Modeling Quasi-Lattice With Octagonal Symmetry

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

doi:10.7868/s0044451014110091

Cited by 2 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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Modelling of Lattices of Two-Dimensional Quasi-Crystals

Gіrzhon¹,

Smolyakov²

2019

Usp. Fiz. Met.

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Modelling of lattices of two-diMensional Quasi-crystals We propose the method for modelling of quasi-periodic structures based on an algorithm being a geometrical interpretation of the Fibonacci-type numerical sequences. The modelling consists in a recurrent multiplication of basis groups of the sites, which possess the 10-th, 8-th or 12-th order rotational symmetry. The advantage of the proposed method consists in an ability to operate with only two-dimensional space coordinates rather than with hypothetical spaces of dimension more than three. The correspondence between the method of projection of quasi-periodic lattices and the method of recurrent multiplication of basis-site groups is shown. As established, the six-dimensional reciprocal lattice for decagonal quasi-crystals can be obtained from orthogonal six-dimensional lattice for icosahedral quasi-crystals by changing the scale along one of the basis vectors and prohibiting the projection of sites, for which the sum of five indices (corresponding to other basis vectors) is not equal to zero. It is shown the sufficiency of using only three indices for describing diffraction patterns from quasi-crystals with 10-th, 8-th and 12-th order symmetry axes. original algorithm enables direct obtaining of information about intensity of diffraction reflexes from the quantity of self-overlaps of sites in course of construction of reciprocal lattices of quasi-crystals.

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Modeling Quasi-Lattice With Octagonal Symmetry

Cited by 2 publications

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Modeling of quasicrystal lattices with a 4-fold symmetry axis

Modeling of quasicrystal lattices with a 4-fold symmetry axis

Modelling of Lattices of Two-Dimensional Quasi-Crystals

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