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Volume 38, Issue 7, 01 June 1967

Temperature‐Induced Changes in Optical Path Length for a Nd‐Doped Glass Rod during Pumping
View Description Hide DescriptionFrame‐camera interferogram data for a neodymium‐doped glass rod taken during the laser pumping process have been analyzed in terms of changes in optical path length due to: (1) explicit temperature‐induced changes in length and index of refraction, and (2) temperature‐induced stress birefringence. Criteria for compatibility of the interferogram data, the formalism, and independently determined values for the phenomenological constants involved are set up and met, after which the temperature over the rod cross section obtains. The minimum in the temperature distribution found accounts for the observed split fringes, and our qualified estimate of the temperature rise at the center of the rod is ∼16°C. Estimates of the changes in optical path length due to the various effects are made, and values for the temperature coefficients of expansion and refractive index of 0.97×10^{−5}/°C±6% and −7.2×10^{−7}/°C±60%, respectively, are submitted.

Theory of Dynamic Optical Distortion in Isotropic Laser Materials
View Description Hide DescriptionIn this paper, Fermat's principle is applied to the analysis of pump‐induced optical distortion in isotropic laser materials. This approach leads to expressions for the slope and trajectories of rays through a laser amplifier rod for a plane‐wave input. These results are then used to predict ray refraction, beam divergence, and optical path length through the rod as a function of radius, time, and polarization. The index of refraction of the material is considered to change both as a result of thermal effects and as a result of the presence of an excited ion population.

Measurements of Dynamic Optical Distortion in Nd‐Doped Glass Laser Rods
View Description Hide DescriptionThis paper quantitatively describes the optical distortion in neodymium‐doped glass which is induced by pump radiation. We have found the optical path length at 6328 Å dependent on four primary effects: (1) change in physical length; (2) change in refractive index due to temperature rise; (3) change in index resulting from stress; (4) change in index associated with an excited‐state population of neodymium ions. Section I presents the experimental techniques used and the results obtained. Included in this section are measurements of optical‐path‐length variations, pump‐induced birefringence, change in physical length, change in refractive index, bulk temperature rise, and the deflection of a pencil of rays. Section II compares the results of Section I with the theory set forth in the previous paper. Good agreement between theory and experiment is achieved provided a term which takes account of the index change associated with an excited‐state population of neodymium ions is included. This term arises from the fact that the polarizability of the neodymium ion in its excited ^{4} F _{3/2} level is different from its value in the ^{4} I _{9/2} ground level. The inclusion of this new term in the expression for the change in refractive index implies that large optical distortions can exist in ``athermalized'' glass.

Space‐Charge‐Limited Currents in Copper Phthalocyanine Thin Films
View Description Hide DescriptionMeasurements of space‐charge‐limited currents have been made on evaporated thin films of the compound copper phthalocyanine using Ohmic contacts. A complete study of the current as a function of voltage, temperature, thickness, and illumination indicates that all the results are consistent with the assumption of an exponential distribution of trapping states of the form N_{t} (E) = kT_{c}P _{0} exp (E/kT_{c} ), where kT_{c}P _{0} is a parameter related to the total trap density.
Practical techniques for obtaining values for the mobility, density of states, total trap density, trap distribution in the vicinity of the Fermi level, and trap capture cross section are outlined and values reported.

Electrical Properties of Copper Phthalocyanine Thin Films as Influenced by the Ambient
View Description Hide DescriptionMeasurements of currents in evaporated thin films of copper phthalocyanine as a function of temperature and ambient have yielded information about the effects of nitrogen, hydrogen, and oxygen ambients on the conductivity, trap density, and mobility. Above a transition voltage the currents are space‐charge‐limited and can be correlated with a trap distribution that decreases exponentially with energy as the distance from the valence band edge increases. The parameters that govern the distribution as well as the position of the Fermi level depend on sample preparation, and some systematic correlation exists between annealing and the subsequent values of these parameters, based on consideration of the crystal changes that occurs on heating.
The value of the intrinsic conductivity σ_{0}=3(Ω cm)^{−1} and mobility μ=0.013±0.007 cm^{2}/Vsec have been determined and are found to be relatively independent of preparation and subsequent treatment.

