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Volume 48, Issue 2, 01 February 1977

Copper electromigration in aluminum
View Description Hide DescriptionThe apparent effective charge Z ^{**} _{Cu}, of copper in aluminum was measured using a quasi‐steady‐state technique. Z ^{**} _{Cu} was measured in the temperature range 325–500 °C at several current densities. The measured values ranged between −4.1 and −14.9. No clear current density or temperature dependence could be seen, except for a possible increase in Z ^{**} _{Cu} with decreasing temperature.

Microstructural investigation of polycrystalline iron whiskers
View Description Hide DescriptionThe microstructure of polycrystallineironwhiskers, produced by chemical vapor decomposition in a magnetic field, is found to consist of a core extending the length of the whiskers surrounded by a series of approximately cylindrical layers made up of particles whose diameters are about 1000–3000 Å. These layers of particles are arranged to form a series of nearly concentric cylinders centered on the core. The grain size in both the core and the surrounding particles is found to be between 50 and 200 Å. The very high strength of these whiskers, 800 MPa, is considered a result of extreme grain refinement strengthening.

Stage I _{ E } recovery of electron‐irradiated pure silver and of its dilute alloys with cadmium and indium
View Description Hide DescriptionIrradiations of silver specimens with electrons in the energy range 0.4–1.7 MeV were performed at liquid‐helium temperatures. A subthreshold phenomenon has been observed which is taking over below ∼750 keV. After separation of this effect, we have studied the annealing spectra of pure silver and of A gCd (25 and 50 ppm Cd) and A gIn (15 and 50 ppm In) diluted alloys following irradiation with different doses of 1.7‐MeV electrons and after irradiationdoping. The stage I _{ E } recovery has been analyzed in terms of the chemical reaction rate theory. The corresponding rate equations have been solved numerically yielding the following values for the capture radii of a silver self‐interstitial atom by a Cd and an In impurity: r _{Cd} ^{Ag}=0.15r _{ v }, r _{In} ^{Ag}= (0.05–0.10) r _{ v }, where r _{ v } is its annihilation radius at a vacancy. The best fit was obtained with a value of E _{ m }=88 meV for the migration energy of a self‐interstitial.

Elastic constants and electrical resistivity of Fe_{3}Si
View Description Hide DescriptionThe electrical resistivity and elastic constants of slowly cooled single‐crystal specimens of the ordered alloy Fe_{3}Si (cubic, DO_{3}structure) were measured from 4.2 °K to room temperature. The residual resistivity (ρ_{ o }) was determined to be 0.6 μΩ cm. We infer from this that had the composition been exactly stoichiometric, which it was not, and the crystal free of internal voids generated during growth from the melt, the ρ_{ o } would have approached zero—a behavior that has not been reported previously for a (non‐superconducting) long‐range ordered alloy. The temperature dependences of the directly measured adiabatic elastic constants were found to be as follows (uncorrected for thermal contraction; T in °K): C _{ L }(T) ={3.410−0.2696/[exp(367/T)−1]}×10^{11} N/m^{2}; C (T) ={1.405−0.0563/[exp(227/T)−1]} ×10^{11} N/m^{2}; C′ (T) ={0.4183−0.1132/[exp(393/T)−1]}×10^{11} N/m^{2}. Calculated values for the isothermal Young’s modulus (E), the shear modulus (G), and the Poisson ratio (ν) of a polycrystalline aggregate of Fe_{3}Si possessing a random distribution of crystallite orientations are, for T=295 °K, as follows: E=2.15×10^{11} N/m^{2}, G=0.828×10^{11} N/m^{2}, and ν=0.299. The Debye temperature of the alloy at 0 °K is 501.1 °K.

Empirical T ^{3/2} law for atomic thermal vibration parameters
View Description Hide DescriptionThe Debye‐Waller factor, as measured by x‐ray and neutron diffraction and Mössbauer techniques, is shown to be of the form a+b T ^{3/2} over an extensive temperature range in a diverse set of crystalline solids. This two‐parameter empirical relationship may be interpreted within the framework of the Debye theory, modified to include quasiharmonic effects.

