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1 Apr 1967

Volume 38, Issue 5, pp. 1999-2412

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Periodic Dislocation Distributions in a Half‐Space

D. R. J. Owen and T. Mura

J. Appl. Phys. 38, 1999 (1967); http://dx.doi.org/10.1063/1.1709818 (11 pages) | Cited 1 time

Online Publication Date: 29 June 2004

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A solution is given to the stress field produced by an arbitrary periodic distribution of dislocations (or plastic distortion) in a half‐space. It is shown how the known results for discrete dislocations are obtained quite simply from this. The solution to the problem of a Frank dislocation network near a free surface is given and its stability examined. The whole‐space stress field decreases exponentially with the distance from the plane of the network, as do the stress terms due to the free surface which decrease exponentially with the distance from this surface. It is shown that the network always experiences a force attracting it to the free surface.

The Elastic Anisotropy of Crystals

D. H. Chung and W. R. Buessem

J. Appl. Phys. 38, 2010 (1967); http://dx.doi.org/10.1063/1.1709819 (3 pages) | Cited 46 times

Online Publication Date: 29 June 2004

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Essentially, the elastic properties of all the known crystals are anisotropic. This paper presents a convenient method to describe the degree of the elastic anisotropy in a given cubic crystal and then discusses its practical values. On the basis of the well‐known Voigt and Reuss schemes to average the single‐crystal elastic constants for polycrystalline behavior, the degree of elastic anisotropy has been defined as A* = [3(A−1)2]∕[3(A−1)2+25A], where A is the usual anisotropy factor given by A = 2c44∕(c11−c12). It is shown that the present A* has the folowing properties of practical importance: (a) A* is zero for the crystals of the elastic isotropy, i.e., A = 1. (b) For an anisotropic crystal, A* is a single‐valued measure of the elastic anisotropy regardless of whether A < 1 or A > 1. (c) A* gives a relative magnitude of the actual elastic anisotropy possessed by a crystal.

Intrinsic Brittle Strength of Magnesium Oxide Bicrystals

F. F. Lange and W. R. Buessem

J. Appl. Phys. 38, 2013 (1967); http://dx.doi.org/10.1063/1.1709820 (7 pages) | Cited 4 times

Online Publication Date: 29 June 2004

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The intrinsic brittle strength (i.e., without dislocation motion) was obtained for MgO bicrystals of various misorientations. Bicrystal fracture always occurred at the grain boundary. Strength values ranged between 70 000 psi and 370 000 psi. Two modes of fracture were observed: intergranular and intragranular fracture. The latter occurred only at high strain energies. Secondary cracks, believed to originate from flaws on the grain‐boundary surface, were observed for all bicrystal specimens that fractured in a brittle manner.
Tensile stresses as high as 400 000 psi were obtained on single crystals of MgO before ductile fracture occurred.

Pulsed Flashover in Vacuum

Alan Watson

J. Appl. Phys. 38, 2019 (1967); http://dx.doi.org/10.1063/1.1709821 (5 pages) | Cited 37 times

Online Publication Date: 29 June 2004

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Experiments on the vacuum flashover of dielectric frusta subjected to 35 and 75 nsec pulses show the strong influence of cone angle on insulation strength. A theory is presented to explain the formative process leading to flashover for one polarity. It is proposed that positive surface charge grows by emission of hot electrons during the application of the electric field. When the surface field intensity is sufficient to draw other electrons into it, they will multiply by secondary emission until the critical breakdown condition is achieved. Flashover is thus initiated by secondary emission, but the formative time lag is governed by thermionic emission of electrons. The experimental data are analyzed and interpreted in the light of this theory.

