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1 Dec 1966

Volume 37, Issue 13, pp. 4599-5015

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Theory of Grain Growth in Porous Compacts

F. A. Nichols

J. Appl. Phys. 37, 4599 (1966); http://dx.doi.org/10.1063/1.1708102 (4 pages) | Cited 49 times

Online Publication Date: 17 June 2004

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Following a suggestion by Kingery and Francois, the theory of grain growth in porous compacts controlled by the migration of pores with the boundaries is developed for all possible transport processes. Contrary to the assumption of these authors, it is shown that the cubic rate law reported for both UO2 and Al2O3 compacts, if it is due to pore migration, must be interpreted as being controlled by vapor transport through the pore with the pressure maintained at 2γ∕r, where γ is the surface tension and r the pore radius. Available data for UO2 and Al2O3 are analyzed according to this model and found to give satisfactory agreement, with the calculated activation energies being reasonably close to the heats of vaporization for the two oxides. An interesting prediction of the model is that the compact should in fact show a decrease in density during grain growth. This behavior has been observed in the case of UO2 but apparently has not yet been reported for Al2O3.

Damping Peaks in Deformed Nickel

Alfred W. Sommer and Daniel N. Beshers

J. Appl. Phys. 37, 4603 (1966); http://dx.doi.org/10.1063/1.1708103 (12 pages) | Cited 9 times

Online Publication Date: 17 June 2004

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The internal‐friction spectrum of zone‐refined nickel [R(273°K)∕R(4.2°K)=600] has been examined at 30 kc∕sec, in the temperature range 77°‐350°K. Plastic deformation produces two prominent relaxation peaks, each the sum of several simple peaks. At 30 kc∕sec, one peak, which occurs at 138°±7°K, has been identified as the Niblett and Wilks peak, and the other, which has its maximum at 248°±40°K, has been shown to be the Bordoni peak. Both peaks have been studied as a function of cold work, grain size, state of annealing, and strain amplitude.
One major result of these studies is a demonstration that the Bordoni peak is only large at low‐to‐moderate flow stresses and vanishes at high flow stress (greater than 50 000 psi) with the Niblett and Wilks peak being the predominant feature of the damping spectrum at the higher‐flow stresses (greater than 30 000 psi). Moreover, the present results in Ni show such similarity to results obtained on deformation‐induced peaks in bcc metals that, if the definition of the Bordoni peak given by Niblett and Wilks is broadened to include Ni, then the peaks in bcc metals can also be included under the definition. Arguments are presented to show that the Bordoni relaxation is best described by the Seeger—Paré hypothesis.

Upper Bound to the Energy of Cross‐Tie Walls

Amikam Aharoni

J. Appl. Phys. 37, 4615 (1966); http://dx.doi.org/10.1063/1.1708104 (6 pages) | Cited 5 times

Online Publication Date: 17 June 2004

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A simple mathematical model is suggested for the magnetization variation inside a cross‐tie domain wall in ferromagnetic films. The exchange and anisotropy energies are calculated analytically for this model. The magnetostatic self‐energy is overestimated by adding essentially the contribution of volume charge at an infinite film thickness to the contribution of the surface charge at zero film thickness, and this gives an upper bound of about 10 erg∕cm2 for the total wall energy at any thickness. Neglecting the volume charge yields an energy of 0.27 erg∕cm2 for zero thickness, while neglecting the surface charge yields 7.7 erg∕cm2 for an infinite thickness. The latter should be an upper bound for the energy in any thickness, if the energy is a monotonic increasing function of the thickness. The radius of a Bloch line is found to be of the order of 100 Å, while the distance between crosses is found to be of the order of 10‐4 cm in Permalloy, which is of the order of experimentally observed values.

