Volume 28, Issue 3, 01 March 1957

Dispersion Relations for Tensor Media and Their Application to Ferrites
View Description Hide DescriptionThe well‐known Kronig‐Kramers integral relations between the real and imaginary parts of the susceptibility are generalized to the case where the susceptibility is a tensor. The consequences of the principle of energy conservation are discussed. The case of a ferrite is discussed in some detail.

Combustion and Detonation in Gases
View Description Hide DescriptionA photographic investigation of combustion in gases was undertaken to observe experimentally the mechanism of initiation and structure of detonation waves. Streak schlieren photographs of hydrogen‐oxygen and carbon monoxide‐oxygen explosions were made in a rectangular shock tube using precision optics and a rotating mirrorcamera.
The photographs show that compression waves generated during the early stages of propagation of the explosion soon steepen into a shock wave which travels ahead of the combustionwave (zone of chemical reaction). This combination of shock and combustionwave is characteristic of a nonsteady detonation state in the moments before stable detonation is initiated. The distance between the two waves narrows as the explosion progresses down the tube due to the continued formation of new combustion centers ahead of the combustionwave by means of auto‐ignitions. Eventually the combustionwave overtakes the shock wave and supplies it directly with energy from the chemical reaction; at this moment stable detonation is initiated.
The internal structure of steady state detonations is found to be different from nonsteady state detonations; for example, whereas the distance between the shock and the zone of chemical reaction is of the order of several centimeters in the nonsteady state detonation, this distance in the steady state detonation is too small to be resolved by the optical system (i.e., less than 1 mm). Other structural features such as spinning detonation and a high‐frequency oscillation of propagation velocity are also illustrated.

Solar Radiation and Atmospheric Attenuation at 6‐Millimeter Wavelength
View Description Hide DescriptionA microwaveradiometer of the Dicke type for the 6‐mm wavelength range has been built and operated to measureradiation from the sun and attenuation in the earth's atmosphere. The total vertical attenuation in the earth's atmosphere on four clear summer days averages 1.2 db. It is presumably due principally to oxygen, since the 6‐mm wavelength is well up on one wing of the 5‐mm absorption line. The quoted values are in agreement with a line‐width constant of 0.02 cm^{−1}. Attenuation in clouds is highly variable. An additional 1 db above the fair‐weather value is typical for a thin overcast.
Measurements during the summer of 1956 indicate an effective solar temperature of about 4500°K. This value is appreciably lower than temperatures reported at 7.5 and 8.5 mm, and it favors a model of the lower chromosphere which assumes temperatures well below the optical surface value of 5700°K.

Theory of the Microstrip
View Description Hide DescriptionA procedure is presented for finding by successive approximation the current distribution, and thus the electromagnetic field, of the lowest mode of the microstrip transmission line. The approximation is valid provided that the strip is not too wide and the dielectric sheet not too thick. Each iteration consists of essentially solving two electrostatic problems.

Extension of Babinet's Principle to Absorbing and Transparent Materials, and Approximate Theory of Backscattering by Plane, Absorbing Disks
View Description Hide DescriptionA rigorous formulation of Babinet's Principle has been found by Copson and by Meixner for perfect conductors. A recently published theory of diffraction by holes in absorbing and transparent screens suggests a generalization of Babinet's Principle to absorbing and transparent materials. The generalized form of Babinet's Principle is not a rigorous statement; it holds only for certain approximate solutions. In this paper it is used to calculate backscattering by circular disks of various reflection coefficients from zero to unity. Experimental results by Severin and v.Baeckmann support this theory. It is expected that, in a succeeding paper, it can be shown that scattering by solid bodies may be calculated in a similar way if the bodies are bounded by plane surfaces large compared to wavelength.

Dynamics of a Spinning Rocket with Varying Inertia and Applied Moment
View Description Hide DescriptionThe dynamic motion of a spinning rocket of varying moments of inertia under the influence of a varying torque is analyzed. The varying moments of inertia result from the rapid expenditure of fuel. The varying torque is produced by a constant rocket thrust asymmetrically applied while the body center of gravity location varies as the fuel burns. Aerodynamic forces are assumed negligible. The analysis is performed through the direct application of Euler's equations, which have a special applicability to this type of problem. The resulting motion is described in terms of Euler angles and resembles the motion of an ordinary top with nonsteady precession. The motion is compared to that of a body of fixed moments of inertia caused by a torque of fixed magnitude. It is shown that the variable aspects of the general problem create important characteristics of the resulting motion.

Electroluminescence Deterioration
View Description Hide DescriptionElectroluminescence intensity of phosphor layers decreases with running time; this decay can be described by the empirical expression, proposed by Roberts, L=L _{0}/(1+t/t _{½}), where t _{½} is the time to half‐intensity. It is also observed that, during electroluminescence decay at room temperature, (1) photoluminescence remains constant, (2) a component of the dark capacitance decreases in proportion to the light output, (3) photoconductivity and dark conductivity show a similar decrease, and (4) the light output wave form shows marked progressive changes. Also, (5) decay at 80°K proceeds at a much slower rate. An approximate derivation of an expression describing trap or donor depletion by electrolysis serves to correlate the data and the empirical expression in the foregoing.

