Volume 33, Issue 6, 01 June 1962

Elastoresistance Effect in Iron Single Crystals
View Description Hide DescriptionThe potentiometer circuit designed for measuring minute variations in small resistances developed by P. W. Bridgman has been used to measure the effect of tension, applied in a direction parallel to that of the current, on the resistance of ironsingle crystals (elastoresistance). Correction for strain permitted the calculation of the more informative physical characteristic, the elastoresistivity. In order to obtain at least an indication of the expected anisotropy of elastoresistivity, two single crystals of different orientations were investigated. Deformation temperatures of +30° and −78°C were used to observe the effect of temperature on the (relative) elastoresistivity. The increase in Δρ/ρ with decreasing temperature was larger than anticipated. The elastoresistivity and elastoresistance showed considerable anisotropy.

Comparison of the Size of Spherical Particles of Iron, Cobalt, and Alloys of Iron‐Cobalt in Mercury as Determined by Various Methods
View Description Hide DescriptionThe sizes of particles prepared in mercury with diameters less than about 3000 Å were determined by electron microscope examination, analysis of the magnetization curve, calculation from the temperature dependence of magnetic remanence,tinadsorption, and analysis of their growth kinetics. The results of the various methods were found to be in reasonable agreement.

Scattering of Light by Polymer Films Possessing Correlated Orientation Fluctuations
View Description Hide DescriptionA theory for the scattering of light from a film of a polymer possessing randomly correlated oriented fluctuations of anisotropic elements is presented. The case for the film possessing both density and orientation fluctuations is considered. It is shown that one can separate these contributions from measurements obtained using polarized light. The consequences of non‐randomly correlated fluctuations are qualitatively considered.

Internal Friction in Al‐Cu Alloy
View Description Hide DescriptionMeasurements of the internal friction in pure Al and two aluminium alloys with 2 and 2.95 wt % Cu were made using a torsional pendulum. With solution‐treated and quenched alloys a weak internal friction peak (peak I) was obtained at the same temperature range at which grain boundary relaxation occurred in pure Al. The peaks disappeared after a few minutes of aging due to the blocking of grain boundary relaxation on precipitation. The activation energyH corresponding to this peak is 32±1 kcal/mole for both the 2 and 2.95% alloys. A grain boundary peak also appeared in furance‐cooled 2% alloy with H = 31±1 kcal/mole, but instead of a peak an inflexion point appeared in 2.95% alloy. For pure Al,H = 32.4 kcal/mole was obtained. Due to re‐solution of the precipitates at higher temperatures another strong internal friction peak (peak II) appeared a few degrees below the solubilitytemperatures for both the alloys. The position of the peak is insensitive to the frequency of measurements but the peak height decreases on increasing the frequency. From the rigidity modulus measurements the solubilitytemperatures for the 2 and 2.95 wt % Cu in Al are obtained and are found to be in good agreement with previous results. An internal friction peak due to Zener relaxation, however, has not been observed in these alloys.

Dependence of the Thermoelectric Figure of Merit on Energy Bandwidth
View Description Hide DescriptionThe thermoelectric figure of merit Tz of a semiconductor is calculated as a function of the width of the conduction band. It is found that Tz approaches zero as the bandwidth goes to zero. The existence of an optimum bandwidth is established; however, the magnitude cannot be ascertained on the basis of the simple model used here.

Calculation of Averages for Primary Recoil Distributions
View Description Hide DescriptionThe slowing down of an energetic particle in a random assembly of scattering centers is discussed. Certain averages for physically interesting quantities can be calculated in a very general form, including unequal masses of scattering and slowing down particles. The averages refer to quantities such as the total distance traveled (L) and the vector distance to the final positions (x_{i} ) and powers thereof. Two assumptions simplify the evaluation of the general results considerably: (α) The mean free path λ is a simple power of the energy E: λ(E)∼E^{μ} ; (β) the distribution g(E; ε) of energies ε after one collision with initial energy E does not change its shape with E: Eg (E; ε)=κ(ε/E). A special distribution of this kind is the hard core distribution. Under assumptions α and β all calculations are reduced to the evaluation of an integral like ∫κ(η)η^{μ} dη. For equal masses and the hard core distribution, one can easily calculate averages of any power of L and obtain the distribution function of L, this being proportional to L ^{1/μ} exp(−L/λ). Under the assumption β alone, with arbitrary λ(E), results are given for special distributions and equal masses (including the hard core distribution). The evaluation of the averages now requires simple integrals over λ for linear averages and double integrals for quadratic averages with known integral kernels. For unequal masses, approximations are discussed.

