Showing papers in "Journal of Applied Physics in 1955"

Theory of elasticity and consolidation for a porous anisotropic solid

Abstract: The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

Study of the Initial Stages of Sintering Solids by Viscous Flow, Evaporation‐Condensation, and Self‐Diffusion

Abstract: The mechanism of material transport in sintering can be elucidated in some cases by direct observation of the rate of interface growth and approach of centers between spherical particles. Measurements with glass, sodium chloride, and copper indicate that with these materials viscous flow, evaporation-condensation, and self-diffusion are the rate-determining mechanisms. Values of viscosity, vapor pressure, and diffusion constants have been determined, but calculations of diffusion constants from these data are subject to uncertainties of interpretation. A model is presented for the behavior of copper during the initial stages of sintering, which is in agreement with available experimental data, and which requires vacancy elimination at dislocations or grain boundaries. Data for refractory oxides indicate the importance of purity and fabrication pressure, but the sintering mechanism for these materials is not determined by the present data.

Theory of Steady‐State Creep Based on Dislocation Climb

Abstract: A theory of steady‐state creep is developed using Mott's mechanism of dislocation climb. It is assumed in the analysis that the rate‐controlling process is the diffusion of vacancies between dislocations which are creating vacancies and those which are destroying them. The concentration of vacancies along a dislocation line is determined by setting the change in the free energy caused by a decrease or increase in the number of vacancies equal to the change in the elastic energy occuring during dislocation climb. The creep equation that results from the analysis is creep rate=const (σα/kT)exp(−Q/kT) where α is a constant (α∼3 to 4), Q is the activation energy of self‐diffusion, kT has its usual meaning, and σ is the stress. This equation is valid in the stress range from the critical shear stress to a stress about equal to 108 to 109 dynes/cm2. At larger stresses the creep rate increases much more rapidly with stress.

Numerical Solutions of Spherical Blast Waves

Abstract: The strong‐shock, point‐source solution and spherical isothermal distributions were used as initial conditions for a numerical integration of the differential equations of gas motion in Lagrangean form. The von Neumann‐Richtmyer artificial viscosity was employed to avoid shock discontinuities. The solutions were carried from two thousand atmospheres to less than one‐tenth atmospheres peak overpressure. Results include overpressure, density, particle velocity, and position as functions of time and space. The dynamic pressure, the positive and negative impulses of both dynamic pressure and static overpressure, positive and negative durations of pressure and velocity, and shock values of all quantities are also described for various times and radial distances. Analytical approximations to the numerical results are provided.

Theory of Non‐Newtonian Flow. I. Solid Plastic System

Abstract: The relaxation process of viscous flow may be visualized as the sudden shifting of some small patch on one side of a shear surface with respect to the neighboring material on the other side of the shear surface. Any shear surface will divide a mosaic of such patches lying on the two sides of the surface. Except for the simplest systems, this mosaic of patches will be heterogeneous and can be described by groups each characterized by its mean relaxation time βn, by xn the fractional area of the shear surface which the group occupies and by αn, a characteristic shear volume divided by kT. The resulting generalized expression for viscosity is η= ∑ n=1nxnβnαnsinh−1βnṡβnṡ, where ṡ is the rate of shear. This equation is applied to masticated natural rubber, polystyrene, X‐672 GR‐S, X‐518 GR‐S rubber, and Vistanex LM‐S polyisobutylene. All applications give good agreement with experiment. The known criticisms of Eyring's simple relaxation theory for viscous flow are reviewed, and are apparently taken care of in ...

Calculation of the Space Charge, Electric Field, and Free Carrier Concentration at the Surface of a Semiconductor

Abstract: In the study of the surface properties of semiconductors, it is valuable to know the relation between carrier density at the surface and the shift in electrostatic potential from the bulk to the surface. By a solution of Poisson's equation utilizing Boltzmann statistics, the space charge, electric field, and change in free carrier concentration have been calculated for a semiconductor surface. The results are expressed as a function of the deviations of the Fermi energy from its intrinsic value in the bulk and at the surface. The calculated curves may be used for any nondegenerate semiconductor at any temperature, provided that the donor and acceptor levels are completely ionized. Numerical values are given for germanium and silicon at room temperature.

