Showing papers in "Journal of Applied Physics in 1970"

Elastic Constants of Compression-Annealed Pyrolytic Graphite

Abstract: The elastic constants of pyrolytic graphite which has been highly ordered by annealing under compressive stress have been determined by ultrasonic, sonic resonance, and static test methods. Ultrasonic tests yielded the elastic constants c11, c12, c33, c44 = 1/s44, and the stress derivative of c33. The moduli 1/s11 and c44 were determined from the free flexural resonant vibrations of bars, and the shear modulus c44 also was determined from the fundamental torsional resonance of the bars and from the resonance of compound torsion oscillators composed of thin graphite disks with steel end pieces. Static tension, compression, and torsion tests on the pyrolytic graphite yielded a complete set of compliances (s11, s12, s13, s33, and s44). The following self‐consistent set of elastic constants (cij in units of 1011 dyn/cm2; sij in 10−11 cm2/dyn) has been deduced from the results: c11 = 106±2, c12 = 18±2, c33 = 3.65±0.10, c13 = 1.5±0.5, c44 = 0.018 to 0.035, 1/s11 = 102±3, 1/s33 = 3.65±0.10, s12 = −0.0016±0.0006,...

Shock‐Wave Studies of PMMA, Fused Silica, and Sapphire

Abstract: The shock‐wave propagation characteristics of polymethyl methacrylate (PMMA), fused silica, and sapphire were measured for both compressive and rarefaction waves using plate‐impact experiments and interferometer instrumentation techniques The peak stress levels in the experiments were 22, 65, and 120 kbar, respectively The high‐resolution measurements of the stress wave profiles showed the PMMA to be a complex material whose wave propagation is influenced by nonlinearity, strain‐rate dependence, and elastic‐plastic effects in which plastic working increases the zero‐pressure volume of the material The fused silica is very well characterized as a nonlinear elastic material having the interesting property of propagating stable rarefaction shock waves The sapphire was nearly linear elastic to 120 kbar The use of these three transparent materials as ``windows'' in laser interferometer instrumented shock‐wave studies of other materials is discussed The effect of the shock‐induced variation of the index o

Tunneling Conductance of Asymmetrical Barriers

Abstract: The voltage‐dependent tunneling conductance of trapezoidal potential barriers has been calculated using two extreme models of (1) the WKB approximation and (2) perfectly sharp boundaries between the metal electrode and the insulator. We show that for both models the conductance‐voltage plot is roughly parabolic at low voltages (≲0.4 V). The minimum conductance is not at zero bias unless the barrier is symmetrical and identical Fermi energies are chosen for the two metal electrodes. The inclusion of image forces does not radically alter the shape of the conductance‐voltage dependence. Using reasonable barrier shapes, the asymmetry of the calculated conductance about V=0 is not as large as we frequently observe experimentally. We point out that this extreme asymmetry appears to be associated with the presence of organic impurities in the oxide layer of the junction.

Maker Fringes: A Detailed Comparison of Theory and Experiment for Isotropic and Uniaxial Crystals

Abstract: A complete theory of Maker fringes in nonabsorbing isotropic and uniaxial crystals has been derived which includes all the corrections necessary for making precise determinations of nonlinear optical co‐efficients. These corrections include finite beamwidth effects and multiple reflection corrections. Comparison of this theory with extensive experimental data on the Maker fringes in quartz, ADP, and KDP shows agreement to within the experimental accuracy of about 5% on the Maker fringe envelopes and to better than 1% on the coherence lengths. We conclude from this study that a careful analysis of Maker fringes can yield precise values of the nonlinear optical coefficients and coherence lengths in isotropic and uniaxial crystals. This is of great importance in establishing accurate and reliable standards in the field of nonlinear optics.

Accommodation of Misfit Across the Interface Between Crystals of Semiconducting Elements or Compounds

Abstract: Misfit dislocations are often transported to the interface between crystals by glide. In materials with the diamond or sphalerite structures, glide is inhibited by the Peierls stress. The aim of this paper is to present a theory for misfit accommodation which includes the effect of the Peierls stress. It is used to explain the elastic strains present in films of germanium on gallium asrenide and to explain the reduction of these strains by a high‐temperature anneal. The strains in germanium on gallium arsenide, and the effect of temperature upon them, are not explained by earlier theories for the accommodation of misfit between one crystal and another.

