Nonequilibrium dynamics of a diffusion-limited reaction driven by a cluster-memory mechanism

The diffusion-limited reaction A+AA+B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis ind=1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously studied reaction A+AA. Ford>1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work ind=1, 2, and 3.     

Evolution of the structural stability of large Cu,Ni, Pd,and Ag clusters with size: An analysis within the embedded atom method

A study of the structural stability of clusters made up of a single component has been carried out within the Embedded Atom Method. Perfect icosahedral and cuboctahedral Cu, Ni, Pd, and Ag clusters with up to 5083 atoms have been compared. The icosahedron is found to be the stable structure for small clusters, and a change of structure from icosahedral to cuboctahedral is found as the cluster size increases. A contraction of the interatomic distances results when the cluster size decreases.     

Defect clusters and precipitation/oxidation of MgO-Co1−xO solid solution

MgO and Co_1−xO powders in 9:1 and 1:9 molar ratio (denoted as M₉C₁ and M₁C₉, respectively) were sintered and homogenized at 1600°C followed by annealing at 850°C and 800°C, respectively to form defect clusters and precipitates. Analytical electron microscopic observations indicated the protoxide remained as rock salt structure with complicated planar diffraction contrast for M₉C₁ sample, however with spinel paracrystal precipitated from the M₁C₉ sample due to the assembly of charge- and volume-compensating defects of the 4:1 type, i.e., four octahedral vacant sites surrounding one Co³⁺-filled tetrahedral interstitial site. The spacing of such defect clusters is 4.5 times the lattice spacing of the average spinel structure of Mg-doped Co_3−δO₄, indicating a higher defect cluster concentration than undoped Co_3−δO₄. The {111} faulting of Mg-doped Co_3−δO₄/Co_1−xO in the annealed M₁C₉ sample implies the possible presence of zinc blend-type defect clusters with cation vacancies assembled along oxygen close packed (111) plane.     

Modellbetrachtungen zum Verständnis unerwarteter Eigenschaften der metalloiden Clusterverbindung [Ga84(N(SiMe3)2)20][Li6Br2(THF)20]·2Toluol

Towards the Understanding of the Unexpected Properties of the Metalloid Cluster Compound [Ga₈₄(N(SiMe₃)₂)₂₀][Li₆Br₂(THF)₂₀]·2Toluol In several short communications we have recently reported on the electrical and superconducting properties of the crystalline title compound 1 which contains anionic Ga₈₄R₂₀‐moieties. Here we present a collection of these results, complemented and interpreted by using DFT‐calculations on model clusters (Ga₈₄(NH₂)₂₀^?). These calculations allow a) a first insight into the dynamics of the Ga₈₄‐moieties (e.g. a rotation of the central Ga₂‐dumbbell) and thus an explanation of the temperature‐dependent Ga‐NMR‐spectra described recently, and b) estimations on the lattice energy of 1 and its resulting unexpected energetic stabilization compared to metallic gallium. A possible contribution of the cations in the electrical conduction mechanism of 1 can also be made feasible with model calculations. The basis for all the results presented is to be found in the “perfect” arrangement of nanoscopic Ga₈₄‐clusters in the crystal. This theoretically predicted condition for superconductivity in a “chain” of identical metal cluster molecules is a requirement which can hardly be realized by means of physical fabrication methods. Therefore, on the one hand the results presented here make for some disillusionment in the field of nanoscience, but on the other hand, especially in the field of synthetic chemistry, they present rewarding challenges for fundamental work in the future.     

(BN)_n团簇的结构和稳定性

用HF方法、密度泛函理论的B3LYP以及微扰理论的MP2方法 ,在 6 3 1G(d)基组水平上 ,对 (BN) n(n =1～ 16)团簇的各种可能结构进行了优化 .讨论了环状与笼状稳定团簇的几何构型、自然键轨道 (NBO)、振动频率、结合能、核独立化学位移 (NICS)和能量二次差分 ,得到了 (BN) n(n =1～ 16)团簇结构的稳定性信息 .比较了HF ,B3LYP以及MP2三种理论方法对(BN) n 团簇的适应性所表现出的差异 .     

Synthesis,molecular structures,and thermal decomposition of heterometallic (π-cyclooctadiene)platinum-bis(tricarbonyliron-μ3-chalcogenides)[Fe—Fe], (π-C8H12)Pt(μ3-X)2Fe2(CO)6, where X = S,Se, or Te

Transmetallation of the Fe₃(₃-X)₂(CO)₉ clusters (X = S, Se, or Te) under the action of (-C₈H₁₂)PtCl₂ afforded new heterometallic clusters (-C₈H₁₂)Pt(₃-X)₂Fe₂(CO)₆ (2—4, respectively), which were characterized by X-ray diffraction analysis. The (-C₈H₁₂)Pt fragment in these clusters is bound to two ₃-bridging chalcogen atoms X. The iron atoms are linked to each other. The coordination environment about the Pt atom is planar-square; the Pt...Fe distance is larger than 3.2 . In the synthesis of cluster 4, a new Pt complex was also obtained for which the structure (CO)₂Pt(-Te)₂Pt(CO)₂ (5) was proposed. According to the results of differential scanning calorimetry, thermal decomposition of complex 5 gave rise only to PtTe, whereas complexes 1—4 gave products with the empirical formula Fe₂PtX₂C₂O₂. The influence of the steric effects on the geometry of the clusters is discussed.     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Preparation of Nano-Sized γ-Al2O3 Supported Iron Catalyst for Fischer-Tropsch Synthesis by Solvated Metal Atom Impregnation Methods

Two types of small iron clusters supported on γ-Al2O3-RT(dehydroxylated at room temperature) and γ-Al2O3-800 (dehydroxylated at 800 ℃) were prepared by solvated metal atom impregnation (SMAI) techniques. The iron atom precursor complex, bis(toluene)iron(0) formed in the metal atom reactor, was impregnated into γ-Al2O3 having different concentrations of surface hydroxyl groups to study the effect of surface hydroxylation on the crucial stage of iron cluster formation. Catalysts prepared in this way were characterized by TEM, M(o)ssbauer, and chemisorption measurements, and the results show that higher concentration of surface hydroxyl groups of γ-Al2O3-RT favors the formation of more positively charged supported iron cluster Fen/γ-Al2O3-RT, and the lower concentration of surface hydroxyl groups of γ-Al2O3-800 favors the formation of basically neutral supported iron cluster Fen/γ-Al2O3-800. The measured results also indicate that the higher concentration of surface hydroxyl groups causes the rapid decomposition of precursor complex, bis(toluene)iron(0), and favors the formation of relatively large iron cluster. Consequently, these two types of catalysts show different catalytic properties in Fischer-Tropsch reaction. The catalytic pattern of Fen/γ-Al2O3-RT in F-T reaction is similar to that of the unreduced α-Fe2O3 and that of Fen/γ-Al2O3-800 is similar to that of the reduced α-Fe2O3.