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1 Oct 1965

Volume 36, Issue 10, pp. 2975-3364

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Nonlinear Rubberlike Viscoelasticity—A Molecular Approach

J. C. Halpin

J. Appl. Phys. 36, 2975 (1965); http://dx.doi.org/10.1063/1.1702913 (8 pages) | Cited 13 times

Online Publication Date: 14 July 2004

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The difference between the dynamic and equilibrium tension in a macromolecular chain is expressed as a ``functional'' of the variation of the nonlinear strain function ϕ(r*) developed in the kinetic theory of elasticity, with respect to time through the interval (0,t) r* ≡ r/rm where r is the vectorial end‐to‐end distance of the molecular chain and rm is the maximum separation). The ``functional'' is expanded in an integral series analogous to Taylor's series and higher terms are neglected to obtain a linear integral equation for the viscously retarded response of the network chain. The equation obtained is a generalized one‐dimensional Boltzmann's superposition equation. It is then shown that the time‐dependent response of the molecular chain is independent of the magnitude of the deformation and, consequently, is of the same analytical form whether the deformation is infinitesimal or finite. From this it necessarily follows that there cannot be an inconsistency at finite stress and strain which is not allowed at infinitesimal excitations. Thus the response at finite excitations can be treated generally by employing the ``generalized'' superposition equation and the same techniques which have been utilized in the linear theories. Employing the usual kinetic theory assumptions, equations are developed for the macroscopic response of a well‐vulcanized rubber. Experimental data obtained in creep, stress relaxation, and dynamic stress‐strain for three different elastomers are presented which support the approach outlined. Some consequences of the theory are discussed.

Some Mechanical Properties of Vitreous Selenium Near Its Glass Transition

L. J. Graham and R. Chang

J. Appl. Phys. 36, 2983 (1965); http://dx.doi.org/10.1063/1.1702914 (4 pages) | Cited 18 times

Online Publication Date: 14 July 2004

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The elastic and anelastic properties (in the megacycle frequency range), viscosity, and electrical resistivity of vitreous selenium near its glass transition temperature were measured as a function of the quench (or melt) temperature between 540° and 720°K. The measurements reveal a correlation between the various properties and the internal molecular structure of the material at the quench temperature. Ultrasonic attenuation below the glass transition temperature of vitreous selenium cannot originate from simple mechanical losses due to viscous flow. A phonon‐phonon scattering mechanism is suggested.

Crystalline Morphology of Synthetic Polypeptides

F. J. Padden and H. D. Keith

J. Appl. Phys. 36, 2987 (1965); http://dx.doi.org/10.1063/1.1702915 (9 pages) | Cited 43 times

Online Publication Date: 14 July 2004

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In an attempt to grow single crystals of synthetic polypeptides, polyglycine, poly‐l‐alanine, and poly‐l‐tyrosine have been precipitated from dilute solution and also cast as films by the slow evaporation of solvent. Polyglycine precipitated from solutions containing equal parts of trifluoroacetic acid (TFA) and trifluoroethanol (TFE) by the addition of water, crystallizes with the polyglycine II structure in the form of lamellar platelets with folded molecular chains. In films of polyglycine cast from these solutions, however, sheaves of ribbonlike crystals are produced, also chain folded and having the same structure. Selected‐area electron diffraction from these various crystals yields corroborative evidence for some of the structural features of polyglycine II. Poly‐l‐alanine cast from solution in TFA and TFE, on the other hand, crystallizes to give platelets and sheaves side by side in the same preparations. Both have the crystal structure of the α form of poly‐l‐alanine, and indirect evidence indicates that chain folding probably occurs in both instances. There is a suggestion that, as grown, the crystals contain solvent complexed chemically with the polymer. Poly‐l tyrosine can be precipitated from solution in mixtures of N,N‐dimethylformamide (DMF) and n‐heptanol in the form of hexagonal platelets and these too probably consist of folded molecules complexed with solvent. A tentative correlation between conformation in solution and crystalline morphology is suggested in the case of poly‐l‐tyrosine, but no definitive conclusion can be reached without further study of the conformation of the polymer held in solution under the conditions prevailing during crystallization.

