Effect of phosphorus additions on the spacing between primary silicon particles in a Bridgman solidified hypereutectic Al-Si alloy

The effect of 100 ppm addition of phosphorus on primary silicon particle number density per unit area N _A and corresponding interparticle spacing is reported for a Bridgman solidified Al-20 wt%Si base alloy. The phosphorus (added as Al-Fe-P base or Al-Cu-P alloys) results in a factor of 3 increase in N _A and a factor of 2 reduction in for the range of conditions studied. In its absence the results conform to = 256 ± 24 m (K/s)_1/3 where is cooling rate during solidification in good agreement with earlier data. When published data on the effect of 0.02 to 0.2 wt%P are included the combined results are well represented by = 250 – 215 (wt%P)^0.17 ( in m, in K/s).     

Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation

Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols a General dependent variable - a ^(mn) Terms of the asymptotic expansion of a(x) - b Characteristic length - c Scalar curvature components in the normal direction - c , c , , c Cosine of , respectively - C Material constant with units of a Young's modulus - e _i Deformed local orthonormal basis associated with (, s, n)(x ₁, x ₂, x ₃) coordinates - Undeformed cylindrical coordinate basis - Intermediate coordinate basis - g Shear correction factor - H Horizontal stress resultants - l ₁ Strain invariant - k Scalar curvature components - L Undeformed cylinder length - M Moment resultants - M _r, M , M _z Moment resultant components in the basis - N Membrane stress resultants - p Internal pressure - p _H, p _v Horizontal and vertical surface loads, respectively - p _i Thickness-averaged surface tractions - Q Transverse shear stress resultants - , r Radial coordinate prior to, after deformation - R Undeformed cylinder radius - , s Meridional coordinate prior to, after deformation - s , s _x, , s Sine of , respectively - , S Reference surface prior to, after deformation - S ₁, S ₂ Shear stress resultants parallel to the reference surface - S ₃ Average transverse normal stress resultant - t Undformed shell thickness - T Axial torque - V Vertical stress resultants - w Two-dimensional strain-energy density function - w _n Terms in expansion for w - W Three-dimensional strain-energy density function - x Undeformed axial coordinate in cylinder - , z Axial coordinate prior to, after deformation     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Phonon Vibration and Conduction of La2 ? xSrxCuO4 ? δ and La1.85 ? xSr0.15 + xCu1 ? xCoxO4 ? δ

Polycrystalline samples La_{2 – x} Sr _x CuO_{4 –} (0.06 x 0.5) and La_{1.85 – x} Sr_{0.15 + x} Cu_{1 – x} Co _x O_{4 –} (0 x 1) were synthesized by a conventional solid state reaction method. The structure, phonon vibration, and conduction were investigated by means of XRD, infrared (IR) spectra, and resistance. It is found that the increase of itinerant hole carriers could mask the in-plane stretching vibration mode (689 cm^–1). The softening of the phonon vibration mode gives an index of the weakening of hybridization. The distortion of CuO₆ octahedron and the microstructural inhomogeneity induced by Co doping lead to the widening of the IR absorption peaks.     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

A Monte Carlo Study of Disorder in the High Pressure Mixed Crystal N2-Ar

In order to obtain a better notion of the experimental results in our laboratory, Monte Carlo calculations have been performed of the N ₂-Ar crystal on the N ₂-rich side, in the p-T region where the and phases exist in pure N ₂. Considering the enthalpy, the system prefers the Ar atoms to be located on the sphere positions. The * phase is present for mixtures down to but is most likely metastable. The *-* transition shifts to lower temperatures with decreasing . The 2 ^nd order transition within the phase continues to exist to even smaller . In contrast to the * -* transition, the transition temperature for the 2 ^nd order transition does not shift to lower temperatures. For a mixture of it is within 5 K from the pure 2 ^nd order transition at a pressure of 7.0 GPa.     

