Showing papers in "Journal of Applied Physics in 1950"

Diffusional Viscosity of a Polycrystalline Solid

Abstract: According to a suggestion of Nabarro, any crystal can change its shape by self‐diffusion in such way as to yield to an applied shearing stress, and this can cause the macroscopic behavior of a polycrystalline solid to be like that of a viscous fluid. It is possible that this phenomenon is the predominant cause of creep at very high temperatures and very low stresses, though not under more usual conditions. The theory underlying it is developed quantitatively, and calculations of rate of creep, or equivalently of effective viscosity, are given for aggregates of quasi‐spherical grains and for wires composed of cylindrical grains. Allowance is made for the effect of tangential stress relaxation at the grain boundaries. It is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may be unable to serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation differen...

A Method for the Numerical Calculation of Hydrodynamic Shocks

Abstract: The equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks. The quantitative influence of these terms can be made as small as one wishes by choice of a sufficiently fine mesh for the numerical integrations. A set of difference equations suitable for the numerical work is given, and the condition that must be satisfied to insure their stabilty is derived.

Second‐Order Transition Temperatures and Related Properties of Polystyrene. I. Influence of Molecular Weight

Abstract: Dilatometric and viscometric data on fractionated polystyrenes containing diethylbenzene end groups are presented over wide temperature ranges. The second‐order transition temperature, viscosity‐temperature coefficient, and specific volume all change rapidly with increasing molecular weight toward asymptotic limits which are practically reached at M≅30,000. Empirical expressions are presented relating these properties to molecular weight and temperature. In each case the dependence on molecular weight is expressed as a simple function of Mn−1. These observations are interpreted and correlated on the basis of the hypothesis that the local configurational order in a liquid polymer is disturbed by the introduction of end groups to a degree that is proportional to their number. The second‐order transition does not represent an isoviscous state. The internal local configurational structure appears to be equivalent, and independent of temperature, in all polystyrenes below their second‐order transition tempera...

Transmission of Elastic Waves through a Stratified Solid Medium

Abstract: The transmission of a plane elastic wave at oblique incidence through a stratified solid medium consisting of any number of parallel plates of different material and thickness is studied theoretically The matrix method is used to systematize the analysis and to present the equations in a form suitable for computation

Formation of Crystal Nuclei in Liquid Metals

Abstract: The known facts about nucleation phenomena in liquid metals are interpreted satisfactorily on the basis of the critical size and interfacial energy concepts. In large continuous masses nucleation is almost always catalyzed by extraneous interfaces. However, in very small droplets the probability that a catalytic inclusion is present is so much less that their minimum nucleation frequencies are reproducible and form a consistent set of values.Interfacial energies, σ, between crystal nuclei and the corresponding liquids have been calculated from nucleation frequencies of small droplets on the basis of the theory of homogeneous nucleation. Energies of interfaces, σg, one atom thick and containing N atoms were calculated from the σ's. The ratio of σg to the gram atomic heat of fusion, ΔHf, was approximately 0.45 for most metals but ∼0.32 for H2O, Bi, Sb, and Ge.The effect of relative complexity of crystal structure upon the supercooling behavior of pure metals apparently is a reflection of its effect upon ΔHf.

The Effect of Cold‐Work Distortion on X‐Ray Patterns

Abstract: With modern experimental technique, it is possible to measure a peak shape with sufficient accuracy to justify an interpretation based on the precise shape of the reflection. The corrected shape is represented by a cosine Fourier series and a set of An coefficients determined. A plot of the An coefficients vs. n will distinguish between distortion and particle size broadening. From the An coefficients, root mean square values of strain averaged over lengths na3 are obtained. The decrease in these values for increasing length na3 is a direct indication of the non‐uniform nature of the strains in cold‐worked metal. By measuring several orders of a given plane, it is theoretically possible to obtain a distribution function of the strains directly from a Fourier transform of the An coefficients.

