Volume 22, Issue 12, 01 December 1951
Index of content:

Contact Potential Variations on Freshly Condensed Metal Films at Low Pressures
View Description Hide DescriptionThe reason for contact differences of potential is discussed. Since it is purely a surface phenomenon, subject to wide variation as the result of adsorbed and chemically combined surface layers, it is of interest to observe the change of contact potential as a function of time for various freshly evaporated metalfilms in high vacuums. The results thus obtained indicate characteristically different behavior for each of the six metals studied. Electrical resistancemeasurements made on similar metalfilms under similar conditions are correlated with contact potentialmeasurements.

Volta Potentials of the Copper‐Nickel Alloys and Several Metals in Air
View Description Hide DescriptionVolta potentials of various metals approximately parallel the emf series. Metals abraded wet are more noble than when abraded dry, the transition metals changing an average of 0.28 volt compared with 0.07 volt for the nontransition metals. This owes possibly to the greater tendency of the transition metals to chemisorb oxygen, especially in the presence of moisture. All metals change in the noble direction upon aging in air, the average value being 0.3 volt after six days.
Potentials for copper‐nickel alloys, plotted with composition, fall on a sigmoid curve, whereas potentials for compositeelectrodes made up of separate nickel and copper areas are linear with percent area of nickel exposed. Commercial nickel‐copper alloys above 50 percent nickel age more rapidly than laboratory alloys. The cause may lie in deoxidizers like magnesium or aluminum, present in commercial alloys, but absent in the laboratory alloys. This suggests a nondestructive method for detecting impurities of this kind in metals.

A Technique for Preparing Beta‐Ray Autoradiographs of Metals and Minerals
View Description Hide DescriptionA technique for preparing autoradiographs of metals and minerals on a microscale is described. Limitations of this technique and possible variations are indicated. Illustrative examples of autoradiographs are presented and interpreted.

Ultrasonic Propagation in Liquids under High Pressures: Velocity Measurements on Water
View Description Hide DescriptionThe problem under discussion is the velocity of ultrasonics in liquids, specifically water, at various temperatures and high pressures. This report deals with the apparatus, and with some representative results obtainable with it.
The electrical apparatus makes use of a presentation unit (Dumont 256 or A/R 'scope) which synchronizes the sequence of operations by internally generated trigger signals at low repetition rates. Three‐ to five‐microsecond pulses at controllable amplitude and approximately 15 Mc/sec carrier frequency are imposed on an X‐cut quartz crystal which has been placed inside a pressure‐supporting vessel containing the test sample. The resulting ultrasonic pulses in the liquid are reflected back and forth over a definite path length between the transducer and a mirror. After amplification in a receiver strip the complete echo‐pattern becomes available for visual comparison on the presentation screen. The timed relative delay (and the measurable amplitude differences) between successive pulses furnish data for velocity (and attenuation) measurements when certain corrections are attended to.
Representative data are given for the velocity in water (to 0.1 percent) as a function of pressure to about 6000 atmospheres. From the data on water, information is derived on the temperature coefficient of sound velocity and on the ratio of specific heats at increasing pressures. The latter results are compared with those obtained directly from purely static experiments, and the advantages of the ultrasonicmeasurement technique for the derivation of some of the thermodynamic coefficients are cited.

The Propagation in a Compressible Fluid of Finite Oblique Disturbances with Energy Exchange and Change of State
View Description Hide DescriptionTheory is presented for oblique shock waves involving (1) heat exchange, k _{1}, (2) transfer of part of the compressible fluid, k _{2}, to an incompressible state, and (3) change in specific heat ratios, k _{3}. By matching mass flow, momentum, and energy relations across an oblique finite disturbance it is shown that these additional conditions introduce new terms in the solution of the form k_{i} u _{1}/(u _{1}−u _{2}). For k_{i} not zero a minimum shock angle is found which always exceeds the Mach angle by a definite increment. For air‐flow at u _{1}/a* of 1.5 with dew point −20°F this increment is calculated as 3.1 degrees. For expansion about a corner such flow differs from the Prandl‐Meyer type and in supersonic nozzles, for example, oblique shock waves are predicted which can explain anomalous pressure losses, the presence of extraneous waves, and non‐isentropic effects. Hodographs of the velocity solution include a triply infinite set of curves, one, the usual set, introduced by Mach number as parameter and the other two by k_{i} . The theory includes physically possible normal and oblique flows involving increase of supersonic velocities and subsonic velocities of which oblique flame fronts are indicated as one form. Applied to air condensations in hypersonic flows isentropic disturbances having appreciable angular flow shift and stagnation pressure losses are predicted.

