Array Of Unit Cells Research Articles

A macroscopic model for plastic flow in metal-matrix composites

Abstract A micromechanically based continuum model is developed to analyze the enhancement of plastic properties of particulate-reinforced metal-matrix composites over matrix materials. The composite is idealized as uniformly distributed periodic arrays of unit cells. Each unit cell consists of a rigid inclusion surrounded by a plastically deforming material. An energy method is adopted to obtain the overall constitutive relation for the composite on the basis of the local nonuniform deformation fields. Effects of particle volume fractions and shapes (e.g. whiskers, discs, etc.) as well as the matrix properties on the flow properties of the composite are obtained. The results are in good agreement with experimental observations and finite element analyses found in the literature. An explicit expression is also proposed, providing a means for evaluating various factors affecting the strength of composites.

Fabrication of two dimensional step edge YBa2Cu3O7 Josephson junction arrays

Laser ablated thin YBa 2 Cu 3 O 7 (YBCO) films on SrTiO 3 substrates were used to fabricate step edge Josephson junction arrays. After forming the substrate into a checkerboard arrangement of steep mesas of lattice parameter 7.5μ m, a YBCO film was deposited and patterned into a square network with the same lattice parameter. The arrays thus consist of 10 3×10 3 wires, 1.5 μ m wide and some 10 6 junctions at the sites of the steps. In a perpendicular magnetic field the conductance of the arrays shows up to 40 periodic oscillations, the periodicity corresponding to one flux quantum per array unit cell.

Analysis of infinite arrays of microstrip-fed dipoles printed on protruding dielectric substrates and covered with a dielectric radome

A method for analyzing infinite arrays of antennas printed on both sides of substrates protruding from a ground plane and covered with a dielectric radome is described. Using the equivalence principle, the array unit cell is decomposed into homogeneous regions where the fields are expressed as Floquet summations, and an inhomogeneous cavity region where the fields can be found by a combination of the method of moments and modal analysis. The approach is rigorous in the sense that the combined effects of the radiating element and feed geometry printed on opposite sides of a protruding substrate are taken into account. The method is quite general, capable of modeling any antenna elements with substrate currents that are perpendicular and/or parallel to the ground plane. In addition, both the radiating and scattering/receiving modes of operation are treated in the analysis. The method is used to calculate the active element impedance of an infinite array of dipoles transmission line-coupled to microstrip feeds. Examples of numerical results are presented for various scan conditions and the effects of a near-field dielectric radome are demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically folds opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile. >

Analytical treatment of circulant nonuniform multiconductor transmission lines

The authors analytically study a certain class of nonuniform multiconductor transmission lines (NMTL). This class is described by circulant impedance and admittance matrices. Due to the properties of circulant matrices (which form a special set of normal matrices) it is shown that the NMTL equations can be simultaneously diagonalized with the aid of the position-independent so-called Fourier matrix. Thereby, the NMTL equations decouple completely and the resulting equations for the modal components of the voltages and currents may be solved with techniques and methods already known from the analyses of single nonuniform transmission lines. Application examples covering the high-frequency propagation on NMTL and an exact solution (in the frequency domain) a coupled transmission line model for a unit cell of a periodic array of wave launchers are presented. The methods are also applied to a diverging pair of conductors above a perfectly conducting plane. Special interest, however, is focused on C/sub N/ and C/sub Nc/ symmetry of the NMTL configurations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Deformation studies of metal matrix composites using electron backscatter patterns

Electron backscatter patterns (EBSPs) are known to be degraded by specimen deformation. Quantification of the EBSP diffuseness and its variation with strain was made for the aluminium alloy 6061 using digital image analysis and discrete Fourier methods. The local distribution of matrix deformation was examined in a unidirectional continuous fibre composite which had been failed in transverse tension. Large matrix strains (above 10%) were only found in a region extending approximately 1 fibre radius from the fracture surface. The distribution of matrix dislocations was established qualitatively for a general unit cell of the fibre array. A failed cross-ply laminate with fibres at 0° and 90° to the tensile load axis was also examined. In particular the increased matrix deformation near a break in a 0° fibre was demonstrated.

Two-dimensional spatial light modulators fabricated in Si/PLZT

We report in this paper the use of Si/PLZT technology in the fabrication of 2-D electrically and optically addressed spatial light modulators. First, a 12 x 12 electrically matrix addressed array was fabricated using simultaneous laser assisted diffusion and crystallization. Then, NMOS transistors exhibiting electron mobility of 550 cm(2)/V-s were fabricated in each unit cell of the matrix array and used to control the PLZT modulator. A dynamic range of 35:1 was achieved. A 16 x 16 optically addressed SLM array was also fabricated. In this case, to improve the optical sensitivity, a three-transistor CMOS detector-amplifier circuit was included in each unit cell of the array.

Metal matrix composites microfracture: Computational simulation

Fiber/matrix fracture and fiber-matrix interface debonding in a metal matrix composite (MMC) are computationally simulated. These simulations are part of a research activity to develop computational methods for microfracture, microfracture propagation and fracture toughness of metal matrix composites. The three-dimensional finite element model used in the simulation consists of a group of nine unidirectional fibers in a three by three unit cell array of SiC/Ti15 metal matrix composite with a fiber volume ratio of 0.35. This computational procedure is used to predict the direction of crack growth based on strain energy release rate. It is also used to predict stress redistribution to surrounding matrix/ fibers due to initial and progressive fracture of fiber/matrix and due to debonding of the fiber-matrix interface. Microfracture results for various loading cases such as longitudinal, transverse, shear and bending are presented and discussed. Step-by-step procedures are outlined to evaluate composite microfracture for a given composite system.

