Identification of the kinematical forbidden reflections from precession electron diffraction

2009 ◽  
Vol 1184 ◽  
Author(s):  
Jean-Paul Morniroli ◽  
Gang Ji
Keyword(s):  
Electron Diffraction ◽  
Dark Field ◽  
Double Diffraction ◽  
Precession Angle ◽  
Space Groups ◽  
Ewald Sphere ◽  
Precession Electron Diffraction

AbstractThe visibility of the kinematical forbidden reflections due to glide planes, screw axes and Wyckoff positions is considered both on experimental and theoretical electron precession patterns as a function of the precession angle. The forbidden reflections due to glide planes and screw axes become very weak and disappear at large precession angle so that they can be distinguished from the allowed reflections and used to deduce the space groups. Contrarily, those due to Wyckoff positions remain visible and strong provided they are located on a major systematic row. This difference of behavior between the forbidden reflections is confirmed by observation of the corresponding dark-field LACBED patterns and is interpreted using the Ewald sphere and the Laue circles from the availability of double diffraction paths. This study also proves that dynamical interactions remain strong along the main systematic rows present on precession patterns.

scholarly journals A complicated quasicrystal approximant ∊16 predicted by the strong-reflections approach

2010 ◽  
Vol 66 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Mingrun Li ◽  
Junliang Sun ◽  
Peter Oleynikov ◽  
Sven Hovmöller ◽  
Xiaodong Zou ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Unit Cell ◽  
Space Groups ◽  
Inverse Fourier Transformation ◽  
Transmission Electron ◽  
Structure Factors ◽  
Precession Electron Diffraction ◽  
Density Map ◽  
Electron Density Map ◽  
Good Agreement

The structure of a complicated quasicrystal approximant ∊16 was predicted from a known and related quasicrystal approximant ∊6 by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ∊16 were deduced from those of the known ∊6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ∊16. An electron-density map of ∊16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊6, the predicted structure of ∊16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊16 is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ∊16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.

scholarly journals Identifying almost identical phases by 3D electron diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C373-C373
Author(s):  
Stéphanie Kodjikian ◽  
Holger Klein ◽  
Christophe Lepoittevin ◽  
Céline Darie ◽  
Pierre Bordet ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Structural Information ◽  
Quantum Spin ◽  
Parameter Determination ◽  
Space Groups ◽  
Cell Parameters ◽  
3 Dimensional ◽  
Precession Electron Diffraction ◽  
The Difference ◽  
Two Phases

Magnetically frustrated materials have been the subject of many studies over the last decades. In search for a 3-dimensional quantum spin liquid, where quantum-mechanical fluctuations prevent magnetic order, different phases of stoichiometry Ba3NiSb2O9 have recently [1] been synthesized some of them at high pressure. Two of these phases are hexagonal. The hexagonal phases (space groups P63/mmc and P63mc, respectively) have different structures but cell parameters that differ by less than 1%. Similar phases have been obtained with Cu [2] or Co [3]. These phases are well distinguished by powder X-ray diffraction when they appear in sufficient quantity in a newly synthesized powder. When these phases are present only in minor quantities, which is a common situation when synthesizing new materials, only transmission electron microscopy can give structural information on a very local scale. However, the accuracy of unit cell parameter determination by electron diffraction (usually 1% or worse) and the identical extinction conditions for the 2 space groups don't permit to distinguish between the two phases. Convergent beam electron diffraction could show the difference between the centrosymmetric and non-centrosymmetric space groups provided a suitably oriented particle can be found. In this work we propose a different method of distinguishing structures in such complicated cases by actually solving the structure. Sufficient in-zone axis precession electron diffraction and/or electron diffraction tomography data can be obtained from any crystal regardless of its orientation. In the subsequent structure solution we have tested both space groups. The quality (or absence thereof) of the structure solutions obtained clearly makes it possible to distinguish between the two hexagonal structures.

Struktur und thermisches Verhalten von Wachstumszwillingen in dünnen kubisch flächenzentrierten Metallschichten

1965 ◽  
Vol 20 (9) ◽  
pp. 1201-1207 ◽  
Author(s):  
H. Schlötterer
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Hexagonal Phase ◽  
Stacking Faults ◽  
Dark Field Image ◽  
Dark Field ◽  
Periodic Lattice ◽  
Double Diffraction ◽  
Polycrystalline Films ◽  
Matrix Orientation

Single crystal films prepared by evaporation of silver, gold, copper, and nickel on heated cleaved rocksalt crystals and polycrystalline films of silver, gold, copper, platinum, aluminum, and nickel have been studied by transmission electron microscopy and electron diffraction. By means of electron microscope dark-field image and selected area diffraction technique the existence of small growth twins in the films is shown. Extra spots observed in the electron diffraction diagram can be explained partly as spots of the four twin orientations, partly as arising from double diffraction of the (100) matrix orientation and of a twin orientation. In the case of polycrystalline films the double diffraction mechanism results in additional diffraction rings seeming not to belong to the normal face-centred cubic lattice. The assumption of an hexagonal phase or of stacking faults or of periodic lattice defects cannot explain all the extra spots and additional rings.The changing diffraction contrast of thick and thin microtwins obviously depends on the different reflection conditions in the electron microscope. It is shown that it is very complicated to distinguish stacking faults from microtwins, but some criteria of distinction are given.By means of a heating stage the single crystals have been heated in the electron microscope up to more than 1000 °C. The thermal behaviour of the twins has been studied in detail. It can be observed that up to 95% of the twins become invisible by transformation from the twin orientation to the (100) matrix orientation. It is concluded from the experiments that the transformation nucleates at the top or bottom of the thin films. Nevertheless more than 1013 twins and stacking faults per cm3 remain unchanged inspite of heating to temperatures near the melting point of the bulk metal.