Studies in Nonlinear Vibration Theory
View Description Hide DescriptionIn his paper, the author determines the stability of periodic solutions of (1) the general forced Duffing equation without damping, , f(x) a polynomial, ε≪1; (2) the forced Duffing equation with damping, ; and (3) the general forced Van der Pol equation, , f(ẋ) an odd polynomial, ε≪1, by seeking conditions necessary to insure periodic or almost‐periodic solutions of the corresponding variational equation. The former are obtained rigorously by means of an existence proof and the latter formally by perturbation series. A vertical tangent theorem is derived which states that the locus of the points of contact of the vertical tangents to the response curves is a stability boundary, since it coincides, in the first approximation, with the locus of periodic solutions of the variational equation. These techniques are illustrated by considering the forced vibrations of a triode oscillator with a fifth‐order tube characteristic, this being a particular case of (3), where we set .

A Critical Study of the Circuit Concept
View Description Hide DescriptionFrom Maxwell's equations, an expression for the complex power associated with a wire circuit is formulated and broken into a complex input power and a complex power into the external fields associated with the circuit, the latter including the radiated power. From these powers, the internal and external impedances of the circuit are obtained such that the current is not required to be everywhere in time phase within the circuit. This concept is extended to coupled circuits, bringing out some of the relations between some conventional methods for obtaining the driving point impedance of antenna arrays. The theory does not require the current distributions to be postulated, but in practical applications such a postulate becomes necessary unless the solution is obtained by a method such as the integral equation method. The resulting circuitry may readily be reduced to that for lumped elements. A more critical study of the impedance formulas is given in the appendix, based upon the reciprocity theorem which is derived therein.

Free Convection Heat Transfer from Electrically Heated Wires
View Description Hide DescriptionIn this paper the author discusses the heat transfer by free convection from electrically heated wires (copper and iron) to distilled water between freezing and boiling, to water boiling at atmospheric conditions and to air at room temperature. The wire surface temperatures needed for the heat transfer determination are calculated from the theoretical temperature distribution in the wire. The experimental results show maximum heat transfer rates of about 2,200,000 Btu/hr, ft^{2} near freezing and 450,000 Btu/hr, ft^{2} near boiling. For boiling water, as the temperature difference between the wire surface and water is increased, the heat transfer coefficient first increases reaching a maximum, then decreases reaching a minimum and increases again (because of radiation) until the wire fails by melting. For copper the maximum film coefficient of 9100 Btu/hr, ft^{2}, °F is observed at 49 degrees temperature difference and the minimum of 136 Btu/hr, ft^{2}, °F at a temperature difference of 690 degrees F. Corresponding values for iron are 12,300 Btu/hr, ft^{2}, °F at a 33 degree temperature difference and 142 Btu/hr, ft^{2}, °F at a 620 degree difference. When air at room temperature surrounds the wire the heat transfer coefficient for copper with an oxide film varies from 0 to 30 and for iron from 0 to 26 Btu/hr, ft^{2}, °F as the surface temperature of the wires is raised until failure occurs.

A Finite Difference Treatment of a Helium Cryostat Design Problem
View Description Hide DescriptionA mathematical expression is derived for computing dimensions of a liquid helium cryostat of specified performance characteristics. Use is made of a finite difference summation scheme applied to a simple thermomechanical model, using T as the independent variable, for a liquid evaporating in a container with good exchange to the walls. The scheme thus takes into account the heat capacity of the gas between the boiling point and the upper cryostat temperature. The results obtained are compatible with the actual performance of cryostats in operation.

