Showing papers by "National Institute of Standards and Technology published in 1970"

Stress Corrosion and Static Fatigue of Glass

Abstract: Stress corrosion cracking of six glasses was studied using fracture mechanics techniques. Crack velocities in water were measured as a function of applied stress intensity factor and temperature, and apparent activation energies for crack motion were obtained. Data were consistent with the universal fatigue curve for static fatigue of glass, which depended on glass composition. Of the glasses tested, silica glass was most resistant to static fatigue, followed by the low-alkali aluminosilicate and borosilicate glasses. Sodium was detrimental to stress corrosion resistance. The crack velocity data could be explained by the Charles and Hillig theory of stress corrosion. It is probable that stress corrosion of glass is normally caused and controlled by a chemical reaction between the glass and water.

Submodular functions, matroids, and certain polyhedra

Abstract: The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all bases have the same cardinality. (See Van der Waerden, Section 33.)

Solubility of CaHPO4 · 2H2O in the System Ca(OH)2-H3PO4-H2O at 5, 15, 25, and 37.5 °C.

Abstract: Solubility isotherms of beta-tricalcium phosphate, β-Ca(PO4)2, prepared by heating mixtures of CaCO3 and CaHPO4 above 800 °C, were determined in the ternary system Ca(OH)2-H3PO4-H2O at 5, 15, 25, and 37 °C in the pH range 6.0-7.5 by equilibration with dilute H3PO4 solutions. The results indicate that β-Ca3(PO4)2 has a negative thermal coefficient of solubility. The solubility product, K s , was determined as a function of temperature by a generalized least-squares procedure; the resulting equation is log K s = - 45723.26 / T + 287.4536 - 0.546763 T ; the values of K s and its dispersion at 25 and 37 °C are 1.20(0.056), and 0.283(0.011) × 10-29. Thermodynamic functions for the dissolution of the salt at the four experimental temperatures are reported. When treated as an adjustable constant, the Ca/P ratio in these β-Ca3(PO4)2 solutions was found to have the value 1.514(0.010), confirming that the stoichiometry of the high temperature form of this salt is correctly indicated by the above formula. The computed isotherms at 25 °C for several calcium phosphates are compared; it is shown that β-Ca3(PO4)2 is, next to Ca5(PO4)3OH, the most stable at pH's above 6.36. The singular points of the β-Ca3(PO4)2 isotherm with those of CaHPO4 · 2H2O and CaHPO4 are at pH's 5.88 and 6.36, respectively.

Metastable Immiscibility Surface in the System Na2O‐B2O3‐SiO2*

Abstract: Opalescence and clearing techniques were used to determine the metastable immiscibility surface for sodium borosilicate solutions. These results indicate that a three-liquid region, which may or may not be metastable to two-liquid regions, underlies the immiscibility surface.

Bremsstrahlung and Photoneutrons from Thick Tungsten and Tantalum Targets

Abstract: Monte Carlo calculations have been made of electron-photon cascades in thick tungsten targets bombarded by electrons with energies up to 60 MeV. The following information has been obtained: (1) the bremsstrahlung efficiency, (2) the angular distribution of the emitted bremsstrahlung intensity, (3) the spectra of the bremsstrahlung emitted in various directions, (4) the transmission of primary and secondary electrons through the target, (5) energy deposition as function of the depth in the target, (6) the differential photon track length distribution inside the target, and (7) the yield of photoneutrons. The paper also includes various comparisons with experimental data.

Landau Diamagnetism from the Coherent States of an Electron in a Uniform Magnetic Field

Abstract: A complete set of coherent-state wave packets has been constructed for an electron in a uniform magnetic field. These states are nonspreading packets of minimum uncertainty that follow the classical motion. Use was made of the ladder operators that generate all the eigen-states of the Hamiltonian from any one energy eigenstate. The coherent states are the eigenstates of the two ladder operators that annihilate the zero-angular-momentum ground state. We have calculated the partition function, exploiting advantages of the coherent-state basis. The Landau diamagnetism and the de Haas-van Alphen oscillations are contained in the coherent-state framework.

