scholarly journals The continuous theory of dislocations for a material containing dislocations to one Burgers vector only

2014 ◽  
pp. 27-42
Author(s):  
Hans-Dieter Alber
Keyword(s):  
Burgers Vector ◽  
Continuous Theory

Dislocations in alumina deformed by prismatic slip

1978 ◽  
Vol 36 (1) ◽  
pp. 606-607
Author(s):  
J. Cadoz ◽  
J. Castaing ◽  
J. Philibert
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Basal Slip ◽  
Prismatic Slip ◽  
Compression Tests ◽  
Thin Sections ◽  
Burgers Vector ◽  
Maximum Deformation ◽  
Transmission Electron ◽  
Mechanical Thinning

Plastic deformation of alumina has been much studied; basal slip occurs and dislocation structures have been investigated by transmission electron microscopy (T.E.M.) (1). Non basal slip has been observed (2); the prismatic glide system <1010> {1210} has been obtained by compression tests between 1400°C and 1800°C (3). Dislocations with <0110> burgers vector were identified using a 100 kV microscope(4).We describe the dislocation structures after prismatic slip, using high voltage T.E.M. which gives much information.Compression tests were performed at constant strainrate (∿10-4s-1); the maximum deformation reached was 0.03. Thin sections were cut from specimens deformed at 1450°C, either parallel to the glide plane or perpendicular to the glide direction. After mechanical thinning, foils were produced by ion bombardment. Details on experimental techniques can be obtained through reference (3).

Defects in ion implanted silicon

1978 ◽  
Vol 36 (1) ◽  
pp. 386-387
Author(s):  
J.A. Lambert ◽  
P.S. Dobson
Keyword(s):  
Defect Structure ◽  
Dislocation Loops ◽  
Frank Loop ◽  
Burgers Vector ◽  
Temperature Range ◽  
Perfect Dislocation ◽  
Contrast Analysis ◽  
Image Position ◽  
Ion Implanted

The defect structure of ion-implanted silicon, which has been annealed in the temperature range 800°C-1100°C, consists of extrinsic Frank faulted loops and perfect dislocation loops, together with‘rod like’ defects elongated along <110> directions. Various structures have been suggested for the elongated defects and it was argued that an extrinsically faulted Frank loop could undergo partial shear to yield an intrinsically faulted defect having a Burgers vector of 1/6 <411>.This defect has been observed in boron implanted silicon (1015 B+ cm-2 40KeV) and a detailed contrast analysis has confirmed the proposed structure.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

Black-white contrast of dislocation loops

1978 ◽  
Vol 36 (1) ◽  
pp. 328-329
Author(s):  
J. J. Hren ◽  
W. D. Cooper ◽  
L. J. Sykes
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Dislocation Loops ◽  
Major Premise ◽  
Burgers Vector ◽  
Transmission Electron ◽  
Primary Means ◽  
Contrast Analysis ◽  
Dot Product ◽  
Imaging Conditions

Small dislocation loops observed by transmission electron microscopy exhibit a characteristic black-white strain contrast when observed under dynamical imaging conditions. In many cases, the topography and orientation of the image may be used to determine the nature of the loop crystallography. Two distinct but somewhat overlapping procedures have been developed for the contrast analysis and identification of small dislocation loops. One group of investigators has emphasized the use of the topography of the image as the principle tool for analysis. The major premise of this method is that the characteristic details of the image topography are dependent only on the magnitude of the dot product between the loop Burgers vector and the diffracting vector. This technique is commonly referred to as the (g•b) analysis. A second group of investigators has emphasized the use of the orientation of the direction of black-white contrast as the primary means of analysis.

Direct structure images of 30° partial dislocation cores in silicon

1987 ◽  
Vol 45 ◽  
pp. 242-243
Author(s):  
J. C. Barry ◽  
H. Alexander
Keyword(s):  
Dislocation Core ◽  
Preparation Technique ◽  
Burgers Vector ◽  
Vector Type ◽  
Sample Preparation Technique ◽  
Lattice Images ◽  
Dislocation Core Structure ◽  
Type Lattice ◽  
Direct Inspection

Dislocations in silicon produced by plastic deformation are generally dissociated into partials. 60° dislocations (Burgers vector type 1/2[101]) are dissociated into 30°(Burgers vector type 1/6[211]) and 90°(Burgers vector type 1/6[112]) dislocations. The 30° partials may be either of “glide” or “shuffle” type. Lattice images of the 30° dislocation have been obtained with a JEM 100B, and with a JEM 200Cx. In the aforementioned experiments a reasonable but imperfect match was obtained with calculated images for the “glide” model. In the present experiment direct structure images of 30° dislocation cores have been obtained with a JEOL 4000EX. It is possible to deduce the 30° dislocation core structure by direct inspection of the images. Dislocations were produced by compression of single crystal Si (sample preparation technique described in Alexander et al.).

Quantitative structure determination of interfaces through Z-contrast imaging and electron energy loss spectroscopy

1996 ◽  
Vol 54 ◽  
pp. 104-105
Author(s):  
S. J. Pennycook ◽  
P. D. Nellist ◽  
N. D. Browning ◽  
P. A. Langjahr ◽  
M. Rühle
Keyword(s):  
Grain Boundaries ◽  
Cuprate Superconductors ◽  
Structure Refinement ◽  
3D Structure ◽  
Real Space ◽  
Contrast Imaging ◽  
Coordination Polyhedra ◽  
Burgers Vector ◽  
Z Contrast ◽  
Contrast Image

