Clustering in alloys

Discrete and Extended Metal Clusters in Alloys With Mercury and Other Croup 12 Elements... 

Ab-initio studies of surface segregation in alloys are based on the Ising-type Hamiltonian, whose parameters are the effective cluster interactions (ECI). The ECIs for alloy surfaces can be determined by various methods, e.g., by the Connolly-Williams inversion scheme , or by the generalized perturbation method (GPM) . The GPM relies on the force theorem , according to which only the band term is mapped onto the Ising Hamiltonian in the bulk case. The case of macroscopically inhomogeneous systems, like disordered surfaces is more complex. The ECIs can be determined on two levels of sophistication ... 

Cryophotochemical techniques have been developed that (i) allow a controlled synthetic approach to mini-metal clusters 112), Hi) have the potential for "tailor-making small, bimetallic clusters (mini-alloy surfaces) 114,116), Hi) permit the determination of relative extinction-coefficients for naked-metal clusters 149), and iv) allow naked-cluster, cryophotochemical experiments to be conducted in the range of just a few atoms or so 112,150,151). 

Figure 4.28. STM image of a PtRh(lOO) surface. Although the bulk contains equal amounts of each element, the surface consists of 69% of platinum (dark) and 31 % of rhodium (bright), in agreement with the expected surface segregation of platinum on clean Pt-Rh alloys in ultrahigh vacuum. The black spots are due to carbon impurities. It is seen that platinum and rhodium have a tendency to cluster in small groups of the same elements.

Because of- the similarity in the backscattering properties of platinum and iridium, we were not able to distinguish between neighboring platinum and iridium atoms in the analysis of the EXAFS associated with either component of platinum-iridium alloys or clusters. In this respect, the situation is very different from that for systems like ruthenium-copper, osmium-copper, or rhodium-copper. Therefore, we concentrated on the determination of interatomic distances. To obtain accurate values of interatomic distances, it is necessary to have precise information on phase shifts. For the platinum-iridium system, there is no problem in this regard, since the phase shifts of platinum and iridium are not very different. Hence the uncertainty in the phase shift of a platinum-iridium atom pair is very small. 

PdPt [96,111], CuPt [112], PdRh [113], FeRu [114], FePt [114], FeNi [115], CuNi [116], BiNi [117] nanoparticle alloys or cluster-in-cluster structures by simultaneous reduction were reported, as summarized in Table la and b. 

Up till now anionic mercury clusters have only existed as clearly separable structural units in alloys obtained by highly exothermic reactions between electropositive metals (preferably alkali and alkaline earth metals) and mercury. There is, however, weak evidence that some of the clusters might exist as intermediate species in liquid ammonia [13]. Cationic mercury clusters on the other hand are exclusively synthesized and crystallized by solvent reactions. Figure 2.4-2 gives an overview of the shapes of small monomeric and oligomeric anionic mercury clusters found in alkali and alkaline earth amalgams in comparison with a selection of cationic clusters. For isolated single mercury anions and extended network structures of mercury see Section 2.4.2.4. 

Zintl ions are polyanions formed by anion clustering in ionic alloys. Two categories were considered those that fit the so-called Zintl-Klemm concept and those that are electron-deficient. 

Smaller tetrel element clusters like the tetrahedral [E4] ions were observed for the first time in the alloy NaPb [38] and are present in AE phases for E = Si to Pb and A = Na-Cs. Although these phases are not soluble, ammoniates of [Pb4]" have been obtained from liquid ammonia solutions of the binary phase RbPb [39]. The Zintl phases Ai2Sii7 (A = K, Rb, Cs) and KgRb6Sii7, which in the solid state contain [Si4]" and [Sig]" anions in the ratio 2 1, readily dissolve in liquid ammonia, and recently it has been shown that both cluster anions [Si4]" [37] and [Sig]" [40] are retained in solution. Corresponding pentel element clusters in bulk solids are [Pn7] and [Pnn] (Table 1). 

Recently, we and others demonstrated that appropriate germanide Zintl clusters in non-aqueous liquid-crystalline phases of cationic surfactants can assemble well-ordered mesostructured and mesoporous germanium-based semiconductors. These include mesostructured cubic gyroidal and hexagonal mesoporous Ge as well as ordered mesoporous binary intermetallic alloys and Ge-rich chalcogenide semiconductors. 

The spectra of silver and gold nanoclusters are intense and distinct (Table 4). They are thus particularly suitable to detect the evolution of a cluster composition during the construction of a bimetallic cluster in mixed solution. The system studied by pulse radiolysis was the radiolytic reduction of a mixed solution of two monovalent ions, the cyano-silver and the cyano-gold ions Ag(CN)2 and Au(CN)2 (Fig- 7) [66]. Actually, the time-resolved observation demonstrated a two-step process. First, the atoms Ag and Au are readily formed after the pulse and coalesce into an alloyed oligomer. However, due to... 