Dislocation Cell Formation in Metals

Abstract: It is shown by an analysis similar to that for the spinodal decomposition of a supersaturated solution that an array of dislocations, modelled by parallel screw dislocations, of uniform density, is unstable; the dislocations move to form a structure having a modulated dislocation density. It is suggested that the instability grows ultimately into a dislocation cell structure and that the cell size is given by the dominant wavelength of the density modulation. This wavelength λm is found to be proportional to ρ−1/2 and furthermore the wavelength is given by λm ≈ Kc·ρ−1/2=rc, where Kc is a constant, ρ is the dislocation density and rc is defined as a dislocation‐dislocation interaction distance. Data in the literature relating to cell size are shown to support this result. Restrictions on the applicability of the analysis are discussed.

Generalized Equation for the Elastic Moduli of Composite Materials

Abstract: A generalized equation is proposed for the relative elastic moduli of composite materials. By the introduction of a generalized Einstein coefficient and a function which considers the maximum volumetric peaking fraction of the filler phase, the moduli of many types of composite systems can be calculated.

Design and Operation of Stable rf‐Biased Superconducting Point‐Contact Quantum Devices, and a Note on the Properties of Perfectly Clean Metal Contacts

Abstract: Point‐contact devices are described which have exhibited long‐term stability and reliability. A particular mode of operation of the devices as rf‐biased low‐frequency detectors is described in detail, including a description of how the device drives a resonant circuit to which it is coupled. In this mode of operation the sensitivity of the devices to low‐frequency fields is of the order of 10−9 G per root cycle bandwidth. Perfectly clean contacts were made by breaking a notched niobium member at 4.2°K and then remaking contact at the break. Quantum behavior of such contacts is identical to that of ordinary contacts, but effects of microscopic multiple connections at the contact were not observed.

Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces

Abstract: Models for initial‐, intermediate‐, and final‐stage densification under pressure have been developed, which explicitly include both the surface energy and applied pressure as driving forces. For the initial stage, the time dependences and size effects given by the integrated equations are identical to those reported earlier for surface energy (alone) as the driving force. The only modification is that the surface energy (γ) is expanded into (γ+PaR/π), where Pa is the applied pressure and R is the particle radius. For the intermediate stage of the process, the Nabarro‐Herring and Coble creep models may be adapted to give approximate (∼4×) densification rates for lattice and boundary diffusion models, respectively. In these cases the complex driving force is written as: (Pa/D+γk), where D is the relative density, and k is the pore surface curvature. At the final stage of the process those models are invalid; an alternate model is developed based on diffusive transport between concentric spherical shells which will give a better assessment of the time dependence of densification high density (>95%); the driving force is (Pa/D+γk) in this case also. Because of the fact that the pore size is some unknown function of density, the rate equations cannot be integrated without further information. It is shown that of the various relations which have been assumed in development of models for hot pressing, for the effective stress in relationship to the applied stress and the porosity, (Pa/D) is the only form which satifies the criteria demanded by self‐consistency in generation of steady‐state diffusion models.

Diffusion‐Limited Phase Transformations: A Comparison and Critical Evaluation of the Mathematical Approximations

Abstract: Mathematical analyses previously made for diffusion‐limited growth and dissolution of spherical and planar precipitates have been reviewed. The analyses include the invariant‐field (Laplace), the invariantsize (stationary interface) and the linear‐gradient approximations, and where possible, exact solutions of the differential time‐dependent diffusion equation and of the independent flux balance. The kinetic parameters are calculated and the different solutions compared. For virtually all cases of practical interest it is shown that the stationary‐interface approximation is the best one. By considering a reversed‐growth analysis and showing that it is merely an approximation to the dissolution of a spherical precipitate, it is thereby shown that growth and dissolution cannot be generally considered as simply conjugate processes.

Magnetic Properties of Stable Dispersions of Subdomain Magnetite Particles

Abstract: Stable colloidal dispersions of subdomain‐size magnetic particles have been prepared that retain their liquid characteristics in the presence of a magnetic field. Magnetization versus applied field curves were obtained as a function of particle size and volumetric solids concentration for magnetite dispersions in a wide variety of carrier liquids. The magnetic properties of these colloidal dispersions have been corrolated by superparamagnetic theory in terms of the size distribution of the suspended particles and their volumetric concentration, correcting for the formation of a nonmagnetic surface mantle one‐unit‐cell thick.