The simultaneous use of Z-contrast imaging with parallel detection EELS in the STEM provides a powerful means for determining the atomic structure of grain boundaries. The incoherent Z-contrast image of the high atomic number columns can be directly inverted to their real space arrangement, without the use of preconceived structure models. Positions and intensities may be accurately quantified through a maximum entropy analysis. Light elements that are not visible in the Z-contrast image can be studied through EELS; their coordination polyhedra determined from the spectral fine structure. It even appears feasible to contemplate 3D structure refinement through multiple scattering calculations.The power of this approach is illustrated by the recent study of a series of SrTiC>3 bicrystals, which has provided significant insight into some of the basic issues of grain boundaries in ceramics. Figure 1 shows the structural units deduced from a set of 24°, 36° and 65° symmetric boundaries, and 24° and 45° asymmetric boundaries. It can be seen that apart from unit cells and fragments from the perfect crystal, only three units are needed to construct any arbitrary tilt boundary. For symmetric boundaries, only two units are required, each having the same Burgers, vector of a<100>. Both units are pentagons, on either the Sr or Ti sublattice, and both contain two columns of the other sublattice, imaging in positions too close for the atoms in each column to be coplanar. Each column was therefore assumed to be half full, with the pair forming a single zig-zag column. For asymmetric boundaries, crystal geometry requires two types of dislocations; the additional unit was found to have a Burgers’ vector of a<110>. Such a unit is a larger source of strain, and is especially important to the transport characteristics of cuprate superconductors. These zig-zag columns avoid the problem of like-ion repulsion; they have also been seen in TiO2 and YBa2Cu3O7-x and may be a general feature of ionic materials.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

scholarly journals Dislocation Arrangement in a Thick LEO GaN Film on Sapphire

2000 ◽  
Vol 5 (S1) ◽  
pp. 97-103
Author(s):  
Kathleen A. Dunn ◽  
Susan E. Babcock ◽  
Donald S. Stone ◽  
Richard J. Matyi ◽  
Ling Zhang ◽  
...  
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Threading Dislocations ◽  
X Ray Diffraction ◽  
Burgers Vector ◽  
X Ray ◽  
The Third ◽  
Dislocation Arrangement ◽  
Image Position ◽  
Gan Film

Diffraction-contrast TEM, focused probe electron diffraction, and high-resolution X-ray diffraction were used to characterize the dislocation arrangements in a 16µm thick coalesced GaN film grown by MOVPE LEO. As is commonly observed, the threading dislocations that are duplicated from the template above the window bend toward (0001). At the coalescence plane they bend back to lie along [0001] and thread to the surface. In addition, three other sets of dislocations were observed. The first set consists of a wall of parallel dislocations lying in the coalescence plane and nearly parallel to the substrate, with Burgers vector (b) in the (0001) plane. The second set is comprised of rectangular loops with b = 1/3 [110] (perpendicular to the coalescence boundary) which originate in the coalescence boundary and extend laterally into the film on the (100). The third set of dislocations threads laterally through the film along the [100] bar axis with 1/3<110>-type Burgers vectors These sets result in a dislocation density of ∼109 cm−2. High resolution X-ray reciprocal space maps indicate wing tilt of ∼0.5º.

The effect of a footprint on perceived surface roughness

1986 ◽  
Vol 405 (1829) ◽  
pp. 303-327 ◽  
Keyword(s):  
Surface Roughness ◽  
Weighting Function ◽  
Sampling Interval ◽  
Asymptotic Convergence ◽  
Reference Surface ◽  
Two Dimensional ◽  
Random Surface ◽  
Spectral Density Functions ◽  
Continuous Theory ◽  
Discrete Theory

A two-dimensional homogeneous random surface { y ( X )} is generated from another such surface { z ( X )} by a process of smoothing represented by y ( X ) = ∫ ∞ d u w ( u – X ) z ( u ), where w ( X ) is a deterministic weighting function satisfying certain conditions. The two-dimensional autocorrelation and spectral density functions of the smoothed surface { y ( X )} are calculated in terms of the corresponding functions of the reference surface { z ( X )} and the properties of the ‘footprint’ of the contact w ( X ). When the surfaces are Gaussian, the statistical properties of their peaks and summits are given by the continuous theory of surface roughness. If only sampled values of the surface height are available, there is a corresponding discrete theory. Provided that the discrete sampling interval is small enough, profile statistics calculated by the discrete theory should approach asymptotically those calculated by the continuous theory, but it is known that such asymptotic convergence may not occur in practice. For a smoothed surface { y ( X )} which is generated from a reference surface { z ( X )} by a ‘good’ footprint of finite area, it is shown in this paper that the expected asymptotic convergence does occur always, even if the reference surface is ideally white. For a footprint to be a good footprint, w ( X ) must be continuous and smooth enough that it can be differentiated twice everywhere, including at its edges. Sample calculations for three footprints, two of which are good footprints, illustrate the theory.

Investigation of Defect Formation in 4H-SiC(0001) and (000-1) Epitaxy

2008 ◽  
Vol 600-603 ◽  
pp. 267-272 ◽  
Author(s):  
Hidekazu Tsuchida ◽  
Isaho Kamata ◽  
Masahiro Nagano
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Defect Formation ◽  
Grazing Incidence ◽  
Microscopic Structure ◽  
Threading Dislocation ◽  
Simultaneous Generation ◽  
Burgers Vector ◽  
X Ray ◽  
Transmission Electron

Defect formation in 4H-SiC(0001) and (000-1) epitaxy is investigated by grazing incidence synchrotron reflection X-ray topography and transmission electron microscopy. Frank-type faults, which are terminated by four Frank partials with a 1/4[0001] type Burgers vector with the same sign on four different basal planes, are confirmed to be formed by conversion of a 1c threading edge dislocation (TSD) in the substrate as well as simultaneous generation of a 1c TSD during epitaxy. The collation between the topography appearance and the microscopic structure and the variety of Frank faults are shown. Formation of carrot defects and threading dislocation clusters are also investigated.

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