Contrast factors of dislocations in the hexagonal crystal system

2002 ◽  
Vol 35 (5) ◽  
pp. 556-564 ◽  
Author(s):  
I. C. Dragomir ◽  
T. Ungár
Keyword(s):  
Lattice Distortion ◽  
Dislocation Model ◽  
Size Distributions ◽  
Hexagonal Crystal ◽  
Strain Anisotropy ◽  
Dislocation Densities ◽  
Contrast Factor ◽  
Parameter Values ◽  
Hexagonal Crystals ◽  
Hexagonal Materials

Strain anisotropy can be well accounted for by the dislocation model of lattice distortion. In a texture-free powder or polycrystal, or if all possible Burgers vectors are equally populated, the dislocation contrast factors are a linear function of the fourth-order invariants of thehklindices. Using this relation the dislocation contrast factors have been evaluated numerically and compiled for a number of common hexagonal materials. A procedure is presented to match experimentally determined contrast factor parameters with the numerically obtained parameter values. The procedure can be used as a tool to extract the microstructure from strain anisotropy in terms of Burgers vector populations, dislocation densities, crystallite size and size distributions in hexagonal crystals. Its practical use is illustrated by the application to plastically deformed titanium.

scholarly journals Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals

2001 ◽  
Vol 34 (3) ◽  
pp. 298-310 ◽  
Author(s):  
T. Ungár ◽  
J. Gubicza ◽  
G. Ribárik ◽  
A. Borbély
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Fourier Coefficients ◽  
Profile Analysis ◽  
Nanocrystalline Powder ◽  
Dislocation Model ◽  
Size Distributions ◽  
Strain Anisotropy ◽  
Diffraction Profile ◽  
X Ray

Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well establishedab initiofunctions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results.

Contrast Factors and Character of Dislocations in Cubic and Hexagonal Crystals

2004 ◽  
Vol 443-444 ◽  
pp. 95-98 ◽  
Author(s):  
Iuliana C. Dragomir ◽  
András Borbély ◽  
Tamás Ungár
Keyword(s):  
Crystallite Size ◽  
The Internet ◽  
Slip Systems ◽  
Burgers Vector ◽  
Dislocation Densities ◽  
Contrast Factor ◽  
Diffraction Peaks ◽  
The Individual ◽  
Hexagonal Crystals ◽  
Active Slip

Anisotropic strain broadening of diffraction peaks can be parameterised by dislocation contrast factors. A comprehensive software has been developed and made available through the internet to determine the individual and averaged contrast factors which are also compiled for cubic and hexagonal crystals. Using the theoretical and the measured values of contrast factor the microstructure of the specimen can be characterised in terms of active slip systems, Burgers vector populations, dislocation densities and crystallite size- and size distribution.

Origin of the alternate bright/dark contrast in HREM images of hexagonal crystals, particularly 6H-SiC

1993 ◽  
Vol 51 ◽  
pp. 914-915
Author(s):  
J.S. Bow ◽  
R.W. Carpenter ◽  
M.J. Kim
Keyword(s):  
High Resolution ◽  
Incident Beam ◽  
Hexagonal Crystal ◽  
Detailed Explanation ◽  
Similar Character ◽  
High Resolution Images ◽  
The Difference ◽  
Zigzag Shape ◽  
Hexagonal Crystals ◽  
Dark Contrast

A prominent characteristic of high-resolution images of 6H-SiC viewed from [110] is a zigzag shape with a period of 6 layers as shown in Fig.1. Sometimes the contrast is same through the 6 layers of (0006) planes (Fig.1a), but in most cases it appears as in Fig.1b -- alternate bright/dark contrast among every three (0006) planes. Alternate bright/dark contrast is most common for the thicker specimens. The SAD patterns of these two types of image are almost same, and there is no indication that the difference results from compositional ordering. O’Keefe et al. concluded this type of alternate contrast was due to crystal tilt in thick parts of the specimen. However, no detailed explanation was given. Images of similar character from Ti3Al, which is also a hexagonal crystal, were reported by Howe et al. Howe attributed the bright/dark contrast among alternate (0002) Ti3Al planes to phase shifts produced by incident beam tilt.

