Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals

0578765 - FZÚ 2024 RIV GB eng J - Journal Article
Hornfeck, Wolfgang
Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals.
Acta Crystallographica Section A-Foundation and Advances. Roč. 79, č. 6 (2023), s. 570-586. ISSN 2053-2733. E-ISSN 2053-2733
R&D Projects: GA ČR(CZ) GA18-10438S
Institutional support: RVO:68378271
Keywords : chiral properties * spiral structures * cyclic twins
OECD category: Condensed matter physics (including formerly solid state physics, supercond.)
Impact factor: 1.8, year: 2022
Method of publishing: Open access

A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ. By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them.
Permanent Link: https://hdl.handle.net/11104/0347677