Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

Determination of hydrogen ordering within the β-RH2+xphase (R= Ho, Y) using electron diffraction techniques

2000 ◽  
Vol 33 (5) ◽  
pp. 1246-1252 ◽  
Author(s):  
Elizabeth J. Grier ◽  
Amanda K. Petford-Long ◽  
Roger C. C. Ward
Keyword(s):  
Electron Diffraction ◽  
Neutron Scattering ◽  
Diffraction Pattern ◽  
Computer Simulations ◽  
Fluorite Structure ◽  
Long Range Order ◽  
Hydrogen Atoms ◽  
Ordered Structures ◽  
Diffraction Patterns

Computer simulations of the electron diffraction patterns along the [\bar{1}10] zone axes of four ordered structures within the β-RH2+xphase, withR= Ho or Y, and 0 ≤x≤ 0.25, have been performed to establish whether or not the hydrogen ordering could be detected using electron diffraction techniques. Ordered structures within otherRH2+x(R= Ce, Tb) systems have been characterized with neutron scattering experiments; however, for HoH(D)2+x, neutron scattering failed to characterize the superstructure, possibly because of the lowxconcentration or lack of long-range order within the crystal. This paper aims to show that electron diffraction could overcome both of these problems. The structures considered were the stoichiometric face-centred cubic (f.c.c.) fluorite structure (x= 0), theD1 structure (x= 0.125), theD1astructure (x= 0.2) and theD022structure (x= 0.25). In the stoichiometric structure, with all hydrogen atoms located on the tetrahedral (t) sites, only the diffraction pattern from the f.c.c. metal lattice was seen; however, for the superstoichiometric structures, with the excess hydrogen atoms ordered on the octahedral (o) sites, extra reflections were visible. All the superstoichiometric structures showed extra reflections at the (001)f.c.c.and (110)f.c.c.type positions, with structureD1 also showing extra peaks at (½ ½ ½)f.c.c.. These reflections are not seen in the simulations at similar hydrogen concentrations with the hydrogen atoms randomly occupying theovacancies.

Electron Diffraction Study of α-AlMnSi Crystals Along Non-Crystallographic Zone Axes

1998 ◽  
Vol 12 (22) ◽  
pp. 2279-2303 ◽  
Author(s):  
G. L. Song ◽  
L. A. Bursill
Keyword(s):  
Electron Diffraction ◽  
Significant Proportion ◽  
Group Symmetry ◽  
Structural Basis ◽  
Quasicrystalline Phase ◽  
Thickness Variation ◽  
Crystal Thickness ◽  
Space Group Symmetry ◽  
Space Group ◽  
Diffraction Patterns

The structure of crystalline α-AlMnSi is examined by electron diffraction. Six distinct zone axes are examined, including both normal crystallographic and non-crystallographic zone axes, allowing the space group symmetry of α-AlMnSi to be studied. A method for indexing the non-crystallographic zone axis diffraction patterns, which involve reflections from several nearby crystallographic zone axes, is described and applied to electron diffraction patterns of the quasi-5-fold, 3-fold and 2-fold axes of the icosahedral building units of cubic α-AlMnSi. These are compared with electron diffraction patterns from the corresponding 5-fold, 3-fold and 2-fold axes of the quasicrystalline phase i-AlMnSi, from which we may make some conclusions concerning the occupancies of the icosahedral units in i-AlMnSi. Electron diffraction patterns characteristic of [Formula: see text] were obtained for thicker specimens. However, for thin specimens, as used for HRTEM imaging, the electron diffraction patterns were characteristic of [Formula: see text] space group symmetry. This unusual behaviour arises because the structural basis for the [Formula: see text] to [Formula: see text] phase transition is a weak effect, involving changes in occupancy of the icosahedral structural elements located at the corners (double-MacKay icosahedra) and body-centers (MacKay icosahedra) of the cubic unit cell. The effects of changing the occupancies of the outer shells of the MI and DMI structural units on the diffraction intensities of the weak reflections were examined. Thus, calculation of the dynamical diffraction amplitudes shows that in fact the weak reflections characteristic of [Formula: see text] only develop sufficient intensity if two conditions are satisfied: namely (1) the crystal thickness exceeds approx. 50 nm and (2) if a significant proportion of [Formula: see text] occupancies are included in the structural model. By fitting the observed thickness variation of the diffraction intensities we propose a new set of occupancies for α-AlMnSi, which is consistent with the electron, X-ray and neutron diffraction data.