Magnetic Induction and Coercive Force Data on Members of the Series BaAl_{ x }Fe_{12−x }O_{19} and Related Oxides
View Description Hide DescriptionOxides having the magnetoplumbite structure and a wide range of magnetic properties have been examined. The magnetic saturations of the compositions M^{II}Fe_{12}O_{19} can be lowered by replacing part of the iron with the ionsAl^{3+}, Ga^{3+}, Mn^{3+}, Cr^{3+}, and Ge^{3+} amongst others. M^{II} in the above formula can be Ba^{2+}, Sr^{2+}, or Pb^{2+}. Calcium can replace these ions in part. Even the samples with magnetic saturations below 200 gauss can be prepared as crystallographically oriented compacts. Contrary to its behavior in ferrites, Ga^{3+} does not appear to occupy tetrahedral sites in the magnetoplumbite structure.
Evidence is presented for the occurrence of points of magnetic compensation in the BaAl_{ x }Fe_{12−x }O_{19} series. As the aluminum contents of the materials increase toward such a point, the ratio 2K/I (where K is the magnetocrystalline anisotropy constant and I is the saturation magnetization) also increases. As a consequence the ferromagnetic resonance frequencies associated with the materials move to higher frequencies, and extremely high coercive forces are realized.

Magnesium‐Copper‐Manganese‐Aluminum Ferrites for Microwave Applications
View Description Hide DescriptionMagnesium‐manganese‐aluminum ferrites prepared by dry pressing techniques are usually fired in the temperature range between 1350 and 1400°C for extended periods of time to obtain samples having high relative densities. When about ten percent of the magnesium in such a system is replaced by copper, as in the series Mg _{0.9} Cu _{0.1}Al_{ x }Fe_{1.75−x } Mn_{0.04}O_{4±}, it is possible to obtain samples with high relative densities and dc resistivities by firing in the 1250 to 1300°C range. Such materials are suitable for microwave applications.
The preparation of ferrites of this type is discussed and data presented on the saturation inductions, Curie temperatures, densities, and dc resistivities.

Thermionic Constants and Sorption Properties of Hafnium
View Description Hide DescriptionThermionic emission measurements on polycrystallinehafnium in the temperature range 1250 to 1820°K have yielded a work function of 3.60 ev and a thermionic constant A of 22.9 amp cm^{−2} deg^{−2}. Intermittent heating thereafter for a total of 46 hours at temperatures above 2100°K and at pressures below 1×10^{−9} mm Hg did not change these parameters appreciably. No gas was desorbed from the hafnium when it was flashed to 2150°K after having been cold for 64 hours. A second sample of hafnium was used as a target in apparatus for studying electron ejection by ions. It was more brittle than the first and thus more contaminated with gas. Its work function was found to be 3.91 ev and the constant A to be 20.5 amp cm^{−2} deg^{−2} after repeated flashing to 2150°K. Evidence from the electron ejection work indicates that the surface of this second hafnium sample was covered with an appreciable fraction of a monolayer immediately after cooling from high temperature. One can conclude that the work function of hafnium increases as the metal irreversibly absorbs gas on heating.

Equipment to Measure the Energy Absorption of Films at High Strain Rates
View Description Hide DescriptionThe design and performance of equipment to measure film toughness under impact loading is described. The measured quantity is the amount of energy absorbed by a film when a ball is projected through it. The velocity of the ball can be varied from about 20 ft/sec to 800 ft/sec. A conditioning chamber permits testing over a temperature range of −40°C to +80°C. Individual tests require a specimen of film of about 1¼×1¼ in. and can be made at the rate of about 2/min. Results are given for films of several commercial materials.

Theory of Thermal Grooving
View Description Hide DescriptionA theory is presented which describes the development of surface grooves at the grain boundaries of a heated polycrystal. The mechanisms of evaporation‐condensation and surface diffusion are discussed with the use of the Gibbs‐Thompson formula and the assumption that the properties of an interface do not depend on its orientation. For the idealized case in which only one of the mechanisms is operative, the groove profile is shown to have a time‐independent shape whose linear dimensions are proportional to t ^{½} for evaporation‐condensation, and to t ^{½} for surface diffusion. The proportionality constants are evaluated, and criteria are developed which permit one to estimate which process predominates in practice. Order of magnitude agreement is obtained with estimates of actual grooving speeds and profiles.

