Deep Learning Enables Rapid Identification of a New Quasicrystal from Multiphase Powder Diffraction Patterns.

Since the discovery of the quasicrystal, approximately 100 stable quasicrystals are identified. To date, the existence of quasicrystals is verified using transmission electron microscopy; however, this technique requires significantly more elaboration than rapid and automatic powder X-ray diffraction. Therefore, to facilitate the search for novel quasicrystals, developing a rapid technique for phase-identification from powder diffraction patterns is desirable. This paper reports the identification of a new Al-Si-Ru quasicrystal using deep learning technologies from multiphase powder patterns, from which it is difficult to discriminate the presence of quasicrystalline phases even for well-trained human experts. Deep neural networks trained with artificially generated multiphase powder patterns determine the presence of quasicrystals with an accuracy >92% from actual powder patterns. Specifically, 440 powder patterns are screened using the trained classifier, from which the Al-Si-Ru quasicrystal is identified. This study demonstrates an excellent potential of deep learning to identify an unknown phase of a targeted structure from powder patterns even when existing in a multiphase sample.

Growth of a quasicrystal-related structure and superstructure for ultrathin Ce-Ti-O films on Pt(111).

Herein, oxide quasicrystal-related (OQC-R) structure and Ce-Ti-O-(3 × 3) superstructure ultrathin films were prepared on Pt(111) and characterized using scanning tunneling microscopy (STM) and low-energy electron diffraction. The OQC-R structure with dodecagonal clusters consisting of triangles, squares, and rhombuses was observed in STM images. The first discovery of the OQC-R structure with a magnetic rare earth metal expands the possibility of discovering new oxide quasicrystals with novel magnetism or superconductivity. By depositing Ti on an OQC-R ultrathin film and post-annealing, a honeycomb lattice of the Ce-Ti-O-(3 × 3) superstructure was prepared. From X-ray photoelectron spectroscopy (XPS) and resonant-photoelectron spectroscopy, the chemical states of the Ce and Ti atoms in the OQC-R structure corresponded to the Ce3+ and Ti2+ states, while those for the Ce-Ti-O-(3 × 3) superstructure corresponded to the Ce3+, Ti3+, and Ti2+ states. The phase transformation from the OQC-R structure to the Ce-Ti-O-(3 × 3) honeycomb superstructure likely occurred when the amount of Ti increased and was more oxidized. The elemental atomic density was also calibrated using XPS and Rutherford backscattering spectroscopy. These results propose tentative structural models of the OQC-R structure as Ce18Ti14O41 and the Ce-Ti-O-(3 × 3) superstructure as CeTi6O9.

A four-dimensional model for the Ba-Ti-O dodecagonal quasicrystal.

A four-dimensional (4D) model is presented of the first oxide dodecagonal quasicrystal found in a Ba-Ti-O ultra-thin film on a Pt(111) single-crystal substrate. The 4D model, with a 4D dodecagonal lattice constant ad = 8.39 Å, was derived by considering a tile decoration model of dodecagonal Niizeki-Gähler tiling composed of squares, triangles and 30° rhombuses. The model consists of four kinds of occupation domain, and 4D positional vectors defining the shape of each occupation domain are given. Moreover, the atomic arrangement of two Ba-Ti-O periodic approximants, the sigma-phase approximant and a 25.6 Šapproximant were derived from the 4D model by the introduction of linear phason strains.

Experimental Observation of Long-Range Magnetic Order in Icosahedral Quasicrystals.

Quasicrystals (QCs), first discovered in 1984, generally do not exhibit long-range magnetic order. Here, we report on long-range magnetic order in the real icosahedral quasicrystals (i QCs) Au-Ga-Gd and Au-Ga-Tb. The Au65Ga20Gd15 i QC exhibits a ferromagnetic transition at TC = 23 K, manifested as a sharp anomaly in both magnetic susceptibility and specific heat measurements, along with an appearance of magnetic Bragg peak below TC. This is the first observation of long-range magnetic order in a real quasicrystal, in contrast to the spin-glass-like behaviors observed for the other magnetic quasicrystals found to date. Moreover, when Gd is replaced by Tb, i.e., for the Au65Ga20Tb15 i QC, a ferromagnetic behavior is still retained with TC = 16 K. Although the sharp anomaly in the specific heat observed for the Au65Ga20Gd15 i QC becomes broadened upon Tb substitution, neutron diffraction experiments clearly show marked development of magnetic Bragg peaks just below TC, indicating long-range magnetic order for the Au65Ga20Tb15 i QC also. Our findings can contribute to the further investigation of exotic magnetic orders formed on real quasiperiodic lattices with unprecedented highest global symmetry, i.e., icosahedral symmetry.

