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.     

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.     

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.     

The Smallest Correction of an Inconsistent System of Linear Inequalities

The problem of calculating a point x that satisfies a given system of linear inequalities, A x #x2265; b, arises in many applications. Yet often the system to be solved turns out to be inconsistent due to measurement errors in the data vector, b. In such a case it is useful to find the smallest perturbation of b that recovers feasibility. This motivates our interest in the least correction problem and its properties.Let A x #x2265; b be an inconsistent system of linear inequalities. Then it is always possible to find a correction vector y such that the modified system A x #x2265; b #x2212; y is solvable. The smallest correction vector of this type is obtained by solving the least correction problem Let denote the convex cone which consists of all the points for which the system A x #x2265; u is solvable. Let denote the polar cone of . It is shown that the least correction problem has a simple geometric interpretation which is based on the polar decomposition of into and . A further insight into the least correction concept is gained by exploring the duality relations that characterize such problems.     

Analysis of a family of unstable lattice orientations in (110) channel die compression

Summary The family of f.c.c. crystal orientations defined by loading direction (110) and any channel die constraint direction between ( ) and ( ) is kinematically unstable. We establish that the experimentally observed finite rotation of the lattice about the loading axis, for initial orientations in this range, is uniquely predicted by the constraints and critical slip-system inequalities without regard to particular hardening theory. We further establish that experimental information on the changing constraint stress would serve to distinguish among theories. Predictions of three specific hardening rules, including classical Taylor hardening and the simple theory, are illustrated for initial constraint directions ( ) and ( ). For the first of these orientations the predictions include constraint stress, lattice rotation, active and latent hardening, and overall crystal shearing to a logarithmic compressive strain of 1.0.     

Effect of the addition of Y2O3 on the structure, microstructure and piezoelectric properties of PZT(53/47)

In this work, an attempt is made to study system with x=0.0125, 0.025, 0.050, 0.075 and 0.1. It was shown that there is limited solid solubility (0.625 mol %) of or 1.25 mol % of in PZT(53/47). For higher levels of dopant, mainly two other extra second phases were detected. The first was a Zr-rich phase in which some and small amounts of was dissolved. The second one was a Pb solid solution composed of mainly PbO, and which was initially also seen in calcined samples. The formation of Zr-rich phase is thought possibly to originate due to the sublimation of Pb from source during the sintering process. For higher x values, a structural shift towards Ti-rich region of PZT's phase diagram is seen. All piezoelectric parameters of the doped samples such as , are seen to decline sharply compared to that of undoped samples. Increasing the level of dopant gave rise to the increase of conductivity and dielectric loss of sintered samples. The formation of non-ferroelectric extra phases, and the Zr/Ti change of the main formed phase is believed to be responsible for this behavior.     

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.     

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 variational principle motivated by the optimal rod theory

Summary In this work we show that a number of well known nonlinear second order ODE appearing in theoretical physics provide the necessary condition for the minimum of the functional with the Lagrangian . Also we prove that those second-order differential equations may be viewied as conservation laws for the corresponding Euler-Lagrange equations that are the fourth-order ODE. Several special cases that have importance in physics, mechanics and optimal rod theory are studied in detail.     

Computer-aided design of small patch antenna using (Al, Mg)TaO2 ceramics

The microwave dielectric properties of (AMT) ceramics and the design of small coplanar waveguide fed antenna (CPWFA) have been investigated. ( and ( have orthorhombic and tetragonal structure, respectively. As ( concentration increased, AMT ceramics transformed into the tetragonal structure. Specimens having tetragonal single phase could be obtained above x=0.6. As ( concentration increased, the grain size, dielectric constant and quality factor (Q) significantly increased and the temperature coefficient of resonant frequency changed from negative to positive. The of was realized at x=0.65 and the Q · f _O value and for this composition were 112 470 GHz and 26.1, respectively. Newly developed dielectric materials were used for 1.5 GHz band CPWFA design and fabrication. The size of the CPWFA can be reduced by using high dielectric constant AMT ceramics, insetting slits into the patch, and fabricating CPW feed line in the ground plane. The slits play a role in not only lowering a center frequency but also fine tuning for the proposed antenna together with the open stub of CPW feed line. The CPWFA with slits has a lower center frequency than the conventional CPWFA, which suggests that the antenna size can be reduced by as much as 16.3%. The structure simulations of the CPWFAs have been performed to obtain impedance matching and to investigate the effects of slits. Experimental results of the fabricated device were in good agreement with the simulation.     

Electrical and magnetic properties of BaTiO3−(Ni0.3Zn0.7)Fe2.1O4 composites

Ceramic composites consisting of ferroelectric and ferrite ( were synthesized by the mixed oxide route. The phase assemblage, electrical and magnetic properties of the samples were investigated. The results indicates that the phase is compatible with ( phase, and dense diphasic composite ceramics were obtained. Electrical resistivity of composites varies with increasing amounts of ( phase, and shows a percolation-like drop. Magnetic hysteresis loops were observed in the composites.     

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.     

