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1 Apr 1955

Volume 26, Issue 4, pp. 359-492

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Extensions of the Rouse Theory of Viscoelastic Properties to Undiluted Linear Polymers

John D. Ferry, Robert F. Landel, and Malcolm L. Williams

J. Appl. Phys. 26, 359 (1955); http://dx.doi.org/10.1063/1.1721997 (4 pages) | Cited 79 times

Online Publication Date: 14 May 2004

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The Rouse theory for viscoelastic properties of very dilute solutions is modified for application to undiluted linear polymers. With the effective segment mobility expressed in terms of steady‐flow viscosity, the theory is applied to polymers of rather low molecular weight essentially without further change. In high molecular weight polymers, it is assumed that for modes of motion with relaxation times above a critical value the effective segment mobility drops abruptly, in accordance with the effect of entanglement coupling on steadyflow viscosity as described by Bueche. Properties in both the transition region between glasslike and rubberlike consistency and the rubberlike or plateau region are predicted semiquantitatively with no arbitrary parameters. In an alternative application to the transition region, the average effective friction coefficient per monomer unit can be calculated for both linear and lightly cross‐linked systems.

Rate of Formation of Film on Metals and Alloys

G. P. Chatterjee

J. Appl. Phys. 26, 363 (1955); http://dx.doi.org/10.1063/1.1721998 (3 pages) | Cited 1 time

Online Publication Date: 14 May 2004

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The rate of atmospheric corrosion of Cu☒Zn and Cu☒Mg alloys are retarded by Al or Mn, and the law of the growth of film in the case of Cu☒Zn alloys changes over from the parabolic to the logarithmic law on the addition of Al or Mn. For Cu☒Mg alloys under a given set of conditions the law of the growth of film is governed by
math
,where x is the film thickness, t is time, and k1 and k2 are constants. It has been indicated that some experimental data on the corrosion of metals and alloys may be quantitatively represented if two or more functions, representing different mechanisms of the growth of film, are taken into consideration simultaneously.

Creep of Aluminum under Cyclotron Irradiation

M. R. Jeppson, R. L. Mather, A. Andrew, and H. P. Yockey

J. Appl. Phys. 26, 365 (1955); http://dx.doi.org/10.1063/1.1721999 (3 pages) | Cited 5 times

Online Publication Date: 14 May 2004

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The effect of cyclotron irradiation by 38‐Mev alpha particles on the steady‐state creep rate (ca 10−6 per second) of aluminum has been measured at beam densities up to 1.2×1013 particles per cm2 per second. The data, which were taken on a 0.016‐inch thick aluminum specimen for a stress range of 600 to 2500 psi and over a temperature range of 160° to 330°C, showed a slight decrease in rate (up to 19 percent) during irradiation. Since the effect is small, apparently independent of beam density, and is comparable to the usual deviations in the absence of radiation, it can be considered a null result.

Azimuthal Surface Waves on Circular Cylinders

Robert S. Elliott

J. Appl. Phys. 26, 368 (1955); http://dx.doi.org/10.1063/1.1722000 (9 pages) | Cited 9 times

Online Publication Date: 14 May 2004

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Solutions of Maxwell's equations are presented which satisfy the boundary conditions for corrugated and dielectric‐clad circular conducting cylinders. These solutions have the physical interpretation of leaky azimuthal surface waves. Values of the complex propagation constant are given as functions of the geometry. For large cylinders the leakage is small and the transmission properties are approximately those of a trapped wave on a flat surface. A coarse experiment gives reasonable agreement with the theory. Some possible applications to transmission lines and antennas are indicated.

Thermoelectric Power and Electrical Resistivity of Dilute Alloys of Silicon in Copper, Nickel, and Iron

C. A. Domenicali and F. A. Otter

J. Appl. Phys. 26, 377 (1955); http://dx.doi.org/10.1063/1.1722001 (4 pages) | Cited 8 times

Online Publication Date: 14 May 2004

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Data are given on the thermoelectric power and on the resistivity of the dilute alloys, Cu☒Si, Ni☒Si, and Fe☒Si, from −195° to +500°C (and higher for some of the alloys). The Cu☒Si thermopower at first decreases with increasing Si content and then again increases, the minimum being at about 2 or 3 atomic percent Si, depending on the temperature. The Cu☒Si resistivity is typical of Cu‐base alloys, the resistivity increases per atomic percent Si changing from 7.2 μΩ cm at −190°C to 8.7 μΩ cm at 840°C. The thermopower and resistivity curves for Ni☒Si show a characteristic knick at the Curie temperature of each alloy. The Fe☒Si thermopowers are positive at lower temperatures and become negative at a temperature T0 which decreases with increasing Si content. Furthermore, T0 changes from about 300°C for pure iron to about +70°C for 2 atomic percent Si. The resistivity of Fe☒Si alloys increases faster than linearly with temperature, and this is also the case for the Ni☒Si alloys below the Curie temperature. Above the Curie temperature, the Ni☒Si resistivities vary linearly with temperature. The increase in resistivity per atomic percent Si in Fe is 10.5 μΩ cm at all temperatures within the measured range.

