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.

Dislocations, crystallite size, and planar faults in nanocrystalline ceria

2009 ◽  
Vol 24 (3) ◽  
pp. 228-233 ◽  
Author(s):  
S. R. Aghdaee ◽  
V. Soleimanian
Keyword(s):  
Grain Size ◽  
Dislocation Density ◽  
Crystallite Size ◽  
Cerium Oxide ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Nanocrystalline Ceria ◽  
Hall Plot

The modified Williamson–Hall and Warren–Averbach methods were used successfully for analyzing experimentally observed anisotropic X-ray diffraction line broadening and for determining reliable values of crystallite size and dislocation density in cerium oxide. The modified Williamson–Hall plot gives 22.3(2) nm for volume-weighted crystallite size, while the modified Warren–Averbach produces 18.0(2) nm for area-weighted grain size. The dislocation density and effective outer cut-off radius of dislocations obtained from the modified Warren–Averbach method are 1.8(3)×1015 m−2 and 15.5(1) nm, respectively.

Study of Dislocation Densities of Thick GaN Films

2014 ◽  
Vol 989-994 ◽  
pp. 387-390
Author(s):  
Yon Gan Li ◽  
Xiang Qian Xiu ◽  
Xue Mei Hua ◽  
Shi Ying Zhang ◽  
Shi Pu Gu ◽  
...  
Keyword(s):  
High Resolution ◽  
Dislocation Density ◽  
Screw Dislocation ◽  
Edge Dislocation ◽  
Thick Films ◽  
X Ray Diffraction ◽  
X Ray ◽  
Dislocation Densities ◽  
Edge Dislocations

The dislocation density of GaN thick films has been measured by high-resolution X-ray diffraction. The results show that both the edge dislocations and the screw dislocation reduce with increasing the GaN thickness. And the edge dislocations have a larger fraction of the total dislocation densities, and the densities for the edge dislocation with increasing thickness reduce less in contrast with those for the screw dislocation.

scholarly journals Распределение интенсивности трехволновой дифракции от дислокационных эпитаксиальных слоев в обратном пространстве

2018 ◽  
Vol 60 (4) ◽  
pp. 691
Author(s):  
Р.Н. Кютт
Keyword(s):  
Dislocation Density ◽  
Intensity Distribution ◽  
Wave Diffraction ◽  
Block Structure ◽  
Reciprocal Space ◽  
X Ray Diffraction ◽  
X Ray ◽  
Common Peak ◽  
Edge Dislocations ◽  
Voigt Function

AbstractThe three-wave X-ray diffraction in strongly disordered epitaxial layers of GaN and ZnO is experimentally investigated. The charts of the intensity distribution in the reciprocal space are plotted in coordinates q _θ and q _ϕ for the most intensive three-wave combination (1010)/(1011) by means of subsequent θ- and ϕ-scanning. A nontrivial shape of the θ-sections of these contours at a distance from the ϕ center of reflection is revealed; it is different for different samples. For the θ-curves at the center of reflection, we observed a common peak that may be approximated by the Voigt function with a power-low decrease in the intensity at the wings; the decrease law (from–4.5 to–5.0) is found to be considerably greater than that for the similar curves of two-wave diffraction and not depending on the dislocation density and distribution in layers. In some films we observed a coarse-block structure; in addition, it follows from the distribution in the reciprocal space that these blocks are turned with respect to each other around a normal to the surface, which allows us to suggest the existence of low-angle boundaries between them, consisting exclusively of edge dislocations.

Dislocations in thin metal films observed with X-ray diffraction

2001 ◽  
Vol 673 ◽  
Author(s):  
Léon J. Seijbel ◽  
Rob Delhez
Keyword(s):  
Fourier Coefficients ◽  
Metal Films ◽  
Thin Metal ◽  
Diffraction Line ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Dislocation Arrangement ◽  
Dislocation Densities ◽  
Metal Layers

ABSTRACTX-ray diffraction has been used to measure the stress, the crystallite size and the dislocation distribution in thin metal layers. By measuring two orders of a reflection, the contribution of the size distribution to the diffraction line broadening can be eliminated. A model equation is fitted to the strain Fourier coefficients of the diffraction line from which the dislocation arrangement can be obtained. For untextured nickel on steel or on silicon the dislocation densities have been obtained. It is demonstrated that for highly textured layers more information can be obtained than for untextured layers. It was found that a heated molybdenum layer on oxidized silicon showed only inclined screw dislocations.