Periodic dislocation configuration analysis by lattice distortion evaluation: micromechanical approach and X-ray diffraction line broadening

2004 ◽  
Vol 37 (2) ◽  
pp. 270-278 ◽  
Author(s):  
H. Bougrab ◽  
K. Inal ◽  
H. Sabar ◽  
M. Berveiller
Keyword(s):  
Dislocation Density ◽  
Fourier Coefficients ◽  
Lattice Distortion ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
Range Interaction ◽  
Dislocation Configuration ◽  
Micromechanical Approach ◽  
Contrast Factor ◽  
Edge Dislocations

This work concerns dislocation microstructure analysis in order to assess stored elastic energy using Fourier coefficients of diffraction lines. These coefficients are related to the lattice distortion heterogeneity evaluated using a micromechanical approach. The lattice distortion formulation is based on dislocation density and Green's function tensors. The first tensor, which is a state quantity, characterizes the distortion incompatibility, while the second one characterizes the interaction phenomena between spatial positions. The proposed approach considers a given dislocation configuration in order to calculate the exact associated fields in a deterministic way. Periodic dislocation distributions were examined and the lattice distortion was calculated as a function of the distanceHbetween two successive dislocations (dislocation density). A short-range interaction effect was found for two values:H= 50 and 100 Å. Then Fourier coefficients of {h00}, {hhh} and {hkl} diffraction lines were estimated. It was observed that the sensitivity of the Fourier coefficients toHdepends strongly on the choice of the diffraction vector. Since the dislocation configurations were crystallographically defined, the contrast factor is included directly in our approach. For the considered slip system, it is shown that the screw periodical distribution has a higher Fourier coefficient variation than the periodical edge dislocations.

Description of the Atomic Positions Around Interfacial Ledges in Terms of the Somigliana Dislocation Model

1991 ◽  
Vol 238 ◽  
Author(s):  
R. Bonnet ◽  
M. Loubradou
Keyword(s):  
Experimental Evidence ◽  
Displacement Field ◽  
Elastic Field ◽  
Point Of View ◽  
Low Energy ◽  
Elastic Displacement ◽  
Dislocation Model ◽  
Structural Units ◽  
Hexagonal Crystals ◽  
Translation State

ABSTRACTIn many materials, crystalline interfaces are facetted. The experimental evidence is that on each side of an interfacial ledge, or along the facets meeting along a common line, low energy atomic structural units are preserved which accommodate elastically angular or/and length misfit(s). Each facet can be considered as a Somigliana dislocation (SD) whose core is extended on the facet. The elastic displacement field of a SD is derived in an anisotropic continuum, for any orientation of the facet relative to a given Cartesian frame. From an atomic point of view, the translation state of the two crystals on each side of the facet is defined. The dislocation content attached to a ledge or a dihedral angle formed by two joining facets along a common side is also analyzed. The local elastic field related to these cases are derived and applications are presented for depicting the positions of the atomic columns in theoretical plots. Comparisons are made with some other theoretical works and HRTEM images. Examples illustrate the application of the Somigliana model to grain boundaries in hexagonal crystals (Mg, WC), and an interphase interface Ni3AI/Ni3Nb.

Dislocation densities and crystallite size distributions in nanocrystalline ball-milled fluorides,MF2(M= Ca, Sr, Ba and Cd), determined by X-ray diffraction line-profile analysis

2005 ◽  
Vol 38 (6) ◽  
pp. 912-926 ◽  
Author(s):  
G. Ribárik ◽  
N. Audebrand ◽  
H. Palancher ◽  
T. Ungár ◽  
D. Louër
Keyword(s):  
Crystallite Size ◽  
Line Profile ◽  
Interference Effect ◽  
Profile Analysis ◽  
Line Profile Analysis ◽  
Size Distributions ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Line Profile ◽  
Dislocation Densities

The dislocation densities and crystallite size distributions in ball-milled fluorides,MF2(M= Ca, Sr, Ba and Cd), of the fluorite structure type have been determined as a function of milling time by X-ray diffraction line-profile analysis. The treatment has been based on the concept of dislocation contrast to explain strain anisotropy by means of the modified Williamson–Hall and Warren–Averbach approaches and a whole-profile fitting method using physically based functions. In most cases, the measured and calculated patterns are in perfect agreement; however, in some specific cases, the first few measured profiles appear to be narrower than the calculated ones. This discrepancy is interpreted as the result of an interference effect similar to that described by Rafaja, Klemm, Schreiber, Knapp & Kužel [J. Appl. Cryst.(2004),37, 613–620]. By taking into account and correcting for this interference effect, the microstructure of ball-milled fluorides is determined in terms of dislocation structure and size distributions of coherent domains. A weak coalescence of the crystallites is observed at longer milling periods. An incubation period in the evolution of microstrains is in correlation with the homologous temperatures of the fluorides.

