The symmetry of electron diffraction zone axis patterns

1976 ◽  
Vol 281 (1301) ◽  
pp. 171-194 ◽  
Keyword(s):  
Electron Microscopy ◽  
Group Theory ◽  
Graphical Representation ◽  
Zone Axis ◽  
Fast Electrons ◽  
Extinction Contour ◽  
Symmetry Properties ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Convergent Beam

The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallelsided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.

A study of the high-Cu Al–Cu–Co decagonal phase

1993 ◽  
Vol 8 (7) ◽  
pp. 1473-1476 ◽  
Author(s):  
B. Grushko
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Electron Diffraction ◽  
Diffuse Scattering ◽  
Nonequilibrium State ◽  
Zone Axis ◽  
Decagonal Phase ◽  
Diffraction Patterns ◽  
Scanning Electron

The decagonal phase was studied by transmission and scanning electron microscopy in an Al62Cu24Co14 alloy annealed at 550–850 °C. The electron diffraction patterns of the decagonal phase exhibited weak quasiperiodic odd-n reflections in the [1-2100] zone axis corresponding to the equilibrated structure. The relative intensities of these reflections were significantly lower in the Al62Cu24Co14 than in the Al68Cu11Co21 decagonal phase. Diffuse scattering observed previously at the same positions can be related to a nonequilibrium state of the decagonal phase.

Effective Extinction Distances in Zone Axis Silicon

2000 ◽  
Vol 6 (S2) ◽  
pp. 1028-1029
Author(s):  
Z. Yu ◽  
R. R. Vanfleet ◽  
J. Silcox
Keyword(s):  
Electron Microscopy ◽  
Plane Waves ◽  
Normal Incidence ◽  
Sample Surface ◽  
Bloch Wave ◽  
Zone Axis ◽  
Image Recording ◽  
Intensity Measurements ◽  
Digital Image Recording ◽  
Convergent Beam

Many scientific questions encountered in electron microscopy require quantitative deductions from the observations. Comparisons of experimental observations with simulations are however, still relatively rare since measurements of intensity are normally difficult. In this paper we discuss the use of experimental observations of the effective extinction distances for zone axis silicon using a convergent beam STEM mode for comparison with a number of simulations. On the experimental side, the measurements were made with a STEM that provides accurate intensity measurements directly with a digital image recording system. Two theoretical schemes widely used in electron microscopy simulations, multislice simulation and Bloch-wave calculation, were employed for the simulations. In each case, both a TEM case and a STEM case were calculated for comparison.The multislice simulations were carried out using codes available from Kirkland. For the TEM case with plane waves at normal incidence on the sample surface, the unscattered (0,0) exit beam gives the Bright Field (BF) intensity.

(111)p microtwinning in SrRuO3 thin films on (001)p LaAlO3

2009 ◽  
Vol 65 (6) ◽  
pp. 694-698 ◽  
Author(s):  
Y. Han ◽  
I. M. Reaney ◽  
D. S. Tinberg ◽  
S. Trolier-McKinstry
Keyword(s):  
Electron Microscopy ◽  
Thin Films ◽  
Transmission Electron Microscopy ◽  
Orientation Relationship ◽  
Room Temperature ◽  
Pulsed Laser ◽  
Zone Axis ◽  
Laser Deposition ◽  
Transmission Electron ◽  
Diffraction Patterns

SrRuO3 (SRO) thin films grown on (001)p (p = pseudocubic) oriented LaAlO3 (LAO) by pulsed laser deposition have been characterized using transmission electron microscopy. Observations along the 〈100〉p directions suggests that although the SRO layer maintains a pseudocube-to-pseudocube orientation relationship with the underlying LAO substrate, it has a ferroelastic domain structure associated with a transformation on cooling to room temperature to an orthorhombic Pbnm phase (a − a − c + Glazer tilt system). In addition, extra diffraction spots located at ±1/6(ooo)p and ±1/3(ooo)p (where `o' indicates an index with an odd number) positions were obtained in 〈110〉p zone-axis diffraction patterns. These were attributed to the existence of high-density twins on {111}p pseudocubic planes within the SrRuO3 films rather than to more conventional mechanisms for the generation of superstructure reflections.

