Volume 36, Issue 4, 01 April 1965
Index of content:
36(1965); http://dx.doi.org/10.1063/1.1714294View Description Hide Description
A general expression for the time‐independent transmission coefficient of a double barrier is derived. Unity double barrier transmission is found possible for all energy levels above or below the double barrier potential energy levels. The conditions under which unity transmission occurs are obtained and discussed.
Application of the general theory to a piecewise constant potential model indicates that double barrier effects in thin film devices may be most noticeable for a majority of current carriers at energy levels near the maximum potential energy level of the double barrier. The small width of the transmission resonances in the examples considered indicates that double barrier effects would probably not be detected, and if they were detected would probably not be interpreted as such, unless investigation of this particular phenomenon was an objective of the research being conducted.
36(1965); http://dx.doi.org/10.1063/1.1714295View Description Hide Description
A new technique for anomalous skin‐effect studies is described. At low temperatures (∼4°K) it measures both surface reactance and surface resistance over a wide band of frequencies extending to below 100 cps. For the transition region from classical to anomalous behavior, experimental results on high‐purity copper show excellent agreement with theory, assuming diffuse scattering of electrons at the metallic surface. A new numerical table of theoretical values is included.
36(1965); http://dx.doi.org/10.1063/1.1714296View Description Hide Description
A technique is developed for treating each of the waves generated by an arbitrary current source in a partly ionized gas with no steady magnetic field. Starting with Maxwell's equations and three sets of coupled hydrodynamicequations (for the electrons, ions, and neutral molecules), it is shown that one can obtain a separate inhomogeneous wave equation for each type of wave in the plasma, with the source term for the transverse and longitudinal waves dependent, respectively, on the curl and divergence of the current source.
36(1965); http://dx.doi.org/10.1063/1.1714297View Description Hide Description
It is shown that an electronavalanche travels with a velocity v_ that is dependent upon Townsend's ionization coefficient α and the diffusion coefficient for the electronsD_. Specifically, v_=μ_E+αD_, where μ_ is the electron mobility, and the applied field E is assumed constant. Numerical machine calculations have been made to study the effect of diffusion and secondary ionization at the cathode in pulsed Townsend discharges. Illustrative examples show the utility of these calculations in measurements of the Townsend ionization coefficients as well as electron and ion mobilities. It is shown that the diffusion‐broadened avalanche for high values of αd (d is the gap distance) requires more than the electron transit time d/v_ to make a gap crossing.
36(1965); http://dx.doi.org/10.1063/1.1714298View Description Hide Description
In order to calculate the limiting magnetic field for superconductivity of a type II superconductor, the free‐energy contributions of the Abrikosov mixed state and the electron spin paramagnetism are combined. The solutions which result are applied to the niobium—zirconium alloy system and compared with the available resistive critical field data, as a function of composition. The calculated curve is generally closer to the experimental curve than either the paramagnetic limit or H c2 alone, and rather good agreement is obtained for niobium‐rich alloys.
36(1965); http://dx.doi.org/10.1063/1.1714299View Description Hide Description
An oscillographic study of the ozonizer discharge under normal operating conditions is made and is discussed in the light of known mechanisms active in glass vessels with external electrodes. The investigation is extended to various gases and the features of the breakdown attributable to the glass itself are distinguished from those depending on the nature of the gas.
36(1965); http://dx.doi.org/10.1063/1.1714300View Description Hide Description
In the presence of a population inversion, fluorescent lifetimes are reduced as a result of stimulated emission. Effective fluorescent lifetimes have been calculated using a Monte Carlo method for ruby rods with Brewster‐angle ends and roughened sides. The calculations take into account the dependence of gain and reflectivity on polarization and the dependence of gain on frequency. The reflection characteristics of the roughened surface are assumed to be those of an ideal diffuse reflector. Results show that effective fluorescent lifetimes are quite insensitive to rod length but strongly dependent on rod diameter. They also indicate the possibility of oscillation in a random mode for rods of sufficiently large diameter.