Injected Current Carrier Transport in a Semi‐Infinite Semiconductor and the Determination of Lifetimes and Surface Recombination Velocities

W. Van Roosbroeck

J. Appl. Phys. 26, 380 (1955); http://dx.doi.org/10.1063/1.1722002 (12 pages) | Cited 122 times

Online Publication Date: 14 May 2004

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With both surface and volume recombination taken into account, time‐dependent and steady‐state Green's functions are obtained for a point source of added carriers in a semi‐infinite semiconductor, and for infinite line and plane sources parallel to the surface. Small‐signal theory is employed, and a compact Stieltjes‐integral derivation is given. The Green's functions are specialized to provide: the time dependence of surface concentration following the instantaneous injection of carriers at a point on the surface; that following instantaneous injection which is uniform over the surface; and the distance dependences for steady point, infinite‐line, semi‐infinite plane, and semi‐infinite line surface sources. Steady flows of minority carriers from these sources into a p—n junction perpendicular to the surface are also calculated. Analytical approximations are found for the steady‐source cases. Theoretical and experimental aspects of the determination of lifetimes and surface recombination velocities from data by means of these results are discussed.

Diffraction of Electromagnetic Waves by a Metallic Wedge of Acute Dihedral Angle

W. W. Grannemann and R. B. Watson

J. Appl. Phys. 26, 392 (1955); http://dx.doi.org/10.1063/1.1722003 (2 pages) | Cited 1 time

Online Publication Date: 14 May 2004

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In the rigorous theory of diffraction by a conducting wedge as developed by Sommerfeld and extended by Pauli, the total field is represented by the terms given by geometrical optics plus a contour integral which represents the diffracted waves. If the faces of the wedge form a dihedral angle of π∕m, m=1, 2, 3 … the contour integral vanishes identically and the solution given by geometrical optics is exact. This prediction has been tested and checked by measurements and calculations of the diffraction patterns of wedges whose dihedral angles were 90° and 30°. The measurements were made at a wavelength of 1.25 cm.

Moderation of Neutrons in SiO2 and CaCO3

Jay Tittman

J. Appl. Phys. 26, 394 (1955); http://dx.doi.org/10.1063/1.1722004 (5 pages) | Cited 1 time

Online Publication Date: 14 May 2004

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The spatial distributions of indium resonance neutrons about a ``point'' Ra‐Be source have been measured in pure CaCO3 (limestone) and SiO2 (sand) out to r2≈9τ. Both media show nearly Gaussian distributions corresponding to Fermi ages τ(SiO2)=1906±90 cm2 and τ(CaCO3)=461±23 cm2 over most of the range observed. Excess resonance flux near the source, more pronounced in CaCO3 than in SiO2, appears to be due to inelastic scattering although such interpretation is not unambiguous. Space integrals indicate ∼10 percent more absorption in CaCO3 than in SiO2 during moderation. Data were corrected for 4.5‐hr activity, 54‐min activation by high energy neutrons, and edge effects; consideration was given to the 3.9‐ and 9‐ev In levels in defining the mean detection energy and to the nonmonoenergetic nature of the Ra‐Be source in affecting the shape of the indium resonance spatial distribution.

Re‐Examination of the Nonsteady Theory of Jet Formation by Lined Cavity Charges

R. J. Eichelberger

J. Appl. Phys. 26, 398 (1955); http://dx.doi.org/10.1063/1.1722005 (5 pages) | Cited 11 times

Online Publication Date: 14 May 2004

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A new type of analysis is applied to observations on jets from lined cavity charges in order to test the nonsteady‐state hydrodynamic theory of a jet formation. The results support previous findings that the theory is qualitatively accurate, but give evidence of departures from the ideal situation assumed in the theory. An attempt is made to assess one of the more likely sources of error, the neglect of acceleration of the liner.

