Application of the pattern matching approach for EBSD calibration and orientation mapping, utilising dynamical EBSP simulations

The characterisation of dental enamel using transmission Kikuchi diffraction in the scanning electron microscope combined with dynamic template matching

The remarkable physical properties of dental enamel can be largely attributed to the structure of the hydroxyapatite (HAp) crystallites on the sub-micrometre scale. Characterising the HAp microstructure is challenging, due to the nanoscale of individual crystallites and practical challenges associated with HAp examination using electron microscopy techniques. Conventional methods for enamel characterisation include imaging using transmission electron microscopy (TEM) or specialised beamline techniques, such as polarisation-dependent imaging contrast (PIC). These provide useful information at the necessary spatial resolution but are not able to measure the full crystallographic orientation of the HAp crystallites. Here we demonstrate the effectiveness of enamel analyses using transmission Kikuchi diffraction (TKD) in the scanning electron microscope, coupled with newly-developed pattern matching methods. The pattern matching approach, using dynamic template matching coupled with subsequent orientation refinement, enables robust indexing of even poor-quality TKD patterns, resulting in significantly improved data quality compared to conventional diffraction pattern indexing methods. The potential of this method for the analysis of nanocrystalline enamel structures is demonstrated by the characterisation of a human enamel TEM sample and the subsequent comparison of the results to high resolution TEM imaging. The TKD - pattern matching approach measures the full HAp crystallographic orientation enabling a quantitative measurement of not just the c-axis orientations, but also the extent of any rotation of the crystal lattice about the c-axis, between and within grains. Results presented here show how this additional information highlights potentially significant aspects of the HAp crystallite structure, including intra-crystallite distortion and the presence of multiple high angle boundaries between adjacent crystallites with rotations about the c-axis. These and other observations enable a more rigorous understanding of the relationship between HAp structures and the physical properties of dental enamel.

Accurate and fast localization of EBSD pattern centers for screen moving technology

The authors of this study develop an accurate and fast method for the localization of the pattern centers (PCs) in the electron backscatter diffraction (EBSD) technique by using the model of deformation of screen moving technology. The proposed algorithm is divided into two steps: (a) Approximation: We use collinear feature points to obtain the initial value of the coordinates of the PC and the zoom factor. (b) Subdivision: We then construct a deformation function containing the three parameters to be solved, select a large region for global registration, use the inverse compositional Gauss-Newton (ICGN) to optimize the objective function, and obtain the results of iteration of the PC and the zoom factor. The proposed algorithm was applied to simulated patterns, and yielded an accuracy of measurement of the PCs that was better than 4.6×10-6 of their resolution while taking only 0.2 s for computations. Moreover, the proposed algorithm has a large radius of convergence that makes it robust to the initial estimate. We also discuss the influence of factors of mechanical instability on its results of calibration during the insertion of the detector, and show that errors in measurements caused by the tilt motion of the camera are related only to the tilt angle of its motion and the detector distance, and are unrelated to the distance moved by it.

Kikuchi pattern simulations of backscattered and transmitted electrons

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 TKD can be affected by changes in the order of 10 - 3 - 10 - 2 if excess-deficiency features are not considered in the theoretical model underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer from biases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.

Integrated correction of optical distortions for global HR-EBSD techniques

Optical distortions caused by camera lenses affect the accuracy of the elastic strains and lattice rotations measured by high-angular resolution techniques. This article introduces an integrated correction of optical distortions for global HR-EBSD/HR-TKD approaches. The digital image correlation analysis is directly applied to optically distorted patterns, avoiding the pattern pre-processing step conducted so far while preserving the numerical efficiency of the Gauss-Newton algorithm. The correction implementation is first described and its numerical cost is assessed considering a homography-based HR-EBSD approach. The correction principle is validated numerically for various levels of first-order radial distortion over a wide range of disorientation angles (0 to 14°) and elastic strain (0 to 5×10^-2). The errors induced when neglecting such distortions as well as the influence of both the radial distortion coefficient and the pattern centre and optical centre locations are quantified. Even when both reference and target patterns are distorted, the correction appears necessary whatever the disorientation between those patterns. The required accuracy on the true distortion parameters for an effective correction is consequently determined.

