A new method of complex structure analysis by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 628-629
Author(s):  
V.V. Rybin ◽  
E.V. Voronina
Keyword(s):  
Complex Structure ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Plastic Strains ◽  
Base Position ◽  
Structural Regularity ◽  
Orientation Matrix ◽  
Computerized Processing ◽  
Fully Automatic ◽  
Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

On ab initio indexing of Laue diffraction patterns

2021 ◽  
Vol 54 (1) ◽  
pp. 333-337
Author(s):  
Adam Morawiec
Keyword(s):  
Data Processing ◽  
Ab Initio ◽  
Reciprocal Lattice ◽  
Structural Studies ◽  
Laue Diffraction ◽  
Automatic Software ◽  
Fully Automatic ◽  
Diffraction Patterns ◽  
The Impact ◽  
Laue Method

The Laue method allows for fast pattern acquisition, but its use in structural studies is limited by the complexity of data processing. In particular, automatic ab initio indexing of Laue patterns is not trivial. This paper describes measures improving the effectiveness of indexing software. The first such measure is to adjust the positions of Laue spots on the basis of a mesh of lines fitted in a consistent way. Two other modifications enlarge the set of cells tested as potential primitive lattice cells. The last modification concerns eliminating solutions representing superlattices of the true reciprocal lattice. The impact of using these schemes on the chances of obtaining correct indexing solutions is illustrated. The described procedures can be implemented to create fully automatic software for ab initio indexing of Laue patterns.

A program for simulation of changes in diffraction patterns with crystal rotations

1990 ◽  
Vol 48 (1) ◽  
pp. 544-545
Author(s):  
F.C. Mijlhoff ◽  
H.W. Zandbergenl
Keyword(s):  
Electron Microscope ◽  
Reciprocal Lattice ◽  
Extensive Training ◽  
Diffraction Mode ◽  
Diffraction Patterns ◽  
Electron Microscopist

Orientation of crystals for HREM is done in diffraction mode. To do this efficiently thorough knowledge of the electron microscope and the reciprocal lattice of the investigated material is essential. With respect to the electron microscope extensive training is required to obtain the ability to tilt a crystal in the desired orientation. Familiarity with the reciprocal lattice of the investigated materials has to be obtained by tilt experiments on a relatively large number of crystals in the electron microscope. Even for experienced electron microscopists this can be very time consuming.In order to be able to practice tilt experiments without using the electron microscope, a program to simulate the electron microscope in diffraction mode was developed. The inexperienced electron microscopist may use the program to practice tilting of crystals. The experienced microscopist can use the program to familiarize with the reciprocal lattice of materials, which have not been studied by him before.

scholarly journals Solidified Fillings of Nanopores

2005 ◽  
Vol 876 ◽  
Author(s):  
Patrick Huber ◽  
Klaus Knorr
Keyword(s):  
Pore Diameter ◽  
Stacking Faults ◽  
Pore Geometry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Medium Length ◽  
Close Packed Structure ◽  
Packed Structure ◽  
Diffraction Patterns ◽  
Selection Of

AbstractWe present a selection of x-ray diffraction patterns of spherical (He, Ar), dumbbell- (N2, CO), and chain-like molecules (n-C9H20, n-C19H40) solidified in nanopores of silica glass (mean pore diameter 7nm). These patterns allow us to demonstrate how key principles governing crystallization have to be adapted in order to accomplish solidification in restricted geometries. 4He, Ar, and the spherical close packed phases of CO and N2 adjust to the pore geometry by introducing a sizeable amount of stacking faults. For the pore solidified, medium-length chainlike n-C19H40 we observe a close packed structure without lamellar ordering, whereas for the short-chain C9H20 the layering principle survives, albeit in a modified fashion compared to the bulk phase.

Crystallography and Diffraction

2021 ◽  
pp. 220-276
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Real Space ◽  
Crystalline Materials ◽  
Space Groups ◽  
Ewald Sphere ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Point Line ◽  
Periodic Arrangement

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

Determination of Tilt Parameters in Electron Diffraction Patterns of 3D-Microcrystals

1997 ◽  
Vol 3 (S2) ◽  
pp. 1049-1050
Author(s):  
E. Dimmeler ◽  
K.C. Holmes ◽  
R.R. Schröder
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Diffraction Spot ◽  
Spot Intensity ◽  
Crystal Face ◽  
Ewald Sphere ◽  
Exact Determination ◽  
Current Experimental Data ◽  
Diffraction Patterns

Electron crystallography of thin three-dimensional (3D) protein crystals requires very exact determination of tilt angles and spot profiles to obtain correct merging of diffraction spot amplitudes. The reciprocal lattice of 3D microcrystals consists of ellipsoidal spot profiles which are very extended in the direction normal to the crystal face (z*). To extrapolate from the intensity measured in a section to the total spot intensity, two features need to be known very exactly: 1. the orientation of reciprocal lattice relative to the Ewald sphere, 2. the 3D-shape of the spot cloud.Fig. 1 shows a tilt series of one frozen hydrated catalase crystal, in the order of recording. The third diffraction pattern gives the highest resolution because it is untilted and therefore the electrons have the shortest path length. In the current experimental data taken at 120 keV electron energy inelastic scattering within the crystal leads to a dramatic loss of elastic information in highly tilted patterns.

