Volume 26, Issue 12, 01 December 1955

Dielectric Constant of Quartz as a Function of Frequency and Temperature
View Description Hide DescriptionMeasurements of dielectric constant and power loss were made from 1 to 90 kc/sec and from 20°C to 400°C. The dielectric constant parallel to the optic axis for all frequencies shows a sharp rise, which occurs at successively higher temperatures for higher frequencies. The loss at a given frequency has a temperature maximum which is higher, the higher the frequency. The results are partially explained by assuming that ions are present in ``tunnels'' parallel to the optic axis. The density and mobility of these ions are obtained. The density is temperature dependent in such a way as to lead to an activation energy of 17.7 kcal per mole. Lithium ions were introduced into the crystals, and the effects caused by these ions were at least compatible with the assumption that lithium ions were originally present. Perpendicular to the optic axis none of the above effects exist.

High Field Electron Emission from Irregular Cathode Surfaces
View Description Hide DescriptionElectron emission from a cathode surface produced by an applied field E is enhanced by the presence of projections on the emitter surface which cause a local increase in E. The nature of this enhancement factor μ(z), which is a function of the distance z from the cathode, is discussed more fully than hitherto and its magnitude is calculated for certain ideal but realistic geometries. Although such a factor may be large on the surface (z=0), it decreases rapidly as z increases so that the mean field magnification , which is required in the Schottkythermionic emissiontheory, is unlikely to be >2 and is probably near to unity even for fields as great as 5×10^{5} v/cm. This fact will mean that the Fowler‐Nordheim theory frequently used to explain emission results at these fields is not applicable and that a Schottkytheory should be used.
It is also shown that is itself field dependent and produces departures from the Schottky law in such a way that the slope of the current vs E ^{½} plot increases rapidly for E<10^{3} v/cm, remains approximately constant for 10^{3}<E<10^{4} v/cm, and then increases again at higher fields. A similar reasoning shows that deviations from the Fowler‐Nordheim law for fields >10^{6} v/cm can also be expected.
Finally, the assumption of a constant emitting area for rough cathodes is also shown to give departures from the emission laws in such a manner that the estimated current density at high fields is appreciably less than the expected values.
These deductions help to explain some of the anomalous results frequently found in many conduction experiments in gases and liquids.

New Active Circuit Element Using the Magnetoresistive Effect
View Description Hide DescriptionA new multistable element is described, and the conditions under which it may operate are discussed. It is found that a bistable element (flip‐flop) with reasonable resolving time may be achieved, though it might be necessary to operate it at low temperatures. A tristable element is found to be possible, but not practical. A slowly operating model is described.

Hexagonal Microstructure of Ice Crystals Grown from the Melt
View Description Hide DescriptionElectron microscopy of etched and nascent surfaces of single ice crystals shows a characteristicmicrostructure of elongated, hexagonal prisms. The small hexagonal units vary greatly in size with an expected width of the order of 3 microns and a length of 6 microns. The coordination among microcrystalline units characterizes a particular single crystal, the size of which may be determined by processes of freezing and subsequent history, but the sizes of the microcrystalline units of which they are composed appear to be independent of the rates of freezing. The etchedsurfaces show that the center of the hexagonal unit etches to a greater depth than does the outer area, indicating a higher degree of crystal disorder along the axis of symmetry.
Icesurfaces in process of growing from the melt also appear to consist of hexagonal pyramidal pits which are built up by concentric steps around the C‐axis. This structure appears to be consistent with that of the etchedsurfaces. Observations of growing‐icesurfaces formed from cesium fluoride solutions reveal that the fluoride impurity tends to reduce the prominence of the pyramidal microstructure in a manner dependent upon concentrations such that the structure disappears for concentrations greater than 10^{−3} M.