Nonlinear liquid oscillations in spherical systems under zero-gravity

Summary Nonlinear free oscillations of the interface of a concentric frictionless immiscible liquid system in a spherical container are investigated in a zero-gravity environment. The natural frequencies are determined for the axisymmetric and asymmetric oscillations of the interfacial surface with the diameter ratio and density ratio as parameters. It was found that for small outer- to inner liquid density ratio the oscillations exhibit softening, while for large density ratios it renders hardening oscillation. The asymmetric oscillations exhibit in the softening range softer and in the hardening range harder liquid oscillations. For a liquid layer around a rigid center sphere the oscillations of the free liquid surface yields softening behavior, where for thinner layers the softening effect is more pronounced.Nomenclature a radius of spherical container, or radius of rigid center sphere - b radius of undisturbed interfacial surface, or radius of undisturbed free liquid surface - k=a/b diameter ratio - pressure - pressure (dimensionless) - , , spherical coordinates - dimensionless radius - R _i main radii of curvaturei=1, 2 time - dimensionless time - v _i liquid velocity (j=1 spherical layer region,j=2 inner liquid sphere region) - V volume of the liquid - Y _nm tesseral surface harmonics - _i density of liquids - velocity potential - dimensionless velocity potential - interfacial surface- or free surface elevation - dimensionless interfacial surface- or free surface elevation - ₀ maximum elevation - circular frequency - circular frequency - _n0 axisymmetric natural frequency - _n1 asymmetric natural frequencym=1 - _nm ⁽⁰⁾ natural frequency of linearized liquid system - mean curvature - _nm Kronecker symbol With 10 Figures     

Response of a spinning liquid column to axial excitation

Summary The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀).Notation a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - P liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _02n –1 natural frequency of harmonic axial response With 8 Figures     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

Neutron Diffraction Studies of Nuclear Magnetic Ordering in Silver

Nuclear antiferromagnetism in fcc silver metal, already investigated by NMR measurements, has been studied in a single crystal of ¹⁰⁹ Ag by neutron absorption and diffraction techniques. Below the Neel temperature T_N , a (001) Bragg reflection with a resolution limited width demonstrates long range order in a simple type-I AFM structure with the ordering vector k = (2/a)(001) (up-down structure). The entropy at the transition, ln 2 in zero magnetic field, corresponding to a critical polarization P_c = 0.75 and T_N = 700 ± 80 pK. Magnetic field B versus entropy S phase diagrams of the (001) structure have been constructed for two directions of B: [001] and The critical field extrapolated to S = 0 is 100 ± 10 T, and for both field directions S_c is highest around B = 30 T. The transition to the paramagnetic state is presumably of second order. The nuclear magnetization was measured by transmission of unpolarized neutrons, and the dimensionless static volume susceptibility in SI units was found to be 0.36 ± 0.01 in the ordered state independently of B and S. The ac susceptibility at 7.9 Hz showed a kink at the transition only when the sample was not exposed to neutrons.     

A quantitative study of the quantum interferometer in pure magnesium

The quantum interferometer oscillations observed in the transverse magnetoresistance of Mg at liquid helium temperatures forJ[11 0] andH[1 00] have been experimentally investigated in detail. A new method of analyzing these quantum interference oscillations has been developed which permits direct line shape comparison between the experimentally observed magnetoresistance oscillations and theoretical calculations based on the stacked-mirror model of quantum transport. By using the stacked-mirror model in conjunction with the line shape comparison technique, virtually all of the approximations made in the initial studies of the quantum interferometer have been eliminated. Distinct and striking line shape changes in the magnetoresistance oscillations, critically dependent on the angle between the direction of the applied magnetic field and the basal plane of the Mg crystal, have also been observed and analyzed. This phenomenon provides direct evidence for the existence of long-range quantum phase coherence of the electron states in the Mg crystal over dimensions of 0.3 mm, corresponding to a quantum state lifetime of 3.5×10^–10 sec. Experimental values for the three magnetic breakdown parameters that characterize the quantum interferometer in pure Mg areH ₁(k _H =0)=3000±75 G,H ₂(k _H =0)=10,000±1500 G, andH ₃(k _H =0)=1000±250 G. Experimental evidence is also presented which shows a magnetic field dependence of the quantum state lifetime for some of the crystals studied.Presented as a thesis to the Department of Physics, The University of Chicago, in partial fulfillment of the requirements for the Ph.D. degree.Supported by NSF Grant GS-39932.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

