Procedures for Point and Space Group Analysis

Special Issue ◽

Zeroth Order ◽

Space Group ◽

Space Groups ◽

Flow Charts ◽

Crystal Space ◽

Description of general procedures for point- and space-group determination by convergent-beam electron diffraction(CBED) soon appears in a special issue of J. Electron Microsc. Tech. The essence of them was already given in the flow charts in ref.2. We here demonstrate the procedures using an example of La2 CuO4 - 6, which is the end member of a 40K class superconductor La2-x Mx CuO4 - 6 (M = Ba, Sr and Ca). The CBED method has utilized to date only dynamical extinction(GM lines) appearing in zeroth-order Laue-zone(ZOLZ) reflections for the space-group determination. We emphasize that the use of GM lines appearing in higher-order Laue-zone(HOLZ) reflections makes it easy to determine crystal space-groups.The substance was already known to belong to the orthorhombic system with the lattice parameters of a=5.3548Å, b=5.4006Å and c=13.1592Å. Fig. 1(a) shows a CBED pattern taken at the [001] incidence, Fig.l(b) being the central part of Fig.l(a). The whole pattern has a symmetry 2mm. This indicates that the crystal has two mirror symmetries perpendicular to each other and that the point group is mmm or mm2.

A practical method of three-dimensional space-group analysis using convergent-beam electron diffraction

Acta Crystallographica Section A ◽

10.1107/s0567739475001738 ◽

1975 ◽

Vol 31 (6) ◽

pp. 804-810 ◽

Cited By ~ 55

Author(s):

P. Goodman

Keyword(s):

Electron Diffraction ◽

Dimensional Space ◽

Group Analysis ◽

Three Dimensional ◽

Practical Method ◽

Beam Electron ◽

Space Group ◽

Convergent Beam ◽

Three Dimensional Space

Bloch-wave interpretations of Gjønnes–Moodie lines in convergent-beam electron diffraction for non-symmorphic space-group crystals

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273321003211 ◽

2021 ◽

Vol 77 (3) ◽

pp. 222-231

Author(s):

Hirofumi Matsuhata

Keyword(s):

Electron Diffraction ◽

Dimensional Space ◽

High Energy ◽

Bloch Wave ◽

Bloch Waves ◽

Beam Electron ◽

Space Group ◽

Space Groups ◽

The contrast of Gjønnes–Moodie (GM) lines which appear in convergent-beam electron diffraction patterns for non-symmorphic space-group crystals is explained using Bloch waves. In the two-dimensional space groups p2mg and pg the Bloch waves for electron diffraction are described. In both space groups along the Δ line, Bloch waves are arranged as two different types, and it is shown that the two types of Bloch waves do not contribute to the intensity of forbidden reflections. Along the position where the forbidden reflection satisfies the Bragg condition, degeneracies of two Bloch waves are found and it is shown that the degenerated pair of Bloch waves do not contribute to the intensity. These Bloch-wave results provide a new perspective in the understanding of the contrast mechanism of GM lines previously described using scattering polynomials. They also advance the understanding of Bloch-wave behaviour in high-energy electron diffraction.

Progress in Transmission Electron Microscopy 1 - Springer Series in Surface Sciences ◽

Point Group and Space Group Identification by Convergent Beam Electron Diffraction

10.1007/978-3-662-09518-8_9 ◽

2001 ◽

pp. 273-299

Author(s):

Yi Liu

Keyword(s):

Electron Diffraction ◽

Group Identification ◽

Point Group ◽

Beam Electron ◽

Space Group ◽

Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

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 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

Point group symmetry of cadmium arsenide thin films determined by convergent beam electron diffraction

Physical Review Materials ◽

10.1103/physrevmaterials.3.084202 ◽

2019 ◽

Vol 3 (8) ◽

Cited By ~ 2

Author(s):

Honggyu Kim ◽

Manik Goyal ◽

Salva Salmani-Rezaie ◽

Timo Schumann ◽

Tyler N. Pardue ◽

...

