Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling

Sinclair, J. E.; Gehlen, P. C.; Hoagland, R. G.; Hirth, J. P.

doi:10.1063/1.325395

Cited by 142 publications

(91 citation statements)

References 22 publications

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“…This therefore simulates an isolated dislocation in an infinite elastic medium. A variant of the method consists in relaxing atoms at the surface using lattice Green functions [25,26,27]. This may be necessary in ab-initio calculations because of the small size of the unit cell that can be simulated.…”

Section: The Cluster Approachmentioning

confidence: 99%

Elastic energy of a straight dislocation and contribution from core tractions

Clouet

2009

Philosophical Magazine

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We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than the ones gliding in {112} planes.

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Section: The Cluster Approachmentioning

confidence: 99%

Elastic energy of a straight dislocation and contribution from core tractions

Clouet

2009

Philosophical Magazine

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“…by preventing the change of volume attendant to a discrete dislocation. Flexible boundary methods have been proposed which overcome this difficulty, most notably those of Sinclair and co-workers (Sinclair 1971, Sinclair et al 1978, Gehlen et al 1972. However, some features of these approaches contribute to making their implementation onerous.…”

Section: Introductionmentioning

confidence: 99%

A harmonic/anharmonic energy partition method for lattice statics computations

Gallego

Ortiz

1993

Modelling Simul. Mater. Sci. Eng.

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A method of lattice statics analysis is developed. Consideration of anharmonic effects is reslricted to finite regions surrounding lattice defecls. All displacements of the nysral are expressed as the effect of unknown forces applied to a perfect harmonic lattice of infinite extent.Displacements are related m the unknown applied forces by means of the Green function of the perfect harmonic lactice. so that equilibrating forces need only be applied to the anharmonic region. The unknown forces are determined so as to maximize the complementary energy of the crjsral, which yields a lower bound to the potential energy. The method daes not require the explicit enforcement of equilibrium or compatibility conditions acmss the boundary beween the harmonic and anharmonic regions. The performance of the method is assessed on the basis of selected numerical examples. The rate of convergence of the method with increasing domain size is found to be cubic. This is one or two orders of magnitude faster than rigid boundary methods based on the harmonic and continuum solutions. respectively.

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“…Sinclair et al, 12 later redeveloped for crack propagation 13 and for dislocations and dislocation kinks 14 -made possible the relaxation of the core geometry of an isolated dislocation. For a review of density-functional theory methods applied to dislocations, see [15].…”

Section: Introductionmentioning

confidence: 99%

Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces

Trinkle

2008

Phys. Rev. B

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Computing the atomic geometry of lattice defects-point defects, dislocations, crack tips, surfaces, or boundaries-requires an accurate coupling of the local strain field to the long-range elastic field. Periodic boundary conditions used by classical potentials or density-functional theory may not accurately reproduce the correct bulk response to an isolated defect; this is especially true for dislocations. Recently, flexible boundary conditions have been developed to produce the correct long-range strain field from a defecteffectively "embedding" a defect in a finite cell with infinite bulk response, isolating it from either periodic images or free surfaces. Flexible boundary conditions require the calculation of the bulk response with the lattice Green function (LGF). While the LGF can be computed from the dynamical matrix, for supercell methods (periodic boundary conditions) it can only be calculated up to a maximum range. We illustrate how to accurately calculate the lattice Green function and estimate the error using a cutoff dynamical matrix combined with knowledge of the long-range behavior of the lattice Green function. The effective range of deviation of the lattice Green function from the long-range elastic behavior provides an important length scale in multiscale quasi-continuum and flexible boundary-condition calculations, and measures the error introduced with periodic boundary conditions.

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Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling

Cited by 142 publications

References 22 publications

Elastic energy of a straight dislocation and contribution from core tractions

Elastic energy of a straight dislocation and contribution from core tractions

A harmonic/anharmonic energy partition method for lattice statics computations

Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces

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