Burgers vector analyses

The main reason for requiring rapid acquisition of different images is for detailed strain analysis. We have seen in Chapter 8 that the Burgers vector of dislocations can be found by noting that there is zero contrast for a screw... 

Ashby and Brown (1963b) extended the analysis to cover the type of strain field found around platelike precipitates whose mismatch with the surrounding crystal is appreciable only in a direction normal to the plate. The analysis is also applicable to the strain normal to the plane of a prismatic dislocation loop of Burgers vector b. When the plane of the loop or precipitate is more or less normal to the foil, the images are similar to that... 

For many purposes, we will find that antiplane shear problems in which there is only one nonzero component of the displacement field are the most mathematically transparent. In the context of dislocations, this leads us to first undertake an analysis of the straight screw dislocation in which the slip direction is parallel to the dislocation line itself. In particular, we consider a dislocation along the X3-direction (i.e. = (001)) characterized by a displacement field Usixi, X2). The Burgers vector is of the form b = (0, 0, b). Our present aim is to deduce the equilibrium fields associated with such a dislocation which we seek by recourse to the Navier equations. For the situation of interest here, the Navier equations given in eqn (2.55) simplify to the Laplace equation (V ms = 0) in the unknown three-component of displacement. Our statement of equilibrium is supplemented by the boundary condition that for xi > 0, the jump in the displacement field be equal to the Burgers vector (i.e. Usixi, O" ") — M3(xi, 0 ) = b). Our notation usixi, 0+) means that the field M3 is to be evaluated just above the slip plane (i.e. X2 = e). 

Molecule Crystal lattice Homogeneous surface Lattice defect Irregular structure Rotation/reflection Spatial translation Surface translation Homotopy Dilation (self-similarity) Molecular point group Space group 2-dimensional unit cell Burgers vector Fractal dimension Spectroscopy X-ray analysis Adsorption studies Crysttd properties Scaling laws... 

The dislocation substructures were obtained by TEM. Standard g.b analysis was carried out to determine the Burgers vectors of isolated dislocations. The 3D nature of the dislocation arrangement was determined using stereo pairs obtained... 

A very plausible alignment mechanism involves movement of defects. Here, forces on defect structures in an electric field are described. The actual material contains a large number of defects in many configurations, so a full analysis would be prohibitively complex. However, it is instructive to consider instead some simple ca.ses a general wall defect, a +1/2, -1/2 pair of parallel disclination lines, and two compound edge dislocations with opposing Burgers vector. 

Diffraction contrast imaging is also widely used in analysis other defects such as dislocation loops, partial dislocations, strain field introduced by small precipitates, etc. In Eig. 5.4c, the Burgers vector for the dislocation loop always points to the center, so the areas perpendicular to the diffraction g show no contrast since g-b = 0. 

First characterizations of the Burgers vector of metadislocations were carried out by means of Bragg-contrast analysis [39]. Their Burgers vector direction was determined as parallel to the [001] direction. Since the line direction is parallel to the [010] direction, metadislocations are pure edge dislocations. 

Deformation, slip, slip system analysis. Burgers vector 176... 

Analysis of TEM images of dislocations, together with structural considerations, indicate that the Burgers vectors for r-, f-, and c-slip are, respectively, (2 0 21),... 

The interfaces between finescale exsolution lamellae of ilmenite in hematite have been investigated and most were shown to be coherent and dislocation free [251]. Due to differences in lattice parameters, dislocation arrays decorate the interface [Fig. 8(b)]. Contrast analysis revealed a hexagonal grid of rhombohedral dislocations [250] rather than dislocations with basal Burgers vectors [252]. The ordering phase transition in ferrian ilmenite from the high-temperature R3c disordered structure to a R3 lower-temperature ordered structure results in the creation of twin domains [253,254]. No dislocations were involved. 

Burgers vector and dislocation line analysis of naturally deformed aug/tc-enstatite crystals indicate activation of many slip systems such as (100)[001], 110 1<110>, 110 1<112>, (100)[010], (010)[100], (010)<101>, and 110 < 111 >, the first two being the most active [311,312]. The study demonstrates that most dislocations are dissociated and stacking faults are produced that can be interpreted based on the complex structure of these chain silicates. In naturally deformed augite from a pyroxenite with lamellar exsolution [lOl] dislocations in (010) combine single to double chains, yielding so-called chain multiplicity faults [316]. 

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