put in pulse operation. Decays of 2–50 percent are observed during 150‐μs pulses. The decay tends to disappear when the tubes are aged under pulse conditions. The peak current is a linearly decreasing function of the logarithm of the duty cycle, even when there is no perceptible decay during the pulses. The rate of decrease is independent of the pulse repetition rate and decreases with cathode temperature.
Current‐voltage characteristics during the pulse and recovery periods are obtained by short sampling pulses. A comparison of these characteristics with computed ideal characteristics does not discriminate unambiguously between a variation of emission and a variation of internal cathode impedance as a source of current decay. Studies to separate the contributions of these effects are in progress.

Measurement of the Internal Energy in Copper Introduced by Cold Work
View Description Hide DescriptionA determination was made of the ratio of the stored energy to the energy expended in cold‐working copper by twisting. Ratios of about 0.03 were found in three cylindrical samples which were cold‐worked to the extent of 8 to 12 cal/g.

Production of Monochromatic X‐Radiation for Microradiography by Excitation of Fluorescent Characteristic Radiation
View Description Hide DescriptionIn several types of applications of microradiography, particularly for histochemical and microchemical analysis by x‐ray absorption spectroscopy, it is desirable to use monochromatic radiation of a wavelength selected specifically with reference to an absorption edge of the element of interest. An x‐ray tube having as its target a material whose K _{α}characteristic wavelength is suitable is the most usual source of monochromatic x‐radiation. In many cases, however, an otherwise desirable target is physically unsuitable for use as a target inside a vacuum tube. Hence, the possibility of producing fluorescent characteristic radiation with intensities sufficient for microradiography becomes of interest. The very high intensity of the primary x‐ray beam made available by the newly developed beryllium‐window x‐ray tubes suggests new possibilities for the excitation of fluorescent radiation.
This paper reports the results of exploratory work attempting to establish the factors governing the intensity and degree of monochromaticity of fluorescent x‐radiation. Several materials, ranging from titanium (atomic number 22) to molybdenum (42) were studied comparatively, with exciting radiations of various characteristics;titanium was studied in greater detail. It is concluded that a considerably higher degree of monochromaticity is obtainable by this method than by direct bombardment and that intensities useful for some aspects by microradiography are obtainable.

Longitudinal and Transverse Ultrasonic Waves in a Synthetic Rubber
View Description Hide DescriptionVelocity and attenuation of both transverse and longitudinal ultrasonic waves are measured in a buna‐N vulcanizate at 2, 5, and 10 megacycles, over a range of temperatures. The method involves use of solid transmission media to conduct pulsed signals into a thin flat specimen. Values of the bulk modulus and of the complex shear modulus are computed from the measurements. It is found that longitudinal‐wave losses in this particular synthetic rubber are substantially accounted for by the relaxation phenomena measured in shear, but this conclusion is subject to considerable quantitative uncertainty arising from experimental errors estimated to be as large as 5 percent for longitudinal‐wave acoustic data and 10 percent for transverse‐wave acoustic data. It is found that below approximately −25°C the shear‐modulus loss tangent becomes relatively independent of temperature and frequency in the present range.

Space Charge Reduction of Low Frequency Fluctuations in Thermionic Emitters
View Description Hide DescriptionThe methods of measuring the space charge reduction factor for shot noise are briefly reviewed, and attention is drawn to the difficulties of making a similar measurement for flicker noise. An indirect qualitative test is described in which a triode is used both in normal manner and as a diode under retarding field conditions. Noise measurements at a high and a low frequency show that the effect of space charge on flicker noise exceeds that for shot noise. The diode results are used to estimate the value of the flicker noise reduction factor which is then seen to have a value less than the corresponding shot noise reduction factor at all current levels.

Electron Microscopy of Synthetic Latices
View Description Hide DescriptionA study has been made by electron microscopy of the size and size distribution of 22 synthetic latices. Included are GR‐S latices Types II, III, and V, polystyrene latices, and several latices of special character.
Details are given on sample preparation, measurement, application of corrections, calculation of number, volume to surface, and molecular weight average diameters, as well as the number and weight average distributions.
The weight average particle size range covered was 730 to 3920A. The smallest sizes were shown by Type II latices, followed in order by Type III, polystyrene, Type V, and some of the special latices. The latices were all nonhomogeneous in size and showed size distributions both on a number and weight basis which in some instances contained single and in some cases double maxima.

The Dirac Delta‐Function and the Summation of Fourier Series
View Description Hide DescriptionThe summation of Fourier series is attained by use of ordinary linear differential equations with constant coefficients having inputs that depend on certain combinations of the Dirac delta‐function. The method is illustrated by several examples representative of those series that arise in applications.

Electromagnetic Back‐Scattering from Cylindrical Wires
View Description Hide DescriptionThe problem of electromagnetic back‐scattering or radar response from cylindrical wires has been investigated using a variational method. The relation between this method and the induced emf method is discussed. To demonstrate the flexibility of the variational calculation different trial functions have been used to determine the numerical values of the back‐scattering cross section for the case of broadside incidence. The boundary condition regarding the currents at the ends of the wire is also carefully examined.

Thermal Force on an Aerosol Particle in a Temperature Gradient
View Description Hide DescriptionData on the thermal forces acting on aerosol particles in a temperature gradient are relatively few. Measurements are reported here on droplets of paraffin oil and castor oil suspended in air, showing the effect of temperature gradient, particle size, and particle material. The thermal force is directly proportional to the temperature gradient prevailing in the gas and to the particle diameter. It is an inverse function of the thermal conductivity of the aerosol material. The agreement between the experimental data and the theory of P. S. Epstein [Z. Physik 54, 537 (1929)] is satisfactory, a fortunate result in view of the approximations to the actual physical situation made in the derivation of the theoretical equation. The velocity of migration of aerosol particles in a temperature gradient can be estimated from Epstein's formula.

Free Molecular Flow in the Sample Inlet to the Mass Spectrometer
View Description Hide DescriptionThe aspects of free molecular flow in the sample inlet to the mass spectrometer are pointed out and the conditions under which such flow can occur are described. Methods for calculating the leak diameter and sample pressure for various flow rates are developed. These principles are illustrated by consideration of the flow characteristics in the mass spectrometer leak detector, and by an example from reaction kinetic studies.
The decrease in pressure in the sample reservoir is also described. This is applied to a determination of molecular weights. The effect of the pressure decrease on apparent fragmentation patterns is pointed out and a rational expression for spectrometer sensitivity is suggested which is based on the fraction of molecules which flow through the spectrometer which appear as ions.