36(1965); http://dx.doi.org/10.1063/1.1714301View Description Hide Description
This work is the examination of a cavity mode approach to the mode structure of a laser. Solutions of the vector wave equation for electromagnetic fields in and between perfectly conducting oblate spheroidal cavities are examined for the case of wavelengths much less than cavity dimensions. These solutions are the field modes in Fabry—Perot type resonators with equal‐radius concave spherical mirrors, or with concave—convex spherical mirrors, when the parameters of the oblate spheroids are chosen so that the radii of curvature and spacing on the axis of rotation match those of the resonatormirrors. Expressions for the transverse and longitudinal mode structures are derived. The eigenvalue equations are written, and are solved for the case of the two lowest‐order modes.
36(1965); http://dx.doi.org/10.1063/1.1714302View Description Hide Description
Electrode geometry effects neglected by previous investigators are shown to be significant for electrical breakdown in vacuum for gap lengths 0 to 1 mm exhibiting breakdown at 0 to 60 kV for Al, Cu, and stainless steel electrodes. In particular, data demonstrating curvature, area, and polarity effects are reported. The effects of material transfer, particle inertia, protrusion formation,erosion, and patterned deposits are also reported.
36(1965); http://dx.doi.org/10.1063/1.1714303View Description Hide Description
The solutions of the rate equations describing the Q‐spoiled and pulsed‐transmission‐mode (PTM) operation of a three‐level laser are given. These solutions were carried out in two time regions: (1) the delay time followed by (2) the pulse time. Region (1) was tractable with approximate analytic methods, while in region (2) the equations were solved by analog computer. The effect of the duration of the Q switch on the delay time and on the PTM operation is investigated. It is found that Q‐switch times as long as 20 nsec give satisfactory PTM operation.
Change of Elastic Constants through the Ferroelectric to Antiferroelectric Phase Transition in a Pb(Ti,Zr,Sn)O3 Ceramic36(1965); http://dx.doi.org/10.1063/1.1714304View Description Hide Description
Ultrasonic pulse‐echo measurements are used to determine the changes in c 11 E , c 33 D , c 44 D , c 44 E , and c 12 E through the reversible ferroelectric—antiferroelectric phase transition in a Pb(Ti, Zr, Sn)O3ceramic. The results indicate that after the transition is enforced by hydrostatic pressure the material loses both electrical and mechanical orientation and becomes elastically isotropic.
36(1965); http://dx.doi.org/10.1063/1.1714305View Description Hide Description
The mechanisms of ion formation in cesium plasmas at relatively low electron temperatures (3500°K) and pressures of a few Torr are investigated. It is concluded that most of the ions are molecular and that they are formed by collisions between cesium atoms in the first excited state. The excited atoms are predominantly produced by inelastic electron collisions.
The excitation cross section is computed by means of the impact parameter method. It has a maximum value of 100×10−16 cm2 at 7 eV. The de‐excitation cross section is computed and found to be approximately constant at 50×10−16 cm2. Radiation trapping and diffusion of excited atoms are also studied.
The ionization cross section is calculated by means of statistical thermodynamics from the measured recombination coefficient for the inverse of the ionizing process. It is found to be 1450×10−16 cm2. The plasma is uniform throughout its volume except in the immediate vicinity of the bounding electrodes.
The proposed mechanism results in performance characteristics for cesium thermionic converters, operating in the ``ignited mode,'' which are in qualitative and quantitative agreement with experimental data.
36(1965); http://dx.doi.org/10.1063/1.1714306View Description Hide Description
We wished to determine if an electrode polarity effect existed in vacuum breakdown conditioning. To investigate this conditioning effect, we used a three‐electrode experimental tube constructed in such a manner that one electrode (1) could be made to oppose either of the other two (2 or 3) without destroying the vacuum. High‐current arcs were drawn between both possible electrode pairs to bring them to a reproducible state of apparent deconditioning. These pairs (1 vs 2 and 1 vs 3) were then, in turn, conditioned by a series of high‐voltage pulses at a gap of 2.3 mm. The following conclusions were drawn: (1) within experimental error, all conditioning took place at the pulse cathode, (2) when the arc and pulse polarities were similar, the subsequent pulse breakdown voltage was lower than when the polarities were opposed, and (3) conditioning was not due to the removal of a gas layer from the electrode, but, rather, to removal of cathode deformations. Predictions concerning the polarity effect in vacuum breakdown conditioning were drawn from the major theories of vacuum breakdown, and compared with our experimental results. We found that our results agreed with the predictions of some vacuum breakdown theories, flatly contradicted the predictions of others, and tended to disagree with the predictions of a third group of theories.