Space‐Charge Distribution in a Static Magnetron
View Description Hide DescriptionThe space‐charge distribution in a static magnetron was investigated by a method involving measurement of the radiation intensity from excited gas atoms at low pressure. Results of the measurements show that space charge extends to the anode under all conditions. Evidence is presented to show that a considerable fraction of the space charge consists of electrons that are trapped for exceedingly long times within the interaction space.

Application of the Engravement Method to the Study of Particle Velocity Distribution in Explosively Loaded Cylinders
View Description Hide DescriptionApplication of the engravement method to the study of particle velocity distribution in the wall of a thick‐walled metal cylinder internally loaded with an explosive charge is described. Tests were conducted with this method on modified cylinders of annealed low‐carbon steel and of brass. Even though each of the modified cylinders broke into a number of fragments, the engravements were well enough preserved to furnish considerable data. Many measurements were obtained from each cylinder by using a large number of pellets of several thicknesses. Particle velocity data were obtained to within inch from the metalexplosive interface. Temporal particle velocity distribution curves are presented for each of the cylinders.

Thickness‐Shear and Flexural Vibrations of Rectangular Crystal Plates
View Description Hide DescriptionEquations governing thickness‐shear and flexural vibrations of crystal plates are solved for the infinite plate, the simply‐supported rectangular plate and the rectangular plate with one pair of parallel edges free and the other pair simply‐supported. The equations permit three types of sinusoidal waves, with sinusoidal crests, in an infinite plate. Each of these undergoes a simple reflection upon normal incidence at a simply‐supported straight edge, so that the frequency spectrum of a simply‐supported rectangular plate has a relatively simple character. The results of a typical computation are given for the AT‐cut of quartz. At a free edge each type of incident wave gives rise, in general, to all three types of reflected wave. Consequently, the frequency spectrum of a plate with a pair of parallel, free edges exhibits an intricate coupling of three infinite systems of modes. The development of the coupling is traced continuously by means of a solution involving elastically supported edges.

Space‐Charge Waves in Crossed Electric and Magnetic Fields
View Description Hide DescriptionThe problem of space‐charge waves propagating along a neutralized electron stream moving in a medium pervaded by crossed static electric and magnetic fields is discussed. From energy considerations it is shown that gain can be realized either by conversion of the electron kinetic or potential energy into electromagnetic energy. A small signal analysis shows that for the first case the TE and TM modes are coupled in general. However, when the electron velocity is much smaller than the velocity of light the coupling coefficients are negligible and the gain realized is identical with that of the conventional traveling‐wave tube. A similar analysis for the second case, which is that of the traveling‐wave magnetron tube, yields the interesting result that the TE and TM modes separate even when the electron velocity is comparable with the velocity of light.

Theory of Scattering by an Inhomogeneous Solid Possessing Fluctuations in Density and Anisotropy
View Description Hide DescriptionThe theory of Debye and Bueche for the scattering of light by an amorphous solid is extended to the case where fluctuations in anisotropy as well as density are considered. A generalized correlation function is defined, which gives the probability of a simultaneous occurrence of fluctuations in polarizability in two volume elements a distance r apart. The fluctuations are specified by the magnitudes of the polarizabilities and the directions of the optic axes. The correlation function is assumed to depend on r, on the angle between the axes of the fluctuations, and on the angle giving the position of the second element with respect to the optic axis of the first. The intensities of the horizontal and vertical components of the scattered light are expressed as integrals over the correlation function of explicit functions of r and the two angles. From the initial slopes and intercepts of the intensities plotted against sin^{2}(θ/2) where θ is the scattering angle, one can obtain average values and average dimensions of the fluctuations, and a measure of the extent to which fluctuations in density and anisotropy are correlated. The theory is applicable to glasses,gels, and liquid crystals.

