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Volume 22, Issue 7, 01 July 1951
22(1951); http://dx.doi.org/10.1063/1.1700063View Description Hide Description
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 sinteringtemperature; 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 sinteringtemperatures. 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 linear and in agreement with the results of previous workers with ionization energies varying from 1.4 to 2.4 ev. Back reflection x‐ray patterns indicate an increase in the lattice spacing after sintering; the change can be correlated with the presence of interstitial zinc atoms. The forbidden gap is taken to be about 3 ev, corresponding to an ultraviolet absorption edge and luminescence peak at 3.2 ev; the yellowing of worked or highly conducting or heated samples is attributed to a shift of this absorption edge into the visible. Room temperature impedance measurements show a frequency dependent reactance and resistance attributable to capacitive shunting of the high resistivity grain boundaries (ν∼107 cps). It is shown that the low frequency conductivity of the sintered samples is determined by the conductivity and relative thickness of the grain boundarymaterial while the Hall coefficient depends mainly on the carrier concentration in the semiconducting grains; uncritical use of low frequency and dc results thus would lead to spuriously low values of the conductivity and mobility in relation to the true properties of the grains.
22(1951); http://dx.doi.org/10.1063/1.1700064View Description Hide Description
The complex relationship between body profile and pressure distribution is important in the design of high‐speed undersea bodies. For slender axisymmetric bodies integration of the equations for irrotational flow has been accomplished, the coordinates of the body profile being related to the pressure distribution through coefficients of Legendre polynomials. The limitations and applications of this approximate analysis have been demonstrated through comparisons with preassigned conditions and with the results of experiments. Computed values closely approach those preassigned or measured throughout the central portion of the body if the maximum diameter does not exceed three‐tenths of the length. The analysis is accordingly useful in designing bodies with low coefficients of drag and low incipient cavitation numbers.
22(1951); http://dx.doi.org/10.1063/1.1700065View Description Hide Description
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.
22(1951); http://dx.doi.org/10.1063/1.1700066View Description Hide Description
The classical Sommerfeld‐Runge method for deriving the laws of geometric optics in isotropic inhomogeneous media from Maxwell's equations is applied to problems in ``weakly'' anisotropic and inhomogeneous media. This leads to a generalized Hamilton‐Jacobi partial differential equation for the phases of the two waves (eikonals) which can propagate with finite velocity in such a medium. If one restricts oneself to a limited class of stress distributions, one derives a very powerful method of solving axially and spherically symmetric problems which would be very difficult to treat by the direct solution of the classical equations of elasticity. The Maxwell‐Neumann law is derived in variational form so that, in principle, one can estimate in any given case the error involved in the conventional assumption that the paths are straight lines instead of the actual Fermat paths.
The last section treats the so‐called general problem of photoelasticity in which the principal stress directions in the plane of the wave front rotate arbitrarily as the latter propagates through the medium. Again the Sommerfeld‐Runge method gives one a solution which claims that if the rate of rotation is small in a wavelength one can ignore the contributions of the rotation to the integrated phase. An experiment is proposed to check this claim.
22(1951); http://dx.doi.org/10.1063/1.1700067View Description Hide Description
Converging shock waves offer interesting possibilities of attaining very high temperatures and pressures. A theoreticaltreatment 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.
22(1951); http://dx.doi.org/10.1063/1.1700068View Description Hide Description
A rigorous formula for the radiation field of a helical antenna is derived on the assumption of an empirical current distribution obtained experimentally by Kraus. For a helix of several turns this formula yields results very nearly the same as those obtained from an approximate method by Kraus, and it has the additional advantages of greater simplicity of computation and applicability to helices of nonintegral numbers of turns. It appears that this empirical current distribution is of a most fortuitous form, but no theoretical basis for it has yet been found.
22(1951); http://dx.doi.org/10.1063/1.1700069View Description Hide Description
The theory of air‐coupled flexural waves in a floating ice sheet is derived for the case of an impulsive point source situated either in the air or in the water. It is found that new branches are introduced to the dispersion curve of flexural waves as a result of coupling to compressional waves in the atmosphere. Experimental data are briefly reviewed.
22(1951); http://dx.doi.org/10.1063/1.1700070View Description Hide Description
An investigation of the effects of rolling and annealing on the orientation of individual grains in siliconferrite strip yielded results which led to the formulation of a theory for the appearance of the ``magnetic'' orientation in the final processed strip. It is proposed that, in a fine‐grained strip of siliconferrite, those grains which are already in the ``magnetic'' orientation before rolling will keep that mean orientation during rolling but become more highly strained than other grains, and therefore, they will become the portions of the cold‐rolled strip with highest free energy. In the annealing process these highest energy regions will recrystallize first, becoming lowest energy regions which will be able to consume the now higher energy regions surrounding them. Since these nuclei have the ``magnetic'' orientation, the final product also attains the ``magnetic'' orientation.
