Modeling of decagonal quasicrystal lattice

Gіrzhon, V. V.; Kovalyova, V.M.; Smolyakov, O. V.; Zakharenko, M.

doi:10.1016/j.jnoncrysol.2011.09.017

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…The expressions (5) and (6) coincide with the expressions presented in [13] by Cahn for the indexing of the icosahedral QC diffraction patterns using two integers (N, M). Similar results have been obtained in the papers [10][11][12] for the octagonal, decagonal, and dodecagonal QC reciprocal lattice indexing. Mentioned QC's are periodic along the highest order symmetry axis; hence their powder diffraction patterns can be indexed using three integers (N, M, L).…”

Section: Modeling Of the Reciprocal Quasilattice With A Four-fold Symsupporting

confidence: 89%

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Modeling of quasicrystal lattices with a 4-fold symmetry axis

Smolyakov

2018

JPhysElectron

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The construction method of a quasilattice with a four-fold rotational symmetry axis is proposed. The described method is based on the recurrent generation of the initial group of lattice points, which are a set of vertices of a square. The aperiodic crystal reciprocal lattice modeling algorithm is analyzed. Used modeling technique is compared with conventional projection approach. The orthogonal basis of a four-dimensional hypercubic lattice is proposed. This lattice produces two-dimensional quasicrystal with a four-fold symmetry axis after it projection on a flat surface. It is shown that the indexation of diffraction pattern of similar quasiperiodic structures can be carry out using 3 integer indexes, which is analogous to the indexing system proposed by Cahn for application to icosahedral quasicrystals.

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Section: Modeling Of the Reciprocal Quasilattice With A Four-fold Symsupporting

confidence: 89%

“…In the works [10][11][12] a method of modeling two-dimensional octagonal, decagonal and dodecagonal structures is proposed. It is based on the recurrent generation of a group of points, which have a symmetrical property of a lattice that is being modeled.…”

Section: Modeling Of the Reciprocal Quasilattice With A Four-fold Symmentioning

confidence: 99%

Modeling of quasicrystal lattices with a 4-fold symmetry axis

Smolyakov

2018

JPhysElectron

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“…In 1989, two types of dislocation in decagonal quasicrystals were confirmed by the comparative analysis of electron diffraction [6]. Based on the multiplication of the basis sites' groups, Girzhon et al proposed the model of the reciprocal lattice of decagonal quasicrystal [7]. By atomic resolution high-angle annular dark-field scanning transmission electron microscopy, Ma and He observed the largest decagonal subunits, which expanded to 5.2 nm in a decagonal shape [8].…”

Section: Introductionmentioning

confidence: 99%

A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Zhang,

et al. 2024

Crystals

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Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here.

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