Estimation of surface layer structure from Rayleigh wave dispersion: Dense data case
View Description Hide DescriptionThe problem of determining subsurface structure of a material from the measured dispersion of Rayleigh surface waves is obviously important in nondestructive testing and in the operation of surface acoustic wavedevices. As is typical of many inverse problems this one is ill‐posed and thus the use of special approaches is indicated. One approach is to represent possible profiles of the subsurface structure by trial functions containing a finite set of adjustable parameters and then find the parameter values giving the best fit to the dispersion data. Here we present an approach using a nonparametric version of estimation theory. This involves a mathematical model representing measurement errors and all possible profiles with reasonable a p r i o r i probability weightings. The present paper is limited to the case in which the dispersion data are dense (i.e., in a practical sense the data points are sufficiently dense on the frequency axis that interpolation can be performed with impunity). Later related papers will deal with the sparse data case. To elucidate the nature of the ill‐posedness, a formal solution of the inverse problem is given in closed form. The application of estimation theory yields tractable estimator which corresponds to the inclusion of a convergence factor in the formal solution. The properties of the estimator are given by a set of auxiliary measures relating to statistical bias, model vs data dominance, resolution and reduction of variance. Because of the present lack of actual data sufficiently dense in a practical sense, synthetic test data, with and without simulated measurement noise, are used to investigate the performance of the estimator.

Some aspects of piezoelectricity and pyroelectricity in uniaxially stretched poly(vinylidene fluoride)
View Description Hide DescriptionThe piezoelectric constant of a uniaxially stretched and polarized poly(vinylidene fluoride) film decreases monotonically with increasing temperature in the range from 65 to 165 °C. After a specimen is cooled under open‐circuit conditions, the thermally stimulated current reverses in sign and exhibits a peak at around the glass‐transition temperature T _{ g }. Reversible changes in infrared spectra before and after the poling process suggest that the dipoles in the β crystals of poly(vinylidene fluoride) can be aligned along the direction of an applied electric field. The alignment is strongly influenced by the amorphous region; the coercive field in P‐Ehysteresis curve observed at 50 Hz increases rapidly at around T _{ g }. Under a high electric field, the uniaxially stretched poly(vinylidene fluoride) film behaves above T _{ g } in the same way as ferroelectricceramics.

Inclusions in cadmium telluride: Estimates for damage thresholds
View Description Hide DescriptionOne problem frequently encountered in high‐power laser systems is the thermal extrinsic damage to the laser materials, which arises from absorbing inclusions. Absorbing inclusions are impurities with physical and optical properties which differ substantially from those of the host material. Such inclusions may absorb sufficient radiation from the incident laser beam to produce major stresses within the host. In this paper, estimates of the maximum tensile stress as a function of inclusion size, laser pulse width, and laser power are computed for the common precipitates in CdTe. Our computations suggest that the heating of such precipitates when subjected to power densities of about 100 MW/cm^{2} may produce stresses comparable to or greater than the breaking strength of the CdTe host.

Interaction of ultrasonic waves incident at the Rayleigh angle onto a liquid‐solid interface
View Description Hide DescriptionThe behavior of a Gaussian ultrasonic beam incident on a liquid‐solid interface at the Rayleigh angle, the angle at which surface waves are excited on the interface, has been studied in some detail. The reflected beam is displaced in the manner predicted by Schoch; however, the ’’Schoch displacement’’ in general is too large. Good agreement is obtained between experimental results and the theory of Bertoni and Tamir, which assumes that the incident beam couples resonantly into a leaky surface wave at the Rayleigh angle and that the energy reradiated from this leaky surface wave interferes with specularly reflected energy. The propagation distance of the ultrasonic beam is explicitly included in describing the ultrasonic wave reflection at the Rayleigh angle.