Morphology of Epitaxial Growth of GaAs by a Molecular Beam Method: The Observation of Surface Structures

Abstract: Homoepitaxial growth of GaAs was studied in situ in an ultrahigh‐vacuum high‐energy electron diffraction (HEED) system. Two surface structures, GaAs(111)−(19)1/2 and GaAs(111)−2, were observed during growth. The transition from one surface structure to the other was found to be a function of the deposition rate and the substrate temperature, with the high‐temperature structure being the (111)−(19)1/2. The film growth morphology was studied by the carbon replication technique. Growth by a step mechanism was observed on a bromine‐methanol etched surface while three‐dimensional nuclei were observed on a polished or contaminated surface.

Thermal Currents from Corona Charged Mylar

Abstract: Thermal currents have been obtained from corona‐charged Mylar. The results are interpreted in terms of electron and/or ion trapping and subsequent release upon reheating. A theory is developed for thermal release of these ``near surface'' charged specimens when no external field is applied. A new method is presented to obtain energies for a series of peaks present in complex thermal current spectra. The trapping parameters are also determined using both the initial rise analysis of Garlick and Gibson, and the curve fitting technique of Cowell and Woods. The results are consistent with four discrete traps in Mylar at depths of 0.55, 0.85, 1.4 and 2.2 (all ±0.1) eV. The 0.55‐ and 0.85‐eV traps are electronic, that at 1.4 eV is either an electronic trap with a Coulomb barrier, or ionic. The 2.2‐eV trap is either ionic, interfacial, or involves dissociation of a complex with subsequent release of an electron to the conduction band. Assuming that the traps empty under monomolecular conditions, analysis of the ...

Structural Investigation of Noncrystalline Nickel‐Phosphorus Alloys

Abstract: The structure of noncrystalline electrodeposited Ni–P alloys, 73.8–81.4 at.% Ni, has been investigated by x‐ray scattering and by physical density measurements. The x‐ray interference functions, I(k), are qualitatively inconsistent with those calculated for fcc‐, hcp‐, and Ni3P‐type crystallites. Calculated radial distribution functions RDF(r) indicate that the alloys have a better defined short‐range order than that observed in liquid noble metals above their melting points. The observed I(k) are very similar to the I(k) calculated by Dixmier, Doi, and Guinier [in Physics of Noncrystalline Solids, J. A. Prins, Ed. (North‐Holland Publ. Co., Amsterdam, 1965), p. 67] from their model. However, the parameters needed to fit the experimental results are inconsistent with the atomic sizes expected for nickel and phosphorus. The noncrystalline alloys are between 0.6% and 1.4% less dense than the corresponding mixtures of fcc Ni and Ni3P, both of which are essentially close packed. A grain boundary density defici...

Temperature Dependence of the Transport Properties of Gallium Arsenide Determined by a Monte Carlo Method

Abstract: Transport properties of gallium arsenide in an electric field have been calculated in the temperature range 77°–500°K using a Monte Carlo technique. In intrinsic material it is found that the threshold field for the onset of negative differential mobility changes only slightly over this temperature range increasing from 3.1 kV/cm at 77°K to 3.7 kV/cm at 500°K, while the negative differential mobility reduces from 4200 to 1000 cm2/V sec over the same temperature rise. The influence of impurity scattering on the velocity field characteristic has been considered at 77°K for impurity concentrations of 1015 and 1017 cm−3 and at 300°K for concentrations for 1013, 1015, and 1017cm−3. The threshold field for the onset of negative differential mobility is found to change only slightly while the peak‐to‐valley ratio decreases significantly with increasing impurity concentration. The temperature dependence of the low‐field mobility has been calculated for impurity concentrations of 1015, 1016, and 1017 cm−3.

