1. Two Examples of Synergy between Experiment and Computation in Nano- Science Sanjay V. Khare Department of Physics and Astonomy University of Toledo Ohio 43606 http://www.physics.utoledo.edu/~khare/

2. Outline About the nano-scale Length Scales and Techniques My lines of research, some examples –Medium range order in a-Si – Pt-Ru and Pt clusters on carbon, structure and electronic properties Summary

3. The scale of things: Sub-nanometer to Macro Natural Manmade Adapted from http://www.sc.doe.gov/bes/

4. What Happens at the Nanoscale?  Surfaces/interfaces between materials often exhibit different properties (geometric, electronic, and magnetic structure, reactivity, …) from bulk due to broken symmetry and/or lower dimensionality.  New surface and interface properties are the origin of new technological developments: high-density magnetic recording, phase-change recording, catalysis, “lab-on-a-chip” devices, and biomedical applications (gene therapy, drug delivery and discovery).

5. Theoretical Techniques and Length Scales 10 – 100 nm and above: Continuum equations, FEM simulations, numerically solve PDEs, empirical relations. 1-10 nm: Monte Carlo Simulations, Molecular Dynamics, empirical potentials. < 1 nm Ab initio theory, fully quantum mechanical. Integrate appropriate and most important science from lower to higher scale.

6. Intermediate length scale 10 nm Length scale: 10 nm Materials: amorphous semiconductors, disordered metal alloys, silica, (a-Si, a-SiO 2, a-Al 92 Sm 8 ) Phenomenon: Structural properties, order-disorder transition, Techniques: Monte Carlo, Molecular dynamics, Image simulation Example Length scale: 10 nm Materials: a-Si Phenomenon: Structural properties of a-Si Techniques: Monte Carlo simulation, image simulation Motivation: Solar cells, medium range order

7. (low variance V(k) in I(k))(high variance V(k) in I(k)) Measuring MRO by Fluctuation Transmission Electron Microscopy P. M. Voyles, Ph.D. Thesis, UIUC (2000).

8. Typical Variance Data 15 Å image resolution peaks at a-Si diffraction maxima average of 8-10 V(k) traces error bars: one  mean Courtesy, Nittala et al.

9. All materials observed to date, a-Si, a-Ge, a-HfO 2, a-Al 92 Sm 8, a-Ge 2 Sb 2 Te 5 show medium range order. Hypothesis: PC grains are frozen-in subcritical crystal nuclei Medium range order (MRO) everywhere Data for a-Si from Voyles et al.

10. Para-crystalline (p-Si) model of a-Si c-Si nano-crystals continuous random network (CRN) matrix += CRN + nano = p-Si c-Si Grains are randomly Orientated and highly strained ==> Material is diffraction amorphous. p-Si has medium range order (MRO)

11. Order in Crystalline Si crystalline Si Crystalline Si: Each atom has 4 bonds and bond angles are fixed. There is short range order and long range order

12. Continuous random network (CRN) of Si continuous random network (CRN) matrix CRN: Each atom has 4 nearest neighbors but bond angles vary. There exists short-range order. But no long range order.

13. Algorithm to make p-Si models 1.First place grains of bulk terminated c-Si in a fixed volume V. Atoms in these grains are called grain atoms. 2.Then randomly distribute atoms in the remaining volume to create a correct density of a-Si. These atoms are matrix atoms. 3.Connect all matrix atoms in a perfect 4-fold random network. 4.Sew the grain surfaces to the matrix such that the (grains + matrix) form a perfectly 4-fold coordinated network. At this stage of construction: Note bonds can be un-physically large. Bonds are just nearest neighbor tables not chemical bonds!

14. Modified WWW Dynamics 1.Do bond switches similar to WWW method to lower the energy. 2.Use Monte Carlo probability. 3.Use Keating potential for relaxation and bond switches. 4.After all moves are exhausted anneal at kT = 0.2-0.3 eV. 5.Go back to step 1 till no more convergence can be achieved.

15. MRO increases smoothly with T s. Voyles, Gerbi, Treacy, Gibson, Abelson, PRL 86, 5514 (2001) Change in peak heights ratio with substrate T s

16. Questions for theory and modeling General: How does the structure of the disordered material affect the V(k) data? Specific for today: When is the second peak higher than the first?