Formation of Dislocation Networks in Gallium Single Crystals

S. H. McFarlane and C. Elbaum

J. Appl. Phys. 38, 2024 (1967); http://dx.doi.org/10.1063/1.1709822 (6 pages) | Cited 2 times

Online Publication Date: 29 June 2004

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The development of dislocation networks in gallium crystals, initially free of detectable dislocations, has been studied at room temperature by an x‐ray diffraction topographic technique. The condition required for the development of these networks is the existence of spatial periodic fluctuations in impurity content. The networks develop, in the absence of an external stress, from individual loops which are first detected 3 to 10 days after the crystal has been grown. These loops grow for days at a uniform rate of 10−8 cm∕sec and reach a size of a few hundred microns. No specific nucleation mechanism for these loops has been identified. It it is assumed that the loops expand by climb (by the addition of vacancies), their rate of growth and observed densities are consistent with a formation energy for vacancies Uf in the range 0.2 to 0.3 eV and a migration energy for vacancies Um in the range 0.4 to 0.7 eV. No values of Uf, Um, or Uf+Um determined from other experiments have been reported and a comparison is not possible at the present time. The change of initially straight dislocation lines into jagged lines has been observed and is interpreted as the climb of screw dislocations into irregular helical dislocations. A marked anisotropy in the growth of the loops and helices was observed and is attributed to an anisotropic coefficient of self‐diffusion.

Dependence of 50‐ and 100‐keV Bremsstrahlung on Target Thickness, Atomic Number, and Geometric Factors

R. C. Placious

J. Appl. Phys. 38, 2030 (1967); http://dx.doi.org/10.1063/1.1709823 (9 pages) | Cited 9 times

Online Publication Date: 29 June 2004

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Experimental data have been obtained for the bremsstrahlung spectra produced with 50‐ and 100‐keV electrons incident on different targets. The spectrum per unit solid angle per incident electron is measured for photon emission angles of 30, 70, and 110 deg, for normal and oblique incidence of the electrons on the targets having atomic numbers of 13, 50, and 79, and for four target thicknesses equal to different fractions of the electron range in the given material. Also, results are given for the bremsstrahlung production efficiencies per unit solid angle at a given emission angle. The experimental results at normal incidence show good agreement with the theoretical predictions of Berger and Seltzer, which are based on thin‐target bremsstrahlung cross sections and which employ Monte Carlo calculations to account for multiple scattering and energy‐loss effects. Similar calculations for other geometries should produce reliable estimates of the emitted bremsstrahlung spectra in this same energy region.

Effect of Stress on the Hall Coefficient of Chromium Films

Chih‐shun Lu and Alvin A. Milgram

J. Appl. Phys. 38, 2038 (1967); http://dx.doi.org/10.1063/1.1709824 (4 pages) | Cited 4 times

Online Publication Date: 29 June 2004

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Hall‐coefficient measurements have been made on vapor‐deposited chromium films in the temperature range from −195° to 150°C. The stress in the chromium films was estimated by the shift of Néel temperature and the differential thermal‐expansion coefficients between the substrate and the film. It was observed that compressive stress reduces the Hall coefficient of chromium and tensile stress increases it. A suggestion is made concerning the similarity between the effects of pressure and the effects of changing the number of 3d electrons in chromium.

New Phase Transformation in InSb at High Pressure and High Temperature

M. D. Banus and Mary C. Lavine

J. Appl. Phys. 38, 2042 (1967); http://dx.doi.org/10.1063/1.1709825 (5 pages) | Cited 15 times

Online Publication Date: 29 June 2004

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A new phase transformation at high pressure and elevated temperature has been found in the InSb pressure‐temperature phase diagram. This transformation to a new phase designated as InSb‐III has been established by measurements of superconducting transition temperature (Tc) as a function of annealing temperature at several pressures and by x‐ray determinations on the new phase, both retained at one atmosphere and at high pressure and temperature. The higher Tc for InSb‐III (Tc = 4.1°±0.1°K) and the x‐ray results lead to the conclusion that InSb‐III is a new phase different from the orthorhombic phase (Tc = 3.5°K).

