Showing papers in "Journal of Applied Physics in 1958"
828 citations
TL;DR: In this paper, it was shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated.
Abstract: Equations describing the flow of a Newtonian liquid on a rotating disk have been solved so that characteristic curves and surface contours at successive times for any assumed initial fluid distribution may be constructed. It is shown that centrifugation of a fluid layer that is initially uniform does not disturb the uniformity as the height of the layer is reduced. It is also shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated. Contour surfaces for a number of exemplary initial distributions (Gaussian, slowly falling, Gaussian plus uniform, sinusoidal) have been constructed. Edge effects on rotating planes with rising rims, and fluid flow on rotating nonplanar surfaces, are considered.
696 citations
TL;DR: In this article, a simple soda-lime glass has been investigated in relation to the sensitivity of this glass to atmospheric corrosion and an analysis of the failure process has been given which is based on the concept that inherent surface flaws grow by corrosive mechanisms to critical dimensions by virtue of a reaction between water vapor in the atmosphere and components of the glass.
Abstract: Static fatigue of a simple soda‐lime glass has been investigated in relation to the sensitivity of this glass to atmospheric corrosion. An analysis of the failure process has been given which is based on the concept that inherent surface flaws grow by corrosive mechanisms to critical dimensions by virtue of a reaction between water vapor in the atmosphere and components of the glass. The rate of this reaction is determined by the stress conditions around local areas and the temperature, pressure, and composition of the surrounding atmosphere. Since the experimental work shows a close relationship between the temperature dependence of the failure process and that of the self diffusion of sodium ion in bulk glass it is concluded that alkali content is responsible for the very low long time strengths of most inorganic glasses.
691 citations
TL;DR: In this article, the energy loss resulting from eddy currents was calculated for magnetic sheet materials with a simple domain configuration, and the results were in a form more suitable for quantitative comparison with measured values on materials, such as grain oriented silicon iron, than have been available.
Abstract: The energy loss resulting from eddy currents is calculated for magnetic sheet materials with a simple domain configuration. The domain model used is considered to be applicable for any induction up to saturation and for the frequency range up to that used in most electrical power applications. The eddy current losses have been calculated explicitly for the case of sinusoidal induction excitation, and expressed in terms of the ratio of domain wall spacing to sheet thickness. The results are in a form more suitable for quantitative comparison with measured values on materials, such as grain oriented silicon iron, than have been available.
538 citations
TL;DR: In this paper, the effects of nonuniform electric fields on nonconducting liquids have been investigated, and the results show that the effect can be used to produce a fairly efficient pumping action of nonconducted liquids, to cause continuous and easily measureable separations in coarse suspensions, to produce selective precipitation, and to produce mixing.
Abstract: Some of the more interesting effects of nonuniform electric fields are described in this report. Experimental and theoretical studies show the effects to be rather striking for particles larger than molecular size. The results show that the effect can be used to produce a fairly efficient pumping action of nonconducting liquids, to cause continuous and easily measureable separations in coarse suspensions, to cause selective precipitation, and to produce mixing.By this means, liquids may be thrown several feet into the air with an electromechanical efficiency of about 25%. A separation factor of at least 2.5 in continuous separatory operation may be produced in a suspension of polyvinyl chloride in carbon tetrachloride‐benzene mixture. Suspensions of polar materials in less polar liquids may be either dispersed or precipitated. In one interesting ``demonstration'' type experiment, drops were ``hung'' in mid‐air.
383 citations
TL;DR: A simple theory of radiation enhanced diffusion has been worked out which describes the dependence of this enhancement on flux and temperature under steady state conditions as discussed by the authors, and the theoretical study also shows that the measurement of enhanced diffusion as a function of temperature can indicate the mechanism by which defects are removed from the lattice.