PyQCstrc.ico: a computing package for structural modelling of icosahedral quasicrystals.

The atomic structure of quasicrystals (QCs) is described as a section of a higher-dimensional structure that consists of a periodic arrangement of occupation domains (ODs). Determination of the shape of ODs and their partitioning is crucial in the structural analysis of QCs. However, owing to the complicated shape of ODs, building the initial structure model requires a great deal of time and effort. Thus, a computer program for building structure models of QCs is needed. Presented here is a Python3 package for structure modelling of icosahedral QCs.

Structural-transition-driven antiferromagnetic to spin-glass transition in Cd-Mg-Tb 1/1 approximants.

The magnetic susceptibility of the 1/1 approximants to icosahedral quasicrystals in a series of Cd85-xMgxTb15 (x = 5, 10, 15, 20) alloys was investigated in detail. The occurrence of antiferromagnetic to spin-glass-like transition was noticed by increasing Mg. Transmission electron microscopy analysis evidenced a correlation between the magnetic transition and suppression of the monoclinic superlattice ordering with respect to the orientation of the Cd4 tetrahedron at T > 100 K. The possible origins of this phenomenon were discussed in detail. The occurrence of the antiferromagnetic to spin-glass-like magnetic transition is associated with the combination of chemical disorder due to a randomized substitution of Cd with Mg and the orientational disorder of the Cd4 tetrahedra.

Magnetic properties of icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems.

A systematic investigation has been performed to elucidate effects of rare earth type and structural complexity on magnetic properties of icosahedral quasicrystal (iQC) and their cubic approximants (APs) in the ternary Cd-Mg-RE (RE = Gd, Tb, Dy, Ho, Er, and Tm) systems. At low temperatures, iQCs and 2/1 APs exhibit spin-glass-like freezing for RE = Gd, Tb, Dy, and Ho, while for Er and Tm they do not show freezing behavior down to the base temperature ∼2 K. The 1/1 APs exhibit either spin-glass-like freezing or antiferromagnetic (AFM) ordering depending on their constituent Mg content. The T f values show increasing trend from iQC to 2/1 and 1/1 APs. In contrast, the absolute values of Weiss temperature for iQCs are larger than those in 2/1 and 1/1 APs, indicating that the total AFM interactions between the neighboring spins are larger in aperiodic, rather than periodic systems. Competing spin interactions originating from the long-range Ruderman-Kittel-Kasuya-Yoshida mechanism along with chemical disorder of Cd/Mg ions presumably account for the observed spin-glass-like behavior in Cd-Mg-RE iQCs and APs.

Formation of an Intermediate Valence Icosahedral Quasicrystal in the Au-Sn-Yb System.

We report on the formation of a new icosahedral quasicrystal (iQC) in the Au-Sn-Yb alloy system. This iQC has a primitive icosahedral lattice with a lattice constant aico of 0.5447(7) nm and a composition that was determined to be Au60.0Sn26.7Yb13.3. X-ray absorption spectroscopy measurement of the near Yb L3 edge demonstrates that the Yb valence in the iQC is an intermediate valence between divalent (4f14) and trivalent (4f13) at ambient pressure and was determined to be 2.18+. The results are compared to those for a corresponding 2/1 cubic approximant crystal. The formation of this new iQC is discussed in terms of the atomic size factor (δ) and the valence electron-to-atom ratio (e/a).

Synthesis and Atomic Structure of the Yb-Ga-Au 1/1 Quasicrystal Approximant.

