1. Energetics and Structural Evolution of Ag Nanoclusters Rouholla Alizadegan (TAM) Weijie Huang (MSE) MSE 485 Atomic Scale Simulation

2. Outline Background and Introduction Background and Introduction Simulation Method Simulation Method Results and Discussion Results and Discussion Summary Summary References 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 Baletto and Ferrando, RMP, 77, 371, 2005 Icosahedron (Ih) Decahedron (Dh) Ino Marks Truncated Octahedron (TO) Single twin

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

6. Simulation Method Classical Molecular Dynamics using Embedded- Atom-Method (EAM) potential Classical Molecular Dynamics using Embedded- Atom-Method (EAM) potential Initialize velocities from Maxwell-Boltzmann distribution Initialize velocities from Maxwell-Boltzmann distribution Construct the neighbor-list and calculate the forces on each atom (Particle motion controlled by EAM potential) 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 Velocity Verlet algorithm was used to integrate the equations of motion and update silver atom positions No PBC: free standing cluster No PBC: free standing cluster Temperature controlled schemes: Temperature controlled schemes: annealing and quenching 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. 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. 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). An attractive interaction which models ''Embedding'' a positively charged pseudo-atom core in the electron density and a pairwise part (which is primarily repulsive).   pairs ij atoms i rnFRV)()()(    j iji rn)( 

8. Temperature Control Annealing: Gradually force temperature to target by a control speed Quenching: Heat up instantaneously to high temperature and drop down slowly

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 (>1000) clusters.

10. Internal Strain As size increase, bulk contribution (internal stress) increases leading to the increase of Δ. Among all the structural motifs investigated, icosahedra have the highest internal strain, which suggests that this structure is energetically unfavorable for relatively large clusters (>500 atoms).

11. Lowest energy shape of TO 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 (γ(100)/γ(111)=1.076) by Baletto et al. (J. Chem. Phys. 116, 3856, 2002) Wulff Construction:

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 (100~300 atoms) -> partial Ih Dh (less than 100 atoms) -> asymmetric shapes Reg- and Ino-Dh -> marks-Dh Ih (less than 200 atoms) -> decahedra. Clusters larger than 300 atoms found to be very stable upon annealing. Reg-Dh Ih Reg-Dh Marks-Dh Dh(287) -> Ih(287)

14. Dh to Ih Transition

15. Ih-to-Dh transition Ih (less than 200 atoms) -> dh Ih (>200 atoms) stable upon annealing But Ih has higher energy at large sizes: barrier to transform to other shapes too high (involve internal melting) Ih(147) Annealing Dh

16. Ih-to-Dh Transition: Quenching Quenching Ih(309) Ih (>200 atoms) stable upon annealing

17. Summary Small-sized Ag clusters of different structures are investigated using EAM potential 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 (>300 atoms). While at a narrow intermediate range (200 300 atoms). While at a narrow intermediate range (200<N<300), it has a lower energy than decahedron Decahedron (Reg.,Ino and Marks) and TO are closed in energy and stability 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 For Ag clusters, surface energy difference between (111) and (100) is small Melting temperature of a TO Ag cluster is depressed to 800~850C Melting temperature of a TO Ag cluster is depressed to 800~850C 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 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. J. Chem. Phys. 116, 3856 (2002) F. Baletto et al. RMP 77, 371 (2005) F. Baletto et al. RMP 77, 371 (2005) M. Valden et al. Science 281, 1647 (1998) M. Valden et al. Science 281, 1647 (1998) A. L. Mackay Acta Cryst. 15, 916 (1962) A. L. Mackay Acta Cryst. 15, 916 (1962) L. D. Marks Rep. Prog. Phys. 57, 603 (1994) L. D. Marks Rep. Prog. Phys. 57, 603 (1994)   Koga, Sugawura, Surface Science, 529, 23 (2003)