Abstract: A simple theory of radiation enhanced diffusion has been worked out which describes the dependence of this enhancement on flux and temperature under steady‐state conditions. The theoretical study also shows that the measurement of enhanced diffusion as a function of temperature can indicate the mechanism by which defects are removed from the lattice. Alpha‐brass was chosen for the experimental work because it is a kinetically simple system, not complicated by nucleation, in which diffusion is easily followed by measuring the electrical resistivity changes associated with changes in short‐range order. The enhanced diffusion rate during irradiation in the Brookhaven reactor has been measured in this alloy at several temperatures in the range 0 to 190°C. This enhancement is independent of temperature from 0 to 150°C, in excellent agreement with the theoretical predictions for the case where the radiation induced defects finally disappear at internal surfaces. Some implications of radiation enhanced diffusion and suggestions for further study are also discussed.
325 citations
TL;DR: In this paper, the dependence of the rate of the oxidation of silicon in oxygen-helium mixtures on gas composition at 1410°C is discussed theoretically, and it is shown that at low oxygen contents of the gas, no layer of solid silica is expected to occur and the rate due to formation of volatile SiO is proportional to the oxygen partial pressure in the bulk gas.
Abstract: The dependence of the rate of the oxidation of silicon in oxygen‐helium mixtures on gas composition at 1410°C is discussed theoretically. At low oxygen contents of the gas, no layer of solid silica is expected to occur and the rate of attack due to formation of volatile SiO is supposed to be proportional to the oxygen partial pressure in the bulk gas. Above a critical oxygen partial pressure, solid silica may be formed and the rate of attack under steady‐state conditions may drop by several powers of ten.
296 citations
252 citations
TL;DR: In this article, the inert gas ions Ne+, A+, Kr+, and Xe+, at energies between 30 and 400 ev, were detected and recorded in a 180° mass spectrometer of 5.5 inch radius.
Abstract: Silver, germanium, and germanium‐silicon alloy surfaces have been bombarded with the inert gas ions Ne+, A+, Kr+, and Xe+, at energies between 30 and 400 ev. Primary beam intensities between one and ten μa/cm2 were obtained in an oscillating electron source of the Heil type. The secondary particles sputtered off, neutrals as well as positive and negative ions, were identified and recorded in a 180° mass spectrometer of 5.5‐inch radius. They are partly background gases adsorbed on the surface, partly atoms and molecules characteristic of the sample. Among the latter particles, neutrals were about 100 times more abundant than those emitted as positive ions. Rather low yields (about one sample atom per 100 incident ions with 400‐ev energy) and relatively high threshold energies (40–50 ev for an angle of 30° between beam and surface) are believed to be due to surface contamination. Retarding potential measurements showed that over 80% of the particles sputtered have initial energies of less than 5 ev. After bombardment, the Ge and Ge‐Si surfaces showed oval‐shaped hillocks, possibly due to appreciable carbon concentrations in the samples studied. If the effects of surface contamination can be reduced, this method promises to be useful in the analysis of solid surfaces.
242 citations
238 citations
TL;DR: In this paper, an analytical model which is applicable to static fatigue of lime glass, has been extended to account for dynamic fatigue of the same glass, which successfully predicts the room temperature strain rate sensitivity of the failure process in lime glass and indicates a method by which the stress concentration relationship, applicable to microscopic flaws on glass surfaces, may be obtained by experiment.
Abstract: An analytical model, which is applicable to static fatigue of lime glass, has been extended to account for dynamic fatigue of the same glass. The model successfully predicts the room temperature strain rate sensitivity of the failure process in lime glass and indicates a method by which the stress concentration relationship, applicable to microscopic flaws on glass surfaces, may be obtained by experiment. Resulting experiments showed that the stress concentration relationship proposed by Inglis is valid.
TL;DR: In this article, a detailed static and dynamic theory based on the above anisotropy energy and the Landau-Lifshitz dynamical equation is presented, and experimental verification of the theory is given.
