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1 Atomic & Molecular Clusters / 原子分子团簇 / 王金兰 Department of Physics Southeast University

2 What is nanometer? Nano is Small ( m; nm) 10 0 m 10-1 m 10-2 m 10-3 m 10-4 m 10-5 m 10-6 m 10-7 m 10-8 m 10-9 m m 1 nanometer=10-9 meter=10-6 micrometer ~ width of 10 H atoms 一尺之棰, 日取其半, 万世不竭 -- 庄子 天下篇 0.33m/2 28 = m=1.23nm 一尺之棰, 日取其半, 月至纳米 -- 纳米科学家

3 Carbon Materials at nanoscale Nano is Small ( m; nm) 10 0 m 10-1 m 10-2 m 10-3 m 10-4 m 10-5 m 10-6 m 10-7 m 10-8 m 10-9 m m Macroscopic carbon NANO We have more choices at nano scale Carbon at nanosize 100 nm 10 nm 1 nm Nano Diamond Nanohorns Nanopeapod Carbon onion MWNT Graphene Some most studied carbon nanomaterials Large Fullerene DWNT Bucky Ball SWNT Smallest SWNT

4 Feynman: There's Plenty of Room at the Bottom What I want to talk about is the problem of manipulating and controlling things on a small scale. Why cannot we write the entire 24 volumes of the Encyclopedia Brittanica on the head of a pin? The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom. It is not an attempt to violate any laws; it is something, in principle, that can be done; but in practice, it has not been done because we are too big. December 29th of 1959, APS annul meeting at CALTECG, Feynman made the famous speech of There s Plenty of Room at the Bottom: An Invitation to Enter a New Field of Physics, beginning of nano research.

5 Milestones in nanoscience and nanotechnology 1982, Binning, Roher: invention of STM 1991, Iijima: synthesis of carbon nanotubes 1989, IBM Scientists: Manipulating atoms by STM 1984, Gleiter: nanocrystalline materials 1985, Kroto, Curl, Smalley: discovery of C , Reed: self-assembling molecular junction

6 Fantastic nanoworld Nanopeapods Nanocar Nanospring Nano kids Nanogear Nanocable

7 Outline What are clusters? Types of cluster What is special of clusters Why study clusters? Aspects of cluster studies

8 What Are Clusters? Aggregates of 2 10 n (n 6 or 7) particles (atoms or molecules). Constituent particles may be identical or they can be two or more different species. Clusters may be studied in the gas phase, in a cluster molecular beam, adsorbed onto a surface or trapped in an inert matrix.

9 The Abundance of Clusters Clusters are formed by most of the elements in the periodic table even the noble gases! Clusters of the coinage metals (copper, silver and gold) are found in stained glass windows. Silver clusters are important in photography. Molecular clusters are present in the atmosphere. Carbon nanoclusters (e.g. C 60 and related fullerenes) may be present in soot and even in space.

10 现代的元素周期表 网上元素周期表 :

11 Metal Clusters Types of Cluster (1) s-block metals (e.g. alkali and alkaline earth metals) bonding is metallic (delocalised and nondirectional) involving mainly the valence s- orbitals. sp-metals (e.g. aluminium) bonding has some covalent character. Transition metals greater degree of covalency and directionality in the bonding - involving the valence d orbitals.

12 Types of Cluster (2) Semiconductor Clusters Composed of elements (e.g. C, Si & Ge) which are semiconductors in the solid state. Includes compound semiconductor (heteroatomic) clusters, with polar covalentbonds (e.g. Ga x As y ). Bonding is covalent bonds are directional and strong.

13 Types of Cluster (3) Ionic Clusters Heteroatomic clusters composed from atoms with large difference in electronegativity. Bonding is predominately ionic (electrostatic). Examples: alkali metal halides [Na x Cl y ] (x y)+ and magnesium oxides [Mg x O y ] 2(x y)+.

14 Types of Cluster (4) Rare Gas Clusters Form at low temperatures. Bound by weak van der Waals dispersion forces. Inter-atomic attraction increases with increasing atomic mass (He Rn).