Diffraction of Spherical Scalar and Vector Waves at Axial Points of a Circular Aperture and Disk
View Description Hide DescriptionThe following work treats Kottler's saltus problem of diffraction of electromagnetic waves emitted by a Hertzian oscillator source and the analogous Kirchhoff's scalar problem of waves emitted by a point source. The medium is a homogeneous isotropic dielectric. In the vector case a new exact solution of the basic integrals is presented, at axial points only, (a) behind a circular aperture in a ``black'' screen, and (b) behind its complementary ``black'' disk. The relative time‐averaged intensity of energy flow is plotted for the disk only. It is shown that the scalar theory predicts considerably larger values than the electromagnetic theory for identical geometrical dispositions.

Electrical Conduction and the Photovoltaic Effect in Semiconductors with Position‐Dependent Band Gaps
View Description Hide DescriptionThe semiphenomenological transport equations that are commonly used in the theory of semiconductors have been rewritten in variables appropriate to the discussion of an illuminated isothermal semiconductor in which the band gap is a linear function of one of the position coordinates. It has been found necessary to neglect those terms in the transport equations that arise from variations in mobility and effective mass. The first section considers electrical conduction in a uniformly doped specimen under weak illumination; deviations from Ohm's law were found to be small. In the second section, the potential distribution in a highly illuminated sample of such material, both with and without a junction present, is found. The major contribution to the total potential is the same as that found earlier by Tauc. These results are then used to determine the best geometry for a solar‐energy converter in which such materials are used, and to calculate the efficiency of this converter as a function of illumination. The greatest efficiency possible was found to be 43%.

Point Defect Trapping in Crystal Growth
View Description Hide DescriptionThe possibility of trapping significant quantities of point defects during growth of a crystal is considered. Calculations are based on the well‐established theory of growth from the vapor on vicinal surfaces and the results are applied approximately to more complex cases. Concentrations of point defects, either above or below equilibrium, can be trapped under some conditions. In most cases the effect is insignificant. The crucial characteristic of a growth condition is defined by the dimensionless parameter D_{v} /Rd where D_{v} is the bulk diffusion coefficient for point defects(vacancies),R is the growth rate, and d is the ``effective thickness'' of the surface. The value of d is about 1 atom layer in most cases, but may be greater at solid‐melt interfaces. Large supersaturations of point defects may be trapped if D_{v} /Rd is small. For very large values of D_{v} /Rd, subsaturation concentrations of vacancies may be trapped. Growth trapping accounts for the loss of dislocations from metal whisker crystals during growth and may support a simple explanation of some substructure formation during solidification of pure single crystals.

On the Theory of Monolayer Evaporation
View Description Hide DescriptionA theory of evaporation of a monolayer is here presented in which the evaporation of individual atoms, without interaction, is treated by statistical methods and in which the effect of interactions between atoms when the coverage is finite is treated by the thermodynamic reasoning developed by Langmuir. By combining these two approaches an expression is obtained which has, formally, only one adjustable constant, namely, the binding energy at zero coverage. The types of interactions taken into account are (following Langmuir): (a) finite size of surface atoms, and (b) dipole repulsion. Values of dipole moment are derived from thermionic emission. Assumptions have to be made regarding the partition functions relating to a surface atom. On the assumption that the only energy states available to a surface atom are those of translation parallel to the surface, agreement within the spread of currently available data for thorium on tungsten is obtained by using a binding energy at zero coverage of 7.61 ev. More precise data are required for determination of whether there must be some other and more complete specification of the partition functions for surface atoms.

