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1 Dec 1956

Volume 27, Issue 12, pp. 1399-1563

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Uses of Carbon Replicas in Electron Microscopy

D. E. Bradley

J. Appl. Phys. 27, 1399 (1956); http://dx.doi.org/10.1063/1.1722278 (14 pages) | Cited 20 times

Online Publication Date: 14 May 2004

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Some of the early techniques for the preparation of carbon films and replicas for the electron microscope are compared with the method of vacuum evaporation developed by the author. The basic techniques for the production of replicas from evaporated carbon are described, and the high resolution obtainable is demonstrated and discussed. Some properties of evaporated carbon replicas are mentioned.
Descriptions are given of the carbon replica methods used in metallurgy and some applications are illustrated. Applications of carbon replicas in the following fields of research are also described: microbiology, biology, botany, entomology, chemistry, and industrial applications including the study of fibers.
It is concluded that evaporated carbon can be used as the final replica in any multistage replica process, and that it can be applied with advantage in almost every field of research in which the electron microscope is employed.
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Dislocation Etch Pits in Silicon Crystals

F. L. Vogel and L. Clarice Lovell

J. Appl. Phys. 27, 1413 (1956); http://dx.doi.org/10.1063/1.1722279 (3 pages) | Cited 12 times

Online Publication Date: 14 May 2004

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A method for suitably etching dislocations in silicon crystals is reported. Using this etch, dislocations in various arrays were observed: low angle boundaries, slip lines, polygonization walls, and bent crystal distributions.

Effect of Electron Irradiation on Young's Modulus

H. Dieckamp and A. Sosin

J. Appl. Phys. 27, 1416 (1956); http://dx.doi.org/10.1063/1.1722280 (3 pages) | Cited 19 times

Online Publication Date: 14 May 2004

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Young's modulus and internal friction measurements are reported on high‐purity copper following electron bombardment. The modulus is observed to rise rapidly with electron flux reaching an early saturation followed by a slow decrease. The rapid saturation is attributed to dislocation pinning. The rate of saturation is temperature dependent in the range from −195°C to about 0°C suggesting defect migration at low temperatures. The slow decrease is attributed to a ``bulk effect'' due to interstitial‐vacancy pairs.

Electrical Conductivity of Barium Oxide Single Crystals as a Function of Temperature and Excess Barium Density

R. T. Dolloff

J. Appl. Phys. 27, 1418 (1956); http://dx.doi.org/10.1063/1.1722281 (9 pages) | Cited 1 time

Online Publication Date: 14 May 2004

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Four‐electrode conductivity measurements over the temperature range from 500 to 1000°K have been made on clear BaO single crystals and on crystals colored blue by excess barium densities between 0.3 and 6×1017 per cc. Barium was introduced into the crystals by heating in a barium atmosphere and the excess barium densities were computed by the Smakula formula from the 2.0‐ev optical absorption band following the method of Sproull, Bever, and Libowitz. The conductivities of the clear crystals attain values of 10−4 mho∕cm at 1000°K whereas the blue crystals show a conductivity maximum of about 1 mho∕cm at about 900°K. The assumption of an electron mobility of 5 cm2∕volt sec leads to an agreement of the saturation electron density and the excess barium density to within a factor of three.

Xenon Arc Transients, Electrical and Optical

George W. LeCompte and Harold E. Edgerton

J. Appl. Phys. 27, 1427 (1956); http://dx.doi.org/10.1063/1.1722282 (4 pages) | Cited 11 times

Online Publication Date: 14 May 2004

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The growth of the luminous area of a high current discharge in an electronic xenon‐filled flashtube has been studied by means of a sequence of timed short‐exposure photographs taken with a magneto‐optic shutter. Electrical measurements show that the tube conductance is approximately proportional to the luminous area of the arc channel. The ionized gas has a volume conductivity of about 90 mho∕cm averaged over the luminous path during the buildup for the conditions investigated.

Diffusion of Aluminum in Single Crystal Silicon

R. C. Miller and A. Savage

J. Appl. Phys. 27, 1430 (1956); http://dx.doi.org/10.1063/1.1722283 (3 pages) | Cited 31 times

Online Publication Date: 14 May 2004

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The diffusion of aluminum into silicon has been reinvestigated to clear up certain discrepancies in the existing aluminum data. The diffusion constants found in this work are in good agreement with those determined by Fuller and Ditzenberger and an order of magnitude less than those reported in another investigation. Aluminum solid solubilities in the neighborhood of 1019 atoms∕cm3 have been found over the 1200 to 1400°C temperature range. These concentrations are several orders of magnitude larger than those reported in other aluminum diffusion investigations. The p‐n junction penetrations and transition capacitances of the diffused samples were used to determine diffusivities and solid solubilities.

