Showing papers in "Journal of Applied Physics in 1951"

Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free‐Space

Abstract: In 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 dataAn 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

Calculation of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion

Abstract: Diffusion in solids is known to occur along grain boundaries and over free surfaces more rapidly than through the interiors of crystals. In order to facilitate quantitative investigation of grain boundary and surface diffusion, a mathematical analysis of the problem has been completed, assuming that grain boundary diffusion is analogous to the diffusion of heat along a thin copper foil imbedded in cork. The calculated diffusion‐penetration relationship for grain boundary diffusion is shown to agree with the experimentally determined grain boundary self‐diffusion of silver.

The Motion and Precipitation of Suspensoids in Divergent Electric Fields

Abstract: The motion of suspensoid particles relative to that of the solvent resulting from polarization forces produced by an inhomogeneous electric field is defined as ``dielectrophoresis.'' It is analogous to the related phenomenon of electrophoresis, in which motion of suspensoid particles is produced by the action of an electrostatic field on the charged particles.From a consideration of theoretical calculations and from experimental observations it is concluded that the phenomena of ``dielectrophoresis'' and ``dielectro‐precipitation'' can be observed under rather ideal conditions, though it is ordinarily often difficult to do so because of the presence of the more easily produced electrophoresis or ion‐type migration of charged particles.The usefulness of dielectrophoresis (and/or electrophoresis) for removing suspended solid particles from polymer solutions during analysis is described.

Scattering of Electromagnetic Waves from Two Concentric Spheres

Abstract: A solution is given for the problem of the scattering of plane electromagnetic waves from a sphere with a concentric spherical shell. The solution is general, and under appropriate conditions is reduced to the well‐known solution for scattering from a single sphere.

On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence

Abstract: The one‐ and three‐dimensional spectral equations for a field of isotropic temperature fluctuations in an isotropic turbulence are derived from the correlation equation. Then, except for the degenerate case of simple conductive decay, stationary fluctuation fields are postulated. Largely by dimensional reasoning and some simple postulates, forms of the temperature fluctuation power spectrum for particular wave number ranges are deduced and are compared with the results of previous analyses giving corresponding segments of the velocity spectrum. Finally, the relative ``effective cut‐off'' wave numbers of the two spectra are compared in terms of the fluid Prandtl number.

Applications of the Radiation from Fast Electron Beams

Abstract: The radiation from fast electron beams passing through a succession of electric or magnetic fields of alternating polarity is examined. The radiation of maximum frequency is emitted in the forward direction. If the deflecting fields are not too large, a semiqualitative argument shows that the maximum frequency is the lowest possible harmonic. The frequencies emitted are determined by studying the Doppler effect, and the angular distribution of radiated energy as well as the total radiation are calculated in a simple straight‐forward manner with reference to well‐known formulas of special relativity. The question of the coherence of the radiation is discussed. The spectral distribution of radiated energy is then calculated more exactly. It is concluded that several applications of the radiation appear possible. A scheme for obtaining millimeter‐waves of considerable power is outlined. The upper limit of the power in a band extending down to a wave‐length of 1 millimeter is calculated to be of the order of several kilowatts for a beam of one ampere and an energy of 1.5 megavolt. The use of the radiation for speed monitoring of beams with energies up to 1000 megavolt is discussed.

The Nature of the Static and Kinetic Coefficients of Friction

Abstract: Experiments have been carried out to determine the transition between static and kinetic conditions when stationary metal surfaces are set into motion, a simple method being used which measures the energy that has to be given to one of the bodies to start it moving. The method is confined to cases in which the static coefficient exceeds the kinetic. Using a load of 1 kg and metal surfaces of various kinds, it is found that the static coefficient persists for distances of the order of 10−4 cm, and then gradually falls off to values corresponding to the kinetic coefficient. This behavior is shown to be consistent with a simple model based on the assumption that the friction force is needed to shear metallic junctions formed between the metal surfaces. The action of boundary lubricants is discussed, and it is shown that they can act either by diminishing the metallic interaction directly, or by preventing its increase during the sliding process.