Plasma Waveguides as Low Loss Structures
View Description Hide DescriptionThe dispersion relation for propagation of an electromagnetic wave between two semi‐infinite slabs of plasma is found under the assumption of infinite magnetic field along the slabs. Provided the plasma frequency is above the applied frequency, a fast wave solution exists, with a sinusoidal field distribution in the free‐space region between the plasma slabs, and exponential decay into the slabs. A complex plasma frequency is introduced to account for collision losses in the plasma, and substituting this complex plasma frequency into the dispersion relationship, the attenuation constant of the wave is found. The imaginary part of the plasma frequency is computed from collision theory and found to give damping considerably smaller than that obtained with metal guides. An application to high‐field linear accelerators is treated in detail.

Filamentary Standing‐Wave Pattern in a Solid‐State Maser
View Description Hide DescriptionThe filamentary maser action in a ruby is explained as caused by minute randomly distributed variations in index of refraction. Relations are derived for the density of filaments and their size in terms of a Fourier resolution of the inhomogeneities. These are so small that it seemed that thermal motion might play a part, but this is shown to be orders of magnitude too small at room temperature.

Magnetic Field Reversal by Relativistic Electrons Which Slow Down While Circulating in a Uniform Impressed Magnetic Field
View Description Hide DescriptionThe prior restriction to conservative motion of the electrons has been removed, but scattering has still been neglected. The rate of energy loss has been used to derive the stationary distribution over a range of energy (or momentum) and canonical angular momentum for an arbitrary magnetic field distribution. A necessary ingredient is the retardation of the electrons; the radiative component of this has been estimated, but not included; the dynamical friction component, arising from motion through a uniform, fully ionized plasma, has been used as the sole contributor to energy loss. This friction also affects the canonical angular momentum and the latter's change in one cycle relative to the energy change has been formulated. Maxwell's equation connecting magnetic field with current density, applied to the stationary distribution, has permitted the formulation of the relation between field and the other variables. This completes the number of relations required to determine the magnetic field (eigenfunction) arising from a given rate of electron injection (eigenvalue): The trajectory equations have been derived.
It has been necessary to picture physically the complete evolution of a trajectory from injection to stopping, both to understand what the mathematics says and to devise an adequate machine program. When field reversal occurs, then just before the electrons die, the electron swarm divides into two counter‐rotating eddies. Two iterative solution techniques have been used to calculate the field distributions for a range of initial energies, field strengths, and injection rates. A striking result is that once reversal of field occurs by increasing the injection rate, it is generally true that the reversed field varies little, but the layer becomes progressively thinner as the injection rate increases further. At some rate the layer thickness passes through zero and thereafter the injection radius lies not at the apocenter of the initial trajectory but at the pericenter, the layer protruding from its prior position.
For full‐energy radii of gyration which are less than about one‐third the injection radius, anomaolus solutions appear which are unstable. A number of aspects of the problem of incorporating an E layer into a thermonuclear device are briefly discussed, namely, the effect of scattering, the possibility of two‐beam instability, the injection of the electrons, effects of end reflection in a finite‐length layer, electrodynamic effects, and plasma diamagnetism.

Tunnel Emission into Vacuum
View Description Hide DescriptionTunnel emission into vacuum is obtained from thin‐film sandwiches of (a) aluminum‐alumina‐aluminum and (b) aluminum‐alumina‐platinum. The alumina layer is made by oxidizing an evaporated film of aluminum in air. Cesium processing, to lower the work function, results in an increase of emission of five orders of magnitude.

Etch‐Tunnels in Lithium Fluoride Crystals
View Description Hide DescriptionThe dissolution and growth behavior of lithium fluoride crystals in aqueous solutions containing long‐chain fatty acids as step‐poisons has been investigated. Both positive crystals (whiskers and platelets) and negative crystals (etch‐tunnels) can be grown, respectively, from supersaturated and undersaturated solutions of lithium fluoride containing identical concentrations of stearic acid (∼2×10^{−6} N). Dissolution behavior in stagnant environments is of particular interest for etch‐tunnels some 0.5 μ in diameter and more than 100 μ in length (negative whiskers) have been observed. Two types of etch‐tunnel can be distinguished; those nucleated at a surface defect—such as a cleavage step or the point of emergence of a dislocation (D type)—and those nucleated at apparently random points on the crystal surface (R type). Metallographic observations reveal that dislocations are not essential to negative crystal growth and it is proposed that tunnels grow simply because dissolution is less efficiently inhibited at the end of a tunnel than at the external surface of the crystal. This is a consequence of the reduced number of poison molecules available to inhibit kink and step motion at the end of a tunnel because of their slow rate of diffusion in a stagnant environment. Vigorous agitation of the environment suppresses etch‐tunnel formation.