The Yb-Ga-Au 1/1 quasicrystal approximant (AP) composition ranges from Yb14.0Ga20.6Au65.4 to Yb14.8Ga46.3Au38.9, and single crystals of the 1/1 AP having the composition Yb13.8Ga26.1Au60.1 were obtained by the self-flux technique. X-ray structural analysis demonstrated that the atomic structure [space group Im3; a = 14.6889(9) Å] can be described by the body-centered packing of Tsai-type rhombic triacontahedron (RTH) clusters. The positional disorder in these clusters, interpreted as the average of an orientationally disordered tetrahedron and triangle, results in positional disorder in the outer shells. The elemental distributions and positions of mixtures of Au and Ga atoms in the RTH clusters correspond to those in the isostructural Yb15Al36Au49 1/1 AP.

Probing Single Pt Atoms in Complex Intermetallic Al13Fe4.

The atomic structure of a 0.2 atom % Pt-doped complex metallic alloy, monoclinic Al13Fe4, was investigated using a single crystal prepared by the Czochralski method. High-angle annular dark-field scanning transmission electron microscopy showed that the Pt atoms were dispersed as single atoms and substituted at Fe sites in Al13Fe4. Single-crystal X-ray structural analysis revealed that the Pt atoms preferentially substitute at Fe(1). Unlike those that have been reported, Pt single atoms in the surface layers showed lower activity and selectivity than those of Al2Pt and bulk Pt for propyne hydrogenation, indicating that the active state of a given single-atom Pt site is strongly dominated by the bonding to surrounding Al atoms.

Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal.

The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections.

Short- and long-range ordering during the phase transition of the Zn6Sc 1/1 cubic approximant.

Using in situ x-ray scattering and synchrotron radiation, we have experimentally elucidated the mechanism of the cubic to monoclinic phase transition in the Zn6Sc 1/1 approximant to an icosahedral quasicrystal. The high-temperature cubic phase is described as a bcc packing of a large Tsai-type icosahedral cluster whose center is occupied by an orientationally disordered Zn4 tetrahedron. A clear monoclinic distortion has been found to take place within 2 K around Tc = 157 K, in excellent agreement with the observed anomalies in the electrical resistivity and heat capacity. Also, a rapid variation of the super-structure reflection intensity is observed. The low-temperature monoclinic phase, as determined by single-crystal x-ray diffraction at 40 K, has been confirmed to consist of ordered Zn4 tetrahedra, oriented in an anti-parallel way along the [[Formula: see text]] direction. Above Tc, a diffuse scattering signal is observed at the position of the super-structure reflections, which evidences that a short-range ordering of the Zn4 tetrahedra takes place. In a way similar to a second-order phase transition, the correlation length describing this short-range ordering increases rapidly when the temperature diminishes and almost diverges when the temperature is close to Tc, going from 200 Å at 220 K to reach the very large value of 1200 Å at 161 K. Finally, using single-crystal x-ray diffraction, the atomic structure of the low-temperature monoclinic super-structure (space group C2/c) could be solved. The ordering of the Zn4 tetrahedra is accompanied by a strong distortion of the surrounding shells.

Ordering and dynamics of the central tetrahedron in the 1/1 Zn6Sc periodic approximant to quasicrystal.

Periodic approximants to quasicrystals offer a unique opportunity to better understand the structure, physical properties and stabilizing mechanisms of their quasicrystal counterparts. We present a detailed study of the order-disorder phase transition occurring at about 160 K in the Zn(6)Sc cubic approximant to the icosahedral quasicrystal i-MgZnSc. This transition goes along with an anti-parallel ordering of the tetrahedra located at the centres of large atomic clusters, which are packed on a bcc lattice. Single crystal x-ray diffuse scattering shows that the tetrahedra display pre-transitional short range ordering above T(c) (Yamada et al 2012 in preparation). Using quasielastic neutron scattering (QENS) we clearly evidence this short range order to be dynamical in nature above T(c). The QENS data are consistent with a model of tetrahedra 'jumping' between almost equivalent positions, which is supported by molecular dynamics simulations. This demonstrates a unique dynamical flexibility of the Zn(6)Sc structure even at room temperature.