Glue Atoms Research Articles

A Cluster–Resonance Criterion for Al‐TM Quasicrystal Compositions

AbstractCompositions of binary Al‐TM (TM=Cr to Ni) quasicrystals are interpreted with a unified cluster formula [icosahedron](glue)1 using the newly developed cluster–resonance model and the e/a formalism. The icosahedra are chosen from the corresponding approximants by considering large radial atomic density, high degree of isolation, and narrow distribution of the shell atoms. Icosahedral quasicrystals are expressed by an icosahedron plus one averaged icosahedron atom as the glue atom [icosahedron](icosahedron/13)1, characterized by e/a ∼1.83–1.85, while decagonal quasicrystals are expressed by an icosahedron plus one TM atom, with e/a ∼1.71–1.78. The total electrons accommodated in unit cluster formulas of different Al‐TM quasicrystals have the same value approaching 24, which implies that the cluster formulas are both chemical and electronic structural units.

Structure of the orthorhombic Al13Co4(100) surface using LEED, STM, andab initiostudies

In a combined scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), and density functional theory (DFT) study of the surface of Al${}_{13}$Co${}_{4}$(100), all techniques have found that after annealing to 1165 K, the surface structure is consistent with a dense Al-rich plane with surface Co atom depletion. Various structure models were considered, and in the LEED study, the best agreement was found with a model that consists of Al-rich terminating planes with no Co atoms, and otherwise a structure similar to the bulk puckered layers. This structure was also found to be stable in the DFT study. The best-fit structural parameters are presented for the two domains of this structure, which contain bipentagons that can be related to the pentagonal bipyramidal structures in the bulk, plus additional glue atoms between them. These domains are not strictly related to each other by symmetry, as they have different surface relaxations. The STM study found significant differences in the surfaces of samples grown by different methods and is able to explain a different interpretation made in an earlier study.

The e/ a values of ideal metallic glasses in relation to cluster formulae

The electrons per atom ratio e/ a is an important factor in discussing the stabilization mechanism of metallic glasses. However, the e/ a assignment is complicated by hybridization effects, particular in transition metal systems. We have previously proposed the “cluster-plus-glue-atom” model for metallic glasses and the relevant cluster formula [cluster](glue atom) x , x ∼ 1 or 3. In the present paper, this model is combined with Häussler’s global-resonance model into a so-called cluster-resonance model. This model allows the calculation of the Fermi vector and hence the effective e/ a of an ideal metallic glass. By assuming an ideal dense packing of the clusters, the atomic density can be obtained and e/ a becomes associated with the number of atoms in the unit cluster formula Z. Experiments are carried out to verify these correlations. Alloys like Cu 8Zr 5Al, Ni 4Zr 9Al 2 and [Ni 7Nb 5Zr]Ni 3, possessing locally the highest glass-forming abilities, are interpreted by cluster formulae, with their Zs being determined by their e/ a values. Such verifications not only validate the proposed e/ a calculation schemes and the models behind them, but also support the ideal metallic glass feature of bulk metallic glasses with high glass-forming abilities.

Composition formulae of ideal metallic glasses and their relevant eutectics established by a cluster-resonance model

Composition formulae for ideal metallic glasses are explored by combining the cluster-plus-glue-atom model with the global resonance model, termed the cluster-resonance model for short. The former model gives the [cluster]1(glue atom) x cluster formulae, stressing the local cluster order of a glassy structure; the latter model extends the local cluster order to a medium-range one by introducing spherical periodicity that relates the cluster size with Fermi vector, k F. Such a correlation allows the calculation of Fermi energy, E F, and electrochemical potential of electrons of the system from any local clusters. The cluster-resonance model also implies the equilibrium of the electrochemical potentials of electrons between different clusters so that the number of glue atoms matching one cluster (x in the cluster formula) can be determined. Examples in the Cu–Zr–Al and B–Co–Si–Ta systems are given to show the effectiveness of the proposed model and the resulting cluster formulae in interpreting multicomponent metallic-glass compositions as well as their relevant binary eutectic points.

