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Heterogeneous structures like composites often need a fine-scale resolution of micro-effects which influence the macroscopic overall response. This is of particular relevance in the fully non-linear range of large strains and inelastic material response of the constituents. Suitable solution methods introduce a multifield scenario of hierarchically superimposed states on different length scales. For big differences of micro- and macro-scales, the argument of scale separation induces the application of homogenization methods. Such types of physical multiscale approaches can be treated by nested multilevel finite element analyses that discretize both the fine-scale micro-structure as well as the macroscopic boundary-value problem. In contrast, small-scale differences require full resolution of the heterogeneous structure. Effective solution methods for the resulting large-scale problems with strongly oscillating properties are suitably designed geometric multigrid techniques, which may be considered as numerical multiscale approaches. In both scenarios, a key ingredient is the suitable formulation of scale bridging algorithms that govern the transfer between different scales. The paper outlines new mesh-bridging techniques in a deformation-driven context for fully non-linear response, which exploit in a non-trivial manner weak constraints on the average deformation in typical finite element patches. The framework is based on an incremental variational structure of finite inelasticity. The proposed new formulations provide variational-based homogenization algorithms for physical multiscale scenarios and problem-dependent optimal finite element grid transfers for numerical multiscale scenarios of heterogeneous materials. Copyright © 2007 John Wiley & Sons, Ltd.

Transmission x-ray microscopy with the x-ray magnetic circular dichroism as a contrast mechanism was used to image the field dependent evolution of magnetic domains in artificially nanostructured strips of a multilayered Fe/Gd system. A diversity of domain configurations have been imaged for different strengths of the applied magnetic field and different widths of the strips, varying between 100 nm and 1 μm. Undulating domain patterns, analogous to those observed in other condensed matter systems could be found.

The paper investigates a numerical procedure for the computation of the overall macroscopic elasticity moduli of linear composite materials with periodic micro-structure. We consider a homogenized macro-continuum with locally attached representative micro-structure which characterizes a representative cell of a composite. The deformation of the micro-structure is assumed to be coupled with the local deformation at a typical point of the macro-continuum by three alternative constraints of the microscopic fluctuation field. The underlying key approach is a finite element discretization of the boundary value problem for the fluctuation field on the micro-structure of the composite. This results into a distinct closed-form representation of the overall elasticity moduli in terms of a Taylor-type upper bound term and a characteristic softening term which depends on global fluctuation stiffness matrices of the discretized micro-structure. With this representation in hand, overall moduli of periodic composites can be computed in a straightforward manner for a given finite element discretization of the micro-structure. We demonstrate the concept for three types of periodic composites and compare the results with well-known analytical estimates.

Continuous films and nanostructures of atomically stacked epitaxial Fe(0 0 1)/Au(0 0 1) multilayers have been studied by soft X-ray and Lorentz microscopy as well as micromagnetic simulations. Domain imaging shows about 65 nm wide magnetic stripe domains, in which the magnetization is oriented perpendicular to the film plane. These results are confirmed by micromagnetic simulations, which also yield additional information about the internal structure of domains and walls.

The paper reports some investigations made with VITROVAC 6025 X ribbons and their applicability for parallel-gated configuration sensors. During appropriate stress annealing a hard axis anisotropy was induced in the ribbon. The effect depends both on the pre-annealing temperature and its duration and on the applied longitudinal tensile stress. The obtained results are discussed in terms of the magnetization processes which take place within the ribbon. The applicability of VITROVAC 6025 X amorphous alloy for parallel-gated configuration sensors was proved by developing TFS-3 type sensors. Measurements of the functional parameters indicated good thermostability, lower magnetic noise levels and lower offset values for the sensors using suitably heat treated VITROVAC 6025 X ribbons.

