New electron diffraction method to identify the chirality of enantiomorphic crystals

A new CBED (convergent-beam electron diffraction) method is proposed for the identification of the chirality of enantiomorphic crystals, in which asymmetry in the intensity of the reflections of Bijvoet pairs in an experimental symmetrical zone-axis CBED pattern is compared with that of a computer-simulated CBED pattern. The intensity difference for reflections of these Bijvoet pairs results from multiple scattering (dynamical nature of electron diffraction) among relevant Bijvoet pairs of reflections, each pair of which has identical amplitude and different phase angles. Therefore, the crystal thickness where chiral identification is made with the present method is limited by the extinction distance of Bijvoet pairs of reflections relevant to multiple scattering to produce the intensity asymmetry, which is usually of the order of a few tens of nanometers. With the present method, a single CBED pattern is sufficient and chiral identification can be made for all the possible enantiomorphic crystals that are allowed to exist in crystallography.

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Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767398008903 ◽

1999 ◽

Vol 55 (2) ◽

pp. 188-196 ◽

Cited By ~ 1

Author(s):

R. Høier ◽

C. R. Birkeland ◽

R. Holmestad ◽

K Marthinsen

Keyword(s):

Electron Diffraction ◽

Phase Structure ◽

Diffraction Method ◽

Convergent Beam Electron Diffraction ◽

Beam Electron ◽

Structure Factors ◽

Refinement Method ◽

Three Phase ◽

Phase Sensitive ◽

Convergent Beam

Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for parameter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depend on the choice of the initial parameters in the refinement. Even unrealistic starting assumptions and incorrect temperature factor lead to stable results for the structure invariant. The examples show that the accuracy varies from 1 to 10° in the electron three-phase invariants determined and from 0.5 to 5% for the amplitudes. Individual phases could not be determined in the present case owing to spatial intensity correlations between phase-sensitive pixels. However, for the three-phase structure invariant, stable solutions were found.

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The kinematic convergent-beam electron diffraction method for nanocrystal structure determination

Journal of Applied Physics ◽

10.1063/1.3238312 ◽

2009 ◽

Vol 106 (7) ◽

pp. 074309 ◽

Cited By ~ 9

Author(s):

J. T. McKeown ◽

J. C. H. Spence

Keyword(s):

Electron Diffraction ◽

Structure Determination ◽

Diffraction Method ◽

Convergent Beam Electron Diffraction ◽

Beam Electron ◽

Convergent Beam

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Enantiomorph identification of crystals belonging to the point groups 321 and 312 by convergent-beam electron diffraction

Journal of Applied Crystallography ◽

10.1107/s0021889806055877 ◽

2007 ◽

Vol 40 (2) ◽

pp. 241-249 ◽

Cited By ~ 2

Author(s):

Haruyuki Inui ◽

Akihiro Fujii ◽

Hiroki Sakamoto ◽

Satoshi Fujio ◽

Katsushi Tanaka

Keyword(s):

Electron Diffraction ◽

Diffraction Method ◽

Convergent Beam Electron Diffraction ◽

Zone Axis ◽

The Other ◽

Zeroth Order ◽

Beam Electron ◽

First Order ◽

Point Groups ◽

Convergent Beam

The recently proposed CBED (convergent-beam electron diffraction) method for enantiomorph identification has been successfully applied to crystals belonging to the point groups 321 and 312. The intensity asymmetry of zeroth-order Laue zone and/or first-order Laue zone reflections of Bijvoet pairs is easily recognized in CBED patterns with the incidence along appropriate zone-axis orientations for each member of the enantiomorphic pair. The intensity asymmetry with respect to the symmetry line is reversed upon changing the space group (handedness) from one to the other. Thus, enantiomorph identification can be easily performed in principle for all crystals belonging to the point groups 321 and 312.

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Convergent-beam electron diffraction studies of domains in tetragonal phase of lead zirconate titanate ceramics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010012518x ◽

1987 ◽

Vol 45 ◽

pp. 26-27

Author(s):

M.L.A. Dass

Keyword(s):

Electron Diffraction ◽

Lead Zirconate Titanate ◽

Tetragonal Phase ◽

Diffraction Method ◽

Rhombohedral Phase ◽

Lead Zirconate ◽

Convergent Beam Electron Diffraction ◽

Beam Electron ◽

Zirconate Titanate ◽

Convergent Beam

Lead zirconate titanate Pb(ZrxTi(1-x))O3 (PZT) ceramics are ferroelectrics formed as solid solutions between PbTiO3 and PbZrO3. Among the different phases in the ferroelectric state, the primary ones are the Ti+4 rich tetragonal phase and the Zr+4 rich rhombohedral phase. The coexistence of both T and R phases at the boundary composition has been reported using the convergent beam electron diffraction method. In an attempt to characterize the ferroelectric domains in the different phases, a study on the tetragonal phase is reported here, as such an analysis is useful in identifying the phases at the phase boundary.The ceramic used in this study was prepared by conventional ceramic processing and the composition of the sample examined was Pb(Zr0.55Ti0.45)O3. The structure has been found to be tetragonal with lattice parameters a=4.0155Å and c=4.1033Å using X-ray diffraction studies of powder samples.

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A DigitalMicrograph™ Script for Crystal Thickness Measurements Using Convergent Beam Electron Diffraction

Microscopy and Microanalysis ◽

10.1017/s1431927604881637 ◽

2004 ◽

Vol 10 (S02) ◽

pp. 1380-1381 ◽

Cited By ~ 5

Author(s):

Vincent Hou

Keyword(s):

Electron Diffraction ◽

Convergent Beam Electron Diffraction ◽

Crystal Thickness ◽

Beam Electron ◽

Convergent Beam ◽

Thickness Measurements

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.

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Identification of the chirality of intermetallic compounds by electron diffraction

MRS Proceedings ◽

10.1557/proc-842-s5.8 ◽

2004 ◽

Vol 842 ◽

Author(s):

S. Fujio ◽

H. Sakamoto ◽

K. Tanaka ◽

H. Inui

Keyword(s):

Electron Diffraction ◽

Intermetallic Compounds ◽

Multiple Scattering ◽

Zone Axis ◽

Intensity Difference ◽

Phase Angles

ABSTRACTA new CBED method is proposed for the identification of the chirality of enantiomorphic crystals, in which asymmetry in the intensity of the reflections of Bijvoet pairs in an experimental symmetrical zone-axis CBED pattern is compared with that of a computer-simulated CBED pattern. The intensity difference for reflections of these Bijvoet pairs results from multiple scattering among relevant Bijvoet pairs of reflections, each pair of which has identical amplitude and different phase angles. With the method, a single CBED pattern is sufficient and chiral identification can be made for all possible enantiomorphic crystals that are allowed to exist in crystallography. The method is successfully applied to some chiral intermetallic compounds.

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