Cluster-plus-glue-atom model in bcc solid solution alloys

In the present work we propose the cluster-plus-glue-atom model for bcc solid solutions by establishing periodic packing geometries of CN14 basic clusters in bcc lattice to reflect the idealized chemical short-range order near solute atoms. The model is expressed by cluster formula (glue)x, where the cluster center is occupied by a solute having the largest negative enthalpy, mixed with the solvent, and other solute atoms serves as glues or substitute for the solvents in cluster shell. The 1 ∶1 cluster model (glue atom)1 is specially emphasized that guarantees to a maximum extent the glue-cluster nearest neighbors and hence forms a most efficient configuration. This 1 ∶1 model is conducible to the design of a low-V hydrogen-storage V1 alloy and a Nb1 alloy with low Youngs modulus combined with high strength.

Alloy phases and metallic glass formation understood via cluster formulas

Alloy phase structures and compositions in glass-forming Al–Ni–Zr system are analyzed by cluster-plus-glue-atom model and cluster line approach. Clusters in crystalline phases are shared with their neighboring clusters and the effective clusters after sharings are used to express the phases: phase = [effective cluster](glue atoms). This cluster formulas similar to molecular formulas for chemicals, contain key structure and composition information of the alloy phases. Cluster phases that require glue atoms and contain periodicity-incompatible clusters have close relationships with metallic glass formation. By avoiding cluster sharings, good glass forming compositions can be expressed by [isolated cluster](glue atom) x , x = 1–3.

CLUSTER--PLUS--GLUE--ATOM MODEL AND COMPOSITION DESIGN OF BCC Ti--Mo--Nb--Zr SOLID SOLUTION ALLOYS WITH LOW YOUNG'S MODULUS

利用＂团簇＋连接原子＂结构模型研究了典型低弹bccβ-Ti固溶体合金的成分特征.对现有低弹β-Ti固溶体合金的成分分析表明它们均满足团簇式[CN14团簇]（连接原子）x.根据该式,设计了Ti-Mo-Nb-Zr系列合金[MoTi（14）]Ti（质量分数表达时为Ti-11.8Mo）,[MoTi（14）]Nb（Ti-11.2Mo-10.8Nb）,[MoTi（14）]Nb2（Ti-10.1Mo-19.5Nb）和[Mo（Ti（13）Zr）]Nb2（Ti-9.2Zr-9.6Mo-18.7Nb）,并采用Cu模吸铸快冷技术制备直径为3和6 mm的合金棒.结果表明,吸铸制备的合金均为bcc结构;当连接原子由Ti变成更低弹的Nb时,合金弹性模量降低;低弹Zr替代Ti进一步降低了合金的弹性模量,[Mo（Ti（13）Zr）]Nb2合金的弹性模量E=72 GPa.铸态样品经过固溶和水淬处理后弹性模量降低.

Complex Alloys Containing Double-Mackay Clusters and (Sb1−δZnδ)24 Snub Cubes Filled with Highly Disordered Zinc Aggregates: Synthesis, Structures, and Physical Properties of Ruthenium Zinc Antimonides

A series of cluster-based ruthenium zinc antimonides with a large unit cell were obtained. Their structures were solved by the single crystal X-ray diffraction methods. They crystallize in the cubic space group of Fm3̅c (No. 226) with cell dimensions of 25.098(3), 24.355(3), 24.307(3), and 24.376(3) Å for Ru(26)Sb(24)Zn(67) (CA), Ru(13)Sb(12)Zn(83.4) (CB), Ru(13)Sb(6.29)Zn(91.56) (CC), and Ru(13)Sb(17.1)Zn(74.8) (CD), respectively. By all indications, compounds CA and CB are two phases showing pronounced distinctions regarding compositions, lattice parameters, thermal and transport properties, but they are not members of an extended solid solution. Compounds CB, CC, and CD are three members of a same solid solution. Topologically, these four compounds contain face-centered cubic packing of double-Mackay type clusters and (Sb(1-δ)Zn(δ))(24) snub cubes filled with highly disordered zinc aggregates, with or without glue atoms between them. Both phases CA and CB are diamagnetic. There is a difference of ∼170 K between their thermally stable temperatures. CA exhibits rather low thermal conductivity with the value of ∼0.9 W m(-1) K(-1) at room temperature, which is about one-third that of CB. The electrical resistivity of CB is almost temperature independent. The Seebeck coefficient of CB is small and negative, while that of CA exhibits a complicated temperature dependence and undergoes a transition from p- to n-type conduction around room temperature.