Ultimate Tensile Properties of Elastomers. IV. Dependence of the Failure Envelope, Maximum Extensibility, and Equilibrium Stress‐Strain Curve on Network Characteristics

Thor L. Smith and J. E. Frederick

J. Appl. Phys. 36, 2996 (1965); http://dx.doi.org/10.1063/1.1702916 (10 pages) | Cited 15 times

Online Publication Date: 14 July 2004

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Uniaxial tensile data from tests at different rates of extension over a wide temperature range are considered for butyl, silicone, Viton B, SBR, and natural rubber vulcanizates (series A) and for six Viton A‐HV vulcanizates (series B) of differing crosslink densities. For series A and for A‐6 in series B, equilibrium stress‐strain data were obtained at large deformations by an indirect method. The ultimate tensile properties of all vulcanizates were previously characterized by a time‐ and temperature‐independent failure envelope. The failure envelope's maximum extension ratio, (λb)max, is shown to be equal to or less than (λ∞)max, the maximum extension ratio (hypothetical) in the absence of rupture and also the maximum extension ratio of network models. Failure and equilibrium data for series A vulcanizates are represented by a specific function of the equilibrium modulus and the maximum extensibility; except for SBR and possibly Viton B, equilibrium and failure data are sensibly identical; thus, (λb)max ≅ (λ∞)max. For series B vulcanizates, qualitative considerations indicate that (λ∞)max∕(λb)max is greater than unity and possibly dependent on crosslink density. Consideration of network models suggests that (λ∞)max should be directly proportional to Mc☒ and inversely proportional to (〈r2〉0∕M)☒. For series A, no correlation between (λb)max and (〈r2〉0∕M)☒ was found. For series B, it is shown that (λb)max∝Mcβ, where β is a constant in the neighborhood of 0.7. For all vulcanizates, (σb)max ≅ 104(λb)max−1, where (σb)max is the stress in psi (based on the undeformed cross section) at (λb)max.

Dynamic Birefringence and Mechanical Loss Spectra of Crystalline Polymers

Ryo Yamada and R. S. Stein

J. Appl. Phys. 36, 3005 (1965); http://dx.doi.org/10.1063/1.1702917 (8 pages) | Cited 15 times

Online Publication Date: 14 July 2004

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The variation of the real parts of the dynamic modulus E′, the dynamic strain‐optical coefficient K′, the mechanical loss tangent tan δ, and the optical loss tangent tan α have been measured as a function of temperature between −40° and +120°C at constant frequency of 1 cps for low‐density polyethylene, high‐density polyethylene, polypropylene, and nylon‐6. The results are interpreted in terms of both phenomenological theory and molecular mechanisms. The results for these polymers may be understood in terms of differing contributions by the processes of (a) spherulite or superstructure deformation, (b) delayed crystal reorientation within the deformed superstructure, and (c) relaxation of crystal orientation. For low‐density polyethylene, processes (b) and (c) are the principal contributors while for high‐density polyethylene, (a) becomes important at the lower temperatures. For polypropylene, (a) dominates and (b) begins to contribute at the higher temperatures, while for nylon‐6, (a) gives way to (c) without any appreciable region of important contribution of (b).

Initiation of Spherulite Growth: The Case of Concurrent Homogeneous and Heterogeneous Nucleation

Fred Gornick

J. Appl. Phys. 36, 3012 (1965); http://dx.doi.org/10.1063/1.1702918 (3 pages) | Cited 5 times

Online Publication Date: 14 July 2004

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Direct determination of the rate of homogeneous spherulite initiation requires the subdivision of the melt into a large enough number of droplets so that all undesired nucleation catalysts (heterogeneities, motes, etc.) will be confined to a relatively small number of them. If the undesired heterogeneities nucleate very rapidly, the droplets free of them will freeze at a rate proportional to their volumes and the inherent (homogeneous) nucleation frequency per unit volune. In many cases, however, the time‐dependent freezing process is pseudohomogeneous, i.e., the result of concurrent homogeneous and heterogeneous (but sporadic or nearly sporadic) nucleation. A method is presented for analyzing data corresponding to this case and for determining the limits within which the droplet nucleation experiment can be expected to yield fruitful results.
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Some Comments on the ``Avrami'' Equation

F. P. Price

J. Appl. Phys. 36, 3014 (1965); http://dx.doi.org/10.1063/1.1702919 (3 pages) | Cited 15 times

Online Publication Date: 14 July 2004

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The ``Avrami'' equation applies rigorously only to a system which does not change volume on transformation and where the developing regions are spheres. The consequences of the impossibility of achieving these conditions in real systems is discussed. It is shown that excessive approximation combined with the use of weight rather than volume fractions can lead to errors in the exponent n of as much as 0.3. It is emphasized that only at very low conversions can meaningful interpretations be made of the exponent.