Keyword(s):

Thin Films ◽

Electron Diffraction ◽

Point Group ◽

Group Symmetry ◽

Point Group Symmetry ◽

Beam Electron ◽

Determination of space group of BaPb0.75Bi0.25O3 by convergent-beam electron diffraction

Physica C Superconductivity ◽

10.1016/s0921-4534(02)01259-5 ◽

2002 ◽

Vol 382 (4) ◽

pp. 422-430 ◽

Cited By ~ 2

Author(s):

Takuya Hashimoto ◽

Kenji Tsuda ◽

Junichiro Shiono ◽

Junichiro Mizusaki ◽

Michiyoshi Tanaka

Keyword(s):

Electron Diffraction ◽

Beam Electron ◽

Space Group ◽

Space Group Determination of the Room-Temperature Phase ofα '-NaV2O5Using Convergent-Beam Electron Diffraction

Journal of the Physical Society of Japan ◽

10.1143/jpsj.69.1939 ◽

2000 ◽

Vol 69 (7) ◽

pp. 1939-1941 ◽

Cited By ~ 8

Author(s):

Kenji Tsuda ◽

Shuichi Amamiya ◽

Michiyoshi Tanaka ◽

Yukio Noda ◽

Masahiko Isobe ◽

...

Keyword(s):

Electron Diffraction ◽

Room Temperature ◽

Temperature Phase ◽

Beam Electron ◽

Space Group ◽

Normally supportive sublattices of crystallographic space groups

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s205327331901218x ◽

2020 ◽

Vol 76 (1) ◽

pp. 7-23

Author(s):

Miles A. Clemens ◽

Branton J. Campbell ◽

Stephen P. Humphries

Keyword(s):

Normal Subgroup ◽

Point Group ◽

Group Extension ◽

Normal Subgroups ◽

Symbolic Form ◽

Space Group ◽

Space Groups ◽

Significant Step ◽

Crystal Class ◽

Crystallographic Space Groups

The tabulation of normal subgroups of 3D crystallographic space groups that are themselves 3D crystallographic space groups (csg's) is an ambitious goal, but would have a variety of applications. For convenience, such subgroups are referred to as `csg-normal' while normal subgroups of the crystallographic point group (cpg) of a crystallographic space group are referred to as `cpg-normal'. The point group of a csg-normal subgroup must be a cpg-normal subgroup. The present work takes a significant step towards that goal by tabulating the translational subgroups (a.k.a. sublattices) that are capable of supporting csg-normal subgroups. Two necessary conditions are identified on the relative sublattice basis that must be met in order for the sublattice to support csg-normal subgroups: one depends on the operations of the point group of the space group, while the other depends on the operations of the cpg-normal subgroup. Sublattices that meet these conditions are referred to as `normally supportive'. For each cpg-normal subgroup (excluding the identity subgroup 1) of each of the arithmetic crystal classes of 3D space groups, all of the normally supportive sublattices have been tabulated in symbolic form, such that most of the entries in the table contain one or more integer variables of infinite range; thus it could be more accurately described as a table of the infinite families of normally supportive sublattices. For a given pair of cpg-normal subgroup and normally supportive sublattice, csg-normal subgroups of the space groups of the parent arithmetic crystal class can be constructed via group extension, though in general such a pair does not guarantee the existence of a corresponding csg-normal subgroup.

Identification of the impurity phase in high-purity CeB6 by convergent-beam electron diffraction

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273319000354 ◽

2019 ◽

Vol 75 (3) ◽

pp. 489-500

Author(s):

Ding Peng ◽

Philip N. H. Nakashima

Keyword(s):

Electron Diffraction ◽

High Purity ◽

Density Functional ◽

Impurity Phase ◽

Lattice Parameters ◽

Beam Electron ◽

Space Group ◽

Convergent Beam ◽

Very High

The rare earth hexaborides are known for their tendency towards very high crystal perfection. They can be grown into large single crystals of very high purity by inert gas arc floating zone refinement. The authors have found that single-crystal cerium hexaboride grown in this manner contains a significant number of inclusions of an impurity phase that interrupts the otherwise single crystallinity of this prominent cathode material. An iterative approach is used to unequivocally determine the space group and the lattice parameters of the impurity phase based on geometries of convergent-beam electron diffraction (CBED) patterns and the symmetry elements that they possess in their intensity distributions. It is found that the impurity phase has a tetragonal unit cell with space group P4/mbm and lattice parameters a = b = 7.23 ± 0.03 and c = 4.09 ± 0.02 Å. These agree very well with those of a known material, CeB4. Confirmation that this is indeed the identity of the impurity phase is provided by quantitative CBED (QCBED) where the very close match between experimental and calculated CBED patterns has confirmed the atomic structure. Further confirmation is provided by a density functional theory calculation and also by high-angle annular dark-field scanning transmission electron microscopy.