Energetics and Structural Energetics and Structural Evolution of Ag Evolution of Ag NanoclustersNanoclusters

Rouholla Alizadegan (TAM)Rouholla Alizadegan (TAM)Weijie Huang (MSE)Weijie Huang (MSE)

MSE 485 Atomic Scale SimulationMSE 485 Atomic Scale Simulation

OutlineOutline

Background and IntroductionBackground and Introduction Simulation MethodSimulation Method Results and Discussion Results and Discussion SummarySummary ReferencesReferences

Why study small clusters?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)

Small cluster structuresSmall cluster structures

Baletto and Ferrando, RMP, 77, 371, 2005

Icosahedron (Ih)

Decahedron (Dh)

Ino

Marks

Truncated Octahedron (TO)

Single twin

Questions aimed to answerQuestions aimed to answer

Energetics and stabilities of Energetics and stabilities of different cluster structures as a different cluster structures as a function of size;function of size;

Structural transition between Structural transition between different structural motifs;different structural motifs;

Equilibrium (lowest-energy) Equilibrium (lowest-energy) morphology for small FCC cluster;morphology for small FCC cluster;

Melting temperature of small FCC Melting temperature of small FCC cluster.cluster.

Simulation MethodSimulation Method Classical Molecular Dynamics using Embedded-Classical Molecular Dynamics using Embedded-

Atom-Method (EAM) potentialAtom-Method (EAM) potential Initialize velocities from Maxwell-Boltzmann Initialize velocities from Maxwell-Boltzmann

distribution distribution Construct the neighbor-list and calculate the Construct the neighbor-list and calculate the

forces on each atom (Particle motion controlled forces on each atom (Particle motion controlled by EAM potential) by EAM potential)

Velocity Verlet algorithm was used to integrate Velocity Verlet algorithm was used to integrate the equations of motion and update silver atom the equations of motion and update silver atom positions positions

No PBC: free standing clusterNo PBC: free standing cluster Temperature controlled schemes:Temperature controlled schemes: annealing and quenchingannealing and quenching

Embedded-Atom-Method (EAM) Embedded-Atom-Method (EAM) potentialpotential

Metallic potential (Metals have an inner core plus valence Metallic potential (Metals have an inner core plus valence electrons that are delocalized. Hence pair potentials do not electrons that are delocalized. Hence pair potentials do not work for them very well. work for them very well.

Good for spherically symmetric atoms: Cu, Al, Pb but not for Good for spherically symmetric atoms: Cu, Al, Pb but not for metals with covalent bonds.metals with covalent bonds.

An attractive interaction which models ''Embedding'' a An attractive interaction which models ''Embedding'' a positively charged pseudo-atom core in the electron density positively charged pseudo-atom core in the electron density and a pairwise part (which is primarily repulsive).and a pairwise part (which is primarily repulsive).

pairs

ijatoms

i rnFRV )()()(

j

iji rn )(

Temperature ControlTemperature ControlAnnealing: Gradually force temperature to target by a control speed

Quenching:Heat up instantaneously to high temperature and drop down slowly

Potential Energy/AtomPotential Energy/AtomAs 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.

Internal StrainInternal 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).

Lowest energy shape of TOLowest 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:

Melting temperature for TO (147 atoms)Small clusters are believed to have a depressed melting temperaturedue to the higher surface/volume ratio.

Structural TransitionStructural 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-DhMarks-Dh Dh(287) -> Ih(287)

Dh to Ih TransitionDh to Ih Transition

Ih-to-Dh transitionIh-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

Ih-to-Dh Transition: QuenchingIh-to-Dh Transition: Quenching

Quenching

Ih(309)

Ih (>200 atoms) stable upon annealing

SummarySummary Small-sized Ag clusters of different structures are Small-sized Ag clusters of different structures are

investigated using EAM potentialinvestigated using EAM potential Among all the structural motifs studied here, icosahedron Among all the structural motifs studied here, icosahedron

has an increasingly higher energy at relatively large sizes has an increasingly higher energy at relatively large sizes (>300 atoms). While at a narrow intermediate range (>300 atoms). While at a narrow intermediate range (200<N<300), it has a lower energy than decahedron(200<N<300), it has a lower energy than decahedron

Decahedron (Reg.,Ino and Marks) and TO are closed in Decahedron (Reg.,Ino and Marks) and TO are closed in energy and stabilityenergy and stability

For Ag clusters, surface energy difference between (111) For Ag clusters, surface energy difference between (111) and (100) is smalland (100) is small

Melting temperature of a TO Ag cluster is depressed to Melting temperature of a TO Ag cluster is depressed to 800~850C800~850C

Structural transition occurs between Dh and Ih, whose Structural transition occurs between Dh and Ih, whose direction depends on sizes. Transition from Ih to Dh is direction depends on sizes. Transition from Ih to Dh is thermodynamically preferred but has to overcome a large thermodynamically preferred but has to overcome a large barrierbarrier

ReferencesReferences 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)