Morphology of Solution‐Grown Polypropylene Crystal Aggregates

J. A. Sauer, D. R. Morrow, and G. C. Richardson

J. Appl. Phys. 36, 3017 (1965); http://dx.doi.org/10.1063/1.1702920 (5 pages) | Cited 42 times

Online Publication Date: 14 July 2004

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Polypropylene aggregates, consisting of interwoven arrays of single‐crystal lamellae, have been obtained by crystallization of samples of isotactic polypropylene from dilute solutions held at constant temperatures between 85° and 115°C. The solvent used was α‐chloronaphthalene with polymer concentrations ranging from 0.4% to 0.01% by weight. The resulting crystalline aggregates were examined by means of phase contrast and electron microscopy. Similar crystal aggregates have been studied by Khoury and found to be incipient spherulites. These aggregates tend to occur in the form of open weave structures, with characteristic cusps. Lath‐like lamellar crystals, with well‐defined faces, are found at the edges of these structures. These edge lamellae produce a single‐crystal electron‐diffraction pattern corresponding to the monoclinic structural form of isotactic polypropylene. On the basis of the experimental findings, it is suggested that folding occurs in monoclinic polypropylene only along a given set of parallel fold planes, viz. {010}. Preliminary results of a study of the fracture characteristics of the crystal lamellae tend to support the suggested hypothesis.

Photographic Light Scattering and Photomicroscopy of Deformed Ringed Spherulites

Robert S. Moore and Chester Gieniewski

J. Appl. Phys. 36, 3022 (1965); http://dx.doi.org/10.1063/1.1702921 (6 pages) | Cited 7 times

Online Publication Date: 14 July 2004

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Polyethylene films were studied by photographic light scattering and photomicroscopy at successive increments of strain, usually 5%. Photomicrographs were taken at times sufficiently long after sample deformation so that the light scattering patterns were constant with respect to intensity and shape. Analysis of such scattering patterns and photomicrographs indicated that upon spherulite deformation, the ring spacing (hence the twist‐distance) increased in the direction of tensile strain and decreased at right angles to the strain direction, as noted in earlier experiments on samples subjected to tensile stress. At about 30% strain the wide‐angle parallel polarizer scattering pattern (polarization and strain directions horizontal) split into a set of 4 arcs nearly parallel to the meridian. With increasing strain (analyzer and strain directions vertical) the arcs of the 4‐arc wide‐angle crossed polarizer scattering pattern, originally at 45° to the polarizer and analyzer axes, occurred nearer the meridian and became nearly parallel to the equator. Photomicrographs indicated that at 30% strain the ring spacing at right angles to the strain direction was extremely small or in some cases not resolvable and that discontinuities occurred in the rings. Immediately adjacent to the axis of sample deformation in many spherulites there was a discontinuity in the rings such that they appeared to cross the axis at an angle of 50° to 60°. The relationship between the changes observed by light scattering and the changes observed by microscopy is shown. Photomicrographs and light scattering patterns are presented and a brief analysis of the changes is given in terms of mechanisms of spherulite deformation.

Thermodynamic Properties of Drawn Linear Polyethylene

A. Peterlin and G. Meinel

J. Appl. Phys. 36, 3028 (1965); http://dx.doi.org/10.1063/1.1702922 (6 pages) | Cited 22 times

Online Publication Date: 14 July 2004

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Measurements of melting curves, density, and long period of undrawn and drawn PE as a function of the draw ratio and the annealing temperature between 118° and 129.8°C for different annealing times were performed. Melting experiments show a linear increase of melting point and a reduction of heat content of the noncrystalline component with increasing draw ratio. As a consequence of plastic deformation during drawing, the tied macromolecules partly incorporated in more than one crystal are under high strain. This reduces not only the entropy but also the intra‐ (trans instead of gauche conformation) and interchain (aligned extended chains are more closely packed) energy of the amorphous regions. Annealing nearly instantaneously removes the strain on tied chains, restores the enthalpy and entropy to the values in a nearly completely relaxed supercooled melt, and increases crystallinity and long period. Subsequent prolonged annealing produces only slight additional changes.
The variation of enthalpy and entropy rather well explains the observed drastic changes in sorption and diffusion of solvent molecules as a consequence of drawing and annealing.

