Pattern Matching Analysis of Electron Backscatter Diffraction Patterns for Pattern Centre, Crystal Orientation and Absolute Elastic Strain Determination: Accuracy and Precision Assessment

Pattern matching between target electron backscatter patterns (EBSPs) and dynamically simulated EBSPs was used to determine the pattern centre (PC) and crystal orientation, using a global optimisation algorithm. Systematic analysis of error and precision with this approach was carried out using dynamically simulated target EBSPs with known PC positions and orientations. Results showed that the error in determining the PC and orientation was < 10$^{-5}$ of pattern width and < 0.01{\deg} respectively for the undistorted full resolution images (956x956 pixels). The introduction of noise, optical distortion and image binning was shown to have some influence on the error although better angular resolution was achieved with the pattern matching than using conventional Hough transform-based analysis. The accuracy of PC determination for the experimental case was explored using the High Resolution (HR-) EBSD method but using dynamically simulated EBSP as the reference pattern. This was demonstrated through a sample rotation experiment and strain analysis around an indent in interstitial free steel

Direct detection of electron backscatter diffraction patterns.

We report the first use of direct detection for recording electron backscatter diffraction patterns. We demonstrate the following advantages of direct detection: the resolution in the patterns is such that higher order features are visible; patterns can be recorded at beam energies below those at which conventional detectors usefully operate; high precision in cross-correlation based pattern shift measurements needed for high resolution electron backscatter diffraction strain mapping can be obtained. We also show that the physics underlying direct detection is sufficiently well understood at low primary electron energies such that simulated patterns can be generated to verify our experimental data

Strong grain neighbour effects in polycrystals

Anisotropy in single crystal properties of polycrystals controls both the overall response of the aggregates and patterning of local stress/strain distributions, the extremes of which govern failure processes. Improving the understanding of grain-grain interactions has important consequences for in-service performance limits. Three-dimensional synchrotron X-ray diffraction was used to study the evolution of grain resolved stresses over many contiguous grains in Zr and Ti polycrystals deformed in situ. In a significant fraction of grains the stress along the loading axis was found to decrease during tensile plastic flow just beyond the macroscopic yield point; this is in the absence of deformation twinning and is a surprising behaviour. It is shown that this phenomenon is controlled by the crystallographic orientation of the grain and its immediate neighbours, particularly those adjacent along the loading axis

Tetragonality of Fe-C martensite -- a pattern matching electron backscatter diffraction analysis compared to X-ray diffraction

Measurements of the local tetragonality in Fe-C martensite at microstructural length-scale through pattern matching of electron backscatter diffraction patterns (EBSPs) and careful calibration of detector geometry are presented. It is found that the local tetragonality varies within the complex microstructure by several per cent at largest and that the scatter in the axial ratio is increased at higher nominal carbon content. At some analysis points the local crystal structure can be regarded as lower symmetry than simple body centred tetragonal. A linear relation between the nominal carbon content and averaged local tetragonality measured by EBSD is also obtained, although the averaged axial ratio is slightly below that obtained from more classical X-ray diffraction measurements.Comment: 33 pages, 12 figures, 2 Table

An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD)

For high (angular) resolution electron backscatter diffraction (HR-EBSD), the selection of a reference diffraction pattern (EBSP0) significantly affects the precision of the calculated strain and rotation maps. This effect was demonstrated in plastically deformed body-centred cubic and face-centred cubic ductile metals (ferrite and austenite grains in duplex stainless steel) and brittle single-crystal silicon, which showed that the effect is not only limited to measurement magnitude but also spatial distribution. An empirical relationship was then identified between the cross-correlation parameter and angular error, which was used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD

Dislocation interactions in olivine control postseismic creep of the upper mantle.

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, commonly induce a period of transient creep, which is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at temperatures ≤600 °C, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25 °C or 1150-1250 °C both preserve stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 μm. The similar stress distributions formed at these different temperatures indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle

Bayesian Optimised Collection Strategies for Fatigue Testing : Constant Life Testing

This paper presents a statistical framework enabling optimal sampling and robust analysis of fatigue data. We create protocols using Bayesian maximum entropy sampling, which build on the staircase and step methods, removing the requirement of prior knowledge of the fatigue strength distribution for data collection. Results show improved sampling efficiency and parameter estimation over the conventional approaches. Statistical methods for distinguishing between distribution types highlight the role of the protocol in model distinction. Experimental validation of the above work is performed, showing the applicability of the methods in laboratory testing.Comment: 25 pages, 12 figures + 1 SI figur

Applications of Multivariate Statistical Methods and Simulation Libraries to Analysis of Electron Backscatter Diffraction and Transmission Kikuchi Diffraction Datasets

Multivariate statistical methods are widely used throughout the sciences, including microscopy, however, their utilisation for analysis of electron backscatter diffraction (EBSD) data has not been adequately explored. The basic aim of most EBSD analysis is to segment the spatial domain to reveal and quantify the microstructure, and links this to knowledge of the crystallography (eg crystal phase, orientation) within each segmented region. Two analysis strategies have been explored; principal component analysis (PCA) and k-means clustering. The intensity at individual (binned) pixels on the detector were used as the variables defining the multidimensional space in which each pattern in the map generates a single discrete point. PCA analysis alone did not work well but rotating factors to the VARIMAX solution did. K-means clustering also successfully segmented the data but was computational more expensive. The characteristic patterns produced by either VARIMAX or k-means clustering enhance weak patterns, remove pattern overlap, and allow subtle effects from polarity to be distinguished. Combining multivariate statistical analysis (MSA) approaches with template matching to simulation libraries can significantly reduce computational demand as the number of patterns to be matched is drastically reduced. Both template matching and MSA approaches may augment existing analysis methods but will not replace them in the majority of applications.Comment: manuscript submitted after review at Ultramicroscop