Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

Determination of Atomic Positions in SiC 4H Using Quantitative Convergent Beam Refinements

1997 ◽  
Vol 3 (S2) ◽  
pp. 1051-1052
Author(s):  
R. Holmestad ◽  
J.-P. Morniroli ◽  
J.M. Zuo ◽  
J.C.H. Spence
Keyword(s):  
Electron Diffraction ◽  
Crystal Form ◽  
Hexagonal Structure ◽  
Double Layers ◽  
Stacking Sequence ◽  
X Ray Diffraction ◽  
Small Probe ◽  
Convergent Beam ◽  
Synthesized Materials

Silicon carbide (SiC) is a widely used ceramic material, with many structural and electronic applications. It exists in many polytypes, differing from one another only by the stacking sequence of close packed double layers of Si and C atoms. The polytype called 4H has the hexagonal structure shown in figure 1. The double layers here have a stacking sequence of ABACABAC.. The distance z between the Si and the C layers (shown in figure 1) is an adjustable parameter, which is not exactly known. The aim of this work is to determine the atomic positions in the c-direction by quantitative convergent beam electron diffraction (QCBED). The goal is to develop a general refinement approach for structure determination by electron diffraction. Many newly synthesized materials are available in only very small quantities in the single crystal form and/or mixed with other phases, making X-ray diffraction methods difficult. SiC is often full of stacking faults. For these types of materials, the CBED method is ideal because of the small probe that can be used; areas of less than 100 Å can be studied.

Determination of crystal symmetry for Bi4Ti3O12-based ferroelectrics by using electron diffraction

2013 ◽  
Vol 46 (3) ◽  
pp. 798-800 ◽  
Author(s):  
Wanneng Ye ◽  
Chaojing Lu ◽  
Peng You ◽  
Kun Liang ◽  
Yichun Zhou
Keyword(s):  
Electron Diffraction ◽  
Room Temperature ◽  
Monoclinic Space Group ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Electron Diffraction Technique ◽  
Convergent Beam

In recent years, inconsistent space groups of monoclinicB1a1 and orthorhombicB2cbhave been reported for the room-temperature ferroelectric phases of both Bi4Ti3O12and lanthanide-substituted Bi4Ti3O12. In this article, the electron diffraction technique is employed to unambiguously clarify the crystal symmetries of ferroelectric Bi4Ti3O12and Bi3.15Nd0.85Ti3O12single crystals at room temperature. All the reflections observed from the two crystals match well with those derived fromB1a1, but the observed reflections 010, 030, {\overline 2}10 and {\overline 2}30 should be forbidden in the case ofB2cb. This fact indicates that both the ferroelectrics are of the space groupB1a1 rather thanB2cb, which is confirmed by convergent-beam electron diffraction observations. On the basis of the monoclinic space groupB1a1, the lattice parameters of both the ferroelectrics were calculated by the Rietveld refinement of powder X-ray diffraction data.

Microstructure and crystal symmetry of Pb2Sr2(Y/Ca)Cu3O9−δ

1990 ◽  
Vol 48 (4) ◽  
pp. 64-65
Author(s):  
Y. P. Lin ◽  
J. S. Xue ◽  
J. E. Greedan
Keyword(s):  
Electron Diffraction ◽  
High Temperature Superconductors ◽  
Carbon Film ◽  
Basic Structure ◽  
Crystal Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Space Groups ◽  
New Family ◽  
Convergent Beam

A new family of high temperature superconductors based on Pb2Sr2YCu3O9−δ has recently been reported. One method of improving Tc has been to replace Y partially with Ca. Although the basic structure of this type of superconductors is known, the detailed structure is still unclear, and various space groups has been proposed. In our work, crystals of Pb2Sr2YCu3O9−δ with dimensions up to 1 × 1 × 0.25.mm and with Tc of 84 K have been grown and their superconducting properties described. The defects and crystal symmetry have been investigated using electron microscopy performed on crushed crystals supported on a holey carbon film.Electron diffraction confirmed x-ray diffraction results which showed that the crystals are primitive orthorhombic with a=0.5383, b=0.5423 and c=1.5765 nm. Convergent Beam Electron Diffraction (CBED) patterns for the and axes are shown in Figs. 1 and 2 respectively.

