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.

Structure model for the τ(μ) phase in Al–Cr–Si alloys deduced from the λ phase by the strong-reflections approach

2006 ◽  
Vol 62 (1) ◽  
pp. 16-25 ◽  
Author(s):  
H. Zhang ◽  
Z.B. He ◽  
P. Oleynikov ◽  
X. D. Zou ◽  
S. Hovmöller ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Unit Cell ◽  
Structure Model ◽  
Common Features ◽  
Structure Factors ◽  
Icosahedral Clusters ◽  
Diffraction Patterns ◽  
Good Agreement

There are very obvious common features in the electron diffraction patterns of the λ and τ(μ) phases in the Al–Cr–Si system. The positions of the strong reflections and their intensity distributions are similar for the two structures. The relation of the reciprocal lattices of the λ and τ(μ) phases is studied. By applying the strong-reflections approach, the structure factors of τ(μ) are deduced from the corresponding structure factors of the known λ phase. Rules for selecting reflections for the strong-reflections approach are described. Similar to that of λ, the structure of τ(μ) contains six layers stacked along the c axis in each unit cell. There are 752 atoms in each unit cell, 53 of them are unique. The corresponding composition of the τ(μ) model is Al3.82 − x CrSi x . Simulated electron diffraction patterns from the structure model are in good agreement with the experimental ones. The arrangement of interpenetrated icosahedral clusters in the τ(μ) phase is discussed.

Electron-density maps

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Electron Density ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Unit Cell ◽  
Density Maps ◽  
Wave Cycle ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an electron-density map. The electron-density map is the Fourier transform of the structure factors (with their phases). If the resolution and phases are good enough, the electron-density map may be interpreted in terms of atomic positions. In practice, it may be necessary to alternate between study of the electron-density map and the procedures mentioned in Chapter 10, which may allow improvements to be made to it. Electron-density maps contain a great deal of information, which is not easy to grasp. Considerable technical effort has gone into methods of presenting the electron density to the observer in the clearest possible way. The Fourier transform is calculated as a set of electron-density values at every point of a three-dimensional grid labelled with fractional coordinates x, y, z. These coordinates each go from 0 to 1 in order to cover the whole unit cell. To present the electron density as a smoothly varying function, values have to be calculated at intervals that are much smaller than the nominal resolution of the map. Say, for example, there is a protein unit cell 50 Å on a side, at a routine resolution of 2Å. This means that some of the waves included in the calculation of the electron density go through a complete wave cycle in 2 Å. As a rule of thumb, to represent this properly, the spacing of the points on the grid for calculation must be less than one-third of the resolution. In our example, this spacing might be 0.6 Å. To cover the whole of the 50 Å unit cell, about 80 values of x are needed; and the same number of values of y and z. The electron density therefore needs to be calculated on an array of 80×80×80 points, which is over half a million values. Although our world is three-dimensional, our retinas are two-dimensional, and we are good at looking at pictures and diagrams in two dimensions.

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.

scholarly journals Precession Electron Diffraction Assisted Orientation Mapping in the Transmission Electron Microscope

2010 ◽  
Vol 644 ◽  
pp. 1-7 ◽  
Author(s):  
Joaquim Portillo ◽  
Edgar F. Rauch ◽  
Stavros Nicolopoulos ◽  
Mauro Gemmi ◽  
Daniel Bultreys
Keyword(s):  
Electron Diffraction ◽  
X Ray Diffraction ◽  
Promising Technique ◽  
Electron Backscattered Diffraction ◽  
Transmission Electron ◽  
Orientation Mapping ◽  
Precession Electron Diffraction ◽  
Electron Microscopes ◽  
Ebsd Technique ◽  
Scanning Electron Microscopes

Precession electron diffraction (PED) is a new promising technique for electron diffraction pattern collection under quasi-kinematical conditions (as in X-ray Diffraction), which enables “ab-initio” solving of crystalline structures of nanocrystals. The PED technique may be used in TEM instruments of voltages 100 to 400 kV and is an effective upgrade of the TEM instrument to a true electron diffractometer. The PED technique, when combined with fast electron diffraction acquisition and pattern matching software techniques, may also be used for the high magnification ultra-fast mapping of variable crystal orientations and phases, similarly to what is achieved with the Electron Backscattered Diffraction (EBSD) technique in Scanning Electron Microscopes (SEM) at lower magnifications and longer acquisition times.