[001] imaging of rutile: A problem in high-resolution microscopy

1983 ◽  
Vol 41 ◽  
pp. 292-293
Author(s):  
Peter G. Self ◽  
Peter R. Buseck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Computer Simulations ◽  
Zone Axis ◽  
Severe Problem ◽  
Diffraction Patterns ◽  
High Resolution Microscopy

HRTEM images of the [001] zone of rutile (fig. 1) show 0.32 nm fringes near the edge of the crystal, but these rapidly change to 0.46 nm in the thicker parts of the crystal. This change in spacing is only possible if the intensities in the dynamically forbidden {100} reflections become comparable to the intensities of the {110} reflections. The {100} reflections are dynamically forbidden because the structure has 2-fold screw axes parallel to a and b and n-glides perpendicular to a and b. The presence of 0.46 nm rather than 0.32 nm fringe spacings in images of the thicker crystal regions presents a severe problem in matching the images to computer simulations. Fig. 2 shows [001] zone axis images for thin and thick crystals. As expected from symmetry, the computed images show only 0.32 nm spacings. In an attempt to explain the mismatch between computed and experimental images several effects not normally included in image calculations, and which could cause a change in the symmetry of electron diffraction patterns, were investigated, all without success.

Observation of Dynamic Extinction Lines in the (420) Diffraction Disks of the MgAl2O4 Spinel CBED Pattern

1990 ◽  
Vol 48 (2) ◽  
pp. 506-507
Author(s):  
Dangrong R. Liu
Keyword(s):  
Electron Diffraction ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
Beam Electron ◽  
Space Group ◽  
Mgal2o4 Spinel ◽  
Principal Axes ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Dynamic Scattering

Many people have observed dynamic extinction lines in the {200} diffraction disks of the <100> zone axis CBED (convergent beam electron diffraction) patterns of the MgAl2O4 spinel. These dark lines are manifestation of the space group of the material and can easily be explained with the Gjønnes-Moodie theory. However, in addition to the extinction lines in the {200} disks, We have also been able to observe dynamic extinction lines present in the {420} diffraction disks in the same CBED pattern.The CBED work in this work was carried out with a JEOL-2000FX microscope operated at 100.15 kV. One <100> zone axis CBED pattern is shown in Fig. 1. The dark lines are clearly shown in the {420} disks running through the two perpendicular non-principal axes, in exactly same way as the dark lines in {200} disks.One can easily explain the dynamic extinction lines in the {200} disks with the Gjønnes-Moodie theory by drawing dynamic scattering pairs oG-Ga and oH-Ha, oK-Ka and oL-La etc. in the diagram (Fig. 2).

Theory and practice of energy-filtered electron diffraction using the HB5 STEM

1992 ◽  
Vol 50 (1) ◽  
pp. 350-351
Author(s):  
L.C. Qin ◽  
A.J. Garratt-Reed ◽  
L.W. Hobbs
Keyword(s):  
Electron Diffraction ◽  
Amorphous Materials ◽  
Distribution Functions ◽  
Theory And Practice ◽  
Background Intensity ◽  
Intensity Data ◽  
Electron Diffraction Technique ◽  
Aperiodic Structure ◽  
Fast Electron Beam ◽  
Diffraction Patterns

Electron diffraction patterns obtained in TEM have long been an important part of microstructural characterizations. Certain materials, such as crystalline silicas, are amorphized in the fast electron beam of the TEM, and their aperiodic (metamict) structure is of interest. For amorphous materials, both elastically and inelastically scattered electrons contribute to the diffuse diffraction pattern. Analysis of aperiodic structure, however, requires intensity data from only elastically scattered electrons, and it is therefore it is necessary to obtain energy-filtered electron diffraction patterns. With the energy-filtered electron diffraction technique, the background intensity that is mainly due to inelastically scattered electrons is removed. This makes possible the derivation of radial distribution functions (RDFs) from collected electron diffraction intensity data for uniform aperiodic structures.

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