Correlation of the Elastic Properties in Steady‐State Flow and Vibrational Experiments

W. Philippoff

J. Appl. Phys. 36, 3033 (1965); http://dx.doi.org/10.1063/1.1702923 (6 pages) | Cited 8 times

Online Publication Date: 14 July 2004

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A comparison between steady‐state and vibrational techniques for measuring the elastic properties of polymer solutions has shown an unexpected anomaly at high frequencies. The steady‐state technique used was flow birefringence which relates elasticity (recoverable shear, s) to the extinction angle χ: s=2 cot 2χ. The vibrational technique used, both the ultrasonic crystal and the Birnboim instruments, relates elasticity to the loss angle, δ′: cot δm′=η2∕(η1−η solv). The solutions investigated included a monodisperse polystyrene, S111, at concentrations of 2% and 4% in a chlorinated biphenyl (Aroclor 1248), a polydisperse polystyrene, PF‐139 and polyisobutylenes in oil. The same solutions were used in both kinds of instruments.
In the lower range of frequencies (taken as equivalent to low shear rates) the steady‐state and dynamic instruments showed excellent agreement for the monodisperse polystyrene. In this range the curve agreed with the Zimm theory. But at higher frequencies the results from the two techniques diverged rapidly. The steady‐state measurements showed s to increase continually, whereas the dynamic measurements showed cot δm′ to pass through a flat maximum and then decrease slowly out to 2×106 sec−1. This lack of agreement was unexpected and is unexplained. It does show that steady‐state elasticity cannot always be predicted from high‐frequency dynamic experiments. The steady‐state viscosity could be satisfactorily predicted from η1 using Pao's theory, but only for the monodisperse polymers.

Superheating of Linear High‐Polymer Polyethylene Crystals

E. Hellmuth and B. Wunderlich

J. Appl. Phys. 36, 3039 (1965); http://dx.doi.org/10.1063/1.1702924 (6 pages) | Cited 74 times

Online Publication Date: 14 July 2004

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The time dependence of melting of morphologically different crystals of polyethylene was investigated. New DTA and calorimeter techniques were developed. A microscope hot stage allowing heating rates of up to 3000°C∕min was built for melting‐point determinations. The superheating of extended‐chain crystals was clearly demonstrated by qualitative DTA and isothermal quantitative calorimetry. Smaller crystals and folded‐chain crystals showed decreasingly less superheating. Crystals which are less perfect and have large surfaces show increasing reorganization. A region of approximately zero entropy production melting seems to lie between reorganization at slow heating rates and superheating at faster heating rates.

Extension of Unoriented Nylon 66 Filaments. III. Superposition of Data

Malcolm L. Williams and Malcolm F. Bender

J. Appl. Phys. 36, 3044 (1965); http://dx.doi.org/10.1063/1.1702925 (6 pages) | Cited 10 times

Online Publication Date: 14 July 2004

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In an effort to understand the molecular mechanism of cold drawing, the tensile creep of unoriented nylon 66 monofilaments as a function of load has been obtained at three different combinations of temperature and moisture content. Qualitatively, an increase in either load, temperature, or moisture content will shift the creep curve to shorter times. These data can be quantitatively correlated by plotting the elongation ϵ against log t−a+bx+cT+c1σ∕(c2+σ). Here t is time, x is % H2O, T is temperature in °K, σ is an average stress in dynes∕cm2, and a, b, c, c1, and c2 are constants. The parameters b and c are identical with those previously found to apply to the moisture and temperature dependence of the elastic extension of oriented nylon 66 fibers. The free‐volume theory frequently employed for amorphous polymer behavior is shown to be inapplicable since moisture sorption decreases the free volume although it quickens cold drawing. Application of dislocation concepts enables an estimate of the stress dependence of dislocation velocity to be calculated.

