Cluster (physics)

A cluster refers to a collection of atoms or molecules, the atomic number is between 3 and 50,000.

Due to their small size clusters have properties that differ from those of a macroscopic solid. Concepts of atomic and molecular physics often fail when it comes to explaining properties of such small particles. The properties of the clusters thus provide a link between atomic and molecular physics on the one hand, and solid state physics on the other side dar. subject of research in this area is how to develop the macroscopic properties of a solid from the properties of an atom or molecule. For many of the properties, the ratio of surface area to volume of atoms is critical to the properties of the cluster.

It further distinguishes a free cluster of a deposited clusters. The latter is located on a surface, while the free cluster moves freely in the room. Are cluster spatially distributed in a different physical medium, it is called the total system then colloid.

Classification

Generally, the clusters are classified according to the number of atoms (s):

• N = 3-12 atoms ( micro- clusters): has not yet been micro- cluster all the components of the cluster on the surface. Concepts and methods of atomic and molecular physics and surface physics are applicable and useful.
• N = 13-100 atoms ( small clusters ): The properties of small clusters are crucially determined by quantum effects. The electronic energy levels are indeed quite close to each other, but for a band structure in the solid state the number of atoms is still too low. The installation of an additional atom or molecule may change very much. Often there are many isomeric cluster structures with closely spaced energy levels. Molecular concepts lose their usefulness. Also plays the surface physics, due to the large ratio of surface to volume atoms atoms of the cluster, is still a very important role.
• N = 100-1000 atoms (large cluster): It is observed a gradual transition to the properties of the solid body, such as transitions in crystal lattices (Chrome has, for example, at about n = 490 a transition from fcc (< 490) to bcc ( > 490), these values ​​have a range of variation of 100 atoms).
• N > 1000 atoms ( small particles or nanocrystals )

Some, but not all properties of solids have developed. From about 50,000 atoms, the properties have now so well developed that one speaks of a solid from then on.

Classification of the chemical bond

• Metallic clusters: half-full band of delocalized electrons Examples: alkali metal clusters, Al, Cu, Fe, Pt, W, Hg clusters; each with n> 200 atoms, average binding energy: 0.5-3 eV
• Covalent clusters: aligned by sp hybridization bonding electron pairs; Examples: C- cluster ( the best known example are the fullerenes, see the image above carbon nanotubes and diamond cluster also belong to the carbon clusters. ); Si, Hg cluster; each with 30
• Ionic clusters: binding by Coulomb forces between ions, examples: (KF ) -, ( CaI2 ) clusters, average binding energy 2-4 eV
• Clusters with hydrogen bond: strong dipole - dipole attraction, examples: ( HF) -, (H2O ) cluster, average binding energy: 0.15-0.5 eV
• Molecular clusters: Van der Waals clusters, plus weak covalent shares examples: (I2 ) - ( AS4 ) - (S8 ) -, organic molecular clusters, average binding energy: 0.3-1 eV
• Van der Waals clusters: induced dipole interaction between atoms and molecules with closed electronic shell, examples: noble gas ( H2) - (CO2) -, Hg - clusters; each with n < 10 atoms, average binding energy: 0.001-0.3 eV

Structure of free clusters

Of outstanding importance for the structure of free clusters is the rule of Friedel:

From this rule, most structures occurred after the pattern of the Platonic solids:

Hexahedron

Octahedron; only micro- clusters

Dodecahedron; only micro- clusters

Icosahedron

Particularly important here is the structure of the icosahedron ( structure on the right), which is particularly prevalent for clusters with an atomic number of n> 12. In each corner of the body and in the interior of an icosahedral atom is placed. Due to the 12 corners so there is a 13 -atom cluster 12 surface atoms and 1 volume of atom. For larger numbers of atoms a new shell with atoms is padded on the icosahedral shape, which can be accommodated due to the longer bond length in the kth shell 10k ² 2 atoms in the shell. There exists therefore for the first shell 12 atoms, for the second shell there is room for exactly 42 more atoms, for the third shell 92 atoms, etc. In all of these dishes are as in the k = 1 cup 12 atoms at the corners an icosahedron and additionally 10k ² -10 atoms on the surfaces. These concentric icosahedral must we imagine as matryoshkas, on whose surface the atoms. As in atomic physics with the stable noble gas atoms there are also very stable clusters due to the shell closures. A closed shell cluster structure results only for a few cluster sizes: n = 13, n = 55, n = 147, n = 309, n = 561, n = 923 and n = 1415; they are referred to as "magic numbers ". This very stable clusters are commonly called with filled atomic shells also Mackaysche icosahedron. The Platonic solids of the figure above occur at the micro- clusters, the hexahedron even for larger clusters.

The magic cluster numbers can be prepared by the following formula: