Tenfold twins in a rapidly quenched NiZr alloy

Chiral spiral cyclic twins

A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.

Atomic scale analyses of {\bb Z}-module defects in an NiZr alloy

This article describes the observation and determination of -module defects (twins, translation faults and module dislocations) in NiZr by high-resolution electron microscopy (HREM), and scanning transmission electron microscopy bright-field (STEM-BF) and high-angle annular dark-field (STEM-HAADF).

Some specific structures of intermetallic alloys, like approximants of quasicrystals, have their unit cells and most of their atoms located on a periodic fraction of the nodes of a unique -module [a set of the irrational projections of the nodes of a (N > 3-dimensional) lattice]. Those hidden internal symmetries generate possible new kinds of defects like coherent twins, translation defects and so-called module dislocations that have already been discussed elsewhere [Quiquandon et al. (2016 ▸). Acta Cryst. A72, 55–61; Sirindil et al. (2017 ▸). Acta Cryst. A73, 427–437]. Presented here are electron microscopy observations of the orthorhombic phase NiZr – and its low-temperature monoclinic variant – which reveal the existence of such defects based on the underlying -module generated by the five vertices of the regular pentagon. New high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) observations demonstrate the agreement between the geometrical description of the structure in five dimensions and the experimental observations of fivefold twins and translation defects.

A tenfold twin of the CrB structure type

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 {\bb Z}-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.

Quasicrystal nucleation and [Formula: see text] module twin growth in an intermetallic glass-forming system

While quasicrystals possess long-range orientational order they lack translation periodicity. Considerable advancements in the elucidation of their structures and formative principles contrast with comparatively uncharted interrelations, as studies bridging the spatial scales from atoms to the macroscale are scarce. Here, we report on the homogeneous nucleation of a single quasicrystalline seed from the undercooled melt of glass-forming NiZr and its continuous growth into a tenfold twinned dendritic microstructure. Observing a series of crystallization events on electrostatically levitated NiZr confirms homogeneous nucleation. Mapping the microstructure with electron backscatter diffraction suggests a unique, distortion-free structure merging a common structure type of binary alloys with a spiral growth mechanism resembling phyllotaxis. A general geometric description, relating all atomic loci, observed by atomic resolution electron microscopy, to a pentagonal [Formula: see text] module, explains how the seed's decagonal long-range orientational order is conserved throughout the symmetry breaking steps of twinning and dendritic growth.

High-resolution electron microscopy and domain structures of pentagonal Frank-Kasper phases

The Laboratory of Atomic Imaging of Solids is dedicated to the direct imaging of materials in various fields of solid-state sciences at the atomic or molecular level. The main programs of this laboratory are briefly described, including quasicrystals, new phases and microdomains in Frank-Kasper phases, suboxides of metals, catalysts, minerals found in China, and molecular structure of organic substances. A recent systematic investigation of domain structures consisting of juxtaposed icosahedral columns is also presented.