Nature of disorder and localization in amorphous carbon

The electronic structure of amorphous diamond-like carbon is studied. Analysis of the participation ratio shows that π states within the σ-σ* gap are localized. The localization arises from dihedral angle disorder. The localization of π states causes the mobility gap to exceed the optical gap, which accounts for the low carrier mobility and the flat photoluminesence excitation spectrum. © 1998 Elsevier Science B.V. All rights reserved.

Electronic structure and surface properties of SrBi2Ta2O9 and related oxides

The electronic structure of SrBi2Ta2O9 and related oxides such as SrBi2Nb2O9, Bi2WO6 and Bi3Ti4O12 have been calculated by the tight-binding method. In each case, the band gap is about 4.1 eV and the band edge states occur on the Bi-O layers and consist of mixed O p/Bi s states at the top of the valence band and Bi p states at the bottom of the conduction band. The main difference between the compounds is that Nb 5d and Ti 4d states in the Nb and Ti compounds lie lower than the Ta 6d states in the conduction band. The surface pinning levels are found to pin Schottky barriers 0.8 eV below the conduction band edge.

Doping mechanism in tetrahedral amorphous carbon

Doping in hydrogenated amorphous silicon occurs by a process of an ionised donor atom partially compensated by a charged dangling bond. The total energies of various dopant and dopant/bonding combinations are calculated for tetrahedral amorphous carbon. It is found that charged dangling bonds are less favoured because of the stronger Coulombic repulsion in ta-C. Instead the dopants can be compensated by weak bond states in the lower gap associated with odd-membered π-rings or odd-numbered π-chains. The effect is that the doping efficiency is low but there are not charged midgap recombination centres, to reduce photoconductivity or photoluminescence with doping, as occurs in a-Si:H.

Properties of tetrahedral amorphous carbon deposited by a filtered cathodic vacuum arc

The properties of a highly sp3 bonded form of amorphous carbon denoted ta-C deposited from a filtered cathodic vacuum arc (FCVA) are described as a function of ion energy and deposition temperature. The sp3 fraction depends strongly on ion energy and reaches 85% at an ion energy of 100 eV. Other properties such as density and band gap vary in a similar fashion, with the optical gap reaching a maximum of 2.3 eV. These films are very smooth with area roughness of order 1 nm. The sp3 fraction falls suddenly to almost zero for deposition above about 200 °C.

Electronic structure of the layered ferroelectric perovskite SrBi2Ta2O9

The band structure of the Bi layered perovskite SrBi2Ta2O9 (SBT) has been calculated by the tight binding method. We find both the valence and conduction band edges to consist of states primarily derived from the Bi-O layer rather than the perovskite Sr-Ta-O block. The valence band maximum arises from O p and some Bi s states, while the conduction band minimum consists of Bi p states, with a band gap of 5.1 eV. It is argued that the Bi-O layers largely control the electronic response of SBT while the ferroelectric response originates from the perovskite Sr-Ta-O block. Bi and Ta centered traps are calculated to be shallow, which may account in part for the excellent fatigue properties of SBT.

Electronic structure of the ferroelectric layered perovskite SrBi2Ta2O9

The band structure of the layered perovskite SrBi2Ta2O9 (SBT) was calculated by tight binding and the valence band density of states was measured by x-ray photoemission spectroscopy. We find both the valence and conduction band edges to consist of states primarily derived from the Bi-O layer rather than the perovskite Sr-Ta-O blocks. The valence band maximum arises from O p and some Bi s states, while the conduction band minimum consists of Bi p states, with a wide band gap of 5.1 eV. It is argued that the Bi-O layers largely control the electronic response whereas the ferroelectric response originates mainly from the perovskite Sr-Ta-O block. Bi and Ta centered traps are calculated to be shallow, which may account in part for its excellent fatigue properties. © 1996 American Institute of Physics.

A microstructural investigation of deformation in fine SiC particulate- and whisker-reinforced aluminium-matrix composites

Aluminium-based composites, reinforced with low volume fractions of whiskers and small particles, have been formed by a powder route. The materials have been tested in tension, and the microstructures examined using transmission electron microscopy. The whisker composites showed an improvement in flow stress over the particulate composites, and this was linked to an initially enhanced work-hardening rate in the whisker composites. The overall dislocation densities were estimated to be somewhat higher in the whisker composites than the particulate composites, but in the early stages of deformation the distribution was rather different, with deformation in the whisker material being far more localized and inhomogeneous. This factor, together with differences in the internal stress distribution in the materials, is used to explain the difference in mechanical properties.

Experimental and micromechanical study of size effects in the constrained deformation of metallic foams

Previous investigations have unveiled size effects in the strength of metallic foams under simple shear - the shear strength increases with diminishing specimen size, a phenomena similar to that shown by Fleck et al. (Acta Mat., 1994, Vol. 42, p. 475.) on the torsion tests of copper wires of various radii. In this study, experimental study of the constrained deformation of a foam layer sandwiched between two steel plates has been conducted. The sandwiched plates are subjected to combined shear and normal loading. It is found that measured yield loci of metallic foams in the normal and shear stress space corresponding to various foam layer thicknesses are self-similar in shape but their size increases as the foam layer thickness decreases. Moreover, the strains profiles across the foam layer thickness are parabolic instead of uniform; their values increase from the interfaces between the foam layer and the steel plates and reach their maximum in the middle of the foam layer, yielding boundary layers adjacent to the steel plates. In order to further explore the origin of observed size effects, micromechanics models have been developed, with the foam layer represented by regular and irregular honeycombs. Though the regular honeycomb model is seen to underestimate the size effects, the irregular honeycomb model faithfully captures the observed features of the constrained deformation of metallic foams.

