Helical Substructures of Close-Packed Metals Determined by a Universal Building Unit (Tetrablock)

Талис, А. Л.; Everstov, A. A.; Крапошин, В. С.

doi:10.1007/s11041-022-00792-z

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Examples of such linear substruc-tures in the cubic crystals ofand -Mn were considered by us in the present work (Figs. 1 and 2), as well as by Talis et al (2020Talis et al ( , 2021Talis et al ( , 2022. In particular, Fig.…”

Section: Unions Of Two Congruent 20/9 Helices Into 40/9 and 40/11 Hel...mentioning

confidence: 78%

“…Realizations in E 3 of the 8/3 and 11/4 approximants of the 30/11 axis of the {3, 3, 5} polytope were demonstrated by us using examples of slightly deformed tetrahedral rods in the crystalline structures of Mn (Talis et al, 2020(Talis et al, , 2021(Talis et al, , 2022. However, the same crystal ß-Mn is also determined by the sixdimensional B 6 lattice (Lidin & Fredrickson, 2012).…”

Section: Tetrahedral Polytope Class Of the Fractional Axesmentioning

confidence: 93%

“…1(e)]. Thus, using the 20/9 helix of flat tetrablocks (Talis et al, 2022) can be no less fruitful than using the 30/11 tetrahelix.…”

Section: Introductionmentioning

confidence: 99%

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Non-crystallographic helices in polymers and close-packed metallic crystals determined by the four-dimensional counterpart of the icosahedron

Talis,

Kucherinenko

2023

Acta Crystallogr Sect B

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Non-crystallographic fractional screw axes are inherent to the constructions of n-dimensional crystallography, where 3 < n ≤ 8. This fact allows one to consider experimentally obtained helices as periodic approximants of helices from the four-dimensional {3, 3, 5} polytope and its derivative constructions. For the tetrahedral Coxeter–Boerdijk helix (tetrahelix) with a 30/11 axis from the {3, 3, 5} polytope, approximants with 11/4 and 8/3 axes in three-dimensional Euclidean space {\bb E}^{3} are considered. These determine the structure of rods composed of deformed tetrahedra in close-packed crystals of α-Mn and β-Mn. In the {3, 3, 5} polytope, highlighted here for the first time, is a 40-vertex helix with a 20/9 axis composed of seven-vertex quadruples of tetrahedra (tetrablocks), whose 7/3 approximants determine in a crystal of an α-Mn rod of deformed tetrablocks with the same period as the 11/4 approximant of the tetrahelix. In the spaces of the three-dimensional sphere and {\bb E}^{3}, the parameters of 20/9, 40/9 and 40/11 helices, as well as of their 20- and 40-vertex approximants, are calculated. The parameters of the approximant of the 40/11 helix in {\bb E}^{3} correspond to experimentally determined parameters of the α-helix, which allows us to explain the versatility of the α-helix in proteins by the symmetry of the polytope. The set of fractional axes of all periodic approximants of helices with 30/11, 20/9, 40/9, 40/11 axes, as well as the powers of these axes, are combined into a tetrahedral-polytope class of 50 basic axes. The basic axes as well as composite (defined as a combination of basic ones) fractional axes of this class cover all fractional axes known to us according to literature data for polymers, biopolymers and close-packed metals.

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Section: Unions Of Two Congruent 20/9 Helices Into 40/9 and 40/11 Hel...mentioning

confidence: 78%