On the Theory of Dislocations

Abstract: If, in a multiply‐connected elastic solid, discontinuities are permitted across a stationary barrier in either the strain or its first derivatives or both, dislocations of a more general type than encountered in classical theory are possible. A number of these more general dislocations have been obtained for states of plane and anti‐plane strain in a hollow right circular cylinder when the surface of discontinuity is a single stationary plane barrier. Some of the dislocations found possess the characteristic that although the strain is continuous across the barrier the displacement discontinuity is not one which would be possible in a rigid body. Examination of the conditions for the uniqueness of solution of the boundary value problems of elasticity reveals that when dislocations of the more general type are admitted appropriate data must be given at each point on the specified barrier in addition to the usual information.

Surface Waves and Their Application to Transmission Lines

Abstract: In this paper the applicability of non‐radiating surface waves for transmission lines is investigated. Two types of waves are considered. The first one, originally studied by A. Sommerfeld, is guided by a cylindrical conductor of finite conductivity. Although this wave type has (under comparable conditions) much lower attenuation than the waves in coaxial cables or rigid wave guides, its practical application is restricted by the fact that the extension of the field is very large. Efficient excitation and undisturbed propagation of this wave mode are feasible only for very high frequencies. The other wave type considered in this paper has not been treated in the literature. It is guided by a conductor which is coated with a dielectric layer or the surface of which is otherwise modified; for example, by being threaded. The field of this wave type has a structure similar to that of Sommerfeld's wave, but the extension of the field can be controlled by the surface modification. Thus low loss transmission lines on the basis of this wave type become feasible for frequencies above 100 megacycles. The information necessary for the design of such lines is given and the agreement between the theoretically expected transmission losses and the measured transmission losses is checked.

Effect of Change of Scale on Sintering Phenomena

Abstract: It is shown that when certain plausible assumptions are fulfilled simple scaling laws govern the times required to produce, by sintering at a given temperature, geometrically similar changes in two or more systems of solid particles which are identical geometrically except for a difference of scale. It is suggested that experimental studies of the effect of such a change of scale may prove valuable in identifying the predominant mechanism responsible for sintering under any particular set of conditions, and may also help to decide certain fundamental questions in fields such as creep and crystal growth.

X‐Ray Measurement of Order in Single Crystals of Cu3Au

Abstract: X‐ray diffraction methods have been used to measure long‐ and short‐range order parameters for single crystals of the alloy Cu3Au held at elevated temperatures. It is shown that short‐range order parameters may be obtained by a three‐dimensional Fourier analysis of the ``scattering power'' for the diffuse background scattering of x‐rays, expressed as a function of reciprocal lattice coordinates. Appropriate experimental and computational procedures are outlined. Intensity measurements have been made with a special arrangement of a bent‐crystal monochromator and a Geiger‐counter spectrometer. Short‐range parameters are given for the first ten shells of atoms surrounding a given atom for three temperatures above the critical temperature of Cu3Au. These results, and those for the long‐range order parameter agree well with theoretical predictions.

Microscopic Observation of the Solidification of Small Metal Droplets

Abstract: The solidification behavior of small metal (10 to 100 micron diameter) droplets has been observed on a high temperature microscope stage. An abrupt change in surface appearance and in the case of high melting metals a sudden brightening (``blick'') accompanies solidification. The solidification temperatures observed for a collection of droplets may be widely distributed, but a significant, usually the major, fraction of the droplets supercool some maximum amount (ΔT‐)max that is reproducible and characteristic of the metal. For many metals (ΔT‐)max≈0.18 times the absolute melting temperature. (ΔT‐)max is not much changed by wide variations in the cooling rate and droplet size. The growth rate of metal crystals is very great so that the solidification rate of the droplets is controlled by the nucleation frequency.