17. CRN reduction increases second peak Big matrix Small CRN matrix same grain size

18. Grain alignment increases second peak Non-aligned grains Aligned grains

19. Effect of crystallite shape on relative peak heights

20. Large aligned fraction of paracrystalline grains give a higher second peak. Similar questions such as dependence of V(k) on grain size distribution can be explained by detailed modeling. “Evidence from atomistic simulations of fluctuation electron microscopy for preferred local orientations in amorphous silicon,” S. V. Khare, S. M. Nakhmanson, P. M. Voyles, P. Keblinski, and J. R. Abelson, App. Phys. Lett. (85, 745 (2004). Available at: http://www.physics.utoledo.edu/~khare/pubs/ Synopsis of a-Si modeling

21. Small length scale 1 nm Length scale: 1 nm Materials: Metals, semi-conductors (Ag, Pt, Si, Ge, Pt-Ru clusters, Graphite) Phenomenon: Energetics, structural and electronic properties Techniques: Ab initio, molecular dynamics, Image simulation Example Length scale: 1 nm Materials: Pt-Ru and Pt clusters on carbon Phenomenon: Structural and electronic properties Techniques: Ab initio method Motivation: Fuel cells, adsorbate substrate interaction

22. Motivation and Conclusions Pure Pt is used extensively as a catalyst Pt-Ru alloys are used a catalysts at the anode in fuel cells in the oxidation reaction: 2CO + O 2 2CO 2 Ru prevents Pt from being poisoned. Model system to study binay nano-cluster properties Existing experiments at UIUC Close-packing geometry preferred by the clusters Pt segregates on top of Ru Novel substrate mediated effects influence the structure Nanoassemblies are supported for functional “devices”. Supports add (semi-infinite) periodicity and affect properties.

23. Supported nano-cluster production PtRu 5 C(CO) 16 clusters were deposited on various graphitic C surfaces Pure Pt clusters were deposited on various graphitic C surfaces by a similar process Topology of both pure Pt and Pt-Ru clusters were then studied using various probes such as STEM, EXAFS, XANES. The structures exhibit a raft like shape

24. Chemistry of inter-metallic nano-cluster deposition Nucleation and growth of bimetallic nanoparticles [PtRu5] n from the cluster precursors PtRu 5 C(CO) 5 as observed by EXAFS, occurring on C substrate. Pt atoms segregate from the core at 400-500 K to the surface at ~700 K. Experiment: C. W. Hills et al., Langmuir 15, 690 (1999); M. S. Nashner et al., J. Am. Chem. Soc. 120, 8093 (1998); 119, 7760 (1997); A. I. Frenkel et al., J. Phys. Chem B 105, 12689 (2001).

25. Features of the nano-clusters Ru Pt Graphitic carbon support (2) Cube-octohedral fcc(111) stacking (3) Magic sizes: 10, 37, 92 … atoms (1) Self-organized nano-clustering on carbon, cluster size 1.0 - 2.0 nm Pt

26. Pt goes on top and bulk bond lengths Ru Pt Graphitic carbon support Pt 92 Pt 6 Ru 31 (5) Even small 37 and 92 atom clusters show bond lengths equal to that in the bulk metals, on “inert” graphitic substrate! (4) In Pt-Ru clusters Pt goes to the top layer

27. Surprise about bulk bond lengths Average bond lengths in clusters from the experiment are 99% - 100%. In 37 free atom cluster only 8% atoms are fully coordinated. In 92 free atom cluster only 20% of atoms are fully coordinated. Substrate carbon must be playing a significant role!

28. Theoretical line of attack Must do ab initio to get structure reliably! Do Pt/Ru and Ru/Pt complete surfaces with full coverage and clusters Cannot do large clusters on graphite with ab initio Do large clusters in vacuum only Do small ones on graphite and vacuum Compare results in vacuum against results on graphite for small clusters Compare with experiment

29. Some checks on our ab initio method 100%99.74%99.36%T/E % 2.453.913.76Theory (T) 2.453.923.78Experiment (E) C (Honeycomb Graphite) Bulk Pt Bulk Ru Ab initio theory reproduces bond distances very well! Table of lattice constants in Å.

30. Pt on top of Ru always wins theoretically Simulated cube-octohedral nanocluster of Pt 6 Ru 31 with Pt on top is stable Simulated cube-octohedral nanocluster of Pt 6 Ru 31 with Pt in the middle breaks cube-octohedral symmetry and is unstable Theoretically Pt on top wins over Pt sub-surface by 0.31 eV/(surface atom) for hcp(111) Ru surface. Theoretically Pt on top wins over Pt sub-surface by 0.48 eV/(surface atom) for fcc(111) Ru surface. Pt sub-surface Pt on top

31. Pt 6 Ru 31 neighbour shell distances (Å) Expt. Theory NN shellPt-PtPt-RuRu-Ru 1 st 2.69 2.702.70 2.622.67 2.52 2 nd 3.78 N/A3.79 3.713.78 3.53 3 rd 4.66 4.674.70 4.504.68 4.41 4 th 5.38 5.305.40 5.055.42 5.12 % of bulk Both ~ 97%Expt. ~99% Theory 93-96% Expt. ~ 100+% Theory ~ 94-96% Theory: PtRu simulated in vacuum Expt.: From fits to EXAFS data on C Percentages are comparisons with bulk values