Measurement of Dislocation Density in Cold-Drawn Steel Wires by Means of X-Ray Bragg Profiles Analysis

2012 ◽  
Vol 184-185 ◽  
pp. 1054-1059
Author(s):  
Fan Yang ◽  
Ying Ying Fan ◽  
Yi Ming Jin
Keyword(s):  
Dislocation Density ◽  
True Strain ◽  
Pearlitic Steel ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Line Profile ◽  
Steel Wires ◽  
Initial Dislocation Density ◽  
Cold Worked

Cold-drawn pearlitic steel wires are widely used in numerous engineering fields. One of the most powerful analysis methods on determining the dislocation character of this heavily cold worked material is to investigate the X–ray diffraction line-profile broadening. Fourier line–broadening analysis in steel wires with near eutectoid composition indicates that with cumulative true strains, the initial dislocation density of 6×1014m-2in the rods increases at least one magnitude in wires. Up to 1.5×1016m-2of dislocation density is found in the ferrite lamella of wires with a true strain of 2.77.

scholarly journals Ice-lattice distortion along the deepest section of the Vostok core from X-ray diffraction measurements

2004 ◽  
Vol 39 ◽  
pp. 501-504 ◽  
Author(s):  
Akira Hori ◽  
Takeo Hondoh ◽  
Mitsugu Oguro ◽  
Vladimir Ya. Lipenkov
Keyword(s):  
Dislocation Density ◽  
Lattice Distortion ◽  
Ice Core ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Core ◽  
Glacier Ice ◽  
Climatic Record ◽  
Accretion Ice ◽  
Ice Lattice

AbstractWe performed X-ray diffraction measurements on eight ice samples taken between 3200 and 3611 m depth of the Vostok (Antarctica) ice core to observe lattice distortions of ice crystals. Selected samples represent three distinct sections of the core: (i) glacier (meteoric) ice with well-preserved climatic record (down to 3310 m), (ii) ‘shear zone’ at the base of the glacier ice (3450– 3537 m) within which the climatic record is disturbed by ice deformation, and (iii) accretion ice formed by freezing of subglacial Vostok lake waters at the base of the ice sheet (from about 3537 m depth to the bottom of the core). The dislocation density decreases from 1012 to 108m–2 with increasing depth. In the accretion ice, lattice distortion tends to decrease with depth. However, the dislocation density does not reach a level typical for laboratory-grown columnar ice even at 3610 m. This reflects plastic deformation which accretion ice has undergone after its formation.

Kinematical diffraction by distorted crystals – dislocation X-ray line broadening

2007 ◽  
Vol 222 (3-4) ◽  
Author(s):  
Radomír Kužel
Keyword(s):  
Line Width ◽  
Diffraction Line ◽  
Orientation Factor ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Orientation Contrast ◽  
Current State ◽  
Contrast Factor ◽  
Method Of Evaluation

The current state of the description and evaluation of dislocation-induced X-ray diffraction line broadening has been reviewed. The diffraction-line broadening can be analyzed in terms of line width, moments or Fourier coefficients. However, in the last years, whole pattern fitting has become the most popular method of evaluation. The line width is proportional to the Burgers vector of dislocations, to the square-root of dislocation density and to the so-called orientation (contrast) factor. The orientation factor determines the

Structural Analysis of X-ray Diffraction Peaks of Thin Film Gallium Arsenide

1970 ◽  
Vol 14 ◽  
pp. 441-452
Author(s):  
E. J. Charlson ◽  
D. H. Hu ◽  
M. R. Farukhi
Keyword(s):  
Thin Film ◽  
Structural Analysis ◽  
Partial Pressure ◽  
Fourier Coefficients ◽  
Stacking Faults ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Gaas Films ◽  
Diffraction Peaks

AbstractA least-squares polynomial approximation of the Warren-Averbach Fourier coefficients line broadening analysis has shown flash-evaporated GaAs films to be characterized by De(lll) ≤ 400 Å and >εL2<½ ⋍ 0.002. Though twinning is the dominant faulting mechanism, a considerable amount of single and double deformation stacking faults are also present. Growth under a partial pressure of arsenic and tin has enhanced crystallite size by a factor of four.

Asymmetric X-ray line broadening of plastically deformed crystals. I. Theory

1988 ◽  
Vol 21 (1) ◽  
pp. 47-54 ◽  
Author(s):  
I. Groma ◽  
T. Ungár ◽  
M. Wilkens
Keyword(s):  
Dislocation Density ◽  
Mean Square ◽  
Line Profiles ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Average Dislocation Density ◽  
Mean Square Fluctuation ◽  
The Mean ◽  
Dipole Polarization

X-ray diffraction line profiles of plastically deformed Cu single crystals orientated for ideal multiple slip were recently found to be markedly asymmetric. A theory is developed to interpret this kind of asymmetric line broadening in terms of the average dislocation density, the dipole polarization of the dislocation structure and the mean square fluctuation of the dislocation density.

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