Determination of Crystallite Size with the X‐Ray Spectrometer

Abstract: The accuracy of the Scherrer crystallite size equation is limited in part by the uncertainty in β, the experimentally deduced pure diffraction broadening. Currently used procedures for estimating β from the observed breadth of a Debye‐Scherrer line are not, in general, applicable to the x‐ray spectrometer.By making use of a scheme of convolution analysis for analyzing the effect of geometrical factors in broadening the pure diffraction contour, a correction curve is developed for determining β from the experimentally measured line breadths b and B (Jones' notation). The degree of reliability of this correction procedure is ascertained by applying Stokes' direct Fourier transform procedure for determining the form of the pure diffraction contour free of instrumental effects.Suggestive procedures are given for crystallite size determination with the x‐ray spectrometer in different size ranges, and several examples are described.

Strain Induced Grain Boundary Migration in High Purity Aluminum

Abstract: A method has been developed for the study of grain boundary migration in high purity aluminum, which allows positive determination of the direction of grain boundary movements. By means of this method it was confirmed that the migration of grain boundaries resulting from surface energy takes place in the direction toward the centers of curvature of the boundaries. On the other hand, strain induced grain boundary migration, such as occurs in recrystallization, proceeds in a direction away from the centers of curvature of the moving boundaries. It was also found that certain strained grains serve as nuclei for strain‐free grains of the same orientation which grow at the expense of neighboring strained grains. Most of the strain‐free grains formed during the annealing of high purity aluminum cold rolled up to about 40 percent are produced by this mechanism of strain‐induced boundary migration, without the formation of new nuclei.

The Propagation of Plastic Deformation in Solids

Abstract: The stress wave caused by a longitudinal impact at the end of a cylindrical bar has been analyzed in the case where the impact velocity is large enough to produce plastic strain. The theory gives a method for computing the stress distribution along the bar at any instant during impact. It is shown that for a given material, there is a critical impact velocity such that when subjected to a tension impact with a velocity higher than the critical, the material should break near the impacted end with negligible plastic strain. An experimental investigation was made concurrently with the theoretical study. Some of the most significant experimental results are presented in this paper.

The Thermal Conductivity of Soils

Abstract: The thermal conductivity of soils of varying moisture content is calculated on a physical basis. The results of this computation are, in a range of moisture contents from 5 to 25 percent, in agreement with experimental data in the literature. The influence of soil composition on conductivity is also explained by the theory. The use for practical purposes of an average resistivity value of 60 to 70 thermal ohms appears justified in the light of this analysis.

Formation of Annealing Twins During Grain Growth

Abstract: It is proposed that annealing twins form during grain growth as a result of a decrease in the interfacial free energy of grain boundaries that would not be achieved in the absence of twinning. Experiments designed to permit detection of the changes in grain boundary free energy accompanying the formation of twins give results in agreement with this concept. The abundance of twins found in annealed copper depends on the texture in a manner that is consistent with the theory.

Interference of Growing Spherical Precipitate Particles

Abstract: The exact theory of the rate of growth of spherical precipitate particles has previously been developed for the initial stage where the individual precipitate particles do not interfere with one another. In the present paper this theory is carried one stage further to include their mutual interference. It is found that in the particular case of a very dilute solution this interference may be accounted for in a relatively simple manner. The applicability of the theory has been tested by new observations upon the precipitation of carbon from α‐iron. Good agreement is found up to 95 percent completion of precipitation.

Thermoelastic Stress in the Semi-Infinite Solid

Abstract: The solution of the elasticity equations for the center of dilatation in the semi‐infinite solid is introduced into Goodier's theory of thermoelastic stress. It is shown that the problem of potential to be solved is identical with that for the solid of indefinite extent. The results are applied to the case of an expanding (or contracting) spherical inclusion embedded in an elastic body near its surface.

An Extension of Wiener's Theory of Prediction

Abstract: The theory of prediction described in this paper is essentially an extension of Wiener's theory. It differs from the latter in the following respects.1. The signal (message) component of the given time series is assumed to consist of two parts, (a) a non‐random function of time which is representable as a polynomial of degree not greater than a specified number n and about which no information other than n is available; and (b) a stationary random function of time which is described statistically by a given correlation function. (In Wiener's theory, the signal may not contain a non‐random part except when such a part is a known function of time.)2. The impulsive response of the predictor or, in other words, the weighting function used in the process of prediction is required to vanish outside of a specified time interval 0≤t≤T. (In Wiener's theory T is assumed to be infinite.)The theory developed in this paper is applicable to a broader and more practical class of problems than that covered in Wiener's theory. As in Wiener's theory, the determination of the optimum predictor reduces to the solution of an integral equation which, however, is a modified form of the Wiener‐Hopf equation. A simple method of solution of the equation is developed. This method can also be applied with advantage to the solution of the particular case considered by Wiener. The use of the theory is illustrated by several examples of practical interest.