Cross terms in the thermodynamic diffusion equations for multicomponent alloys

Abstract: The kinetic equations for the atom fluxes in a multicomponent alloy are derived in terms of atomic driving forces for a random alloy model. In this model, the contribution to each atom flux from the vacancy wind effect is directly proportional to the vacancy flux. The kinetic equations when written in the same form as the thermodynamic diffusion equations allow theL ik coefficients to be identified. The cross terms relating the flux of speciesi to the chemical potential gradients of other speciesk are found to be nonzero. These cross terms can have an appreciable effect on the atom fluxes and can lead to negative intrinsic diffusion coefficients even in ideal systems. Neglecting the cross terms can lead to serious inaccuracies. TheL ik in ann-component system depend on then tracer diffusion coeficients. In this respect, it still is possible to express then atom fluxes in terms of onlyn coefficients.

Crack Healing in Glass

Abstract: Cracks in soda-lime-silica glass specimens closed spontaneously; the recovery in strength was determined by fracture mechanics techniques. Approximately 80% strength was recovered in cracks formed by mechanical shock, whereas approximately 20% was recovered in cracks that closed after being held open to the atmosphere for several minutes. The high strength recovery in the mechanically shocked specimens is attributed to the very active surface formed during fracture. If the surface is allowed to adsorb O2 or H2O vapor, the activity is reduced, and healing is less complete. Crack healing can introduce surface flaws into glass that cannot be detected by current methods of nondestructive testing.

Hydrogen Stark broadening calculations with the unified classical path theory.

Abstract: The unified theory has been generalized for the case of upper and lower state interaction by introducing a more compact tetradic notation. The general result is then applied to the Stark broadening of hydrogen. The thermal average of the time development operator for upper and lower state interaction is presented. Except for the time ordering it contains the effect of finite interaction time between the radiator and perturbers to all orders, thus avoiding a Lewis type cutoff. A simple technique for evaluating the Fourier transform of the thermal average has been developed. The final calculations based on the unified theory and on the one-electron theory are compared with measurements in the high and low electron density regime. The unified theory calculations cover the entire line profile from the line center to the static wing and the simpler one-electron theory calculations provide the line intensities only in the line wings.

Surface States on Tungsten

Abstract: The energy distribution of field-emitted electrons from single-crystal faces of tungsten exhibits structure which is extremely sensitive to surface contaminants. The structure for the (100) plane has the correct shape and energy expected for surface states resulting from spin-orbit---split bands. These results are in good agreement with recent theoretical predictions.

A Report on the Accuracy of Some Widely Used Least Squares Computer Programs

Abstract: Linear least squares test problems based on fifth degree polynomials have been run on more than twenty different computer programs in order to assess their numerical accuracy. The programs tested, all in present-day use, included representatives from several statistical packages as well as some from the SHARE library. Essentially five different algorithms were used in the various programs to obtain the coefficients of the least squares fits. The tests were run on several different computers, in double precision as well as single precision. By comparing the coefficients reported, it was found that those programs using orthogonal Householder transformations, classical Gram-Schmidt orthonormalization or modified Gram-Schmidt orthogonalization were generally much more accurate than those using elimination algorithms. Programs using orthogonal polynomials (suitable only for polynomial fits) also proved to be superior to those using elimination algorithms. The most successful programs accumulated inner...

Crystallization of sheared polymer melts

Abstract: The Crystallization kinetics of molten polyethylene subjected to a constant shear stress were investigated theoretically and experimentally. The rate of crystallization depends on the difference of entropy (Δs) between the crystalline and molten state. The constant shear stress in the melt decreases Δs causing an abrupt increase in the rate of crystallization and a decrease of the thickness of the folded-chain lamellar crystals.