scholarly journals Huge unit cell Sr64.1Bi27.7Ni8.2Oxsolved by precession electron diffraction

2011 ◽  
Vol 67 (a1) ◽  
pp. C694-C694
Author(s):  
H. Klein ◽  
M. Bacia ◽  
A. Rageau ◽  
P. Strobel ◽  
M. Gemmi
Keyword(s):  
Electron Diffraction ◽  
Unit Cell ◽  
Precession Electron Diffraction

Density-modification procedures: improving a calculated map before interpretation

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Electron Density ◽  
Uniform Density ◽  
Anomalous Scattering ◽  
Molecular Replacement ◽  
Small Proteins ◽  
Isomorphous Replacement ◽  
Structure Factors ◽  
Density Map ◽  
Solvent Molecules ◽  
Electron Density Map

Procedures to determine the phases of the structure factors, by isomorphous replacement, by anomalous scattering, or by molecular replacement, were described in the Chapters 7–9. Using one or more of these methods, phases are generated which allow an electron-density map to be calculated, at a resolution to which the phases are thought to be reliable. In many cases this electron density can be confidently interpreted in terms of atomic positions. But this is not always the case. Quite often, the procedures so far described offer a tantalizing puzzle map, with some features which I think I can interpret, but raising many questions. Before devoting effort to interpreting an unsatisfactory electron-density map, a number of procedures are available, which might make a striking improvement. Perhaps the most important strategy is to seek out more isomorphous and anomalous scattering derivatives. Before doing that, there are other possibilities which may improve an electron-density map without any more experimental data. These methods are known collectively as density modification. The first group of methods exploits features of the electron density which result from the packing of molecules into a crystal. Macromolecular crystals composed of rigid molecules have voids between the molecules filled with disordered solvent, often including the precipitants used in the crystallization process. These solvent regions present featureless density between the structured density of the macromolecules. A high-quality electron-density map will show these featureless regions clearly. In a map of poorer quality, the voids between molecules may be clearly defined, but far from featureless. This provides a method to improve the map. Although some solvent molecules are immobilized on the surface of the macromolecule, those further from the surface are in a disordered liquid-like state which presents a uniform density. Except in very small proteins, the majority of solvent is disordered. If such uniform solvent regions can be recognized, they allow surfaces to be defined which separate solvent regions from protein regions. Two procedures are described below. It has become almost a matter of routine to use one or both of these methods.

New Applications of Electron Diffraction in the Pharmaceutical Industry: Polymorph Determination by Using a Combination of Electron Diffraction and Synchrotron X-ray Powder Diffraction Techniques

2002 ◽  
Vol 8 (2) ◽  
pp. 134-138 ◽  
Author(s):  
Z.G. Li ◽  
R.L. Harlow ◽  
C.M. Foris ◽  
H. Li ◽  
P. Ma ◽  
...  
Keyword(s):  
Pharmaceutical Industry ◽  
Electron Diffraction ◽  
Powder Diffraction ◽  
Unit Cell ◽  
X Ray ◽  
Cell Parameters ◽  
Synchrotron Powder Diffraction ◽  
Transmission Electron ◽  
Diffraction Patterns ◽  
New Applications

Electron diffraction has been recently used in the pharmaceutical industry to study the polymorphism in crystalline drug substances. While conventional X-ray diffraction patterns could not be used to determine the cell parameters of two forms of the microcrystalline GP IIb/IIIa receptor antagonist roxifiban, a combination of electron single-crystal and synchrotron powder diffraction techniques were able to clearly distinguish the two polymorphs. The unit-cell parameters of the two polymorphs were ultimately determined using new software routines designed to take advantage of each technique's unique capabilities. The combined use of transmission electron microscopy (TEM) and synchrotron patterns appears to be a good general approach for characterizing complex (low-symmetry, large-unit-cell, micron-sized) polymorphic pharmaceutical compounds.

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.

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