Tsutomu Ishimasa

Icosahedral quasicrystals in Zn–T–Sc (T = Mn, Fe, Co or Ni) alloys

Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a 6D ranging from 7.044 to 7.107 Å. They have valence electron concentrations e/a ranging from 2.01 to 2.14, and almost the same ratios between the edge length a R of the Penrose tile and the averaged atomic diameter . Moreover other Zn- and Cd-based quasicrystals, including the same type of atomic Tsai–type cluster, have the same values of e/a ≈ 2.1 and . The equality in e/a indicates that the Hume-Rothery mechanism plays an important role for the formation of these quasicrystals.

Icosahedral quasicrystal and 1/1 cubic approximant in Au–Al–Yb alloys

A P-type icosahedral quasicrystal is formed in an Au–Al–Yb alloy with a six-dimensional lattice parameter a 6D = 7.448 Å. The composition of the quasicrystal was analyzed to be Au51Al34Yb15. The quasicrystal is formed in as-cast alloys and is regarded as metastable with decomposition to other crystalline phases during annealing at 700°C. Among Tsai-type quasicrystals, this quasicrystal is situated just between the Zn–Sc group with a smaller a 6D and the larger Cd–Yb group. The intermediate valence of Yb recently observed in this quasicrystal may be due to this unique situation, namely a smaller major component in Au-Al-Yb than in Cd–Yb. The predominant phase in the annealed specimen is a 1/1 cubic approximant with lattice parameter a = 14.500 Å belonging to the space group Im . This phase is stable at the composition Au51Al35Yb14 at 700°C. Rietveld structural analysis indicated that the crystal structure is a periodic arrangement of Tsai-type clusters with four Au–Al atoms at their centers. Chemical ordering of Au and Al is characteristics of this approximant.

A New Series of Icosahedral Quasicrystals in Zn-M-Sc (M = Ag, Au, Pd, Pt) Alloys

A new series of icosahedral quasicrystals has been found in Zn75M10Sc15 (M = Ag, Au, Pd and Pt) as-cast alloys. Electron and powder X-ray diffraction analyses indicated that these quasicrystals are of the P-type (primitive type) and have six-dimensional lattice parameters a6D=0.7112–0.7151 nm. The quasicrystals are formed as main phases in these alloys. In the Zn80Ag5Sc15 alloy annealed at 981 K for 24 h, a Zn85Sc15-type cubic phase is formed exclusively, which has the lattice parameter a=1.3867 nm. The cubic phase is interpreted as a 1/1 approximant of Zn75Ag10Sc15. This observation, as well as intensity similarity in the X-ray diffraction patterns, suggests that Zn75M10Sc15 quasicrystals belong to the same group as the Zn80Mg5Sc15 quasicrystal from the viewpoint of a local atomic configuration.

A Zn-based icosahedral quasicrystal classified into the same structure type as Cd-based icosahedral quasicrystals?

Abstract New icosahedral quasicrystals have been discovered in Zn–Mg–Sc and Zn–Mg–Ti alloy systems. The former forms at the alloy composition of Zn80Mg5Sc15, and belongs to P-type (aP=0.7111 nm) showing high degree of structural perfection. The icosahedral atomic cluster included in 1/1 approximant crystal, Zn17Sc3, suggests that the Zn–Mg–Sc icosahedral quasicrystal has structural similarity to the Cd-based icosahedral quasicrystals recently reported. Preliminary study of Zn–Mg–Ti alloys has revealed that two types of icosahedral quasicrystals form near the alloy composition of Zn84Mg8Ti8; namely P-type icosahedral quasicrystal with aP=0.7023 nm, and F-type icosahedral quasicrystal exhibiting very weak superlattice reflections. The Zn–Mg–Sc and Zn–Mg–Ti quasicrystals have common features on diffraction intensity, stoichiometric composition, and average concentration of valence electrons.

New icosahedral quasicrystals formed in Cu-based ternary alloys

New Cu-based P-type icosahedral quasicrystals have been observed in the ternary Cu–(Ga or Al)–Sc alloy systems. The Cu–Ga–Sc quasicrystal forms almost exclusively in a rapidly quenched Cu48Ga34Sc18 alloy, and has a six-dimensional lattice parameter a 6D = 0.6930 nm. The as-cast alloy with the same composition contains no quasicrystal but has a 1/1 bcc approximant as its main phase. The Cu–Al–Sc quasicrystal forms at the alloy composition Cu46Al38Sc16 both in an as-cast alloy and in alloys aged at 776 and 873 K, and has a lattice parameter a 6D = 0.6959 nm. Although electron diffraction patterns exhibit rather strong deviation from the ideal symmetric positions for weak reflections, the presence of the quasicrystal in the aged Cu–Al–Sc alloys indicates that this phase is a candidate of a stable phase in this ternary system.