Creep response of sandwich beams with a metallic foam core

The creep response of metallic foam sandwich beams in 3-point bend is investigated numerically for the case of a metallic foam core and two steel faces. The face sheets are treated as elastic, while the foam core is modeled by a viscoplastic extension of the Deshpande-Fleck yield surface. This power-law creeping constitutive law has been implemented within the commercial finite element code ABAQUS. It is found that the beams creep by a variety of competing mechanisms, depending upon the choice of material properties and the geometric parameters. A failure map is constructed and effect of rate dependence on the load-deflection curves is quantified, and compared against the available experimental data.

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Two-dimensional Cartesian air-gap element (CAGE) for dynamic finite-element modeling of electrical machines with a flat air gap

This paper extends the air-gap element (AGE) to enable the modeling of flat air gaps. AGE is a macroelement originally proposed by Abdel-Razek et al.for modeling annular air gaps in electrical machines. The paper presents the theory of the new macroelement and explains its implementation within a time-stepped finite-element (FE) code. It validates the solution produced by the new macroelement by comparing it with that obtained by using an FE mesh with a discretized air gap. It then applies the model to determine the open-circuit electromotive force of an axial-flux permanent-magnet machine and compares the results with measurements.

Fine scale structures from deformation of aluminium containing small alumina particles

Microstructures and mechanical properties have been studied in aluminium containing a fine dispersion of alumina particles, deformed by cold-rolling to strains between 1.4 and 3.5. The microstructure was characterised by TEM. The deformation structures evolved very rapidly, forming a nanostructured material, with fine subgrains about 0.2 μm in diameter and a fraction of high-angle boundaries which was already high at a strain of 1.4, but continued to increase with rolling strain. The yield stress and ductility of the rolled materials were measured in tension, and properties were similar for all materials. Yield stress measurements were correlated with estimates made using microstructural models. The role of small particles in forming and stabilising the deformation structure is discussed. This nanostructured cold-deformed alloy has mechanical properties which are usefully enhanced at comparatively low cost. This gives it, and similar particle-strengthened alloys, good potential for commercial exploitation. © 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

The effect of hole size upon the strength of metallic and polymeric foams

Tensile and compressive tests have been performed on centre-hole panels, made from three types of metallic foams and two polymeric foams. In compression, the foams fail in a ductile, notch-insensitive manner, in support of a "net section strength" criterion. In tension, a ductile-brittle transition is observed for some of the foams at sufficiently large specimen sizes: for a small hole diameter the net section strength criterion is obeyed, whereas for a large hole a local stress criterion applies and the net section strength is reduced. For a number of the foams, the panel size was not sufficiently large to observe this ductile-brittle switch in behaviour. The predictions of a cohesive zone model are compared with the measured strengths and are found to be in good agreement. © 2001 Elsevier Science Ltd. All rights reserved.

Plastic collapse of sandwich beams with a metallic foam core

Plastic collapse modes of sandwich beams have been investigated experimentally and theoretically for the case of an aluminum alloy foam with cold-worked aluminum face sheets. Plastic collapse is by three competing mechanisms: face yield, indentation and core shear, with the active mechanism depending upon the choice of geometry and material properties. The collapse loads, as predicted by simple upper bound solutions for a rigid, ideally plastic beam, and by more refined finite element calculations are generally in good agreement with the measured strengths. However, a thickness effect of the foam core on the collapse strength is observed for collapse by core shear: the shear strength of the core increases with diminishing core thickness in relation to the cell size. Limit load solutions are used to construct collapse maps, with the beam geometrical parameters as axes. Upon displaying the collapse load for each collapse mechanism, the regimes of dominance of each mechanism and the associate mass of the beam are determined. The map is then used in optimal design by minimizing the beam weight for a given structural load index.

Mode I crack growth resistance of metallic foams

A Dugdale-type cohesive zone model is used to predict the mode I crack growth resistance (R-curve) of metallic foams, with the fracture process characterized by an idealized traction-separation law that relates the crack surface traction to crack opening displacement. A quadratic yield function, involving the von Mises effective stress and mean stress, is used to account for the plastic compressibility of metallic foams. Finite element calculations are performed for the crack growth resistance under small scale yielding and small scale bridging in plane strain, with K-field boundary conditions. The following effects upon the fracture process are quantified: material hardening, bridging strength, T-stress (the non-singular stress acting parallel to the crack plane), and the shape of yield surface. To study the failure behaviour and notch sensitivity of metallic foams in the presence of large scale yielding, a study is made for panels embedded with either a centre-crack or an open hole and subjected to tensile stressing. For the centre-cracked panel, a transition crack size is predicted for which the fracture response switches from net section yielding to elastic-brittle fracture. Likewise, for a panel containing a centre-hole, a transition hole diameter exists for which the fracture response switches from net section yielding to a local maximum stress criterion at the edge of the hole.