Ultrasonic Attenuation Caused by Thermoelastic Heat Flow

Kurt Lücke

J. Appl. Phys. 27, 1433 (1956); http://dx.doi.org/10.1063/1.1722284 (6 pages) | Cited 43 times

Online Publication Date: 14 May 2004

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Expressions for the attenuation of sound waves in a standard linear viscoelastic body have been derived and have been applied to the attenuation due to the thermoelastic effect.
The thermoelastic attenuation for sound waves has been computed for single crystals and polycrystalline materials under application of the high‐frequency approximation of sound propagation. For single crystals the attenuation in the main propagation directions have been computed explicitly for cubic and hexagonal crystals taking into account the anisotropy of the elastic properties and thermal expansion.
Comparison with experiments in the megacycle region shows that the attenuation caused by heat flow between the grains of a polycrystalline specimen is usually overpowered by scattering at the grain structure. Also the computed attenuation caused by heat flow between the regions of compressions and rarefaction of the wave is for many materials much smaller than the measured values.
For single crystals of certain metals, however, the computed and the measured values have the same order of magnitude. It can be shown that in these cases the attenuation is composed of a thermoelastic component and of a component resulting from dislocations. In zinc the two components can be separated experimentally and the agreement between the measured and the computed thermoelastic damping is very good.

Lifetime Measurements of Excess Carriers in Semiconductors

N. J. Harrick

J. Appl. Phys. 27, 1439 (1956); http://dx.doi.org/10.1063/1.1722285 (4 pages) | Cited 16 times

Online Publication Date: 14 May 2004

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A technique is described whereby bulk carrier lifetimes in semiconductors can be measured over a wide range of injection level without making any electrical connections to the sample. The excess carriers are created by visible light and their distribution is measured by absorption of infrared radiation. The most important advantage of this technique is that the electric field term can be neglected in the continuity equation which describes the carrier distribution and the diffusion length can thus be determined directly. It appears that this technique may be used even in the presence of trapping. Some measurements are described for germanium where it is found that the carrier lifetime may increase or decrease with injection level. This is consistent with the Hall‐Shockley‐Read theory of carrier recombination.

Some Statistical Properties of Signal Plus Narrow Band Noise Integrated over a Finite Time Interval

L. C. Maximon and J. P. Ruina

J. Appl. Phys. 27, 1442 (1956); http://dx.doi.org/10.1063/1.1722286 (7 pages) | Cited 1 time

Online Publication Date: 14 May 2004

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The variance of narrow band noise plus c.w. signal after detection and integration over a finite time interval is derived. The problem is solved for Ideal, Gaussian, and High Q Single Tuned filters with square law and linear detection, the latter for large predetection signal‐to‐noise ratio. In addition to these filters the analysis is carried through for a model which considers the envelope of narrow band noise plus signal as a function which is constant for intervals of duration equal to the reciprocal of the noise band width and statistically independent in different intervals. Graphs of the mean square deviation divided by the mean power for noise alone are given for all filters and the model, with square law detection and predetection signal‐to‐noise ratios 0, 0.5, 1, 2.

Magnetic Granulometry and Super‐Paramagnetism

C. P. Bean and I. S. Jacobs

J. Appl. Phys. 27, 1448 (1956); http://dx.doi.org/10.1063/1.1722287 (5 pages) | Cited 82 times

Online Publication Date: 14 May 2004

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The magnetic technique of particle size measurement based on the work of Elmore consists of a comparison of a modified Langevin curve with the observed magnetization curve for an appropriate system of ferromagnetic particles. The average magnetic moment per particle is obtained from this analysis, and the average particle size is thus determined. The prediction by Néel of thermal relaxation in single‐domain ferromagnetic particles broadens the range of applicability of the granulometry method, with special emphasis on the size range from 20 A to about 100 A. A possible objection to the method, arising from evidence for an abnormal temperature dependence of the saturation magnetization of very small magnetic particles, is re‐examined experimentally and found to be invalid. Several examples are presented that demonstrate the predicted thermal relaxation and that point to a wide utilization of the granulometry technique.