Behavior of Manganese in GaAs
View Description Hide DescriptionHall measurements on manganese‐doped gallium arsenide reveal a single acceptor level for this impurity with an ionization energy of 0.1 ev. The ionization energy and segregation coefficient, k_{s} =0.05, appear to be independent of concentration over the range N_{A} =6×10^{17}−1×10^{20}/cm^{3}.

Control of Population Inversion in Pulsed Optical Masers by Feedback Modulation
View Description Hide DescriptionThe output power level of an optical maser is dependent on the level of inversion which can be reached. Using a technique in which the optical feedback is modulated by a shutter disk, an enhancement of the output power level of a pulsed ruby optical maser was observed. The higher level of output power occurred for only a short pulse. An explanation is given and the observed effect compared to the expected value.

Sputtering of Gold by Low Energy Inert Gas Ions
View Description Hide DescriptionThe sputtering yield of gold bombarded by low energy (20–100 ev) helium, neon, and argon ions has been measured by the increase in electrical resistance of a thin goldfilm. It has been shown that for neon and argon the yield decreases rapidly with decreasing ion energy from 100 to 40 ev; below 40 ev the decrease is less rapid and no definite threshold has been found. With 40‐ev neon ions the yield is proportional to the ion current density, but with argon ions of this energy the yield is independent of the current: For currents greater than 100 μa/cm^{2} neon is more efficient than argon in sputteringgold. To explain the variation of yield with ion current for low energy neon ions it is suggested that the sputtering may take place by a two‐stage process: the first stage being the creation of defects in the gold by the ions, and the second stage, ejection of gold atoms from the neighborhood of these defects.

A Technique for Pulling Single Crystals of Volatile Materials
View Description Hide DescriptionA technique has been developed to pull single crystals of volatile materials using standard pulling apparatus. This has been accomplished by covering the surface of the material to be pulled with a substance that is liquid at the pulling temperature. Crystals of PbTe and PbSe were pulled using molten B_{2}O_{3} as the surfaceliquid.

Atom Ejection in Low Energy Sputtering of Single Crystals of fcc Metals and of Ge and Si
View Description Hide DescriptionThe spatial distribution of atoms ejected from low index planes of Cu, Ni, Au, Al, Ge, and Si have been studied for bombardment by Hg^{+}, Ne^{+}, and Ar^{+} ions of energies up to 800 ev. In addition, the atom ejection for Hg^{+}‐ion bombardment of various Ge planes (12° apart) belonging to the [110] zone has been investigated in detail. For the fcc crystals, ejection was observed in 〈110〉 directions at all energies, in〈100〉 directions at higher energies, and in 〈411〉 directions under certain conditions. The ejection in the 〈110〉 and 〈100〉 directions are interpreted to be the result of focusons intercepting the surface with sufficient energy to cause a surface atom to be ejected. It is shown that a reasonable interpretation of the atom ejection in 〈411〉 directions is that a 〈110〉 focuson may intercept and eject a surface atom which is in a twin position rather than a normal position. For ion bombardment of Ge and Si atom ejection is observed in 〈111〉 and 〈100〉 directions. A possible interpretation is that many of the natural interstitial positions are filled near the surface as a result of the bombardment and that the structure resembles more that of a bcc structure. The systematic deviation in ejection directions from the associated crystallographic direction observed for the Hg^{+}‐ion bombardment of various Gesurfaces suggests that the atomic collisions resulting in atom ejection for Ge and Si occur in the outer few surface layers.