The Symmetry of Ordered Cubic γ-Fe2O3 Investigated by TEM

2006 ◽  
Vol 61 (6) ◽  
pp. 665-671 ◽  
Author(s):  
Klemens Kelm ◽  
Werner Mader
Keyword(s):  
Electron Diffraction ◽  
Spinel Structure ◽  
Intermediate Phase ◽  
Dark Field ◽  
Continuous Group ◽  
Cubic Phase ◽  
Bright Field ◽  
Space Groups ◽  
Octahedral Sites ◽  
Diffraction Patterns

Well-crystallized particles of cubic and tetragonal γ -Fe2O3 embedded in a Pd matrix were produced besides other oxides by internal oxidation of a Pd-Fe alloy in air. Particles of tetragonal γ -Fe2O3 consist of orientation domains with the c axes normal to each other. Particles of the ordered cubic γ -Fe2O3 appear single crystalline in bright field and in dark field images with reflections of the basic spinel structure. In dark field images enantiomorphous domains were observed using reflections of the ordered phase. From the analysis of electron diffraction patterns in the principal zone axes the description of ordered cubic γ -Fe2O3 in the enantiomorphous space groups P4132/P4332 follows without further presumptions. In the sequence from space group Fd3m of disordered cubic γ -Fe2O3 via P4132/P4332 of the ordered cubic phase to the pair P41212/P43212 of tetragonal γ -Fe2O3 a continuous group-subgroup relation can be derived. This relation shows that ordered cubic γ -Fe2O3 is an intermediate phase upon ordering of vacant octahedral sites towards tetragonal γ -Fe2O3

scholarly journals Hafnium-Silicon Precipitate Structure Determination in a New Heat-Resistant Ferritic Alloy by Precession Electron Diffraction Techniques

2013 ◽  
Vol 20 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Désirée Viladot ◽  
Joaquim Portillo ◽  
Mauro Gemí ◽  
Stavros Nicolopoulos ◽  
Núria Llorca-Isern
Keyword(s):  
Electron Diffraction ◽  
Structure Determination ◽  
Three Dimensional ◽  
Direct Methods ◽  
Extinction Condition ◽  
Orbital Theory ◽  
Orthorhombic Unit Cell ◽  
Precession Angle ◽  
Ferritic Alloy ◽  
Precession Electron Diffraction

AbstractThe structure determination of an HfSi4 precipitate has been carried out by a combination of two precession electron diffraction techniques: high precession angle, 2.2°, single pattern collection at eight different zone axes and low precession angle, 0.5°, serial collection of patterns obtained by increasing tilts of 1°. A three-dimensional reconstruction of the associated reciprocal space shows an orthorhombic unit cell with parameters a = 11.4 Å, b = 11.8 Å, c = 14.6 Å, and an extinction condition of (hkl) h + k odd. The merged intensities from the high angle precession patterns have been symmetry tested for possible space groups (SG) fulfilling this condition and a best symmetrization residual found at 18% for SG 65 Cmmm. Use of the SIR2011 direct methods program allowed solving the structure with a structure residual of 18%. The precipitate objects of this study were reproducibly found in a newly implemented alloy, designed according to molecular orbital theory.

scholarly journals Precession Electron Diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C12-C12
Author(s):  
Paul Midgley
Keyword(s):  
Electron Beam ◽  
Electron Diffraction ◽  
High Energy ◽  
Specimen Thickness ◽  
Coulombic Interaction ◽  
Precession Angle ◽  
Data Set ◽  
X Ray ◽  
Starting Point ◽  
Precession Electron Diffraction

The strong Coulombic interaction between a high energy electron and a thin crystal film gives rise to electron diffraction patterns encoded with information that is remarkably sensitive to the crystal potential. That exquisite sensitivity can be advantageous, for example in the determination of local symmetry and bonding, but can also be problematic in that in general the dynamical scattering inherent in electron diffraction prohibits the use of conventional crystallographic methods to recover structure factor phase information and solve unknown structures. One way to reduce this problem is to use precession electron diffraction (PED), introduced 20 years ago [1] as the electron analogue of Buerger's X-ray technique, in which the electron beam is first rocked in a hollow cone above the sample and then de-rocked below, the net effect of which is equivalent to precessing the sample about a stationary electron beam. PED is now used almost routinely as a starting point to solve crystal structures that cannot be solved for a variety of reasons using x-ray or neutron methods. In this keynote lecture we explore why the PED technique has been successful for structure determination, focussing on the PED geometry, the variation of intensities with precession angle and specimen thickness, and how this `mimics' kinematic behaviour, and the use of unconventional structure solution and refinement approaches [2]. New acquisition geometries will be discussed that rely on tilt series of PED patterns to yield a more complete 3D data set. The lecture will focus on how PED has been used also as a method for nanoscale orientation mapping [3], providing more information than conventional electron diffraction and a robust method with which to determine local crystallographic orientation. By scanning the beam, accurate orientation images can be derived from series of PED patterns and, by combining with tomographic methods, sub-volume orientation information is also available.

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