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- Electron backscatter diffraction (19)
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We discuss a refined simulation approach which treats Kikuchi diffraction patterns in electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction (TKD). The model considers the result of two combined mechanisms: (a) the dynamical diffraction of electrons emitted coherently from point sources in a crystal and (b) diffraction effects on incoherent diffuse intensity distributions. Using suitable parameter settings, the refined simulation model allows to reproduce various thickness- and energy-dependent features which are observed in experimental Kikuchi diffraction patterns. Excess-deficiency features are treated by the effect of gradients in the incoherent background intensity. Based on the analytical two-beam approximation to dynamical electron diffraction, a phenomenological model of excess-deficiency features is derived, which can be used for pattern matching applications. The model allows to approximate the effect of the incident beam geometry as a correction signal for template patterns which can be reprojected from pre-calculated reference data. As an application, we find that the accuracy of fitted projection centre coordinates in EBSD and TKDcan be affected by changes in the order of 10−3–10−2 if excess-deficiency
features are not considered in the theoreticalmodel underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer frombiases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.
CALM is software for determining the Bravais lattice type and the resulting lattice parameters from a single Kikuchi pattern. It requires the definition of 4 bands and a single bandwidth from which all other band positions as well as bandwidths are derived. For band detection, it uses the Funk transform, which allows detection of twice as many bands as usual. CALM works for any symmetry and requires low-noise patterns of at least 320x240 pixels. The resulting errors are <2% even for such small patterns, assuming good quality. The relative errors are <0.5%. However, this requires a projection centre position best derived from a sample of a cubic phase in CALM. However, this must have been recorded under identical conditions. Hundreds of Kikuchi patterns of phases with different symmetries were examined.
CALM is software for determining the Bravais lattice type and the resulting lattice parameters from a single Kikuchi pattern. It requires the definition of 4 bands and a single bandwidth from which all other band positions as well as bandwidths are derived. For band detection, it uses the Funk transform, which allows detection of twice as many bands as usual. CALM works for any symmetry and requires low-noise patterns of at least 320x240 pixels. The resulting errors are <2% even for such small patterns, assuming good quality. The relative errors are <0.5%. However, this requires a projection centre position best derived from a sample of a cubic phase in CALM. However, this must have been recorded under identical conditions. Hundreds of Kikuchi patterns of phases with different symmetries were examined.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
The program PowderCell is a crystallographic tool for visualization of Crystal structures. However, it offers also non-conventional features like the fulautomatical generation of subgroups or the consideration of non-standard settings of space-group types. On the one Hand the program is very useful for non-crystallographers who like to get an impression of the atomic arrangement within the unit cell. But also for crystallographers it is recommendable because it contains a lot of additional information which can be extracted and used like data given in the International Tables for Crystallography, Vol. A. However, the most important advantage of the program is the simultaneous calculation of the X-ray or neutron diffraction powder patterns for a mixture of up to 10 crystalline phases. Between more than 7 different characteristic radiations can be chosen and their influence on the resulting powder pattern can be studied. Furthermore, experimental diffractograms can be analysed using a refinement procedure. The implemented LeBail-algorithm allows the investigation of unknown phases. In combination with the refinement algorithm an interface to Shelx offers the possibility for a step by step ab initio structure analysis. Certainly, the user-friendly shell is one reason that especially users who are not so familar with space-group symmetry, crystal structure data or diffractometry use this powerful tool for the solution of scientific or analytical problems as well as in teaching.
X-ray stress analysis on crystalline materials is based on the determination of elastic lattice strains. The strains described by the shift of peak positions are converted to stresses by the means of theory of elasticity. The development of the sin2ψ-method of X-ray stress analysis introduced an enormous progress in X-ray stress analysis during the last decades. This report outlines some important elements of X-ray physics and fundamentals of theory of elasticity. The Standard measuring procedure are described and special experimental differences to the common powder diffractometry are outlined.
During focused ion beam microscopy (FIB) of crystalline materials imaging contrast and milling result are effected by orientation of the crystals with respect to the incident ion beam. This is due to the possibility of ion channeling along preferred crystal directions which effects the depth at which interaction between ions and specimen atoms takes place. As a result of channeling emission of ion induced secondary electrons (iiSE) and secondary ions (SI) as well as the sputter rate decreases.
Theoretical channeling orientations and critical angles can be calculated.
These effects have been studied quantitatively for polycrystalline recrystallized Cu as a typical model case.
The competitive growth of columnar grains in a single-grain selector, which is used for directional solidification of single-crystal blades from nickel-based superalloys, has been investigated by electron backscattered diffraction and local X-ray diffraction analysis. It has been found that the competitive grain growth in a starter block is determined by the crystallographic factor: rapidly growing grains with the axial orientation close to the [001] direction dominate in this part of the casting. For the competitive grain growth in a helicoidal separator, the geometric factor (the position of a grain at the input of the separator) is also important. The results obtained suggest that an appropriate geometry of the single-grain selector was chosen. In addition, the distribution of the orientations of columnar grains obtained by electron backscattered diffraction, can be used for approximate estimation of the yield of suitable (i.e., with the deviation of the axial orientation from the [001] direction within a specified tolerance) single-crystal blades.
Fatigue crack propagation investigations have been performed in austenitic-ferritic duplex stainless steel H22N5M3 in air and during hydrogen charging, using various frequencies of loading. Strong differences of crack propagation velocity depending on the test conditions were noticed. Lower frequency with applied hydrogen charging led to the huge increase of crack propagation velocity compared to the tests performed in air. To understand such a behaviour in each case and characterize crack mode, the samples were observed using electron back-scattered diffraction (EBSD). It was shown that in air, the fatigue crack propagation involved plastic deformation and the resulting cracks had ductile character. The presence of hydrogen led to more brittle mode of cracking. This effect was also connected with frequency of loading: lower frequency, which assured longer time for hydrogen-crack tip interaction, resulted in the highest crack propagation velocity and the brittle cracking mode with lower amount of plastic deformation. The performed observations indicated that the path of the crack went mostly transgranularly through both austenite and ferrite phases. Phase and grain boundaries were not the preferred paths for crack propagation.