Quasiperiodic long-range ferrimagnetic order in Ising model simulation in an icosahedral quasicrystal model structure

Abstract A new type of ferrimagnetic order was found in a Monte Carlo simulation of quasiperiodic magnetic system at low temperatures, which includes Ising spins arranged on the F-type quasiperiodic lattice. The spin occupation domains (or acceptance regions) in the phason space revealed the new type of ferrimagnetism consisting of two subdomains corresponding to up- and down-spins, which definitely indicated the quasiperiodic long-range nature of this ferrimagnetic order. A structure model of the Zn–Mg–Ho icosahedral phase was adopted as a three-dimensional quasicrystal model for this simulation. Ruderman–Kittel–Kasuya–Yosida (RKKY)-like alternating exchange interaction was assumed to extend to the fourth shortest distance. The elastic magnetic diffraction patterns from spin-dependent scattering consisted of sharp spots indicating a long-range order of the magnetic structure. Each diffraction spot could be indexed by six integers of all odd or all even, and this fact indicated F-type symmetry of the ferrimagnetic order which reflects the F-type symmetry of the structure.

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

Quasicrystals are long-range ordered materials that 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.

Phason space analysis and structure modelling of 100 Å-scale dodecagonal quasicrystal in Mn-based alloy

The dodecagonal quasicrystal classified into the five-dimensional space group P126/mmc, recently discovered in a Mn–Cr–Ni–Si alloy, has been analysed using atomic-resolution spherical aberration-corrected electron microscopy, i.e. high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and conventional transmission electron microscopy. By observing along the 12-fold axis, non-periodic tiling consisting of an equilateral triangle and a square has been revealed, of which common edge length is a = 4.560 Å. These tiles tend to form a network of dodecagons of which size is a ≈ 17 Å in diameter. The tiling was interpreted as an aggregate of 100 Å-scale oriented domains of high- and low-quality quasicrystals with small crystallites appearing at their boundaries. The quasicrystal domains exhibited a densely filled circular acceptance region in the phason space. This is the first observation of the acceptance region in an actual dodecagonal quasicrystal. Atomic structure model consistent with the electron microscopy images is a standard Frank-Kasper decoration of the triangle and square tiles that can be inferred from the crystal structures of Zr4Al3 and Cr3Si. Four kinds of layers located at z = 0, ±1/4 and 1/2 are stacked periodically along the 12-fold axis, and the atoms at z = 0 and 1/2 form hexagonal anti-prisms consistently with the 126-screw axis. The validity of this structure model was examined by means of powder X-ray diffraction.

Approximant of dodecagonal quasicrystal formed in Mn–Si–V alloy

The crystal structure of a hexagonal phase formed in Mn70Si20V10 has been analyzed by the Rietveld method using synchrotron radiation diffraction data. Analysis was carried out by assuming an average metallic element Mn0.875V0.125 via high resolution electron microscopy. The space group of the refined model is P6/mmm (No. 191) and the unit cell includes 18.9 Si and 78.1 metallic atoms. The lattice parameters are a = 17.058(6) Å, c = 4.640(1) Å. This hexagonal phase is regarded as an approximant of a dodecagonal quasicrystal. The electron diffraction pattern along the c-axis exhibits pseudo 12-fold diffraction symmetry. In the c-projection, the structure is interpreted as the tiling of two types of local structural units, namely an equilateral triangle and square with the same edge length of 4.57 Å, which correspond to A15-type and Zr4Al3-type structures in the three dimensions, respectively. Both bond orientational order and scaling property, characteristic of a dodecagonal quasicrystal, are imitated in this periodic tiling.

Dodecagonal quasicrystal in Mn-based quaternary alloys containing Cr, Ni and Si

A dodecagonal quasicrystal showing 12-fold symmetry forms in Mn-rich quaternary alloys containing 5.5 or 7.5 at.% Cr, 5.0 at.% Ni and 17.5 at.% Si. After annealing at 700 °C for 130 h, the quasicrystal precipitated in a matrix of β-Mn-type crystalline phase. The shape of the quasicrystal is needle-like having a length of several tens of micrometres. Electron diffraction as well as powder X-ray diffraction experiments has revealed the following characteristics of the quasicrystal: diffraction symmetry 12/mmm, the presence of systematic extinction for h1h2h2h1h5-type reflections with odd h5 index, and then five-dimensional space group P126/mmc. Indexing of the reflections indicated that the dimension of the common edge in the equilateral triangle–square tiling is 4.560 Å, and the periodicity is 4.626 Å along the 12-fold axis. This is the first example of the dodecagonal quasicrystal synthesized by ordinary metallurgical method in 3-d transition-metal alloys.