On the Determination of Magnetocrystalline Anisotropy Constants from Torque Measurements
View Description Hide DescriptionAccording to simple theory,torque measurements on cubic single‐crystal disks should give values for the crystal anisotropy constants, K _{1} and K _{2}, that are independent of field above some minimum saturating field. Our experiments on {100} and {110} disks of 3¼% silicon‐iron, and previous experiments of others, show that this theory is inadequate. In a more refined theory it is assumed that the edges of the disk are not saturated even in high fields. The observed increase in the peak values of the torque with increasing field can be attributed to a very small variation of the net magnetization I as the disk is rotated in the field. This variation must be such that I is largest in the hard directions of magnetization and smallest in the easy directions. Direct observation of the domain patterns on a {100} disk appears to confirm these assumptions. For both {100} and {110} disks, K _{1}′ (the effective value of K _{1}) varies as 1−c/√H over the range 1000 to 20 000 oersteds. The corresponding K _{2}′ values for the {110} disk show a more complicated dependence on H. Values of K _{1}′ found from torque peaks differ somewhat from those obtained from torque slopes; the difference between the smaller K _{2}′ values is much more serious. The discrepancy is attributed to the particular way in which I varies with disk rotation.

Reproducing the Properties of Alnico Permanent Magnet Alloys with Elongated Single‐Domain Cobalt‐Iron Particles
View Description Hide DescriptionSingle‐domain particles of 40:60 cobalt‐iron alloy have been prepared with a median diameter of 200 angstrom units, a median elongation of 5.4:1, and an intrinsic coercive force of 1950 oersteds. By compacting these particles to various packing densities and degrees of alignment, shape anisotropy fine‐particle magnets have been made with magnetic properties duplicating those of each of the Alnico permanent magnet alloys, including maximum energy product values above five million gauss‐oersteds. It is concluded that the Alnico alloys and the fine‐particle magnets derive their properties from very similar, but not identical, shape anisotropy effects.

Noise in Nonlinear Oscillators
View Description Hide DescriptionA method is presented for estimating the nonlinear noise contribution in an oscillator at low levels of oscillation. This involves obtaining an approximate solution of a nonhomogeneous van der Pol type of nonlinear differential equation driven by noise. The method of solution is based upon the reduction of the equation to a linear form. The nonlinear contribution can then be obtained by computing the power spectrum output of a cube law rectifier. The calculations indicate a variation of nonlinear noise with rf level. Such variation is observed in nuclear and electronic magnetic resonancedevices used for the detection of magnetic absorption in paramagnetic materials.

U‐Effect‐III; Effect of Liquid Drop Motion in Mercury‐Electrolyte Capillary Tubes
View Description Hide DescriptionWhen a glass capillary tube filled with alternating drops of mercury and electrolyte is made to vibrate mechanically, an alternating voltage is available across terminals inserted in its ends. This effect has been attributed to changes in the surface area of the interfaces [E. Yeager and F. Hovorka, J. Acoust. Soc. Am. 25, 447 (1953)]. New experimental evidence indicates that at low frequencies the output voltage depends on motion of the liquid drops with respect to the capillary tube. A first‐order approximation theory which takes into account the tube compliance and the relative motion of the liquid drops with respect to the capillary tube has been obtained and is found to agree qualitatively with the experimental data relating: (1) tube output voltage to frequency at fixed amplitude of vibration; (2) tube output voltage to relative motion of the drops at fixed frequency; and (3) short‐circuit current output to relative motion for fixed capillary radius, independent of mercury‐electrolyte proportions for a given electrolyte.Theory indicates that the voltage is a function of the length of mercury in a tube rather than of the number of interfaces; this result seems to be in agreement with the data.

Steady‐State Creep through Dislocation Climb
View Description Hide DescriptionA dislocation climb creep model is considered which does not require the production of immobile dislocations. The creep equation that results from the analysis is

Thermoelastic Damping at the Boundary between Dissimilar Solids
View Description Hide DescriptionThe problem of thermoelastic damping at the boundary between dissimilar solids is investigated for the case of small, sinusoidal, longitudinal disturbances of long‐wavelength propagating normally through the interface. The relevant equations are derived from thermodynamic considerations, and it is found that the mechanical energy absorption per unit time is proportional to the square root of the disturbance frequency.

Activation Field and Coercivity of Ferroelectric Barium Titanate
View Description Hide DescriptionThe activation field of BaTiO_{3} c‐domain crystals may be calculated from an experimental determination of the frequency dependence of the coercivity. The ratio of activation fields above and below the orthorhombic transition is equal to the respective ratio of coercivities. The decrease in coercivity in passing through this transition is related to the change in thickness of the space charge layer within the ferroelectric.

Dynamics of a Projectile Penetrating Sand
View Description Hide DescriptionThe experiment reported in this paper was designed to obtain data on the dynamics of a nonrotating, conical‐nosed projectile penetrating randomly‐packed sand. Position versustime measurements for the projectile in sand were obtained by means of a photographic‐electronic chronograph developed for the purpose. The striking velocity v _{0} of all rounds was about 700 m/sec. The negative acceleration of a 5‐in. long, 0.50‐caliber, 80‐gram projectile was found to be roughly expressible by the equation where the coefficients α, β, and γ are positive constants. This general relation includes as special cases the conventional penetration formulas of Robins‐Euler, Poncelet, and Résal. A new theory of penetration is proposed based on the equations: where the coefficients α, β, γ are positive constants and α<β. An abrupt transition in the drag force that occurs at the critical velocity v_{c} of about 100 m/sec is believed due to transition from inelastic to quasi‐elastic impact.