Decay of 175Hf and 181Hf

Nuclear-physical properties of ¹⁷⁵Hf and ¹⁸¹Hf produced by neutron irradiation of natural hafnium in the SM-3 nuclear reactor were studied. The X-ray and -ray spectra were measured with high-energy-resolution HPGe and Ge(Li) detectors. The half-lives T1/2 (days) were determined: ¹⁷⁵Hf 71.9±1.3 and ¹⁸¹Hf 42.12±0.25. The relative intensities (rel. units) of the -ray lines (keV) of ¹⁸¹Hf are as follows: 133.03, 54.0±1.6; (136.28 + 136.86), 8.9±0.3; 345.919, 20.4±0.6; and 482.193, 100. The ratios of the intensities in the X-ray spectrum were measured: , , , and .     

Extrudate distortion studies of polystyrene using an extrusion rheometer

Uncorrected and corrected logarithmic flow-curves for a general purpose polystyrene (MW=261000 and MW/MN=4.4) obtained using a Davenport Extrusion Rheometer are shown for the range 160 to 200° C. The uncorrected flow curves show a change in slope, but at the lower extrusion temperatures this change occurs after the appearance of distorted extrudates. The onset of extrudate distortion obtained from observation does not coincide with the change in slope of the graph. The corrected logarithmic flow curves show no change in slope. Values of and _c from both sets of graphs show that is inversely proportional to _c, and for the higher melt temperatures the corrected _c values increase with temperature. The high value of critical wall stress at 160° C is attributed to the increase in melt elasticity with decreasing temperature being a greater effect than the decrease in elasticity due to a decrease in .     

Liquidus Relations in the Na2WO4–LiPO3–WO3System

The liquidus relations in the Na₂WO₄–LiPO₃–WO₃system (diagonal section of the quaternary mutual system Li,Na||PO₃,WO₄,WO₃) were studied by thermal analysis at WO₃contents of 60 mol %. The results demonstrate that, in the composition region studied, the liquidus surface comprises the primary-crystallization fields of Na₂WO₄, LiPO₃, and the congruently melting compounds Na₂WO₄· WO₃, 3LiPO₃· WO₃, Na₂WO₄· NaPO₃, and 2Li₂WO₄· LiPO₃. The low-melting compositions revealed in the system studied are of interest for the preparation of Li _x Na _y WO₃bronzes.     

Group codes on certain algebraic curves with many rational points

We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq ² over _q , whereq = 2q ₀ ² andq ₀ = 2 ⁿ , such that dimension + minimal distance q ² + 1 – q ₀ (q – 1). The codes are ideals in the group algebra _q [S], whereS is a Sylow-2-subgroup of orderq ² of the Suzuki-group of orderq ² (q ² + 1)(q – 1). The curves used for construction have in relation to their genera the maximal number of GF _q -rational points. This maximal number is determined by the explicit formulas of Weil and is effectively smaller than the Hasse—Weil bound.Supported by Deutsche Forschungsgemeinschaft while visiting Essen University     

Pressure dependence of the melting and α-β phase transition temperatures of carbon monoxide

The pressure dependences of the melting temperatureT _m and crystallographic phase transition temperatureT of carbon monoxide have been measured as a function of hydrostatic pressure to 1.75 kbar by using associated changes in the nuclear spin-spin relaxation timeT ₂ of¹³C as an indicator of the transitions. From the Clausius-Clapeyron equation the volume increments at zero pressure are deduced to beV _m =2.50±0.07 andV =0.92±0.02 cm³/mole. The CO phase diagram is compared with that of N₂.Research performed with support from National Science Foundation Grant DMR75-20161 and under auspices of U.S. ERDA.Visiting Professor of Physics, University of Florida, 1975–6.