Nuclei of Strain in the Semi‐Infinite Solid

Abstract: Stress functions are given for forty nuclei of strain in the semi‐infinite elastic solid. The corresponding stresses have the property that the traction vanishes across the plane boundary of the solid. The nuclei are derived, by processes of superposition, differentiation and integration, from the solution of the elasticity equations for the single force in the interior of the semi‐infinite solid.

The Use of Spraying Methods and of Volatile Suspending Media in the Preparation of Specimens for Electron Microscopy

Abstract: Developments have been made in the use of spraying methods in the preparation of specimens for examination in the electron microscope. At the same time, two wholly volatile diluents, containing electrolytes and adjusted to normal pH, have been developed for use in forming the spray drops. The use of volatile electrolytes makes it unnecessary to wash the specimen after the droplet patterns have been formed on the specimen screens.There are several qualitative and quantitative uses and advantages of the spray technique as described. The qualitative ones are these: (1) the brief drying time of the droplets helps to preserve the shapes of particles upon drying, and also allows studies to be made of rapidly reacting systems; (2) since the drop patterns are reproducibly representative samples of the suspension under investigation, qualitative assays of the particulate composition of the suspension can be made, and a comparison of the particulate composition of two closely similar suspensions can be made under i...

Work Functions of the Elements

Abstract: Like the chemical properties of the elements, the work function φ is a periodic function of atomic number, as shown clearly by a new compilation of published data for 57 elements. The progressive rise and fall of work function values throughout the table of the elements appears to be sufficiently regular to permit approximations to be made of values for the metallic and semimetallic elements on which no data has yet been published. Since the first ionization potential Ei and electrode potential E0 exhibit a similar periodic function of atomic number, a striking resemblance exists among the respective plots of φ, Ei, and E0.

Stress Analysis for Compressible Viscoelastic Materials

Abstract: Mathematical methods of stress analysis are presented for linear, compressible, viscoelastic, or anelastic, materials such as metals at high temperatures or high polymers with small strains. For such materials stress, strain and their time derivatives of all orders are related by linear equations with coefficients which are material constants. Fourier integral methods are used to show that static elasticity solutions can be used to determine the time dependent stresses in viscoelastic bodies with any form of boundary conditions.If stress and double refraction and their time derivatives are also linearly related, the standard photoelastic techniques can be used to determine the directions and difference in magnitude of the time dependent principal stresses, even though the principal stress axes do not coincide with the polarizing axes and both vary with time. When viscoelastic models are used in photoelastic studies, the time variation of the stress distribution in the model represents a first approximatio...

A Bending Method for Measurement of the Tensile Strength and Young's Modulus of Glass Fibers

Abstract: The tensile strength and Young's modulus of Johns‐Manville experimental drawn glass fibers were measured by a bending method which consists of twisting a loop in a fiber and pulling the ends until the loop breaks. The tensile strength observed by this method was two to three times higher than observed by the conventional straight fiber method, while Young's modulus was practically unchanged. These results may be accounted for by the presence of flaws, since the probability is small that the weakest flaw will occur in the loop, while the straight fiber will always break at the weakest flaw. The apparatus used, a modified Chainomatic balance, is described and the equation of the looped fiber is derived. The method is used to measure the maximum tensile stress and strain attained at the point of minimum radius of curvature of the loop as well as the breaking tensile stress and strain at the actual break point of the fiber. The stress at the break point was found to be as small as one‐half the maximum attained in the loop, showing that the strength of the fiber was not uniform.