15 Types of Cluster (5) Molecular Clusters Clusters of molecules. Types of bonding include: van der Waals, dipole-dipole interactions, higher- order multipolar interactions and hydrogen bonding. Examples: (N 2 ) n ; (C 6 H 6 ) n ; (HF) n ; (H 2 O) n.

16 Types of Cluster (6) Inorganic and Organometallic Cluster Rich chemistry of inorganic and organometallic clusters developed over the second half of the 20 th century. Generally thermodynamically and/or kinetically stable with respect to coalescence and can exist in the solid, liquid and vapour phases. Examples: Fe(C 5 H 5 ) 2 ; V(C 6 H 6 ) 2.

17 What is special of clusters Finite Size Effects Surface Effects Magic Number Macky Icosahedron

18 Cluster Size Effect (1) bulk diamond lattice reconstruction discrete levels continuous band dispersions Ge 15 cluster

19 Cluster Size Effects (2) Size-induced structural phase transitions

20 Electronic, optical, magnetic properties: size-dependence HOMO-LUMO gap, Zn Ionization potentials, Cd Polarizabilities, Ge Optical adsorption, Cu Magnetic moments, Fe, Co, Ni

21 Surface Effect (1) Large surface-to-volume: 纳米微粒直径 D(nm) 包含总原子数 表面原子所占比例 (%) 当直径小于 10nm, 纳米粒子的比表面积总和将大于 100m 2 /g 由于表面原子数增多, 原子配位不足及高的表面能, 使表面效应增强, 如高的反应活性

22 Why gold become so expensive? An example 表面科学研究和密度函数理论计算表明, 在 Au 的光洁表面, 低于 473K 时不可能发生 H 2 和 O 2 的离解吸附 (dissociative adsorption), 表明 Au 对于氢化和氧化反应是惰性的 直径小于 2nm 的 Au 颗粒, 对于许多反应, 诸如 CO 氧化和丙稀环氧化 (propylene epoxidation) 变得惊人的活泼, 特别是在低温下 CO 吸附需要金属 Au 表面, 其周围成为与 O 2 反应的区域 2nm 的 Au 团簇 (cluster size: ~300atoms)

23 Magic Numbers (1) abundant peak, magic number : atomic & electronic structures Typical setup for time-of-fight mass spectrum Electron shells in Na clusters: W.D.Knight, PRL52, 2141(1984).

24 Magic Numbers (2) Competition of electronic and geometry effects in clusters Electron shell metal clusters with free electrons Geometry space-filling icosahedrons for inert gas clusters

25 Superatom (1)

26 Superatom (2)

27 Mackay Icosahedron

28 Cluster Size Regimes (1) Cluster Size N Diameter / nm Small Medium Large > 10 4 > 8.6

29 Cluster Size Regimes (2) MACROSCOPIC MESOSCOPIC MICROSCOPIC D >10 4 Å N > D ~ Å N ~ D ~ Å N ~ D < 10 Å N < 10 BULK COLLOIDS NANOCLUSTERS ATOMS & MOLECULES

30 Scaling Laws (1) Large Medium Small Liquid Drop Behaviour Quantum Size and Surface Effects EJPD(1987).

31 Scaling Laws (2) Examples Ionisation energies of potassium clusters (N 100): IP IP ( ) ( ) R / ev = R / Å 1 ( N) / ev = N 3 Melting temperatures of gold clusters: T m ( ) ( ) R / K = R / Å 1 1

32 Scaling Laws (3) Deviations from Scaling Laws Large deviations (oscillations about the smooth trend) are observed for many properties in the medium and (especially) the small cluster size regimes. Deviations arise due to Quantum Size Effects (electronic shell closings) and Surface Effects (geometric shell closings).

33 Spherical Cluster Approximation (1) N-atom cluster modelled by sphere. Cluster volume: V c = NV a Atom Radius = R a Cluster radius: R c = N 1/3 R a Cluster surface area: A c = N 2/3 A a Cluster No. surface atoms: N s = 4N 2/3 R c Fraction of surface atoms: F s = N s /N = 4N 1/3 F s < 0.01 (1%) for N > 64,000,000 atoms.

34 Spherical Cluster Approximation (2) Plot of fraction of surface atoms (F s ) against N 1/3 for icosahedral shell clusters. N ( K ) = (10K + 15K + 11K + 3) 3 K number of shells.

