Tsai-type Cluster Research Articles

Formation of 2/1 and 1/1 approximants in a quaternary Al–Pd–Au–Yb system

In this study, 2/1 and 1/1 approximants in a quaternary Al–Pd–Au–Yb system were synthesized by substituting Au into original Al–Pd–Yb quasicrystals. In the Al50Pd24Au10Yb16 and Al52Pd22Au10Yb16 alloys, 2/1 and 1/1 phases were formed, respectively, and the lattice constants were relatively small—2.314 and 1.431 nm for the 2/1 and 1/1 phases, respectively. Scanning transmission electron microscopy revealed that both approximants comprise Tsai-type atomic clusters. Inverse magnetic susceptibility for the approximants obeyed the Curie–Weiss law, indicating the presence of paramagnetism. The effective magnetic moments were estimated to be 3.20 μB and 2.94 μB for the 2/1 and 1/1 phases, respectively, indicating that Yb in both approximants adopts an intermediate valence state.

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

ABSTRACT 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, has been proposed. Here τ 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.

Concomitant singularities of Yb-valence and magnetism at a critical lattice parameter of icosahedral quasicrystals and approximants

Non-Fermi-liquid (NFL), a significant deviation from Fermi-liquid theory, usually emerges near an order-disorder phase transition at absolute zero. Recently, a diverging susceptibility toward zero temperature was observed in a quasicrystal (QC). Since an electronic long-range ordering is normally absent in QCs, this anomalous behaviour should be a new type of NFL. Here we study high-resolution partial-fluorescence-yield x-ray absorption spectroscopy on Yb-based intermediate-valence icosahedral QCs and cubic approximant crystals (ACs), some of which are new materials, to unveil the mechanism of the NFL. We find that for both forms of QCs and ACs, there is a critical lattice parameter where Yb-valence and magnetism concomitantly exhibit singularities, suggesting a critical-valence-fluctuation-induced NFL. The present result provides an intriguing structure–property relationship of matter; size of a Tsai-type cluster (that is a common local structure to both forms) tunes the NFL whereas translational symmetry (that is present in ACs but absent in QCs) determines the nature of the NFL against the external/chemical pressure.

Atomic-Scale Tuning of Tsai-Type Clusters in RE-Au-Si Systems (RE = Gd, Tb, Ho).

Tsai-type quasicrystals and approximants are distinguished by a cluster unit made up of four concentric polyhedral shells that surround a tetrahedron at the center. Here we show that for Tsai-type 1/1 approximants in the RE–Au–Si systems (RE = Gd, Tb, Ho) the central tetrahedron of the Tsai clusters can be systematically replaced by a single RE atom. The modified cluster is herein termed a “pseudo-Tsai cluster” and represents, in contrast to the conventional Tsai cluster, a structural motif without internal symmetry breaking. For each system, single-phase samples of both pseudo-Tsai and Tsai-type 1/1 approximants were independently prepared as millimeter-sized, faceted, single crystals using the self-flux synthesis method. The full replacement of tetrahedral moieties by RE atoms in the pseudo-Tsai 1/1 approximants was ascertained by a combination of single-crystal and powder diffraction studies, as well as energy dispersive X-ray spectroscopy (EDX) analyses with a scanning electron microscope (SEM). Differential scanning calorimetry (DSC) studies revealed distinctly higher decomposition temperatures, by 5–35 K, for the pseudo-Tsai phases. Furthermore, the magnetic properties of pseudo-Tsai phases are profoundly and consistently different from the Tsai counterparts. The onset temperatures of magnetic ordering (Tmag) are lowered in the pseudo-Tsai phases by ∼30% from 24 to 17 K, 11.5 to 8 K, and 5 to 3.5 K in the Gd–Au–Si, Tb–Au–Si, and Ho–Au–Si systems, respectively. In addition, the Tb–Au–Si and Ho–Au–Si systems exhibit some qualitative changes in their magnetic ordering, indicating decisive changes in the magnetic state/structure by a moment-bearing atom at the cluster center.

Analyzing by the Two-Level System and Conduction Mechanism of Icosahedral Quasicrystals CdYb and CdMgYb

We have presented one of possible mechanisms for anomalous transport properties in Tsai-type quasicrystals CdYb and CdMgYb. The tunneling process between the Tsai-type clusters has been argued in dilute bound approximation of dynamics of the two-level system.