Etching Phenomena in the {111} Plane of Niobium

E. Zedler

J. Appl. Phys. 38, 2046 (1967); http://dx.doi.org/10.1063/1.1709826 (8 pages) | Cited 4 times

Online Publication Date: 29 June 2004

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For single‐ and polycrystalline niobium the relation between etch figures and dislocations is qualitatively demonstrated. Repeated etching allows investigation of the movement and multiplication of dislocations. Besides triangular etch hillocks there often occur etch traces or walls, respectively, and networks that may be interpreted as dislocations lying nearly parallel to the observation plane. Etch figures of helical dislocations have been found too.

Thermally Engraved Gratings using a Giant‐Pulse Laser

H. J. Gerritsen and M. E. Heller

J. Appl. Phys. 38, 2054 (1967); http://dx.doi.org/10.1063/1.1709827 (4 pages) | Cited 8 times

Online Publication Date: 29 June 2004

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Previous investigators have demonstrated the efficient and cataclysmal removal of material from surfaces hit by a giant‐pulse laser. Experimental evidence is presented here that very fine patterns, defined to 0.1 μ, can be engraved directly in metals or insulators by using the interference from two beams. Besides possible practical uses, the study of the structure of such patterns is expected to further our understanding of the mechanisms involved in damage by giant‐pulse laser impact.

Ferroelectric Rare‐Earth Molybdates

Hans J. Borchardt and Paul E. Bierstedt

J. Appl. Phys. 38, 2057 (1967); http://dx.doi.org/10.1063/1.1709828 (4 pages) | Cited 65 times

Online Publication Date: 29 June 2004

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The molybdates of Sm, Eu, Tb, and Dy are isotypic with ferroelectric Gd2(MoO4)3. Other compositions of this structure occur in the pseudoternary system Gd☒La☒Y‐molybdate and in the pseudobinary system Gd2(MoO4)3☒Gd2(WO4)3. A representative number of these compositions were grown as single crystals and tested for ferroelectricity. Each was found to be ferroelectric as evidenced by a ferroelectric hysteresis loop and by visual observation of domains. The Curie temperatures (TC), spontaneous polarizations (Ps), and coercive fields (Ec) were determined, with values ranging as follows: TC, 148°–190°C; Ps, 0.14–0.23 μC∕cm2 at 25°C; Ec, 5.0–14.5 kV∕cm at 25°C.

Magnetostriction and Compositional Gradients in Boat‐Evaporated Permalloy Films

T. C. Penn and F. G. West

J. Appl. Phys. 38, 2060 (1967); http://dx.doi.org/10.1063/1.1709829 (5 pages) | Cited 4 times

Online Publication Date: 29 June 2004

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Magnetostriction measurements on Permalloy films prepared by vacuum evaporation from a tungsten boat indicate an average Fe enrichment of about 2% above the original melt composition. In addition it is shown that the film composition varies continuously through the thickness from 4% to 7% per 1000 Å for typical evaporation conditions. Compositional gradients of even smaller magnitude are capable of pinning spin waves. Since filament and boat evaporation are used widely in preparing laboratory films, the anomalous spin‐wave results frequently reported in the literature may be due to thickness‐compositional gradients.

Boron Detection in Metals by Alpha‐Particle Tracking

J. S. Armijo and H. S. Rosenbaum

J. Appl. Phys. 38, 2064 (1967); http://dx.doi.org/10.1063/1.1709830 (6 pages) | Cited 29 times

Online Publication Date: 29 June 2004

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Track‐etching techniques were used to detect boron in austenitic steels. The technique involved placing polymers which were known to be sensitive to alpha particles in intimate contact with the polished metal surface, exposing the specimen to neutrons, and then etching the polymer detector. Alpha tracks that result from the 10B(n, α)7Li reaction were developed in the polymer by etching in an aqueous NaOH solution. The boron concentration in the steels was quantitatively determined and the results compared with more conventional analytical techniques. It is seen that in addition to measuring the total boron content, the track‐etch method allows one to map the distribution of boron within the microstructure of the metal alloy. The detector materials used were cellulose nitrate and cellulose acetate butyrate. The technique is useful for measuring boron concentrations in the parts‐per‐million range.

