Abstract
Questions, like who mentioned and used the term clusters for the first time, and who found and interpreted the nuclear and electronic shells of clusters, are answered. The definition, history, discovery of electronic shells and synthesis of clusters are presented. The evolution of small clusters to nanoclusters and their function in nanotechnology are discussed. The terms magic numbers in nature and their relationship to clusters are explained. The nuclear, electronic, atomic, and magnetic shells are introduced.
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References
W.D. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, M.Y. Chow, M.L. Cohen, Electronic shell structure and abundances of sodium clusters. Phys. Rev. Lett. 52, 2141 (1984)
H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C\(_{60}\): buckminsterfullerene. Nature 318, 162–163 (1985)
D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)
I. Boustani, W. Pewestorf, P. Fantucci, V. Bonaić-Kouteckỳ, J. Kouteckỳ, Systematic ab initio configuration-interaction study of alkali-metal clusters: relation between electronic structure and geometry of small Li clusters. Phys. Rev. B 35, 9437 (1987)
A. Kornath, A. Kaufmann, A. Zoermer, R. Ludwig, Raman spectroscopic investigation of small matrix-isolated lithium clusters. J. Chem. Phys. 118, 6957 (2003)
I. Boustani, Systematic LSD investigation on cationic boron clusters B\(_{n} (n=2-14)\). Int. J. Quantum Chem. 52, 1081 (1994)
H.J. Zhai, B. Kiran, J. Li, L.-S. Wang, Hydrocarbon analogues of boron clusters - planarity, aromaticity and antiaromaticity. Nat. Mater. 2, 827 (2003)
Z.A. Piazza, H.-S. Hu, W.-L. Li, Y.-F. Zhao, J. Li, L.-S. Wang, Planar hexagonal B\(_{36}\) as a potential basis for extended single-atom layer boron sheets. Nat. Commun. 5, 3113 (2014)
I. Boustani, A. Quandt, Nanotubes of bare boron clusters. Ab initio and density functional theory. Europhys. Lett. 39, 527 (1997)
I. Boustani, A. Quandt, E. Hernández, A. Rubio, New boron based nanostructured materials. J. Chem. Phys. 110, 3176 (1999)
D. Ciuparu, R.F. Klie, Y. Zhu, L. Pfefferle, Synthesis of pure boron single-wall nanotubes. J. Phys. Chem. B 108, 3967 (2004)
F. Liu, C.-M. Shen, Z.-J. Su, X.-L. Ding, S.-Z. Deng, J. Chen, N.-S. Xu, H.-J. Gao, Metal-like single crystalline boron nanotubes: synthesis and it in situ study on electric transport and field emission properties. J. Mater. Chem. 20, 2197 (2010)
I. Boustani, Systematic ab initio investigation of bare boron clusters: determination of the geometry and electronic structures of B\(_n (n=2-14)\). Phys. Rev. B 55, 16426 (1997)
X.-F. Zhou, X. Dong, A.R. Oganov, Q. Zhu, Y.-J. Tian, H.-T. Wang, Semi-metallic two-dimensional boron allotrope with massless Dirac fermions. Phys. Rev. Lett. 112, 085502 (2014)
A.R. Oganov, J. Chen, C. Gatti, Y.-M. Ma, T. Yu, Z. Liu, C.W. Glass, Y.-Z. Ma, O.O. Kurakevych, V.L. Solozhenko, Ionic high-pressure form of elemental boron. Nature 457, 863–867 (2009)
S. Iijima, Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004)
R. Tenne, L. Margulis, M. Genut, G. Hodes, Polyhedral and cylindrical structures of tungsten disulphide. Nature 360, 444–446 (1992)
S. Seifert, H. Terrones, M. Terrones, G. Jungnickel, T. Frauenheim, Structure and electronic properties of MoS\(_2\) nanotubes. Phys. Rev. Lett. 85, 146 (2000)
http://www.angelo.edu/faculty/kboudrea/periodic/physical_metals_fig1.gif. Accessed 26 Oct 2014
G.C. Benson, R. Shuttleworth, The surface energy of small nuclei. J. Chem. Phys. 19, 130–131 (1951)
F.A. Cotton, Metal atom clusters in oxide systems. Inorg. Chem. 3(9), 1217–1220 (1964)
J.J. Burton, Anomalous heat capacity of spherical clusters of atoms. Chem. Phys. Lett. 3, 594–596 (1969)
K. Wade, The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. J. Chem. Soc. D 792–793 (1971)
K. Wade, Structural and bonding patterns in cluster chemistry. Advances in Inorganic Chemistry and Radiochemistry, vol. 18 (1976), pp. 1–66
M.M. Balakrishnarajan, E.D. Jemmis, Electronic requirements of polycondensed polyhedral boranes. J. Am. Chem. Soc. 122, 4516–4517 (2000)
E.D. Jemmis, Building relationships between polyhedral boranes and elemental boron. Chemtracts Inorg. Chem. 18, 620–628 (2005)
G. Audi, The history of nuclidic masses and of their evaluation, arXiv:physics/0602050v1. Accessed 1 Oct 2014
Rikenresearch: http://www.riken.jp/en/research/rikenresearch/highlights/6041/. Accessed 1 Oct 2014
J.J. Burton, Configuration, energy, and heat capacity of small spherical clusters of atoms. J. Chem. Phys. 52, 345–352 (1970)
K.J. Klabunde, R.M. Richards, Nanoscale Materials in Chemistry, 2nd edn. (Wiley, Inc., Hoboken, 2009)
http://homepage.hispeed.ch/bakowies/graphics/fullerenes_allfullerenes.jpg. Accessed 1 Oct 2014
https://en.wikipedia.org/wiki/File:Ionization_energies.png. Accessed 1 Jun 2019
N.N. Greenwood, A. Earnshaw, Chemistry of Elements (Pergamon Press, Oxford, 1984)
P. Cottle, Nuclear physics: doubly magic tin. Nature 465, 430–431 (2010)
http://profmattstrassler.files.wordpress.com/2013/02/nuclear_force.png. Accessed 1 Oct 2014
https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcRD1GBCA6O9RIZaapQKVx5TJK_Wbo9xlvn-SSupjvCMalDmqwEz0A. Accessed 1 Oct 2014
O. Echt, K. Sattler, E. Recknagel, Magic numbers for sphere packings: experimental verification in free xenon clusters. Phys. Rev. Mod. Lett. 47, 1121–1124 (1981)
W.A. de Heer, The physics of simple metal clusters: experimental aspects and simple models. Rev. Mod. Phys. 65, 611–676 (1993)
T.P. Martin, Shells of atoms. Phys. Rep. 273, 199–241 (1996)
I. Boustani, Ab initio quantum chemical calculations of Fe\(_{16}\) planar cluster (2017). Unpublished results
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Boustani, I. (2020). Magic Numbers. In: Molecular Modelling and Synthesis of Nanomaterials. Springer Series in Materials Science, vol 290. Springer, Cham. https://doi.org/10.1007/978-3-030-32726-2_2
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DOI: https://doi.org/10.1007/978-3-030-32726-2_2
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