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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.
Characterization of the fcc/bcc orientation relationship by EBSD using pole figures and variants
(2004)
The orientation relationship (OR) between fcc and bcc lattices are described by crystallographic fundamentals using the example of Kurdjumov-Sachs (K-S) and Nishiyama-Wassermann (N-W). Complete pole figures containing all variants will be used to distinguish even between slightly different ORs. EBSD on iron meteorites and duplex steel has been used to analyse a large number of crystal orientations with regard to a high statistical significance and a high probability to capture all variants in a single measurement. It is shown that the use of fixed OR models like K-S, N-W, Bain, Pitsch, or Greninger-Troiano does not satisfacturally reflect the observed experimental pole distributions. It is not convenient to use high-indexed lattice planes and directions to describe the small deviations from the given models. The Euler subspace representation offers a readily comprehensible tool to get an idea about the characteristic of the experimentally detected OR.
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.
Kikuchi diffraction patterns can provide fundamental information about the lattice metric of a crystalline phase. In order to improve the possible precision and accuracy of lattice parameter determination from the features observed in Kikuchi patterns, some useful fundamental relationships of geometric crystal-lography are reviewed, which hold true independently of the actual crystal symmetry. The Kikuchi band positions and intersections and the Kikuchi band widths are highly interrelated, which is illustrated by the fact that all lattice plane trace positions of the crystal are predetermined by the definition of only four traces. If, additionally, the projection centre of the gnomonic projection is known, the lattice parameter ratios and the angles between the basis vectors are fixed. A further definition of one specific Kikuchi band width is sufficient to set the absolute sizes of all lattice parameters and to predict the widths of all Kikuchi bands. The mathematical properties of the gnomonic projection turn out to be central to an improved interpretation of Kikuchi pattern data, emphasizing the importance of the exact knowledge of the projection centre.
Electron backscatter diffraction (EBSD) and scanning electron microscopy were combined to study the effect of residual defect density on corrosion initiation in aluminium alloy AA2024-T3. EBSD was used to determine the level of misorientation (MO), from pixel to pixel, within individual grains. The MO can be determined with respect to either the average orientation angle of the grain or with respect to the average orientation angle of the surrounding pixels (in this instance, a matrix of 7×7 surrounding pixels has been applied). Herein, the MO, determined using the surrounding pixels, was used as the means for the assessing the level of defect density within a grain. It was found that there was a noteworthy, but not definitive, correlation of MO with corrosion initiation after 1 min exposure to 0.1 M NaCl solution. Additionally, the S and θ-phase particles were also identified using EBSD, displaying a range of MO and therefore defect density.
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.
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.
The effect of electrochemical charging of hydrogen on the structure of a lean duplex stainless steel LDX 2101® (EN 1.4162, UNS S32101) was examined by both Time-of-Flight secondary ion mass spectrometry and electron back-scatter diffraction. The goal is to correlate hydrogen concentration and induced structural changes. Chemical and structural characterizations were done for the same region at the sample's surface with sub-micron spatial resolution. Regions of interest were varying in size between 50 × 50 μm and 100 × 100 μm. The results show a phase transformation of austenite to mainly a defect-rich BCC and scarcely a HCP phase. The phase transformation occurred in deuterium rich regions in the austenite.
Automated electron backscatter diffraction (EBSD) is generally unable to distinguish between multiple cubic phases in a specimen without additional information, such as that obtained by simultaneous energy dispersive X-ray spectroscopy (EDS). Small particles of phases with relatively similar compositions push the limits of phase identification using simultaneous EBSD and EDS, and a mismatch exists between the spatial resolutions of these two techniques due to them having different electron interaction volumes. In a recent paper, the present authors explored using backscatter detectors mounted on top of the EBSD detector to obtain atomic number (Z) contrast images that could be used for phase segmentation in cases where the results from the EBSD and EDS signals remain ambiguous. In the present work, we show that similar information can be obtained from the raw EBSD patterns themselves at higher spatial resolution than was obtained from the backscatter detectors, with the additional advantage of having no spatial mismatch between the data collection grids.
Synthesis of Molybdenum and Niobium Mono- and Binary Silicides by the Method of SHS-Metallurgy
(2016)
The process of self-propagating high-temperature synthesis of the Mo–Nb–Si silicides from the powder mixtures has been investigated. Based on performed experiments, the composition of powder mixtures as well as technological parameters are proposed which provide the synthesis of monosilicides MoSi₂, NbSi₂, and binary silicides Mo₁-хNbxSi₂ with different ratios of Nb/Mo by adding different contents of MoO₃ and Nb₂O₅. Microstructure and phase compositions of the obtained silicide ingots are characterized by scanning electron microscopy, electron probe microanalysis, X-ray diffraction, and backscatter electron diffraction.
The locally varying tetragonality in martensite grains of a high-carbon steel (1.2 mass percent C) was resolved by electron backscatter diffraction (EBSD) with a spatial resolution in the order of 100 nm. Compared to spatially integrating X-ray diffraction, which yielded an average tetragonality fo c/a=1.05, the EBSD measurements in the scanning electron microscope allowed to image a local variation of the lattice papameter ration c/a in the range of 1.02 ≤ c/a ≤ 1.07. The local variation of tetragonality is confirmed by two different EBSD data analysis approaches based on the fitting of simulated to experimental EBSD patterns. The resulting EBSD-based tetragonality maps are pointing to a complex interaction of carbon concentration and local lattice distortions during the formation process of martensitic structures.
In the present work, the influence of deuterium on the microstructure of a duplex stainless steel type EN 1.4462 has been characterized by Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) supported by scanning electron microscopy (SEM), focused ion beam (FIB), electron back scattered diffraction(EBSD) and energy dispersive x-ray (EDX) investigations. Characterization has been carried out before and after electrochemical charging with deuterium which has been used as a tracer, due to its similar behavior to hydrogen in the steel microstructure. In a first approach, the distribution of the deuterium occurring at temperatures above 58 °C has been visualized. Further it turned out that sub-surface micro blisters are formed in the ferrite-austenite interface, followed by the formation of needle shaped plates and subsequent cracking at the ferrite surface. In the austenite phase, parallel cracking alongside twins and hexagonal close packed (martensitic) regions has been observed. In both phases and even in the apparent interface, cracking has been associated with high deuterium concentrations, as compared to the surrounding undamaged microstructure. Sub-surface blistering in the ferrite has to be attributed to the accumulation and recombination of deuterium at the ferrite-austenite interface underneath the respective ferrite grains and after fast diffusing through this phase. Generally, the present application of chemometric imaging and structural analyses allows characterization of hydrogen assisted degradation at a sub-micron lateral resolution.
Signal optimization for transmission Kikuchi diffraction (TKD) measurements in the scanning electron microscope is investigated by a comparison of different sample holder designs. An optimized design is presented, which uses a metal shield to efficiently trap the electron beam after transmission through the sample. For comparison, a second holder configuration allows a significant number of the transmitted electrons to scatter back from the surface of the sample holder onto the diffraction camera screen. It is shown that the secondary interaction with the sample holder leads to a significant increase in the background level, as well as to additional noise in the final Kikuchi diffraction signal. The clean TKD signal of the optimized holder design with reduced background scattering makes it possible to use small signal changes in the range of 2% of the camera full dynamic range. As is shown by an analysis of the power spectrum, the signal-to-noise ratio in the processed Kikuchi diffraction patterns is improved by an order of magnitude. As a result, the optimized design allows an increase in pattern signal to noise ratio which may lead to increase in measurement speed and indexing reliability.