Ternary Quasicrystals Research Articles

Compositions of Al-Based Quasicrystals Interpreted by Cluster Formulae

It is known previously that bulk metallic glass compositions satisfy cluster formulae [cluster](glue atom)1,3 of 24 valence electrons as deduced from our cluster-resonance model. In the present work, it is further shown that compositions of Al-based binary and ternary quasicrystals are also explained by 24-electron cluster formulae of the types [icosahedron](glue atom)0,1, where the icosahedral cluster is identi ed from a corresponding crystalline approximant according to dense atomic packing and cluster isolation criteria, and the glue atom site is either vacant for an icosahedral quasicrystal or equal to one for a decagonal quasicrystal. Ternary quasicrystals are formulated with the same formulae as their basic binary ones but the icosahedron shell sites are substituted by third elements. The 24-electron cluster formulae are then the chemical and electronic structural units of quasicrystals, mimicking the molecular formulae of chemical substances.

Crystal chemistry and chemical order in ternary quasicrystals and approximants

In this work we review our current understanding of structure, stability and formation of icosahedral quasicrystals and approximants. The work has special emphasis on Cd–Yb type phases, but several concepts are generalized to other families of icosahedral quasicrystals and approximants. The paper handles topics such as chemical order and site preference at the cluster level for ternary phases, valence electron concentration and its influence on formation and composition, fundamental building blocks and cluster linkages, and the similarities and differences between different families of icosahedral quasicrystals and approximants.

A cluster line approach for composition rules of quasicrystals and bulk metallic glasses

This paper analyzes the structure and composition characteristics of ternary quasicrystals and bulk metalic glasses from the viewpoint of atomic clusters. It is pointed out that quasicrystals and bulk metallic glasses satisfy a cluster line rule. The cluster line refers to a straight composition line linking a specific cluster to the third element in a ternary alloy phase diagram. A ternary quasicrystal or bulk metallic glass composition is located at the intersection point of two cluster lines. Ternary quasicrystal and bulk metallic glass compositions can be the expressed with a cluster-plus-glue-atom model which can predict new ternary bulk metallic glasses.

Cluster-based composition rule for stable ternary quasicrystals in Al-(Cu, Pd, Ni)-TM systems

Although hundreds of quasicrystals have been found, little is known about their quantitative composition rules that can help design new materials. In this paper we propose a cluster-based approach to decipher the composition rules. Our approach consists of the following steps: (1) selection of a known basic cluster in the constituent binary systems; (2) construction of a cluster line linking the binary cluster composition to a third element; and (3) the intersection of the two cluster lines points to a new quasicrystal composition if the e/a ratio falls in the appropriate range, typically from 1.8 to 2.0. The predicted compositions agree satisfactorily with experimental values.

Quasicrystals in the Ti–Zr–Ni alloy system

The empirical compositional criteria for ternary quasicrystals (QCs) based on the QCs’ phase diagram features are applied in the Ti–Zr–Ni alloy system. The ideal quasicrystals-forming composition Ti 40Zr 40Ni 20 has been identified, which lies at the crossing point of the two specific lines, termed as e/ a-constant and e/ a-variant lines. Bulk quasicrystalline Ti/Zr-based alloys are obtained in region of (Ti x Zr 100− x ) 100− y Ni y (43.75⩽ x⩽81.25, y=17, 20 in at.%) by copper mold casting. It was confirmed that Ti 40Zr 40Ni 20 is the optimal QC-forming composition, where a nearly pure bulk quasicrystal rod, 6 mm in diameter, can be formed. With a small deviation from this ideal composition, the Ti(Zr) solid solution phases and/or C14-type Laves phase, though as minority phases, are found coexisting with the majority icosahedral phase. At the same time, the explanation of the e/ a-variant line is explored.

Thermoelectric Properties of Binary Cd–Yb Quasicrystal and Its Approximant

The thermoelectric properties of the binary quasicrystal Cd84.6Yb15.4 and its approximant Cd6Yb are reported. The thermopowers decrease linearly from 14 and 12 µV/K, respectively, with decreasing temperature from 300 K. The resistivities at 300 K are 180 and 150 µΩ·cm, respectively, and decrease rapidly on cooling below 100 K. These results indicate that Cd–Yb compounds possess a metallic nature, in contrast to the semiconductor-like behavior of conventional ternary quasicrystals. The phonon thermal conductivity κph(T) of Cd–Yb compounds shows no maximum, but is described by a power law, κph∝Tn, with n=0.5 and 1.0, respectively, for Cd84.6Yb15.4 and Cd6Yb. The thermoelectric dimensionless figures of merit ZT are estimated to be 0.003 and 0.004 at 300 K, respectively.