Elastic Deformation of Field‐Ion‐Microscope Tips

Klaus D. Rendulic and Erwin W. Müller

J. Appl. Phys. 38, 2070 (1967); http://dx.doi.org/10.1063/1.1709831 (3 pages) | Cited 8 times

Online Publication Date: 29 June 2004

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During the imaging process the specimen in a field ion microscope is subject to a stress of 105 kg∕cm2. The extent to which the elastic deformation caused by this stress appears in the image of W, Ta, and Mo specimens is investigated. Depending on the tip shape one observes an increase or a decrease in local magnification. When the electric field is increased from 220 MV∕cm to 450 MV∕cm the change in the projection angle does not exceed ±1.5°.

Steady Laminar Flow of Elasticoviscous Liquid through a Pipe with Suction or Injection

Shankar Prasad Mishra and Jyotirmoy Sinha Roy

J. Appl. Phys. 38, 2072 (1967); http://dx.doi.org/10.1063/1.1709832 (9 pages) | Cited 1 time

Online Publication Date: 29 June 2004

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The problem of steady laminar flow of elasticoviscous liquids through a porous pipe in the presence of suction or injection has been studied in this paper. The perturbation method has been used to obtain the axial velocity regarding the Reynolds number `R' as the perturbation parameter. The effect of elastic elements in the viscous liquid on the axial velocity, axial pressure drop, and the shearing stress have been shown graphically.

Dislocation Pile‐Ups against a Locked Dislocation of a Different Burgers Vector

Y. T. Chou

J. Appl. Phys. 38, 2080 (1967); http://dx.doi.org/10.1063/1.1709833 (6 pages) | Cited 19 times

Online Publication Date: 29 June 2004

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The classical analysis of Eshelby, Frank, and Nabarro of a linear dislocation pile‐up is generalized to include the case in which the locked dislocation may have a Burgers vector of mb, where b is the Burgers vector of free dislocations and m is a positive real number. The equilibrium positions of (n−1) free dislocations piled up against the locked dislocation under a uniform applied stress are given by the roots of the Laguerre polynomial Ln−1(2m−1). Simple expressions for the distance between the locked and nearest free dislocation, x1, the length of the pile‐up, L, and the stress at its tip, σtip, are obtained. Increasing m will increase x1 and decrease σtip, while L is only slightly extended. For large n the stress field within a certain distance range around the tip is found to be independent of m.
Based on the Petch model of yielding it is shown that increasing m increases the Hall‐Petch slope by a factor of (m)1∕2. The effect of m on the coalescence of leading dislocations leads to a higher‐fracture stress if m is increased.

Method for Determining Molecular‐Attachment Kinetics during Crystal Growth. Theory

L. A. Tarshis and S. O'Hara

J. Appl. Phys. 38, 2086 (1967); http://dx.doi.org/10.1063/1.1709834 (7 pages) | Cited 1 time

Online Publication Date: 29 June 2004

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The phenomenon of planar faceting of an otherwise curved interface is re‐examined and shown to provide an experimental means of determining crystal‐growth laws and magnitude of kinetic constants. Facets are often observed to form during crystal growth as a result of the large driving force required to generate new layer sources. This driving force is shown to be orders of magnitude larger than that required for layer‐edge passage. As a result, the interface must depart from its equilibrium morphology and facet in those crystallographic directions requiring source generation. This nonequilibrium departure is related to the actual interfacial undercooling through the temperature gradient at the interface. The effect of the non‐regular morphology on the steady‐state temperature gradient is considered. Pertinent experiments are described in detail and exemplary cases are cited.