Direct Observation of Dislocation Networks in Folded‐Chain Crystals of Polyethylene

V. F. Holland and P. H. Lindenmeyer

J. Appl. Phys. 36, 3049 (1965); http://dx.doi.org/10.1063/1.1702926 (8 pages) | Cited 44 times

Online Publication Date: 14 July 2004

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The direct observation of networks of dislocations between platelets of folded‐chain polyethylene crystals has been accomplished using diffraction contrast electron microscopy. The networks are composed of dislocations, primarily in their screw orientation, having Burgers vectors [110], [100], and [010]. The [110] dislocations are invariably dissociated into ribbons and there is evidence that the other two also tend to dissociate. Singularities in the networks are interpreted in terms of interactions between the partial edge dislocations previously detected by moiré patterns and glissile screw dislocation ribbons. These observations prove that folded‐chain surfaces are sufficiently regular to pack crystallographically and that slip between folded‐chain platelets can occur by the motion of dislocations.

Cold Drawing of Glassy Polystyrene under Dead Load

D. H. Ender and R. D. Andrews

J. Appl. Phys. 36, 3057 (1965); http://dx.doi.org/10.1063/1.1702927 (6 pages) | Cited 20 times

Online Publication Date: 14 July 2004

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The deformation of glassy polystyrene under a fixed tensile dead load can take place in three different modes: (a) drawing by formation and propagation of a neck, (b) drawing by proliferation of deformation bands without necking, and (c) homogeneous creep. Which mode is observed depends primarily on stress level and temperature. In homogeneous creep, deformation bands are not found; however, they are always observed in connection with the two types of drawing. At any given temperature a boundary stress is observed above which drawing takes place and below which only creep is observed. This critical stress decreases with increasing temperature. It is believed that this is the stress necessary either for the formation or propagation of deformation bands. It seems likely that drawing by shear band proliferation is the ideal mode which would be obtained in a perfectly homogeneous and uniform sample; however, drawing usually goes over into the necking mode because of nonuniformities in specimen geometry or uneven temperature. Neck initiation is delayed for a certain time interval after application of the dead load. The logarithm of the delay time is found to be a linear function of stress and, also, an approximately linear function of temperature.

Birefringence Effects in Acrylonitrile Polymers. II. The Nature of the 140°C Transition

R. M. Kimmel and R. D. Andrews

J. Appl. Phys. 36, 3063 (1965); http://dx.doi.org/10.1063/1.1702928 (9 pages) | Cited 19 times

Online Publication Date: 14 July 2004

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Birefringence measurements on solvent‐cast films of polyacrylonitrile homopolymer under dead load are reported as a function of temperature and as a function of time at constant temperature. It is shown that a large positive birefringence effect is associated with the 240°C aromaticization reaction in PAN. The high negative birefringence state produced by temperature cycling and first reported in Part I of the present series is found to require a small dead load on the sample during cooling for its formation, and is observed to form under conditions of almost constant length. From the interaction between the large negative effect and the positive effects of the nitrile conjugation reaction, it is deduced that the magnitude of the large negative effect is directly proportional to the concentration of nitrile groups present. It is proposed that the 140°C transition in PAN is a result of the association‐dissociation equilibrium between nitrile dipoles on adjacent chains. The temperature dependence of the equilibrium constant for this association is calculated from the birefringence ``cooling curve,'' giving an enthalpy change of 48 kcal∕mole, which suggests that association of dipole multiples is involved. Creep, dynamic mechanical, and dielectric loss data from the literature are correlated on the basis of this proposal concerning the nature of the transition.

Scattering of Light by Two‐Dimensional Spherulites

S. Clough, J. J. Van Aartsen, and R. S. Stein

J. Appl. Phys. 36, 3072 (1965); http://dx.doi.org/10.1063/1.1702929 (14 pages) | Cited 57 times

Online Publication Date: 14 July 2004

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The low‐angle light scattering for anisotropic disks (representing two‐dimensional polymer spherulites) is calculated for the cases of (1) the optic axis lying in the plane of the disk and tilted at the angle β to the radius, (2) the optic axis rotating cylindrically about the radius through the angle ω while making a constant angle β to the radius where (a) ω rotates randomly and (b) ω varies linearly with the distance r from the center of the disk, and (3) affine deformation of the disk to an ellipsoid. For case (1) the scattering pattern is shown to rotate azimuthally through the angle β from that previously described where β=0° in agreement with experimental observations on polytetrafluoroethylene. Case (2) is shown to predict an azimuthal dependence of the wide‐angle scattering maxima of a type experimentally observed for banded spherulites. Case (3) predicts a deformation of the scattering pattern of a type observed for deformed polyethylene spherulites.
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Brush Cathode Plasma—A Well‐Behaved Plasma