Theory of Do for Atomic Diffusion in Metals

Abstract: The theory of the entropy of activation ΔS previously given for interstitial diffusion in metals is herein extended to self‐ and to chemical diffusion. It is concluded that this entropy of activation will always be positive; and it is shown that in the case of self‐diffusion and of chemical diffusion at very low concentrations, the better the empirical ΔS the better does it correlate with the theoretical positive ΔS. The large negative apparent ΔS frequently found for chemical diffusion at higher concentrations must be attributed either to inaccuracies in experiments or to the presence of short circuiting diffusion paths. It is predicted that the presently reported negative values of ΔS will become positive when very small concentrations are used in large grain size specimens.

Lattice and Grain Boundary Self‐Diffusion in Silver

Abstract: The lattice and grain boundary self‐diffusion coefficients of high purity silver have been measured over extended temperature ranges. It has been found that the lattice diffusion coefficients are described by the equation, DL=0.895 exp(−49500/RT) cm2 sec−1 and are independent of the thermal history of the crystals within wide limits. The absolute grain boundary diffusion coefficients fit the equation, DB=0.03 exp(−20,200/RT) cm2 sec−1 and are independent of the grain size of the specimens.

Axially Symmetric Systems for Generating and Measuring Magnetic Fields. Part I

Abstract: This is Part I of a systematic discussion of axially symmetric magnetic fields, both central and remote from the origin, search coils reporting the field or gradient at a single point, and mutual inductances. Here the central uniformity of symmetrical fields and gradients is analyzed by zonal harmonic expansion. Laplace's equation and symmetry restrict these fields to a few types, regardless of the detailed geometry of the generating system. Universal error‐contour maps are derived for the central field or gradient in systems having errors of second, fourth, or sixth order, and for hybrid types combining second and fourth. One hybrid has an oblate error field suitable for cloud‐chamber and orbital applications.Source systems include circular filaments, cylindrical or plane circular current sheets, and thick solenoids of rectangular or notched section. Each type of source may be designed to produce any of the field patterns. To this end, source constants derived for the particular source type are combined ...

Maxwell's Demon Cannot Operate: Information and Entropy. I

Abstract: In an enclosure at constant temperature, the radiation is that of a ``blackbody,'' and the demon cannot see the molecules. Hence, he cannot operate the trap door and is unable to violate the second principle. If we introduce a source of light, the demon can see the molecules, but the over‐all balance of entropy is positive. This leads to the consideration of a cycle Negentropy→Information→Negentropy for Maxwell's demon as well as for the scientist in his laboratory. Boltzmann's constant k is shown to represent the smallest possible amount of negative entropy required in an observation.

A Mechanical Determination of Biaxial Residual Stress in Sheet Materials

Abstract: A method is given for determining the residual stress in a sheet material by removing successive uniform layers of material from the surface of a test specimen and measuring the resulting curvature. From the condition of equilibrium of a free specimen, a stress vs curvature relation is derived which holds over the depth to which material has been removed. The method applies when the stress is constant in the plane of the specimen and varies through the thickness. An experimental technique is described which is believed to satisfy the essential requirement that the removal of surface layers should not affect the stress in the remaining material, and a practical example is given.

Atomic size effect in the x-ray scattering by alloys

Abstract: In 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, γAA, γAB, and γBB. 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 Cu3Au and a powder pattern of Ni3Au2. An asymmetry in the wings about a fundamental reflection is a result of the size effect.

Thickness‐Shear and Flexural Vibrations of Crystal Plates

Abstract: The theory of flexural motions of elastic plates, including the effects of rotatory inertia and shear, is extended to crystal plates. The equations are solved approximately for the case of rectangular plates excited by thickness‐shear deformation parallel to one edge. Results of computations of resonant frequencies of rectangular, AT‐cut, quartz plates are shown and compared with experimental data. Simple algebraic formulas are obtained relating frequency, dimensions, and crystal properties for resonances of special interest in design.

Studies in Newtonian Flow. I. The Dependence of the Viscosity of Liquids on Temperature

Abstract: It is shown that the Walther and Andrade equations, while very satisfactory for moderate ranges of temperature, are not adequate to define the dependence of the viscosity of liquid normal paraffins on temperature over extended ranges. One method of developing a viscosity‐temperature relationship is presented that gives equations defining this dependence with satisfactory validity. The purpose of this paper is to show that the precise dependence of the viscosity of liquids on temperature is complicated. This is in contrast to the relatively simple relation for the precise dependence of the viscosity of liquids on free‐space which will be presented in subsequent papers.