Effect of Alloying on Aluminum K and Copper L X‐Ray Emission Spectra in the Aluminum‐Copper System

William L. Baun and David W. Fischer

J. Appl. Phys. 38, 2092 (1967); http://dx.doi.org/10.1063/1.1709835 (5 pages) | Cited 14 times

Online Publication Date: 29 June 2004

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Data for the Al K emission band, Al Kα satellites and Cu LIII band in Al‐Cu alloys (10%–100% Al) are presented. Significant changes in the spectra are noted with changes in composition. The Al K emission band is split and the long‐wavelength component shifts to longer wavelengths and becomes dominant with a decrease in Al concentration. The short‐wavelength component shifts only slightly and maintains the typical sharp, short wavelength‐emission edge seen in pure aluminum. Separation between high‐ and low‐energy components in the Al K band is as much as 4 eV (10% Al) and extrapolates to about 4.5 eV for very dilute alloys, which is nearly the calculated excitation energy of 3s2→3s3p in Al+. The Al K satellites Kα3 and Kα4 show corresponding intensity changes with alloy composition. The intensity ratio Kα4∕Kα3 changes linearly (for 6‐kV excitation) from 0.48 in Al to 0.70 in 10 Al‐90 Cu.
The Cu LIII band also shows changes in shape with alloying but the changes are not as large as observed for the Al K band. The copper band shifts linearly to lower energy as more and more aluminum is added.

Infrared Absorption of the Gamma‐Induced Surface Layer on Germanium

K. C. Lin and L. Lee

J. Appl. Phys. 38, 2097 (1967); http://dx.doi.org/10.1063/1.1709836 (2 pages)

Online Publication Date: 29 June 2004

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A thin layer on the surface of single‐crystal germanium produced by 60Co‐gamma irradiation has been found. This layer can only be produced on specimens which were irradiated in air. Several infrared absorption bands with peak absorptions at 3, 6, 6.85, 11.5, and 12.7 μ are associated with the layer. Of these bands, only the 11.5‐μ band has been identified as resulting from germanium dioxide which was formed on the surface by chemical reaction of germanium with oxygen and∕or ozone. The origins of other bands as well as the layer remain unknown.

Thermoluminescence and Color Centers in LiF

R. W. Christy, N. M. Johnson, and R. R. Wilbarg

J. Appl. Phys. 38, 2099 (1967); http://dx.doi.org/10.1063/1.1709837 (8 pages) | Cited 38 times

Online Publication Date: 29 June 2004

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Thermoluminescence emission above room temperature and optical absorption have been studied in LiF crystals irradiated by gamma rays, with emphasis on conditions which are of greatest interest for applications to radiation dosimetry. The specimens were Harshaw crystals of differing purity, and the purpose was to correlate the electron and hole traps and recombination centers involved in the thermoluminescence with optical‐absorption bands produced by the trapped carriers. The dominant glow peak in suitably treated crystals occurs at about 200°C, and this is correlated with an absorption band at 310 mμ, through thermal and optical bleaching of the thermoluminescence and optical absorption. A smaller glow peak at 100°C is correlated with an absorption band at 380 mμ. The F center absorbing at 250 mμ appears to be the electron trap associated with both glow peaks. It is concluded that the 310‐ and 380‐mμ centers are trapped‐hole centers, and the thermoluminescence occurs after they are thermally ionized. The recombination center which produces the visible‐light emission is believed to be not the F center, however, but an impurity center which absorbs at 196 mμ. An energy‐level diagram is suggested, which can account for the observed optical and thermal transitions. It depends on electron tunneling from the F center to the 196‐mμ center. Available evidence indicates that the 310‐ and 380‐mμ centers involve Mg; the impurity responsible for the 196‐mμ center may be Al.

Wave Interactions with Moving Boundaries

C. S. Tsai and B. A. Auld

J. Appl. Phys. 38, 2106 (1967); http://dx.doi.org/10.1063/1.1709838 (10 pages) | Cited 14 times

Online Publication Date: 29 June 2004

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The general theory of the double Doppler effect is reviewed for both vacuum and material media. Frequency and amplitude changes in the reflected and transmitted waves at a partially reflecting moving interface are calculated for cases in which the medium behind the interface: (a) moves at a different velocity than the interface; (b) moves at the interface velocity; (c) is stationary. The advantages of case (c) for practical frequency conversion are discussed.
Multiple moving interfaces in a stationary medium are also considered. On the basis of this theory, Doppler shifts at moving, tapered transition regions are analyzed as a series of discrete, closely spaced steps. This shows that the frequency conversion of the transmitted wave is independent of the slope of the taper. By use of a transmission line model, a simple physical explanation is given for the double Doppler effect in a moving taper.