Hot Electron Energy Loss in Tunnel Cathode Structures

Robert M. Handy

J. Appl. Phys. 37, 4620 (1966); http://dx.doi.org/10.1063/1.1708105 (9 pages) | Cited 52 times

Online Publication Date: 17 June 2004

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A variety of scattering processes occur within the metal—oxide—metal tunnel cathode, with the result that most of the injected electrons fail to escape into vacuum. By considering the over‐all behavior it is possible to identify the most important loss mechanisms and where they occur.
Electron emission measurements suggest that the internal hot electron velocity distribution in the exit metal films is isotropic as a result of numerous phonon scattering events. It is also found that the electron attenuation length in the exit metal film is not a strong function of energy over most of the observable range. As a direct consequence one obtains the result that the shape and mean energy of the emitted electron energy distribution are determined principally by the scattering in the oxide layer. Collision ionization is unlikely; hence optical phonon scattering is believed to be the principal oxide energy loss mechanism. If the scattering is random and independent of energy, both the mean energy loss (ΔE) and mean square deviation (δ2) should depend linearly on oxide thickness (x). Within the limits of the available data this is shown to be reasonably correct, and a mean rate of energy loss dE∕dx≈0.03 eV∕Å is obtained. This corresponds to about one optical phonon emission event for every 4‐Å travel measured along the field direction. The consistency of the argument is tested by showing that δ2 also varies linearly with oxide thickness. The minimum ingredients for a model of the hot electron scattering processes are outlined.

Thermodynamics and the Manley—Rowe Equations

Paul Penfield

J. Appl. Phys. 37, 4629 (1966); http://dx.doi.org/10.1063/1.1708106 (2 pages)

Online Publication Date: 17 June 2004

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An unproved hypothesis is made: a physical system obeys the Manley—Rowe frequency‐power formulas if, and only if, it is reversible in the thermodynamic sense. A general proof of this hypothesis is not available, and the exact conditions under which it is true are not yet known, but it is demonstrated for a three‐frequency upconverter pumped sinusoidally and exchanging noise at the other two frequencies.

Ultrasonic Attenuation in Cadmium Sulfide from 1.8° to 300°K

A. E. Lord and R. Truell

J. Appl. Phys. 37, 4631 (1966); http://dx.doi.org/10.1063/1.1708107 (3 pages) | Cited 2 times

Online Publication Date: 17 June 2004

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Ultrasonic attenuation measurements have been made at 12, 30, and 46 Mc∕sec and from 1.8°K to room temperature on a cadmium sulfide specimen. The specimen had a dark room temperature conductivity of about 10‐2 (Ω⋅cm)‐1. A very large attenuation peak was observed in the neighborhood of 15°‐20°K. Conductivity values showed that the peak is undoubtedly due to relaxation effects in the space‐charge bunching caused by the acoustic wave, the mechanism proposed by Hutson and White.

The Wiedemann—Franz Ratio of Metallic Uranium at Elevated Temperatures

Gidon Erez and Uzy Even

J. Appl. Phys. 37, 4633 (1966); http://dx.doi.org/10.1063/1.1708108 (2 pages) | Cited 1 time

Online Publication Date: 17 June 2004

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The electric resistivity, heat capacity, and temperature diffusivity of uranium at temperatures from 50°‐800°C were measured on the same sample. The Wiedemann—Franz ratio was then calculated. A transition seems to occur at 250°C.

Stress—Strain Isotherms for Poly‐(Dimethylsiloxane) Networks

J. E. Mark and P. J. Flory

J. Appl. Phys. 37, 4635 (1966); http://dx.doi.org/10.1063/1.1708109 (5 pages) | Cited 43 times

Online Publication Date: 17 June 2004

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Stress—strain isotherms are presented for poly‐(dimethylsiloxane) networks of different degrees of cross linking, swollen to various extents by a diluent. Results are interpreted in terms of the equation f*v2⅓V*/(α−α−2) = 2C1+2C2α−1, where f* is the tension per unit initial area (unswollen) exhibited by a network when swollen to a polymer volume fraction v2 and elongated to the relative length α, 2C1 is a parameter of the network structure established by the molecular theory of rubber elasticity, and 2C2 is an additional parameter found to give a better representation of experimental data. Values of C2 obtained for networks are found to decrease as the degree of cross linking is decreased, and the degree of swelling is increased.