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.

Structural origin of the high glass-forming ability in Y-doped bulk metallic glasses

Structural origin of the high glass-forming ability (GFA) in multicomponent bulk metallic glasses (BMGs) caused by minor alloying was investigated using state-of-the-art synchrotron radiation techniques. It is found that a two-shell icosahedral cluster with one Y center is the basic structural unit in the representative Cu46Zr42Al7Y5 BMG, which may be densely packed with the help of shared and glue atoms, leading to enhanced ordering at short and medium range. This cluster dense packing may play a key role in achieving the high GFA in CuZrAlY alloy, which also explains the strong dependence of GFA on Y content observed in many experiments. The present work may be extended to a series of multicomponent amorphous alloys, the formation of which is strongly dependent on minor alloying.

Ni-based Ni-Fe-B-Si-Ta bulk metallic glasses

The glass-forming ability and properties of Ni-based Ni-Fe-B-Si-Ta bulk metallic glasses are explored in this work. The alloy compositions are determined by using a combination of the cluster line approach, the multi-alloying strategy and the substitutions of similar elements. Bulk metallic glasses with diameters of 3 mm take shape at compositions formulated under the cluster-plus-glue-atom model [M9B]B∼[(Ni1−xFex)7.71(Si0.66Ta0.34)1.29B]B0.94=(Ni1−xFex)70.5B17.7Si7.8Ta4, x=0.35–0.45, where the bracketed part is the cluster and the unbracketed part is the glue atoms. These alloys exhibit good magnetic properties. The maximum Is is found in the (Ni0.55Fe0.45)70.5B17.7Si7.8Ta4 alloy which reaches 0.51 T, with its Hc as low as 8.5 A/m. Interestingly, these alloys display dual glass transitions at (Ni0.65Fe0.35)70.5B17.7Si7.8Ta4, (Ni0.60Fe0.4)70.5B17.7Si7.8Ta4 and (Ni0.55Fe0.45)70.5B17.7-Si7.8Ta4 as unveiled by Temperature-Modulated Differential Scanning Calorimetry.

Formation rule of β-FeSi2 phases in (Fe, M)Si2 ternary alloys

Binary β-FeSi2 phase is an important semiconductor metal silicide with narrow band-gaps. The formation of this phase in ternary alloys was investigated for the search of ternary semiconductor silicides. Using the cluster line approach as the theoretical guideline, a structure model is established with one cluster and one glue atom, and alloy series of Fe3Si8M(M=B, Cr, Ni, Cu, Co, Al) were designed by replacing the glue atom Fe in binary β-FeSi2. To obtain homogenous alloys, high vacuum suction casting and melt spinning method were used for the preparation of alloy rods and ribbons. Microstructure and composition analysis showed that the β phase could dissolve 15%—20% Ni, 4%—13% Cu, 7%—10%Co and 7%—10%Cr (molar content). However, in contrary to the designed formula, the added Al replaces Si rather than Fe. There were trace amounts of amorphous particles in Fe3Si8B and Fe3Si8Cr ribbon samples, which showed under the rapid cooling conditions, the addition of B and Cr was favorable for the amorphous phase formation.

Glass forming abilities of binary Cu100−xZrx (34, 35.5, and 38.2 at. %) metallic glasses: A LAMMPS study

Using large-scale atomic/molecular massively parallel simulator (LAMMPS), we have studied the liquid behaviors of Cu61.8Zr38.2, Cu64.5Zr35.5, and Cu66Zr34 amorphous alloys including their pair distribution functions, distributions of Voronoi clusters with different coordination numbers, and mean square displacements of Cu and Zr atoms. Compared to Cu61.8Zr38.2 and Cu66Zr34, we found high concentrations of distorted icosahedra with indices of ⟨0,2,8,2⟩ and ⟨0,4,4,4⟩, high numbers of Cu-centered Cu8Zr5 and Cu9Zr4 clusters, and reduced atomic diffusivity of Cu and Zr atoms in molten Cu64.5Zr35.5 alloy. These effects would benefit glass formation in Cu64.5Zr35.5 alloy. Meanwhile, from the viewpoints of local cluster structure, the majority of the glue atoms are Cu atoms in Cu64.5Zr35.5 amorphous alloy, which leads to denser packing and better glass forming ability.