Bei der Umsetzung von reduzierten Phillips-Katalysatoren mit Ethylen bei 300 °C wird der Katalysator nach kurzer Zeit desaktiviert; gleichzeitig entstehen tragergebundene Chrom-Organyle. Diese konnen vom Silicagel-Trager mit HCl und anderen Sauren gespalten und mit CH3OH extrahiert werden. Durch Chromatographie werden Fraktionen von Organochrom-Verbindungen erhalten, die sich um CH2-Einheiten unterscheiden. XPS-, 1/2H-NMR- und Massenspektren sowie magnetische Messungen beweisen, das Homologe des Typs (RnCp)CrCl2(CH3OH) (RnCp = alkyliertes Cyclopentadienyl) vorliegen. Der RnCp-Ligand bildet sich durch oxidative Verknupfung, – ggf. unter CC-Spaltung – von Chrom-gebundenem Olefin. Gemas UV/Vis- und Massenspektren konnen Cl– und CH3OH durch andere Anionen und Donormolekule ersetzt werden. Ohne Donor werden zweikernige, Cl-verbruckte Molekule erhalten, von denen [(1,2,3-Me3Cp)CrCl2]2 durch Kristallstrukturanalyse gesichert wurde. Einwirkung von O2 fuhrt reversibel zu Chrom(V)-Derivaten vom Typ (RnCp)Cr(O)Cl2. Surface Compounds of Transition Metals. XLI [1] Preparation and Properties of Organochromium Compounds by Reaction of Phillips Catalysts with Ethylene Reaction of reduced Phillips catalysts with ethylene at 300 °C deactivates the catalyst; supported organochromium compounds are formed. These can be cleaved from the silica support by HCl and other acids, and transferred into solution by extraction with CH3OH. Chromatography yields fractions of organochromium compounds which differ by CH2 moieties. XPS, 1/2H NMR, and mass spectra as well as magnetic measurements prove that an ensemble of (RnCp)CrCl2(CH3OH) (RnCp = alkylated cyclopentadienyl) has been formed. The RnCp ligand results from a chromium-assisted oxidative coupling of the olefin with or without CC-cleavage. According to UV/Vis and mass spectroscopy Cl– and CH3OH can be substituted for other anions and donor molecules. Without a donor dinuclear, Cl-bridged molecules are obtained, of which [(1,2,3-Me3Cp)CrCl2]2 was established by crystal structure analysis. Reaction with O2 reversibly leads to chromium(V) compounds of the type (R2Cp)Cr(O)Cl2.

The combination of magnetic circular dichroism as a magnetic contrast mechanism and a transmission x-ray microscope allows imaging of magnetic structures with lateral resolutions down to 25 nm. Results on magneto-optical Tb25(Fe75Co25)75 layers system with thermomagnetically written bits of various sizes were obtained at the x-ray microscope XM-1 at the Advanced Light Source in Berkeley, CA. The results prove the thermal stability of the bits in the recording process. Furthermore the capability of soft x-ray microscopy with respect to the achievable lateral resolution, element specificity and sensitivity to thin magnetic layers is demonstrated. The potential of imaging in applied magnetic fields for both out-of-plane and in-plane magnetized thin magnetic films is outlined.

Heterogeneous structures like composites often need a fine-scale resolution of micro-effects which influence the macroscopic overall response. This is of particular relevance in the fully nonlinear range of large strains and inelastic material response of the constituents. Suitable solution methods introduce a multifield scenario of hierarchically superimposed states on different length scales. For big differences of micro- and macro-scales, the argument of scale separation induces the application of homogenization methods. Such types of physical multiscale approaches can be treated by nested multilevel finite element analyses that discretize both the fine-scale micro-structure as well as the macroscopic boundary-value problem. In contrast, small scale differences require full resolution of the heterogeneous structure. Effective solution methods for the resulting large-scale problems with strongly oscillating properties are suitably designed geometric multigrid techniques, which may be considered as numerical multiscale approaches. In both scenarios, a key ingredient is the suitable formulation of scale bridging algorithms that govern the transfer between different scales. The paper outlines new mesh-bridging techniques in a deformation-driven context for fully nonlinear response, which exploit in a nontrivial manner weak constraints on the average deformation in typical finite element patches. The framework is based on an incremental variational structure of finite inelasticity. The proposed new formulations provide variational-based homogenization algorithms for physical multiscale scenarios and problem-dependent optimal finite element grid transfers for numerical multiscale scenarios of heterogeneous materials.