Steady‐State Theory of an Intermediate‐Pressure Discharge Column in a Magnetic Field
View Description Hide DescriptionA steady‐state theory of a discharge column in a magnetic field is presented which covers the intermediate pressure range where the ion mean free path is neither much greater than, nor much less than, the discharge radius. With increasing pressure and magnetic field, its predictions tend to those obtainable from ambipolar diffusion theory. With decreasing pressure they approximate those of low‐pressure discharge theory based on the use of the third‐moment equation for the ions. The analysis in this paper is based on continuity and momentum‐transfer equations for the electrons and ions, but in contrast to linear ambipolar diffusion theory, the nonlinear ion inertia term is retained. In the plasma approximation, retention of this term gives rise to a plasma‐sheath boundary, where the density is nonzero and the potential finite, located where the ambipolar drift velocity reaches the isothermal sound speed [k(T_{e} +T_{i} )/m_{i} ]^{1/2}. Numerical solutions are presented for the profiles of density, velocity, and potential, for planar and cylindrical discharges. These indicate that potential inversion can occur, and that under such conditions the potential rises to a maximum and then decreases towards the plasma‐sheath boundary.

Decorated Dislocations in LiNbO_{3} and LiTaO_{3}
View Description Hide DescriptionIt has been found that dislocations in LiNbO_{3} and LiTaO_{3}single crystals can be decorated by electric‐field‐enhanced diffusion of platinum or gold into the crystals at temperatures in the order of 600°C with voltages in the range of 250 to 1000 V/cm. To demonstrate the use of the technique, examples of low‐angle boundary networks in LiNbO_{3} and LiTaO_{3} are shown. The general characteristics of the as‐grown dislocation network in a [101̄0]‐growth‐axis LiNbO_{3} crystal are described, and the effect of annealing on the dislocation array in LiTaO_{3} crystals is discussed.

Renormalization and the First‐Order Ferroelectric Transition in Perovskites
View Description Hide DescriptionA renormalization of the Hamiltonian H, previously devised by Silverman and Joseph to calculate the temperature‐dependent ferroelectric‐mode frequency in perovskites exhibiting a second‐order transition, is extended to the case of a first‐order phase change. The extension involves inclusion in H of all anharmonic terms to sixth order which give rise, after a thermal average is taken, to polarization and temperature dependences in the internal energy, which are similar to those appearing in the phenomenological theory of Devonshire. Validity of the latter theory in high electric fields can now be understood as a consequence of field independence of the acoustic modes, which make the dominant contribution to the temperature dependence of the internal energy. Since the optical frequencies must depend on field under these circumstances, so that validity of the Devonshire theory requires that they make little contribution to thermal properties, the optical branch should lie above the acoustic, except in (001) planes where the unstable modes occur which are responsible for the transition. From domain‐wall calculations in the tetragonal phase of bariumtitanate, it is concluded that dispersion is weak in the (001) planes, so that all frequencies with k in such a plane will be low. This suggests that (001) planes should be surfaces of discontinuity in frequency, which leads in turn to the prediction that the electric susceptibility and switching rate in tetragonal bariumtitanate will exhibit thickness dependence of purely lattice‐dynamical origin, with the thickness dependence of the latter exceeding that of the former. The theory thus provides a means of correlating the field and thickness dependence of switching and polarization with the structure and temperature dependence of the lowest transverse optic branch.

