Energetics and Structural Evolution of Ag Nanoclusters

1
Energetics and Structural Evolution of Ag
Nanoclusters

• Rouholla Alizadegan (TAM)
• Weijie Huang (MSE)
• MSE 485 Atomic Scale Simulation

2
Outline

• Background and Introduction
• Simulation Method
• Results and Discussion
• Summary
• References

3
Why study small clusters?

• Unique structures
• crystalline or
• noncrystalline
• Non-bulk properties
• lattice spacings,
• melting temperature,
• electronic properties

Valden et al. Science 281, 1647 (1998)
Koga, Sugawura, Surface Science, 529, 23 (2003)
4
Small cluster structures
Decahedron (Dh)
Truncated Octahedron (TO)
Icosahedron (Ih)
Single twin
Ino
Marks
Baletto and Ferrando, RMP, 77, 371, 2005
5
Questions aimed to answer

• Energetics and stabilities of different cluster
  structures as a function of size
• Structural transition between different
  structural motifs
• Equilibrium (lowest-energy) morphology for small
  FCC cluster
• Melting temperature of small FCC cluster.

6
Simulation Method

• Classical Molecular Dynamics using
  Embedded-Atom-Method (EAM) potential
• Initialize velocities from Maxwell-Boltzmann
  distribution
• Construct the neighbor-list and calculate the
  forces on each atom (Particle motion controlled
  by EAM potential)
• Velocity Verlet algorithm was used to integrate
  the equations of motion and update silver atom
  positions
• No PBC free standing cluster
• Temperature controlled schemes
• annealing and quenching

7
Embedded-Atom-Method (EAM) potential

• Metallic potential (Metals have an inner core
  plus valence electrons that are delocalized.
  Hence pair potentials do not work for them very
  well.
• Good for spherically symmetric atoms Cu, Al, Pb
  but not for metals with covalent bonds.
• An attractive interaction which models
  ''Embedding'' a positively charged pseudo-atom
  core in the electron density and a pairwise part
  (which is primarily repulsive).

8
Temperature Control
Quenching Heat up instantaneously to high
temperature and drop down slowly
Annealing Gradually force temperature to
target by a control speed
9
Potential Energy/Atom
As the sizes of clusters increase, the average
potential energies decrease. Energies of
Reg-Dh, Marks-Dh, Ino-Dh and TO are closed for Ag
clusters, being insensitive to the size (54 to
5394 atoms). Icosahedra clusters have a
slightly higher energy compared to the other
structures, especially for very small (55) and
very large (gt1000) clusters.
10
Internal Strain
As size increase, bulk contribution (internal
stress) increases leading to the increase of ?.
Among all the structural motifs investigated,
icosahedra have the highest internal strain,
which suggests that this structure is
energetically unfavorable for relatively large
clusters (gt500 atoms).
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Lowest energy shape of TO
Wulff Construction
N M of Atoms Energy/atom
Delta 7 5 1385 -2.725
2.17 7 6 1463
-2.724 2.225 7 7 1469
-2.723 2.226 8 4
1415 -2.723 2.216
9 4 1583 -2.717
2.365 10 4 1663 -2.712
2.46 11 4 1687
-2.701 2.47
N
M
Ag cluster is not very sensitive to the surface
ratio between (100) and (111) facets, agrees
qualitatively with the results
(?(100)/?(111)1.076) by Baletto et al. (J.
Chem. Phys. 116, 3856, 2002)
12
Melting temperature for TO (147 atoms)
Small clusters are believed to have a depressed
melting temperature due to the higher
surface/volume ratio.
13
Structural Transition

• Dh (100300 atoms) -gt partial Ih
• Dh (less than 100 atoms) -gt asymmetric shapes
• Reg- and Ino-Dh -gt marks-Dh
• Ih (less than 200 atoms) -gt decahedra.
• Clusters larger than 300 atoms found to be very
  stable upon annealing.

Reg-Dh
Ih
Reg-Dh
Marks-Dh
Dh(287) -gt Ih(287)
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Dh to Ih Transition
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Ih-to-Dh transition

• Ih (less than 200 atoms) -gt dh
• Ih (gt200 atoms) stable upon annealing
• But Ih has higher energy at large sizes barrier
  to transform to other shapes too high (involve
  internal melting)

Annealing
Ih(147)
Dh
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Ih-to-Dh Transition Quenching
Ih (gt200 atoms) stable upon annealing
Quenching
Ih(309)
17
Summary

• Small-sized Ag clusters of different structures
  are investigated using EAM potential
• Among all the structural motifs studied here,
  icosahedron has an increasingly higher energy at
  relatively large sizes (gt300 atoms). While at a
  narrow intermediate range (200ltNlt300), it has a
  lower energy than decahedron
• Decahedron (Reg.,Ino and Marks) and TO are closed
  in energy and stability
• For Ag clusters, surface energy difference
  between (111) and (100) is small
• Melting temperature of a TO Ag cluster is
  depressed to 800850C
• Structural transition occurs between Dh and Ih,
  whose direction depends on sizes. Transition from
  Ih to Dh is thermodynamically preferred but has
  to overcome a large barrier

18
References

• F. Baletto et al. J. Chem. Phys. 116, 3856
  (2002)
• F. Baletto et al. RMP 77, 371 (2005)
• M. Valden et al. Science 281, 1647 (1998)
• A. L. Mackay Acta Cryst. 15, 916 (1962)
• L. D. Marks Rep. Prog. Phys. 57, 603 (1994)
• Koga, Sugawura, Surface Science, 529, 23 (2003)