5:15 PM - 6:45 PM
[SCG45-P05] Development of electron diffraction/microscopy simulation based on dynamical scattering theory and its application to mineralogy and petrology
Keywords:Electron Backscattered Electron Diffraction, dynamical scattering theory, Scanning Transmission Electron Microscopy
Scanning transmission electron microscopy (STEM) and electron backscatter diffraction (EBSD) methods have become widespread as powerful tools for crystal phase identification, structural analysis, and orientation analysis at the nanometer scale, and are essential analytical techniques in many material science fields, including mineralogy and petrology. In recent years, the importance of these techniques has increased even further with the development of brighter electron guns and the widespread use of high-sensitivity CMOS cameras, enabling fast and quantitative acquisition of diffraction intensities. Electron microscopy images and electron diffraction patterns are modulated by multiple scattering effects and aberrations of electromagnetic lenses, making precise simulation essential for quantitative data analysis. Against this background, the author has been developing the open-source crystallography software ReciPro for many years. This presentation introduces the recent overview of ReciPro, its main computational algorithms, and future prospects.
ReciPro is software that offers functions such as searching crystal databases, visualizing crystal structures and goniometers, stereonet projection, simulating diffraction patterns and (S)TEM images, and indexing diffraction spots. ReciPro incorporates symmetry operation information for space groups (230 standard notations) as well as those considering axis interchange (530 types), enabling the reproduction of any crystal structure in the software. It also includes the American Mineralogist Crystal Structure Database (AMCSD) in its installation files, allowing for the use of over 20,000 mineral structure models even in offline environments. The crystal rotation state is synchronized across all functions (3D crystal structure, stereonet, single crystal diffraction, etc.), and rotating the crystal in any function immediately reflects in the others.
One of its main features is the simulation of single crystal diffraction, allowing for the selection of X-rays, electrons, or neutrons as incident waves. For X-ray and neutron sources, calculations are based on the kinematic scattering approximation (first-order perturbation theory), where diffraction intensity is estimated simply from the square of the amplitude of the crystal structure factor and the excitation error. For electron beams, dynamic effects are calculated based on the Bloch wave method (Bethe, 1928). This method describes the state of electrons in the crystal using the wave equation and Bloch's theorem, calculates the Bloch waves that can exist in a periodic potential field, and then computes the amplitude of the diffracted waves by smoothly connecting the incident/exit waves at the sample interface. ReciPro supports dynamic scattering simulations for selected area electron diffraction (SAED), precession electron diffraction (PED), (large-angle) convergent-beam electron diffraction ((LA)-CBED), and electron backscatter diffraction (EBSD). CBED and EBSD represent the converging electron beam as a superposition of many plane waves. Although the Bloch wave method generally has a high computational cost, algorithmic improvements and CPU parallelization have achieved computation speeds that are practical for use.
Furthermore, ReciPro is capable of calculating high-resolution TEM (HRTEM) and STEM images. The former (HRTEM) is simulated at arbitrary magnification/resolution, taking into account the modulation effects of spherical aberration and defocusing of the objective lens, partial spatio-temporal coherence of the electron beam, and changes in sample thickness due to dynamic scattering effects. The latter (STEM) represents the incident converging electrons as a multitude of plane waves, similar to CBED, and calculates the effect of inelastic scattering due to phonon excitation (thermal diffuse scattering, TDS) by integrating over the scattering angle, enabling simulation of STEM images using annular detectors (e.g., STEM-HAADF). ReciPro is distributed under the MIT license (github.com/seto77/ReciPro/releases/latest/) as completely free software and runs on the Microsoft .NET Desktop 8.0 runtime. All source code and detailed documentation are available at the above GitHub repository.
ReciPro is software that offers functions such as searching crystal databases, visualizing crystal structures and goniometers, stereonet projection, simulating diffraction patterns and (S)TEM images, and indexing diffraction spots. ReciPro incorporates symmetry operation information for space groups (230 standard notations) as well as those considering axis interchange (530 types), enabling the reproduction of any crystal structure in the software. It also includes the American Mineralogist Crystal Structure Database (AMCSD) in its installation files, allowing for the use of over 20,000 mineral structure models even in offline environments. The crystal rotation state is synchronized across all functions (3D crystal structure, stereonet, single crystal diffraction, etc.), and rotating the crystal in any function immediately reflects in the others.
One of its main features is the simulation of single crystal diffraction, allowing for the selection of X-rays, electrons, or neutrons as incident waves. For X-ray and neutron sources, calculations are based on the kinematic scattering approximation (first-order perturbation theory), where diffraction intensity is estimated simply from the square of the amplitude of the crystal structure factor and the excitation error. For electron beams, dynamic effects are calculated based on the Bloch wave method (Bethe, 1928). This method describes the state of electrons in the crystal using the wave equation and Bloch's theorem, calculates the Bloch waves that can exist in a periodic potential field, and then computes the amplitude of the diffracted waves by smoothly connecting the incident/exit waves at the sample interface. ReciPro supports dynamic scattering simulations for selected area electron diffraction (SAED), precession electron diffraction (PED), (large-angle) convergent-beam electron diffraction ((LA)-CBED), and electron backscatter diffraction (EBSD). CBED and EBSD represent the converging electron beam as a superposition of many plane waves. Although the Bloch wave method generally has a high computational cost, algorithmic improvements and CPU parallelization have achieved computation speeds that are practical for use.
Furthermore, ReciPro is capable of calculating high-resolution TEM (HRTEM) and STEM images. The former (HRTEM) is simulated at arbitrary magnification/resolution, taking into account the modulation effects of spherical aberration and defocusing of the objective lens, partial spatio-temporal coherence of the electron beam, and changes in sample thickness due to dynamic scattering effects. The latter (STEM) represents the incident converging electrons as a multitude of plane waves, similar to CBED, and calculates the effect of inelastic scattering due to phonon excitation (thermal diffuse scattering, TDS) by integrating over the scattering angle, enabling simulation of STEM images using annular detectors (e.g., STEM-HAADF). ReciPro is distributed under the MIT license (github.com/seto77/ReciPro/releases/latest/) as completely free software and runs on the Microsoft .NET Desktop 8.0 runtime. All source code and detailed documentation are available at the above GitHub repository.