Lattice‐Dynamical Theory of Switching in Barium Titanate Single Crystals
View Description Hide DescriptionA lattice‐dynamical approach to calculation of the switching probability is developed for use in connection with the Miller‐Weinreich model of 180° domain‐wall motion in bariumtitanatesingle crystals. According to the new approach, the nuclei of permanently reversed polarization, which appear on the domain‐wall surface in the presence of a field, are produced by a superposition of optic modes. The probability that this superposition will attain the amplitude required to switch a nucleus can be calculated as the probability for the outcome of a random walk. This probability is a function of the optical frequency and of the number of modes which contribute to switching. From a previous renormalization of the Hamiltonian which describes the lowest transverse optic mode, the field and thickness dependence of the parameters which govern switching can be determined. In this way it is predicted that (1) the product of field and activation energy will increase with the field; and (2) the thickness dependence of the switching activation energy, which is primarily of lattice‐dynamical origin, should exceed the corresponding thickness dependence of the electric susceptibility measured on the same crystal. The role of the surface layer is assumed, following Janovec, to lie in the production of backswitched microdomains behind the advancing domain wall. This backswitching can produce electrostatic fields which retard the wall in the same way as depolarization fields which earlier theories have attributed to charges deposited on the inner surface of an unswitched layer. This picture of retardation permits us to separate the mechanism which slows the wall from that which accounts for the thickness dependence of switching and thus to avoid contradictions which have arisen in attempts to explain the latter effect by depolarization fields.

Time Dependence of Avalanche Processes in Silicon
View Description Hide DescriptionAn analysis of the time dependence of avalanche processes encountered in silicon junctions, including the effects of different ionization rates and velocities of the two charge carriers, is presented. An earlier analysis of Read was restricted to equal ionization rates and velocities; that restriction has been removed but the frequency limitation of his analysis has been retained here. Various solutions of the generalized differential equation are obtained, including a steady‐state solution to a sinusoidal perturbation of the avalanche‐field maximum. The important features of this steady‐state solution are that it describes the avalanche current for all explicit values of the multiplication M≥1, is valid for highly nonlinear responses to the sinusoidal perturbation, and contains both the in‐phase and out‐of‐phase parts of the fundamental‐frequency component of the avalanche response.
The analysis is applied to solid‐state photomultipliers, is used to explain an anomalous rectification observed in operating Read structures, and, lastly, the small‐signal limit of the avalanche response is compared with susceptance measurements of a uniformly avalanching junction as a function of the multiplication and saturation current over a frequency range of 20 to 200 MHz.

Analysis of the Q Factor, Efficiency, Stability, and the Design of Read Structures in the Nonlinear Range
View Description Hide DescriptionUsing time‐dependent solutions of the avalanche current generalized for unequal ionization rates and velocities of the two charge carriers, compact formulas for the Q and the efficiency of the Read structure are derived, which are valid from zero to very large oscillation amplitudes. A method is developed to properly account for the internal‐field adjustment (which may be variably positive or negative) that is caused by the nonlinearly rectified avalanche‐current component flowing through the drift region. These developments clearly show that the behavior of the Q at intermediate and large signals cannot be correctly derived unless the avalanche analysis retains terms related to both the in‐phase and out‐of‐phase components of the avalanche current.
The behavior of Q vs oscillation amplitude is numerically calculated for a successfully operated prototype and compared with experimental observation. These experimental observations in conjunction with the analytical development also permit an interpretation and assessment of the effects due to inhomogeneities in multiplication found in junctions.
Design considerations of Read structures are discussed, particularly how various parameters that are critical in optimizing the efficiency and stability may be controlled by design of the electric‐field distribution of the avalanche. It is shown how advantage may be taken of the asymmetry of ionization rates of the two charge carriers to achieve even higher efficiencies than the 30% Read predicted for the case of equal ionization rates. Finally, certain circuit criteria for achieving dynamic stability are discussed and solutions given.

X‐Ray K Absorption Edges of Alloys. I. Correlation to Band Models
View Description Hide DescriptionIt is possible to identify portions of the fine structure appearing in the x‐ray K absorption edges of pure metals with their respective energy bands. The areas of these portions are proportional to the density of unoccupied states in each band and changes in their occupation density accompanying alloying. Face‐centered‐cubic Ni, Co, and Fe have similar fine structures that are characteristically different from that of body‐centered‐cubic Fe. An analysis of the latter suggests that the overlapping 3d+4s+4p bands in α‐Fe are split into two sub‐bands separated by ∼8 eV. A direct comparison of changes in the areas under the curves of Cu‐Ni alloys shows that a systematic decline in Ni 3d holes and Cu 4s holes takes place with increasing copper content. An apparent saturation takes place at 56 at.% copper in agreement with magnetic saturation and NMR measurements.

