5:15 PM - 7:15 PM
[SMP29-P05] Development of Simulation of Electron Backscattering Diffraction Based on Monte Carlo Method and Dynamical Diffraction Theory
Keywords:Electron backscatter electron diffraction, dynamical diffraction theory, Bloch wave, Crystallographic preferred orientation orientation
One of the most powerful tools for identifying mineral phases and analyzing crystallographic orientations is the SEM-EBSD method. This method is widely used for evaluating rock samples, ceramic materials, and metal materials because it is relatively easy to prepare samples and can analyze a wide area of samples in a short time. However, if the EBSD images simulated in the computer are inaccurate, it is impossible to perform accurate indexing. Indexing geological samples is particularly difficult in many cases, and for example, the success rate for indexing serpentine, which is one of the main minerals that make up fault rock, is only around 70% [1], and for talc, the success rate is only around 10–20% [2]. The inaccuracy of EBSD simulations is due to the fact that many of the analysis software packages currently in use calculate based on kinematic approximations (first-order perturbation theory). In actual electron diffraction, it is necessary to take into account the process of electrons being scattered multiple times, and this effect (kinetic diffraction) not only changes the intensity of the bands, but also significantly changes the position and curvature of the bands. Due to this problem, most of the published EBSD analysis results have undergone a considerable amount of “data correction and adjustment” based on human judgment, and objectivity is not always guaranteed.
In this study, in order to accurately handle the phenomenon of backscattered electron diffraction, we performed dynamical diffraction calculations based on the Bloch wave method. This method describes the electron wave in a crystal using the wave equation and Bloch's theorem, and obtains the amplitude of the scattered wave (diffracted wave) by smoothly connecting the incident/exit waves with the Bloch wave in the crystal at the sample interface. The derivation of the Bloch wave is reduced to an eigenvalue problem, and solving this is the most computationally expensive part, but once the eigenvalues have been obtained, the scattering amplitude for a sample of any thickness can be calculated immediately. In this study, the directional space was divided into a fine grid (1000000-10000000), and the eigenvalues and eigenvectors were calculated from any depth/directions. The depth of penetration, escape direction and intensity of the backscatter electrons were calculated using Monte Carlo simulation. In recent years, the authors have published an algorithm for performing electron diffraction simulations based on the Bloch wave method at high speed [3], and we have applied this method. As a result, the dynamical simulations can reproduce the contrast between the brightness of the inside and outside of the band, as well as the brightness of the overlapping parts of multiple bands (crystal band axes), whereas kinematic simulations can only reproduce the geometric arrangement of the bands. In the future, the authors plan to perform more accurate calculations by incorporating absorption effects and the orientation dependence of scattering intensity.
[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, in order to accurately handle the phenomenon of backscattered electron diffraction, we performed dynamical diffraction calculations based on the Bloch wave method. This method describes the electron wave in a crystal using the wave equation and Bloch's theorem, and obtains the amplitude of the scattered wave (diffracted wave) by smoothly connecting the incident/exit waves with the Bloch wave in the crystal at the sample interface. The derivation of the Bloch wave is reduced to an eigenvalue problem, and solving this is the most computationally expensive part, but once the eigenvalues have been obtained, the scattering amplitude for a sample of any thickness can be calculated immediately. In this study, the directional space was divided into a fine grid (1000000-10000000), and the eigenvalues and eigenvectors were calculated from any depth/directions. The depth of penetration, escape direction and intensity of the backscatter electrons were calculated using Monte Carlo simulation. In recent years, the authors have published an algorithm for performing electron diffraction simulations based on the Bloch wave method at high speed [3], and we have applied this method. As a result, the dynamical simulations can reproduce the contrast between the brightness of the inside and outside of the band, as well as the brightness of the overlapping parts of multiple bands (crystal band axes), whereas kinematic simulations can only reproduce the geometric arrangement of the bands. In the future, the authors plan to perform more accurate calculations by incorporating absorption effects and the orientation dependence of scattering intensity.
[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.