cluster (rus. кластер) — a compact isolated group of interconnected atoms, molecules or ions, whose properties differ in varying degrees from properties of its constituent elements.


In different areas of knowledge the term “clusters” refers to very different objects. In nuclear physics clusters are correlated groups of elementary particles. In chemistry and materials science clusters most often refer to one of the intermediate states between a single atom (molecule, ion) and a solid body (nanoparticle).

According to the latter point of view, a cluster is a group of a small, often variable, number of interacting atoms, ions or molecules. Depending on the type of the particles, all clusters are divided into atomic, ionic and molecular; depending on their composition – into metal, carbon, etc. It is reasonable to include in the concept of clusters the particles of such size, whose observed properties differ significantly from the properties of the macroobject, or whose properties change with the addition of another constituent element. For example, here we speak about a discrete, rather than band-type electronic spectrum. Thus, the particle sizes concerned do not exceed one to two thousand atoms, and are frequently much smaller. There may be observed nonmonotonic dependence of the properties on the cluster size, especially in small clusters, where at different sizes various competing structural types can occur.

Most methods of producing metal clusters are based on the evaporation of metals, alloys and binary compounds by thermal, plasma, electron beam, or laser exposure with subsequent condensation. The main requirement for the conditions of condensation is a high nucleation rate at a minimum growth rate of the particles formed, which can be achieved at the maximum condensable vapour cooling rate (supersonic flow of metal vapour into vacuum, evaporation in a rarefied inert gas atmosphere, etc.). The method of low temperature matrix isolation (see also cryochemistry) is widely used in the synthesis and study of clusters. Clusters can exist in the gas phase; the structure and composition of such clusters can differ markedly from the properties of clusters in the condensed state. Mass spectrometry and various spectroscopic methods of gas phase analysis are actively used to study the processes of cluster formation in this case.

Along with the cluster particles of metals and alloys, there are also cluster compounds, in which the metal core is stabilised by ligands, sometimes having a very complex chemical composition. In molecules of such compounds ligands surround a frame of metal atoms located at distances up to 0.35 nm and allow direct metal-metal interaction. By nuclearity (q), i.e. the number of metal atoms that form the frame of a cluster compound, all clusters are divided into small (q = 3-12), medium (q = 13-40), large (q = 41-100) and extra-large, "giant" (q> 100). Cluster compounds are typical of transition metals, and of many non-transition elements. There exist homometallic clusters, whose frame is composed of atoms of one metal, and heterometallic clusters, whose frame is composed of atoms of two, three or more metals. The metal frame of cluster molecules is covered by a dense layer of ligands, both terminal and bridging, which may consist of individual atoms (H, Cl, Br, I, Se, etc.), or groups of atoms or molecules (CO, NO, olefins, arenas, etc.).

Sometimes monatomic ligands (N, C, H, P, etc.) are located inside the cavities of the metal frame having other ligands on the outside. Another important class of cluster compounds are clusters of semiconductor substances, such as selenide or cadmium telluride. Such clusters can be synthesised using traditional solution-based methods of organometallic chemistry, by etching the macroscopic particles of the material, but also with use of porous matrices to obtain the required particle size. As in the previous case, the chemical stability of such clusters can be achieved by protecting their surface with organic ligands or surfactants (SAS). Such clusters can be used as quantum dots, in particular, in blue light-emitting diodes and luminescent tags or objects. In general, the possible applications of metal or semiconductor clusters include catalysis, the creation of nanoelectronic devices and metamaterials on the basis of their spatially ordered arrays, such as photonic crystals.

Other important types of clusters include colloidal clusters, fullerenes Cn (n ≥ 20) and their outer-sphere derivatives, endohedral fullerenes M@Cn, metallocarbohedrenes or metallocarbons M8C12 (M is the transition metal: Ti, Zr, Hf, V, Cr, Mo and Fe), as well as “inorganic fullerenes”, i.e. multilayer polyhedra formed of molybdenum or tungsten sulphides and of some inorganic oxides and halides, some of which show high lubricating performance.


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Ti8C12 molecular cluster represented by a dodecahedron. Titan atoms are marked blue and carbon atoms are red.


  • Goldt Ilya V.
  • Gusev Alexander I.
  • Shlyakhtin Oleg A.


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  2. Gusev A. I. Nanomaterials, Nanostructures, and Nanotechnologies (in Russian) // Fizmatlit, Moscow (2007) - 416 pp.
  3. Gusev A. I., Rempel A. A. Nanocrystalline Materials. — Cambridge: Cambridge International Science Publishing, 2004. — 351 p.