X‐Ray K Absorption Edges of Alloys. II. Nickel‐Cobalt and Nickel‐Iron Solid Solutions
View Description Hide DescriptionChanges taking place in the fine structure of the cobaltK edge in Ni‐Co solid solutions indicate a decline in the 3d‐4shole density at cobalt atom sites. Changes in the NiK edge in the same alloys suggest that the hole density at nickel atoms increases, thus supporting the rigid‐band model for these alloys.
Significant changes in the NiK edges of fcc (gamma) Ni‐Fe solid solutions suggest that the rigid‐band model may be valid for these alloys also. It does not appear to be applicable, however, to bcc (alpha) solid solutions. In both alloy types, the fine structure at the Fe K edge remained unchanged. Good agreement was obtained with magnetic measurements on bcc Ni‐Fe alloys.

Dislocation Configurations in Cylindrical Coordinates
View Description Hide DescriptionGeneral expressions are derived for the stress components due to an arbitrary continuous distribution of dislocations prescribed in a cylindrical coordinate system. Results are obtained for the stress field of a helical dislocation of uniform shape with the Burgers vector along its axis. The additional energy arising from the interaction of a point defect with the helix is obtained and the behavior of the defect examined.
It is also shown how results for circular dislocation loops are readily obtained from the general expressions and in particular the problem of a rotational loop, which is formed by twisting the two faces of the slip surface relative to each other, is solved.

Magnetic Annealing Effects in Silicon‐Doped Garnets
View Description Hide DescriptionMany properties of polycrystallineyttriumirongarnet (YIG) and reduced single‐crystal YIG have been attributed to the presence of Fe^{2+}ions which provide mobile electrons that can diffuse locally through the lattice. It was the purpose of this research to study the modification to the low‐temperature anisotropy caused by the presence of Fe^{2+}ions in silicon‐doped YIG, Y_{3}Fe_{5−δ}Si_{δ}O_{12} with 0<δ<0.18. Silicon‐doped YIG demonstrates a time‐dependent induced anisotropy proportional to doping when magnetically annealed to low temperatures. The kinetics and temperature dependence of this induced anisotropy have been studied. It is further found that these dopedgarnets show a constant, high‐field component of rotational hysteresis which is both frequency‐ and temperature‐dependent.
The intrinsic, unannealed anisotropy behaves in a novel way. At room temperature the anisotropy coincides with normal YIG, while between 150°K and 300°K  K _{1}  increases above that of pure YIG Below about 150°K the curves develop asymmetry and appear to be no longer purely cubic. At 4.2°K the easy axis has shifted to the [100] direction (>3% doping) indicative of a change in sign in K _{1}. Silicon‐doped lutetiumirongarnet and polycrystallinelutetiumirongarnet were found to behave in a similar manner.
The results are interpreted in terms of an electron‐diffusion model which enables the Fe^{2+} ion to effectively wander among four nonequivalent octahedral sites. A simple kinetic rate theory is at least partially successful in explaining: (1) the time dependence of the torque curves, (2) the rotational hysteresis, and (3) some of the apparent low‐temperature deviations from cubic symmetry.