Bias-voltage dependent STM images from the 2–fold surface of the icosahedral Ag-In-Yb quasicrystal

The 2–fold surface of the icosahedral (i-)Ag–In–Yb quasicrystal has been investigated using scanning tunnelling microscopy (STM). STM data reveals a bias-voltage dependency. At high positive bias, bright protrusions are observed. At negative bias, new protrusions appear while the size of the original protrusions decreases. The STM features at both positive and negative bias polarities can be related to atomic planes intersecting the centre of Tsai-type clusters (the building blocks of the bulk structure). The bias-dependency can be explained by a change in contribution in tunnelling current from Yb and Ag/In, as expected from density of states calculations.

Icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Y, Sm, Gd, Tb, Dy, Ho, Er, Tm) systems

The formation and stability of icosahedral quasicrystals and their cubic approximants in the Cd-Mg-RE (RE = Y, Sm, Gd, Tb, Dy, Ho, Er, Tm) systems are studied in detail, with a focus on the effects of Mg substitution as well as the dependence on temperature and RE species. The results show that the compositional region of the icosahedral phase in the ternary phase diagram shrinks gradually as the RE element becomes smaller in atomic size. This phenomenon is correlated with the geometric ‘stability’ of a so-called Tsai-type cluster described as a packing of spheres that represent the atomic radii of the constituent elements. Moreover, the icosahedral quasicrystals are found to be stabilized at lower RE concentrations (12–13.5 at.%) and temperatures (T < 773 K) compared to their cubic approximants, contrary to earlier findings for the Cd-Mg-Yb system. Single grains of the icosahedral, 2/1 and 1/1 cubic approximant phases with, respectively, rhombic triacontahedron, octahedron and rhombic dodecahedron morphologies ranging ≈1.5–2.5 mm in diameter are further synthesized using a self-flux method. It is confirmed that the bounding facets of the single grains are {111} and {110} for the 2/1 and 1/1 cubic approximants, respectively, through orientation analysis using electron backscatter diffraction. Finally, microstructures involving the Cd-Mg-RE icosahedral quasicrystal and Cd-Mg hexagonal solid solution are analysed to show parallel alignment of 2-fold rotational axes of the former with the 6-fold and 2-fold rotational axes of the latter. This orientation relationship is further discussed in terms of the coincidence of interplanar spacings between the two phases.

Formation of Ga–Pd–Sc icosahedral quasicrystal and approximant phases

ABSTRACTWe report the formation of an icosahedral quasicrystal and its approximant in the Ga–Pd–Sc alloy. The primitive-type quasicrystal with a six-dimensional lattice constant of 0.713 nm formed in the melt-quenched Ga53Pd30Sc17 alloy, with a similar composition to that of the Ga55Pd30Sc15 1/1 approximant. The atomic-scale observation and chemical analysis of the 1/1 approximant by scanning transmission electron microscopy and energy-dispersive X-ray spectroscopy showed that the approximant consisted of Tsai-type clusters with a characteristic chemical ordering. Furthermore, a series of approximants were observed in the Ga55Pd30RE15 alloys by replacing Sc with other rare-earth elements (REs) (RE = Y, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu). These approximants, which have relatively small lattice constants and consequently smaller RE–RE distances compared with those for other RE-containing Tsai-type approximants, may be candidates for materials with novel electronic and magnetic properties similar to those observed in Au-based quasicrystals and approximants.

Atomic structures of ternary Yb–Cd–Mg icosahedral quasicrystals and a 1/1 approximant

Atomic structures of ternary icosahedral (i) Yb–Cd–Mg quasicrystals (QCs) with five different Mg contents up to 46.4 at.% and a corresponding 1/1 approximant (AP), which has a composition of Yb13.3Cd70.3Mg16.5, have been analysed by single-crystal X-ray diffraction. The structures of the iQCs were found to be isostructural to the parent i-YbCd5.7, which consists of a so-called Tsai-type rhombic triacontahedron (RTH) cluster and double Friauf polyhedron, and that of the 1/1 AP was found to be isostructural to YbCd6, which is described by a body-centred packing of the same type of RTH cluster. In the iQCs, it was found that there are three types of Cd/Mg occupation, namely, Cd preferential site, Mg preferential site and Cd/Mg mixed site, and the occupation probabilities of Mg atoms at the Mg preferential site show a saturation behaviour around the Mg content of 20 at.%. This selective Mg occupation is identified as a cause of the non-linear increase in the icosahedral lattice constant with increasing Mg content. The 1/1 AP has a similar selective Mg occupation to that of the iQCs in terms of the shell structures of the Tsai-type RTH cluster. In both iQCs and the 1/1 AP, the Mg preferential sites have a smaller number of Yb atoms among their coordination numbers. Moreover, short-range order (s.r.o.) diffuse scattering was observed on the diffraction patterns of the iQCs at the positions corresponding to a face-centred-type (F-type) icosahedral superlattice. The F-type s.r.o. was found to result from the Mg substitution.