Approximant-based orientation determination of quasicrystals using electron backscatter diffraction

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.

Comparison of Orientation Mapping in SEM and TEM

Multiple experimental configurations for performing nanoscale orientation mapping are compared to determine their fidelity to the true microstructure of a sample. Transmission Kikuchi diffraction (TKD) experiments in a scanning electron microscope (SEM) and nanobeam diffraction (NBD) experiments in a transmission electron microscope (TEM) were performed on thin electrodeposited hard Au films with two different microstructures. The Au samples either had a grain size that is >50 or <20 nm. The same regions of the samples were measured with TKD apparatuses at 30 kV in an SEM with detectors in the horizontal and vertical configurations and in the TEM at 300 kV. Under the proper conditions, we demonstrate that all three configurations can produce data of equivalent quality. Each method has strengths and challenges associated with its application and representation of the true microstructure. The conditions needed to obtain high-quality data for each acquisition method and the challenges associated with each are discussed.

Refined Calibration Model for Improving the Orientation Precision of Electron Backscatter Diffraction Maps

For the precise determination of orientations in polycrystalline materials, electron backscatter diffraction (EBSD) requires a consistent calibration of the diffraction geometry in the scanning electron microscope (SEM). In the present paper, the variation of the projection center for the Kikuchi diffraction patterns which are measured by EBSD is calibrated using a projective transformation model for the SEM beam scan positions on the sample. Based on a full pattern matching approach between simulated and experimental Kikuchi patterns, individual projection center estimates are determined on a subgrid of the EBSD map, from which least-square fits to affine and projective transformations can be obtained. Reference measurements on single-crystalline silicon are used to quantify the orientation errors which result from different calibration models for the variation of the projection center.

Prediction of potential pseudo-symmetry issues in the indexing of electron backscatter diffraction patterns

A new methodology to predict potential pseudo-symmetric or systematically mis-indexed orientations for an arbitrary crystal structure is presented. The method leverages the recently proposed spherical indexing algorithm to index electron backscatter diffraction patterns. Potential pseudo-symmetric orientations are interpreted as secondary peaks in the autocorrelation of the Kikuchi sphere. The generality of the method is illustrated using a number of crystal systems, ranging from nickel, where no significant pseudo-symmetric issues are expected, to SrTiO3, with mild occurrence of such issues, to the olivine series, γ-TiAl and U-6%Nb systems, where the traditional Hough method systematically mis-indexes the pseudo-symmetric variants. Furthermore, the method predicts the severity of potential pseudo-symmetric matches and ranks all variants using a normalized autocorrelation coefficient.

A New and Unexpected Spatial Relationship Between Interaction Volume and Diffraction Pattern in Electron Microscopy in Transmission

The finding of this study is that the interaction volume in electron microscopy in transmission is well ordered laterally, with a remarkable and unexpected consequence being that lateral subsections of the interaction volume produce subsections of the Kikuchi diffraction pattern. It makes the microstructure of samples directly visible in Kikuchi patterns. This is first illustrated with polycrystalline Ti-10Al-25Nb with an on-axis transmission Kikuchi diffraction set-up in a scanning electron microscope. It is then shown via a Monte Carlo simulation and a large-angle convergent-beam electron diffraction experiment that this phenomenon finds its origin in the nature of the differential elastic and quasi-elastic cross sections. This phenomenon is then quantified by a careful image analysis of Kikuchi patterns recorded across a vertical interface in a silicon sample specifically designed and fabricated. A Monte Carlo simulation reproducing all the geometric parameters is conducted. Experiments and simulations match very well qualitatively, but with a slight quantitativity gap. The specificity of the thermal diffuse scattering cross-section, not available in the simulation, is thought to be responsible for this gap. Beside Kikuchi diffraction, the case of diffraction spots and diffuse background present in the pattern is also discussed.