Electron Microscopic Replica Studies of Porosity in Fused Iron Catalysts
View Description Hide DescriptionThe preparation of various replicas of a fused iron catalyst is described. Micrographs of these replicas show comparable fine structures that are attributed to the pores developed in the catalyst upon reduction. Dimensions of these fine structures compare reasonably well with pore diameters calculated from pore volume‐surface area determinations.

A Method of Growing Single Crystals of Lead Telluride and Lead Selenide
View Description Hide DescriptionSingle crystals of lead telluride measuring up to 1¼‐cm diameter and 6 cm long have been grown in sealed silica crucibles by the Bridgman‐Stockbarger method of lowering a melt slowly through a freezing level. The crystals have been grown for the purpose of testing the semiconducting and allied properties of lead telluride in that form. Extreme purity of the materials and cleanliness of the crucible have been found essential for successful growth. X‐ray tests have shown that the specimens are single crystals. The purest crystal grown so far had a conductivity corresponding to an electron concentration of 5×10^{14} per cc. Attempts to introduce excess of one of the constituents—lead or tellurium into the crystal lattice during growth have not so far been successful.

General Theory of Electromagnetic Horns
View Description Hide DescriptionExact equations for the propagation of electromagnetic waves in a perfectly conducting horn of arbitrary shape are given. They take the form of an infinite set of simultaneous ordinary linear differential equations, and can be interpreted as the equations of propagation of a system of coupled E‐ and H‐waves. If the coupling is neglected, we need only consider a single differential equation for each E‐ and H‐wave, which can be solved approximately by the W.K.B. method. This approximate solution brings out the distinction between ``transmission regions'' and ``attenuation regions'' of the horn, as found by Barrow and Chu for the sectoral horn.
It is shown that the error due to neglect of coupling is, in general, of the order of the square of the flare angle as far as the variation of the field along the horn is concerned, but is of the first order in the flare angle as regards the variation of the field over the cross section. The coupling cannot, however, be neglected between modes of propagation which have the same cut‐off frequency for all cross sections. The propagation characteristics of several special shapes of horn are discussed in detail.

Exact and Approximate Equations for Wave Propagation in Acoustic Horns
View Description Hide DescriptionExact equations are given for the propagation of acoustic waves in horns of arbitrary shape. These equations are similar to, though simpler than, the equations previously found for electromagnetic horns, and can be regarded as giving rise to an infinite number of coupled modes of propagation. If the coupling is neglected, the equation for the fundamental mode is the familiar one, but the theory also furnishes equations for the higher modes. The error involved in neglecting coupling is discussed.

Evaporation Rate of Liquid Helium. I
View Description Hide DescriptionIn connection with a study of the emissivity of metals at low temperatures, a quantitative analysis has been made of the factors involved in the design of storage containers for liquid helium. Experiments confirm the analysis, which has resulted in an exceedingly simple liquid‐nitrogen‐protectedliquid helium container having a heliumevaporation rate of 1 percent per day.
The hemispherical emissivity of mechanically polished copper at 4.23°K was determined for blackbody radiation. For radiation corresponding to that emitted by a blackbody at 77.1°K and 297.1°K, the measured emissivities are 6.9×10^{−3} and 1.29×10^{−2}, respectively. These data are discussed in relation to the recent theoretical work of Reuter and Sondheimer.
The heat of vaporization of helium at 4.228°K was determined to be 4.93 cal g^{−1}, in substantial agreement with the data of Dana and Kamerlingh Onnes. Kistemaker's thermodynamic considerations questioning the accuracy of these data are evaluated in terms of the new determination.

Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free‐Space
View Description Hide DescriptionIn this paper it is shown that the viscosity of the liquid normal paraffins can be accurately defined as a simple function of relative free‐space except for values in the neighborhood of the freezing points of each compound. A novel method of extrapolating the specific volumes of this family of compounds to absolute zero is described which permits the calculation of reliable values of the relative free‐space from density data.
An expression of the same form as the author's function, but in which temperature rather than free‐space is the primary variable (the so‐called Andrade equation), fails to reproduce the viscosity of n‐heptadecane over the same range of temperatures within the limits of the known accuracy of the measurements.

Convection Currents in Porous Media. IV. Remarks on the Theory
View Description Hide DescriptionDifferential equations for critical stability of a fluid in a porous medium and heated from below are solved by an approximate method not hitherto used. A single formula is obtained for the thermal environment at critical stability, apparently valid over a wide range of conditions, which allows for temperature dependence of viscosity and nonlinear temperature distributions. New experiments are reported in which initial convection has been detected by visual, thermal, and radioactive‐trace means. Experimental mean thermal gradients for critical stability deviated from values predicted by the new solution of theory by the following average amounts: visual, 150 percent; thermal, 32 percent; radioisotopic, 11 percent.

Dosimetry of X‐Rays and Gamma‐Rays by Radiophotoluminescence
View Description Hide DescriptionThe effects of high energyradiation on the luminescence properties of solids are surveyed. Of the four effects considered—radiophotoluminescence, radiophotostimulation, radiothermoluminescence, and the ``killing'' of luminescence by x‐rays or gamma‐rays—the first effect is shown to have advantages in principle over the others as a basis for dosimetry.
The absorption, excitation, emission, sensitivity, energy dependence, and stability characteristics of a radiophotoluminescent Ag‐activated phosphate glass are described. It is shown that dosage measurements can be made with this material, employing a simple fluorophotometer, from 10 roentgens to a few thousand roentgens of gamma‐rays. By proper shielding, such a dosimeter element can be made reasonably independent of energy. The dosage indication obtained is quite stable with time and is not seriously affected by exposure of the glass to visible or ultraviolet light or to temperatures in the range of −70° to +100°C. Because of its sensitivity range and its stability over a wide range of ambient conditions, the dosimeter appears to be particularly suited for monitoring personnel that may be exposed to rather high doses of gamma‐rays, such as may be encountered in A‐bomb explosions.

The Crystallographic Aspect of Slip in Body‐Centered Cubic Single Crystals. II. Interpretation of Experiments
View Description Hide DescriptionA new method for determining the ratios of the critical shear stresses has been applied to data taken from the literature and to original results. Measurements of yield strength were found to be not too satisfactory for the investigation of the slip behavior of the body‐centered cubic materials. On the other hand, any method which determined the slip plane and the orientation of the tensile axis gave useful results. In all instances where the data were available, the ratio of the critical shear stresses on {123} and {112} was very close to one, and did not change with temperature. The ratio of the critical shear stresses on {123} and {110} changes with temperature and composition, with the value of S_{123} generally being higher than that for S_{110}.

Atomic Size Effect in the X‐Ray Scattering by Alloys
View Description Hide DescriptionIn a random solid solution, if the two atoms have appreciably different sizes, the nearest‐neighbor distances and to a lesser extent the higher neighbor distances will be of three kinds, γ_{ AA }, γ_{ AB }, and γ_{ BB }. The effect produces modulations in the diffuse intensity similar to those produced by short‐range order. The size effect is important when the difference in scattering power is large, the difference in size is large, and the short‐range order is small. The size effect is illustrated by a single crystal pattern of Cu_{3}Au and a powder pattern of Ni_{3}Au_{2}. An asymmetry in the wings about a fundamental reflection is a result of the size effect.

Propagation of Disturbances in One‐Dimensional Accelerated Electron Streams
View Description Hide DescriptionThe propagation of small sinusoidal modulations in the infinite, parallel‐plane diode is studied. A second‐order differential equation is obtained for the ac convection current. Solutions are found in closed form for the cases of a drift‐stream, space‐charge‐limited acceleration, and acceleration with an arbitrary current density less than the space‐charge‐limited value.