Presentation Information
[R2-02]EBSD simulation integrating backscattered-electron transport and Bloch-wave dynamical diffraction
*Yusuke SETO1, Yukitaka Ohyama1 (1. Osaka Metropolitan University)
Keywords:
Electron backscatter diffraction,Dynamical theory,Backscatter erectron
The phases, crystallographic orientations, and microstructures of rock-forming minerals provide fundamental information in mineralogy and petrology, including discrimination of polymorphs, reconstruction of deformation histories, and interpretation of seismic anisotropy through lattice-preferred orientation. SEM-EBSD is the most powerful technique for obtaining such information at the grain scale; however, its reliability essentially depends on the accuracy of reference pattern simulations. Indexing of geological samples is often difficult: the success rate is at most ~70% for serpentine [1] and only 10–20% for talc [2]. Most conventional software relies on the kinematical approximation and cannot reproduce the intensity contrast, position shift, or curvature of Kikuchi bands caused by dynamical (multiple) scattering. Moreover, the actual intensity of EBSD patterns is also governed by the energy, depth, and angular distributions of backscattered electrons (BSEs). A physically correct prediction of the patterns therefore requires a unified framework that combines electron transport and dynamical diffraction.
In this study, we decompose the problem into three processes: (i) BSE transport, (ii) dynamical diffraction within the crystal, and (iii) projection onto the detector plane. Monte Carlo simulations tracking millions of electron trajectories, employing Mott elastic cross-sections (NIST database) and a dielectric-response inelastic model, yield the joint distribution of the exit direction, energy, and depth of BSEs, from which the energy and depth ranges required for the dynamical calculation are determined automatically. Using the reciprocity theorem, the exit problem is converted into an equivalent incidence problem, and energy- and depth-resolved master patterns are computed by the Bloch wave method with our fast algorithm [3] and stored on a Rosca–Lambert equal-area grid; nonlocal absorption and thermal diffuse scattering background can be optionally included. Kikuchi patterns are finally synthesized by interpolating the master patterns along the direction subtended by each detector pixel and weighting them with the BSE distributions.
The whole procedure is implemented in the open-source crystallographic software ReciPro [3], directly linked to crystal-structure databases such as AMCSD and COD. It enables quantitative evaluation of how chemical composition, absorption, accelerating voltage, and sample tilt affect the visibility and contrast of Kikuchi bands, supporting reliable phase identification of complex minerals and optimization of measurement conditions prior to experiments. In particular, even for minerals whose Kikuchi bands are intrinsically low in sharpness (band slope) owing to their chemical composition, the present framework correctly reproduces such diffuse patterns as they are, since the energy and depth distributions of BSEs are explicitly taken into account. As validation, we performed pixel-by-pixel image comparisons with experimental EBSD patterns of major rock-forming minerals and confirmed good agreement. Kikuchi lines, band indices, and zone-axis indices can be overlaid on the dynamical patterns, and the crystal orientation is synchronized with the structure viewer and stereonet, making the simulator a useful educational tool for understanding the correspondence among real space, reciprocal space, and orientation space. We will present the computational procedure and validation results, and discuss prospects for applications to minerals that are difficult to index.
[1] Nagaya, Wallis, Seto, et al. Journal of Structural Geology 95, 127–141, 2017. [2] Nagaya, Okamoto, Oyanagi, Seto, et al. American Mineralogist 105, 873–893, 2020. [3] Seto & Ohtsuka. Journal of Applied Crystallography 55, 397–410, 2022.
In this study, we decompose the problem into three processes: (i) BSE transport, (ii) dynamical diffraction within the crystal, and (iii) projection onto the detector plane. Monte Carlo simulations tracking millions of electron trajectories, employing Mott elastic cross-sections (NIST database) and a dielectric-response inelastic model, yield the joint distribution of the exit direction, energy, and depth of BSEs, from which the energy and depth ranges required for the dynamical calculation are determined automatically. Using the reciprocity theorem, the exit problem is converted into an equivalent incidence problem, and energy- and depth-resolved master patterns are computed by the Bloch wave method with our fast algorithm [3] and stored on a Rosca–Lambert equal-area grid; nonlocal absorption and thermal diffuse scattering background can be optionally included. Kikuchi patterns are finally synthesized by interpolating the master patterns along the direction subtended by each detector pixel and weighting them with the BSE distributions.
The whole procedure is implemented in the open-source crystallographic software ReciPro [3], directly linked to crystal-structure databases such as AMCSD and COD. It enables quantitative evaluation of how chemical composition, absorption, accelerating voltage, and sample tilt affect the visibility and contrast of Kikuchi bands, supporting reliable phase identification of complex minerals and optimization of measurement conditions prior to experiments. In particular, even for minerals whose Kikuchi bands are intrinsically low in sharpness (band slope) owing to their chemical composition, the present framework correctly reproduces such diffuse patterns as they are, since the energy and depth distributions of BSEs are explicitly taken into account. As validation, we performed pixel-by-pixel image comparisons with experimental EBSD patterns of major rock-forming minerals and confirmed good agreement. Kikuchi lines, band indices, and zone-axis indices can be overlaid on the dynamical patterns, and the crystal orientation is synchronized with the structure viewer and stereonet, making the simulator a useful educational tool for understanding the correspondence among real space, reciprocal space, and orientation space. We will present the computational procedure and validation results, and discuss prospects for applications to minerals that are difficult to index.
[1] Nagaya, Wallis, Seto, et al. Journal of Structural Geology 95, 127–141, 2017. [2] Nagaya, Okamoto, Oyanagi, Seto, et al. American Mineralogist 105, 873–893, 2020. [3] Seto & Ohtsuka. Journal of Applied Crystallography 55, 397–410, 2022.