<i>Theory of Dislocations</i> and <i>Theory of Crystal Dislocations</i>

Hirth, J. P.; Lothe, J.; Nabarro, F. R. N.; Smoluchowski, R.

doi:10.1063/1.3035074

Cited by 345 publications

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“…Any chiral tube can be viewed as a basic zigzag, but with a ''defect''-a running through the center-hollow screw dislocation of a Burgers vector b (Fig. 1B-D) (19). (The reason to choose the zigzag tube rather than armchair as a basic one will become clear later.)…”

Section: Resultsmentioning

confidence: 99%

“…Along with this geometrical consideration, it is important to note a qualitative difference from the case of solid bulk or nanowire [which also displays Eshelby twist (20)]. In the last 2 cases, the screw dislocation adds strain, whose energy Ϸ͉b͉ 2 impedes the larger Burgers vectors (19). In contrast, in a 1-atom-thin CNT wall, the axial screw dislocation carries no energy penalty, thus permitting different magnitudes of ͉b͉ and therefore various chiralities.…”

Section: Resultsmentioning

confidence: 99%

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Dislocation theory of chirality-controlled nanotube growth

Ding

Harutyunyan

Yakobson

2009

Proc. Natl. Acad. Sci. U.S.A.

308

374

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The periodic makeup of carbon nanotubes suggests that their formation should obey the principles established for crystals. Nevertheless, this important connection remained elusive for decades and no theoretical regularities in the rates and product type distribution have been found. Here we contend that any nanotube can be viewed as having a screw dislocation along the axis. Consequently, its growth rate is shown to be proportional to the Burgers vector of such dislocation and therefore to the chiral angle of the tube. This is corroborated by the ab initio energy calculations, and agrees surprisingly well with diverse experimental measurements, which shows that the revealed kinetic mechanism and the deduced predictions are remarkably robust across the broad base of factual data.carbon ͉ catalysis ͉ kinetics ͉ nucleation ͉ synthesis

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Dislocation theory of chirality-controlled nanotube growth

Ding

Harutyunyan

Yakobson

2009

Proc. Natl. Acad. Sci. U.S.A.

308

374

View full text Add to dashboard Cite

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“…In a continuum setting, sub-grain dislocation networks have been studied analytically [4,5,[11][12][13] and computationally [9,[14][15][16]. Analytical studies have been for the most part limited to infinite planar dislocation arrays and based on simple kinematics and geometrical arguments such as Frank's relation or on line-tension models that neglect elastic interactions and the structure of the dislocation nodes [4,11,13].…”

Section: Introductionmentioning

confidence: 99%

“…Analytical studies have been for the most part limited to infinite planar dislocation arrays and based on simple kinematics and geometrical arguments such as Frank's relation or on line-tension models that neglect elastic interactions and the structure of the dislocation nodes [4,11,13]. Computational models that regard dislocations as elastic line defects are often beset by the cost of evaluating the long-range elastic interactions between each pair of dislocation segments and by the sensitivity of the results to the choice of the interaction cut-off radius [14].…”

Section: Introductionmentioning

confidence: 99%

A multi-phase field model of planar dislocation networks

Ortiz¹

2004

Modelling Simul. Mater. Sci. Eng.

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In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289-98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957 to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers.

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“…A dislocation creates around it a perturbation that can be seen as an elastic field. Under an exterior strain, a dislocation moves according to its Burgers vector which characterizes the intensity and the direction of the defect displacement (see Hirth and Lothe [17] for an introduction to dislocations).…”

Section: Presentation and Physical Motivationsmentioning

confidence: 99%

A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

Hajj

Forcadel

2007

Math. Comp.

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Abstract. In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence and uniqueness result for the solution of this model. We also propose a convergent numerical scheme and we prove a Crandall-Lions type error estimate between the continuous solution and the numerical one. As far as we know, this is the first error estimate of Crandall-Lions type for Hamilton-Jacobi systems. We also provide some numerical simulations.

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Theory of Dislocations and Theory of Crystal Dislocations

Cited by 345 publications

References 0 publications

Dislocation theory of chirality-controlled nanotube growth

Dislocation theory of chirality-controlled nanotube growth

A multi-phase field model of planar dislocation networks

A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

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