Elastic Green's function of icosahedral quasicrystals

Bachteler, J.; Trebin, Hans‐Rainer

doi:10.1007/s100510050383

Cited by 26 publications

(16 citation statements)

References 19 publications

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“…De and Pelcovits [12] found the two-dimensional Green functions for pentagonal (2D) quasicrystals and Ding et al [13] calculated the explicit expressions of two-dimensional Green tensors for various forms of planar (2D) quasicrystals. Bachteler and Trebin [14] gave an approximative solution for the three-dimensional Green tensor of icosahedral (3D) quasicrystals, assuming that the coupling between phonons and phasons is small (perturbation method).…”

Section: Introductionmentioning

confidence: 99%

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops

Lazar

Agiasofitou

2014

Philosophical Magazine

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The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is the generalized Burgers equation for arbitrary sources and the generalized Mura-Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach-Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach-Koehler stress formula, Mura-Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.

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Section: Introductionmentioning

confidence: 99%

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops

Lazar

Agiasofitou

2014

Philosophical Magazine

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“…The constant Γ ,⊥ enters the shape of the diffuse tails around Bragg peaks [6], can drive a quasicrystal phase unstable with respect to a related crystal phase [7,8], and affects the strain fields of dislocations in quasicrystals, which have been studied by diffraction contrast in transmission electron microscopy [9,10]. Previous authors [5,6,10,11] simply assumed Γ ,⊥ was small compared with the other elastic constants.…”

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confidence: 99%

Phonon-phason coupling in icosahedral quasicrystals

Zhu

Henley

1999

Europhys. Lett.

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received ; accepted ) PACS. 61.44Br -Quasicrystals. PACS. 62.20Dc -Elasticity, elastic constants. PACS. 61.10Dp -Theories of X-ray diffraction and scattering. PACS. 71.15Pd -Molecular dynamics calculations (Car-Parrinello) and other numerical simulations.Abstract. -From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the two alloys studied, i-AlMn and i-(Al,Cu)Li; a dimensionless measure of its magnitude relative to the phonon and phason elastic constants is of order 1/10, suggesting its effects are small but detectable. We also give a criterion for when phonon-phason effects are noticeable in diffuse tails of Bragg peaks.( * ) Present address: IBM T.

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“…µ 3 = 0. Isotropy in phason elasticity is given in the spherical approximation µ 4 = µ 5 discussed in [6], in addition to the condition µ 3 = 0.…”

Section: 1 Some Fundamentalsmentioning

confidence: 99%

Elastic theory of icosahedral quasicrystals - application to straight dislocations

2001

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In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three-and fivefold straight screw-and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three-and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders.

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Elastic Green's function of icosahedral quasicrystals

Cited by 26 publications

References 19 publications

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops

Phonon-phason coupling in icosahedral quasicrystals

Elastic theory of icosahedral quasicrystals - application to straight dislocations

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