Electrical Properties of Inert Gas Plasmas Generated in Thermionic Cold‐Cathode Diodes by Radiation in a Nuclear Reactor36(1965); http://dx.doi.org/10.1063/1.1714307View Description Hide Description
The electrical properties of inert gas (Xe, Kr, Ar) plasmas have been studied in a nuclear reactor environment at gamma radiation dose rates up to 6×108 rad/h. The measurements are made by inserting a gas‐filled thermionic diode into the core of a 5‐MW nuclear reactor. The space‐charge neutralization effects caused by the ion‐electron pairs generated in the gas are measured and interpreted in terms of plasma properties of the gas. The electrical conductivity of the plasma, at a constant radiation level, goes through a maximum as a function of pressure in the range of 1–300 Torr. If the radiation dosage is varied, keeping all other factors the same, one finds the electrical conductivity monotonically increases with dose rate in the range of 106−6×108 rad/h.
Experiments are described which indicate that electrons can be removed from a low work function ``cold'' electrode into the plasma by a mechanism different from either thermionic or field emission. A physical model is proposed to explain this phenomenon.
36(1965); http://dx.doi.org/10.1063/1.1714308View Description Hide Description
Kesaev's recent data on the stability of vacuum arcs for a wide variety of solid and liquidcathodes furnish a greatly expanded range of criteria for determining the mechanism of the cathode spot. The large effects of phase and crystalline texture of the cathode suggest that an essential process occurs within the cathodemetal itself. This is thought to be secondary electron emission produced by positive ions through a diffusion‐controlled neutralization process. Each secondary initiates a short burst of thermal ionization in front of the cathode, which supplies practically all of the arc current. Survival of the arc depends on the emission of at least one new secondary within the period of the burst, and this depends on the current and on the rate of diffusion of ions into the cathode, the secondary emission being greater the larger the current and the slower the diffusion. Relative diffusion rates are estimated for most of the cathodemetals used by Kesaev and it is found that the current required for a given arc lifetime increases regularly with the rate of diffusion of ions into the cathodemetal. The analysis yields five new heats of diffusion—polycrystalline mercury and bismuth 16.2 and 18.3 kcal/mole, respectively; and liquidbismuth,thallium, and aluminum, 8.8, 3.2, and 3.4 kcal/mole, respectively.
The diffusion rate is correlated with cathode temperature, dislocations, and vacancies, and the moving spot probes in all directions for areas of low diffusion rate. The arc is extinguished when all parts of the cathode line lie on micro‐areas of high diffusion. The arc lifetime data furnish estimates of the concentrations of dislocations in all the solid and liquid (transient existence) metals as prepared by Kesaev. The concentration of edge dislocations is found to be approximately inversely proportional to the fourth power of the heat of vaporization.
The statistics of arc lifetime as a function of current may be correlated by the Poisson formula, with each burst of ionization counting as a single Poisson trial, which is successful if it produces one or more secondary electrons. The analysis for liquid indium indicates that the bursts have a lifetime of about 5×10−7 sec.
The random motion of the free spot on mercury is thought to be determined by random radial temperature‐fluctuation gradients at the edge of the spot. The velocity of the free spot on mercury is limited to about 104 cm/sec because the spot must not outrun its secondary emission, which lags behind positive ion incidence on the cathode by about the 10−7 sec required for the diffusionsecondary emission process in mercury. Retrograde motion of the spot in a magnetic field is found, qualitatively and semiquantitatively, to be due to the temperature gradient set up across the spot by the Righi—Leduc thermomagnetic effect. The retrograde velocity on bulk liquidmercury is subject to the same velocity limit of about 104 cm/sec as is the random velocity in zero field. A spot at a mercury—molybdenum boundary can jump to a substantially higher velocity when the Righi—Leduc gradient is high enough, and when, also, the increased velocity is great enough to permit the spot to operate on a mercury layer so thin that the diffusing ions have access to the molybdenum surface, where the more abundant supply of electrons accelerates the neutralization process, and thus decreases the time‐lag of secondary emission.
