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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.
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.
In this paper one refined approach is applied to determine the exact orientation of bipyramidal TiO2 nanoparticles prepared with good dispersion as almost isolated particles on a carbon TEM grid. The advantages of the recently developed high-throughput Transmission Kikuchi Diffraction (TKD) are used to identify quickly and reliably the geometrical orientation of the crystalline TiO2 nanoparticle bipyramids (anatase) on a statistically relevant number of particles.
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.
A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 x 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.
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.
Inconel 718 is a precipitation strengthened, nickel-based super alloy of interest for the Additive Manufacturing (AM) of low volume, complex parts to reduce production time and cost compared to conventional subtractive processes. The AM process involves repeated rapid melting, solidification and reheating, which exposes the material to non-equilibrium conditions that affect elemental segregation and the subsequent formation of solidification phases, either beneficial or detrimental. These variations are difficult to characterize due to the small length scale within the micron sized melt pool. To understand how the non-equilibrium conditions affect the initial solidification phases and their critical temperatures, a multi-length scale, multi modal approach has been taken to evaluate various methods for identifying the initial phases formed in the as-built Inconel 718 produced by laser-powder bed fusion (L-PBF) additive manufacturing (AM). Using a range of characterization tools from the bulk differential thermal analysis (DTA) and x-ray diffraction (XRD) to spatially resolved images using a variety of electron microscopy tools, a better understanding is obtained of how these minor phases can be properly identified regarding the amount and size, morphology and distribution. Using the most promising characterization techniques for investigation of the as-built specimens, those techniques were used to evaluate the specimens after various heat treatments. During the sequence of heat treatments, the initial as-built dendritic structures recrystallized into well-defined grains whose size was dependent on the temperature. Although the resulting strength was similar in all heat treated specimens, the elongation increased as the grain size was refined due to differences in the precipitated phase distribution and morphology.
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.
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 describe a lattice-based crystallographic approximation for the analysis of distorted crystal structures via Electron Backscatter Diffraction (EBSD) in the scanning electron microscope. EBSD patterns are closely linked to local lattice parameter ratios via Kikuchi bands that indicate geometrical lattice plane projections. Based on the transformation properties of points and lines in the real projective plane, we can obtain continuous estimations of the local lattice distortion based on projectively transformed Kikuchi diffraction simulations for a reference structure. By quantitative image matching to a projective transformation model of the lattice distortion in the full solid angle of possible scattering directions, we enforce a crystallographically consistent approximation in the fitting procedure of distorted simulations to the experimentally observed diffraction patterns. As an application example, we map the locally varying tetragonality in martensite grains of steel.