Ballistic Demagnetizing Factor in Uniformly Magnetized Cylinders

R. I. Joseph

J. Appl. Phys. 37, 4639 (1966); http://dx.doi.org/10.1063/1.1708110 (5 pages) | Cited 42 times

Online Publication Date: 17 June 2004

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A simple, closed‐form expression is obtained for the ballistic demagnetizing factor of a uniformly magnetized cylinder. Detailed comparison is made between the present results and both the previously derived series expansion (in which the radial variation of magnetization is neglected), valid for p(=length∕diameter) ≥10, and the numerical extrapolation of the latter to the range 0≤p≤100. An alternate derivation of a result for the magnetometric demagnetizing factor of a uniformly magnetized cylinder is presented. Detailed comparison is made between the demagnetizing factors in the uniformly magnetized cylinder (ballistic, magnetometric) and the demagnetizing factor of an inscribed ellipsoid of revolution.

Thermal Properties of Molecular Crystals. I. Heat Capacity and Thermal Expansion

A. Bondi

J. Appl. Phys. 37, 4643 (1966); http://dx.doi.org/10.1063/1.1708111 (5 pages) | Cited 2 times

Online Publication Date: 17 June 2004

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The lattice heat capacity Cvs and especially the difference Cps‐Cvs of molecular crystals composed of rigid molecules is shown to be well represented by a suitably modified form of the Leibfried and Ludwig theory of anharmonic crystals. Crystals of low packing density (ρ*<0.65) such as benzene require a (fairly large) heat capacity correction for the heat of lattice defect formation. An empirical correction of the theory is proposed to adapt it for the estimation of Cvs of crystals composed of flexible molecules.
The expansion coefficient (αs) of molecular crystals composed of rigid molecules at 0.7Tm<T<0.9Tm is represented by a universal value of the dimensionless number αs* = αsΔHs/Cvs first proposed by Grueneisen and also derivable from Ludwig's theory of anharmonic oscillator crystals. Variants of αs* are discussed also for hydrogen‐bonded crystals and for crystals composed of flexible molecules.

Thermal Properties of Molecular Crystals. II. Thermal Conductivity

A. Bondi

J. Appl. Phys. 37, 4648 (1966); http://dx.doi.org/10.1063/1.1708112 (1 page)

Online Publication Date: 17 June 2004

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A corresponding states type correlation of the thermal conductivity of polycrystalline molecular crystals is presented which requires as input information only the heat of sublimation, the van der Waals volume of the molecules, and the number of external degrees of freedom per molecule.

Impurity Effects on the Basal Plane Solidification Kinetics of Supercooled Water

Alan S. Michaels, P. L. T. Brian, and Peter R. Sperry

J. Appl. Phys. 37, 4649 (1966); http://dx.doi.org/10.1063/1.1708113 (13 pages) | Cited 8 times

Online Publication Date: 17 June 2004

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Growth rates of ice on the basal plane from pure water and from dilute solutions of selected ionic salts, surfactants, and water‐soluble polymers were measured by an improved technique of capillary crystallization for supercoolings ranging from 0.03° to 0.2°C. The corresponding velocities ranged from 10‐6 cm∕sec to 5×10‐4 cm∕sec. Corrections for bulk mass transfer and heat transfer effects were applied to the kinetic data.
The kinetic data for pure water, although in agreement with those of Hillig near supercoolings of 0.07°C, diverge from the earlier results toward lower velocities at both lower and higher supercoolings. The data nonetheless support the general conclusion of Hillig that growth of undamaged ice crystals on the basal plane proceeds by two‐dimensional nucleation.
Both growth‐rate enhancements (up to a factor of about five) and retardations (up to a factor of about three) were observed during crystallization in the presence of additives. The type of effect and its magnitude were dependent on the nature of the additive, its concentration, and upon the degree of supercooling. Certain effects of ionic salts appear related to freezing potential phenomena reported by several earlier workers. Growth acceleration, found to occur to varying degrees with all classes of additive, may have been a consequence of dislocations introduced in the crystal by the additive during growth.

