Long-range in-plane elastic displacement fields of double vacancies in graphene

2021 ◽  
pp. 115075
Author(s):  
Ilya E. Golentus
Keyword(s):  
Long Range ◽  
Elastic Displacement ◽  
Displacement Fields

Atomic Displacements Around Nitrogen Interstitial Impurities in Ta and Nb

1986 ◽  
Vol 82 ◽  
Author(s):  
S. Rao ◽  
E. J. Savino ◽  
C. R. Houska
Keyword(s):  
Long Range ◽  
Theoretical Calculations ◽  
Attenuation Factor ◽  
Scattering Data ◽  
Elastic Displacement ◽  
Force Model ◽  
The Core ◽  
Atomic Displacements ◽  
The Green Function ◽  
Experimental Findings

ABSTRACTThe core as well as the long range elastic displacements around N octahedral interstitial atoms in Ta and Nb are modelled using the Green Function – Kanzaki force method. The theoretical calculations are compared with experimental attenuation factor and diffuse scattering data, reported in the literature, for both N in Nb and N in Ta [1,2,3]. It is shown that a third neighbor radial Kanzaki force model is needed to explain the experimental findings, and the long range elastic displacement field is non-spherical.

General expressions for the elastic displacement fields induced by dislocations in quasicrystals

1995 ◽  
Vol 7 (28) ◽  
pp. 5423-5436 ◽  
Author(s):  
Di-Hua Ding ◽  
Renhui Wang ◽  
Wenge Yang ◽  
Chengzheng Hu
Keyword(s):  
Elastic Displacement ◽  
Displacement Fields

X-ray scattering: a wonderful tool to probe lattice strains in materials with small dimensions

2004 ◽  
Vol 840 ◽  
Author(s):  
Olivier Thomas ◽  
Audrey Loubens ◽  
Patrice Gergaud
Keyword(s):  
Disordered Systems ◽  
Elastic Displacement ◽  
X Ray Diffraction ◽  
Displacement Fields ◽  
X Ray ◽  
Atomic Displacements ◽  
X Ray Scattering ◽  
Lattice Strains ◽  
Individual Unit ◽  
Ray Scattering

ABSTRACTX-ray diffraction was recognized from the early days as highly sensitive to atomic displacements. Indeed structural crystallography has been very successful in locating with great precision the position of atoms within an individual unit cell. In disordered systems it is the average structure and fluctuations about it that may be determined. In the field of mechanics diffraction may thus be used to evaluate elastic displacement fields. In this short overview we give examples from recent work where x-ray diffraction has been used to investigate average strains in lines, films or multilayers. In small objects the proximity of surfaces or interfaces may create very inhomogeneous displacement fields. X-ray scattering is again one of the best methods to determine such distributions. The need to characterize displacement fields in nanostructures together with the advent of third generation synchrotron radiation sources has generated new and powerful methods (anomalous diffraction, coherent diffraction, microdiffraction, …). We review some of the recent and promising results in the field of strain measurements in small dimensions via X-ray diffraction.

On the computation of diffraction peaks from discrete defects in continuous media: comparison of displacement and strain-based methods

2014 ◽  
Vol 47 (3) ◽  
pp. 861-878 ◽  
Author(s):  
Manas Vijay Upadhyay ◽  
Laurent Capolungo ◽  
Levente Balogh
Keyword(s):  
Fourier Method ◽  
Continuous Media ◽  
Dislocation Dynamics ◽  
Elastic Displacement ◽  
Average Strain ◽  
Displacement Fields ◽  
Discrete Dislocation ◽  
Peak Broadening ◽  
Diffraction Peaks ◽  
Displacement Based

This study introduces a numerical tool to generate virtual diffraction peaks from known elastic displacement or strain fields arising in the presence of discrete straight or curved dislocations in continuous media. The tool allows for the generation of diffraction peaks according to three methods: the displacement-based Fourier method of Warren, the Stokes–Wilson approximate method and a new average-strain-based Fourier method. The trade-off between the accuracy and the demand for computational power of the three methods is discussed. The work is applied to the cases of single-crystal microstructures containing (i) straight dislocations, (ii) low-angle symmetric tilt grain boundaries, (iii) a restrictedly random distribution of dislocations and (iv) complex microstructures generated by discrete dislocation dynamics, to illustrate the differences and domains of validity of the aforementioned methods. Dissimilar diffraction profiles reveal that peak broadening from dislocated crystals has additional contributions coming from strain gradients – a feature that is rejected in the Stokes–Wilson approximation. The problem of dealing with multi-valued displacement fields faced in the displacement-based Fourier method is overcome by the new average-strain-based Fourier method.

Elastic displacement fields induced by dislocations in dodecagonal quasicrystals

1995 ◽  
Vol 200 (2) ◽  
pp. 177-183 ◽  
Author(s):  
Wenge Yang ◽  
Jianlin Lei ◽  
Di-hua Ding ◽  
Renhui Wang ◽  
Chengzheng Hu
Keyword(s):  
Elastic Displacement ◽  
Displacement Fields
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