Field-Emission Studies of Electronic Energy Levels of Adsorbed Atoms

Abstract: The relative changes in the total energy distribution of field-emitted electrons upon adsorption of single atoms have been measured for adsorption of the alkaline-earth atoms (Ba, Sr, and Ca) on several crystal planes of tungsten. The expected perturbations of the energy distribution due to the tunneling resonance through an atomic "virtual level" at various positions relative to the Fermi surface and of various half-widths $\ensuremath{\Gamma}$ is demonstrated by a simple one-dimensional calculation. The measured energy-dependent structure in the current-enhancement factor due to the adsorbate has been interpreted in a tunneling-resonance model to yield the positions and shapes of the atomic "virtual levels." The ground-state $^{1}S$ $6{s}^{2}$ level of Ba is broadened to a half-width ${\ensuremath{\Gamma}}_{S}=0.75$ eV and shifted upward by $\ensuremath{\Delta}{E}^{S}=0.95$ eV. This causes it to overlap and mix with the first two excited states: a triplet $^{3}D$ $6s5d$ and a singlet $^{1}D$ $6s5d$. The observed $^{3}D$ and $^{1}D$ levels were not shifted and had a half-width ${\ensuremath{\Gamma}}_{D}=0.1$ eV. Similarly, the first excited state of Ca, a triplet $^{3}P$ $4s4p$, was shifted by $\ensuremath{\Delta}{E}^{3\mathrm{P}}\ensuremath{\approx}0.4$ eV with a width ${\ensuremath{\Gamma}}_{3\mathrm{P}}\ensuremath{\approx}0.3$ eV ($2\ensuremath{\Gamma}=\mathrm{FWHM}$). The effect of the band structure of the substrate on tunneling resonance is discussed.

Crystal Growth Mechanisms: Energetics, Kinetics, and Transport

Abstract: Publisher Summary This chapter reviews a survey and organizes the extremely diverse phenomena coming under the heading of crystallization, and presents a physics framework for understanding their mechanisms. This framework consists of the application of statistical mechanics, thermodynamics, kinetic theory, and especially transport theory to crystallization problems. The chapter emphasizes the quantitative approach on well-defined systems, both for experiment and theory. The subject of the growth of crystals is an interdisciplinary one, in the sense that contributions to this field have been and continue to be made by scientists and engineers from many professional fields: solid-state physicists, mineralogists, crystallographers, physical chemists, mathematicians, chemical engineers, metallurgists, and probably many others. A similar diversity exists in the wide range of media of publication of the research, and in the departments of universities and research organizations in which the work is performed. The chapter discusses crystallization problems by analyzing them from the point of view of a particular discipline of physics. It begins with the more general disciplines—that is, thermodynamics and statistical mechanics and proceeds to more specialized ones—that is, mass transport and fluid flow.

Proposed Secondary-Standard Wavelengths in the Spectrum of Thorium*

Abstract: Energy levels of Th lines computed from weighted averages of interferometrically measured wavelengths data

Atmospheric Oxygen in 1967 to 1970

Abstract: Observations of atmospheric oxygen in clean air between 50°N and 60°S, mainly over the oceans, yield an almost constant value of 20.946 percent by volume in dry air. Since 1910 changes with time over the globe appear to be either zero or smaller than the uncertainty in the measurements.

Polymorphism in Benzene, Naphthalene, and Anthracene at High Pressure

Abstract: Optical observations, in which a microscope was used with the diamond-anvil pressure cell, were carried out on benzene, naphthalene, and anthracene up to temperatures of about 600 degrees C and pressures of approximately 40 kilobars. New high-pressure phases of benzene (benzene III) and anthracene (anthracene II) were observed, and the existence of the high-pressure polymorph, naphthalene II, was verified. All three materials decompose initially to a reddish-orange liquid, and ultimately to amorphous carbon. The decomposition temperatures decrease with increasing molecular size.

Correction of near-field antenna measurements made with an arbitrary but known measuring antenna

Abstract: We describe a technique for rigorously correcting for the effects of an arbitrary but known measuring antenna (or ‘probe’) in determination of vectorial far-field antenna pattern and power-gain function from near-field measurements.

P-V-T, Thermodynamic and Related Properties of Oxygen from the Triple Point to 300 K at Pressures to 33 MN/m2.

Abstract: The results of new experimental pressure-volume-temperature measurements on oxygen are presented. The data range in temperature from 54 to 300 K and in pressure from 0.1 to about 33 MN/m2. The following properties are tabulated for selected isobars: molar volume, (∂P/∂ρ) T , (∂P/∂T)ρ, internal energy, enthalpy, entropy, specific heats at constant volume and at constant pressure, and the velocity of sound. Additional tables present the above properties for saturated liquid and vapor, the freezing liquid P-V-T relationship, and the derived Joule-Thomson inversion curve. New values for the critical density and triple point density are presented, and the second and third virial coefficients are tabulated.