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Approximant-based orientation determination of quasicrystals using electron backscatter diffraction
(2020)
Orientation mapping of quasicrystalline materials is demonstrated using crystalline approximant structures in the technique of electron backscatter diffraction (EBSD). The approximant-based orientations are symmetrised according to the rotational point group of the quasicrystal, including the visualization of orientation maps using proper colour keys for quasicrystal symmetries. Alternatively, approximant-based orientation data can also be treated using pseudosymmetry post-processing options in the EBSD system software, which enables basic grain size estimations. Approximant-based orientation analyses are demonstrated for icosahedral and decagonal quasicrystals.
Electron backscatter diffraction (EBSD) is a technique to obtain microcrystallographic information from materials by collecting large-angle Kikuchi patterns in the scanning electron microscope (SEM). An important fundamental question concerns the scattering-angle dependent electron energy distribution, which is relevant for the formation of the Kikuchi diffraction patterns. Here we review the existing experimental data and explore the effective energy spectrum that is operative in the generation of backscatter Kikuchi patterns from silicon. We use a full pattern comparison of experimental data with dynamical electron diffraction simulations. Our energy-dependent cross-correlation based pattern matching approach establishes improved constraints on the effective Kikuchi pattern energy spectrum, which is relevant for high-resolution EBSD pattern simulations and their applications.
Orientation determination does not necessarily require complete knowledge of the local atomic arrangement in a crystalline phase. We present a method for microstructural phase discrimination and orientation analysis of phases for which there is only limited crystallographic information available. In this method, experimental Kikuchi diffraction patterns are utilized to generate a self-consistent master reference for use in the technique of Electron Backscatter Diffraction (EBSD). The experimentally derived master data serves as an application-specific reference in EBSD pattern matching approaches. As application examples, we map the locally varying orientations in samples of icosahedral quasicrystals observed in a Ti40Zr40Ni20 alloy, and we analyse AlNiCo decagonal quasicrystals.
Hydrocarbons fuel our economy. Furthermore, intermediate goods and consumer products are often hydrocarbon-based. Beside all the progress they made possible, hydrogen-containing substances can have severe detrimental effects on materials exposed to them. Hydrogen-assisted failure of iron alloys has been recognised more than a century ago. The present study aims to providing further insight into the degradation of the austenitic stainless steel AISI 304L (EN 1.4307) exposed to hydrogen. To this end, samples were electrochemically charged with the hydrogen isotope deuterium (2H, D) and analysed by scanning electron microscopy (SEM), electron back-scatter diffraction (EBSD) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). It was found that deuterium caused a phase transformation from the original γ austenite into ε- and α’-martensite. Despite their low solubility for hydrogen, viz. deuterium, the newly formed phases showed high deuterium concentration which was attributed to the increased density of traps. Information about the behaviour of deuterium in the material subjected to external mechanical load was gathered. A four-point-bending device was developed for this purpose. This allowed to analyse in-situ pre-charged samples in the ToF-SIMS during the application of external mechanical load. The results indicate a movement of deuterium towards the regions of highest stress.
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.
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.
A historical tool for crystallographic analysis is provided by the Hilton net, which can be used for manually surveying the crystal lattice as it is manifested by the Kikuchi bands in a gnomonic projection. For a quantitative analysis using the Hilton net, the projection centre as the relative position of the signal source with respect to the detector plane needs to be known. Interplanar angles are accessible with a precision and accuracy which is estimated to be ≤0.3o. Angles between any directions, e.g. zone axes, are directly readable. Finally, for the rare case of an unknown projection-centre position, its determination is demonstrated by adapting an old approach developed for photogrammetric applications.
It requires the indexing of four zone axes [uvw]i in a backscattered Kikuchi diffraction pattern of a known phase collected under comparable geometric conditions.
To visualize the varying tetragonal distortions in high carbon martensitic steels by EBSD, two different approaches have been applied on backscattered Kikuchi diffraction (BKD) patterns. A band-edge refinement technique called Refined Accuracy (RA) (Oxford Instruments) is compared with a technique called Pattern Matching (PM), which optimizes the fit to a simulated BKD signal. RA distinguishes between hypothetical phases of different fixed 𝑐∕𝑎, while PM determines a best fitting continuous 𝑐∕𝑎 by projective transformation of a master pattern. Both techniques require stored BKD patterns.
The sensitivity of the 𝑐∕𝑎-determination was tested by investigating the microstructure of a ferritic steel with an expected 𝑐∕𝑎 = 1. The influence of the Kikuchi pattern noise on 𝑐∕𝑎 was compared for a single or 40 averaged frames per measuring point, and turned out to be not significant. The application of RA and PM on the martensitic microstructure delivered qualitatively similar maps of 𝑐∕𝑎. The comparison of RA and PM shows that RA is suitably fast and precise during mapping the martensite 𝑐∕𝑎 ratio in analyses of high carbon martensite, especially for fast initial surveys. As RA leads quantitatively to higher noise in 𝑐∕𝑎, the PM analysis can be used for higher precision results.
A glass of the composition 37BaO·16CaO·47SiO2 wt% produced on an industrial scale is crystallized at 970 °C for times ranging from 15 min to 2 h. The crystallization at the immediate surface as well as the crystal growth into the bulk are analyzed using scanning electron microscopy (SEM) including energy dispersive X-ray spectroscopy (EDXS) and electron backscatter diffraction (EBSD) as well as X-ray diffraction in the Θ–2Θ setup (XRD). The immediate surface shows the oriented nucleation of walstromite as well as the formation of wollastonite and an unknown phase of the composition BaCaSi3O8. All three phases also grow into the bulk where walstromite ultimately dominates the kinetic selection and grows throughout the bulk due to a lack of bulk nucleation. Walstromite shows systematic orientation changes as well as twinning during growth. A critical analysis of the XRD-patterns acquired from various crystallized samples indicates that their evaluation is problematic and that phases detected by XRD in this system should be verified by another method such as EDXS.
Oriented surface crystallization on polished diopside glass surfaces has been studied with scanning electron microscopy, electron backscatter diffraction, transmission electron microscopy and laser scanning microscopy.
An orientation preference of [001] parallel to the glass surface was detected for separately growing diopside crystals even as small as 700 nm in size. This finding shows that crystal orientation occurs in the outermost surface layer without crystal-crystal interaction and indicates that the crystal orientation is a result of oriented nucleation. Depending on surface preparation, monomodal crystal orientation distributions with [100] perpendicular to the surface or bimodal distributions with [100] and [010] perpendicular to the glass Surface were detected. It was also shown that the degree of crystal orientation increases with decreasing Surface roughness. The observed orientation of diopside crystals could be explained in terms of the interfacial energies of different crystal faces.