Ab Initio Studies of Size and Coordination Effects

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Ab Initio Studies of Size and Coordination Effects

• Shobhana Narasimhan
• Jawaharlal Nehru Centre for Advanced Scientific
  Research
• Bangalore, India
• shobhana_at_jncasr.ac.in

Kolkata, January 8 2007
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First A Confession
Once upon a time
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Confession (continued)
Today
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Our group
http//www.jncasr.ac.in/shobhana
Use ab initio density functional theory
(DFT) calculations to explore various aspects of
the consequences of reduced co-ordination.
Other applications of DFT to materials problems.
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Reduced Coordination

• Lowering of dimensionality usually accompanied by
  reduction in coordination number.
• Examples surfaces, interfaces, nanotubes,
  nanowires, nanoclusters.
• Reduced coordination results in altered
  structures.
• Differences in other properties too vibrational,
  thermal, electronic, magnetic, chemical
  reactivity, transport.

dimensionality ? ? C.N. ?
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Systems/Phenomena of Interest to Us

• Structure (Reconstruction) of surfaces,
  nanowires, clusters.
• Elastic properties of these systems (e.g., size
  dependence of hardness).
• Vibrational properties of these systems (e.g.,
  surface phonons, etc.).
• Thermal behaviour (e.g., thermal expansion,
  melting) of bulk systems, surfaces, nanosystems
• Reactivity dependence on local environment,
  e.g., rough vs. smooth surfaces, microcrystals
  vs. nanoclusters.
• Magnetic properties especially with reference
  to how magnetism affects the above.

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The Techniques We Use

• Fairly standard implementations of ab initio
  density functional theory (plane wave basis,
  pseudopotentials).
• Density functional perturbation theory for
  vibrational and elastic properties.

• Quasiharmonic approximation / full anharmonicity
  (from frozen phonons) for anharmonic thermal
  properties.
• Nudged elastic band method for reaction
  barriers.
• Parametrized model potentials for larger scale
  problems.

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Reconstruction on close-packed metal surfaces
To reduce surface stress, some surfaces
reconstruct into patterns of alternating domains
of FCC and HCP stacking

• Pt(111) reconstructs into honey-
• comb or triangular pattern on
• -heating above 1330 K
• -placing in supersaturated vapor

• Au(111) reconstructs
• into herringbone pattern

30nm
STM image of Au(111)
STM images of Pt(111)
Barth et al.,1990 Huang et al. 1990 Narasimhan
Vanderbilt, 1991 Sandy et al., 1992 Bott
et al., 1993 Hohage, Michely Comsa, 1995.
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Reconstruction on vicinal (stepped) Au(111)

• Also consist of tilings of FCC HCP domains
• Pattern depends on terrace width and type of
  step.

Repain, Rousset et al.
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Modelling the Reconstruction

• We perform ab initio calculations to parametrize
  a classical
• model.
• Excellent agreement with experiments.

Simulated STM images of the lowest
energy structures on Au(111) ? and Pt(111) ?
Narasimhan Vanderbilt Pushpa Narasimhan
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Self-Ordered Magnetic Nanostructures
These reconstructed surfaces act as templates for
growing ordered arrays of nanomagnets
60 nm STM image of the Au(788) surface. Each
bright dot corresponds to a cobalt cluster
(around 100 atoms each).
STM image of O.1 ML of Co on Au(111)
Repain, Rousset et al.

• Can use to study nanomagnetism
• High-density nanomagnetic storage devices?
• Questions for theorists
• - Site preference
• - Mechanism place exchange or adsorption?
• - Magnetic properties

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Clusters

• Our primary interests
• Algorithms to find lowest energy structures
• Elastic properties
• Vibrational properties
• Melting Behaviour
• Catalysis

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Force Constant Tensor

• k ia,jb ? force induced on atom j in direction
  b,
• upon moving atom i in direction a
  (by unit length)
• Dimensions of energy/length2
• Can obtain from DFT calculations by performing
  frozen phonon calculations or from density
  functional perturbation theory (DFPT).
• Measure of bond stiffness

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Size-dependent trends in nanoclusters
As size reduced
Coordination ?
Bond lengths ?
Frequencies ?
Bond stiffness ?
R. Pushpa, U.V. Waghmare SN
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Coordination-dependent trends in nanoclusters
Bonds in Si clusters are longer and softer than
in bulk
Bonds in Sn (Pb) clusters are (much) shorter and
stiffer than in bulk
Coordination number is the key parameter
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Scaling Relations
Clusters
Periodic systems
Stiffness (length)-11 for a given element
J. Paul SN
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Consequences of enhanced stiffness
Competition between fewer bonds and stiffer
bonds.
Results for elastic modulus for dilation for Si,
Sn and Pb (clusters bulk)

• Clusters softer than bulk
• Data collapse due to scaling relations between
  stiffness, length and coordination.
• Higher the CN in the bulk, less the relative
  softening in clusters.

R. Pushpa, U.V. Waghmare SN
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Consequences of enhanced stiffness
Competition between fewer bonds and stiffer
bonds.

• urms decreases as N decreases (for small N)
  non-monotonically
• Lindemann melting temperature increases as N
  decreases, very non-monotonically

R. Pushpa, U.V. Waghmare SN
When CN in bulk is high/low, clusters have
lower/higher urms higher/lower Tm than bulk
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Enhanced magnetism in low-d systems
Clusters/monolayers tend to be more magnetic than
bulk (Stoner criterion)
Bulk is magnetic
Clusters and monolayers ferromagnetic

• Fascinating magnetic properties
• Lower coordination magnetism affects reaction
  rate when used as catalysts

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Factors affecting catalysis
Model systems

• Catalytic dissociation of NO on Rh
• - Surfaces, monolayers and clusters
• At various lattice constants
• Free standing or on MgO substrates
• Non-magnetic or spin polarized calculations
• Aim to separate out effects of coordination
  number, strain, charge transfer magnetism
• Spin catalysts?

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Spin of Rh clusters NO adsorption
P. Ghosh, R. Pushpa, S.de Gironcoli SN
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Anharmonic Effects

• Expand energy in powers of displacements
• E(x) T ½ c(x-x0)2 g(x-x0)3
  f(x-x0)4
• harmonic
  anharmonic
• Some consequences pressure dependence of bulk
  modulus, Grüneisen parameters, thermal expansion,
  phonon frequency shifts and finite lifetimes,.
• Have studied using frozen phonons, quasiharmonic
  approximation, etc.
• Exchange-correlation errors less for anharmonic
  than harmonic properties(?), increase with
  temperature(?).

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Thermal expansion
Fe
expt.
Ni
GGA.
LDA

• Obtained using quasiharmonic approximation
• Phonon frequencies from DFPT
• GGA OK at low T, underestimates at higher T.

A.J. Hatt, B. Melot S.N.
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Thermal expansion
Fe
expt.
Ni
GGA.
LDA

• Invar Effect
• Anomalously small thermal expansion coefficient
  
• Anti-Invar Effect
• Anomalously large thermal expansion coeff.
  (e.g., fcc Fe)

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Conclusions

• Ab initio DFT is a good way to look at
  low-dimensional systems.
• Magnetism is (obviously) important for low-d
  systems.
• We are interested in growth, catalysis,
  anharmonicity.
• Collaborators
• Prasenjit Ghosh, Jaita Paul,
• Raghani Pushpa
• Alison Hatt, Brent Melot
• Stefano de Gironcoli, Umesh
• Waghmare
• Funding
• DST
• DST/MAE Indo-Italian Programme

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