Cluster packed structures in bulk metallic glasses created from BCC derivative compounds

Molecular dynamics simulations based on plastic crystal model were performed for the Fe69.0Nb10.3B20.7 and Zr57.1Ni28.6Al14.3 alloys to investigate their forming ability and features of the noncrystalline structures. The Fe69.0Nb10.3B20.7 and Zr57.1Ni28.6Al14.3 alloys were created from C6Cr23 and Ti4Ni2O structures, respectively, by assuming the presence of hypothetical clusters in the crystalline structures under a treatment that the clusters and glue atoms are regarded as the components. The analysis with total pair-distribution function, g(r), revealed that these alloys have high tendencies to form noncrystalline structures while their partial g(r) profiles for pairs among components showed the presence of medium range order. Cluster packed structures from bcc derivative compounds cause high forming ability of noncrystalline structure and the medium range order in the noncrystalline structure.

Co- and Fe-based multicomponent bulk metallic glasses designed by cluster line and minor alloying

Bulk metallic glass (BMG) formations in Co- and Fe-based alloy systems are investigated by using our cluster line approach in combination with minor alloying principle. Basic ternary alloy compositions in Co–B–Si, Fe–B–Y, and Fe–B–Si systems are first determined by cluster lines defined by linking special binary clusters to third elements. Then the basic ternary alloys are further minor alloyed with 3 to 5 at.% Nb to improve glass-forming abilities (GFAs) and ϕ3 mm BMGs are formed in (Co8B3–Si)–Nb and (Fe8B3–Y)–Nb but not in (Fe8B3–Si)–Nb, TM8B3 (TM = Fe, Co) being the most compact binary cluster. The BMGs are expressed approximately with a unified simple composition formula: (TM8B3)1M1, M = (Si, Nb) or (Y, Nb). Finally, mutual Fe and Co substitutions further improve the GFAs as well as the soft magnetic properties, e.g., Is reaching 0.98 T and Hc < 6 A/m for the Co–Fe–B–Si–Nb BMGs. Using the (cluster)1(glue atom)1 model, a new ternary BMG Fe8B3Nb1 is obtained.

Cu–Zr–Ag bulk metallic glasses based on Cu 8Zr 5 icosahedron

Based on the cluster line criterion, the Ag addition into the Cu 8Zr 5 cluster composition is investigated for the search of ternary Cu–Zr–Ag bulk metallic glasses with high glass forming abilities. Two initial binary compositions Cu 0.618Zr 0.382 and Cu 0.64Zr 0.36 are selected. The former one corresponds to a deep eutectic point; it is also the composition of the Cu 8Zr 5 icosahedron, which is derived from the Cu 8Zr 3 structure. The latter one, which can be regarded as the Cu 8Zr 5 cluster plus a glue atom Cu, is the best glass-forming composition in the Cu–Zr binary system. Two composition lines (Cu 0.618Zr 0.382) 1− x Ag x and (Cu 0.64Zr 0.36) 1− x Ag x are thus constructed in the Cu–Zr–Ag system by linking these two compositions with the third constitute Ag. A series of Cu–Zr–Ag bulk metallic glasses are found with 2–8 at.% Ag contents in both composition lines. The optimum composition (Cu 0.618Zr 0.382) 0.92Ag 0.08 within the searched region with the highest T g/ T l = 0.633, is located along the cluster line (Cu 0.618Zr 0.382) 1− x Ag x , where the deep eutectic Cu 0.618Zr 0.382 exactly corresponds to the dense packing cluster Cu 8Zr 5. The alloying mechanism is discussed in the light of atomic size and electron concentration factors.