scholarly journals The determination of point groups from imprecise molecular geometries

2021 ◽  
Author(s):  
Peter J. Knowles
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
Simple Function ◽  
Coordinate Frame ◽  
New Approach ◽  
Measure Of Symmetry ◽  
Point Groups

AbstractWe present a new approach for the assignment of a point group to a molecule when the structure conforms only approximately to the symmetry. It proceeds by choosing a coordinate frame that minimises a measure of symmetry breaking that is computed efficiently as a simple function of the molecular coordinates and point group specification.

scholarly journals Coherent convergent-beam time-resolved X-ray diffraction

2014 ◽  
Vol 369 (1647) ◽  
pp. 20130325 ◽  
Author(s):  
John C. H. Spence ◽  
Nadia A. Zatsepin ◽  
Chufeng Li
Keyword(s):  
Single Shot ◽  
Beam Diameter ◽  
X Ray Diffraction ◽  
Single Particles ◽  
Time Resolved ◽  
X Ray ◽  
Challenges And Opportunities ◽  
Phase Sensitive ◽  
Diffraction Patterns ◽  
Convergent Beam

The use of coherent X-ray lasers for structural biology allows the use of nanometre diameter X-ray beams with large beam divergence. Their application to the structure analysis of protein nanocrystals and single particles raises new challenges and opportunities. We discuss the form of these coherent convergent-beam (CCB) hard X-ray diffraction patterns and their potential use for time-resolved crystallography, normally achieved by Laue (polychromatic) diffraction, for which the monochromatic laser radiation of a free-electron X-ray laser is unsuitable. We discuss the possibility of obtaining single-shot, angle-integrated rocking curves from CCB patterns, and the dependence of the resulting patterns on the focused beam coordinate when the beam diameter is larger or smaller than a nanocrystal, or smaller than one unit cell. We show how structure factor phase information is provided at overlapping interfering orders and how a common phase origin between different shots may be obtained. Their use in refinement of the phase-sensitive intensity between overlapping orders is suggested.

scholarly journals The large angle technique and lattice defect identifications

2014 ◽  
Vol 70 (a1) ◽  
pp. C40-C40
Author(s):  
Michiyoshi Tanaka
Keyword(s):  
Lattice Defect ◽  
Large Angle ◽  
Crystal Structure Analysis ◽  
Shift Vector ◽  
Space Groups ◽  
Orientation Difference ◽  
History Of ◽  
Point Groups ◽  
Convergent Beam

The history of the Convergent Beam Electron Diffraction (CBED) is shortly introduced. Symmetry determinations[1] of crystals or the point groups and space groups of 3, 4, 5 and 6 dimensional crystals, and crystal structure analysis including the determination of charge density distribution and potential distribution of a crystal are briefly reviewed.[2] Then, the large angle CBED (LACBED) technique is described.[3] Applications of the LACBED technique to the determinations of the Burgers vector of a dislocation, the shift vector at a stacking fault, the precise orientation difference of a twin domain and the strain of an advanced multi-layer material are reviewed.

Simultaneous Identification of the Bravais Lattice and Glide Planes From Microdiffraction Patterns: Deduction of the Possible Space Groups

1990 ◽  
Vol 48 (2) ◽  
pp. 478-479
Author(s):  
Jean Paul Morniroli ◽  
Michel Gantois
Keyword(s):  
Spot Size ◽  
Bravais Lattice ◽  
High Angular Resolution ◽  
Space Groups ◽  
Small Spot ◽  
3D Information ◽  
Convergent Beam ◽  
Simultaneous Identification ◽  
2D And 3D

Microdiffraction experiments obtained with a small spot size and a nearly parallel electron beam are well-adapted to most specimens and especially to small particles. They are particularly useful when Convergent Beam Electron Diffraction (CBED) patterns do not give the 2D and 3D information required to identify the point and the space groups. They can also be used to start the identification or the determination of a crystal structure. Specific and simplest CBED experiments are later realized to remove left ambiguities.The microdiffraction Zone Axis Patterns (ZAP) are composed of sharp reflections whose high angular resolution helps to appreciate the shifts and the periodicity differences between the Zero (ZOLZ) and First (FOLZ) Order Laue Zones reflection nets. Observations of thin areas at low temperature are recommended in order to produce many well visible FOLZ reflections.It was already indicated that the crystal system and the Laue class are deduced from observation of the whole pattern symmetry of the reflections.