Interface Barrier Energy Determination from Voltage Dependence of Photoinjected Currents

Abstract: Interface barrier energies and their dependence on applied field may be obtained from the voltage dependence of currents produced by electron photoinjection from an electrode. Unlike the conventional Fowler plot method, direct measurement is possible and knowledge of the absorbed light intensity is not required. A theoretical analysis gives the dependence of photocurrent on voltage and photon energy, and it is shown that barrier heights are obtainable by examination of the V‐I characteristics to determine the sign of the second derivative. Theoretical forms of the V‐I characteristics are derived for specific electron energy distributions which should be generally applicable. Experimental results from MIS structures using thermally grown SiO2 on degenerate n‐type silicon are found to be in good agreement with theoretical predictions. Thresholds for emission from the conduction band (3.2 eV) and from the valence band (4.16 eV) are clearly defined in the V‐I characteristics. The fact that the difference betw...

Electromigration Damage in Aluminum Film Conductors

Abstract: Electromigration studies of large‐ and fine‐grain aluminum films showed that fine‐grain films were characterized by a mixed orientation and a grain size of ≈2 μ, and that large‐grain films had a highly preferred 98% 〈111〉 orientation and a grain size of ≈8 μ. Stripes fabricated from the large‐grained films had a consistently longer life, higher activation energy, and lower standard deviation of the life distribution than stripes fabricated from fine‐grained films. These results are interpreted in terms of the nature of flux divergences in the two films. Calculations give the magnitude of vacancy supersaturations at various structural divergences present in the films studied.

Effects of Various Heating Rates on Glow Curves

Abstract: Methods for evaluating activation energies and escape frequency factors from glow curves by the use of various heating rates are discussed. For first‐order peaks, the method of finding the glow parameters by measuring the shift of the maximum temperature with changing heating rate is generalized. This method, known to be true for linear and exponential heating rates, is shown in the present paper to hold true for any monotonically increasing heating function. The method using the variations in the maximum intensity with changing heating rates, previously known to apply for certain thermally stimulated current peaks is proved to be true for all first‐order peaks. Analogous methods are found for general‐order peaks, an important special case of which are the second‐order peaks. Computer calculations as well as experimental results in ZnS:Er3+ samples are given as a check. These methods are of special value when the peaks are not ``clean'' since the quantities used are measured only at the maximum point.

Dielectric Properties of Bismuth Titanate

Abstract: Three‐terminal dielectric measurements of the weak‐field permittivity have been carried out on single crystals of bismuth titanate (Bi4Ti3O12), which contained only ``narrow‐angle'' twin walls. The pseudo‐orthorhombic ea, eb, ec in these twinned monoclinic crystals show strong dispersion in the frequency range 100 Hz‐1 mHz, and only above 1 mHz are the data representative of the intrinsic properties. The dispersion is thought to arise from space charge developed through the high conduction current at elevated temperatures and not from domain wall motion or damped piezoelectric resonance.

Thermal Effects in a Nd:YAG Laser

Abstract: A theoretical model for the thermal lens and birefringent effects induced in a continuously pumped Nd:YAG rod is developed. Experimental measurements of these effects using a 6328‐A probe are described and compared to theory. Excellent agreement between the two types of measurements and theory is obtained. The thermally birefringent and bifocusing phenomena are suggested as causes of reductions in the polarized and fundamental TEM00 powers from a high‐power multimode Nd:YAG laser. Typical results are described using a laser which operates in the 200−300‐W range of average powers.

Fracture of Bone

Abstract: Fracture of bone is investigated by measuring the energy required to propagate a crack and by observing, microscopically, the mechanism of fracture. At low strain rates bone displays very high resistance to crack propagation comparable even to some metallic materials. The type of fracture is similar to fiber‐reinforced composite materials.

Microwave Behavior of Partially Magnetized Ferrites

Abstract: The high‐frequency permeability of partially magnetized ferrites is calculated for some simple domain configurations, comprising only ``up''‐ and ``down''‐domains. The method used is based upon the magnetostatic approximation and neglects exchange effects, but is otherwise substantially rigorous. The components of the effective permeability tensor (ratio of average induction to average magnetic field) in general depends upon details of the domain configuration in addition to the net dc magnetization. When the dc magnetization is cycled between the two states of complete magnetization the high frequency permeability, considered as a function of the dc magnetization, in general shows hysteresis. Detailed calculations of the high‐frequency permeability have been carried out for the case in which the domain configuration is cylindrically symmetric, i.e., invariant under rotation around the direction of magnetization. For any such domain configuration the two relevant components μeff and κeff of the effective ...