Karl‐Birger Persson

J. Appl. Phys. 36, 3086 (1965); http://dx.doi.org/10.1063/1.1702930 (9 pages) | Cited 41 times

Online Publication Date: 14 July 2004

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Results of probe, spectroscopic, and microwave studies are used to describe properties of a novel cold‐cathode discharge. The use of a brush cathode allows stable operation in the abnormal glow region where some of the usual cold‐cathode mechanisms are greatly exaggerated and determine the features of the produced plasma. The cathode fall is about an order of magnitude larger than for the corresponding normal cold cathode. The brush cathode generates a uniform electron beam in the energy range 1 to 10 kV and a corresponding negative glow with a longitudinal dimension (reaching distance of the beam) one to two orders of magnitude larger than for the normal cathode glow. The large dimensions of the negative glow and the fact that it is well‐behaved (no instabilities and no striations) make it ideal for a whole series of investigations in plasma physics and spectroscopy. The electron density in the helium plasma is in the range 1010 to 1014 cm−3, the electron temperature in the range 0.05 to 0.10 eV. The negative glow is beam generated (essentially field free) and recombination dominated making it a practically uniform plasma ideal for the study of rate and transport coefficients. Preliminary measurements of the particle balance give a recombination rate of 5×10−10 cm3 sec−1 at 1100°K and an electron density of 3×1012 cm−3 in agreement with the collisional‐radiative recombination theory developed by Bates, Kingston, and McWhirter. The recombination light emitted by the plasma is sufficiently strong to make spectroscopic methods useful for measurements of the electron density and the electron temperature. Lines in the helium series 2s3S—np3P0 are observed up to the quantum level n=30.

Tripyramid and Raised‐Triangle (111) Diamond‐Lattice Imperfections in Silicon Epitaxial Films

J. E. Lawrence and R. N. Tucker

J. Appl. Phys. 36, 3095 (1965); http://dx.doi.org/10.1063/1.1702931 (7 pages) | Cited 3 times

Online Publication Date: 14 July 2004

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Two epitaxial defects, the raised triangle and the tripyramid, which appear in silicon and germanium films, are discussed with respect to their origin, crystallography, and electrical characteristics. These crystalline defects propagate from substrate surface contamination, such as refractory particles, and grow more rapidly than the defect‐free film. Referred to the substrate lattice, the raised‐triangle defect is bound by the inclined {111} planes; the defect lattice is rotated 180° around the [111] direction. The raised‐triangle defect provides the conditions necessary for the formation of the tripyramid structure. The three crystallite lattices of the tripyramid are rotated relative to the raised‐triangle lattice's [111] direction such that their [111] directions are tilted 4° in the [211] direction. The major exposed faces of the tripyramid crystallites are {110} planes. Both the raised triangle and the tripyramid are centers for soft electrical junctions.

Parallel‐Pumped Magnon Instabilities in a Two‐Sublattice Ferrimagnetic Crystal

Frederic R. Morgenthaler

J. Appl. Phys. 36, 3102 (1965); http://dx.doi.org/10.1063/1.1702932 (10 pages) | Cited 7 times

Online Publication Date: 14 July 2004

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Instability thresholds for parallel‐pumped magnons in a two‐sublattice ferrimagnet are derived by means of a perturbation method. Cases are considered in which the pump frequency is twice a particular magnon frequency or else the sum of two distinct magnon frequencies—one belonging to each branch of the spinwave dispersion relation. The calculations are made within the molecular field approximation for a single crystal of ellipsoidal shape, and include the effects of the volume dipolar energy as well as those due to unequal g factors of the sublattices. The thresholds appropriate to an ``unflopped'' antiferromagnet are also given when the dc magnetic field is applied parallel to the anisotropy axis.
The prospects for experimentally reaching the thresholds, particularly those occurring at submillimeter wavelengths, are evaluated insofar as is possible; in such cases the possibility exists of utilizing a laser for the pump.