Role of structural defects in electron transport properties of copper films
View Description Hide DescriptionKinetics of annealing of the electrical resistivity (ρ), Hall coefficient R _{ H }, mobility μ, and thermoelectric power TEP of thin (160–5000 Å) copperfilms deposited at temperatures ranging from 80 to 600 K have been studied. The activation energy for the associated recovery process has been obtained from the observed isothermal and isochronal changes in the resistance of the films. This energy increases from a value of 0.7 eV at 2000 Å to 1.4 eV at 180 Å for room‐temperature‐deposited Cufilms. Changes in ρ, R _{ H }, and μ on annealing are found to decrease with film thickness and deposition and annealing temperatures. On the other hand, changes in TEP due to annealing increase with film thickness up to 3000 Å; the rate of change depends sensitively on deposition temperature. With decreasing temperature of deposition, the reduction in TEP occurs at successively higher annealing temperature. Annealing does not affect the temperature dependence of R _{ H } and TEP. These results, together with the information on the microstructure of the films and the known scattering behavior of structural defects in the bulk, lead us to conclude that (1) the reduction in ρ, R _{ H }, and μ on annealing is due to the annihilation of vacancies; (2) the corresponding changes in TEP are due to the decrease in the concentration of vacancies as well as the density of dislocations. Quantitative effects of vacancies and dislocations on R _{ H } and TEP have been deduced from the observed data. The enormously large contributions of the defects may be understood qualitatively in terms of the variations in the density of holelike states and/or the energy dependence of conductivity (at the Fermi surface), caused by changes in the extent and/or degree of curvature of the necks at the Fermi surface.

The attractive and repulsive forces on a lattice screw dislocation
View Description Hide DescriptionThe properties of a lattice screw dislocation in a crystal in the form of a strip or a circular cylinder or an infinite crystal with a circualr hole or in a composite crystal composed of a soft matrix surrounded by a rigid second phase are determined. It is shown that the misfit stress field in the lattice is altered due to the image stress field. Some important conclusions have been arrived at on the image stress field on the dislocation in all the above situations.

Measurement of Faraday rotation in the Implosion Heating Experiment
View Description Hide DescriptionA technique for measuringFaraday rotation on the Implosion Heating Experiment (a fast 20‐cm‐radius theta pinch, with n∼10^{15}/cm^{3}, B∼5 kG) is described. Using a polarized CO_{2} laser with a nearly crossed analyzer the Faraday rotation is measured at one position in the plasma. The nearly crossed analyzer is used to minimize errors due to refraction. The Fn d l is measured at the same time and radius using a fractional‐fringe interferometer at the He‐Ne 633‐nm wavelength. From these two measurements the magnetic field is obtained. For comparison the magnetic field is also measured with probes. The results indicate that probes immersed in the plasma are too slow to follow the rapid changes in magnetic field that occur in IHX.

Plasma density measurements in a gas target
View Description Hide DescriptionExperiments are reported on Stark broadening measurements of electron number density in gas targets under intense electron‐beam heating. Plasma recombination is found to be fast on the gasdynamic time scales of the subsonic target configuration studied. The configuration simulates that in the gas‐target neuton generator systems under development for fusion technology research.

Plasma rotation by electric and magnetic fields in a discharge cylinder
View Description Hide DescriptionA theoretical model for an electric discharge is developed consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field, to study the rotation of the discharge plasma in the crossed electric and magnetic fields. The associated boundary‐value problem for the coupled partial differential equations, which describe the electric potential and the plasma velocity fields, is solved in closed form. The electric field,current density, and velocity distributions are discussed in terms of the Hartmann number H and the Hall coefficient ωτ. As a result of the Lorentz forces, the plasma rotates with speeds as high as 10^{6} cm/sec around its axis of symmetry at typical conditions. As an application, it is noted that rotating discharges of this type could be used to develop a high‐density plasma‐ultracentrifuge driven by j×B forces, in which the lighter (heavier) ion and atom components would be enriched in (off) the center of the discharge cylinder.

Study of electron‐beam‐produced plasmas by fast photography and emission spectroscopy
View Description Hide DescriptionThe luminous events produced by a drifting relativistic electron beam (REB) (1–2 MeV, 100 kA, 40 nsec) have been photographed with an image converter of 5‐nsec gate time. Coupled with a transmission spectrograph, time‐gated snapshots (1 μsec) of the spectra have been recorded. For air pressure between 0.1 and 0.3 Torr, the beam is self‐focused and it yields a spark spectrum containing mainly N^{+}, with some O^{+} and N^{++} lines. In 0.8–1 Torr of air, the beam is unfocused and it yields the N_{2} (B←C) but not the (A←B) bands. In the presence of a target, the unfocused beam may again produce an air breakdown. A slitless spectrum then yields a two‐dimensional image of the event, which may be related to the spatial distribution of the beam. The results are discussed in connection with REB and ion acceleration research. In addition, Lichtenberg‐type discharge tracks in a Plexiglas disk irradiated by 2‐MeV beams are photographed and compared with the fluorescence lifetime of the N_{2} (B←C) bands.