Abstract: Thin magnetic films (∼1000 A) evaporated onto a heated glass substrate in the presence of a dc magnetic field develop a uniaxial magnetic anisotropy energy of the form Ek=Ksin2φ, with φ measured from the deposition field. Such films promise to outperform ferrite cores in digital‐computer memory‐systems by several orders of magnitude. A detailed static and dynamic theory based on the above anisotropy energy and the Landau‐Lifshitz dynamical equation is presented. The static theory contains the unique feature of the coercive force parallel to the easy axis being dependent on a field in the plane of the film and perpendicular to the easy axis. Experimental verification of the theory is given.The dynamic theory considers both steady‐state and pulse response. The steady‐state solution is well known; the pulse solution must take very careful account of all the important torques acting in a switching experiment, and numerical results are obtained by the use of a digital computer. Experimentally, steady‐state res...
TL;DR: In this article, the authors show that if the group velocities on the two transmission lines are in the same direction, the direction of power transfer reverses periodically with distance.
Abstract: When two circuits such as filters or transmission lines are coupled together by means of distributed reactances which can vary sinusoidally in time and space, energy can be converted between waves of different frequencies in a variety of ways. If the waves on the two transmission lines are characterized by frequencies ω1 and ω2 and phase constants β1 and β2, while the coupling reactances vary as ω=ω1−ω2 and β=β1−β2+Δβ, power P1 at ω1 is converted into power P2 at ω2 and vice versa in a manner reminiscent of waves on coupled passive circuits, except that a relationship (P2/ω2)=(P1/ω1) is obeyed. If the group velocities on both transmission lines are in the same direction, the direction of power transfer reverses periodically with distance. If they are not in the same direction, the power transfer increases monotonically with distance for small Δβ but reverses periodically for Δβ larger than a certain limit.When the coupling reactance varies as given by ω=ω1+ω2 and β=β1+β2, parametric amplification is possi...
TL;DR: In this paper, the etch pit formation process is described in detail, and the mechanism for pit formation is discussed, which is probably due to the preferential nucleation of unit pits one molecule deep at a dislocation and the movement of the monomolecular steps across the surface.
Abstract: Dislocation etch pits can be formed on LiF by a dilute aqueous solution of FeF3. In this report the etch pit formation is described in detail, and the mechanism for pit formation is discussed. The nature of the etch pits depends on the character of the dislocation, and on the exact composition of the etchant. Edge dislocations and screw dislocations etch slightly differently; the former produce deeper pits. The etching is inhibited by some segregated impurities at dislocations, therefore aged dislocations and fresh dislocations etch much differently. Etch pit formation is probably due to the preferential nucleation of unit pits one molecule deep at a dislocation, and the movement of the monomolecular steps across the surface. The relative rates of these two processes determine the shape of the etch pits. The nucleation rate for unit pits depends upon the dislocation energy, hence upon the character of the dislocation and the impurity content as suggested by Cabrera. The nucleation rate is faster at edge dislocations, because of their higher energy. The nucleate rate is low at dislocations with segregated impurities, because the impurities lower the dislocation energy. The ferric ion is adsorbed on the surface and inhibits the motion of steps, so that steeper, more visible pits are produced as the iron content is increased.
TL;DR: In this article, a new mechanism for bulk viscosity is proposed from the standpoint of the hole theory of liquids and the rate process theory, which can explain the temperature and pressure dependencies of acoustic absorption for associated liquids and very viscous nonassociated liquids.
Abstract: The mechanisms for bulk viscosity are different between associated and nonassociated liquids. Here, a new mechanism for bulk viscosity is proposed from the standpoint of the hole theory of liquids and the rate process theory. This mechanism can explain the temperature and pressure dependencies of acoustic absorption for associated liquids and very viscous nonassociated liquids.
TL;DR: In this paper, a new phenomenological approach to quantitative discussions of the statistics and time dependence of mechanical breakdown is presented, which permits the prediction of relationships between the lifetime distributions to be observed for fibers under different loading histories: dead loads, loads proportional to time, and periodic loads.