On the Form and Growth of Complex Crystals: The Case of Tsai-Type Clusters

Where are the atoms in complex crystals such as quasicrystals or periodic crystals with one hundred or more atoms per unit cell? How did they get there? The first of these questions has been gradually answered for many materials over the quarter-century since quasicrystals were discovered; in this paper we address the second. We briefly review a history of proposed models for describing atomic positions in crystal structures. We then present a revised description and possible growth model for one particular system of alloys, those containing Tsai-type clusters, that includes an important class of quasicrystals.

Crystal electric field excitations in the quasicrystal approximantTbCd6studied by inelastic neutron scattering

We have performed inelastic neutron scattering measurements on powder samples of the quasicrystal approximant, ${\mathrm{TbCd}}_{6}$, grown using isotopically enriched $^{112}\mathrm{Cd}$. Both quasielastic scattering and distinct inelastic excitations were observed below 3 meV. The intensity of the quasielastic scattering measured in the paramagnetic phase diverges as ${T}_{\mathrm{N}}\ensuremath{\sim}22$ K is approached from above. The inelastic excitations, and their evolution with temperature, are well characterized by the leading term, ${B}_{2}^{0}{O}_{2}^{0}$, of the crystal electric field (CEF) level scheme for local pentagonal symmetry for the rare-earth ions [S. Jazbec et al., Phys. Rev. B 93, 054208 (2016)] indicating that the Tb moment is directed primarily along the unique local pseudofivefold axis of the Tsai-type clusters. We also find good agreement between the inverse susceptibility determined from magnetization measurements using a magnetically diluted ${\mathrm{Tb}}_{0.05}{\mathrm{Y}}_{0.95}{\mathrm{Cd}}_{6}$ sample and that calculated using the CEF level scheme determined from the neutron measurements.

Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism

We report on the six-dimensional (6D) structural refinement of three members of the i-$R$-Cd quasicrystals ($R$ = Gd, Dy, Tm) via synchrotron x-ray diffraction from single-grain samples, and show that this series is isostructural to the i-${\mathrm{YbCd}}_{5.7}$ quasicrystal. However, our refinements suggest that the $R$ occupancy on the Yb icosahedron sites within the Tsai-type atomic cluster is approximately 80%, with the balance taken up by Cd. Similarities between the i-$R$-Cd series and i-${\mathrm{ScZn}}_{7.33}$, and their differences with i-${\mathrm{YbCd}}_{5.7}$ and i-${\mathrm{Ca}}_{15}{\mathrm{Cd}}_{85}$, indicate that there are at least two subclasses of Tsai-type icosahedral quasicrystals. We further show from x-ray resonant magnetic scattering (XRMS) measurements on a set of closely related ${\mathrm{Tb}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{Cd}}_{6}$ 1/1 approximants that the dilution of the magnetic $R$ ions on the icosahedron within the Tsai-type cluster by nonmagnetic Y disrupts the commensurate magnetic ordering in the approximant phase.

Origin of Quantum Criticality in Yb–Al–Au Approximant Crystal and Quasicrystal

To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$, the approximant crystal Yb$_{14}$Al$_{35}$Au$_{51}$ is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits $\chi\sim T^{-0.5}$ for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field $T/B$ over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to the strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size.

Superconductivity of Au–Ge–Yb Approximants with Tsai-Type Clusters

We report the emergence of bulk superconductivity in Au64.0Ge22.0Yb14.0 and Au63.5Ge20.5Yb16.0 below 0.68 and 0.36 K, respectively. This is the first observation of superconductivity in Tsai-type crystalline approximants of quasicrystals. The Tsai-type cluster center is occupied by Au and Ge ions in the former approximant, and by an Yb ion in the latter. For magnetism, the latter system shows a larger magnetization than the former. To explain this observation, we propose a model that the cluster-center Yb ion is magnetic. The relationship between the magnetism and the superconductivity is also discussed.

First Observation of Superconductivity in New Alloys with Tsai-Type Clusters

Deguchi et al. have reported the first observation of bulk superconductivity in new alloys of Tsai-type crystalline approximants of quasicrystals.

