Anisotropic flow and fracture in beryl [Be3Al2(SiO3)6]

Flow and fracture resulting from Vickers indentation testing on {0 0 0 1} and {10 0 } planar orientations have been examined. Flow characterized by indent shape differentiation was analysed to belong to the slip system with planes of the types { 10 0} and {11 0}. The ensuing fracture paths were resolved to propagate along {1 0 0} and {1 1 } cleavage planes whileK _c values obtained for them were 0.196 and 0.248 MPam^1/2, respectively.     

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     

Transmission electron microscope study of a directionally solidified Cu-MgCu2 eutectic

The crystallography and the interface structure of a unidirectionally solidified Cu-MgCu₂ eutectic alloy have been examined by transmission electron microscopy. The microstructure of the eutectic was found to be lamellar and regularly interrupted by faults. The preference of the particular orientation relationship could not be explained by relative atomic densities of the planes comprising the interface. Based on the defect contrast observed and extinction distance calculations, it is suggested that the fine array of defects observed at the interface may be characterized as steps with step vectors parallel to or Dislocations were also observed at the interface but they were rarely regular.     

Viscous response of an anchored spinning liquid column to various axial excitations

Summary For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear for < 2 ₀, while in the elliptic range < 2 ₀ the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.Notation a radius of column - h length of liquid bridge - I _n modified Bessel function - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution - Weber number - z ₀ excitation amplitude - liquid density - surface tension - surface tension parameter - Ohnesorge number - liquid surface displacement - kinematic viscosity - ₀ rotational speed - dimensionless rotational speed - forcing frequency - dimensionless forcing frequency - dimensionless forcing frequency for non-viscous liquid - a= root of bi-cubic Eq.(33) - root of bi-cubic Eq.(33)     

Structural features of Σ = 19, [110] GaAs tilt grain boundaries

= 19, [110] tilt grain boundaries have been observed to facet parallel to particular planes; the facets lie along _A/ _B, ( )_A/ )_B and ( )_A/( )_B. The structural unit of the = 19 ( )_A/( )_B [110] boundaries consists of 5- and 7-member rings, which are similar to the core structure of a/2[110] edge dislocations. The polarities in each grain on either side of the boundaries has been confirmed by CBED methods; a lower number of anti-site type cross-boundary bonds occur along the boundaries compared to when the polarity of one grain is reversed. The presence of 7-member rings and anti-site cross-boundary bonds results in a more open atomic structure at the boundary, shortening the distance between the first and the second {331} atomic planes from the boundary plane by 40%.     

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

Eine Erweiterung der Analogie zwischen der Gasdynamik und Flachwasserströmungen auf rotierende Systeme mit konservativen Massenkräften

Zusammenfassung Die bekannte Analogie zwischen den Theorien reibungsfreier flacher Wasserströmung und der isentropen idealen Gasdynamik wird im zweidimensionalen instationären Fall durch Zulassung rotierender Bezugssysteme und konservativer Massenkraftfelder erweitert. Damit kann man in einem rotierenden Wasserbehälter mit geeignet gestaltetem Boden u. a. atmosphärische Probleme näherungsweise studieren.

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Summary The well known analogy of the theories of nonviscous shallow water flows and isentropic ideal gasdynamics is generalized in the two-dimensional nonstationary case to apply to rotating systems with conservative body forces. This enables one, in particular, to simulate atmospheric problems by use of a rotating water tank with suitable bottom shape.

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Liste der verwendeten Symbole spezifische Wärme des Gases bei konstantem Druck - Fr in (2) definierteFroude-Zahl - Gravitationsbeschleunigung - H ortsabhängige Ruhetiefe bei Drehung des Wassers als starrer Körper - Druck - atmosphärischer Druck auf der freien Wasseroberfläche - Bezugslänge - Zeit - absolute Temperatur - Geschwindigkeitskomponenten parallel zu den Achsen - kartesische Koordinaten - durch Abweichung von der Drehung des Wassers als starrer Körper verursachte orts-und zeitabhängige Änderung der Wassertiefe - Verhältnis der spezifischen Wärmen des Gases - zu gehörende Wellenlänge - Dichte - Winkelgeschwindigkeit Mit 1 Textabbildung1 Boden des Wasserbehälters 2 freie Wasseroberfläche II freie Wasseroberfläche bei einer Drehung des Wassers als starrer KörperEin oberer Querstrich gibt an, daß die betreffende Größe eine physikalische Dimension hat; Größen ohne einen solchen Querstrich sind dimensionsfrei.     

Superconducting critical currents in Nb-Cu-Nb sandwiches

A preparation method is presented for Nb-Cu-Nb sandwiches for proximity-effect measurements with a large junction area of about 150×150 µm and intermediate Cu layers of thicknesses between 0.2 and 1.5 µm. The thickness of the Nb layers is about 150 µm. These samples are used to study the dependence of the superconducting critical currentI _c through the Cu layer as a function of a magnetic field applied parallel and perpendicular to the layers. Furthermore, the effects of flux lines trapped in the Nb layers on the critical currentsI _c andI _c are investigated. The results are used to discuss the influence of proximity effects in microcomposite superconductors.     