We discuss different concepts for the construction of transfer operators with regard to the application of multigrid methods to an efficient solving of strongly heterogeneous, linear elastic materials. The micro-structure is assumed to be resolved sufficiently well. The key contribution is the formulation of new physically motivated approaches for linear-elastic composites with arbitrary micro-structures. This task is achieved by means of a numerical homogenization concept based on a variational principle. The efficiency of the new approaches will be compared with alternative techniques in the scope of a representative model problem.

The X-ray magnetic circular dichroism (X-MCD), i.e., the dependence of the absorption of circularly polarized X-rays on the magnetization of the absorber exhibits at L-edges of transition metals values up to 25%. This can serve as a huge magnetic contrast mechanism in combination with a transmission X-ray microscope (TXM) to image magnetic domains providing a lateral resolution down to about 30 nm. The inherent element-specificity, the possibility to record images in varying external fields within a complete hysteresis loop, the relation of the contrast to local magnetic spin and orbital moments, etc. demonstrate the unique applicability to study the magnetic domain structure in current technical relevant systems like magneto-optics for high density storage media, multilayers for GMR applications or nanostructures for MRAM technology.

We discuss different concepts for the construction of transfer operators with regard to the application of multigrid methods to an efficient solving of strongly heterogeneous linear—elastic materials. The key contribution is a new physically motivated approach. In order to take into account the influence of the heterogeneity the idea is to perform a numerical homogenization within a characteristic subdomain. This subdomain is assumed to be resolved by a local finite element discretization. The efficiency of the new approach is demonstrated by means of some fundamental model problems and compared with existing methods.

The aim of the study was to investigate the influence of dental alloys and their components on magnetic resonance imaging of the temporomandibular joint. A plaster and a water- filled acrylic resin phantom - representing the disc and the condyle of the TMJ - were used. Cylindrical crow-type samples of 13 alloys and 14 pure substances were investigated. All alloys were examined with regard to their magnetic susceptibility, using a vibrating sample magnetometer. Metallic artefacts appeared on spin-echo technique as distortions, and on gradient-echo technique signal loss could be observed. Precious alloys were shown to be diamagnetic. The non precious alloys we investigated were paramagnetic. Paramagnetic alloys with a magnetic molar-susceptibility Cmol2000 x10(-6) cm3/mol can produce clinically relevant artefacts.

Mehrgitterverfahren eignen sich ideal zur Losung groser dunnbesetzter Gleichungssysteme, wie sie bei FE-Diskretisierungen komplexer Randwertprobleme auftreten konnen. Im Kontext heterogener Materialien wird eine Vorgehensweise vorgeschlagen, in der Zugange der materialtheoretischen Mehrskalenbildung und Mehrgittermethoden zusammengefuhrt werden. Das neue Mehrgitterkonzept hat sowohl algebraische als auch geometrische Grundstruktur. Die Effizienz des neuen Konzepts wird am Beispiel des geometrischen Mehrgitters anhand reprasentativer Modellprobleme mit bekannten Verfahren verglichen. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mehrgitterverfahren ermoglichen eine effiziente Losung groser Gleichungssysteme, die bei Finite Element-Diskretisierungen nichtlinearer Randwertprobleme auftreten konnen. Bei heterogenen Materialien bedingt der Einsatz solcher Loser die Konstruktion spezieller Transferoperatoren. Diese Aufgabe wird mit Hilfe von Homogenisierungstechniken gelost. Die neuen Strategien werden anhand reprasentativer Modellprobleme mit bekannten Verfahren verglichen.

Die Losung groser Gleichungssysteme infolge der FE-Diskretisierung heterogener Materialien mit Mehrgitterverfahren kann nur mittels geeigneter Transfer- und Grobgitteroperatoren effizient erfolgen. Wesentlicher Aspekt bei der Konstruktion der erforderlichen Operatoren ist die Verknupfung mit einem diskreten Homogenisierungskonzept. Diese neue Strategie wird anhand eines reprasentativen Modellproblems mit bekannten alternativen Verfahren verglichen.

