Partial Fourier approximation of the Lamé equations in axisymmetric domains

In this paper, we study the partial Fourier method for treating the Lamé equations in three‐dimensional axisymmetric domains subjected to non‐axisymmetric loads. We consider the mixed boundary value problem of the linear theory of elasticity with the displacement û , the body force f̂ ϵ (L₂)³ and homogeneous Dirichlet and Neumann boundary conditions. The partial Fourier decomposition reduces, without any error, the three‐dimensional boundary value problem to an infinite sequence of two‐dimensional boundary value problems, whose solutions û _n (n = 0, 1, 2,…) are the Fourier coefficients of û . This process of dimension reduction is described, and appropriate function spaces are given to characterize the reduced problems in two dimensions. The trace properties of these spaces on the rotational axis and some properties of the Fourier coefficients û _n are proved, which are important for further numerical treatment, e.g. by the finite‐element method. Moreover, generalized completeness relations are described for the variational equation, the stresses and the strains. The properties of the resulting system of two‐dimensional problems are characterized. Particularly, a priori estimates of the Fourier coefficients û _n and of the error of the partial Fourier approximation are given. Copyright © 1999 John Wiley & Sons, Ltd.     

Effect of Substitution on the Hysteretic Phase Transition in a Bistable Phenalenyl-Based Neutral Radical Molecular Conductor

The ability to tune the physical properties of bistable organic functional materials by means of chemistry can facilitate their development for molecular electronic switching components. The butylamine-containing biphenalenyl boron neutral radical, [Bu]₂B, crystalline compound has recently attracted significant attention by displaying a hysteretic phase transition accompanied by simultaneous bistability in magnetic, electrical, and optical properties close to room temperature. In this report, substitutional doping was applied to [Bu]₂B by crystallizing solid solutions of bistable [Bu]₂B and its non-radical-containing counterpart [Bu]₂Be. With increasing doping degree, the hysteretic phase transition is gradually suppressed in terms of reducing the height, but conserves the width of the hysteresis loop as observed through magnetic susceptibility and electrical conductivity measurements. At the critical doping level of about 6 %, the abrupt transformation of the crystal structure to that of the pure [Bu]₂Be crystal packing was observed, accompanied by a complete collapse of the hysteresis loop. Further study of the structure–properties relationships of bistable neutral radical conductors based on the [Bu]₂B host can be conducted utilizing a variety of biphenalenyl-based molecular conductors.     

Scaffolding, ladders, chains, and rare ferrimagnetism in intermetallic borides: electronic structure calculations and magnetic ordering

The electronic structures of "Ti(9-n)Fe(2+n)Ru(18)B(8)" (n=0, 0.5, 1, 2, 3), in connection to the recently synthesized Ti(9-n)Fe(2+n)Ru(18)B(8) (n=1, 2), have been investigated and analyzed using LSDA tight-binding calculations to elucidate the distribution of Fe and Ti, to determine the maximum Fe content, and to explore possible magnetic structures to interpret experimental magnetization results. Through a combination of calculations on specific models and using the rigid band approximation, which is validated by the DOS curves for "Ti(9-n)Fe(2+n)Ru(18)B(8)" (n=0, 0.5, 1, 2, 3), mixing of Fe and Ti is anticipated at both the 2b- and 4h-chain sites. The model "Ti(8.5)Fe(2.5)Ru(18)B(8)" (n=0.5) revealed that both Brewer-type Ti-Ru interactions as well as ligand field splitting of the Fe 3d orbitals regulated the observed valence electron counts between 220 and 228 electrons/formula unit. Finally, models of magnetic structures were created using "Ti(6)Fe(5)Ru(18)B(8)" (n=3). A rigid band analysis of the LSDA DOS curves concluded preferred ferromagnetic ordering at low Fe content (n≤0.75) and ferrimagnetic ordering at higher Fe content (n>0.75). Ferrimagnetism arises from antiferromagnetic exchange coupling in the scaffold of Fe1-ladder and 4h-chain sites.     

Scaffolding, ladders, chains, and rare ferrimagnetism in intermetallic borides: synthesis, crystal chemistry and magnetism

Single-phase polycrystalline samples and single crystals of the complex boride phases Ti(8)Fe(3)Ru(18)B(8) and Ti(7)Fe(4)Ru(18)B(8) have been synthesized by arc melting the elements. The phases were characterized by powder and single-crystal X-ray diffraction as well as energy-dispersive X-ray analysis. They are new substitutional variants of the Zn(11)Rh(18)B(8) structure type, space group P4/mbm (no. 127). The particularity of their crystal structure lies in the simultaneous presence of dumbbells which form ladders of magnetically active iron atoms along the [001] direction and two additional mixed iron/titanium chains occupying Wyckoff sites 4h and 2b. The ladder substructure is ca. 3.0 ? from the two chains at the 4h, which creates the sequence chain-ladder-chain, establishing a new structural and magnetic motif, the scaffold. The other chain (at 2b) is separated by at least 6.5 ? from this scaffold. According to magnetization measurements, Ti(8)Fe(3)Ru(18)B(8) and Ti(7)Fe(4)Ru(18)B(8) order ferrimagnetically below 210 and 220 K, respectively, with the latter having much higher magnetic moments than the former. However, the magnetic moment observed for Ti(8)Fe(3)Ru(18)B(8) is unexpectedly smaller than the recently reported Ti(9)Fe(2)Ru(18)B(8) ferromagnet. The variation of the magnetic moments observed in these new phases can be adequately understood by assuming a ferrimagnetic ordering involving the three different iron sites. Furthermore, the recorded hysteresis loops indicate a semihard magnetic behavior for the two phases. The highest H(c) value (28.6 kA/m), measured for Ti(7)Fe(4)Ru(18)B(8), lies just at the border of those of hard magnetic materials.     

Effect of Residual Stresses on Delamination Cracks in Fiber Reinforced Composites

In the processing of cross-ply fiber reinforced materials, residual stresses, as well as possible transverse cracking may arise. These affect the stress field about a delamination between two layers. In this investigation, the effect of residual stresses resulting from curing and transverse cracks is examined. A 0°/90°/0° ply system is considered with a delamination assumed between one of the 0° and 90° layers. The residual stresses along the interface without the delamination are calculated. First, this analysis is done neglecting the transverse cracks in the 90° layer. Then, the transverse cracks are included and several methods are employed to calculate the residual stresses. These include the shear lag method, a semi-analytic method and the finite element method. It is seen that the latter two methods produce similar results. By means of the superposition principle, the stress intensity factors resulting from the residual stresses are obtained for the delamination. Use is made of the conservative M-integral with tractions along the crack faces.     

Optimization of microvia-technology using excimer laser for build-up layer application in microelectronics

In interconnection microelectronics microvias play a key role in the manufacture of high-density circuitry for use in electronic systems such as portable, smart sensors and computing applications. In the current work an excimer laser is used and microvias in the dielectric of the build-up layer are generated with the mask imaging method. Different laser parameters (demagnification factor, energy transmission percentage, fluence) are optimised in order to obtain microvias with different diameters, taper angle and aspect ratio. With electrochemical Cu-deposition interconnections between the upper and the underlying circuitry are realised. A nearly uniform thickness of the plated copper is obtained, and quality of the plating is assessed by means of the degree of delamination of the electrochemically deposited copper.