Abstract: A new phenomenological approach to quantitative discussions of the statistics and time dependence of mechanical breakdown is presented. The theory permits the prediction of relationships between the lifetime distributions to be observed for fibers under different loading histories: dead loads, loads proportional to time, and periodic loads. It also permits the calculation of relationships between the strength of separated individual filaments and the strength of bundles of filaments. The present formulation of the theory is more general than the author's previous work on this subject in that the fibers considered here can ``remember'' their past history as far as breakdown is concerned. It is shown that in the case of periodic loadings, depending on the choice of certain arbitrary functions, the theory can be used to discuss either time‐dependent fatigue or cycle‐dependent fatigue. The relationships between the present approach and the static models used in classical theories of tensile strength distributions for single filaments and bundles are discussed.This article consists of a formal, axiomatic development of the theory. Future publications will contain detailed comparisons of the various results with available experimental data.
TL;DR: In this paper, it was shown that the index of refraction of a variable-index, spherical lens which will form perfect geometrical images of the points of two given concentric spheres on each other.
Abstract: The general solution is obtained for the index of refraction of a variable‐index, spherical lens which will form perfect geometrical images of the points of two given concentric spheres on each other. One conjugate sphere is assumed to be outside the lens or at its surface, while the other may be either inside, outside, or at the surface. If one of the spheres is of infinite radius, the lens will focus a parallel beam perfectly at a point on the other sphere.It is shown that the index of refraction may be specified arbitrarily, subject to two simple conditions, in an outer shell of any desired thickness less than the radius of the lens. The index of the central portion is then expressed in terms of a function which is tabulated, and of an integral involving the index of the outer shell. Some properties of the general solution are discussed, and various special solutions are derived.
TL;DR: The ion-bombardment cleaning method has been successfully applied to the (100) faces of germanium, silicon, and nickel, and to the(0001) face of titanium as mentioned in this paper.
Abstract: The ion‐bombardment cleaning method has been successfully applied to the (100) faces of germanium, silicon, and nickel, and to the (0001) face of titanium. Conditions and precautions necessary for the production of clean surfaces are described. Tests have been made for contamination from the ambient during the cleaning procedure for germanium. It has been shown that contamination approximating one‐half monolayer does not occur under the conditions which were obtained, and that the method is capable of producing surfaces which are atomically clean.Results for clean (100), (111), and (110) germanium faces and the (100) silicon face indicate that the atomic positions in the surface planes are not the same as the corresponding positions in the bulk structure. For (100) nickel and (0001) titanium, the positions of the atoms in the surface planes are in agreement with x‐ray data. In the case of titanium, an unidentified surface structure was present until after several cycles of alternate heating and ion bombardment. In the case of nickel, a double‐spaced surface monolayer and in some cases a single‐spaced, simple‐square structure, attributed to carbon, was present until after several cycles of alternate heating and ion bombardment.
TL;DR: In this article, the electric field at the surface of a semiconductor is obtained as a function of the semiconductor bulk properties and the potential difference across the space charge region, and conditions under which the equation for the field can be conveniently simplified are discussed, and a particular case is treated numerically.
Abstract: The electric field at the surface of a semiconductor is obtained as a function of the semiconductor bulk properties and the potential difference across the space charge region. The treatment is general enough to take into account degenerate free carrier distributions and partial ionization of impurities, either in the neutral bulk or the space charge region, or both. A one‐dimensional model with a spacially homogeneous impurity distribution is assumed. The density of states in the conduction and valence bands is assumed to be that appropriate for spherical and ellipsoidal energy surfaces. The common model for simple donor and acceptor states is used in the main body of the paper. Conditions under which the equation for the field can be conveniently simplified are discussed, and a particular case is treated numerically.The validity of the free carrier distribution functions in the high fields near the semiconductor surface is discussed in Appendix I. The equation for the electric field at the semiconductor...
TL;DR: In this paper, a new type of 180° wall is observed: the main wall is cut at regular intervals by short, right-angle ''cross ties'' which terminate in free, single ends.