An oscillatory interlayer exchange coupling observed in many sandwich and multilayer films can be understood as an interference effect of electron waves partially reflected at each interface with spin dependent reflection coefficients. Consequently, we might expect all magnetic properties in some way related to the density of states to oscillate as a function of the magnetic and nonmagnetic layer thickness. In order to experimentally test this concept we have measured different magnetic properties of Ni/Au multilayer films prepared by magnetron sputtering on glass substrates. The Ni thickness was kept constant at tNi=(7.3±0.5) A while the Au layer thickness was varied between 4 A and 80 A. The films had a coherent fcc structure with (111) texture. The saturation field and the remanence oscillate as a function of tAu with a period which agrees well with a theoretical value calculated from the bulk Fermi surface of Au and proves that indeed an oscillatory exchange coupling is present. The Curie temperature ...

We succeeded in growing ultrathin Fe(110) films in ultrahigh vacuum sandwiched between Au(111), which show ferromagnetic behaviour even below monolayer coverage. For the first time, low-temperature magnetization measurements on such Au-Fe-Au sandwiches reveal a switching of the easy axis from the film plane to the film normal in iron films thinner than 3 monolayers (ML). We interpret this as an interface effect. The usually dominating shape anisotropy is overcompensated by a magnetic interface anisotropy at smaller iron coverages. The effective magnetic anisotropy field at 10 K is proportional to the inverse iron thickness down to 2 ML. The related interface anisotropy field is determined to 40 kOe per single Fe(110)-Au interface.

The magnetic ground state, magnetic anisotropies and spin excitations of surfaces, interfaces and ultra-thin films of ferromagnetic 3d-metals are discussed. Enhanced magnetic ground state moments and altered hyperfine fields as predicted by ab initio band calculations have not been conclusively verified by experiments up to now. Future calculations should take into account dipolar fields and the role of interface roughness. Very large magnetic anisotropies are observed at magnetic surfaces and interfaces. In Ni/Cu multilayered films, the superposition of surface and stress-induced anisotropies was used to switch the easy axis of magnetization from the film plane to a perpendicular orientation by a proper choice of the Ni layer thickness. This could be an attractive possibility to develop new magnetic materials for technical applications. The temperature dependence of the spontaneous magnetization at surfaces and in ultra-thin films deviates from the behaviour of bulk material. Size effects as well as surface effects of spin wave excitations are discussed, comparing theoretical and experimental results. The need for more complete theories including surface exchange, surface anisotropy and realistic surface structures is emphasized.

The overall fall-back angle α50 of thin uniaxial ferromagnetic films was calculated including the effect of the magnetization ripple and the skew. Both, ripple and skew angle were assumed to show a Gaussian distribution with different standard deviations. Ripple and skew are superimposed in a nonlinear manner to give the fall-back angle of the entire film. By direct measurements of the ripple fall-back angle, α500, for very small spots of the film, of the fall-back angle, α50, of the entire film, and of the distribution and standard deviation of the skew, the calculation could be tested, which gave good agreement between experiment and theory. As long as the skew is unknown the fall-back angle alone is not the best measure for the “quality” of an uniaxial film.

Previous investigations of ultra‐thin epitaxial Fe (110) films grown on Ag (111) have indicated that there is a measurable increase at 4.2 K in the magnetic hyperfine field compared with bulk value in iron atoms in the first three surface layers of the films. As these films were produced in ultra‐vacuum and then removed for study by transmission Mossbauer spectroscopy it was necessary to provide a protective overcoat to prevent oxidation of the surface. Because of this it was not possible to rule out interaction of the Fe surface with the overcoat layers as a cause of the increased surface hyperfine field. A series of new films have been made of isotopically pure 56Fe. A thin probe layer of 57Fe ranging in thickness from 4–10 A was then deposited on the film surface and a variety of different overcoat layers subsequently chosen to protect these films. Overcoating materials included Ag, Au, Cu, Ge, MnF2, and NaCl. While there were differences in the hyperfine fields and isomer shifts of the 57Fe probe laye...

The order-disorder transition in Fe-Co thin films has been studied by secondary electron Mossbauer spectroscopy. The inhomogeneous character of the disordering process and the role of lattice defects for the interpretation of asymmetric Mossbauer spectra in the case of Fe-Co are pointed out.