A molecular dynamics-aided fracture mechanics parameter and its application to a tensile problem

Inoue, Hideyuki; Akahoshi, Y.; Harada, Syoji

doi:10.1007/s004660050064

Cited by 4 publications

(4 citation statements)

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“…Alternative expressions for materials with defects, or even how their definition behaved in the presence of such defects, were not considered. An expression for displacement gradient was also developed by Inoue et al (1995), and later used by Jin and Yuan (2005), to calculate a discrete version of the J-Integral, the energetic driving force for crack propagation. Also interested in developing a discrete form of the J-Integral expression, Nakatani et al (2000) used the derivative of a continuous weighting function to selectively include atomic displacement information in the determination of a displacement gradient field.…”

Section: Introductionmentioning

confidence: 99%

Deformation gradients for continuum mechanical analysis of atomistic simulations

Zimmerman

Bammann

Gao

2009

International Journal of Solids and Structures

126

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a b s t r a c tWe present an expression developed for calculating an atomic-scale deformation gradient within atomistic simulations. This expression is used to analyze the deformation fields for a one-dimensional atomic chain, a biaxially stretched thin film containing a surface ledge, and a FCC metal subject to indentation loading from a nanometer-scale indenter. The analyses presented show that the metric established here is consistent with the continuum mechanical concept of deformation gradient (which is known to have a zero curl for compatible deformations) in most instances. However, our metric does yield non-zero values of curl for atoms near loaded geometric inhomogeneities, such as those that form the ledges themselves and those beneath or adjacent to the indentation contact region. Also, we present expressions for higher order gradients of the deformation field and discuss the requirements for their calculation. These expressions are necessary for linking atomistic simulation results with advanced continuum mechanics theories such as strain gradient plasticity, thereby enabling fundamental, atomic-scale information to contribute to the formulation and parameterization of such theories.

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Section: Introductionmentioning

confidence: 99%

Deformation gradients for continuum mechanical analysis of atomistic simulations

Zimmerman

Bammann

Gao

2009

International Journal of Solids and Structures

126

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“…The author therefore developed a molecular-dynamics simulation technique that analyzes diffusion at the interface. Molecular dynamics simulation has been used to study fracture (Inoue et al 1995) and granular¯ows (Zheng and Hill 1998), and it has been considered to be an effective tool in monitoring the atomic positions, velocities, and forces as well as the total energy, work, and potential energy. Using the molecular dynamics approach, we have investigated grain-boundary diffusion during grainboundary sliding (Iwasaki et al 1995) as well as during grain-boundary grooving (Iwasaki et al 1997) in crystalline aluminum.…”

Section: Introductionmentioning

confidence: 99%

Molecular dynamics study of diffusion and atomic configuration in layered structures for Al circuit interconnects

Iwasaki

1999

Computational Mechanics

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Diffusion at Al(1 1 1)/underlay-metal interfaces, which is a dominant factor of electromigration-induced open-circuit failures in Al interconnects, was investigated by molecular dynamics simulation. The author focused on interfaces between the (1 1 1) plane in Al and the plane of greatest atomic density in ®ve kinds of metals that have high melting temperatures: Ti, Cr, Mo, W, and Ta. The calculated self-diffusion coef®cients of Al atoms near the Al/Ti and Al/Cr interfaces were smaller than those near the other three interfaces. This result is consistent with experimental results by other works that showed that Ti and Cr are effective underlay metals for suppressing the diffusion in Al interconnects. This result on the self-diffusion coef®cient was linked to the result on the atomic con®g-urations. The con®gurations of Al atoms at Al/Ti and Al/ Cr interfaces were close to that for bulk Al, while the con®gurations at the other three interfaces were signi®-cantly different from that for bulk Al. It was found that diffusion as well as atomic con®guration at the Al/underlay-metal interface is determined by the lattice mismatch between the (1 1 1) plane in Al and the plane of greatest atomic density in the underlay metal.

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“…Molecular-dynamics simulation has been used to investigate tensile fracture (Inoue et al 1995) and granular ows (Zheng and Hill 1998), and it has been considered to be an effective tool in monitoring microscopic physical quantities such as atomic positions, velocities, and forces as well as macroscopic physical properties such as deformation pro®le and slip velocity. Using a similar molecular-dynamics technique, we simulated grain-boundary diffusion during grain-boundary sliding (Iwasaki et al 1995) in crystalline aluminum.…”

Section: Introductionmentioning

confidence: 99%

Molecular dynamics study of adhesion strength and diffusion at interfaces between interconnect materials and underlay materials

Iwasaki

2000

Computational Mechanics

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A molecular-dynamics technique for determining the adhesion strength and analyzing diffusion at interfaces between different materials has been developed. The adhesion strength is determined by calculating the adhesive fracture energy de®ned as the difference between the total potential energy of the material-connected state and that of the material-separated state. This technique is used to determine the adhesion strength and analyze diffusion at the interfaces between Cu ®lms and highmelting-point materials that are used as underlay materials for Cu interconnects in ULSIs. The adhesive fracture energy shows that the adhesion strength of the Cu/Ru and Cu/Ir interfaces is much higher than that of the Cu/W, Cu/ TiN, and Cu/Ta interfaces. Because the diffusion of Cu atoms at the Cu/Ru and Cu/Ir interfaces is suppressed, the surface smoothness of Cu ®lms on Ru and Ir is much better than that on W, TiN, and Ta. It is also found that adhesion strength and smoothness increase with decreasing lattice mismatch between Cu and the underlay material. These results are con®rmed by SEM (scanning electron microscope) and scratch testing. 2 Analysis method 2.1 Method of adhesion analysisThe adhesion strength is investigated by calculating the adhesive fracture energy de®ned as the difference between

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A molecular dynamics-aided fracture mechanics parameter and its application to a tensile problem

Cited by 4 publications

References 0 publications

Deformation gradients for continuum mechanical analysis of atomistic simulations

Deformation gradients for continuum mechanical analysis of atomistic simulations

Molecular dynamics study of diffusion and atomic configuration in layered structures for Al circuit interconnects

Molecular dynamics study of adhesion strength and diffusion at interfaces between interconnect materials and underlay materials

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