Quasicrystal nucleation and ℤ module twin growth in an intermetallic glass-forming system

Abstract

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 module, explains how the seed’s decagonal long-range orientational order is conserved throughout the symmetry breaking steps of twinning and dendritic growth.

Multi‐Step Crystallization of Self‐Organized Spiral Eutectics

“…That is, the presence of such crystallographic defects causes the spiral growth form. While screw dislocation‐driven growth has been reported in diverse areas of crystallization—and indeed extensions of the Burton–Cabrera–Frank spiral growth model exist—our proposed mechanism on the role of “hidden” polytetrahedral phases in assisting heterogeneous nucleation supports and expands upon recent reports, for instance, metastable quasicrystal‐induced nucleation yielding grain‐refined alloys, among other two‐step solidification pathways.…”

Chiral spiral cyclic twins

“…The case m ¼ 6 is also interesting, insofar as a cyclic twin nucleation has been reported to occur in tin-based solder alloys (Lehman et al, 2010), which strongly resembles the cyclic twin nucleation phenomena observed for NiZr (Hornfeck et al, 2018), yet differs in that the symmetry of the twin is sixfold.…”

“…The twin model of NiZr was constructed by adhering to certain geometrical constraints imposed by NiZr's crystal structure (Hornfeck et al, 2014). Its parametrization by the spiral sequence of equation ( 33) followed only afterwards (Hornfeck et al, 2018;Hornfeck, 2018) and by empirically finding the suitable integer sequences for the baseline and alternating part in the On-line Encyclopedia of Integer Sequences (OEIS; Sloane, 2018). This has several drawbacks.…”

“…The binary intermetallic compound NiZr exhibits a remarkable tendency of forming cyclic tenfold twins from either a vitrified amorphous matrix upon heating (Jiang et al, 1985) or a deeply undercooled melt upon solidification (Hornfeck et al, 2014(Hornfeck et al, , 2018.…”

“…In order to better understand the twin formation process an atomistic model was developed (Hornfeck et al, 2014(Hornfeck et al, , 2018Hornfeck, 2018), based on some idealized geometric properties of NiZr's orthorhombic unit cell, including not only its special axial ratio, in the form of 2 tan À1 ða=bÞ ' 36 , being the prerequisite of tenfold twinning, but also taking into account special values for the atomic coordinates, governed by a Z module. This model has been experimentally confirmed at atomic resolution (Hornfeck et al, 2018) by means of highangle annular dark-field scanning transmission electron microscopy (HAADF-STEM), thereby making NiZr the first example of Z-module twinning (Quiquandon et al, 2016;Sirindil et al, 2017Sirindil et al, , 2018. The atomistic model found (Fig.…”