Hysteresis Loops of Mixtures of Ferromagnetic Micropowders

Abstract: A treatment is given of the hysteresis loops of dilute mixtures of various sizes of ferromagnetic particles. Three ranges of particle size are considered: very small particles called ``super‐paramagnetic'' which are single domain and equilibrate resulting from thermal vibrations, single domain particles which are large enough that they do not equilibrate, and particles large enough to contain many domains in equilibrium. The results are compared to experiment.

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

Abstract: 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.

Silicon Solar Energy Converters

Abstract: Theory is given for the design of silicon solar energy converters commonly known as the Bell Solar Battery. Values are given for the various parameters in the design theory. Experimental data are presented and compared with the theoretical relations based on a simple model.It is found that with present techniques, units can be made with up to 6 percent efficiency in the conversion of solar radiant energy to electrical energy. An important factor in obtaining such high efficiencies is the reduction of the series resistance of the cell to as low a value as possible.

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

Abstract: 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.

Electrical Conductivity of Highly Ionized Argon Produced by Shock Waves

Abstract: Shock tube techniques for the production of shock waves up to Mach number 20 have been developed and reported previously by Resler, Lin, and Kantrowitz, J. Appl. Phys. 23, 1390 (1952). These techniques can produce high temperature gas with accurately known enthalpy (e.g., in argon 25 percent ionization has been produced following an incident shock). Spectroscopic studies of high temperature argon produced this way by Petscheck, Rose, Glick, Kane, and Kantrowitz, ``Spectroscopic studies of highly ionized argon produced by shock waves,'' J. Appl. Phys. 26, 83 (1955), showed that equilibrium ionization can be reached in the time available in these experiments (of the order of 100 microseconds). This paper reports a study of the electrical conductivity of high temperature argon produced by shock waves.At low degrees of ionization (less than 10−3 for argon), the diffusivity of electrons and thus the gas conductivity is determined by the cross section for electron‐atom collisions which has been measured by mobility and by scattering techniques. At high degrees of ionization (larger than 10−3 for argon) the diffusion of electrons is primarily limited by long range Coulomb interaction with positive ions and thus is independent of the chemical nature of the gas. Theoretical treatments of this case have been given by Chapman and Cowling, Cowling, and by Spitzer and Harm. At intermediate degrees of ionization additive effects of both of these resistivity mechanisms would be expected.Preliminary measurements with electrodes indicated large surface resistances. These effects were avoided by the development of an electrodeless technique in which the moving ionized gas deflected a magnetic field. Resultant voltages induced in a search coil were related to the conductivity distribution in the gas following the shock wave. At temperatures greater than 8000–10 000°K (depending on the gas density) the gas conductivity quickly reached a maximum value (up to 80 mhos/cm). The maximum conductivity obtained at these high temperatures agreed within 10 percent with theoretical expectations. It also agreed well with measurement of electrical resistivity in the cesium discharge by F. L. Mohler, Bur. Standards J. Research 21, 873 (1938). At lower temperatures the oscillograms indicated that the conductivity was still rising at the end of the hot region. Under these conditions maximum conductivities reached were much lower than the theoretical values. The ionization rate obtained varied considerably with the gas density.At the highest temperatures the conductivity declined quickly from the maximum value and the rate of decline could be correlated with the expected cooling due to recombination radiation. Indications of a high conductivity associated with luminous shock fronts were obtained.

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

Abstract: 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.

Analysis of Electrode Phenomena in the High-Current Arc

Abstract: An analysis is made of the phenomena at the electrodes of a high‐current short‐time arc. It is shown that the input power density to the anode spot is in the range 5×104 to 1×106 watts/cm2. To a first‐order approximation, all this power can be carried off by evaporation. Power conducted into the metal and lost by radiation is negligible in the probable operating range. For most materials, the anode spot is probably considerably above the boiling temperature. The process of evaporation holds the spot temperature constant at a value such that the input power and evaporation power are equal. Experimental data indicate that for any given metal the anode spot temperature is that for which the evaporation power density is at least 3×105 watts/cm2. As an example, for copper the theoretical limits of temperature are 2490 to 3040°K, while experimental data indicate a temperature of 2920°K. Other metals considered are: Ag, Al, C, Fe, Mo, Sn, Ti, W, Zn, Zr. It is also shown that for the maximum power input that can ...

