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Tomasz Tokarski

Publications and source records attributed to Tomasz Tokarski.

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Resolving Overlapping EBSD Patterns by Experiment -- Simulation Residuals Analysis

In the technique of Electron Backscatter Diffraction (EBSD), the accurate detection and identification of different phases existing in a sample is often limited by overlapping Kikuchi diffraction patterns originating from the extended probing volume of the individual EBSD map points measured in the scanning electron microscope (SEM). We present an iterative approach that uses simulated Kikuchi patterns to resolve several overlapping diffraction signals. For each measured EBSD pattern, our method first identifies the best-fit simulated Kikuchi pattern using dynamic template matching. This simulated, ideal reference pattern is then further processed to optimally match the experimental image, uncovering any underlying weaker signals after subtraction. Repeatedly utilizing dynamic template matching and pattern subtraction on residual signals of subsequent steps enables the identification of minor phases that might otherwise be missed from the probing volume of the EBSD map point. This method significantly improves phase detection in complex materials, addressing a key limitation of conventional EBSD analysis that conventionally assigns a single phase to each map point. The present method does not require a known orientation relationship between the phases of the overlapping patterns or close neighbor experimental patterns like previously published approaches.

cond-mat.mtrl-sci

Simulation-based Super-Resolution EBSD for Measurements of Relative Deformation Gradient Tensors

We summarize a data analysis approach for electron backscatter diffraction (EBSD) which uses high-resolution Kikuchi pattern simulations to measure isochoric relative deformation gradient tensors from experimentally measured Kikuchi patterns of relatively low resolution. Simulation-based supersampling of the theoretical test diffraction patterns enables a significant precision improvement of tensor parameters obtained in best-fit determinations of strains and orientations from low-resolution experimental patterns. As an application, we demonstrate high-resolution orientation and strain analysis for the model case of hardness test indents on a Si(100) wafer, using Kikuchi patterns of variable resolution. The approach shows noise levels near $1 \times 10^{-4}$ in the relative deviatoric strain norm and in the relative rotation angles on nominally strain-free regions of the silicon wafer. The strain and rotation measurements are interpreted by finite element simulations. While confirming the basic findings of previously published studies, the present approach enables a potential reduction in the necessary pattern data size by about two orders of magnitude. We estimate that pattern resolutions in the order of $256\times256$ pixels should be enough to solve a majority of EBSD analysis tasks using pattern matching techniques.

cond-mat.mtrl-sci

Pattern Matching Workflows for EBSD Data Analysis: Quartz Chirality Mapping

Pattern matching approaches to electron backscatter diffraction (EBSD) in the scanning electron microscope (SEM) provide qualitatively new possibilities for the microstructural analysis of chiral non-centrosymmetric phases due to the influence of dynamical electron diffraction effects on the formation of EBSD Kikuchi patterns. In the present study, we analyze the microstructure of polycrystalline alpha-quartz in an agate mineral sample. We identify characteristic intra-grain inversion domains of different handedness which are well-known from classical polarized light microscopy. As a result, the handedness-resolved microstructure of quartz can be imaged with the spatial and orientation resolution provided by EBSD in the SEM.

cond-mat.mtrl-sci

EBSD and TKD analyses using inverted contrast Kikuchi diffraction patterns and alternative measurement geometries

Electron backscatter diffraction (EBSD) patterns can exhibit Kikuchi bands with inverted contrast due to anomalous absorption. This can be observed, for example, on samples with nanoscale topography, in case of a low tilt backscattering geometry, or for transmission Kikuchi diffraction (TKD) on thicker samples. Three examples are discussed where contrast-inverted physics-based simulated master patterns have been applied to find the correct crystal orientation. As the first EBSD example, self-assembled gold nanostructures made of Au fcc and Au hcp phases on single-crystal germanium were investigated. Gold covered about 12% of the mapped area, with only two-thirds being successfully interpreted using standard Hough-based indexing. The remaining third was solved by brute force indexing using a contrast-inverted master pattern. The second EBSD example deals with maps collected at a non-tilted surface instead of the commonly used 70 degree tilted one. As TKD example, a jet-polished foil made of duplex stainless steel 2205 was examined. The thin part close to the hole edge producing normal-contrast patterns were standard indexed. The areas of the foil that become thicker with increasing distance from the edge of the hole produce contrast-inverted patterns. They covered three times the evaluable area and were successfully processed using the contrast-inverted master pattern. In the last example, inverted patterns collected at a non-tiled sample were mathematically inverted to normal contrast, and Hough/Radon-based indexing was successfully applied.

cond-mat.mtrl-sci

Fixing Left and Right: Assignment of Chiral Elemental Crystal Structures using Kikuchi Diffraction

Crystals of the chemical elements manganese, tellurium, and selenium can show the effects of handedness. In order to sense the possible effects of a changing sense of chirality on the properties of samples from these elements, the potential presence of two, enantiomorphic, physically different, variants of these elemental crystal structures needs to be resolved in crystallographic analyses. Due to fundamental limitations of kinematical X-ray scattering in crystals, however, the effects of chirality in single-element crystals are very difficult to sense using standard X-ray diffraction techniques. In the present paper, we show that dynamical Kikuchi diffraction in the scanning electron microscope is sensitive to the local sense of chirality in crystals of single chemical elements. We demonstrate chirality assignment in $β$-manganese, and we determine the sense of crystal chirality from Kikuchi diffraction patterns of the trigonal structures of tellurium and selenium.

cond-mat.mtrl-sci

Tetragonality mapping of martensite in a high-carbon steel by EBSD

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 100nm. Compared to spatially integrating X-ray diffraction, which yielded an average tetragonality of c/a=1.05, the EBSD measurements in the scanning electron microscope allowed to image a local variation of the lattice parameter ratio c/a in the range of 1.02 $\leq$ c/a $\leq$ 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.

cond-mat.mtrl-sci

Standard-Based EBSD: Fingerprinting of Order and Orientation in Materials

Orientation determination does not necessarily require complete knowledge of the local atomic arrangement in a material. We present a method for microstructural phase discrimination and orientation analysis of phases for which there is only limited information available. In this method, experimental Kikuchi diffraction patterns are utilized to generate self-consistent standards for use in the technique of Electron Backscatter Diffraction (EBSD). As an application example, we map the locally varying orientations in samples of icosahedral quasicrystals observed in a Ti40Zr40Ni20 alloy.

cond-mat.mtrl-sci

Mapping of Local Lattice Parameter Ratios by Projective Kikuchi Pattern Matching

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.

cond-mat.mtrl-sci