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Ab Initio Studies of Size and Coordination Effects

Ab Initio Studies of Size and Coordination Effects. Shobhana Narasimhan Jawaharlal Nehru Centre for Advanced Scientific Research Bangalore, India shobhana@jncasr.ac.in. Kolkata, January 8 2007. First: A Confession. Once upon a time…. Confession (continued). Today…. Our group….

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Ab Initio Studies of Size and Coordination Effects

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  1. Ab Initio Studies of Size and Coordination Effects Shobhana Narasimhan Jawaharlal Nehru Centre for Advanced Scientific Research Bangalore, India shobhana@jncasr.ac.in Kolkata, January 8 2007

  2. First: A Confession Once upon a time…

  3. Confession (continued) Today…

  4. 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….

  5. 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. 

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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

  12. Si6 Pb11 Pb14 Si20 Clusters • Our primary interests: • Algorithms to find lowest energy structures • Elastic properties • Vibrational properties • Melting Behaviour • Catalysis

  13. Force Constant Tensor • k ia,jbforce induced on atom jin directionb, • upon movingatomiin 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

  14. Size-dependent trends in nanoclusters As size reduced: Coordination Bond lengths  Frequencies  Bond stiffness  R. Pushpa, U.V. Waghmare & SN

  15. 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

  16. Scaling Relations Clusters Periodic systems Stiffness ~ (length)-11 for a given element J. Paul & SN

  17. 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

  18. Consequences of enhanced stiffness Competition between fewer bonds and stiffer bonds…. • urmsdecreases asN decreases (for small N) non-monotonically • Lindemann melting temperature increases as Ndecreases, very non-monotonically R. Pushpa, U.V. Waghmare & SN When CN in bulk is high/low, clusters have lower/higher urms & higher/lowerTm than bulk

  19. 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

  20. O N Rh 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?

  21. Spin of Rh clusters + NO adsorption P. Ghosh, R. Pushpa, S.de Gironcoli & SN

  22. 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 lessfor anharmonic than harmonic properties(?), increase with temperature(?).

  23. 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.

  24. 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)

  25. 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

  26. Skål!

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