Rigid body translation in the (\bar 211) twin boundary in silicon

The rigid body translation accompanying a ( 11) twin boundary in silicon has been studied by transmission electron microscopy. From a detailed analysis of theα-type fringe systems in the 111, 311 and 2 0 common reflections, the following translation vector is deduced: [011], which is equivalent to [411] in the other crystal element. A slight deviation of this orientation is possible.     

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     

Rheological behaviour and modelling of semi-solid Sn-15% Pb alloy

The rheological behaviour and modelling of a semi-solid, Sn-15% Pb alloy characterized by a special coaxial-cylinder rheometer over a wide range of process conditions is reported. In particular, the effect of shear rate , volume fraction of solid (f _s), and cooling rate on the apparent viscosity () of the semi-solid Sn-15% Pb alloy under isothermal and various cooling conditions was studied. Based on the experimental data, the shear rate used in preparing the semi-solid alloy as well as the volume fraction of solid have the most dominant effects on the rheological properties of the semi-solid Sn-15% Pb alloy. A viscosity model expressed as is proposed in which f _s ^* is the critical solid fraction at which the apparent viscosity goes to infinity, (F _s) corresponds to the asymptotic viscosity at infinity shear rate, and characterizes the transition shear rate between the power-law and Newtonian regions. finally, measurements with a differential scanning calorimeter were made and used to correlate the temperature and volume fraction of solid which, in turn, was corroborated with available data from the literature.     

Fermi surface and extended van Hove singularity in the non-cuprate layered perovskite superconductor Sr2RuO4

With high-resolution (22 meV) angle-resolved photoemission spectroscopy, the Fermi surface of the first copper free layered-perovskite superconductor, Sr₂RuO₄, was determined. We observed three bands to cross the Fermi energy in qualitative agreement with LDA band structure calculations; one electron-like surface encircling the point in the projected Brillouin zone, and two hole-like surfaces around the point. The most striking aspect of the measurements is the observation of an extended van Hove singularity. It is located 17 meV below the Fermi energy and extends around the point for about 0.2 Å^–1 along both the — — and the — — directions.These observations demonstrate that van Hove singularities near the Fermi surface are a more generic feature of layered oxides, and call for a clarification of their exact role in oxide superconductivity.We are grateful to D. Singh for making available his band structure calculations. D. H. Lu thanks the VW Foundation for financial support.     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Load relaxation studies of germanium

A series of compressive load relaxation experiments were conducted on germanium single crystals in the temperature range 400 to 885° C. The curvature of the log-log data obtained from load relaxation tests changes from concave upward to concave downward as the test temperature increases at fixed stress level, or as the strain level increases at fixed temperature. At intermediate temperatures, 600° C, the transition from concave upward to concave downward curvature happens on a single relaxation curve. These observations are consistent with the two-branch rheological model proposed by Hart to explain the deformation behaviour of metals and were analysed in terms of this model. The transition from concave upward to concave downward curvature could be moved to higher temperature by doping germanium with gallium, which decreases the dislocation glide velocity relative to that in pure germanium. The transition could be shifted to lower temperature by compressing samples along [1 1] rather than [1 0] because the [1 1] orientation favours cross-slip while the [1 0] orientation does not. Dislocation dipoles and straight dislocations dominated the microstructure of samples which had concave upward log-log curves, while well-developed dislocation cell structures dominated the microstructure of samples which yielded concave downward curves. The observed changes in the curvature of the load relaxation curves and the dislocation structure both indicate the increased importance of dislocation climb with increasing temperature. When compared through the Orowan equation, the load relaxation results are in good agreement with published stress-dislocation velocity data.     

Multiband superconductivity: A mapping to the extended attractive Hubbard model

Following our recent work which shows that purely repulsive multiband systems effectively reduce to the extended attractive Hubbard model having the on-site repulsion along with nearest-neighbor and next-nearst-neighbor attraction for the cuprate structures, we study the latter model in the mean-field theory.T _c against band filling for various symmetries of pairing is numerically calculated. The results show that, for the region of and expected for the mapping from the original multiband model,T _c has maximum values of the order of 100 K, which is consistent with the experimental results. For certain values of parameters,s- and -wave pairing have similar values of T_c, which may suggest the possibility of a mixed phase of the two.The numerical calculations were done on the HITAC S3800 in the University of Tokyo Computer Centre. This work was in part supported by a Grant-in-Aid from the Ministry of Education, Science, and Culture, Japan.     

Grain growth behaviour of the Al-Cu eutectic alloy during superplastic deformation

Grain growth behaviour of the Al-Cu eutectic alloy was investigated as a function of strain (ε), strain rate and deformation temperature (T) over = 10⁻² s⁻¹ and T=400 to 540°C. The grain size increases with increase in strain and temperature. Upon deformation to a fixed strain, the grain growth is generally seen to be more at lower strain rates. The rates of overall grain growth and due to deformation alone , however, increase with increasing strain rate according to and , respectively. The increase in the grain growth rate with strain rate is attributed primarily to the shorter time involved at higher strain rate for reaching a fixed strain. The activation energy for grain growth under superplastic conditions is estimated to be 79 kJ mol⁻¹.     

