Ab Initio Studies of Size and Coordination Effects：尺寸和协同效应的从头计算研究

1、1Ab Initio Studies of Size and Coordination EffectsShobhana NarasimhanJawaharlal Nehru Centre for Advanced Scientific ResearchBangalore, Indiashobhanajncasr.ac.inKolkata, January 8 20072First: A ConfessionOnce upon a time3Confession (continued)Today4Our group Use ab initio density functional theory

2、(DFT) calculations to explore various aspects of the consequences of reduced co-ordination.+ Other applications of DFT to materials problems.http:/www.jncasr.ac.in/shobhana5Reduced CoordinationLowering of dimensionality usually accompanied by reduction in coordination number.Examples: surfaces, inte

3、rfaces, nanotubes, nanowires, nanoclusters.Reduced coordination results in altered structures.Differences in other properties too: vibrational, thermal, electronic, magnetic, chemical reactivity, transport.dimensionality C.N. 6Systems/Phenomena of Interest to Us Structure (Reconstruction) of surface

4、s, 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 environm

5、ent, e.g., rough vs. smooth surfaces, microcrystals vs. nanoclusters. Magnetic properties: especially with reference to how magnetism affects the above.7The Techniques We Use Fairly standard implementations of ab initio density functional theory (plane wave basis, pseudopotentials). Density function

6、al 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.8Reconstruction on close-p

7、acked metal surfaces Au(111) reconstructs into herringbone pattern*STM image of Au(111)30nm Pt(111) reconstructs into honey- comb or triangular pattern on: -heating above 1330 K* -placing in supersaturated vapor*STM images of Pt(111)*Barth et al.,1990; Huang et al. 1990; Narasimhan & Vanderbilt,

8、 1991* Sandy et al., 1992; * Bott et al., 1993; Hohage, Michely & Comsa, 1995.To reduce surface stress, some surfaces reconstruct into patterns of alternating domains of FCC and HCP stacking:9Reconstruction on vicinal (stepped) Au(111)Repain, Rousset et al. Also consist of tilings of FCC & H

9、CP domains Pattern depends on terrace width and type of step.10Modelling the Reconstruction We perform ab initio calculations to parametrize a classical model. Excellent agreement with experiments.Simulated STM imagesof the lowest energystructures on Au(111) and Pt(111) Narasimhan & Vanderbilt;

10、Pushpa & Narasimhan11Self-Ordered Magnetic NanostructuresThese reconstructed surfaces act as templates for growing ordered arrays of nanomagnets: Can use to study nanomagnetism High-density nanomagnetic storage devices? Questions for theorists: - Site preference - Mechanism: place exchange or ad

11、sorption? - Magnetic propertiesSTM image of O.1 ML of Co on Au(111)60 nm STM image of the Au(788) surface. Each bright dot corresponds to a cobalt cluster (around 100 atoms each). Repain, Rousset et al.12ClustersSi6Pb11Pb14Si20Our primary interests: Algorithms to find lowest energy structures Elasti

12、c properties Vibrational properties Melting Behaviour Catalysis 13 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 p

13、erturbation theory” (DFPT). Measure of bond stiffnessForce Constant Tensor14As size reduced:Coordination Bond lengths Frequencies Bond stiffness Size-dependent trends in nanoclustersR. Pushpa, U.V. Waghmare & SN15Coordination-dependent trends in nanoclustersBonds in Si clusters are longer and so

14、fter than in bulkBonds in Sn (Pb) clusters are (much) shorter and stiffer than in bulkCoordinationnumber is thekey parameter16Scaling RelationsStiffness (length)-11 for a given elementClustersPeriodic systemsJ. Paul & SN17Competition between fewer bonds and stiffer bonds.Results for elastic modu

15、lus for dilation for Si, Sn and Pb (clusters & bulk)Clusters softer than bulkData 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 & SN18Consequences of enhanced stiffnessu

16、rms decreases as N decreases (for small N) non-monotonically Lindemann melting temperature increases as N decreases, very non-monotonicallyCompetition between fewer bonds and stiffer bonds.When CN in bulk is high/low, clusters have lower/higher urms & higher/lower Tm than bulkR. Pushpa, U.V. Wag

17、hmare & SN19Enhanced magnetism in low-d systemsClusters/monolayers tend to be more magnetic than bulk (Stoner criterion)FeCoNiRuRhPdOsIrPtBulk is magneticClusters and monolayers ferromagnetic Fascinating magnetic properties Lower coordination + magnetism affects reaction rate when used as cataly

18、sts20Factors affecting catalysisModel 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 calculationsAim: to separate out effects of coordination number, strain, charge trans

19、fer & magnetismSpin catalysts?NORh21Spin of Rh clusters + NO adsorptionSystemMagnetic moment (bare clusters)(B/Rh atomMagnetic moment (with NO)(B/Rh atom)Eads of NO(eV/NO molecule)N-O bond length ()RhNO3.00.03.231.19Rh2NO2.00.543.101.21Rh3NO1.670.722.891.23P. Ghosh, R. Pushpa, S.de Gironcoli &am

20、p; SN22Anharmonic Effects Expand energy in powers of displacements: E(x) = T + c(x-x0)2 g(x-x0)3 + f(x-x0)4 + harmonic anharmonic Some consequences: pressure dependence of bulk modulus, Grneisen 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(?).23Thermal expansion