Protein crystals can be incommensurately modulated

2008 ◽  
Vol 41 (3) ◽  
pp. 600-605 ◽  
Author(s):  
Jeffrey J. Lovelace ◽  
Cameron R. Murphy ◽  
Lee Daniels ◽  
Kartik Narayan ◽  
Clarence E. Schutt ◽  
...  
Keyword(s):  
Diffraction Pattern ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Chemical Crosslinking ◽  
X Ray Diffraction ◽  
X Ray ◽  
Periodic State ◽  
Orientation Matrix ◽  
Aperiodic Crystals ◽  
Future Work

For a normal periodic crystal, the X-ray diffraction pattern can be described by an orientation matrix and a set of three integers that indicate the reciprocal lattice points. Those integers determine the spacing along the reciprocal lattice directions. In aperiodic crystals, the diffraction pattern is modulated and the standard periodic main reflections are surrounded by satellite reflections. The successful indexing and refinement of the main unit cell andqvector usingTWINSOLVE, developed by Svensson [(2003). Lund University, Sweden], are reported here for an incommensurately modulated, aperiodic crystal of a profilin:actin complex. The indexing showed that the modulation is along thebdirection in the crystal, which corresponds to an `actin ribbon' formed by the crystal lattice. Interestingly, the transition to the aperiodic state was shown to be reversible and the diffraction pattern returned to the periodic state during data collection. It is likely that the protein underwent a conformational change that affected the neighbouring profilin:actin molecules in such a way as to produce the observed modulation in the diffraction pattern. Future work will aim to trap the incommensurately modulated crystal state, for example using cryocooling or chemical crosslinking, thus allowing complete X-ray data to be collected.

Electron diffraction from crystal defects: Fraunhofer effects from plane faults

1966 ◽  
Vol 293 (1433) ◽  
pp. 169-180 ◽  
Keyword(s):  
Electron Diffraction ◽  
Intensity Distribution ◽  
Stacking Faults ◽  
Dynamical Theory ◽  
Crystal Defects ◽  
Similar Calculation ◽  
Selected Area Electron Diffraction ◽  
Periodic Intensity ◽  
Diffraction Patterns ◽  
Calculated Intensity

The selected area electron diffraction patterns from a crystal containing a stacking fault have been observed to exhibit a number of unusual features. In some cases a periodic intensity distribution about the Bragg spot, in other cases streaking. By applying Kirchhoff’s theory of diffraction and using the dynamical theory of electron diffraction this intensity distribution around the Bragg spots in the electron diffraction patterns from stacking faults has been calculated. The calculated intensity distributions compare favourably with experiment. A similar calculation has also been carried out to predict the intensity distribution around Bragg spots in the selected area electron diffraction patterns from a crystal containing a grain boundary.

Indexing of diffraction patterns for determination of crystal orientations

2020 ◽  
Vol 76 (6) ◽  
pp. 719-734
Author(s):  
Adam Morawiec
Keyword(s):  
Computer Vision ◽  
Computer Science ◽  
Reciprocal Lattice ◽  
General Description ◽  
Indexing Methods ◽  
Research Fields ◽  
Underlying Principle ◽  
Star Identification ◽  
Diffraction Patterns

The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

scholarly journals Identification of two allotwins of mica polytypes in reciprocal space through the minimal rhombus unit

2000 ◽  
Vol 56 (4) ◽  
pp. 639-647 ◽  
Author(s):  
Massimo Nespolo ◽  
Giovanni Ferraris ◽  
Hiroshi Takeda
Keyword(s):  
Reciprocal Lattice ◽  
Reciprocal Space ◽  
The Other ◽  
Relative Rotation ◽  
Asymmetric Unit ◽  
X Ray ◽  
Long Period ◽  
Diffraction Patterns

The X-ray investigation (precession method) of the Ruiz Peak oxybiotite, which is well known for the occurrence of a large number of polytypes and twins, revealed two complex diffraction patterns, which cannot be identified as long-period polytypes. These patterns are analysed in terms of the minimal rhombus, a geometrical asymmetric unit in reciprocal space which permits the decomposition of the composite reciprocal lattice of a twin or allotwin into the reciprocal lattices of the individuals. Both the recorded patterns correspond to a 1M–2M 1 allotwin: the relative rotation between the individuals is 120° in one case and 60° in the other. The geometrical criteria for evaluating the presence of twinning or allotwinning are analysed through these two natural examples.

Sign in / Sign up

Export Citation Format

Share Document