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 .     

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.     

Growth of aluminium nitride whiskers by sublimation-recrystallization method

Aluminium nitride (AlN) with various morphologies was fabricated through a sublimation-recrystallization method. The influences of type of reactor and temperature gradient were explored, as well as the orientations and growth mechanism of the obtained AlN whiskers. In the early stage of preparation, a vapour-liquid-solid (VLS) mechanism dominated, producing AlN pillars, whiskers and noncrystalline fibres. In the later stage, as the catalyst liquid was removed by volatilization, the pillars and noncrystalline fibres stopped growing, but the growth of AlN whiskers continued through a vapour-solid (VS) mechanism. By Laue method and rotating-crystal method of x-ray diffraction, together with electron diffraction, most of the AlN whiskers were discovered to grow on planes , or , where l=0, 1, 2, 3, along crystal axes , or , where w=0, 1, 2, 3. Oblique grown whiskers also appeared, with a growth direction at an angle of about 54° to the growth plane, .     

On the torsional waves in an elastic bar with long-range cohesive forces

Summary With reference to some of the results obtained in [1], the equation of motion and the equations of nonlocal stress components in the form of Kroener-Eringen are transformed into the Fourier space. A lengthy calculation using a separable form of the nonlocal elastic moduli leads to the governing equation of the problem with two types of solutions. In each case the nonlocal phase velocity and, respectively, the nonlocal group velocity of the very short waves turn out to be by about 36% less than the velocities of their classical counterparts.Notation a atomic spacing - c ₂ classical speed of shear waves - c _2nonloc nonlocal speed of shear waves - c _a2nonloc,c _b2nonloc nonlocal speeds in rods - k wave number - r radius vector - R radius of the bar - v hoop displacement - Fourier transform ofv - V volume of the rod - z axial coordinate - delta sequence - , Lamé's constants - , nonlocal moduli - transform of - A wave length - * mass density - frequency     

The HREM study of precipitates in an Al−Zn−Mg alloy

A study of precipitate phases in an Al–Zn–Mg alloy in the T74 condition has been conducted by means of high resolution electron microscopy. It has been observed that G.P. zones, and phases exist simultaneously in the matrix. The G.P. zones are plate-like forming on (111) matrix plane. The phase has a hexagonal structure witha=0.496 nm,c=1.403 nm and the orientation relationship with the matrix is . A new orientation relationship between the phase and the matrix is found to be .     

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.

---

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.

---

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     

A note on the turbulent energy as a parameter of turbulent flow

The art of modeling turbulence is a needed tool in the construction of computer codes for turbulent flows. The state to which this art has been developed is inadequate, and quotations from authoritative sources support this point of view. The energy contained in the turbulent fluctuations, i.e., the turbulent energy, is often used as a parameter in the modeling process. The present article attempts to examine this quantity as it is being created, transported, and dissipated. For this purpose experimental evidence from the author's own experiments (free jets), as well as theoretical conclusions from the elementary deductions of the basic equations, the concept of turbulent potential flow, and a general solution to the Navier-Stokes-Reynolds equations, is drawn to attention. Recirculating flow is given special attention. The paper concludes with recommendations for principles that must be satisfied if improved modeling is to be achieved. These principles are necessary; whether they are also sufficient is open to question.Nomenclature A ₀ Constant - b _1/2 Jet's half-width - b ₁ ^2/(0) Jet's half-width at z=z(in0) - E _z Kinetic energy contained in the jet's axial velocity at a given profile - E _r Kinetic energy contained in the jet's radial velocity at a given profile - f() Dimensionless velocity profile [f(0)=1] - F(), H() Defined functions - L _char Jet's characteristic length - m, n Exponents - p Pressure - q Kinetic energy in the turbulent fluctuations - Heat flux - q ² - r, , z Cylindrical coordinates - t Time - û Internal energy - u, v, w Velocity components - Mean velocity components - Mean velocity components - U ₀ Constant - U _plate Plate's velocity - Uskc/(0) Centerline velocity at z=z₀ - X, Y, Z Components of body force - W Total work done by surface stresses - W ₁ Recoverable work done by surface stresses - W ₂ Dissipated work - z ₀ Downstream distance from the nozzle beyond which self-similar velocity profiles occur - Fluid's kinematic viscosity - Fluid's density - Normal stresses - Shear stresses - Normal stresses with the pressure removed - Dimensionless Crossflow coordinate - ₀ Constant - Stress functions - Stress potential Paper dedicated to Professor Joseph Kestin.Definitions of symbols are given under Nomenclature.     

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.     

Solidification and interfacial structure of in situ Al-4.5Cu/TiB2 composite

In situ particle reinforced Al-4.5Cu/TiB₂ composite was fabricated with TiO₂, H₃BO₃, Na₃AlF₆ powders and Al-4.5Cu alloy by reaction in melt. The composite can be directly casted into moulds to make composite parts. TiB₂ particles distribute uniformly in the matrix. The average size of TiB₂ particles is 0.93 m. At the atomic scale, TiB₂ is hexagonal, and exhibits hexagon or quadrilateral shape. The orientation relationships exist in the interfaces between TiB₂ particle and -Al, and between the reinforced small Al₂Cu phase and -Al in the composite. They are . TiB₂ particle is nucleation site for -Al matrix growth in the composite. The interface between TiB₂ particles and the matrix is clean and well bonded. No reaction product has been found through HREM observation. This is beneficial to the strength of the composite. The as-cast Al-4.5Cu/TiB₂ composite exhibits mechanical excellent properties: the tensile strength is 416.7 MPa, the yield strength is 316.9 MPa, and the elongation is 3.3 pct.     