Relation to Diffusion Measurements of Some Beta‐Ray Absorption Phenomena

A. E. Berkowitz

J. Appl. Phys. 26, 403 (1955); http://dx.doi.org/10.1063/1.1722006 (3 pages) | Cited 4 times

Online Publication Date: 14 May 2004

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The absorption in thin layers of nickel, aluminum, and cobalt of beta rays from Co60 was measured in connection with the use of the surface counting method of determining diffusion coefficients. Data was obtained for foils and for evaporated and electroplated layers. In all cases the activity increased between 0 and 4 mg∕cm2. A discrepancy was noted between the data for foils and those for evaporated and electroplated layers. It is shown that this general behavior is predicted by simple scattering and absorption expressions. The implications of these data for the use of the surface counting method are discussed.

Measurement of the Elastic Constants of Single Crystal Cobalt

H. J. McSkimin

J. Appl. Phys. 26, 406 (1955); http://dx.doi.org/10.1063/1.1722007 (4 pages) | Cited 42 times

Online Publication Date: 14 May 2004

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The 5 elastic constants of hexagonal cobalt have been determined using pulse modulated ultrasonic waves which are reflected back and forth within the crystal. Frequencies between 10 and 30 Mc∕sec were used. Values of the constants were derived from 11 measurements of wave velocities for longitudinal and shear modes in 3 crystals, using a phase comparison technique. At 25°C the constants (all in 1012 dynes∕cm2) are: c11=3.071±0.5 percent, c12=1.650±0.5 percent, c13=1.027±1.5 percent, c33=3.581±0.5 percent, c44=0.755±0.5 percent. These are based on a density of 8.836.

Theory of Frequency Modulation Noise in Tubes Employing Phase Focusing

John L. Stewart

J. Appl. Phys. 26, 409 (1955); http://dx.doi.org/10.1063/1.1722008 (5 pages) | Cited 2 times

Online Publication Date: 14 May 2004

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Oscillators employing phase focusing such as magnetrons have fairly well defined spokes whose rotational speed is proportional to the oscillation frequency. Each spoke is composed of a finite number of electrons having random velocities and consequently is subject to random fluctuations about a mean position. This spoke ``jitter'' leads to fluctuations in the oscillation frequency resulting in frequency modulation noise. It is the theoretical evaluation of the parameters of this noise as affecting the power spectrum of the oscillator output that is of interest here. The theoretical results compare favorably with the measured power spectrum of a voltage‐tunable magnetron. The application of the formulas require an estimate of electron temperature although no attempt is made to evaluate this temperature. Amplitude fluctuation noise appears to be relatively unimportant in continuous‐wave phase‐focused oscillators.

Measurement of the Lifetime of Minority Carriers in Germanium

William G. Spitzer, Tomas E. Firle, Melvin Cutler, Robert G. Shulman, and Milton Becker

J. Appl. Phys. 26, 414 (1955); http://dx.doi.org/10.1063/1.1722009 (4 pages) | Cited 4 times

Online Publication Date: 14 May 2004

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Two methods are described for the measurement of lifetime of minority carriers. One depends on pulse injection of carriers in a filament and detection, after a known time, at a collector. The second makes use of the decay of the conductivity modulation caused by minority carriers after injection at a single contact. Both measure the lifetime in a small region rather than the average value over a large part of the sample.

Electron Temperature in the Parallel Plane Diode

T. N. Chin

J. Appl. Phys. 26, 418 (1955); http://dx.doi.org/10.1063/1.1722010 (6 pages)

Online Publication Date: 14 May 2004

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Chandrasekhar's relaxation time is applied to the electron gas in flow. By determining the relaxation time, tR, and the mean transit time, tT, two types of electron flow may be characterized: anisotropic flow if tT«tR, and isotropic flow if tR«tT. It is shown that the electron temperature along the flow decreases as the mean velocity of the electrons increases in a parallel plane diode. In the given examples, the boundary conditions are obtained for a particular model which has been recommended in the study of thermionic emission.

X‐Ray Diffraction Study of Silver Iodide Aerosols

James E. Manson

J. Appl. Phys. 26, 423 (1955); http://dx.doi.org/10.1063/1.1722011 (3 pages) | Cited 3 times

Online Publication Date: 14 May 2004

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A source of silver iodide aerosols has been studied to determine the effect of the temperature of generation on the crystal structure of the particles in the aerosol output. Sampling was done by use of a novel thermal precipitator which gave samples in the proper form for direct analysis in a Debye‐Scherrer x‐ray diffraction camera. Patterns were obtained indicating the presence of both cubic and hexagonal modifications (ZnS and ZnO type). As the source temperature was raised, an increase of the proportion of hexagonal particles was observed, 95 percent hexagonal particles resulted when the source was operated at 800°C. An explanation of this behavior is proposed.