Asymptotic Expansions of Solutions of the Heat Conduction Equation in Internally Bounded Cylindrical Geometry

R. H. Ritchie and A. Y. Sakakura

J. Appl. Phys. 27, 1453 (1956); http://dx.doi.org/10.1063/1.1722288 (7 pages) | Cited 19 times

Online Publication Date: 14 May 2004

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The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the ``radiation'' boundary condition. A problem in the flow of gas through a porous medium is considered in detail.

Vapor Pressure of Plastic Materials

Niels Jensen

J. Appl. Phys. 27, 1460 (1956); http://dx.doi.org/10.1063/1.1722289 (3 pages) | Cited 2 times

Online Publication Date: 14 May 2004

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A method is presented of measuring the equivalent nitrogen vapor pressure of polymeric materials over a range of temperatures. It is found that, for the range of temperatures investigated (300–450°K), the vapor pressure‐temperature characteristics of the polymeric materials studied are described by the empirical relation
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.
The values of the constants A and B in this equation are determined for a number of materials including nylon, Teflon, saran, polyethylene, and mylar.

Simple Modes of Vibration of Crystals

R. D. Mindlin

J. Appl. Phys. 27, 1462 (1956); http://dx.doi.org/10.1063/1.1722290 (5 pages) | Cited 10 times

Online Publication Date: 14 May 2004

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In this paper there are described solutions of the three‐dimensional equations of elasticity and the equations of generalized plane stress pertaining to vibrations of crystal rectangular parallelepipeds and thin plates with traction‐free faces. The modes of motion exist in crystals of certain classes for specific orientations and length‐ratios of the edges. Since the solutions are exact and in closed form, they may be used to advantage in connection with the measurement of elastic constants. Special disposition of electrodes is required for piezoelectric excitation.

Properties of the Shock Transition at Low Temperature

J. J. Gilvarry

J. Appl. Phys. 27, 1467 (1956); http://dx.doi.org/10.1063/1.1722291 (6 pages) | Cited 2 times

Online Publication Date: 14 May 2004

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Bethe's equation for the change of entropy in waves of finite amplitude is shown to be inapplicable for an initial state of temperature arbitrarily close to absolute zero, for a degenerate substance possessing a zero‐point pressure (or energy). Thermodynamic functions for such a substance at low temperature are formulated in general terms applicable to the Fermi‐Dirac gas, the Thomas‐Fermi atom, the Debye solid, and the Mie‐Grüneisen solid as special cases. The conditions under which the equation of state satisfies the Bethe‐Weyl conditions are given. Of the usual four basic properties of the shock transition under the Bethe‐Weyl conditions, two must be modified for the class of substances in question, for an initial state arbitrarily close to zero temperature. The argument follows from extension of Bethe's method, by Taylor expansion of the Hugoniot function about the initial state. The results are shown to be consistent with Weyl's procedure.

Extremely Low‐Frequency Electromagnetic Waves. I. Reception from Lightning

Leonard Liebermann

J. Appl. Phys. 27, 1473 (1956); http://dx.doi.org/10.1063/1.1722292 (4 pages) | Cited 10 times

Online Publication Date: 14 May 2004

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Extremely low‐frequency (ELF) radio waves (10–500 cycles) originating in lightning were received over distances in excess of 15 000 km. Transmission conditions were equally good, day or night. Propagation distances were ascertained by analysis of higher frequency components (>1700 cycles) according to known methods. The receiving antenna employed an arrangement of grounded electrodes which uniquely determined the azimuthal direction of the source. Two distinct classes of ELF pulses are described which are attributed to different conditions of propagation.

Extremely Low‐Frequency Electromagnetic Waves. II. Propagation Properties

Leonard Liebermann

J. Appl. Phys. 27, 1477 (1956); http://dx.doi.org/10.1063/1.1722293 (7 pages) | Cited 7 times

Online Publication Date: 14 May 2004

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Properties of electromagnetic propagation at extremely low frequencies (below 500 cycles) are deduced from analysis of pulse distortion. The source of the transmitted pulse is lightning. Two distinct transmission types are analyzed. Normal, or type I, propagation is shown to behave as if the earth's surface and ionosphere constitute a wave guide composed of two plane parallel surfaces, with one surface partially conducting. This wave guide has no low‐frequency limit on progagation; attenuation formulas are given. The transmission properties of type II, or anomalous propagation, are derived and seen to be inexplicable by means of this wave‐guide model. The analysis leads to a determination of the effective conductivity of the ionospheric reflector at these frequencies: the daytime reflecting layer (D layer) conductivity is 104 esu; the nighttime conductivity (E layer) is 5×104 esu; both results are far lower than deduced by other means.