The Orientation Dependence of the Rate of Grain Boundary Migration

Abstract: Very small recrystallized grains of a large variety of orientations were produced locally in lightly rolled high purity aluminum crystals. The rate of growth of these small grains varied greatly, depending on their relative orientation with respect to the matrix crystal. Grains with an orientation corresponding to a [111] rotation of about 40° showed by far the highest rate of growth. These results indicate that recrystallization textures developing in the spontaneous recrystallization of deformed single crystals can be accounted for by the orientation dependence of the rate of growth.

Separation of Gases by Fractional Permeation through Membranes

Abstract: The permeability of a number of thin organic films toward oxygen and nitrogen has been measured. For an ethyl cellulose film the studies were extended to include CO2, A, He, and H2. The enrichment of a binary gas mixture in a single stage of permeation has been calculated for the extreme cases of perfect mixing and no mixing. Application of these results indicates that the use of a fractional permeation process may be of practical importance in effecting the separation of oxygen from air, helium from natural gas, and hydrogen from coke‐oven gas, as examples.

A General Solution for the Bending of Beams on an Elastic Foundation of Arbitrary Continuity

Abstract: In the analysis of beams which are supported elastically along their entire length, it is usually assumed that the elastic support is provided either by a series of independent springs, or by a completely continuous elastic medium.The present paper proposes a method of solution for the intermediate cases, that is, for foundations of partial continuity, by assuming that such foundations may be represented by beams imbedded into an otherwise discontinuous supporting material. In a foundation of this type, there are three independent elastic constants, the resilience of the discontinuous spring layers above and below the beam that is within the foundation, and the flexural rigidity of the foundation beam itself. By changing the values of these three constants, elastic foundations of a wide variety may be produced or, conversely, the constants may be adjusted in such a manner as to represent approximately the characteristics of any given elastic supporting medium.In the paper a general procedure is presented ...

Production of 2537 Radiation and the Role of Metastable Atoms in an Argon‐Mercury Discharge

Abstract: The average population of 63P1 mercury atoms is calculated from the measured 2537 output and resonance radiation diffusion theory. Average populations of 63P2, 0 are then found by comparing the absorptions of 5461, 4358, and 4047. Populations for a 0.42‐amp. discharge in 3.5‐mm argon of high purity plus Hg vapor at 42°C in a tube 1½ inches in diameter are for 63P2, 1, 0, respectively, 7.6×1011, 1.9×1011, and 3.5×1011 cm−3; these are ⅕, 1/20, and ⅕ of the corresponding Boltzmann populations, for the electron temperature of 11,100°K.Rates of collisions of the first and second kinds involving electrons (average concentration 2.1×1011 cm−3), and the 61S0 and 63P2, 1, 0 states are calculated using known excitation functions and detailed balancing. The results predict populations for 63P2, 1, 0 within 10 percent of those observed; they further predict that ⅔ of the observed 2537, ⅔ of the visible triplet, and ¾ of the 3650 group are produced stepwise via 63P. Quenching collisions involving argon are assumed neg...

The Static Electrification of Dust Particles on Dispersion into a Cloud

Abstract: An extensive study of the charge and size distribution of particles from 0.5 to 30 microns radius in dust clouds of diverse exemplary types dispersed in air under a variety of conditions ranging from blowing with minimum of turbulence to conditions of violent and maximum impact with various types of surfaces was made using adaptations of the Hopper and Laby modification of the oil drop experiment. It was observed that all dusts, including homogeneous dusts with no impacts on solid surfaces, were charged. In homogeneous systems the charges of opposite sign were equal, no net charge resulting, the number of particles of similar size with opposite charges being about the same. The magnitude of charges increased somewhat less rapidly than the surface of the particle. There was no correlation between size and sign of charge. There is strong evidence that charging occurs on separation of the contacts between particles in the dispersion of the cloud. Humidity did not affect the charging. Studies of heterogeneous systems making contact with solid walls of different composition from the powder gave consistent asymmetry of charge of varying degrees depending on the proportion of particles striking the surfaces relative to those just separated.