The Electric Tunnel Effect across Thin Insulator Films in Contacts

Abstract: Existing calculations on the tunnel effect through thin films in contacts apply to very weak and very strong electric fields. It is the main purpose of the present paper to complete the picture by the treatment of intermediate cases, which are important for many contact applications.

The Production and Stability of Converging Shock Waves

Abstract: Converging shock waves offer interesting possibilities of attaining very high temperatures and pressures. A theoretical treatment by G. Guderley which we have confirmed and extended by the method of characteristics indicated that the strength of a strong converging cylindrical or spherical shock varies inversely with a power (0.396 for γ=1.4) of the surface area of the wave, thus becoming very great close to the center of convergence. The experimental production of high temperatures and pressures by means of these converging shocks depends on their ``stability'' of form. A converging wave is said to be stable if it approaches perfect cylindrical or spherical shape, thus damping out random disturbances as it propagates. The experimental work of L. G. Smith on Mach reflection is applied to show that these converging waves are stable for the shock range (M≤2.4) covered by his experiments. Smith's work and the theoretical work of Lighthill indicate that the stability decreases greatly at high Mach numbers.The simplest experimental method of achieving a cylindrical converging shock is by the use of a shock tube with a converging channel. This, however, results in the hottest region of the gas being in close thermal contact with the cold walls. An axially symmetric shock tube has been designed and constructed which produces a complete converging cylindrical shock rather than just a sector and in which the region of convergence is comparatively well isolated thermally from the walls. It has been found possible to converge a moderate strength shock wave (M=1.7) sufficiently to produce considerable luminosity at the center of convergence. Schlieren photographs are presented showing various phases of the formation and stability of these converging waves.

The Mathematical Basis of the Interpretation of Tracer Experiments in Closed Steady‐State Systems

Abstract: The basic equation for the mixing of radioactive isotopes is dR/dt = I grad a, where dR/dt is the flux of radioactivity; a, the relative specific activity; and I, the interfusion constant. The equation is applied to systems of compartments and some electrical analogies are presented. As special cases of the unconstrained systems treated in an earlier paper two constrained systems are discussed in which only a single radioactive isotope is required for the study of transport phenomena. One of these (mammillary system) consists of a central compartment communicating with a number of peripheral compartments. In the other (catenary system) the compartments are arranged chainwise. Equations are derived for the n‐compartment mammillary system relating the time dependent specific activities of the compartments to the exchange rates between the peripheral and central compartments and to their content of substance being exchanged. In analyzing the effect of lumping of a series of compartments into a single equival...

On the Representation of the Electric and Magnetic Fields Produced by Currents and Discontinuities in Wave Guides. I

Abstract: Electromagnetic scattering problems in cylindrical wave guides, including free space, involve the calculation of the fields produced in the presence of geometrical discontinuities by arbitrary currents. Such discontinuities may be replaced by equivalent electric and magnetic currents. The over‐all calculation then leads to two distinct problems: first, the calculation of the fields produced by the prescribed and induced currents in a discontinuity—free guide; second, the self‐consistent determination of the induced currents by the condition that the fields so produced satisfy the boundary conditions at the discontinuity surfaces. The first problem is treated herein by representation of the fields in terms of a complete set of vector modes characteristic of the possible transverse field distributions in the guide cross section. This representation transforms the over‐all field problem into one‐dimensional modal problems of conventional transmission line form. The eigenvalue problem of finding the characteristic modes is discussed in detail for the case of a uniform guide with perfectly conducting walls. The transformation procedure and the solution of the resulting transmission line problem are treated from an impedance point of view. A typical modal analysis and synthesis is presented for the explicit determination of the fields produced by arbitrary electric and magnetic currents in an infinite and semi‐infinite wave guide of arbitrary cross section. The connection with a corresponding dyadic Green's function representation (to be treated in Part II) is pointed out.