Direct Observation of Dislocations in Silicon Web Crystals

E. D. Jungbluth

J. Appl. Phys. 36, 3112 (1965); http://dx.doi.org/10.1063/1.1702933 (4 pages) | Cited 4 times

Online Publication Date: 14 July 2004

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Dislocations in web silicon have been observed by x‐ray diffraction microscopy. Numerous sources of dislocations originate in the dendrite and form low‐angle grain boundaries within the web. Dislocations propagating along the growth direction have [011] and [101] or [110] Burgers vectors, and dislocations aligned along the [110] and [101] directions are product dislocations of a Lomer‐Cottrell reaction. Interactions between the two sets of dislocations are often observed.

Effect of Hydrostatic Pressure on Shock Waves from Underwater Explosions

B. W. Vanzant and R. C. DeHart

J. Appl. Phys. 36, 3116 (1965); http://dx.doi.org/10.1063/1.1702934 (2 pages) | Cited 1 time

Online Publication Date: 14 July 2004

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Techniques for using pressure vessels to study the characteristics of shock waves from high explosives detonated under high hydrostatic pressure have provided empirical observations not previously available in the literature. Results indicate that although peak pressure is not affected by hydrostatic pressure, the duration is shortened and the impulse lowered by increasing the hydrostatic pressure. Also, the negative phase of the pressure pulse appears to increase as the ambient pressure increases.

Optimization of the Cross‐Sectional Geometry of Nernst—Ettingshausen Devices

G. L. Guthrie

J. Appl. Phys. 36, 3118 (1965); http://dx.doi.org/10.1063/1.1702935 (5 pages) | Cited 2 times

Online Publication Date: 14 July 2004

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The cross‐sectional geometry of Nernst—Ettingshausen generators and refrigerators is optimized for essentially rectangular geometry and also for Norwood's spiral screw thread configuration. The magnetic field, heat flow, and electrical current flow are assumed to be mutually perpendicular. The derivation is carried out without any restrictive assumptions concerning electric current distribution. There are no restrictive assumptions about the temperature dependence of κ, σ, or the Nernst coefficient. The expressions for the boundary of the device are given in parametric form with temperature as the parameter. Formulas are given for use in estimating the effect of incomplete optimization.

Mechanisms Contributing to the Noise Pulse Rate of Avalanche Diodes

Roland H. Haitz

J. Appl. Phys. 36, 3123 (1965); http://dx.doi.org/10.1063/1.1702936 (9 pages) | Cited 36 times

Online Publication Date: 14 July 2004

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The noise pulse rate of microplasmas and uniform avalanche diodes is determined by carrier generation within the space‐charge layer of the breakdown region, and by minority carrier diffusion to the breakdown region. By suppressing the minority carrier diffusion from bulk to breakdown region with a suitable geometry, it is possible to investigate the carrier generation within the space‐charge layer of a p‐n junction. Three contributions to the carrier generation rate are found: (1) thermal carriers from generation centers, (2) re‐emission of carriers trapped during preceding periods of avalanche breakdown, and (3) carrier generation by internal field emission (band‐to‐band tunneling). For the case of uniform avalanche diodes, these three contributions are investigated separately. The density of generation and trapping centers within the breakdown region could be reduced by several orders of magnitude by driving the diodes into secondary breakdown. During this process the breakdown region is heated to a temperature of the order of 1000°C at which trapping and generation centers are partly annealed.

Beam Probing of rf Beam∕Plasma Interactions

A. B. Cannara and F. W. Crawford

J. Appl. Phys. 36, 3132 (1965); http://dx.doi.org/10.1063/1.1702937 (4 pages) | Cited 10 times

Online Publication Date: 14 July 2004

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Experimental measurement of rf electric fields in electron‐beam∕plasma interactions requires a non‐perturbing probing technique. Such a technique is described in this paper and has been applied to study cathodic electron beam break‐up and meniscus formation phenomena observed in a low‐pressure mercury‐vapor discharge. Experiments are described in which the deflection of a fine electron‐beam probe directed parallel to the cathode surface is measured to determine the spatial variations of the low‐ and high‐frequency electric fields. A number of supporting experiments are reported which help to clarify the various phenomena occurring in the beam∕plasma interaction region.
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