Crystal Structure of Superconducting 1/1 Cubic Au–Ge–Yb Approximant with Tsai-Type Cluster

We report the synthesis of a single-phase sample of the superconducting crystalline approximant Au64.0Ge22.0Yb14.0 and present a structure model refined by Rietveld analysis for X-ray diffraction data.

Formation of an Icosahedral Quasicrystal and Its Approximant in Au-Al-Sc System

The formation of the icosahedral (i-) and 1/1-approximant (1/1-) phases in the Au-Al-Sc system has been investigated. A primitive-type i-phase was found to form in an Au45Al40Sc15 alloy. This i-phase was shown to be thermodynamically stable at 973K. A stable 1/1-phase was found to form at 1173K for compositions of Au44+xAl41¹xSc15 (x = 0, 1, 2, 3). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) revealed that the 1/1-phase consists of Tsai-type icosahedral clusters. Similar local structures were observed in the HAADF-STEM image for the i-phase, indicating that the i-phase consists of Tsai-type clusters identical to the clusters in the 1/1-phase. The composition of the Au-Al-Sc i-phase is consistent with the formation conditions, including those in the valence electrons per atom ratio and in the atomic size factor, which has been shown previously for other Tsai-type i-phases. This fact demonstrates the importance of these conditions for stabilization of Tsai-type i-phases. [doi:10.2320/matertrans.M2014421]

Synthesis and thermal stability of Au-based quasicrystals and its approximants

Various Tsai-type quasicrystals and crystalline approximants have been found in a variety of systems. These compounds are made of Tsai-type icosahedral clusters. Recently, the existence of long-range magnetic orders was reported in Cd6R and Au-SM-R approximants[1,2]. Therefore, it is of interest to investigate the magnetic properties of new alloys systems which are also composed of Tsai-type clusters. In the present work, in order to search new Tsai-type quasicrystals as well as approximants, we have investigated the phase constitution and phase stability in the Au-In-R(R=rare-earth) systems. In this research, alloys of various compositions were prepared by arc melting and were subsequently annealed under various conditions. The phase constitution and phase stability were investigated by X-ray diffraction and differential thermal analysis. As a result, we have observed the formation of 1/1 approximants in the Au-In-R systems and found that they are stable up to high temperatures of ~1000K. The formation condition and stability of icosahedral quasicrytals will be also reported in the presentation.

Tsai-Type Quasicrystal and Its Approximant in Au-Al-Tm Alloys

A P-type icosahedral quasicrystal with a six-dimensional lattice parameter a6D = 7.411 A is formed as an equilibrium phase in Au Al Tm alloy, of which composition was analyzed to be Au46Al38Tm16 by electron probe microanalysis. This quasicrystal is observed as a predominant phase in both as-cast and Au49Al34Tm17 alloys annealed at 910 ◦C, and as one of main phases in the alloy slowly cooled from 1020 ◦C. A 1/1 approximant, Au48Al38Tm14, is also formed near the composition of the quasicrystal. This is a body-centered cubic structure (space group: Im3) with a lattice parameter a = 14.458 A that is an isostructure to the recently reported 1/1 Tsai-type approximant in Au Al Yb. This approximant is characterized by disorderly arranged four Au Al atoms centered at the Tsai-type cluster, presence of atoms at 8c site, and chemical ordering of Au and Al at sites forming a partial triacontahedron.

Formation of Tsai-type 1/1 approximants in In-Pd-RE (RE: rare earth metal) alloys

The formation of the 1/1 crystal approximant phase (1/1 phase) to the icosahedral phase (i phase) in In-Pd-RE (RE: rare earth metal) systems has been investigated. A new series of 1/1 phases were found in In53Pd33RE14 (RE; Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) alloys. For Y, Sm, Gd, Tb, Dy, and Ho, the 1/1 phases were found in annealed alloys, indicating that they are thermodynamically stable. The atomic structure of the 1/1 phases was directly observed by high-angle annular dark-field imaging performed via scanning transmission electron microscopy, revealing that the 1/1 phases consisted of a periodic arrangement of Tsai-type icosahedral clusters. Further, the atomic size effect on i phase formation, as well as formation conditions previously reported for other Tsai-type i and 1/1 phases were examined. It was found that the ratio of the atomic radius of base metals such as In and Pd affects i phase formation. Moreover, the appropriate range of the radius ratio for i phase formation was narrower than that for 1/1 phase formation.