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).     

Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles,hypotheses, and mathematical model

A model of thermomechanic behavior of a polymer upon its formation in a crystallization process is proposed. Based on methods of nonequilibrium thermodynamics governing relationships are obtained which make it possible to establish the dependence of the final degree of crystallicity of the material on the history of the crystallization process and to explain the mechanism of formation of the remanent stresses in a polymer article.Notation u translation vector - v velocity vector - acceleration vector - absolute temperature - density - c specific heat capacity - deformation tensor - strain tensor - specific enthropy - U ^* internal energy - z specific free enthalpy - _i internal parameters of state - t time - q heat flux vector - matrix of heat conduction coefficients - W ^* energy dissipation - F vector of mass forces - the 4th rank tensor of elastic pliabilities - matrix of heat expansion coefficients - tensor of contribution of structural variations to deformation - function of equilibrium value ^* - p mean pressure - deviator of the tensor of deformations - spherical part of the deformation tensor - deviator of the tensor of stresses - K volume modulus - unity tensor - Q enthalpy of the crystallization process - Q _eq enthalpy of the equilibrium crystallization process - _g glass transition temperature - ^*() the curve obtained in the equilibrium crystallization process - f final degree of crystallicity Institute of Mechanics of Continuous Media of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Institute of Technical Chemistry of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 479–485, May–June, 1995.     

Electrical conduction of partially stabilized zirconia Zr0.94Ca0.06O1.94 as a function of temperature and oxygen partial pressure

Partially stabilized zirconia (PSZ), Zr_0.94Ca_0.06O_1.94was prepared by a hot kerosene drying method and a conventional oxide wet-mixing method. The total d.c. conductivities of these zirconia specimens were measured by the three-terminal technique as a function of temperature in the range 1088 to 1285 K and oxygen partial pressure in the range 1 to 10^–24 bar. The specimen prepared by the hot kerosene drying method showed near oxygen ion conduction with four times higher conductivity than the specimen prepared by the conventional mixing method at T=1088–1285 K and bar. The higher oxygen pressure conductivity tended approximately towards a to dependence, indicative of p-type conduction, whereas the lower oxygen pressure conductivity tended to be virtually independent of oxygen pressure, indicative of oxygenion conduction. The activation energy was found to be 130 kJ mol^–1 at T=1088–1285 K, bar (air) for pure electron-hole conduction and 153kJ mol^–1 at T=1088–1285 K for ionic conduction.     

Stresses in a cylindrical shell supported by a core of a different material

Summary The stress problem of a thin cylindrical shell supported by an elastic core of a different material and subjected to arbitrary loading on its curved surface is considered. The problem is solved by applying the three-dimensional theory of elasticity to the core and using membrane or bending solutions for the shell. Equilibrium and compatibility equations are satisfied at the junction of the shell and the core. It is pointed out that the procedure can easily be extended to the case of a hollow core with or without another shell of another material in it. Numerical results are presented to illustrate the effectiveness of even a weak core in reducing the shell stresses.

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Zusammenfassung Gegenstand der Untersuchung ist eine dünne Kreiszylinderschale, die durch einen elastischen Kern aus einem anderen Werkstoff gestützt ist und eine beliebige Belastung trägt. Die Lösung verbindet die strenge, dreidimensionale Theorie des zylindrischen Kerns mit der Membran- oder Biegetheorie der Schale. An der Grenze zwischen beiden Teilen müssen die Verschiebungen und gewisse Spannungskomponenten stetig übergehen. Es wird darauf hingewiesen, daß die Lösung leicht auf den Fall ausgedehnt werden kann, daß der Kern ein Hohlzylinder ist, der möglicherweise auf der Innenseite mit einer zweiten Zylinderschale verbunden ist. Zahlenergebnisse zeigen, daß selbst ein verhältnismäsig nachgiebiger Kern einen großen (und günstigen) Einfluß auf die Spannungen in der Schale ausübt.

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Principal Symbols a Radius of the middle surface of the shell - t Thickness of the shell - =1–t/2a - u _c,v _c,w _c Displacements respectively in the axial, circumferential and radial directions of a point in the core - X(x), (), (r/a) 3×3 square matrices - ,m Parameters - l Length of the cylinder - c A vector containing constantsc ₁,c ₂ andc ₃ - =r/a - =m+4(1–v _e) - E _c,v _e Elastic constants for the core material - Stresses at a point in the core - D _c - A vector containing _rx , _r and _r - (r/a) A 3×3 matrix - Displacements at the surfacer=a of the core - A vector containing - Amplitudes of displacements - A vector containing - =(x, ,a) - _ij Constants - A A square matrix containing constants _ij - Stress resultants in the shell as defined in reference [3] - p _x,p ,P _r Components of applied loading per unit area of shell's middle surface - () - ()· - u, v, w Displacements of a point on the middle surface of the shell - E _s,v _s Elastic constants for the shell material - D _s - K - k - p _xmn,p _mn,p _rmn Amplitudes of loadsp _x,p , p_r - u _mn, v_mn,w _mn Amplitudes of displacementsu, v, With 1 Figure