The local atomic quasicrystal structure of the icosahedralMg25Y11Zn64 alloy

A local and medium range atomic structure model for the face centred icosahedral (fci)Mg25Y11Zn64 alloy has beenestablished in a sphere of r = 27 Å. The model was refined by least squares techniques using the atomic pair distribution(PDF) function obtained from synchrotron powder diffraction. Three hierarchies of theatomic arrangement can be found: (i) five types of local coordination polyhedra for thesingle atoms, four of which are of Frank–Kasper type. In turn, they (ii) form a three-shell(Bergman) cluster containing 104 atoms, which is condensed sharing its outer shell with itsneighbouring clusters, and (iii) a cluster connecting scheme corresponding to athree-dimensional tiling leaving space for a few glue atoms. Inside adjacent clusters,Y8 cubes are tilted with respect to each other and thus allow for overall icosahedralsymmetry. It is shown that the title compound is essentially isomorphicto its holmium analogue. Therefore, fci-Mg–Y–Zn can be seen as therepresentative structure type for the other rare earth analogues fci-Mg–Zn–RE(RE = Dy,Er, Ho, Tb) reported in the literature.

Medium range real atomic structure of face-centred icosahedral Ho9Mg26Zn65

Abstract A complementary approach to solve quasi crystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho9Mg26Zn65 [a(6D) = 2 × 5.18(3) Å] has been obtained from in-house powder X-ray diffraction data (MoKα 1). For the first time, full profile PDF refinements of a quasicrystal were performed: Starting with rational approximant models, derived from 1/1- and 2/1-Al—Mg—Zn, its local and medium range structure was refined (r < 27 Å; R = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. The basic structural unit is the 3-shell, 104-atom Bergman cluster (d ≈ 15 Å) comprising a void at its center. The clusters are interconnected sharing common edges and hexagonal faces of the 3rd shells. The remaining space is filled by some glue atoms (9% of all atoms), yielding an almost tetrahedrally close packed structure. All Ho atoms are surrounded by 16 neighbours (FK-polyhedron “P”). Most of them (89%) are situated in the 2nd shell and form a Ho8 cube (edge length 5.4 Å); they are completed by 12 Mg atoms to a pentagon dodecahedron. Cubes in neighbouring clusters are tilted with respect to each other; their superposition generates diffraction symmetry 2/m3̅5̅. The remaining Ho atoms act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar when compared to common crystalline intermetallic compounds. From our results, the long range quasiperiodic structure of icosahedral Mg—Zn—RE (RE = Y and some rare earths) is anticipated to be a canonical cell tiling (CCT, after Henely) decorated with Bergman clusters.

Cluster-disordered glue model and role of glue atoms in the icosahedral quasicrystalline structure

We adopt first principles methods for Zn–Mg clusters (related to Al–Zn–Mg quasicrystals) to estimate the energy cost for disorder in the glue region by giving small displacements to only the glue atoms, while keeping the atoms in the icosahedral cages frozen at the ideal icosahedral positions. We compare these estimates of cluster calculations with the energy changes for a structural transition in solids, and find that the glue region disorder costs at least an order of magnitude less energy. These results support the proposition of the cluster-disordered glue model, that the glue region in a quasicrystal may be disordered.

New group of stable icosahedral quasicrystals: structural properties and formation conditions

Structural studies on the icosahedral quasicrystals in Zn–Mg–Sc, Cu–Ga–Mg–Sc, and Zn–Mg–Ti alloys as well as their corresponding 1/1 cubic approximants, have revealed that these quasicrystals belong to a new structural group similar to Cd-based quasicrystals. This group is characterized by a triple-shell icosahedral cluster different from both Mackay- and Bergman-types. The presence of the atomic cluster has been deduced from the structure model of the approximant crystal, Zn 17Sc 3, in which the clusters are embedded in a periodic network of so-called ‘glue atoms’. Density measurement suggested the presence of at least 2.7 Zn atoms in the first shell of the cluster in this approximant. The substitutional relationship in these three quasicrystals indicates the important role of Hume-Rothery rule for the formation of this type of quasicrystal. The occurrence of a P-type icosahedral quasicrystal in Zn–Mg–Yb alloy is also reported.