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- Title
A tenfold twin of the CrB structure type.
- Authors
Hornfeck, Wolfgang
- Abstract
NiZr crystallized from an amorphous matrix or solidified from an undercooled melt exhibits a tenfold twinned microstructure, which is explained by an ideal twin model utilizing special geometric properties of the CrB structure type. The model is unique in several ways: (i) it contains no adjustable parameters other than a scaling factor accounting for the smallest interatomic distance; (ii) it features an irrational shift in the translational part of the twin operation; and (iii) it has many traits commonly observed for quasicrystals, connected to the occurrence of decagonal long‐range orientational order, making NiZr the first experimental example of the recently introduced concept of ‐module twinning. It is shown how these remarkable properties of the tenfold twin's structure model are related to one another and founded in number theory as well as in the mathematical theory of aperiodic order. The structure of the tenfold twins formed by CrB‐type NiZr is explained by an idealization of the NiZr crystal structure, involving atoms occupying the nodes of a pentagonal ‐module, and the chiral twin structure being parameterized by a spiral generating formula.
- Subjects
INTERMETALLIC compounds; NICKEL compounds; CRYSTAL structure
- Publication
Acta Crystallographica. Section A, Foundations & Advances, 2018, Vol 74, Issue 6, p659
- ISSN
2053-2733
- Publication type
Article
- DOI
10.1107/S2053273318011828