Improved Surface Ionization Efficiency by High Work Function Refractory Metals and Alloys

Otto K. Husmann

J. Appl. Phys. 37, 4662 (1966); http://dx.doi.org/10.1063/1.1708114 (9 pages) | Cited 7 times

Online Publication Date: 17 June 2004

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For continuous one‐year operation without deterioration of the surface ionization engine characteristic, the neutral efflux should be in the 0.1% range. For the neutral efflux reduction the Saha equation implies the use of high work function metals. Therefore, tungsten‐rhenium alloys and iridium filaments were investigated. For completeness, tungsten and rhenium filaments were also studied with regard to their thermionic work function and threshold temperature for cesium surface ionization. The data were measured in an all‐metal guard ring diode with directly heated filament under clean surface conditions. The electron work functions and the threshold temperatures of the tungsten‐rhenium alloys increase with increasing amount of rhenium in tungsten. For ϕ‐I≤0.5 eV the electron work function governs the surface ionization.
One porous tungsten‐25% rhenium pellet and two porous tungsten substrates chemically coated with rhenium and iridium yielded work functions below those measured with the corresponding filaments. At 10‐mA∕cm2 cesium ion current density, the neutral efflux from the rhenium coated pellet was, with 2×106 pores∕cm2 (traverse counting technique), 1%±0.1%. Under clean conditions 0.3% neutral efflux may be expected. The increase of the threshold temperature with electron work function leads to increased grain size and lower pore density for long term stability of the porous structure.

Angular Distribution of Radiation Scattered Coherently by a Plasma Cylinder

A. R. Jones and E. R. Wooding

J. Appl. Phys. 37, 4670 (1966); http://dx.doi.org/10.1063/1.1708115 (7 pages) | Cited 2 times

Online Publication Date: 17 June 2004

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The intensity and phase of a wave scattered by a cylindrical plasma column have been computed for the case where R∕λf is near unity. The angular distribution of intensity was measured when a 9.6‐GHz plane wave was incident on a plasma of 2.68‐cm radius with the electric vector parallel to the cylinder axis. The variation of phase with angular position was also determined. A resonance was observed.

Acoustic Relaxations in Zirconium‐Niobium Alloys

C. W. Nelson, D. F. Gibbons, and R. F. Hehemann

J. Appl. Phys. 37, 4677 (1966); http://dx.doi.org/10.1063/1.1708116 (6 pages) | Cited 3 times

Online Publication Date: 17 June 2004

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Acoustic measurements are reported which were made by the composite resonator technique on poly‐crystalline and single‐crystal specimens of Zr‐Nb alloys (0%‐25% Nb). Three distinct thermally activated relaxation peaks have been observed. In the frequency range 80–300 kc∕sec, the relaxations occur in the neighborhood of 160°, 40°, and 12°K, with activation energies of 0.3, 0.05, and ∼0.02 eV, respectively. The relaxation which occurs at 12°K has only been observed in Zr‐5% Nb. The 160° and 40°K relaxations have been demonstrated to be associated with the β → ω, athermal transformation. An atomic model for the 160°K relaxation process is presented and a tentative suggestion made for the origin of the relaxation at 40°K. No mechanism for the 12°K relaxation is attempted.

Crystallography of SiP and SiAs Single Crystals and of SiP Precipitates in Si

C. G. Beck and R. Stickler

J. Appl. Phys. 37, 4683 (1966); http://dx.doi.org/10.1063/1.1708117 (5 pages) | Cited 19 times

Online Publication Date: 17 June 2004

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Transmission electron microscope examinations of silicon single crystals, phosphorus‐diffused at low temperatures from anodic oxide films as phosphorus sources, showed the presence of crystallographically oriented precipitate. X‐ray and electron diffraction investigations of SiP and SiAs single crystals prepared by a vapor‐growth method revealed the orthorhombic crystal structure of the as‐grown compounds. Using these structure data, the precipitate in the diffused silicon could be identified by electron diffraction as SiP. The orientation relationship SiP‐precipitate∕Si‐matrix was determined.

