Three-beam convergent-beam electron diffraction for measuring crystallographic phases

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)753-764
Number of pages12
JournalIUCrJ
Volume5
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • convergent-beam electron diffraction
  • crystallographic phase problem
  • dynamical studies
  • enantiomorph ambiguity
  • multiple scattering
  • nanocrystals
  • structure determination
  • three-phase invariants

Cite this

@article{0efc7253496f4fcc91e2142cd7c7e7a4,
title = "Three-beam convergent-beam electron diffraction for measuring crystallographic phases",
abstract = "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.",
keywords = "convergent-beam electron diffraction, crystallographic phase problem, dynamical studies, enantiomorph ambiguity, multiple scattering, nanocrystals, structure determination, three-phase invariants",
author = "Yueming Guo and Nakashima, {Philip N.H.} and Joanne Etheridge",
year = "2018",
month = "1",
day = "1",
doi = "10.1107/S2052252518012216",
language = "English",
volume = "5",
pages = "753--764",
journal = "IUCrJ",
issn = "2052-2525",
publisher = "International Union of Crystallography (IUCr)",

}

Three-beam convergent-beam electron diffraction for measuring crystallographic phases. / Guo, Yueming; Nakashima, Philip N.H.; Etheridge, Joanne.

In: IUCrJ, Vol. 5, 01.01.2018, p. 753-764.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Three-beam convergent-beam electron diffraction for measuring crystallographic phases

AU - Guo, Yueming

AU - Nakashima, Philip N.H.

AU - Etheridge, Joanne

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - convergent-beam electron diffraction

KW - crystallographic phase problem

KW - dynamical studies

KW - enantiomorph ambiguity

KW - multiple scattering

KW - nanocrystals

KW - structure determination

KW - three-phase invariants

UR - http://www.scopus.com/inward/record.url?scp=85056188286&partnerID=8YFLogxK

U2 - 10.1107/S2052252518012216

DO - 10.1107/S2052252518012216

M3 - Article

VL - 5

SP - 753

EP - 764

JO - IUCrJ

JF - IUCrJ

SN - 2052-2525

ER -