Breakdown Conduction in Al‐SiO‐Al Capacitors
View Description Hide DescriptionDestructive breakdown has been studied in Al‐SiO‐Al capacitors using transmission electron microscopy and electron diffraction, while the capacitors were subjected to controlled electrical stresses. Extensive electrical measurements were made outside the electron microscope on other capacitors. The purpose is to describe destructive breakdown and to relate it to prebreakdown conduction, conditions of fabrication, and capacitor structure.
It is found that breakdowns originate at inhomogeneities in the dielectric which appear in electron micrographs as irregularly shaped dark spots about 0.5 μ in diameter. The structure of these dark spots has not been determined. Breakdowns are not concentrated at pinholes, dust spots, or fissures. Breakdown is accompanied by the growth of crystalline silicon. Electrical measurements with a given capacitor reveal two well‐defined polarity‐sensitive threshold voltages, one for the onset of breakdown and one for the cessation of breakdown. Both are virtually independent of temperature from 80° to 380°K. The voltage threshold for the onset of breakdown varies approximately as w ^{1/2}, where w is the dielectric thickness, while the voltage threshold for the cessation of breakdown is found to be independent of dielectric thickness. The diameter of a typical breakdown is 10 to 100 μ. The conductivity of the breakdown site at the onset of breakdown changes by a factor of about 10^{10} in a time less than 0.1 μsec. Duration of a breakdown is usually about 1 μsec.
A breakdown mechanism is proposed that is based upon an electrochemical solid reaction in the presence of the breakdownelectric field:where the term Si−Si^{+} means the two silicon atoms are in crystalline form and one is singly ionized. A description of the breakdown process is given using this reaction.

Electron‐Bombardment Desorption of Carbon Monoxide Adsorbed on Tungsten
View Description Hide DescriptionThe ion current produced by electron bombardment of the (211) crystal face of a W ribbon is shown to be predominantly O_{16} ^{+}. The only impurity detected, H^{+}, was never more than 4% of the total current even when the ribbon operated in hydrogen with a carbon monoxide impurity as low as 1%.

Study of the Different Operating Modes of an Alkaline‐Metal‐Plasma Machine by Means of Electric Probes
View Description Hide DescriptionThis study includes the design of a fully demountable alkaline‐metal‐plasma machine. The plasma is produced by contact ionization of alkaline metal vapor on a refractorymetal emitter. The properties of this plasma depend on three parameters: emitter temperature, cesium vapor pressure, and potential of an electrode which sets the electric boundary conditions for the medium. Three movable probes analyze the plasma. Measurements are made and results are discussed in terms of the parameters. The first part of the study is devoted to a description of the machine and the probes. The second part analyzes its different operating modes. There are two fundamental modes. The first covers the case where collisions are predominant. The second is a flux mode in which interactions are very improbable. The machine permits continuous transition from the first to the second mode. In the transition zone complex phenomena arise. The study is primarily concerned with an examination of the inflection potentials given by the second derivative of the current‐voltage characteristics of the probes. Interpretation of this inflection potential will differ greatly from one operating mode to another.

Thermoelectric and Galvanomagnetic Measurements on (Bi_{2}Te_{3})_{5}(Bi_{2}Se_{3})_{1} (Sb_{2}Te_{3})_{18}
View Description Hide DescriptionThe galvanomagnetic parameters ρ_{123}, ρ_{1111}, ρ_{1133}, ρ_{1131}, and ρ_{1122} have been measured at 77°K for two samples of p‐type (Bi_{2}Te_{3})_{5}(Bi_{2}Se_{3})_{1} (Sb_{2}Te_{3})_{18} and the results fitted to a six‐ellipsoid model similar to that proposed for Bi_{2}Te_{3}. An anomalous rise in the Hall coefficient with temperature and an apparent change in the effective mass ratios are explained by assuming the existence of impurity banding. The thermal conductivity,thermoelectric power, and electrical resistivity were measured over the temperature range from 77° to 300°K.

Reflection and Transmission of Electromagnetic Waves by a Moving Plasma Medium. II. Parallel Polarizations
View Description Hide DescriptionThe reflection and transmission of electromagnetic waves by a moving dispersive dielectric half‐space or slab are investigated theoretically. The dispersive medium is assumed to be a cold plasma medium. Two cases of the movement are considered: (a) the plasma medium moves parallel to the interface; (b) the plasma medium moves perpendicular to the interface. The electric vector of the incident wave is assumed to be polarized in the plane of incident (parallel polarization). Unlike the normal polarization case which was treated earlier, the reflected and transmitted fields for the present case are functions of the velocity of the moving plasma medium for both cases (a) and (b). An illustrative numerical example is given for case (a) at normal incidence.