Low Shear Capillary Viscometer with Continuously Varying Pressure Head
View Description Hide DescriptionA capillary viscometer is described for the study of the flow behavior of non‐Newtonian fluids at shear stresses of 0.06–20 dynes/cm^{2}. The all‐glass instrument consists of two units connected by a ball joint, one unit of which contains the capillary while the second is essentially a manometer. As the test fluid moves through the capillary, the rate of rise of the fluid in the manometer is observed. This measurement of the column height as a function of time allows calculation of both pressure drop and rate of flow. Different combinations of capillary and manometer units can be employed interchangeably to study liquids of widely varying viscosities. Data and methods are presented which show that the instrument can be used to determine the absolute viscosities of Newtonian liquids and the flow curves of non‐Newtonian fluids over the indicated shear stress region.

Space‐Charge Effects in Electron Optical Systems
View Description Hide DescriptionBeams consisting of charged particles which are all directed towards a given virtual focus will generally not reach this focus but, due to their mutual repulsion, they will pass through a waist and then become divergent. Ray tracing shows that either positive or negative spherical aberration is introduced in a beam passing through a waist. This aberration is caused by the interaction of the electrons; its sign depends on voltage, current, and on the angle of initial convergence of the beam. For sufficiently high voltages or low currents, waist formation no longer occurs, but the electron rays cross the axis of the beam. With decreasing current density, the transition from waist to crossover is found to occur first for the inner rays of the beam while the outer rays still form a waist. All experimental results are found to be in approximate agreement with theoretical predictions.

Dynamic Determination of the Compressibility of Metals
View Description Hide DescriptionEquation of state data for Duralumin in the pressure range from 0.1 to 0.3 megabar have been determined dynamically by measuring shock and free surface velocity electrically in a plate of 24 ST Duralumin that has been stressed by a high explosive detonation. A theory is presented which allows comparison with data obtained by other experimenters, and which yields the relationship between pressure and compression either at constant entropy or constant temperature. The empirical form chosen for the equation of state (p=αμ+βμ^{2}) expresses the pressure as a quadratic function of the compression. Experimental techniques are described in detail. Five points are given for the equation of state of Duralumin in the pressure range from approximately 0.15 megabar to 0.33 megabars. Some data are also presented for cadmium and steel.

Ferroelectric Hysteresis in Barium Titanate Single Crystals
View Description Hide DescriptionThe properties of the dynamic hysteresis loop of a c‐domain BaTiO_{3}single crystal are examined as a function of temperature. Experimental results indicate that the coercivity and hysteresis losses decrease sharply as the crystal passes through a phase transition to a lower order of symmetry. This occurs without a substantial loss in loop rectangularity. The properties of a theoretical model for the hysteresis loop are derived from the Devonshire thermodynamic equations and previously defined experimental parameters. In the tetragonal and orthorhombic crystal phases, good agreement is obtained between the behavior predicted for the theoretical model and the experimental observations made on a c‐domain.

Total Emissivities and Absorptivities of Some Commercial Surfaces at Room and Liquid‐Nitrogen Temperatures
View Description Hide DescriptionThe heat transferred by radiation was measured between surfaces at room temperature and liquid‐nitrogen temperature. The surfaces used were various combinations of electroplated gold and silver and polished copper sheet. From the test data, the approximate total emissivities of the room‐temperature surfaces and the total absorptivities of the liquid‐nitrogen surfaces were computed.
The results of these tests indicated that electroplated silversurfaces have lower emissivities and absorptivities than equivalently treated electroplated goldsurfaces in this temperature range. The best surface tested was a special, bright, unbuffed silver‐plated surface. This surface is known to the trade as ``silver lume.'' The room‐temperature emissivity of this surface was approximately 0.017, and the absorptivity at 77.3°K for radiation from a 300°K surface was about 0.0083. These are the lowest values at these temperatures of which we have knowledge.
It was found that the electroplated surfaces were best used without buffing or any mechanical working of the surface. It is believed that cold working of the metal surface increases its emissivity and absorptivity by increasing its electrical resistivity.