Abstract: Domain‐wall structure in Permalloy films in the thickness range 25 to 2000 A has been studied by the Bitter technique. A new type of 180° wall has been observed: the main wall is cut at regular intervals by short, right‐angle ``cross ties'' which terminate in free, single ends. The cross‐tie period and length are dependent on film thickness, each becoming shorter with decreasing thickness. These patterns can be understood in terms of a new model for the structure of domain walls in thin films of low‐anisotropy material. In the conventional model the atomic moments within the wall rotate about an axis perpendicular to the wall. In a thin film such a configuration leads to a large energy contribution from the large demagnetization factor normal to the film. In the new model, the axis of rotation is itself thought to rotate about the axis of the wall to give a ``corkscrew'' configuration of spins and a large decrease in associated magnetostatic energy. Of several experiments which have been performed which s...
TL;DR: In this paper, the light emission patterns of silicon diffused p-n junctions at breakdown were compared with the etch-pit patterns that reveal dislocations, and it was concluded that avalanche breakdown microplasmas occur preferentially where dislocation pass through the junction.
Abstract: The light emission patterns of silicon diffused p‐n junctions at breakdown have been compared with the etch‐pit patterns that reveal dislocations. It is concluded that avalanche breakdown microplasmas occur preferentially where dislocations pass through the junction. In narrow p‐n junctions, large numbers of dislocations result in enhanced internal field emission and, consequently, a soft reverse characteristic. A qualitative correlation is found between the nature of the light emission pattern (spots for avalanche breakdown, glow for field emission) and the quality of the reverse characteristic. Possible reasons why breakdown should occur preferentially at dislocations are discussed though no precise conclusion is reached. Peculiar singularities observed in the light emission patterns of some junctions were found to coincide with crystal abnormalities revealed in the etch patterns.
TL;DR: In this article, the reflection of a plane electromagnetic wave on a rough surface was analyzed and the boundary condition (7.8) for the case of vertical polarization should read 7.8.
Abstract: I N a previous publicationi we have analyzed the reflection of a plane electromagnetic wave on a rough surface. Due to an error in sign* in Eq. (3.6) of the foregoing reference the sign on the right side of Eqs. (3.7) and (3.9) must also be changed. This amounts to replacing the “roughness parameter” r by -(r throughout the paper. In particular the boundary condition (7.8) for the case of vertical polarization should read
TL;DR: In this paper, the spectrum of modes of oscillation of a ferromagnetic spheroid situated in a uniform dc magnetic field is discussed, and it is shown that for the size of sample usually used in microwave experiments, a part of the spectrum consists of magnetostatic modes for which exchange and propagation may be ignored.
Abstract: The spectrum of modes of oscillation of a ferromagnetic spheroid situated in a uniform dc magnetic field is discussed. It is shown that, for the size of sample usually used in microwave experiments, a part of the spectrum consists of magnetostatic modes for which exchange and propagation may be ignored. The behavior of these modes is discussed at some length and it is shown that the analysis gives a satisfactory description of the observed absorption curves.
TL;DR: In this article, a non-laminar optical model is proposed to calculate trajectories at any point in a long high-density electron beam, where thermal velocities are treated as an integral part of the motion.
Abstract: Most previous treatments of long high‐density electron beams have assumed laminar flow. Recent experiments show that in many cases this assumption is unjustified. The present theory is based on a non‐laminar optical model which treats thermal velocities as an integral part of the motion. A Maxwellian distribution of initial transverse velocities is assumed at the cathode, and a first‐order focusing theory is applied in order to calculate trajectories at any point in the beam. It is shown that whenever a long beam is confined by a focusing field, images of the cathode are formed repeatedly along the axis.When applied to uniform magnetic focusing fields, the theory predicts the periodic formation along the axis of cathode images and crossovers, and a relative rotation of successive images. Such effects have been reported. Values of required focusing fields are derived for given space‐charge and thermal‐velocity conditions, and relations are established between beam spread and transverse velocities. The resu...
