Three-beam convergent-beam electron diffraction for measuring crystallographic phases
Under almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic meth...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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International Union of Crystallography
2018-11-01
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| Series: | IUCrJ |
| Subjects: | |
| Online Access: | http://scripts.iucr.org/cgi-bin/paper?S2052252518012216 |
| _version_ | 1818958288311549952 |
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| author | Yueming Guo Philip N. H. Nakashima Joanne Etheridge |
| author_facet | Yueming Guo Philip N. H. Nakashima Joanne Etheridge |
| author_sort | Yueming Guo |
| collection | DOAJ |
| description | Under almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic method exists. In this work, a set of simple analytical expressions is derived for the intensity distribution in convergent-beam electron diffraction (CBED) patterns recorded under three-beam conditions. It is shown that these expressions can be used to identify features in three-beam CBED patterns from which three-phase invariants can be extracted directly, without any iterative refinement processes. The octant, in which the three-phase invariant lies, can be determined simply by inspection of the indexed CBED patterns (i.e. the uncertainty of the phase measurement is ±22.5°). This approach is demonstrated with the experimental measurement of three-phase invariants in two simple test cases: centrosymmetric Si and non-centrosymmetric GaAs. This method may complement existing structure determination methods by providing direct measurements of three-phase invariants to replace `guessed' invariants in ab initio phasing methods and hence provide more stringent constraints to the structure solution. |
| first_indexed | 2024-12-20T11:23:22Z |
| format | Article |
| id | doaj.art-ce52218a92a742a181fc63f497a07d83 |
| institution | Directory Open Access Journal |
| issn | 2052-2525 |
| language | English |
| last_indexed | 2024-12-20T11:23:22Z |
| publishDate | 2018-11-01 |
| publisher | International Union of Crystallography |
| record_format | Article |
| series | IUCrJ |
| spelling | doaj.art-ce52218a92a742a181fc63f497a07d832022-12-21T19:42:27ZengInternational Union of CrystallographyIUCrJ2052-25252018-11-015675376410.1107/S2052252518012216gq5009Three-beam convergent-beam electron diffraction for measuring crystallographic phasesYueming Guo0Philip N. H. Nakashima1Joanne Etheridge2Department of Materials Science and Engineering, Monash University, Victoria 3800, AustraliaDepartment of Materials Science and Engineering, Monash University, Victoria 3800, AustraliaDepartment of Materials Science and Engineering, Monash University, Victoria 3800, AustraliaUnder almost all circumstances, electron diffraction patterns contain information about the phases of structure factors, a consequence of the short wavelength of an electron and its strong Coulombic interaction with matter. However, extracting this information remains a challenge and no generic method exists. In this work, a set of simple analytical expressions is derived for the intensity distribution in convergent-beam electron diffraction (CBED) patterns recorded under three-beam conditions. It is shown that these expressions can be used to identify features in three-beam CBED patterns from which three-phase invariants can be extracted directly, without any iterative refinement processes. The octant, in which the three-phase invariant lies, can be determined simply by inspection of the indexed CBED patterns (i.e. the uncertainty of the phase measurement is ±22.5°). This approach is demonstrated with the experimental measurement of three-phase invariants in two simple test cases: centrosymmetric Si and non-centrosymmetric GaAs. This method may complement existing structure determination methods by providing direct measurements of three-phase invariants to replace `guessed' invariants in ab initio phasing methods and hence provide more stringent constraints to the structure solution.http://scripts.iucr.org/cgi-bin/paper?S2052252518012216crystallographic phase problemthree-phase invariantsconvergent-beam electron diffractionstructure determinationenantiomorph ambiguitynanocrystalsdynamical studiesmultiple scattering |
| spellingShingle | Yueming Guo Philip N. H. Nakashima Joanne Etheridge Three-beam convergent-beam electron diffraction for measuring crystallographic phases IUCrJ crystallographic phase problem three-phase invariants convergent-beam electron diffraction structure determination enantiomorph ambiguity nanocrystals dynamical studies multiple scattering |
| title | Three-beam convergent-beam electron diffraction for measuring crystallographic phases |
| title_full | Three-beam convergent-beam electron diffraction for measuring crystallographic phases |
| title_fullStr | Three-beam convergent-beam electron diffraction for measuring crystallographic phases |
| title_full_unstemmed | Three-beam convergent-beam electron diffraction for measuring crystallographic phases |
| title_short | Three-beam convergent-beam electron diffraction for measuring crystallographic phases |
| title_sort | three beam convergent beam electron diffraction for measuring crystallographic phases |
| topic | crystallographic phase problem three-phase invariants convergent-beam electron diffraction structure determination enantiomorph ambiguity nanocrystals dynamical studies multiple scattering |
| url | http://scripts.iucr.org/cgi-bin/paper?S2052252518012216 |
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