Measurement of Detonation Velocity by Doppler Effect at Three‐Centimeter Wavelength

Melvin A. Cook, Ray L. Doran, and Glen J. Morris

J. Appl. Phys. 26, 426 (1955); http://dx.doi.org/10.1063/1.1722012 (3 pages)

Online Publication Date: 14 May 2004

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This article describes the application of the Doppler principle to the measurement of detonation velocity with three‐centimeter electromagnetic radiation. The method makes use of the ionized wave front in detonation as a moving reflecting surface for electromagnetic waves. Detonation velocities for four different solid explosives were calculated from the observed Doppler frequencies and the indices of refraction, which were measured by a microwave interferometer. Complexities in the observed Doppler patterns come about because the cylindrical charges act as multimode dielectric wave guides.

Reflection of Sound in the Ocean from a Continuous Stratum Containing a Velocity Extremum

E. O. Cook and H. S. Heaps

J. Appl. Phys. 26, 429 (1955); http://dx.doi.org/10.1063/1.1722013 (5 pages)

Online Publication Date: 14 May 2004

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The reflection of a plane wave of sound from a layer separating regions of different sound velocities, the layer itself containing a velocity variation through an extremum, is considered in terms of its dependence upon the angle of incidence, the layer thickness, and the velocity variation through the layer. It is found that the power reflection coefficient may differ significantly from its value for the corresponding abrupt or monotonic velocity transition. Numerical results are tabulated for various types of layers of thickness from zero to ten wavelengths and with a total velocity transition of ±5 and ±10 ft∕sec.

Dependence of the Electric Strengths of Liquids on Electrode Spacing

A. H. Sharbaugh, J. K. Bragg, and R. W. Crowe

J. Appl. Phys. 26, 434 (1955); http://dx.doi.org/10.1063/1.1722014 (4 pages) | Cited 5 times

Online Publication Date: 14 May 2004

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Using a reproducible pulsed voltage technique, the electric strengths of liquid hexane, heptane, and tetradecane have been measured with small electrode spacings (approximately 2 to 200 microns). The electric strengths are found to change inversely with the logarithm of the separation in accord with theoretical expectation. On the basis of an approximate model of the breakdown process, the measurements on heptane yield values of 9×10−7 cm for the electron mean free path in the liquid and 9 for the number of multiplications per electron required for breakdown.

Barium Getters in Carbon Monoxide

J. Morrison and R. B. Zetterstrom

J. Appl. Phys. 26, 437 (1955); http://dx.doi.org/10.1063/1.1722015 (6 pages) | Cited 3 times

Online Publication Date: 14 May 2004

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The effects of pressure, temperature, and physical state on the ability of a barium getter to sorb carbon monoxide are presented. At pressures in the 10−5‐mm range, a five‐milligram getter is exhausted in about one thousand hours. Temperatures ranging from room temperature to 150°C did not affect greatly the rate of gettering or the capacities of the getters. The observed gettering rates or capacities do not obey any simple law over an extended time.

Crystallization Kinetics in High Polymers. II. Polymer‐Diluent Mixtures

Leo Mandelkern

J. Appl. Phys. 26, 443 (1955); http://dx.doi.org/10.1063/1.1722016 (9 pages) | Cited 68 times

Online Publication Date: 14 May 2004

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The rates of crystallization of two polymer‐diluent mixtures, poly‐(ethylene oxide)‐diphenyl ether and poly‐(decamethylene adipate)‐dimethyl formamide were studied at various temperatures ranging from 6° to 15° below the melting points of the mixtures. The various mixtures investigated encompassed a wide range of compositions; the volume fraction of the diluent v1 ranged from about 0.10 to 0.70. The crystallization behavior observed was strikingly similar to that previously reported for bulk polymers in the first paper of this series. The results are interpreted by making the necessary modifications to the treatment previously employed wherein steady‐state nucleation and growth were assumed to occur simultaneously throughout the process. Agreement obtained between theory and experiment is similar to the corresponding results for the bulk polymer.

