On Diffraction Patterns of Structures Containing Regular Crystallographic Shear Planes

1992 ◽  
Vol 45 (9) ◽  
pp. 1397 ◽  
Author(s):  
G Harburn ◽  
BH Parry ◽  
RJD Tilley ◽  
RP Williams
Keyword(s):  
Electron Diffraction ◽  
Fourier Analysis ◽  
Tungsten Trioxide ◽  
Two Dimensional ◽  
Analysis Study ◽  
Shear Structures ◽  
Crystallographic Shear ◽  
Diffraction Patterns ◽  
Special Case ◽  
Shear Planes

The appearances of the diffraction patterns expected for the phases derived from tungsten trioxide by crystallographic shear have been deduced by Fourier analysis. Study of electron- diffraction patterns and optical analogues confirms the predictions of the theory. The results have been generalized to a two-dimensional continuum of 'infinitely adaptive structures' by use of the shift lattice, of which the crystallographic shear structures are a special case.

Mechanism of the morphotropic transformation between the rutile and corundum structural types

2003 ◽  
Vol 59 (4) ◽  
pp. 456-462 ◽  
Author(s):  
H. Katzke ◽  
R. Schlögl
Keyword(s):  
Simple Model ◽  
Phase Segregation ◽  
Transformation Process ◽  
Transformation Mechanism ◽  
One Dimensional ◽  
X Ray ◽  
Structural Types ◽  
Crystallographic Shear ◽  
Diffraction Patterns ◽  
Shear Planes

The rutile/corundum structural transformation which is based on crystallographic shear is discussed in terms of a one-dimensional disorder model. The transformation process is described by a simple model based on the structural relationship between the rutile-type and corundum-type phases. The model is able to handle randomly spaced crystallographic shear planes, the so-called Wadsley defects, as well as clustered CS planes. Calculations hsow that simply modifying the probability parameters of the model can lead to phase segregation. X-ray powder diffraction patterns are calculated for the proposed transformation mechanism as a function of the stoichiometry x in MO2−x in order to show the influence of such defects on the intensities and linewidths of the Bragg reflections.

The elastic strain energy of crystallographic shear planes in reduced tungsten trioxide

1977 ◽  
Vol 286 (1332) ◽  
pp. 55-85 ◽  
Keyword(s):  
Tungsten Trioxide ◽  
Elastic Strain ◽  
Strain Energy ◽  
Unit Volume ◽  
Elastic Strain Energy ◽  
Nucleation And Growth ◽  
Significant Part ◽  
Ordered Arrays ◽  
Crystallographic Shear ◽  
Shear Planes

Calculations of the elastic strain energy due to crystallographic shear (c.s.) planes lying upon {102}, {103} and {001} planes in reduced tungsten trioxide crystals have been made. The cases analysed in detail are for both isolated c.s. planes and for pairs of c.s. planes. These results are used to determine the elastic strain energy per unit volume for crystals containing ordered arrays of c.s. planes. It was found that the magnitude of the elastic strain energy was in the sequence {001} < {102} < {103} and that at relatively small inter-c.s. spacings the curves of elastic strain energy against c.s. plane separation take the form of a series of peaks and valleys. These results are compared with experimental observations of c.s. plane spacings in substantially reduced crystals containing quasi-ordered arrays of c.s. planes and with observations of c.s. plane nucleation and growth in both slightly and more appreciably reduced crystals. It was found that the elastic strain energy plays a significant part in controlling the microstructure of c.s. plane arrays in such cases.

Accurate lattice-parameter determination from electron diffraction tomography data using two-dimensional diffraction vectors

2018 ◽  
Vol 51 (4) ◽  
pp. 982-989 ◽  
Author(s):  
Jonas Ångström ◽  
Hong Chen ◽  
Wei Wan
Keyword(s):  
Electron Diffraction ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Lattice Parameter ◽  
Parameter Determination ◽  
Data Sets ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
Lower Accuracy ◽  
Diffraction Patterns

Electron diffraction tomography (EDT) has emerged as a successful tool for ab initio atomic structure determination of nanometre-sized crystals. However, lattice parameters obtained from EDT data are often of lower accuracy than those from powder X-ray data, owing to experimental errors and data-processing methods. This work describes a lattice-parameter refinement method for EDT data using two-dimensional diffraction vectors and shows that the accuracy of lattice-parameter determination can be improved significantly. It is also shown that the method is tolerant to sample displacement during data collection and to geometric distortions in the electron diffraction patterns due to lens imperfections. For the data sets tested, the method reduces the 95% confidence interval of the worst errors in angles from ±1.98 to ±0.82° and the worst relative errors of the unit-cell lengths from ±1.8% to ±1.3%, compared with the conventional method using clustering of three-dimensional diffraction vectors. The improvement is attributed to the fact that the new method makes use of the positions of two-dimensional diffraction spots, which can be determined with high accuracy, and disregards the position of the central beam, the orientation of the rotation axis and the angles of the diffraction frames, whose errors all contribute to the errors for lattice-parameter determination using the three-dimensional method.

The Interpretation of Electron Diffraction Patterns of Faulted Structures

1974 ◽  
Vol 32 ◽  
pp. 342-343
Author(s):  
J. M. Cowley
Keyword(s):  
Crystal Structure ◽  
Electron Beam ◽  
Tungsten Trioxide ◽  
Titanium Oxides ◽  
Resolution Electron ◽  
Niobium Titanium ◽  
Diffraction Patterns ◽  
Block Structures ◽  
Shear Planes ◽  
High Resolution Electron Micrographs

In many high resolution electron micrographs of oxides, minerals and other materials, planar faults, often nearly parallel to the electron beam, are visible. When the crystal structure is clearly resolved the nature of the faults may be evident from the images, as in the case of the faults in the periodicities of the block structures of niobium and niobium-titanium oxides (Iijima, 1973; Iijima, Kimura and Goto, 1973), the shear planes (Wadsley defects) occuring in reduced tungsten trioxide (Iijima, in preparation) and the micro-twins occuring in the mineral enstatite (Iijima and Buseck, in preparation).

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