Jianbing Qiang

From clusters to phase diagrams: composition rules of quasicrystals and bulk metallic glasses

Metallic elements having negative enthalpies of mixing tend to form characteristic local atomic clusters. In this review, we use the structural information in the first nearest neighbour shell level, or first-shell atomic cluster, to derive the composition rules of two types of complex alloy phases, quasicrystals and bulk metallic glasses, both being composed of elements with negative enthalpies of mixing. We first show the composition phenomena in quasicrystal-forming systems, where major composition rules such as cluster line, electron concentration and atomic size criteria are derived. Then we analyse the composition rules of bulk metallic glasses using the very same approaches. Finally, we summarize their common composition rules into more general rules and basic theories.

Bulk metallic glasses in the Zr-Al-Ni-Cu system

Abstract Electron concentration and atomic size rules are important criteria for bulk metallic glass formation. According to these rules, a series of new Zr-Al-Ni-Cu amorphous alloys with a constant e/a ratio of 1.4 and an average atomic size of 0.1496 nm was designed. All the alloys have high glass forming abilities, large supercooled liquid regions ΔTx, and large reduced glass transition temperatures Trg. The best glass forming composition is located near Zr63.8Al11.4Ni17.2Cu7.6. Its glass forming ability is higher than that of the Inoue alloy Zr65Al7.5Ni10Cu17.5.

Ternary bulk metallic glasses formed by minor alloying of Cu8Zr5 icosahedron

Icosahedron Cu8Zr5, derived from the Cu8Zr3 phase structure, corresponds to the deepest eutectic Cu0.618Zr0.382. Near this composition is the best glass-forming Cu–Zr composition, Cu0.64Zr0.36. (Cu0.64Zr0.36)1−xMx and (Cu0.618Zr0.382)1−xMx were examined for glass formation, where M represents Nb, Sn, Mo, Si, V, Ag, or Ta. A series of Cu–Zr based bulk metallic glasses are discovered with minor Nb, Sn, Mo, Ag, and Ta additions (lower than 3at.%). The minor alloying mechanism was discussed in the light of atomic size and electron concentration factors.

Composition rule of bulk metallic glasses and quasicrystals using electron concentration criterion

This paper aims at establishing a number of electrons/atom (e/a)-based criterion for searching bulk metallic glasses (BMGs) and quasicrystals with large forming abilities in the Zr-based multicomponent alloy systems. After discussions on the diffraction characteristics corresponding to the Fermi surfaces-Brillouin zone interaction in the Zr-based Hume-Rothery phases, the Hume-Rothery matching rule is well explained when the effective e/a value of the matrix element Zr is taken as 1.5. The BMG- and quasicrystal-related phases are pointed out to be a family of nearly e/a-constant phases in a given alloy system. An e/a-constant criterion is then used to predict the ideal composition of the quasicrystals and BMGs in the Zr-Ti-Ni, Zr-Al-Ni, and Zr-Al-Ni-Cu systems, respectively. Nearly pure bulk Zr-Ti-Ni quasicrystals and a series of BMGs with glass-forming abilities greater than that of the known Zr 6 5 Al 7 . 5 Ni 1 0 Cu 1 7 . 5 alloy are found.

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.

The e/a factor governing the formation and stability of (Zr76Ni24)1−xAlx bulk metallic glasses

Abstract In the present paper (Zr 76 Ni 24 ) 1− x Al x alloys were prepared to investigate the influence of e / a , electron number per atom, on their glass-forming abilities. The bulk metallic glasses (BMGs) obtained in this alloy series have an e / a span from 1.37 to 1.53. Their thermal stability increases with the e / a ratios. The largest thermal stability is found at Zr 60 Al 21 Ni 19 with the highest possible e / a =1.53. These BMGs manifest negative temperature coefficients of resistivity and a nearly linear T -dependence of resistivity within the temperature span 80–293 K. The validity of the Nagel–Tauc conjecture, 2 k f ≈ k p for the stabilities of these BMGs is discussed. The e / a -based rule is a promising way to locate glass-forming compositions in the Zr-based multi-component alloy systems.

Cluster formulae for alloy phases

Composition formulae for alloy phases are developed using first-neighbour coordination polyhedra plus their connections. The resultant cluster formulae [cluster](glue atom) x , similar to molecular formulae for chemicals, contain key structural and composition information on the alloy phases. As examples, Al–Ni–Zr alloy phases are analysed with the objective of revealing cluster formula properties such as the principal cluster, the cluster phase and the definition of complex alloy phases.

24 electron cluster formulas as the ‘molecular’ units of ideal metallic glasses

It is known that ideal metallic glasses fully complying with the Hume-Rothery stabilization mechanism can be expressed by a universal cluster formula of the form [cluster](glue atom)1 or 3. In the present work, it is shown, after a re-examination of the cluster-resonance model, that the number of electrons per unit cluster formula, e/u, is universally 24. The cluster formulas are then the atomic as well as the electronic structural units, mimicking the ‘molecular’ formulas for chemical substances. The origin of different electron number per atom ratios e/a is related to the total number of atoms Z in unit cluster formula, e/a = 24/Z. The 24 electron formulas are well confirmed in typical binary and ternary bulk metallic glasses.

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-Al 72.5 Fe 14.5 Ni 13 and D′-Al 705 Fe 12 Ni 17.5 , that correspond respectively to Al–Fe-based and Al–Ni-based decagonal phases in the same ternary system.

Ti-Zr-Ni bulk quasicrystals prepared by casting

A broad bulk-quasicrystal-forming region, (Ti x Zr100− x )100− y Ni y (43.75 ≤⃒ x ≤⃒ 81.25, 17 ≤⃒ y ≤⃒ 23), has been identified in the Ti-Zr-Ni system, and quasicrystals can be obtained by using a conventional suction-casting method. The quasilattice constant of the icosahedral (i) phase is within the range 0.505-0.530 nm. Ti40Zr40Ni20 is the optimal composition, where nearly pure bulk quasicrystals can be obtained. With a slight deviation from this composition, Ti-Zr solid-solution phases and/or C14-type Laves phase, although minority phases, coexist with the majority i phase. Differential thermal analysis reveals that the i phase in the bulk as-cast Ti40Zr40Ni20 alloy is stable below 953 K and transforms to the C14-type Laves phase and β-Ti-Zr solid solution at higher temperatures.