Electronic properties of ternary quasicrystals in one dimension

The one-electron properties of a certain class of one-dimensional ternary quasicrystals are investigated. In particular, we show in detail the presence of a special kind of critical states called marginal critical states in these QCs. By the use of a real-space renormalization-group method, it is shown that the scaling properties of marginal critical states are characterized by stretched exponentials. These states are virtually localized, so that their presence may make a QC less conductive.

Formation rule for Al-based ternary quasi-crystals: Example of Al–Ni–Fe decagonal phase

After examining ternary Al-based quasi-crystalline phase diagrams, we pointed out that the presence of e/a-constant and e/a-variant lines is a common phenomenon. Ternary quasi-crystal compositions are located at the crossing point of these lines in ternary phase diagrams. Such an empirical rule can be used to predict the ternary quasi-crystal compositions from binary ones. We applied this rule to the Al–Fe–Ni system and clarified the decagonal phase composition zone. There are two decagonal phases, D-Al72.5Fe14.5Ni13 and D′-Al705Fe12Ni17.5, that correspond respectively to Al–Fe-based and Al–Ni-based decagonal phases in the same ternary system.

Physics of complex metals: Temperature-dependent resistivities in ionic superconductors and stable quasicrystals.

Elementary phase-space arguments for electron-phonon scattering in metals give the temperature-dependent resistivity \ensuremath{\rho}(T)\ensuremath{\sim}${\mathit{T}}^{\mathit{n}}$ with n\ensuremath{\ge}3. Similarly for electron-electron scattering n=2. To explain n=1 for superconductive (Bi,Sr${)}_{4}$${\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ over the range 7T700 K one can assume a structural model with punctured semiconductive domain walls. There is strong evidence for this model not only in oxide perovskites, but also in Chevrel compounds such as ${\mathrm{EuMo}}_{6}$${\mathrm{S}}_{8\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{O}}_{\mathit{x}}$, which also exhibit linear \ensuremath{\rho}(T) over a narrower temperature range. In the domain-wall model recoil energy and momentum are absorbed by the walls, much as umklapp momentum is absorbed by the crystal as a whole in pure polyvalent metals. A wide range of experimental data support the model. By-products of the model are explanations of carrier freeze-out as measured by diverse anomalies in the Hall resistance, the correlation of ${\mathit{T}}_{\mathit{c}}$ with the slope of the linear background tunneling conductance of Pb-Bi-O superconductors, a simple qualitative explanation for the first- (second-) order electronic (structural) phase transition observed near x=0.21 in well-annealed ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$, and an explicit mechanism for the origin of c-axis linear resistivities in intercalated Bi-Sr cuprates. A similar microstructural model explains the linear temperature dependence of the hopping conductance in stable ternary quasicrystals. The key factor common to both ionic superconductors and stable quasicrystals is their multinary composition which creates hierarchies of saddle points in the local conductance.

Predicting quasicrystals with quantum structural diagrams

Binary and ternary quasicrystals have been successfully separated by means of quantum structural diagrams in the light of new experimental data, and new potential candidates for the quasicrystalline state are presented. A general and simple classification of alloy systems, consistent with the experimental data, is proposed, which allows predictions of any type of binary and ternary quasicrystals. Quantum coordinates are analyzed and interpreted, and suggestions are given for an improvement of the present method.

Quantum diagrams and the prediction of new ternary quasicrystals.

We use the quantum-diagram technique to identify the chemical factors which favor quasicrystal formation. Expressed diagrammatically, these factors provide severe constraints on compositions at which quasicrystals or high-order rational approximants are likely to form. We outline several computerized search strategies which utilize the diagrammatic conditions to identify compositions for experimental investigation, and give examples of typical results.

Icosahedral quasicrystals and quantum structural diagrams.

Stable crystalline compound analogs of ternary quasicrystals are successfully isolated by quantum structural diagrams, which also predict many possible new quasicrystals. Physical mechanisms responsible for the formation and certain features of quasicrystals are suggested, including the six-dimensionality of the hypercubic protolattices.