For example, when the mixed solution of Ag(CN)2 and Au(CN)2 is irradiated by y-radiolysis at increasing dose, the spectrum of pure silver clusters is observed first at 400 nm, because Ag is more noble than Au due to the CN ligand. Then, the spectrum is red-shifted to 500 nm when gold is reduced at the surface of silver clusters in a bilayered structure [102], as when the cluster is formed in a two-step operation [168] (Table 5). However, when the same system is irradiated at a high dose rate with an electron beam, allowing the sudden (out of redox thermodynamics equilibrium) and complete reduction of all the ions prior to the metal displacement, the band maximum of the alloyed clusters is at 420 nm [102]. 

Figure 12 Top Maximum wavelength of the plasmon band of alloyed gold-silver clusters as a function of the mole fraction x of gold in alloyed gold-silver clusters, produced at the dose rate 7.9 MGy hr and the dose 20 kGy. Experiments, calculated values by Mie model. Bottom Extinction coefficient at the maximum of the plasmon band as a function of the mole fraction x of gold in alloyed gold-silver clusters. Experiments, calculated values from Kreibig equation [74] with r = 5 nm A with r = 3 nm. (From Ref 102.)...

This book is the first attempt to summarize, probably from our subjective point of view, the state of the art in a very rapidly developing theory of many-particle effects in bimolecular reactions in condensed matter, which up to now was a subject of several review papers only [1—10]. We have focused mainly on several basic bimolecular reactions trying not to cover all possible cases (e.g., more complicated reactions, cooperative processes in alloys under irradiation [11] or initial macroscopic separation of reactants, etc.) but to compare critically results and advantages/limitations of numerous approaches developed in the last years. We focused on processes induced by point particles (defects) only the effects of dislocation self-organization are discussed in [12-16] whereas diffusion-limited particle aggregation with a special attention to fractal cluster formation has extensive literature [17-21],... 

An effect other than this ensemble effect has to be invoked in order to explain the increase in M and S for the alloys with 40-70% Cu. Although the origin of this apparent energetic effect is not clear, the effect could be due to differences in size of the nickel clusters in the surface caused by differences in bulk concentration of the alloy, or to adsorption-induced enrichments of nickel in the surface. The latter can also depend on the bulk concentration of the alloys. 

The subject of heteronuclear cluster compounds of the transition metals remains an active area of research interest, and was reviewed in the early 1980s by Geoffroy el al. (1,2). Clusters with novel architectures, exemplified by the star clusters of Stone and co-workers (5), continue to be synthesized. Whereas there is undoubtedly strong academic interest in the structure, bonding, and chemical reactivity of heteronuclear clusters in their own right, additional impetus to this field is given by the important relationship between heteronuclear clusters and bimetallic alloy catalysts. This relationship was the subject of a published symposium (4). 

K.A. Gall et al Finite element analysis of the stress distributions near damaged Si particle clusters in cast Al-Si alloys. Mech. Mater. 32, 277-301 (2000)... 

Molecular cluster ions are very useful because they reveal which elements are in contact in the sample. Of course, this presupposes that such clusters are emitted intact and are not the result of recombination processes above the surface. Oechs-ner [13] collected evidence that direct cluster emission processes predominate in the case when relatively strong bonds exist between neighbor atoms. Direct emission becomes even more likely if the two atoms differ significantly in mass, and when the heavier atom receives momentum from the sputter cascade in the solid. Thus, there is little doubt that clusters of the type ZrO+, FeCl3-, MoS+, CH3+, PdCO+, or Rh2NO+ (which we will encounter in the applications later) stem from direct emission processes and reflect bonds present in the sample [2, 4], Some evidence exists, however, that atomic recombination may play a role in the SIMS of metals, and in alloys where the two constituents have comparable mass... 

In this work we study a number of isolated clusters which may be relevant for understanding the clustering in the liquid alloys. Of course, the behaviour of those clusters in the alloy may be more complicated due to the interaction with the condensed medium, but by studying free clusters we expect to obtain useful information about the tendency of the atoms to cluster in the alloy. A preliminary calculation [9] using the Density Functional Formalism (DFT) [10, 11] and a simplified model for the cluster structure [12] has confirmed the high stability of the A4Pb and A4Pb4 species (with A = Li, Na, K, Rb, Cs). However, the drastic simplification of the cluster structure used in that model calls for more accurate calculations. Consequently, in this work we report the results of ab initio molecular-dynamics DFT calculations. 

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