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

2007 ◽  
Vol 40 (2) ◽  
pp. 241-249 ◽  
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.

Energy Filtered Imaging and Convergent Beam Electron Diffraction (CBED) in the Transmission Electron Microscope (TEM)

1997 ◽  
Vol 3 (S2) ◽  
pp. 973-974
Author(s):  
A.G. Fox ◽  
E.S.K. Menon ◽  
M. Saunders
Keyword(s):  
Electron Diffraction ◽  
Form Factors ◽  
Zone Axis ◽  
X Ray ◽  
Elemental Imaging ◽  
Energy Filtering ◽  
Transmission Electron ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Single Objective

Over the last ten years TEMs have been developed that are capable of HREM, EDX, PEELS and diffraction using a single objective pole piece. More recently these TEMs have been equipped with the capability of energy filtering the electron beam after it has passed through the sample so that energy filtered images and electron diffraction patterns can be obtained. In this work the use of a Topcon 002B TEM equipped with a GATAN PEELS imaging filter (GIF) to generate zero-loss energy filtered zone axis CBED patterns and elemental images from inelastically scattered electrons will be described. An analysis of this energy filtered data indicates that elemental imaging using the GIF is an informative, but semiquantitative technique, whereas zero-loss energy filtered zone axis CBED patterns can be accurately quantified so that the two lowest-angle x-ray form factors of cubic elements can be measured with errors of the order of 0.1% or less.

Replica Extraction Method on Nanostructured Gold Coatings and Orientation Determination Combining SEM and TEM Techniques

2014 ◽  
Vol 20 (6) ◽  
pp. 1654-1661 ◽  
Author(s):  
Christian Bocker ◽  
Michael Kracker ◽  
Christian Rüssel
Keyword(s):  
Electron Microscopy ◽  
Extraction Method ◽  
Electron Backscatter Diffraction ◽  
Substrate Surface ◽  
Complete Removal ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Nanostructured Gold ◽  
Diffraction Patterns ◽  
Convergent Beam

AbstractIn the field of electron microscopy the replica technique is known as an indirect method and also as an extraction method that is usually applied on metallurgical samples. This contribution describes a fast and simple transmission electron microscopic (TEM) sample preparation by complete removal of nanoparticles from a substrate surface that allows the study of growth mechanisms of nanostructured coatings. The comparison and combination of advanced diffraction techniques in the TEM and scanning electron microscopy (SEM) provide possibilities for operators with access to both facilities. The analysis of TEM-derived diffraction patterns (convergent beam electron diffraction) in the SEM/electron backscatter diffraction software simplifies the application, especially when the patterns are not aligned along a distinct zone axis. The study of the TEM sample directly by SEM and transmission Kikuchi diffraction allows cross-correlation with the TEM results.

Precipitation Hardening in Fe-1.03%Cu Structural Steel

2007 ◽  
Vol 561-565 ◽  
pp. 111-114
Author(s):  
Hui Ping Ren ◽  
Hai Yan Wang ◽  
Zong Chang Liu ◽  
Lin Chen
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Precipitation Hardening ◽  
Solution Treatment ◽  
Zone Axis ◽  
High Density ◽  
Nano Scale ◽  
Transmission Electron ◽  
Steel Strength ◽  
Diffraction Patterns

The precipitation of copper during aging at 650oC within ferrite in high-purity Fe-1.03wt%Cu steel was examined by transmission electron microscopy, and the influence of precipitation particles on property of experimental steel was investigated. The microstructure and the corresponding diffraction patterns of different zone axis were analyzed. Nano-scale copper-rich clusters with B2-like structure and high density dislocation around precipitate was observed during either solution treatment or aging. Nano-scale metastable precipitates and high density around them were found to play the most important role for increasing steel strength.