Sheath disassembly in Methanospirillum hungatei strain GP1

Sheaths of Methanospirillum hungatei are very resilient structures and consist of circumferential rings, which have been likened to the hoops of a barrel. The isolated sheaths are dramatically disassembled to the individual hoops upon treatment with β-mercaptoethanol at 90 °C. Sheath disassembly resulted in a large decrease in suspension turbidity and a release of approximately 10% of sheath protein in the form of 4.6 to 7.0 kiloDalton (kDa) peptides. These are referred to as "glue peptides" to suggest a function in linking the hoops together to form the intact sheath. The liberated hoops consisted of a protein surface array crystallized on a matrix material. Intact sheaths, or hoops largely freed of the glue peptides, could be solubilized at 90 °C by (i) a combination of β-mercaptoethanol and sodium dodecyl sulfate, (ii) by alkaline conditions of pH 12 or more, or partially (iii) by carbonate anion at pH 11. Fractionation by liquid chromatography of hoops solubilized by alkaline conditions of pH 12.6 revealed major polypeptides of about 24 and 45 kDa; a smaller peak occurred at 12 kDa. Based on the dimensions of the unit cell of the crystalline array, we suggest that two copies of the 24-kDa polypeptide form the 5.6 × 2.8 nm unit cell as a dimer, which then tends to form larger aggregates. The 2.8-nm subunit may be a dimer of the 12-kDa species. Sheaths of M. hungatei strain JF1 exhibited a similar polypeptide profile, but in this case, the 45-kDa species predominated.

Finite element analysis of a three-dimensional open-celled model for trabecular bone.

Based on a regular array of cubic unit cells, each containing a body-centered spherical void, we created an idealized three-dimensional model for both subchondral trabecular bone and a class of porous foams. By considering only face-to-face stacking of unit cells, the inherent symmetry was such that, except at the surface, the displacements and stresses within any one unit cell were representative of the entire porous structure. Using prescribed displacements the model was loaded in both uniaxial compressive strain and uniaxial shear strain. Based on the response to these loads, we found the tensor of elastic constants for an equivalent homogeneous elastic solid with cubic symmetry. We then compared the predicted modulus with our experimental values for bovine trabecular bone and literature values for an open-celled latex rubber foam.

Magnetic structure of FeSn2, and reflections on FeGe2cells

The intermetallic compound FeSn2 has been studied by neutron diffraction, magnetisation measurements and Mossbauer spectroscopy. This compound is antiferromagnetic (TN=378K) and a second transition occurs at Tt=93K. The unit cell of the antiferromagnetic array is the same size as the chemical cell. Between TN and Tt the magnetic structure is collinear, characterised by ferromagnetic planes (100), coupled antiferromagnetically along the (100) direction; the spin direction lies in the (001) plane near the a axis. AT tt=93K a spin rotation to the (110) direction is observed. Below Tt, FeSn2 becomes non-collinear antiferromagnetic and the iron moments form a canted structure along the c axis. The angle between the two spin dynamics is 18 degrees and the moment per iron atom observed is 16.4+or-0.05 mu B at 5K. This magnetic behavior of FeSn2 is similar to that observed for FeGe2. A new description of the non-collinear structure of FeGe2 is proposed and the moment per iron atom is corrected to mu =1.21 mu B.

Electronic State Calculations of Dislocations in Cadmium Telluride

AbstractUsing a tight binding method the localized electronic states in CdTe connected with the core of 30° and 90° glide partials are calculated. Periodic arrays of large unit cells each containing two 30° or 90° partials with Burgers vectors of opposite sign are considered. Several models of the core structure of each partial are analyzed. The electronic states of dissociated screw and 60° glide dislocations are discussed.

On the Orthogonality of Approximate Waveguide Mode Functions

For many waveguides, only approximate solutions for the mode functions are available and in such cases the question arises, whether the orthogonality property of the exact modes can be preserved. This problem is addressed in the present paper. A fairly general method of solution is considered and it is shown that in spite of two consecutive approximations the resultant mode functions are indeed orthogonal. Examples that have been analyzed include a rectangular waveguide with a septum, a rectangular waveguide with an axial, conducting strip and a (phased array) unit cell waveguide with one or more axial, conducting strips.

Electron states associated with the core region of the 60° dislocation in silicon and germanium

AbstractUsing the tight‐binding method the localized states connected with the 60° dislocation in silicon and germanium are calculated. Periodic arrays of large unit cells each containing two 60° dislocations with Burgers vectors of opposite sign are considered. As a consequence of the broken bonds a one‐dimensional band occurs in the direction of the dislocation line for both silicon and germanium. The dilatation region of the dislocation core is also found to cause a second dislocation band to appear below the conduction band edge.

Semiempirical calculation of deep levels: divacancy in Si

A study of the electronic levels associated with the divacancy in silicon is reported. The extended Huckel theory is shown to reproduce the band structure of silicon. The electronic levels of the divacancy are calculated by considering a periodic array of large unit cells each containing 62 atoms; a 64 atom perfect cell with two atoms removed to form the divacancy. The results are found to be in qualitative agreement with the results of EPR and infrared absorption measurements.

The magnetic structure and hyperfine field of FeGe2

Abstract The magnetic structure of the intermetallic compound FeGe2 has been determined from powder and single crystal neutron diffraction data. The unit cell of the anti-ferromagnetic array is the same size as the chemical cell, and the spins on the four equivalent iron atoms in this cell lie parallel or anti-parallel to two different, but symmetry related, directions in the basal plane of the tetragonal structure. The angle between the two spin directions is 71° ± 6° and the moment per iron atom observed is 0.73±0.06 μB. The temperature dependence of the magnetic scattering indicates a Neel point in the region of 0°c. The hyperfine field at the iron atom as determined from the Mossbauer effect is 148±2 kG.