Nyquist's and Thevenin's Theorems Generalized for Nonreciprocal Linear Networks

Abstract: It is shown that an N‐node nonreciprocal linear network, with a system of internal thermal noise generators at temperature T, is equivalent to the source‐free network together with a set of correlated nodal current generators, with infinite internal impedance, such that 〈iris*〉Avdν=2kT(yrs+ysr*)dν where yrs is an element of the network admittance matrix and ir is the rth nodal noise current with frequency v. The noise sources can also be represented by a system of nodal voltage generators, with infinite internal admittance, such that 〈vrvs*〉Avdν=2kT(zrs+zsr*)dν.The application of these results to a system of coupled antennas in an equi‐thermal enclosure is noted and necessary conditions for the realizability of passive nonreciprocal networks are derived.

Electron Microscopy of Monodisperse Latexes

Abstract: A series of monodisperse polystyrene latexes has been prepared by carefully controlled emulsion polymerizations. The particle diameters of three of these latexes were determined by electron microscopy. The latex particles were dispersed on collodion membranes supported by copper grids. The microscopes had previously been calibrated with collodion replicas of a 30 000 line/inch diffraction grating. In general, the reproducibility of measurements from many photographic exposures was good; however, a few exposures yielded particle diameters considerably higher than the averages.An investigation of this technique indicated that: (1) polystyrene latex particle diameters (collodion membranes—copper grid supports) increased considerably on electron irradiation, (2) collodion diffraction grating replicas (copper grid supports) shrank slightly on electron irradiation, and (3) the magnification of the electron microscope varied slightly from exposure to exposure. It was found that variations of particle diameter re...

Work Function of Tungsten Single Crystal Planes Measured by the Field Emission Microscope

Abstract: The work functions of the low emitting crystallographic planes of tungsten, (011) and (112), are not well known. In previous experiments scattered secondaries and some other disturbing effects covered the small emission particularly of the (011) plane. A method combining the field emission microscope with a probe collector has been applied. The current density in the (011) plane turned out to be 4 to 5 orders of magnitude smaller than in strongly emitting planes. Applying the Fowler‐Nordheim theory, φ011 was found between 5.70 and 5.99 ev and φ112 between 4.65 and 4.88 ev depending on the temperature at which the tungsten crystal has been annealed previously. This is not a temperature effect of the work function, but the result of freezing in thermal imperfections of the planes. The work function of the ideal (011) plane appears to be as high as 5.99 ev. The existence of such a high value is further suggested by the ionization of aluminum on a hot polycrystalline tungsten wire, indicating that a part of t...

Dependence of the Coercive Force on the Density of Some Iron Oxide Powders

Abstract: An experimental investigation has been made of the dependence of the coercive force on the density of some magnetite and gamma ferric oxide powders consisting of different sized and shaped particles. Various aspects of the data are discussed. In particular, an interpretation based on a calculation of the critical single domain size of iron oxide particles with a prolate spheroidal shape is consistent with the experimental results.

Magnetic Materials for Digital‐Computer Components. I. A Theory of Flux Reversal in Polycrystalline Ferromagnetics

Abstract: It is proposed that magnetization reversal in polycrystalline ferro‐ and ferrimagnetic materials is primarily due to the nucleation and growth of 180° Bloch walls. The origin of domains of reverse magnetization is discussed. The rate of growth of these domains is determined by a study of the elastic and frictional forces which retard the motion of their 180°‐Bloch‐wall boundaries. This theoretical model successfully explains the output‐voltage wave forms of polycrystalline materials. A figure of merit for the magnetization reversal of magnetic cores is defined as the switching coefficient Sw=(Hm−H0)τ, where τ is the time required to reverse the magnetization, Hm is the applied magnetic field, and H0 is the threshold field value at which the average domain‐wall velocity is zero. Sw is composed of an eddy‐current contribution Swe and a spin‐relaxation contribution Swr. The value of Sw is derived in terms of various fundamental parameters of the material. It is shown that in ferrites and ultra‐thin metal tap...

Measurement of Carrier Lifetimes in Germanium and Silicon

Abstract: The decay of photoconductivity has been used to measure the lifetime of excess carriers in rectangular samples of germanium and silicon. The sample is illuminated by a short pulse of light and the sample lifetime obtained from an oscilloscope display of the decay of photoconductivity. Analysis of the solution of the diffusion equation yields methods of measuring the bulk lifetime, the surface recombination velocity, and the diffusion constant.