35 Why Study Clusters? (1) Fundamental interest: Their intrinsic structure and properties The central position between condensed matter science. molecular and Potential applications: new functionality materials, device, catalysis, etc.

36 Clusters: bridge between atoms and solids Atomic structures: different from bulk and size-dependent How large must a cluster be before its properties resemble those of the bulk element?

37 Fundamental interest (1) To what extent do cluster properties resemble those of discrete molecules or infinite solids? Can the study of large finite clusters tell us anything about the bonding or explain the properties of bulk solids? How rapidly do cluster structures and other properties converge towards those of the bulk as the nuclearity (size) increases?

38 Fundamental interest (2) Can the evolution of band structure with increasing cluster size be detected? For clusters of metallic elements, at what cluster size is metallic conductivity first observed? Can phase transitions be observed and are they of the same type found for bulk solids and surfaces? By studying the geometric structures of clusters, how their structures change as a function of size, and cluster growth patterns, can we gain an understanding of crystal growth at the microscopic level?

39 Clusters: building block for nanostructured materials Peapods: clusters inside nanotube fullerene-based solid Supported cluster film Free clusters Clusters embedded in matrix Molecular electronic devices Cluster-based solids β-boron

40 Investigation of Clusters Types of clusters Molecular (cluster) beams free clusters Matrix isolated trapped clusters Matrix = liquid, glass or crystal (e.g. zeolites), condensed rare gases etc. Surface adsorbed supported clusters Methodology of studies Experimental studies Theoretical Model and Computational studies

41 Experimental Methods Generic Cluster Experiment Generation Interaction Detection Generation (including Nucleation, Growth & Condensation) Sources Interaction/Investigation Ionization Fragmentation Spectroscopy Reaction Detection Ions Neutrals Photons

42 真空合成 : 溅射 Cluster Generation (1)

43 Cluster Generation (2) 气相合成 : 蒸发和气体冷凝固法

44

45 Cluster Generation (3) 气相合成 : 激光蒸发和激光热解

46 磁控溅射 Cluster Generation (4)

47 Cluster Generation (5) 超声膨胀 : 惰性气体团簇

48 Nucleation, Growth and Condensation Cluster Nucleation M + M + M M 2 + M excess energy removed by third atom (KE) dimer acts as site of further growth and condensation Cluster Growth M N + M M N+1 Cluster Condensation M N + M P M N+P (or M N+P-X + X M)

49 Cluster decay processes and photo- and collision-induced dissociation Experimental Study Mass analyzers Time-of-flight Mass spectroscopy Static dipole polarizabilities Photoionization and Ionization potential Photoelectron Spectroscopy and Electron affinities Stern-Gerlach molecular beam deflection and magnetic properties Optical spectroscopy and optical properties surface plasma resonances in metal clusters

50 Abundance Spectra of Na n Clusters

51 Static dipole polarizabilities

52 Ionization Potential

53 PES and Electron Affinity

54 Stern-Gerlach Molecular Beam Deflection and Magnetic Moment

55 The Importance of Theory Many cluster properties (e.g. cluster geometries, binding energies and energy barriers) are not easily measured directly from experiment. Theoretical models and computational methods have been very useful in helping to interpret spectroscopic (e.g. UV/visible and photoelectron) and mass spectrometric data. Clusters constitute an exacting testing ground for theoretical methods testing the range of validity of theoretical models derived from the extremes of atomic/molecular and solid state physics.

56 C 60 clusters

57 Au clusters Au 20 : T d

58 Computational Searching of cluster geometries Hohenberg-Kohn Theorems E 0 = E 0 (ρ) ρ: electron density Density Functional Theory (DFT) calculations Schrödinge r Equation HΨ = EΨ Ψ: wavefunction Ab initio and semi-empirical molecular orbital calculations Molecular Mechanics E 0 (force field Parameters) mainly Hooke s law Molecular Mechanics (MM) force field calculations Structural and electronic structure calculations Structural calculations

59 计算材料模拟的时间与空间尺度 对于一个物理现象, 从微观原子尺度到宏观尺度各层面进行模拟是一个挑战

60 Number of atoms (electrons)

61

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