Computer programANIZCfor the calculation of diffraction contrast factors of dislocations in elastically anisotropic cubic, hexagonal and trigonal crystals

2003 ◽  
Vol 36 (1) ◽  
pp. 160-162 ◽  
Author(s):  
András Borbély ◽  
Juliana Dragomir-Cernatescu ◽  
Gábor Ribárik ◽  
Tamás Ungár
Keyword(s):  
Computer Program ◽  
Single Crystals ◽  
Programming Language ◽  
Slip Plane ◽  
Anisotropic Medium ◽  
Mechanical Equilibrium ◽  
Strain Anisotropy ◽  
Diffraction Contrast ◽  
Contrast Factor ◽  
Distortion Tensor

The computer programANIZChas been developed using the Pascal programming language for the calculation of diffraction contrast factors of dislocations in elastically anisotropic cubic, hexagonal and trigonal crystals. The contrast factor is obtained numerically by integrating the angular part of the distortion tensor in the slip plane. The distortion tensor is calculated by solving the sextic equation provided by the mechanical equilibrium of a single dislocation in an infinite anisotropic medium. The contrast factors can be used for the interpretation of strain anisotropy as obtained from peak profile measurements made on either single crystals, textured polycrystals or powders.

scholarly journals Фактор предпочтения базисной краевой дислокационной петли в цирконии. Численный анализ

2020 ◽  
Vol 62 (12) ◽  
pp. 2087
Author(s):  
А.В. Бабич ◽  
В.Ф. Клепиков ◽  
П.Н. Остапчук
Keyword(s):  
Elastic Anisotropy ◽  
Elastic Field ◽  
Elastic Interaction ◽  
Growth Theory ◽  
Hexagonal Crystal ◽  
Bias Factor ◽  
Area Of Influence ◽  
Hexagonal Crystals ◽  
Toroidal Geometry

Recent numerical calculations of the diffusion coefficients of radiation point defects in hexagonal crystals have made it clear that the main assumption of the radiation growth theory of zirconium (DAD - diffusional anisotropy difference) does not allow one to describe the radiation growth correctly. Thus, the elastic ideology (EID - elastic interaction difference), based on the concept of the flow bias factor, remains relevant. Therefore, the bias factor for the basic edge loop of zirconium in a toroidal reservoir was calculated numerically (using the finite difference method), taking into account the elastic anisotropy of the hexagonal crystal. The toroidal geometry of the reservoir makes it possible to calculate the flows for a loop of any size and without any correction of the elastic field in its area of influence. The dependences of the loop bias factor on its radius and nature are obtained for various sink densities. The essential role of the form of the boundary condition on the outer surface of the reservoir is shown. The prospects for further research in the construction of the theory of the radiation growth of zirconium based on the elastic ideology are discussed.

Microstructural Investigation of Fluoroapatite Hydrothermally Converted from Hydroxyapatite Synthesized from Crocodile Eggshell

2021 ◽  
Vol 32 ◽  
pp. 21-32
Author(s):  
Reedwan Bin Zafar Auniq ◽  
Weerapong Lerdrattranataywee ◽  
Upsorn Boonyang
Keyword(s):  
Crystal Size ◽  
Ph Value ◽  
Structure Evolution ◽  
Hexagonal Crystal ◽  
Microstructural Investigation ◽  
Unique Structure ◽  
Distinctive Morphology ◽  
Cubic Structure ◽  
Hexagonal Crystals ◽  
Dumbbell Structure

Fluoro/hydroxyapatite (FHAp) were prepared by hydrothermal at 150 °C for 24 hours with different of starting materials. The conversion of hydroxyapatite (HAp) and tricalcium phosphate to FHAp showed the rod-like shape with 200 nm. While, the morphology of FHAp from crocodile eggshell as CaCO3 form with different in phosphorus and fluoride source showed the unique structure evolution from rod-like hexagonal crystals, dumbbell to ball shape. Two distinctive morphology, first when using NaF as fluoride source with (NH4)2HPO4 precursor show the large cubic structure in high magnification it is tufted hexagonal crystal and it bundle like structure. As the pH value decreases in NH4F, it increases crystal size. For H3PO4 as phosphate precursor found that unique structure evolution from rod-like hexagonal crystals to dumbbell structure and then form the sphere assembly with a size of several micrometers.

Dislocation model of strain anisotropy

2008 ◽  
Vol 23 (2) ◽  
pp. 125-132 ◽  
Author(s):  
Tamás Ungár
Keyword(s):  
Line Profile ◽  
Profile Analysis ◽  
Lattice Defects ◽  
Dislocation Model ◽  
Line Profile Analysis ◽  
Strain Anisotropy ◽  
Burgers Vector ◽  
Slip Activity ◽  
Dislocation Type ◽  
Type Lattice

Dislocation model of strain anisotropy is presented. The dislocation theorem of strain broadening is suggested which means that strain broadening can only be caused by dislocation-type lattice defects. Based on this theorem strain anisotropy is modeled and accounted for by assuming that strain broadening is caused by dislocations or dislocation-type lattice defects. The effect of strain anisotropy is summarized in hkl dependent dislocation contrast factors, which can be either averaged over the permutations of hkl indices or are different for each different reflection. The dislocation model of strain anisotropy provides a powerful tool to analyze slip activity, Burgers vector populations, and plasticity on the basis of line profile analysis.

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