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Li Z, Rose H, Madsen J, Biskupek J, Susi T, Kaiser U. Computationally Efficient Handling of Partially Coherent Electron Sources in (S)TEM Image Simulations via Matrix Diagonalization. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2022; 29:1-9. [PMID: 36104826 DOI: 10.1017/s1431927622012387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We introduce a novel method to improve the computational efficiency for (S)TEM image simulation by employing matrix diagonalization of the mixed envelope function (MEF). The MEF is derived by taking the finite size and the energy spread of the effective electron source into account, and is a component of the transmission cross-coefficient that accounts for the correlation between partially coherent waves. Since the MEF is a four-dimensional array and its application in image calculations is time-consuming, we reduce the computation time by using its eigenvectors. By incorporating the aperture function into the matrix diagonalization, only a small number of eigenvectors are required to approximate the original matrix with high accuracy. The diagonalization enables for each eigenvector the calculation of the corresponding image by employing the coherent model. The individual images are weighted by the corresponding eigenvalues and then summed up, resulting in the total partially coherent image.
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Affiliation(s)
- Zhongbo Li
- Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
| | - Harald Rose
- Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
| | - Jacob Madsen
- Faculty of Physics, University of Vienna, Vienna 1090, Austria
| | - Johannes Biskupek
- Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
| | - Toma Susi
- Faculty of Physics, University of Vienna, Vienna 1090, Austria
| | - Ute Kaiser
- Electron Microscopy Group of Materials Science, University of Ulm, Ulm 89081, Germany
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Peters JJP. A Fast Frozen Phonon Algorithm Using Mixed Static Potentials. Ultramicroscopy 2021; 229:113364. [PMID: 34352601 DOI: 10.1016/j.ultramic.2021.113364] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 07/16/2021] [Accepted: 07/23/2021] [Indexed: 10/20/2022]
Abstract
Image simulation in electron microscopy is vital for advanced image analysis but can be prohibitively long. This is especially true when including thermal diffuse scattering through the frozen phonon method, requiring repeat simulations for a number of phonon configurations. Here a method of reducing frozen phonon simulation time is demonstrated by emulating random phonon displacements through randomly mixing a set of precalculated static potentials. This avoids excessive recalculation of atom potentials and can lead to significant time improvement. The validity and limitations of this method are also demonstrated with respect to convergent beam electron diffraction and scanning transmission electron microscopy.
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Pelz PM, Rakowski A, Rangel DaCosta L, Savitzky BH, Scott MC, Ophus C. A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2021; 27:835-848. [PMID: 34225836 DOI: 10.1017/s1431927621012083] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the plane-wave reciprocal-space interpolated scattering matrix (PRISM) algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into “beamlets,” given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer random access memory (RAM). We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM, and partitioned PRISM algorithms.
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Affiliation(s)
- Philipp M Pelz
- Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA94720, USA
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
| | - Alexander Rakowski
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
| | - Luis Rangel DaCosta
- Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA94720, USA
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
| | - Benjamin H Savitzky
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
| | - Mary C Scott
- Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA94720, USA
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
| | - Colin Ophus
- National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
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Madsen J, Susi T. The abTEM code: transmission electron microscopy from first principles. OPEN RESEARCH EUROPE 2021; 1:24. [PMID: 37645137 PMCID: PMC10446032 DOI: 10.12688/openreseurope.13015.1] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/18/2021] [Indexed: 09/27/2023]
Abstract
Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document. This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.
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Affiliation(s)
- Jacob Madsen
- Faculty of Physics, University of Vienna, Vienna, 1090, Austria
| | - Toma Susi
- Faculty of Physics, University of Vienna, Vienna, 1090, Austria
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Madsen J, Susi T. The abTEM code: transmission electron microscopy from first principles. OPEN RESEARCH EUROPE 2021; 1:24. [PMID: 37645137 PMCID: PMC10446032 DOI: 10.12688/openreseurope.13015.2] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/18/2021] [Indexed: 08/31/2023]
Abstract
Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document. This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.
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Affiliation(s)
- Jacob Madsen
- Faculty of Physics, University of Vienna, Vienna, 1090, Austria
| | - Toma Susi
- Faculty of Physics, University of Vienna, Vienna, 1090, Austria
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Analysis of medium-range order based on simulated segmented ring detector STEM-images: amorphous Si. Ultramicroscopy 2019; 200:169-179. [DOI: 10.1016/j.ultramic.2019.02.023] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Revised: 02/22/2019] [Accepted: 02/26/2019] [Indexed: 11/21/2022]
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