Oriented Growth of Semiconductors. III. Growth of Gallium Arsenide on Germanium

L. C. Bobb, H. Holloway, K. H. Maxwell, and E. Zimmerman

J. Appl. Phys. 37, 4687 (1966); http://dx.doi.org/10.1063/1.1708118 (7 pages) | Cited 27 times

Online Publication Date: 17 June 2004

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Gallium arsenide has been grown on germanium using arsenic trichloride and gallium. With optimum growth conditions the epitaxial layers have properties close to those of good‐quality bulk crystals. Comparison between epitaxial and bulk crystals is made in terms of the widths of the x‐ray rocking curves and of the properties of p‐n junctions formed within the epitaxial layer.

Oriented Growth of Semiconductors. IV. Vacuum Deposition of Epitaxial Indium Antimonide

H. Holloway, J. L. Richards, L. C. Bobb, J. Perry, and E. Zimmerman

J. Appl. Phys. 37, 4694 (1966); http://dx.doi.org/10.1063/1.1708119 (6 pages) | Cited 9 times

Online Publication Date: 17 June 2004

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Using flash vaporization, indium antimonide has been grown epitaxially on indium antimonide substrates. The perfection of the epitaxial layers depends critically upon the method used for preparation of the substrate surface. Best results were obtained after the substrates had been ion‐bombarded and annealed. Layers grown under optimum conditions yield x‐ray rocking curves similar to those from good bulk crystals. p‐n junctions made within these layers have characteristics similar to those reported for high‐quality diodes made with bulk indium antimonide.

Yield and Angular Distribution of Cesium‐Sputtered Molybdenum

J. B. Green, N. Thomas Olson, and Harold P. Smith

J. Appl. Phys. 37, 4699 (1966); http://dx.doi.org/10.1063/1.1708120 (4 pages) | Cited 3 times

Online Publication Date: 17 June 2004

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A radioactive tracer technique has been adapted to the measurement of the yield (atoms∕ion) and angular distribution (atoms∕ion∕sr) of molybdenum sputtered by a cesium ion beam normal to the (100) crystallographic face. The energy of the ion was varied from 1 to 7.5 keV, and the target temperature was varied from 77° to 473°K. The yield increased with energy and decreased with target temperature. Preferred emission in the 〈100〉 direction was measured, but emission in the 〈111〉 direction could not be resolved. The importance of ion channeling and the effects of thermal annealing on ion‐induced damage are emphasized.

Direct Determination of the Flow Curves of Non‐Newtonian Fluids. IV. Parallel‐Plane Rotational Viscometer

Irvin M. Krieger and Martin E. Woods

J. Appl. Phys. 37, 4703 (1966); http://dx.doi.org/10.1063/1.1708121 (2 pages) | Cited 5 times

Online Publication Date: 17 June 2004

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Analysis of the laminar flow of a non‐Newtonian fluid between rotating parallel planes permits the viscosity to be calculated as a function of shear rate from data of torque vs angular velocity. Experimental results are presented which show that the non‐Newtonian viscosities thus obtained agree with capillary, Couette, and cone‐and‐plate instruments over a four‐decade shear rate range.

Substitutional‐Interstitial Interaction and the Anomalous Snoek Peak in Fe‐V‐N Alloys

A. J. Perry, M. Malone, and M. H. Boon

J. Appl. Phys. 37, 4705 (1966); http://dx.doi.org/10.1063/1.1708122 (7 pages) | Cited 8 times

Online Publication Date: 17 June 2004

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It has been shown that the anomalous Snoek internal friction peaks observed in Fe‐V‐N alloys by Fast and Meijering2 can be interpreted as being made up of three distinct contributions. From a study of the manner in which these contributions vary with the free nitrogen level in the alloy, a model is proposed and considered in detail in which between one and three nitrogen atoms reside in the six octahedral sites co‐ordinated with a vanadium atom. The three contributions then correspond to jumps by the nitrogen atoms for the cases when one, two, and three interstitials are present. The model allows the evaluation of the interaction energy between a nitrogen atom and either a vanadium atom, a vanadium‐nitrogen pair, or a vanadium‐di‐nitrogen group as about 0.3 eV. The calculated variation of the filling of sites with the free nitrogen level in the alloy is in fair agreement with the resolved contributions to the anomalous peak.