Appropriate zone-axis orientations for the determination of crystal polarity by convergent-beam electron diffraction

2015 ◽  
Vol 48 (3) ◽  
pp. 736-746 ◽  
Author(s):  
Katsushi Tanaka ◽  
Norihiko L. Okamoto ◽  
Satoshi Fujio ◽  
Hiroki Sakamoto ◽  
Haruyuki Inui
Keyword(s):  
Electron Diffraction ◽  
Rotation Axis ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
Mirror Plane ◽  
Axis Orientation ◽  
Beam Electron ◽  
Polarity Determination ◽  
Point Groups ◽  
Convergent Beam

A convergent-beam electron diffraction (CBED) method is proposed for polarity determination, in which polarity is determined from the intensity asymmetry of any of thehkl–\overline h\overline k\overline l Friedel pairs appearing in a zone-axis CBED pattern with a symmetric arrangement of Bijvoet pairs of reflections. The intensity asymmetry occurs as a result of multiple scattering among Bijvoet pairs of reflections in the CBED pattern. The appropriate zone-axis orientations for polarity determination are deduced for 19 of the 25 polar point groups from symmetry considerations so as to observe Bijvoet pairs of reflections symmetrically in a single CBED pattern. These appropriate zone-axis orientations deduced for the 19 polar point groups coincide with nonpolar directions. This is because the nonpolar directions for these point groups are perpendicular to an even-fold rotation axis, which guarantees the symmetric arrangement of Bijvoet pairs of reflections with respect to the symmetry (m–m′) line in a CBED pattern taken along any of the appropriate zone-axis orientations. Them–m′ line in the CBED pattern is proved to be perpendicular to the trace of the even-fold rotation axis. On the other hand, if the nonpolar direction is either perpendicular to a mirror plane or parallel to a roto-inversion axis as in the four point groupsm, 3m1, 31m, \overline 6, the nonpolar direction cannot be used as the appropriate zone-axis orientation for polarity determination because the Bijvoet pairs of reflections are not arranged symmetrically in the CBED pattern. The validity of the CBED method is confirmed both by experiment and by calculation of CBED patterns.

Application of convergent beam electron microscopy in materials science

1978 ◽  
Vol 36 (1) ◽  
pp. 620-621
Author(s):  
J.W. Steeds ◽  
K. K. Fung
Keyword(s):  
Electron Microscopy ◽  
Materials Science ◽  
Zone Axis ◽  
Simple Relationship ◽  
Beam Electron ◽  
Small Probe ◽  
Yield Information ◽  
Semiconductor Contacts ◽  
Chalcogenide Layer ◽  
Convergent Beam

IntroductionWe have used a Philips EM400 electron microscope with a STEM pole- piece to carry out convergent beam electron microscopy on a wide variety of materials, including precipitates in stainless steels, metal/semiconductor contacts, metal oxide catalysts, environmental fibres, metastable phases in evaporated films, and transition metal chalcogenide layer compounds. Two features of this microscope make it particularly suitable for convergent beam work. These are its low hydrocarbon partial pressure which greatly reduces the carbon contamination of the specimen when working with a small probe (̴ 300 Ådiameter) and the very wide angular field of view in the diffraction plane (̴ 16°).Two-dimensional diffraction may be used to yield information about the projected crystal potential. In certain cases a simple relationship has been established between the form of zone axis patterns and the nature of the projected potential, Oneway of using this information is by making measurements of zone axis critical voltages and we have recently extended our measurements to a number of zone axis patterns with 6 mm symmetry having different sorts of projected potential.

Diffraction Patterns Obtained by Scanning Electron Microscope

1972 ◽  
Vol 27 (3) ◽  
pp. 441-444d ◽  
Author(s):  
F Fujimoto ◽  
K Komaki ◽  
S Takagi ◽  
H Koike
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Incident Beam ◽  
Reciprocal Theorem ◽  
Diffraction Patterns ◽  
The Reciprocal Theorem ◽  
Convergent Beam ◽  
Beam Technique ◽  
Transmission Scanning Electron Microscopy ◽  
Scanning Electron

AbstractKossel-Möllenstedt and Kikuchi patterns are obtained by transmission scanning electron microscopy and compared with those obtained by the convergent beam technique from the same portion of the specimen. The identity of corresponding patterns obtained by both techniques shows the validity of the reciprocal theorem in electron diffraction for both elastic and inelastic scattering. The variations of Kossel-Möllenstedt patterns with the conditions of the incident beam and the position of the detector are also shown.

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