Microstructure studies of ZnO nanoneedles

ZnO nanoneedles with uniform diameter and length have been synthesized using thermal evaporation approach. Their microstructure and anisotropic growth mechanism have been studied by means of scanning electron microscopy, high-resolution electron microscopy and convergent-beam electron diffraction. The ZnO polarity induces fast [0001] axial growth of the ZnO nanoneedles which are directed either by high index and planes or by ZnO nanoparticle nuclei formed at the (0001)-Zn growth fronts. Moreover, the {0002} stacking faults are believed to assist the ZnO nanoneedle growth. The slope surfaces at the inactive -O bottom geometrically favor ZnO nanorods growth through twinnings.     

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.     

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.     

Electrical properties of Pd–Au/(In x –Sn1 – x ) Oxide/Si(p)/Al heterojunction diodes

Current–voltage (I–V ) and capacitance–voltage – characteristics of [Pd–Au/( – ) Oxide/Si(p)/Al] semiconductor oxide semiconductor (SOS) solar cells were measured in the temperature range between 300 and 500 K. The dark forward current–voltage curves were found to be independent of temperature. Consequently, the diode quality factor was temperature dependent. Analysis of the data indicated that the predominant carrier transport mechanism of the samples in the intermediate bias voltage region was thermionic field emission and recombination tunneling. From the experimental data it was found that, the open circuit voltage – , the short circuit current – and the fill factor 0.28–0.32, under illumination of 1124 lux.     

Effect of boundary plane on the atomic structure of [0001] Σ 7 tilt grain boundaries in ZnO

The atomic structure of [0001] Σ 7 tilt grain boundaries with { }‖ { }, { }‖ { }, and { }‖ { } boundary planes in ZnO was investigated through high-resolution transmission electron microscopy observation of fiber-textured thin films and atomistic calculations. These boundaries were found to comprise three kinds of common structural units that are characterized by fourfold- to eightfold-coordinated channels along the [0001] direction in contrast to sixfold-coordinated channels in wurtzite structure. The boundary structural units are very similar to the multiple core structures of edge dislocations with Burgers vectors of 1/3 < > . Transformation between two of the three configurations can easily occur through an atom flipping corresponding to dislocation glide. Depending on the orientation of boundary planes with respect to the Burgers vectors, the dislocation-like units exhibit straight or zigzag arrangements with periodicities corresponding to the Σ 7 misorientation.     

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.

---

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.

---

---

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

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.     

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.     

The laminar stagnation-point flow against a solidifying moving shell

Summary This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.Nomenclature A suction velocity in boundary layer variables - a jet width [m] - c specific heat of the solid metal [J/m³K] - h Newtonian heat transfer coefficient [W/m²K] - k velocity gradient in units ofU/a - m dS ^*/dX ^* local inclination of the solidifying phase - S ^* (L)/L average slope of the solidifying phase - S ^* local thickness of the solidified phase [m] - S, S local thickness of the solidified phase in units ofL and , resp. - T absolute temperature [K] - T _f fusion temperature of metal [K] - T ₀ temperature of cooling water [K] - U jet velocity [m/s] - V belt velocity [m/s] - +i complex velocity potential in units ofUa - x coordinate tangential to the solidifying interface in units ofa - X ^* coordinate tangential to the belt [m] - X, X coordinates tangential to the belt in units ofL and , resp. - y coordinate orthogonal to the solidifying interface in units ofa - Y ^* coordinate orthogonal to the belt [m] - Y, Y coordinates orthogonal to the belt in units ofL and , resp. - z x+iy complex coordinates in units ofa - unit vector along the belt - unit vector orthogonal to the belt - local unit normal vector to the solidifying interface - h _f latent heat of fusion of metal [J/m³] - thermal diffusivity of solid metal [m²/s] - belt velocity in units ofU - { _n }, { _n } asymptotic sequences of the outer and inner expansion, resp. - m suction velocity outer variables - velocity potential in units ofUa - jet inclination relative to the local solidifying interface - coordinate orthogonal to the solidifying interface in units of - x c thermal conductivity of solid metal [W/mK] - displacement thickness in units of - v kimematic viscosity of liquid metal [m ²/s] - arctan (dS ^*/dX ^*) local angle of inclination of the solidifying interface - =(T–T ₀)/(T _f –T ₀) dimensionless temperature - perturbation parameter - coordinate tangential to the solidifying interface in units ofa/k - stream function in units ofUa - magnified stream function valid within the boundary layer - solidification constant Dimensionless parameter P _eL VS ^* (L)/ Peclet number - Q h/(cV) Heat flux number - R Ua/v Reynolds number - St Stefan number     

The Validity of Using the Microscopic Hyperbolic Heat Conduction Model Under a Harmonic Fluctuating Boundary Heating Source

The validity of using the microscopic hyperbolic heat conduction model under a harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic hyperbolic heat conduction model is essential when . The phase shift between the electron-gas and solid-lattice temperatures is found to be . This phase shift reaches a fixed value of 1.5708 rad at very large values of . It is found that the use of the microscopic hyperbolic heat conduction model is essential when ¯>1×10⁹ rads^–1 for most metallic layers independent of their thickness.