Gettering of Gas by Titanium
View Description Hide DescriptionTitanium metal has been studied as a getter for oxygen, nitrogen, carbon dioxide, air, water vapor, hydrogen, and methane.Titanium above 700°C will getter oxygen, nitrogen, and carbon dioxide. Hydrogen is absorbed by titanium in the temperature range of 25 to 400°C. Water vapor and methane are readily sorbed when the metal is operated at both elevated and reduced temperatures. Large quantities of gases can be sorbed; sorption of ten to ninety atomic percent is possible. When saturated with gas, the metal becomes brittle and is easily fractured. Hydrogen gas is the only gas which can be released by heating after it has been sorbed by titanium.

Stress‐Strain Relations in Snow under Uniaxial Compression
View Description Hide DescriptionTwo types of tests were performed on the uniaxial compression of snow; experiments at constant strain rate and at constant load. The strain rate can be represented as the product of functions of density, stress, temperature, and time. For densities between γ≃0.3 g/cc and γ≃0.6 g/cc the strain rate is proportional to (γ_{ ice }−γ)/γ to the fourth power. The strain rate varies linearly with stress for low stresses (2<σ<100 g/cm^{2}) but increases to an approximately cubic relationship at higher stresses (1<σ<5 kg/cm^{2}). An activation energy of about 14 000 cal/mole can be derived from the temperature dependence. In the constant load tests the strain is proportional to the time to a power of about 0.8. The effect of snow type is small, being less than the relatively large experimental scatter encountered.

Calculation of the Complex Modulus of Linear Viscoelastic Materials from Vibrating Reed Measurements
View Description Hide DescriptionTwo methods of determining the variation of real and complex modulus with frequency from vibrating reed test results are detailed. One is based on measurements of the relative amplitude and phase lag of the motion of the free and driven ends of the reed, the other on amplitude resonance measurements only. The analysis is based on a general linear viscoelastic law, and takes into account the influence of the frequency dependent moduli of the material on the frequency and amplitude of the resonance peaks. This influence has not been correctly accounted for in previous analyses which have included the assumption that the material behaves according to a particular, simple viscoelastic law, which will in general not be borne out by the final results.
The method is applied to a series of tests. For the material and frequency range used the imaginary part of the complex modulus was small compared with the real part, and the influence mentioned in the foregoing was small. A simpler method of analysis might thus be justified, but in other cases it will be necessary to carry out the complete analysis in order to obtain a satisfactory interpretation of test results.

Angular Distribution of Multiply Scattered Gamma Radiation from a Plane Isotropic Source
View Description Hide DescriptionA method is given for calculating, within the framework of the moment‐method of Spencer and Fano, the angular distribution of radiation from a plane isotropic source. Essential use is made of the simplification introduced by a geometrical feature of radiation from such a source. Sample calculations are presented for a 1‐Mev source in water.

Method for Obtaining Complete Quantitative Pole Figures for Flat Sheets Using One Sample and One Sample Holder
View Description Hide DescriptionThe general expressions for the x‐ray absorption corrections in the reflection region for flat sheets in any orientation are derived. These equations contain, as special cases, the correction factors of previously reported pole figure techniques and also correction factors for a new method, permitting a rapid and accurate determination of complete quantitative pole figures of flat sheets using one sample and one sample holder. For the outer regions of the polar net a low‐order Bragg reflection is used with the technique of Decker, Asp, and Harker; and for the center region a higher order Bragg reflection from the same set of planes is used with a different set of correction factors. Pole figures, obtained by this method, for cold rolled aluminum and magnesium are presented.

Capacitance Measurements on Alloyed Indium‐Germanium Junction Diodes
View Description Hide DescriptionDonor densities in the base material of fused junction diodes, inferred from capacitance data, are used to calculate majority carrier mobilities. The dependence of capacitance on reverse bias at very low biases is found to be given by the sum of two terms, a space charge capacitance and a capacitance due to the flow of holes as given by Shockley's low level p‐n junction theory.