22(1951); http://dx.doi.org/10.1063/1.1700071View Description Hide Description
Previous researches on the helix have made simplifying approximations about the nature of the boundary conditions. In this paper the field equations and boundary conditions are formulated exactly. They are then solved by an expansion in powers of the ratio of the thickness of the wire to the distance between turns.
The method used consists of introducing a new coordinate system, which is such that a helical wire of circular cross section is a surface in which one coordinate is constant. Maxwell's equations and the electromagneticboundary conditions are expressed in terms of this system. Since nonorthogonal coordinates are involved, the equations cannot be solved exactly; but a perturbation procedure may be applied as indicated above.
The result of the analysis is to show that there is a principal mode, which propagates with the free space velocity of light in the direction of the wire. The characteristics of this mode are studied, and they are compared successfully with experiment.
22(1951); http://dx.doi.org/10.1063/1.1700072View Description Hide Description
An experimental investigation has been made of the distributions of current and charge amplitude and phase on cylindrical antennas and on the driving lines. The presence of a stub support modifies the distributions on the antenna only near the junction of the antenna, line, and stub; however, for antenna loads near antiresonance, the distributions on the line as well as the impedances of the structure are altered considerably.
A corrective network is defined for the terminal region of the junction. Impedances of theoretical models of antennas, the network, and conventional transmission line equations may then be used to predict the apparent impedances of the structure.
22(1951); http://dx.doi.org/10.1063/1.1700073View Description Hide Description
Crystals of hexagonal selenium have been grown in a melt. Their microstructures have been compared with those arising in vapor crystals.
The dark resistivity has been studied as a function of axis orientation, temperature, field, and time of application of a field. The thermoelectric power has been measured and attempts made to measure Hall effect. The nature of the acceptor levels has been discussed, the approximate hole densities and mobilities have been determined, and values of the activation energies obtained.
The field effects have been discussed and the phenomenon of an apparent semipermanent polarization occurring at quite low fields has been noted.
22(1951); http://dx.doi.org/10.1063/1.1700074View Description Hide Description
Torsion experiments on an aluminum‐zinc alloy (21 atomic percent zinc) show that precipitation gives rise to large values of internal friction. After prolonged periods of aging, which are sufficient to produce growth of the precipitate particles, the internal friction begins to decrease. The activation energy for the elementary process producing the anelastic behavior is 23 kcal per mole. It is demonstrated, with the help of static measurements, that the curves of internal frictionversus temperature do not show a peak but continue to rise indefinitely with increasing temperature. This behavior cannot readily be interpreted in terms of the usual concept of a relaxation spectrum but requires a new concept of coupled relaxations. Metallographic examination of the specimens reveals that the observations of large internal friction are correlated with the occurrence of discontinuous precipitation. The observed anelasticity is interpreted in terms of the fragmentation of the lattice; i.e., the formation of an irregular network of shear‐relaxing interfaces during discontinuous precipitation. It is demonstrated that in such a network the coupling, produced by an overlapping of regions within which shear stress is relaxed, makes possible a very large total relaxation. Additional measurements of elastic aftereffect in the supersaturated solid solution permit the determination of the mean time of stay of atoms in this solid solution, between 52°C and 72°C, by the anelasticity resulting from pair reorientation. The results obtained are in excellent agreement with the conventional high temperature diffusion data and correspond to a heat of activation for diffusion of 25.4 kcal per mole.
22(1951); http://dx.doi.org/10.1063/1.1700075View Description Hide Description
The capacitance of selenium rectifiers which have been subjected to a voltage pulse in the blocking direction is found to be temporarily decreased after the pulse has ceased. The recovery of the changed capacity to its original value is investigated as a function of pulse height, pulse duration, and temperature. The speed of the recovery can be greatly increased by illumination (through a transparent electrode) with light of the same spectral range which is effective in causing the photoeffect in selenium photovoltaic cells. This is an indication that the phenomenon is of electronic and not of ionic nature.
As an explanation it is proposed that an electric pulse in blocking direction removes electrons from elevated energy states in the electrode‐selenium boundary. Recovery occurs because electrons are returned to the elevated energy states by thermal agitation and also by photoelectric effect if the selenium is illuminated.
22(1951); http://dx.doi.org/10.1063/1.1700076View Description Hide Description
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 are considered.
22(1951); http://dx.doi.org/10.1063/1.1700077View Description Hide Description
A method for measuring the diffusion coefficient of carbon in metallic carbides is proposed. The rate at which excess metallic inclusions are consumed by carbon diffusing in from a surface is used to indicate the extent to which diffusion has taken place. Conditions are derived under which the results are susceptible to simple analytic treatment.
