Quasicrystal structure prediction: A review

Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given structure. We survey the history and current state of these prediction efforts with a focus on methods that have improved our understanding of the structure and stability of known metallic quasicrystal phases. Advances in the structural modeling of quasicrystals, along with first principles total energy calculation and statistical mechanical methods that enable the calculation of quasicrystal thermodynamic stability, are illustrated by means of cited examples of recent work

Quasiperiodic ordering in thick Sn layer on ii-Al-Pd-Mn: A possible quasicrystalline clathrate

Realization of an elemental solid-state quasicrystal has remained a distant dream so far in spite of extensive work in this direction for almost two decades. Here, we report the discovery of quasiperiodic ordering in a thick layer of elemental Sn grown on icosahedral ($i$)-Al-Pd-Mn. The STM images and the LEED patterns of the Sn layer show specific structural signatures that portray quasiperiodicity but are distinct from the substrate. Photoemission spectroscopy reveals the existence of the pseudogap around the Fermi energy up to the maximal Sn thickness. The structure of the Sn layer is modeled as a novel form of quasicrystalline clathrate on the basis of the following: Firstly, from ab-initio theory, the energy of bulk Sn clathrate quasicrystal is lower than the high temperature metallic $\beta$-Sn phase, but higher than the low temperature $\alpha$-Sn phase. A comparative study of the free slab energetics shows that surface energy favors clathrate over $\alpha$-Sn up to about 4 nm layer thickness, and matches $\beta$-Sn for narrow window of slab thickness of 2-3 nm. Secondly, the bulk clathrate exhibits gap opening near Fermi energy, while the free slab form exhibits a pronouced pseudogap, which explains the pseudogap observed in photoemission. Thirdly, the STM images exhibit good agreement with clathrate model. We establish the adlayer-substrate compatibility based on very similar (within 1%) the cage-cage separation in the Sn clathrate and the pseudo-Mackay cluster-cluster separation on the $i$-Al-Pd-Mn surface. Furthermore, the nucleation centers of the Sn adlayer on the substrate are identified and these are shown to be a valid part of the Sn clathrate structure. Thus, based on both experiment and theory, we propose that 4 nm thick Sn adlayer deposited on 5-fold surface of $i$-Al-Pd-Mn substrate is in fact a metastable realization of elemental, clathrate family quasicrystal.Comment: 10 figures in the Manuscript and the 8 figures in the Supplementary materia

Atomic dynamics of the i-ScZnMg and its 1/1 approximant phase: experiment and simulation

International audienceQuasicrystals are long range ordered materials which lack translational invariance so that the study of their physical properties remains a challenging problem. In order to study the respective influence of the local order and of the long range order (periodic or quasiperiodic) on lattice dynamics, we have carried out inelastic x-ray and neutron scattering experiments on single grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant. Besides the overall similarities and the existence of a pseudo gap in the transverse dispersion relation, marked differences are observed, the pseudo gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of pseudo Brillouin zone in the quasicrystal. These results are compared to simulations on atomic models and using oscillating pair potentials which have been fitted against ab-initio data. The simulated response function reproduces both the dispersion relation but also the observed intensity distribution in the measured spectra. The partial vibrational density of states, projected on the cluster shells, is computed from this model

Planar defect in approximant : the case of Cu-Al-Sc alloy

The {110} planar defect formed in the Cu-Al-Sc 1/1 approximant has been studied by means of electron microscopy and 6-dimensional analysis. As the displacement vector of the planar defect, 1/2 has been proposed. Here tau denotes the golden ratio. This vector corresponds to a 6-dimensional translation of type [111000] and also to the c-linkage of Tsai-type clusters. An atomic structure model of the planar defect has been constructed referring to the structural properties of the regular 1/1 approximant; namely truncated triacontahedron framework and embedded clusters. This structural model was validated by the agreement between the observed and simulated HAADF-STEM images. Models of the intersection of two planar defects and the triple point, where three planar defects intersect, were also proposed. All local structures formed at these defects are understood by the concept of so-called canonical cell tiling