Positive column of Na‐Ne‐Ar ac discharges
View Description Hide DescriptionThe positive column of 50‐Hz ac discharges in a mixture of sodium vapor and noble gas (99 vol% Ne–1 vol% Ar) has been investigated experimentally. The experimental conditions were as follows: discharge tube radius 10 mm, noble‐gas pressure 5.5 Torr at 20°C, and sodium density (2.4–5.7) × 10^{19} m^{−3} which corresponds to a tube wall temperature of 519–538 K. The rms values of the current ranged from 0.25 to 1.5 A. The dischargeproperties,measured with the aid of electrostatic probes, show hysteresis effects especially for high rms current values. This behavior can be explained from the combined effects of depletion of sodium atoms and diffusion. It is found that the experimental data on the time‐resolved electron temperature agree with calculated values. Qualitative agreement is obtained between the measured and calculated data on the electron density, electric field strength, and radiated power.

Effect of radial expansion of the laser heating of a magnetically confined plasma
View Description Hide DescriptionThe laser heating behavior of a plasma column confined by a solenoid magnetic field is analyzed. A quasistatic model is used to account for plasma radial expansion. The ion heating process is studied explicitly. Simple analytic expressions are obtained to describe electron and ion temperatures as well as the behavior of axial heating or ’’bleaching’’‐wave propagation.

Interaction of electromagnetic waves with bounded plasmas moving perpendicular to the plane of incidence
View Description Hide DescriptionThis paper describes the reflection and transmission of obliquely incident electromagnetic plane waves by an isotropic and uniaxially anisotropic plasma half‐space moving perpendicular to the plane of incidence. Results for both the parallel and perpendicular polarizations of the incident wave have been obtained. The mechanism of power transmission into the plasma for each of the cases is examined. The effect of the dispersive nature of the plasma medium is illustrated by presenting numerical results of the power reflection coefficient versus incident wave frequency for various values of the medium velocity.

Brewster angle for an E‐polarized electromagnetic wave interacting with a moving dielectric medium
View Description Hide DescriptionThe Brewster‐angle phenomena of total transmission has been investigated with reference to an E‐polarized electromagnetic waveinteracting with a dielectric half‐space moving along the interface. Analytic conditions are derived for the existence of Brewster angles. We also discuss how the Brewster angles are modified by replacing the incident region (in which the incident electromagnetic wave is propagated) with an isotropic or a uniaxially anisotropic plasma. The Brewster angles are found to behave in a remarkably different fashion under various conditions. Numerical results for the Brewster angles, showing their dependence on the nondimensional velocity of the medium β, are presented for several values of the physical parameters.

The disintegration and vaporization of plastic targets irradiated by high‐power laser pulses
View Description Hide DescriptionWe have studied the disintegration of polyethylene and polystyrene targets irradiated by 100‐J 40‐nsec Nd/glass laser pulses. At power densities of ≲10^{12} W/cm^{2} relatively massive targets (6×10^{−5} to 5×10^{−4} cm^{3}) are totally disintegrated to produce finely divided target material and un‐ionized vapor. Both the size of the target and the presence or absence of a laser prepulse strongly influence the proportions of finely divided target material and un‐ionized vapor, especially within the first few microseconds after peak laser power. This disintegration is always preceded by the emission of a hot fully ionized plasma, but only 1% of the target material is contained in the hot plasma. Typically, (1–3) ×10^{19} atoms of un‐ionized vapor are released as a slowly expanding (v∼10^{5} cm/sec) cold dense gas cloud (n _{ o }≳10^{19} cm^{−3}) surrounding the initial target position. This cloud of target material has subsequently been heated by absorption of a 300‐J 100‐nsec CO_{2} laser pulse to produce an approximately fully ionized plasma.