Preparation of Thin Magnetic Films and Their Properties

Abstract: Techniques for the preparation by vacuum evaporation of single thin layers and laminated structures of ferromagnetic alloys (principally in the iron‐nickel system) are described The magnetic properties are related to those parameters of the process which may be chosen to yield materials having desired characteristics A method for producing films with extreme hysteresis loop rectangularity is described Questions of suitable substrate materials, evaporable dielectrics for use in insulating multilayer deposits, and control of alloy composition, are considered in detail

Electrical Breakdown in High Vacuum

Abstract: Currents preceding breakdown have been measured between closely spaced tungsten electrodes in high vacuum. It is found that field emission currents sufficient to evaporate anode metal flow before breakdown. These currents follow the Fowler‐Nordheim equation when field magnification due to surface irregularities on the cathode is taken into account. The field magnification is a function of distance at electrode separations less than 4×10−4 cm.Explanation of the observed breakdown at low voltage and small spacing requires an unusually high yield of electrons at the cathode per ion formed in the gap. Furthermore there is no measurable direct enhancement of the current by ionization even at higher voltages. The high electron yield must therefore exist over the entire observed range of breakdown voltages. This high yield is satisfactorily accounted for by the increase in field emission due to the positive ion space charge, which in turn increases the positive ion current density until there is breakdown. It is...

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

Abstract: 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.

Viscoelasticity of Poly Methacrylates

Abstract: This paper presents an intensive study of the viscous and elastic properties of the poly methacrylates. Variation of these properties is studied as a function of temperature in the range 60

Gettering of Gas by Titanium

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

Tensile Strength of Plastics above the Glass Temperature

Abstract: The times taken for two plastics, polystyrene and polyethyl methacrylate, to break under various constant loads are reported for both the glassy and rubbery states. A theory is presented which describes the strength properties of plastics in the glassy state. The theory predicts that the logarithm of the time taken for the sample to break is proportional to the applied load. Such behavior is actually found by experiment. The tensile data in the rubbery range are adequately represented by a theory previously developed for that region.

An Approximate Theory of Armor Penetration

Abstract: The problem of armor penetration of thin plates is considered from a quasi‐dynamical approach. Equations are derived for the energy dissipation due to plastic deformation and for heating of the projectile target interface. Both the conical and the ogival head are considered in the application of the general equations.

Spectroscopic Studies of Highly Ionized Argon Produced by Shock Waves

Abstract: For the study of high‐temperature gas dynamics, shock‐tube techniques have been developed earlier to produce shock waves strong enough to heat gases to high and accurately known enthalpy (for argon up to 18 000°K or 40 percent ionization at equilibrium). This paper reports a study of the visible radiation from the highly luminous argon following strong shock waves.Preliminary spectrograms showed a strong continuum and that the prominent argon lines were broadened and shifted to the red. Correlation of the frequency shifts with theoretical treatments permitted an evaluation of the ion density in the gas. Development of a drum camera spectrograph (film speed 700 ft/sec) in which time effects could be resolved to about 1 μsec indicated that equilibrium ion density was reached rapidly, and provided a rough measurement of the rate of decline of ion density due to cooling.Absolute photoelectric spectrophotometric measurements of the continuum radiation were made and correlated with theoretical expectations. Con...

Outgassing of Glass

Abstract: The gas evolved from glass at temperatures below the softening point, which is of interest in bake‐out problems, is primarily water. The water evolved from unit surface at constant temperature above 300°C is linear with respect to the square root of the time of bake‐out. The intercept of the linear plot, which can be altered by different surface treatments, is a measure of the easily removed water residing at the surface. The slope is a measure of the rate of evolution of water that has diffused to the surface from the interior.Values of the diffusion constant for water and concentration gradients after bake‐out have been calculated for a soda‐lime glass. The diffusion constant is an exponential function of the reciprocal of the absolute bake‐out temperature. Values of the activation energy for the diffusion process are given for eight glasses.A method of calculating the amount of water that will diffuse from glass for any time‐temperature conditions following any bake‐out is presented.