theoretical simulation of nanoclusters · • in physics, the term clusters (a)small, multiatom...
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Theoretical Simulation of
Nanoclusters
Xiaohu Yu
Moscow Institute of Physics and Technology
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Contents
• Introduction of nanoscience and
theoretical methods;
• The geometric structure of nanocluster;
• The stability of nanocluster;
• The growth of nanocluster;
• The structural transformation of
nanocluster;
• The sintering of nanocluster
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Introduction
Science 327 (2010) 278-279.
Bulk Au is noble;
Au nanoclusters are
active in catalysis;
High-surface area gold
catalysts exhibit
promising properties
suitable for industrial
application.
Green gold catalysis
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Introduction
Nanotechnology defination
Coarse particles: 2500-10000 nm;
Fine particles: 100-2500 nm
Nanoparticles: Ultrafine particle,
1-100 nm;
Nanoclusters: 1-10 nm;
Nanopowers: agglomerates of
nanoparticles or nanoclusters.
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Introduction
• In chemistry, a cluster
(a) an ensemble of bound atoms or molecules;
(b) intermediate in size between a molecule and a bulk
solid;
(c)diverse stoichiometries and nuclearities.
• In physics, the term clusters
(a)small, multiatom particles;
(b)between 3 and 3*107 atoms
• The phase cluster was coined by F.A.Cotton in the early
1960s to refer to compounds containing metal-metal
bonds.
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Introduction
• Atomic cluster can be either pure, formed from a
single atomic species, or mixed, formed from a mixed
atomic species.
• Classifications criteria:
(a)bond nature; (b)atomic count;(c) electric/magnetic
properties
• “magic number” representation in the mass spectra.
• The number of atoms N in perfect icosahedra as well as
fcc cuboctahedra with n complete atomic shells is given by
the sequence; 13, 55, 147, 309, 561, etc.
• N =(10n3+15n2+11n+3)/3Phys. Rev. Lett. 99 (2007) 083402.
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Introduction
• Molecular clusters: Atomic and molecular clusters
are aggregates of 5-105 atomic or molecular units.
• Classified according to the forces holding them together:
Van der Waals clusters; Metallic clusters; ionic clusters;
• Transition metal carbonyl clusters:Ni(CO)4
and Fe(CO)5, Fe2(CO)9,
• Transition metal halide clusters:
• Boron Hydrides: ( Wade’s rule)
• Fe-S clusters in biology: Fe4S4
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Theoretical Methods
• Molecular mechanics
• Finite element methods
• Molecular dynamics
• Monte Carlo methods
• Quantum molecular dynamics
• Nonequilibrium molecular dynamics
• Monte Carlo method
• Brownian dynamics
• Density functional theory
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Theoretical method
• Basin hopping (BH)
• Simulated annealing
• Minima hopping (MH)
• Genetic algorithm (GA)
• Random sampling methods
• Particle swarm optimization (PSO)
• Evolutionary program (USPEX)
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Bottom-up
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Bottom-up (metal)
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Top-down
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Top-down
Chem. Commun. 2010, 46, 5936.J. Mater. Chem. 2010, 20, 10535.
O vacancy formation is greatly facilitated in nanoscale ceria
Ce3+ occupy edge and corner sites
Ce4+ in highly coordinated positions
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The geometric of nanocluster
Phys. Rev. Lett. 75 (1995) 288-291.
Nature 392 (1998) 582-585.
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Stability of nanocluster
• Bind energy: Eb =Eatom-Ecluster/n
• Second energy difference:
Δ2En=En-1+En+1-2En
• Fragmentation energy:ΔEn= Eb(n)-Eb(n-1)
• Ionization potentials (IP):
E(IP) = En+-En
• Electron affinities (EA):
E(EA)=En-En-
• Detachment energies(ED)
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Stability of nanocluster
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Stability of nanocluster
Number of vertices Polyhedron
4 Tetrahedron
5 Trigonal bipyramid
6 Octahedron
7 Pentagonal bipyramid
8 D2d (trigonal)Dodecahedron
9 Tricapped trigonal prism
10 Bicapped square antiprism
11 Edge-contracted icosahedron
12 Icosahedron
4n rules
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Stability of nanocluster
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Stability of nanocluster
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Stability of Cs clusters
Phys. Rev. B 78 (2008) 245423.
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Stability of Cs clusters
Phys. Rev. B 78 (2008) 245423.
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Structures of iron clusters
Comp. Mater. Sci. 35 (2006) 275-278.
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Stability of iron clusters
J. Chem. Phys. 139 (2013) 034314.
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Structures of Au clusters
Phys. Rev. B 66 (2002) 035418.
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Stability of gold clusters
Phys. Rev. B 66 (2002) 035418.
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Optimization of Atomic Clusters
J. Am. Chem. Soc. 132, 6596-6605 (2010).
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Optimization of Atomic Clusters
ACS Nano 3, 1225-1230 (2009).
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Optimization of Atomic Clusters
Nature materials 11, 49-52(2012)
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Mg, Ti, Zn oxides
Nat. Mater. 7 (2008) 937-946.
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Modelling nano-clusters and nucleation
Phys. Chem. Chem. Phys. 12 (2010) 786-811.
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The growth of In2O3
Phys. Chem. Chem. Phys. 12 (2010) 8446-8453.
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The growth of SiO2
Phys. Chem. Chem. Phys. 12 (2010) 786-811.
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The growth of TiO2
Phys. Chem. Chem. Phys. 12 (2010) 786-811.
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The growth of dimer
Phys. Rev. Lett. 77, 51-54 (1996).
Dimer Growth, Structure Transition and Antiferromagnetic
Ordering in Small Cr Clusters
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The growth of Ti cluster
J. Chem. Phys. 118, 2116-2123 (2003).
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Oxidation of Fe cluster
Phys. Rev. Lett. 76, 4853-4856 (1996).
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Oxidation of Si3Ox(1-6) cluster
Phys. Rev. Lett. 78, 4450-4453 (1997).
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Oxidation of Ta cluster
J. Phys. Chem. A. 113, 9804-9813 (2009).
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Doping of nanocluster
Physical Review B 86, 205320 (2012)
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Structural transformations
Phys. Rev. Lett. 99 (2007) 083402.
John-Teller effect
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Structural transformations
The lowest energy structures of 13-atom Fe13-nPtn clusters.The blue and
yellow balls represent the Fe and Pt atoms, respectively.
Frau Sanjubala Sahoo, 2011, dissertation
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Structural transformations
Evolution of the lowest isomer for Ag8 (left) and Au4Ag4 (right), relative
to the energy of the GM isomer (E0)
Nanoscale 4 (2012) 1109-1115.
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Global minimum isomers for the 8-atom Au-Ag clusters, as function of
composition. For Au6Ag2 the two nearly degenerate isomers are shown.
Structural transformations
Nanoscale 4 (2012) 1109-1115.
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Structural transformations
J. Chem. Phys. 138 (2013) 094312.
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Sintering of nanocluster
• Molecular dynamics
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Sintering of Ni nanocluster
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Acknowledgements
Thank you for your attention!
grant of the Government of the Russian
Cuderation № 14.A12.31.0003.