TL;DR: In this paper, a series of germanium-silicon alloys were used for thermoelectric power measurement and it was shown that solid-solution alloying can significantly increase the figure of merit of the thermodynamic properties of these materials.
Abstract: Thermal conductivity measurements have been made on a series of germanium‐silicon alloys. At 300°K for an alloy containing 56 atomic percent Si, the thermal conductivity was found to be six times smaller than the value for pure Ge. Measurements of the thermoelectric power on some alloys are also reported. It is then shown that solid‐solution alloying can significantly increase the figure of merit of thermoelectric materials.
TL;DR: Magnetic properties of 5Fe2O3·3M 2O3 where M represents Gd•Tb•Dy•Ho•Er•Tm•Yb•Lu•Y•Sm•Eu are reported in this article.
Abstract: Magnetic properties of 5Fe2O3·3M2O3 where M represents Gd‐Tb‐Dy‐Ho‐Er‐Tm‐Yb‐Lu‐Y‐Sm‐Eu are reported. The results are interpreted using Neel's molecular field model. A study of the Al substituted gadolinium garnets shows a preference for Al ions to occupy d sites.
TL;DR: In this paper, it was shown that dislocations are nucleated ahead of the tips of cracks that move slower than 6×103 cm/sec in LiF crystals, and that cracks move more slowly in crystals with high dislocation densities than in relatively perfect crystals.
Abstract: It is shown that dislocations are nucleated ahead of the tips of cracks that move slower than ∼6×103 cm/sec in LiF crystals. The motion of cracks that move slower than ∼3×103 cm/sec is unstable; that is, the velocity oscillates.About 2×105 cm/sec is the terminal velocity for (100) cleavage cracks in LiF.For constant driving force, cracks move more slowly in crystals with high dislocation densities than in relatively perfect crystals.
TL;DR: The magnetization reversal process of iron-nickel films (nominally 82% Ni−18% Fe) deposited in the presence of a magnetic field to a thickness of about 1000 A to 4000 A have been examined by the application of appropriate fields.
Abstract: The magnetization reversal process of iron‐nickel films (nominally 82% Ni‐18% Fe) deposited in the presence of a magnetic field to a thickness of about 1000 A to 4000 A have been examined by the application of appropriate fields. Experimental results indicate that at least two different magnetization reversal mechanisms are effective. The first, characterized by relatively long remagnetization periods, involves domain‐wall movement; the second, characterized by relatively short remagnetization periods, is consistent with the rotation of the magnetization in the plane of the film. The threshold for the rotational process is altered by the application of transverse magnetic field in a manner consistent with a simple energy model.
TL;DR: In this article, the authors used micrographic techniques to study dislocations, point defect clusters, and cavities in neutron-irradiated LiF crystals and found that the defect clusters decrease in number and increase in size with increasing annealing temperatures.
Abstract: Micrographic techniques have been used to study dislocations, point defect clusters, and cavities in neutron‐irradiated LiF crystals.No evidence of inhomogeneous damage caused by ``thermal or displacement spikes'' was found. However, a uniform etching effect was found for doses greater than ∼1015 nvt. The etching is believed to be caused by clusters of point defects greater than 2 A but less than 50 A in size. This agrees with previous x‐ray results. The defect clusters decrease in number and increase in size with increasing annealing temperatures. At temperatures greater than ∼400°C only (110) dislocation loops remain and these disappear above ∼600°C. Electron bombardment causes a similar effect.The as‐grown dislocation structure of LiF is not affected by neutron bombardment. However, it becomes increasingly difficult to move fresh dislocations in crystals given neutron doses greater than ∼1012 nvt. The hardening is independent of dislocation velocity and temperature and hence cannot be caused by Cottrellpinning of dislocations. The color changes that accompany hardening suggest that it is caused by defect clusters rather than single defects.At annealing temperatures above ∼600°C crystallographic cavities appear in LiF crystals. They are rectangular parallelepipeds with (100) sides. Evidence is presented to show that the cavities are not caused by fission gases but probably by loss of fluorine from the crystals.