Mathematical morphology stems from set theory and it makes use of properties of point sets. The first point set is an origin image and the second one (usually smaller) is a structuring element. Morphological image transformations are image to image transformations based on a few elementary set operators. Fundamental morphologic operations are dilation, erosion and hit or miss. Next operations described in this work are opening and closing. Originally morphological operators were used for binary images only, later they were generalized for grey tone and color ones. This work describes the basic morphological image processing methods including their practical usage in image filtering and segmentation.

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Within the collaborative research center SFB 920 “Multifunctional Filters for Metal Melt Filtration”, the thermally induced formation of metastable aluminum oxides and related microstructural changes were investigated. It was confirmed that the γ-Al₂O₃ phase possesses a defective spinel structure containing Al vacancies that preserve the stoichiometry of this phase. The presence of vacancies fragments apparently the γ-Al₂O₃ crystallites into nanocrystalline domains, which are separated by non-conservative antiphase boundaries (APBs) of the type {100} ¼<110>. These APBs form a 3D network that is randomly distributed over all crystallographically equivalent lattice planes. This phenomenon causes a starlike (and hkl-dependent) broadening of the reciprocal lattice points that correspond to the aluminum sublattice. It was shown that the extent of the broadening of the reciprocal lattice points can be predicted by employing the phase shift factors. With increasing degree of the APBs ordering, the initial streaks representing the broadened reflections start to split, forming superstructure reflections. This superstructure of γ-Al₂O₃ is commonly known as δ-Al₂O₃. Between the ordered APBs, the crystal structure of δ-Al₂O₃ is closely related to the crystal structure of monoclinic θ-Al₂O₃. The phase transition of γ-Al₂O₃/δ-Al₂O₃ to θ-Al₂O₃ proceeds via migration of just three Al³⁺ cations to the neighboring tetrahedral and octahedral sites in the cubic close packed (ccp) oxygen sublattice. The general migration vector is ⅛<111> (γ-Al₂O₃). Diffraction effects associated with different intermediate states can be explained by an improper long-range ordering of equivalent APBs or certain Al³⁺ cations and the local formation of θ-Al₂O₃ within the δ-Al₂O₃ superstructure. The formation of θ-Al₂O₃ is accompanied by an increase of the occupancy of the tetrahedral sites in the oxygen sublattice by the Al³⁺ cations. In surrounding local γ-Al₂O₃ domains, however, some cations migrate from the tetrahedral to the octahedral sites. Thus, the local formation of θ-Al₂O₃ is nearly invisible for the ²⁷Al 1D magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy. Still, it was recognized by the 2D multiple quantum (MQ) MAS NMR spectroscopy. A continuous formation of the θ-Al₂O₃ domains was confirmed by the Raman spectroscopy, X-ray diffraction (XRD) and selected area electron diffraction (SAED). The proposed microstructure and transformation models helped to explain the thermal stabilization of the metastable alumina phases by Si-doping. For investigation of the thermally induced phase transitions in metastable alumina phases, boehmite (γ-AlO(OH)) was chosen as the starting compound. However, the metastable alumina phases were also observed in endogenous inclusions present in solidified steel melts. For identification of these phases, a procedure for reconstruction of spherical Kikuchi maps from recorded EBSD patterns was developed.

In dieser Arbeit werden das Wachstum mittels Molekularstrahlepitaxie und die Eigenschaften der Ferromagneten Fe und Fe_3Si auf niedrig-symmetirschen GaAs(113)A-Substraten studiert. Drei wichtige Aspekte werden untersucht: (i) Wachstum und strukturelle Charakterisierung, (ii) magnetische Eigenschaften und (iii) Magnetotransporteigenschaften der Fe und Fe_3Si Schichten auf GaAs(113)A-Substraten. Das Wachstum der Fe- und Fe_3Si-Schichten wurde bei einer Wachstumstemperatur von = bzw. 250 °C optimiert. Bei diesen Wachstumstemperaturen zeigen die Schichten eine hohe Kristallperfektion und glatte Grenz- und Oberflächen analog zu [001]-orientierten Schichten. Weiterhin wurde die Stabilität der Fe_(3+x)Si_(1-x) Phase über einen weiten Kompositionsbereich innerhalb der Fe_3Si-Stoichiometry demonstriert. Die Abhängigkeit der magnetischen Anisotropie innerhalb der Schichtebene von der Schichtdicke weist zwei Bereiche auf: einen Beresich mit dominanter uniaxialer Anisotropie für Fe-Schichten = 70 MLs. Weiterhin wird eine magnetische Anisotropie senkrecht zur Schichtebene in sehr dünnen Schichten gefunden. Der Grenzflächenbeitrag sowohl der uniaxialen als auch der senkrechten Anisotropiekonstanten, die aus der Dickenabhängigkeit bestimmt wurden, sind unabhängig von der [113]-Orientierung und eine inhärente Eigenschaft der Fe/GaAs-Grenzfläche. Die anisotrope Bindungskonfiguration zwischen den Fe und den As- oder Ga-Atomen an der Grenzfläche wird als Ursache für die uniaxiale magnetische Anisotropie betrachtet. Die magnetische Anisotropie der Fe_3Si-Schichten auf GaAs(113)A-Substraten zeigt ein komplexe Abhängigkeit von der Wachstumsbedingungen und der Komposition der Schichten. In den Magnetotransportuntersuchungen tritt sowohl in Fe(113)- als auch in Fe_3Si(113)-Schichten eine antisymmetrische Komponente (ASC) im planaren Hall-Effekt (PHE) auf. Ein phänomenologisches Modell, dass auf der Kristallsymmetrie basiert, liefert ein gute Beschreibung sowohl der ASC im PHE als auch des symmetrischen, anisotropen Magnetowiderstandes. Das Modell zeigt, dass die beobachtete ASC als Hall-Effekt zweiter Ordnung beschreiben werden kann. / In this work, the molecular-beam epitaxial growth and properties of ferromagnets, namely Fe and Fe_3Si are studied on low-symmetric GaAs(113)A substrates. Three important aspects are investigated: (i) growth and structural characterization, (ii) magnetic properties, and (iii) magnetotransport properties of Fe and Fe_3Si films on GaAs(113)A substrates. The growth of Fe and Fe_3Si films is optimized at growth temperatures of 0 and 250 degree Celsius, respectively, where the layers exhibit high crystal quality and a smooth interface/surface similar to the [001]-oriented films. The stability of Fe_(3+x)Si_(1-x) phase over a range of composition around the Fe_3Si stoichiometry is also demonstrated. The evolution of the in-plane magnetic anisotropy with film thickness exhibits two regions: a uniaxial magnetic anisotropy (UMA) for Fe film thicknesses = 70 MLs. The existence of an out-of-plane perpendicular magnetic anisotropy is also detected in ultrathin Fe films. The interfacial contribution of both the uniaxial and the perpendicular anisotropy constants, derived from the thickness-dependent study, are found to be independent of the [113] orientation and are hence an inherent property of the Fe/GaAs interface. The origin of the UMA is attributed to anisotropic bonding between Fe and As or Ga at the interface, similarly to Fe/GaAs(001). The magnetic anisotropy in Fe_3Si on GaAs(113)A exhibits a complex dependence on the growth conditions and composition. Magnetotransport measurements of both Fe(113) and Fe_3Si(113) films shows the striking appearance of an antisymmetric component (ASC) in the planar Hall effect (PHE). A phenomenological model based on the symmetry of the crystal provides a good explanation to both the ASC in the PHE as well as the symmetric anisotropic magnetoresistance. The model shows that the observed ASC component can be ascribed to a second-order Hall effect.