Tensile Strength of Whiskers

S. S. Brenner

J. Appl. Phys. 27, 1484 (1956); http://dx.doi.org/10.1063/1.1722294 (8 pages) | Cited 174 times

Online Publication Date: 14 May 2004

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Tensile tests have been performed on whiskers of iron, copper, and silver 1.2 to 15 μ in diameter. The strongest whiskers which were less than 4 μ in diameter exhibited resolved elastic shear strengths of from two to six percent of their shear moduli. Stress‐strain determinations on iron have shown that large deviations from Hooke's law occur beyond two percent strain. As the whiskers increase in size, their strengths decrease with considerable scatter.

Electromagnetic Transmission Characteristics of a Lattice of Infinitely Long Conducting Cylinders

Zohrab A. Kaprielian

J. Appl. Phys. 27, 1491 (1956); http://dx.doi.org/10.1063/1.1722295 (12 pages) | Cited 3 times

Online Publication Date: 14 May 2004

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This investigation is primarily concerned with the study of electromagnetic transmission characteristics of a lattice of infinitely long conducting cylinders. Four approaches to the general problem have been employed and the advantages, disadvantages, and realms of validity of each have been studied. Several of these methods constitute a substantial improvement over previous analyses and are supported by wave‐guide and free‐space experimental work.
The four approaches are: (1) A molecular analogy with a consideration of dipole interactions leading to the Clausius‐Mosotti relations, (2) A transmission line formulation which considers the thick obstacle for both polarizations, (3) An analysis based on the summation of scattered fields which demonstrates that the Clausius‐Mosotti relations are a special case of a more general relation which accounts for the effects of higher order multipoles, and (4) A solution formally valid for all values of spacing and cylinder radius based on integral equation formulation of variational principle.

Reflectionless Transmission through Dielectrics and Scattering Potentials

I. Kay and H. E. Moses

J. Appl. Phys. 27, 1503 (1956); http://dx.doi.org/10.1063/1.1722296 (6 pages) | Cited 129 times

Online Publication Date: 14 May 2004

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A complete solution is given for the problem of constructing a plane stratified dielectric medium having that the property that at a fixed frequency and polarization a plane wave at any angle of incidence will be transmitted without reflection by the medium. This problem can also be interpreted quantum‐mechanically. The dielectric medium of the first interpretation becomes, in the second interpretation, a potential for the one‐dimensional Schrödinger equation such that a particle which is sent in from ‐ ∞ is transmitted with probability one of getting through to + ∞, no matter what the initial kinetic energy of the particle may be.
In addition, the results can be applied to the problem of finding perfectly matched nonuniform transmission lines.

Structure of Bent Zinc Crystals

C. T. Wei and Paul A. Beck

J. Appl. Phys. 27, 1508 (1956); http://dx.doi.org/10.1063/1.1722297 (11 pages) | Cited 9 times

Online Publication Date: 14 May 2004

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Zinc crystals were bent either by wrapping them around a mandrel or by the application of a concentrated load in a direction perpendicular to the basal plane. The structure of the bent crystals was studied by means of suitable x‐ray diffraction techniques, namely the Lambot technique and the Schulz technique. It was found that, after bending around a mandrel of sufficiently small radius, the zinc crystals were subdivided into subgrains, with an average disorientation between neighboring subgrains of approximately 3 minutes of arc. In the dimples formed by a concentrated load the radius of bending is quite large and there is hardly any observable substructure. However, the substructure does develop upon annealing by the polygonization mechanism. The diameter of the dimples formed by a concentrated load increases linearly with the logarithm of the time of load application, for a constant load, and it increases linearly with the load if the time of load application is constant.