Ultrasonic Attenuation in Aluminum Ammonium Alum and Aluminum Potassium Alum

B. J. Marshall, D. O. Pederson, and W. E. Bailey

J. Appl. Phys. 38, 2116 (1967); http://dx.doi.org/10.1063/1.1709839 (5 pages) | Cited 1 time

Online Publication Date: 29 June 2004

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The attenuation of 10‐Mc∕sec sound waves in AlNH4(SO4)2⋅12H2O and AlK (SO4)2⋅12H2O over a temperature range of 300° to 4.2°K has been measured. Results, which are available for both longitudinal and transverse waves propagated in the [111], [110], and [100] directions show that there are some very large absorption peaks occurring in the temperature range between 80° and 120°K.
The complex dielectric constants of these alums have also been measured using the same frequency and directional dependence as that used in the ultrasonic attenuation measurements. The results, presented in this paper, show that the real and imaginary parts exhibit peaks in the same temperature region as that for the ultrasonic attenuation peaks.
It is believed that these results might be associated with a Debye type of relaxation in solids.

Dissolution Spirals on Gamma‐Irradiated Lithium Fluoride

M. B. Ives and T. R. Ramachandran

J. Appl. Phys. 38, 2121 (1967); http://dx.doi.org/10.1063/1.1709840 (3 pages) | Cited 1 time

Online Publication Date: 29 June 2004

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Double‐spiral features have been observed at high resolution on lithium fluoride {100} surfaces etched in distilled water containing from 0.1 to 9 ppm ferric ions. The models proposed for similar features on other materials are reviewed, and suggestions are made regarding the lattice‐defect configurations responsible for the spirals. Radiation‐induced climb of segments of dislocations which are parallel to the surface is introduced as a possibility.

Behavior of Passing Dislocations in Superlattices

M. J. Marcinkowski and G. Lakso

J. Appl. Phys. 38, 2124 (1967); http://dx.doi.org/10.1063/1.1709841 (10 pages) | Cited 22 times

Online Publication Date: 29 June 2004

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A detailed computer analysis has been made of the behavior associated with the passage of pairs of superlattice dislocations on neighboring parallel slip planes for the specific case of the Fe3Si alloy. The treatment has been carried out for superlattice screw and edge dislocations of like and unlike sign for a series of vertical passing distances. In particular, the equilibrium separation between the individual ordinary dislocations constituting the superlattice dislocation has been determined as a function of distance between the pair of superlattice dislocations. In addition, the passing forces as well as the cross slip and climb forces associated with the dislocations have been calculated.
It has been found that cross slip of superlattice screw dislocations with mutual annihilation, if they are of unlike sign, will occur for passing separations of 100 Å or less. Superlattice edge dislocations can, however, be passed by one another at much closer distances, which results in the uncoupling of the superlattice dislocation. Furthermore, the extension of the superlattice dislocations oscillates strongly as they pass one another. All of these results are in general agreement with observations obtained with the Fe3Si superlattice.

Effect of Pressure on the Mössbauer Effect of 57Fe in Nickel Metal

D. L. Raimondi and G. Jura

J. Appl. Phys. 38, 2133 (1967); http://dx.doi.org/10.1063/1.1709842 (4 pages) | Cited 5 times

Online Publication Date: 29 June 2004

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The Mössbauer spectrum of 57Fe in nickel metal was studied to a pressure of 80 kbar. A peak in the internal field at the 57Fe nucleus was observed at 10 kbar, followed by a slow decrease up to 80 kbar. The initial increase of the internal field with pressure is given by d lnH∕dP=10.2×10−4 kbar−1. The isomer shift over the entire pressure range is given by d(IS)∕dP=−4.15×10−5 cm∕sec∕kbar. These results are discussed as they relate to other pressure studies on the properties of pure nickel and iron.
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