Surface Matching of Dielectric Lenses

E. M. T. Jones and S. B. Cohn

J. Appl. Phys. 26, 452 (1955); http://dx.doi.org/10.1063/1.1722017 (6 pages) | Cited 5 times

Online Publication Date: 14 May 2004

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Two methods of cancelling the surface reflections of dielectric lenses are described in this paper. The first utilizes a simulated quarter‐wave matching layer, and the second a reactive wall embedded within the dielectric. The reactive wall may take a variety of physical forms, such as arrays of thin conducting disks which have a capacitive reactance, or arrays of thin wires which have an inductive reactance. Surface matching is obtained when the disks are placed approximately ⅜ wavelength inside the lens, or the wires ⅛ wavelength. Curves are presented that show how the reflections at the air and dielectric boundary are reduced for various angles of incidence and polarization when quarter‐wave layer and reactive‐wall matching are employed.
The reactance of the array of disks for waves incident at various angles and polarizations is computed by means of Bethe's small aperture theory, and Babinet's principle. Measurements in wave guide of the reactance of an array of circular disks for various angles of incidence and for both E‐ and H‐plane polarization show close agreement with the theory.

Field Produced by an Arbitrary Slot on an Elliptic Cylinder

James R. Wait

J. Appl. Phys. 26, 458 (1955); http://dx.doi.org/10.1063/1.1722018 (6 pages) | Cited 3 times

Online Publication Date: 14 May 2004

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A derivation is given for the electromagnetic field produced by an arbitrary slot cut in the surface of an elliptic cylinder of perfect conductivity and infinite length. The electric field tangential to the slot is assumed to be a prescribed function. The integrals in the formal solution are evaluated by the saddle point method for the far zone fields which when specialized to thin transverse or axial slots agree with known results. As illustrative examples, patterns of thin axial and transverse slots on a strip are computed.

Properties of Elastic and Plastic Waves Determined by Pin Contactors and Crystals

Stanley Minshall

J. Appl. Phys. 26, 463 (1955); http://dx.doi.org/10.1063/1.1722019 (7 pages) | Cited 37 times

Online Publication Date: 14 May 2004

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Experimental techniques are described by which one can observe the separation of a shock wave in a metal into an elastic wave and a slower plastic wave. The plastic‐wave velocity was about 15 percent less in steel and 10 percent less in tungsten than the elastic‐wave velocity, at pressures imparted by Composition B explosive. Elastic‐wave velocities were the same, within experimental error, as the measured sound velocities. The pressure in the elastic wave in SAE 1020 steel, deduced from the material and wave velocities, is independent of the plastic‐wave pressure within experimental accuracy, and is about 12 kilobars. SAE 1040 steel, however, does not exhibit a single characteristic elastic‐wave pressure. The pressure initially is about 6 kilobars, and increases to about 12 kilobars before the arrival of the plastic wave.

Orientation and Temperature Effects on the Electrical Resistivity of High‐Purity Magnesium

James L. Nichols

J. Appl. Phys. 26, 470 (1955); http://dx.doi.org/10.1063/1.1722020 (3 pages) | Cited 6 times

Online Publication Date: 14 May 2004

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The effect of crystal orientation on the electrical resistivity of high‐purity magnesium at 24°C may be represented by the equation:
math
,where θ is the angle between the hexagonal axis and the direction of current flow. The effect of temperature on the electrical resistivity for varying orientations shows temperature coefficients of 0.00390 and 0.00408∕°C obtained perpendicular and parallel to the hexagonal axis, respectively, for the temperature range of 24° to 200°C. Magnesium shows rotational symmetry about the hexagonal axis with respect to electrical resistivity. Grain size has little or no effect on the electrical resistivity of magnesium.

Cubic to Orthorhombic Diffusionless Phase Change— Experimental and Theoretical Studies of AuCd

D. S. Lieberman, M. S. Wechsler, and T. A. Read

J. Appl. Phys. 26, 473 (1955); http://dx.doi.org/10.1063/1.1722021 (12 pages) | Cited 112 times

Online Publication Date: 14 May 2004

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A theoretical analysis of the cubic to orthorhombic transformation is presented which predicts for a partly transformed crystal, the interface plane, orientation relationships, and macroscopic distortions from a knowledge only of the lattice parameters of the initial and final phases. Arguments are advanced to show that in order to minimize the strain energy associated with the transformation, the interface plane must be one of zero average distortion. This leads directly to considerations of an inhomogeneous product phase. Experimental studies on an AuCd alloy are described and the observed crystallographic features of the transformation compared with values calculated using the theory. The agreement between calculated and observed results for this alloy system as well as others is strong evidence for the theory of diffusionless phase transformations presented.
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