High Temperature Structure and Thermal Expansion of Some Metals as Determined by X‐Ray Diffraction Data. I. Platinum, Tantalum, Niobium, and Molybdenum

Abstract: The crystal structure and thermal expansion of platinum, tantalum, niobium, and molybdenum have been determined between 1100° and 2500°K. These metals were found to undergo a uniform thermal expansion over the temperature range of this investigation and to undergo no structural change. The permanent elongation of tantalum wires, produced by annealing at temperatures between 2473° and 2773°K, appears to be caused by reorientation of crystal grains in the specimen and to preferred direction of crystal growth during annealing, rather than to a change in crystal structure.Quadratic equations have been developed for the thermal expansion of platinum, tantalum, niobium, and molybdenum. These equations are represented, respectively, by Δa0/a0=7.543×10−6(T−291)+2.362×10−9(T−291)2,Δa0/a0=6.080×10−6(T−291)+7.50×10−10(T−291)2,Δa0/a0=7.591×10−6(T−291)+6.96×10−10(T−291)2, and Δa0/a0=0.987×10−3+2.40×10−6(T−273)+2.20×10−9(T−273)2.Values of the expansion coefficient α were computed for each of the metals by differentiati...

Heat Conduction in Simple Metals

Abstract: The partial differential equation of heat conduction is a nonlinear equation when the temperature dependence of the thermal parameters (i.e., the thermal conductivity, K, and S, the product of the density and the specific heat at constant pressure) is taken into account. It is shown that a mathematical condition for the transformation to linear form of the one‐dimensional, nonlinear, partial differential equation of heat conduction is the constancy of [1/(KS)½](d/dT)log(S/K)½. This discovery is the motivation for an investigation of the relations between the thermal parameters of simple metals on the bases of the theory of solids and available experimental data. It is found that KS is essentially constant, its variation with temperature being much less than that of either K or S considered separately. It is also shown, as a result, that the condition for the above‐mentioned transformation is valid for simple metals. Applications of the transformed equation to the solution of problems in heat conduction ar...

Theory of the Circular Diffraction Antenna

Abstract: The circular diffraction antenna consists of a coaxial wave guide fitted with an infinite‐plane conducting baffle, and open to free space. An equivalent circuit description, appropriate to principal‐mode propagation in the coaxial region, is investigated theoretically. Variational expressions for the circuit parameters are derived, and used for accurate numerical evaluation.

Long‐Range Order in Beta‐Brass and Cu3Au

Abstract: Measurements have been made on single crystals of CuZn and Cu3Au held at various temperatures below Tc to decide whether there is a single‐ordered phase whose order changes with temperature, or whether there is an ordered and a disordered phase the relative amounts changing with temperature. Precision measurements were made of the position and width of the (222) CuZn and (400) Cu3Au reflections. The disordered phase has a larger cell dimension, so that reflections from the ordered and disordered phases are slightly displaced from one another. For both materials, a single peak was observed which was too narrow to correspond to the existence of two phases. At the stoichiometric compositions, it is concluded that below Tc there is only an ordered phase whose long‐range order varies with temperature. Measurements of the long‐range order in Cu3Au have been made on briquets of filings, using quenched samples, and on a sample held at temperature.

Effect of Surface Condition of a Sphere on Its Water-Entry Cavity

Abstract: An investigation of factors which influence the formation of a cavity when a sphere enters water vertically is described. It was found that cavities are formed at much lower entry speeds for contaminated spheres than for clean ones, but that there is little dependence on the type of the contaminant. In regard to the scaling of this effect, the tendency to form a cavity varies little with change of size or specific gravity of the sphere. Water‐entry cavities are observed to form at velocities much lower than those required for incipient cavitation in the water tunnel; consequently, a relation between the two effects appears improbable. Some dependence of cavity formation on viscosity might be inferred from the observation that cavities were formed at lower entry speeds by spheres coated with liquids of high viscosity than by spheres without this coating.

Dosimetry of X‐Rays and Gamma‐Rays by Radiophotoluminescence

Abstract: The effects of high energy radiation 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 ...