Electron Mobility in High‐Purity GaAs

Abstract: The combination of polar optical phonon, piezoelectric acoustic photon, deformation potential acoustic phonon, ionized impurity, and neutral impurity scattering in the relaxation time approximation is shown to give results which are in good agreement with the temperature and concentration dependence of the electron mobility in high‐purity GaAs. For polar optical phonon scattering a relaxation time is defined at each temperature from Ehrenreich's variational calculation. Since most of the parameters are well known, the only adjustable parameter in the calculation is the conduction band deformation potential with the best agreement with experiment given by | E1 | = 7.0 eV. Using this value a 77°K lattice scattering limited mobility of 240 000 cm2/V sec is obtained.

Effect of Pressure on the emf of Chromel‐Alumel and Platinum‐Platinum 10% Rhodium Thermocouples

Abstract: A differential technique has been used to measure the absolute effect of pressure on the emf of Chromel‐Alumel and Pt‐Pt10Rh thermocouples. The experiments were conducted in a solid pressure medium piston‐cylinder apparatus to 35 kbar and 1000°C. Extrapolation of these data shows Chromel‐Alumel to read as much as 28°C high at 50 kbar and 1200°C and Pt‐Pt10Rh as much as 28°C low at 50 kbar and 2000°C. Graphs are presented which show correction voltage versus temperature for various pressures.

Theory of the Static Stability of Cylindrical Domains in Uniaxial Platelets

Abstract: A theory of the static stability of circular cylindrical domains in uniaxial magnetic platelets has been developed. The predictions of the theory agree well with experiments and provide requirements which link material properties to domain geometry. The theory is developed by assuming a model in which the domains have cylindrical walls of zero width and by then calculating the size and stability of the domains, using a straightforward although somewhat lengthy energy method. It is found that in order for domains to exist Ku⪞2πMs2, where Ku is the uniaxial anisotropy constant and Ms is the saturation magnetization. However, the model is most accurate when Ku≫2πMs2, although in this case the domains tend to have a low mobility. A formula relating domain size to the material parameters, the plate thickness and the applied bias field is obtained. More important, static stability considerations indicate that when all parameters except the bias field are held constant the domains are stable only over a 3:1 diam...

Hot Electron Effects and Saturation Velocities in Silicon Inversion Layers

Abstract: Carrier mobility variations were measured for electrons in silicon inversion layers. Near liquid‐helium temperatures and with electron densities less than about 2×1012 cm−2, the mobility increased with field and temperature. Correlation of the electron temperature with field indicates that ΔT varies with the field approximately as F3/2. Temperature dependence of the amplitude of the oscillatory magnetoconductance gave similar consistent results. At very high fields, the mobility decreased at all temperatures and electron densities. The electron drift velocity was measured for different surface orientations, substrate dopings, and ambient temperatures from 4.2° to 300°K. The drift velocity was found to saturate for fields greater than a few times 104 V/cm, depending upon the low field mobility, and was found to be lower than the reported bulk values. For (100), (111), and (110) surfaces, the limiting velocities at 300°K are (6.5±0.5) × 106, (5.5±0.5) × 106, and (4.0±0.5) × 106 cm/sec, respectively.

Mechanism of Inclusion Damage in Laser Glass

Abstract: The mechanism of inclusion damage in laser glass is associated with the temperature rise of particles, or surface regions of particles, relative to the surrounding glass. The particles of greatest concern are metallic, although at very high‐power levels ceramic inclusions containing large concentrations of highly absorbing ions can likewise result in failure. Solutions to the heat‐flow problems of a perfectly conducting sphere in a medium of finite conductivity and of the infinite composite solid indicate that temperatures of metal particles subject to a 20‐J/cm−2, 30‐nsec laser pulse can exceed 10 000°K for a range of particle sizes. These high temperatures produce stresses in the glass adjacent to the particles which can exceed the theoretical strength of the glass, and result in failure. The effects on the breakdown condition of flux level and pulse time, as well as the size, shape, thermal expansivity, and spectral emissivity of the particle, and the heat capacity and thermal conductivity of particle and glass are specified. Observations of damage morphologies are reported and related to the results of the calculations. A fatigue phenomenon is anticipated under certain conditions, and the phenomenon of phase separation is not expected to affect significantly the process of inclusion damage. Likely sources of metallic inclusion particles in laser glasses are considered, and melting conditions most suitable for their avoidance are discussed.