Polynomial-time construction of codes I: Linear codes with almost equal weights

We prove that there are infinite families (C_i)_i0 of codes over F_q with polynomial complexity of construction whose relative weights are as close to as we want and are such that

The effect of temperature on the electric conductivity property of Bi3Zn2Sb3O14 pyrochlore type phase

The electric conductivity characteristic of ceramics was investigated by impedance spectroscopy in the frequency range from 5 Hz to 13 MHz. Electric measurements were performed at temperatures in the range from 25 to 700 °C. The phase type pyrochlore was synthesized by the polimeric precursors method. Ceramic presenting a relative density of 98% of the theoretical density was prepared. The data were presented in Nyquist diagrams form, from which the electric resistivity was determined. The electric conductivity followed the Arrhenius law with an apparent activation energy of the conduction process equal to 1.37 eV. The electric conductivity at room temperature was determined by extrapolation being equal to . Between 400 and 700 °C, the conductivity values were and , respectively.     

The constant stress tensile creep behaviour of a superplastic zirconia-alumina composite

A detailed study was conducted to evaluate the constant stress tensile creep behaviour of a superplastic 3 mol% yttria-stabilized zirconia-20 wt% alumina composite. The comprehensive experimental results indicate that creep deformation may be expressed in the form exp(–585 000/8.3T), where is the steady-state creep rate, is the imposed stress, is the linear intercept grain size andT is the absolute temperature. Microstructural observations revealed that there is very little dislocation activity, or change in grain size or shape. A detailed analysis was conducted to evaluate the possible rate-controlling mechanisms in terms of the experimentally determined mechanical properties and the microstructural observations. Based on the maintenance of an equiaxed microstructure and the strong grain size and stress dependence, it is concluded that creep occurs by a grain-boundary sliding/grain rearrangement process.     

The Dual-Phase-Lag Heat Conduction Model in Thin Slabs Under a Fluctuating Volumetric Thermal Disturbance

In the present work, the thermal behavior of a thin slab, under the effect of a fluctuating volumetric thermal disturbance described by the dual-phase-lag heat conduction model is investigated. It is found that the use of the dual-phase-lag heat conduction model is essential at large frequencies of the volumetric disturbance. It is found that the hyperbolic wave model deviates from the diffusion model when and the dual-phase-lag model deviates from the diffusion model when . where is the angular velocity of the fluctuating wall temperature, is the phase-lag in the heat flux vector and is the phase-lag in the temperature gradient vector.     

Metrological certification of current transformers under service conditions

Conclusions Theoretical analysis and experimental data confirm the statement that Eq. (16) permits the of a CT to be determined under fixed load and current conditions with an error that is smaller by a factor of two or three than the controlled accuracy grade of the standards [1, 2].During operation of a CT in the rated range of currents it is advisable to measure and at several points of the range for a determination of from Eq. (16) or of from Eq. (14).Besides this, when checking a CT in accord with [3] it is permissible to make corrections for the standard CTs. In this case the actual CT load should not differ by more than 20% from the one being corrected. Equation (16) permits a correction for any permissible load to be taken into account without a significant error buildup.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 53–55, August, 1980.     

Heat flux measurement from the temperature field of a heated surface. 2. Inhomogeneous flux

Based on the previously obtained analytical solutions of the three-dimensional space-time problem of recalculating boundary conditions, algorithms are developed and a computational experiment is carried out to reconstruct the heat flux with arbitrary spatial distribution of the temperature field of the heated surface.Notation T(t, ) temperature over the plate surface - q(t ) heat flux to the plate surface - ={x,y} transverse coordinate - t time - k thermal conductivity - a ² thermal diffusivity - L plate thickness - Jacobi theta-function [4] - Fourier parameter - Jacobi theta-function [4] - transversal Laplacian Institute of Atmospheric Optics, Siberian Division, Russian Academy of Sciences, Tomsk, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 622–628, July–August, 1995.     

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 a stability theory of non-selfadjoint mechanical systems

Summary The concept of the Hamiltonian functional is generalized in such a way that a bilinear functional results, which plays the role of the Hamiltonian for non-selfadjoint systems. For this generalized Hamiltonian the condition leads to the so called hybrid Galerkin's equations, and the condition , to the load-frequency reationship. This relationship can be interpreted as a surface in the load-frequency space, the projection of which on the load-planes yields the stability boundaries, i.e. the buckling loads.

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Zu einer Stabilitätstheorie nicht-selbstadjungierter mechanischer Systeme

Zusammenfassung Der Begriff des Hamiltonschen Funktionals wird in solcher Weise verallgemeinert, daß ein bilineares Funktional bei nicht-selbstadjungierten Systemen an seine Stelle tritt. Für dieses verallgemeinerte Hamiltonsche Funktional führt die Bedingung auf die sogenannten hybriden Galerkinschen Gleichungen und die Bedingung auf die Last-Frequenz-Funktion. Diese Funktion kann im Last-Frequenz-Raum als eine Fläche aufgefaßt werden, deren Projektion auf die Last-Ebenen die Stabilitätsgrenzen und damit die Knicklasten liefert.

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Dedicated to Professor Kurt Magnus in honor of his sixtieth birthday.