It is suggested that more sophisticated observation and analysis of cathode‐spot statistics should furnish a valuable metallurgical tool for studying the texture and dislocation properties of metal surfaces. From the analysis of Kesaev's data some speculations are made about the origin and behavior of edge dislocations.
36(1965); http://dx.doi.org/10.1063/1.1714309View Description Hide Description
The anomalous surface reflection of x rays reported recently by Yoneda has been investigated for several materials using MoKα1, CuKα1, and CrKα1 radiation. The experimental evidence speaks strongly in favor of the Warren and Clarke interpretation in terms of totally reflected small‐angle scattering. For clean surfaces the scattering appears to be due to surface irregularities of the bulk material itself. Because of its sensitivity to the roughness and chemical contamination of optically or near‐optically finished surfaces, the Yoneda effect has considerable promise as a new x‐ray tool for studying surfaces and thin films.
36(1965); http://dx.doi.org/10.1063/1.1714310View Description Hide Description
Vacuum distillation methods were demonstrated to be effective for producing high‐purity crystals of LiF. It was established from chemical analyses of condensate products that under the experimental conditions adopted, 995°C and 4 to 5×10−2 Torr, the order of vaporization for the fluorides, NaF, MnF2, LiF, MgF2, and CaF2, corresponds to the order of their decreasing vapor pressures. Under similar experimental conditions LiF containing no more than 200 ppm of oxygen could be produced from mixtures of LiF and Li2O.
36(1965); http://dx.doi.org/10.1063/1.1714311View Description Hide Description
Magnetic susceptibility of iron—tin alloys containing 0.45, 0.82, 1.33, 1.83, and 2.14 at.% tin have been studied as a function of temperature up to 1500°K. Tin influences the magnetic properties of iron in an unusual way. The mass magnetic susceptibility of γ iron is increased by about 1% due to 0.45 at.% tin. The paramagnetic moments of the bcc phase, determined from the susceptibility data between 1300° and 1500°K, show a small increase with increasing tin content. These results are, in principle, consistent with the ferromagnetic properties studied by Fallot (1936) indicating that tin does not act as simple diluent in regard to the magnetic behavior of iron.Electrical resistivities of iron—tin alloys, determined at 4.2°, 77.2°, and 297.0°K, show that tin increases the resistivity of iron very considerably, i.e., about 8 μΩ cm per 1 at.% at 4.2°K. Lattice parameters of iron—tin solid solutions up to 5 at.% tin (quenched from 1013°K) have been measured at 298°K. None of the present theories are capable of explaining satisfactorily the observed behavior.
36(1965); http://dx.doi.org/10.1063/1.1714312View Description Hide Description
An analysis is made of the strain‐energy distribution in a slotted double‐cantilever cleavage specimen. In this type of specimen the crack is medially constrained by a pair of longitudinal slots, so that surface energies can be determined in nonmonocrystalline samples.
The analysis treats the arms of the crack as end‐loaded cantilever beams, and the post crack‐tip region as a pair of elastically supported beams. The web produced by slotting is assumed to act as an elastic foundation for the remaining beam‐like portions of the post crack‐tip region. An expression for the specific surface energy of the material is then derived from conservation of energy at the instant the crack begins to propagate. Linear elastic behavior of the material is assumed and shearing strains are neglected.
Extension of the analysis to conventional (unslotted) specimens in which medial constraint of the crack is obtained through a preferred direction of cleavage, is discussed semiquantitatively in terms of an effective foundation modulus.
36(1965); http://dx.doi.org/10.1063/1.1714313View Description Hide Description
A brief study is described of a simple method for producing plane shock waves in solids at pressures higher than those attainable by conventional explosive methods. Mach reflection of a conically convergent shock in the specimen yields a disk‐shaped front at a pressure of several megabars, depending on the type of explosive employed and the specimen material; this front is accessible to Hugoniot equation‐of‐state measurements. Results for copper at a pressure of 1.9 Mbar are in good agreement with published values.