Role of the Cathode Field Emission in the Streamer‐Spark Transition

E. Nasser

J. Appl. Phys. 37, 4712 (1966); http://dx.doi.org/10.1063/1.1708123 (5 pages) | Cited 12 times

Online Publication Date: 17 June 2004

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In a point‐to‐plane gap in atmospheric air streamers propagate under a voltage pulse from the point anode into the low‐field region at high velocities and under continuous branching. It was found that electron emission from the copper cathode occurs under the effect of the high field between the streamer tips and the cathode just before impact. Photographic evidence by means of paper films placed on the cathode with sensitive emulsion facing it showed that at the points where strong streamer tips approached the back side of the film great concentrations of minute dots appeared. These dots are attributed to electron avalanches produced by those electrons liberated from the cathode and accelerated towards the streamer tip. The liberation of electrons was ascribed to the high field intensities at the tips since radiation cannot penetrate the paper. To confirm this, the back side of the paper was blackened at spots with no change in pictures. To further substantiate this, a thin metallic layer was placed at the back of the paper. No electrons were liberated and no dots appeared opposite the metallic layer because asymmetrical fields cannot build up between the two plane surfaces. The avalanches between film and cathode became diffuse when the air gap was increased to 3 mm since they merged into each other. At a gap of 5 mm, only a few avalanches were observed, of which some formed negative streamers as evidenced by distinct negative Lichtenberg figures on the film.

Technique for Measuring Vacancy Concentrations in Metals at the Melting Point

D. King, A. J. Cornish, and J. Burke

J. Appl. Phys. 37, 4717 (1966); http://dx.doi.org/10.1063/1.1708124 (6 pages) | Cited 5 times

Online Publication Date: 17 June 2004

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A technique is described for measuring vacancy concentrations at the melting point by measuring the difference between the linear thermal expansion and the lattice thermal expansion. The method uses small specimens to facilitate eventual study of alloys and involves separate measurements of length change and lattice parameter change, the former by an interferometric technique and the latter by a diffractometer technique. The results of a study of 99.995% pure aluminum agree closely with the earlier measurements of Simmons and Balluffi, giving a vacancy concentration at the melting point of 8.7±1.2×10−4.

Dielectric Breakdown in LiF Crystals Bombarded by Electrons

Kazuko Kubo

J. Appl. Phys. 37, 4722 (1966); http://dx.doi.org/10.1063/1.1708125 (7 pages) | Cited 2 times

Online Publication Date: 17 June 2004

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Dielectric breakdown phenomena were observed in LiF single crystals bombarded by electrons of 1–2 MeV. The Lichtenberg figures were developed in a layer which included the range plane of the bombarding electrons. The components of the figures lay in the directions 〈221〉, 〈111〉, 〈114〉, and a few 〈100〉, besides dominant 〈110〉, with small angle deviations. Turns and reflections of the path were found at the boundary of the layer. Structural alterations of the crystal, including edge dislocations, were observed around the large paths. These phenomena, which have not been observed in the previous experiments by the conventional method, are suggested to result from the intense ionization and heating due to electronic avalanches occuring in a rather long period of discharge time, superposing on the damage induced by electron bombardment.

Acoustoelectric Waves in Piezoelectric Materials

E. W. Prohofsky

J. Appl. Phys. 37, 4729 (1966); http://dx.doi.org/10.1063/1.1708126 (9 pages) | Cited 2 times

Online Publication Date: 17 June 2004

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The electron‐piezoelectric sound wave interaction gives rise to three distinguishable phenomena: gain, acoustoelectric effects, and nonlinear mixing. The acoustoelectric effects, through coupling to the gain, cause interaction between sound waves which give rise to flux wave propagations. These waves travel at the velocity of sound and can have gain much larger than that of the ordinary peizoelectric waves.
When the nonlinear mixing is taken into account, the mixing may be rapid enough to alter the collective wave to that of a second sound wave with velocity 1∕√3 vs. The nonlinear mixing is examined, and it is proposed that the second sound conditions can only exist when a delicate balance is achieved between coherent gain and loss.
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