Analytische Chemie
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- Electron backscatter diffraction (30)
- EBSD (12)
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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.
An extensive set of information about the diffracting volume is carried by EBSD patterns: the crystal lattice, the reciprocal lattice, the crystal structure, the crystal symmetry, the mean periodic number of the diffracting phase, the source point from where it has been projected (projection centre), the crystal orientation, the sample topography (local tilt), the (preparation) quality of defect density of the crystal, and possible pattern overlaps. Some of this information is used regularly in conventional EBSD analyses software while others are still waiting for a more widespread application. Despite the wealth of information available, the accuracy and precision of the data that are presently extracted from conventional EBSD patterns are often well below the actual physical limits. Using a selection of example applications, we will demonstrate the gain in angular resolution possible using relatively low-resolution patterns of approximately 20k pixels in combination with pattern matching (PM) approaches. In this way, fine details in a microstructure can be revealed which would otherwise be hidden in the orientation noise.
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.
The Bravais lattices and their lattice parameters are blindly determined using electron backscatter diffraction (EBSD) patterns of materials with cubic or tetragonal crystal structures. Since the geometric relationships in a single EBSD pattern are overdetermined, the relative errors of determining the lattice parameters as well as the axial ratios are confined to about 0.7 ± 0.4% and 0.07 ± 0.03%, respectively, for ideal simulated EBSD patterns. The accuracy of the crystal orientation determination reaches about 0.06 ± 0.03°. With careful manual band detection, the accuracy of determining lattice parameters from experimental patterns can be as good as from simulated patterns, although the results from simulated patterns are often better than expermental patterns, which are lower quality and contain uncertain systematic errors. The reasonably high accuracy is obtained primarily because the detection of the diffracting-plane traces and zone axes is relatively accurate. The results here demonstrate that the developed procedure based on the EBSD technique presents a reliable tool for crystallographic characterization of the Bravais lattices of unknown phases.
We use pattern matching of experimental and dynamically simulated backscattered Kikuchi diffraction (BKD) patterns to increase the orientation precision of electron backscatter diffraction (EBSD) measurements. In order to quantify the improvement in orientation precision, we analyze the experimental distribution of the kernel average misorientation (KAM) angles. We find that for the same raw data, i.e. the same EBSD data acquisition time budget, the pattern matching approach improves the KAM resolution by an order of magnitude compared to orientation data delivered from the conventional Hough-transform based data analysis. This quantitative improvement enables us to interpret small orientation changes in plastically deformed materials which are hidden in noisy orientation data delivered from the reference EBSD system.
As an application example, we analyze a ferritic-martensitic steel (P92) sample before and after low-cycle fatigue (LCF) loading (±0.3% strain) at 620 °C. Whereas the low precision of the EBSD orientation data from the manufacturer software does not allow a reliable discrimination of the gradually changing microstructure, we find very clear systematic differences of the local microstructure after the pattern matching orientation refinement of the initial, raw pattern data. For the investigated P92 sample, the KAM-angle histograms are well described by two log-normal distributions indicating the already tempered and the remaining and mostly untempered martensite.
We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle-resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in-depth theoretical modelling of the energy- and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations.
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.
On April 23rd 2013 at 2:07 a.m., a 1.3 kg meteorite fell in the Braunschweig suburb Melverode (52° 13′ 32.19″ N. 10° 31′ 11.60″ E). Its estimated velocity was 250 km/h and it formed an impact pit in the concrete fall site with a diameter of 7 cm and a depth of 3 cm. Radial dust striae are present around the impact pit. As a result of the impact, the meteorite disintegrated into several hundred fragments with masses up to 214 g. The meteorite is a typical L6 chondrite, moderately shocked (S4) – but with a remarkably high porosity (up to 20 vol%). The meteorite was ejected from its parent body as an object with a radius of about 10–15 cm (15–50 kg). The U,Th-He gas retention age of ∼550 Ma overlaps with the main impact event on the L-chondrite parent body ∼470 Ma ago that is recorded by many shocked L chondrites. The preferred cosmic-ray exposure age derived from production of radionuclides and noble gas isotopes is (6.0 ± 1.3) Ma.
Advanced structural characterisation techniques which are rapid to use, non-destructive and structurally definitive on the nanoscale are in demand, especially for a detailed understanding of extended-defects and their influence on the properties of materials. We have applied the electron
backscatter diffraction (EBSD) technique in a scanning electron microscope to non-destructively
characterise and quantify antiphase domains (APDs) in GaP thin films grown on different (001)Si substrates with different offcuts. We were able to image and quantify APDs by relating the asymmetrical intensity distributions observed in the EBSD patterns acquired experimentally and comparing the same with the dynamical electron diffraction simulations. Additionally mean angular error maps were also plotted using automated cross-correlation based approaches to image APDs.
Samples grown on substrates with a 4° offcut from the [110] do not show any APDs, whereas samples grown on the exactly oriented substrates contain APDs. The procedures described in our work can be
adopted for characterising a wide range of other material systems possessing non-centrosymmetric point groups.
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.