Focusing of Low‐Energy Electron Beams

W. W. H. Clarke and L. Jacob

J. Appl. Phys. 27, 1519 (1956); http://dx.doi.org/10.1063/1.1722298 (6 pages)

Online Publication Date: 14 May 2004

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Conventional electrostatic and magnetic lenses were used to focus electron beams in the range of energies 30–70 v, produced by a specially designed experimental tube. The electron distribution in the focused beam was resolved by a series of concentric end collectors and a convention introduced to assess effective beam widths.
With near‐symmetrical lenses of the electrostatic type and for energies above 30 v, the beam, if inside the aberration limits of the lens, appears to be acted on as a whole by the field and a definite focus is obtained; for 30‐v beams, on the other hand, there is no unique focus since maximum and minimum values of effective beam width were recorded as the focus voltage was varied. Such a periodic variation might arise from the existence of standing wave patterns in the space charge in front of the cathode.
A characteristic feature of the focusing which is most marked in the magnetic case is the disappearance on focus of the Gaussian core of the incident beam distribution. With magnetic lenses having apertures in the ratio 2∕1, it was remarkable to find that the smaller aperture lens was the most efficient in bringing beams to a focus. In general, the power of magnetic lenses had to be greatly increased (in the measurements, by a factor of 30) over any expected thin lens performance to achieve a focus. Space charge forces, nonhomocentricity, and potential depression are held to be responsible for the abnormal conditions of focus.

Note on the Reduction of Carrier Lifetime in p‐n Junction Diodes by Electron Bombardment

W. Miller, K. Bewig, and B. Salzberg

J. Appl. Phys. 27, 1524 (1956); http://dx.doi.org/10.1063/1.1722300 (4 pages) | Cited 4 times

Online Publication Date: 14 May 2004

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Commercial encapsulated silicon p‐n junction diodes were bombarded by 2 Mev electrons from a Van de Graaff generator. The reverse transient current and the static I–V characteristics of the junction were measured before and after varying intervals of the bombardment time. The time dependence of the reverse transient current is in close agreement with theory, and the reciprocal of the minority carrier lifetime, as inferred from these data, is found to be a linear function of the bombardment time. The bombardment also produced marked changes in the static I–V characteristics of the diodes. These data are not in agreement with simple p‐n junction theory. A suggested explanation is that the diode behavior is generally similar to that of a p‐i‐n junction.

Stability of Periodic‐Field Beam Focusing

K. K. N. Chang

J. Appl. Phys. 27, 1527 (1956); http://dx.doi.org/10.1063/1.1722301 (6 pages)

Online Publication Date: 14 May 2004

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By taking into consideration both the effects of space‐charge and large‐amplitude scalloping, an analytic solution for periodic‐field beam focusing is obtained through use of successive approximation and Fourier series expansion. The stability limit is then determined by studying a perturbation of the obtained solution. The perturbation results in a Hill's differential equation for the incremental beam radius. This equation yields a stability criterion for periodic‐field beam focusing. It is found that instability starts at some degree of beam scalloping and ends at a higher one, and thus forms an unstable band.

Approximate Theory on the Stability of Interfacial Waves between Two Streams

Chan‐Mou Tchen

J. Appl. Phys. 27, 1533 (1956); http://dx.doi.org/10.1063/1.1722302 (4 pages)

Online Publication Date: 14 May 2004

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The stability of the interface of two superposed streams is studied by extending the theory of Helmholtz stability to include the viscosity and surface tension in the waves. The two uniform layers of incompressible fluids are of different densities, viscosities and stream velocities. Gravity, Taylor acceleration, and surface tension are taken into consideration. An approximate theory is developed and is valid in three ranges of wave numbers. Neutral stability, rate of growth, and rate of decay are illustrated graphically.

Donor Concentration Changes in Oxide‐Coated Cathodes Resulting from Changes in Electric Field

H. J. Krusemeyer and M. V. Pursley

J. Appl. Phys. 27, 1537 (1956); http://dx.doi.org/10.1063/1.1722303 (9 pages) | Cited 3 times

Online Publication Date: 14 May 2004

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Large reproducible changes in work function of oxide cathodes have been observed following step‐like changes in dc current drawn from, as well as to, the coating. One type, with a time constant in the range of 10−2 to 1 second, has been reported by others. It appears to be caused by a redistribution of donors by the field set up in the coating. We studied this phenomenon further as a function of temperature, dc current density, coating composition, and barium deposition.
We also discovered a second type of transient which follows the first. It has a time constant, in the range from 100 to 104 seconds. The amplitude of this change is of the same order as that of the first. The time dependence is in most cases given by a simple exponential. Both amplitude and time constant are a function of the cathode itself as well as its environment. This transient is thought to be caused by a change of the total number of donors. A simple analysis accounting for the exponential form yields values for the donor loss rate.
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