Arcing at Electrical Contacts on Closure. Part I. Dependence upon Surface Conditions and Circuit Parameters22(1951); http://dx.doi.org/10.1063/1.1700078View Description Hide Description
In a low voltage circuit the occurrence of an arc between approaching electrodes is dependent upon the nature of the surfaces and upon the circuit inductance. For carbonsurfaces, or noble metal surfaces which have been ``activated'' by operation in various organic vapors resulting in a carbonaceous layer, the limiting circuit inductance is somewhat above 10−3h, which is much higher than the limiting inductance for clean noble metal surfaces. This activation by organic vapors occurs for noble metals only and for certain vapors; for example, benzene derivatives. In the case of silver and benzene vapor, it has been shown that the activation is due to adsorption of benzene onto a greasy surface layer and its decomposition there by the heat of subsequent closures. A metal surface, which has been activated by organic vapor, remains active indefinitely if there is no arcing at the surfaces; but with continued operation and accompanying arcing, the activating material is burned away, and the surface returns to the inactive condition if no activating vapor is supplied.
Arc voltages, which are independent of current and of ambient gas, as far as tested, have been measured for a number of metals and for carbon; the arc voltage for carbon is quite erratic in the range between 20 and 30 volts, but for each of a number of metals the arc voltage is steady.
Arcing at noble metal surfaces, similar to that induced by carbonaceous material from organic vapors, can be produced also by insulating particles or insulating films. The active condition gradually disappears with continued arcing, unless there is a steady supply of insulating material to the surface.
The minimum arc current has been measured to be 0.6 amp for active silver and for carbon, and 0.03 amp for inactive silver. These are the currents at which an established arc is extinguished.
22(1951); http://dx.doi.org/10.1063/1.1700079View Description Hide Description
Heat treatment in a magnetic field has been found effective for iron‐silicon alloys between two percent and ten percent silicon, the highest maximum permeability being obtained at about 6.5 percent silicon. In a single crystal of this composition, magnetized parallel to a  direction, the hysteresis loop is squared by the magnetic anneal and the maximum permeability is increased from 50,000 to 3,800,000, the highest value yet reported.
22(1951); http://dx.doi.org/10.1063/1.1700080View Description Hide Description
The viscoelastic properties of viscose monofils differing in the degree of orientation were measured by means of the vibrating reed method within the frequency range from 20 to 100 cps. The frequency dependence as well as the orientation dependence of the modulus and viscosity coefficient were discussed and connected with the relaxation mechanism. It could be expected that the anomalous dispersion should occur at frequencies lower than 1 cps and at high frequencies such as 104∼106 cps, the former being due to the motion of secondary cross bonds permitting the chains to slip, and the latter to the motion of segments. In order to supplement the data which support this discussion, measurements were extended to Cellophane, films of cellulose acetate, and Celluloid, and also to films of synthetic high polymers such as Polycaprolactam and polyvinyl chloride. The latter two substances showed noticeably different dynamic properties from that of cellulose, and this could, assumably, be associated with the fact that they lack in crystallization.
22(1951); http://dx.doi.org/10.1063/1.1700081View Description Hide Description
The dynamic Young's moduli of various types of paper were measured by the vibrating reed method. The Young's modulus of paper increases statistically at a rate approximately proportional to the square of its density. The modulus and density of paper increase with the degree of beating. The sulfite and sulfate fibers behave differently during beating. The angular dependence of Young's modulus, tensile strength, and elongation at break was analyzed mathematically; and the results were verified by experiments. According to this theory, the mean value of Young's modulus and tensile strength of machine‐made paper should be expressed by the geometrical mean of the values of the machine and cross directions, whereas the mean value of elongation can be given by the arithmetical mean. The removal of parenchyma cells is very effective in reducing the Young's modulus of dissolving pulp. The viscoelasticproperties of paper were observed within the frequency range from 20 to 180 cps. The dynamic modulus and mechanical loss factor of the sheets employed were found to be smaller than one‐tenth of those of cellulose films. The interfiber deformation influences the dynamic properties of paper.
22(1951); http://dx.doi.org/10.1063/1.1700082View Description Hide Description
The motion of a clamp‐free reed excited by a sinusoidal displacement of the clamped end was analyzed by rigorously solving the fundamental equation for vibration. The real and imaginary parts of the modulus are given in terms of resonant frequency and band width of the frequency curves. The results are compared with those of Nolle which were obtained in an approximate manner by introducing an equivalent electric circuit. As long as the mechanical loss tangent is smaller than 10−1, as is the case in most high polymers, the practical error caused by the approximation is estimated to be insignificant. Nolle's network was interpreted from a purely mechanical standpoint by means of the fundamental equation for vibration.