Some practical aspects of CBED applications in materials science

1989 ◽  
Vol 47 ◽  
pp. 508-509
Author(s):  
D. R. Liu ◽  
D. B. Williams
Keyword(s):  
Materials Science ◽  
Theoretical Foundation ◽  
Point Group ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
X Ray ◽  
Unambiguous Determination ◽  
Convergent Beam ◽  
Electron Energy Loss

The paper by Buxton et al. has firmly laid down the theoretical foundation for the point group determination of a crystal structure with convergent beam electron diffraction (CBED). Numerous examples of successful applications of this theory to materials science problems have been published. However, it has also been observed that, for an unambiguous determination of some crystal structures, more zone axis CBED patterns are needed than it is indicated by the tables in the paper. Yet sometimes ambiguity can still exist as in the case of the point group determination of the MgAl2O4 spinel, where CBED is unable to detect an alleged Al3+ ion displacement of Δb=0.0002∼0.0006 nm along a <111> direction and thus unable to determine whether its point group should be m3m or m. This difficulty might be attributed to the fact that, as for microanalysis, such as x-ray energy dispersive spectroscopy and electron energy-loss spectroscopy, the CBED technique must have its detection limit beyond which the detail in an acquired CBED pattern is not adequate enough to permit an unambiguous determination of its diffraction group.

Determinability of Complete Residual Strain Tensor from Multiple CBED Patterns

2006 ◽  
Vol 524-525 ◽  
pp. 115-120 ◽  
Author(s):  
Adam Morawiec
Keyword(s):  
Strain Tensor ◽  
Convergent Beam Electron Diffraction ◽  
Reasonable Accuracy ◽  
Multiple Diffraction ◽  
Numerical Tests ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
The Impact ◽  
Elastic Strain Tensor

The ambiguity in determination of complete elastic strain tensor by convergent beam electron diffraction can be overcome by simultaneous use of multiple diffraction patterns. Numerical tests of strain determining procedure based on multiple patterns have been carried out. Patterns were simulated using both kinematic and dynamic approaches, and then they were used as input in the tested procedure. The tests indicate that, in practice, at least three patterns are needed in order to determine a complete strain tensor with reasonable accuracy. The strain resolution of two parts per ten thousand was achieved with five diffraction patterns. Moreover, the impact of errors in voltage and camera length is considered. It is shown that within the kinematic description, the deviations from the correct voltage are equivalent to errors in the isotropic part of strain.

Symmetry — breaking in convergent-beam electron diffraction

1988 ◽  
Vol 46 ◽  
pp. 518-519
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Materials Science ◽  
Perfect Crystal ◽  
Convergent Beam Electron Diffraction ◽  
Small Deviations ◽  
Higher Symmetry ◽  
Small Probe ◽  
Superconducting Ceramics ◽  
Major Application ◽  
Convergent Beam

Symmetry determination remains the major application of CBED in materials science. Its power lies not only in the small-probe capability, but in the sensitivity to small deviations from symmetry, and the ability to distinguish centro- and non-centrosymmetric structures. However, there are a large number of artefacts which can lead to lowering of the observed symmetry, so that procedures for CBED point and space-group determinations generally stipulate that, where two different symmetries are observed, the higher-symmetry pattern should be regarded as representative of the perfect crystal (eg.l). This has lead to the occasional controversy (notably in the recent case of the 1-2-3 superconducting ceramics) as to whether symmetry-lowering is “genuine” or not. The purpose of the present paper is to review the possible sources of symmetry-breaking in CBED patterns and to attempt to establish a basis on which to distinguish “genuine” symmetry-breaking from artefacts. The various sources of symmetry-breaking will be addressed in turn.

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