Electrical Breakdown over Insulators in High Vacuum

Abstract: In the investigated range of 5×10−3 to 10−7 mm Hg, the breakdown voltage over insulators in high vacuum is independent of pressure. Currents of 10−11 to 10−8 ampere were observed in the region below breakdown voltage by detecting x‐ray quanta with a Geiger‐Mueller counter. Pinhole camera x‐ray pictures revealed that practically all radiations originate from an area on the anode a distance from the insulator, with a weaker radiation coming from a ring immediately adjacent to the insulator. Current‐voltage relationships as usually observed in these experiments indicate a roughness factor and an emitting area on the cathode similar to previous findings in vacuum gaps. Current bursts were observed which did not develop into complete breakdown. Oscilloscopic observations revealed that sometimes at breakdown over insulators the voltage on the test sample drops to 2.5 kv; in other cases it falls to less than 100 volts. The low voltage arc‐like discharge extinguishes at a current of about one ampere for copper electrodes in contact with Pyrex glass. When a resistance in series with the test sample is increased to keep the maximum current below one ampere, no stable discharge is observed. As in a vacuum gap, the breakdown voltage over an insulator is increased by successive breakdowns. Part of this ``conditioning'' is permanent. The nonpermanent part is dependent on the state of the test sample prior to conditioning. The anode does not appear to influence conditioning. When the resistance in series with the test sample allows a discharge current above one ampere to flow, a fast conditioning usually occurs which results in a high permanent breakdown voltage.

Electromagnetic Scattering from Spheres with Sizes Comparable to the Wavelength

Abstract: By using suitably defined logarithmic derivative functions and the recurrence formulas due to Infeld, the problem of obtaining numerical answers for the scattering of a plane electromagnetic wave by a sphere can be simplified. This is particularly true if the sphere has a complex index of refraction. The nature of these logarithmic derivative functions is shown for one special case involving water spheres.Experimental results are given for the back‐scattering cross sections of water spheres in the electrical size region 0.74≤2πa/λ≤5.90. These results were obtained at a wavelength of 16.230 cm using the standing‐wave method of measurement. It is believed that these were the first laboratory measurements of the back‐scattering cross section made on individual water spheres in this critical size region.Comparison is made between the experimental and theoretical results.

Some Electrical Properties of Zinc-Oxide Semiconductor.

Abstract: Measurements of the dark electrical conductivity σ, and Hall coefficient were made on sintered spectroscopically pure zinc oxide powder samples over a temperature range from 100°K to 625°K and at room temperature on zinc oxide crystals containing lead impurities, using both the usual dc potentiometer‐probe method and an ac (4000 cps) set. In this reproducible range, lnσ is not linear with 1/T for the sintered samples but exhibits maxima occurring at higher T and σ values, the higher the sintering temperature; the electronic carrier concentration of the different samples, calculated from the Hall data, indicates thermal ionization of 1.6×1016 to 9.0×1017 donors/cm3 lying 0.017 to 0.045 ev below the conduction band, with increasing ionization energy and increasing donor concentration, in general, occurring for higher sintering temperatures. Conductivity measurements are also made on sintered samples from 300°K to 1040°K using the ac (4000 cps) voltmeter‐ammeter method; above about 650°K, lnσ versus 1/T is l...

Interfacial Free Energy of Coherent Twin Boundaries in Copper

Abstract: The ratio of the interfacial free energy of coherent twin boundaries to the average grain boundary free energy in copper has been measured by means of the dihedral angles formed at the intersections of twin boundaries and grain boundaries with each other and with a copper/lead vapor interface. The mean value found for the ratio is 0.035±0.006.

A Reinterpretation of Experiments on Intermetallic Diffusion

Abstract: Reported values for the heat of activation, H, for volume chemical diffusion, as obtained from the slope of the best straight line in a semilogarithmic plot of diffusion data against T−1, may often be greatly in error. These values will be too low whenever diffusion along internal surfaces plays a significant role at the lower temperatures of measurement. A method is presented which attempts to avoid such errors in H by using the calculated values of Zener for the intercept of the straight line. When the data is reconsidered in the light of this method, the widely accepted belief that H for chemical diffusion in dilute solid solutions is generally considerably less than H for self‐diffusion of the solvent is brought to question. In fact, it is found that the chemical diffusion activation energy is generally within 15 percent of that for self‐diffusion. It is further concluded that the process of diffusion under a chemical gradient may itself produce internal surfaces which act as short‐circuiting diffusio...