Amorphous versus Crystalline GeTe Films. III. Electrical Properties and Band Structure

Abstract: Various transport studies have been carried out on amorphous and crystalline GeTe films of 80 A to 10 μ thickness. Crystalline GeTe has a low resistivity (∼10−4 Ω·cm at 300°K) which increases with temperature slowly and nearly linearly at low temperatures (below ∼300°K) and rapidly at higher temperatures. The hole concentration (N∼1010−1021 cm−3) increases only slightly with temperature. Mobility varies as N−4/3. These results in conjunction with the tunnel‐spectroscopy and optical data show that crystalline GeTe is a degenerate (and thus metallic conduction), p‐type narrow band gap (∼0.1–0.2 eV) semiconductor with Fermi level ∼0.3–0.5 eV inside the valence band. The linear increase of the susceptibility mass with hole concentration, the constancy of the Hall coefficient up toωLτ=0.35 (ωL=Larmor frequency, τ=collision relaxation time), and the monotonic increase of thermopower with temperature indicate that conduction takes place only in a single valence band. Amorphous GeTe films exhibit activated conduction. The dc resistivity varies from 410° to 77°K as ρ0 exp (Eg/2kT), where Eg is about 0.8 eV and ρ0 is the resistivity of crystalline GeTe films. Ac resistivity decreases with frequency (ω) as ω−n, where n lies between 0.5 and 1.0, depending on the temperature. The activation energy for ac conduction decreases rapidly from the dc value to zero with decreasing temperature as well as increasing frequency. The capacitance of amorphous GeTe at 77°K varies as ω−0.2 while the loss factor is independent of the frequency. With increasing dc field, the linear dependence of current on voltage changes to a power relation Vn, where n varies rapidly from ∼3 to 6 or more in a small range of the applied field. At very high fields, I ∝expβF1/2 (β=constant) is observed. These results, together with the tunnel‐spectroscopy, and optical data suggest that amorphous GeTe may be represented as a p‐type semiconductor with band gap ∼0.8 eV with exponential tailing of the bands and a continum of localized states in the vicinity (both sides) of the band edges. Conduction takes place by two parallel processes of intrinsic excitation across the band gap, and thermally and/or field‐assisted hopping from one localized (trapping) state to another. Dc conduction by hopping at low fields is negligible. At higher fields, trap modified space‐charge‐limited current flow and Poole‐Frenkel effect determine the nonlinear field dependence of current.

Thermal Expansion of Copper from 20 to 800 K—Standard Reference Material 736

Abstract: Copper is the first of a series of materials that will be certified as thermal‐expansion standards by the National Bureau of Standards. The results of tests on five specimens indicate the stock is of consistent quality so that it may be certified as Standard Reference Material 736. A Fizeau interferometer was used for the expansion measurements. Above room temperature a controlled‐atmosphere furnace using a calibrated Pt vs Pt‐10% Rh thermocouple was used. Below room temperature a cryostat capable of operation with both liquid nitrogen and helium was used with a calibrated platinum resistance thermometer. Values of expansivity were calculated between equilibrium temperatures. The expansivity was used in the analysis of the data. Third‐order polynomials were fitted to the data for each of the five specimens in the overlapping temperature ranges from 0 to 70 K, 50 to 270 K, and 210 to 800 K to test for variations between the specimens. The deviations between the five equations were well within the standard deviations of the data for each of the specimens in the respective temperature intervals. All the expansivity data were then pooled and used to obtain an equation for each of the temperature ranges given above. These equations and their integrals were used to calculate the final values of expansivity and expansion, respectively. The results of the statistical analysis of the expansion and expansivity data are presented. A comparison is made with the data in the literature.

Plane Stress Wave Propagation in Solids

Abstract: This paper shows that in general, plane stress waves in solids or fluids exhibit two phase velocities. One of these is associated with the stress profile of the wave and the other with the mass‐velocity profile. These velocities are distinct except for isentropic simple waves, steady flow, or discontinuous fronts, As a result, the determination of time‐dependent constitutive relations from shock‐wave experiments requires more measurements than has heretofore been recognized.