32. Pt 92 neighbour shell distances (Å) Theory: Pt 92 simulated in vacuum Expt.: From fits to EXAFS data Percentages are comparisons with bulk values 5.96[96.16%]6.18[99.71%]5 th 5.34[96.33%]5.52[99.57%]4 th 4.67[97.27%]4.78[99.56%]3 rd 3.81[97.19%]3.91[99.74%]2 nd 2.71[97.77%]2.76[99.57%]1 st Theory [% of bulk]Expt. [ % of bulk] Pt 92 NN shell

33. Small clusters in vacuum and on C trimer capped trimer capped 10-atom 2.602.652.432.5010 2.772.66bulk 2.552.592.332.484 2.442.522.242.543 2.292.431.902.552 Pt in vacuum Pt on CRu in vacuum Ru on C# of atoms dimer Average bond lengths in Å from ab initio theory

34. Bulk-like Bonds: A Substrate-Mediated Effect

35. Relative scales: Substrate versus Ru C-C distance ( ) = 1.42 Å, Center to Center( ) = 2.45 Å Ru dimer on C ( ) = 2.54 Å Ru bulk bond length = 2.66 Å Honeycomb structure of graphene Substrate length scales < adsorbate scales Effect of substrate is not just geometric Lengths not in simple ratios, hence adsorbate clusters are incommensurate Subtle electronic effect due to graphene  electrons

36. Theory Enhances Understanding Nano-assemblies are always substrate-supported Substrate mediated effect Properties highly affected by support For metallic nano-clusters on carbon, bond-lengths and distributions agree with experiment once support is included Theory yields fundamental insight Location and electronic properties can be analyzed atom by atom Not always possible with simple experiment Experimental data is only simulated to fit with measured signal Ab initio methods are reliable for structural and electronic properties! S. V. Khare, D. D. Johnson et al., (In preparation).

37. Collaborators Senior Theorists Experimentalists D. D. Johnson (UIUC) J. R. Abelson (UIUC) A. A. Rockett (UIUC) R. G. Nuzzo (UIUC) Colleagues and Students V. Chirita (U. of Linkoping, Sweden) P. M. Voyles (Wisconsin) P. Keblinski (RPI) S. Nakhmanson (NCSU)

38. Institutional Support Department of Materials Science and Engineering and Frederick Seitz Materials Research Lab University of Illinois at Urbana-Champaign Illinois 61801 USA Support: NSF, DARPA Program, DOE, and ONR.

39. Exciting future for synergy between theoretical modeling and experiments Combination of appropriate theoretical tools for the right length scale and close contact with experimentalists is mutually fruitful! Thank you!

40. Z=0.125 Å Z=0.250 Å Z=0.375 Å Z=0.500 Å Z=0.625 Å Z=0.750 Å Z=1.000 Å Electronic Density Plot: Free Dimer Free Ru 2 bond length = 1.9 Å Different Z slices

41. Ru dimer on C slice through Z = 0.80 Å Electronic Density Plot: Dimer on C Jahn-Teller distortion: Ru dimer ion cores are not at symmetric hexagon centers. A single Ru adatom favors hexagon center not side.

42. Ru dimer on C slice through Z=0.89 Å Bottom Ru ion cores is closer to carbon surface. Ru dimer asymmetrically placed in hexagon and canted. Dimer is canted – not parallel to graphite

43. Ru trimer on C slice through Z=0.18 Å Electronic Density Plot: Trimer on C Close to graphite plane Ru trimer ion cores are not at symmetric hexagon centers.

44. Charge Difference Isosurface of Planar Ru Trimer relative to unsupported trimer ±2 e/A 3 isosurface red red charge deficit yellow yellow charge gain From the bottom Symmetry of the charge distribution matches the symmetry of the substrate - lowering energy. As will all 3-fold and 6-fold symmetric clusters. Hence cub-octahedral stacking occurs on layers that have such symmetry, such a 7-atom layer, … Courtesy of Lin Lin Wang and D.D. Johnson (UIUC)

45. Pt 6 Ru 31 Bond Lengths (Å) per n.n. Shell For Pt 92 cluster (5 shells): 99+% in experiment, 96-99% in theory 99+% (94-99%) of bulk value in experiment (theory). No 2nd n.n. bond for Pt-Pt with Pt atop position! Graphite only important for atoms near graphite surface.

46. Z=1.77 Å Slice through trimer atoms Ru trimer is planar, unlike dimer Average distance from C-graphite remains same as dimer.

47. Ab initio method details LDA, Ceperley-Alder exchange-correlation functional as parameterized by Perdew and Zunger Used the VASP code with generalized ultra-soft Vanderbilt pseudo-potentials and plane wave basis set 14 Å cubic cell in vacuum with (4x4) graphite surface cell, 7 layers of vacuum 18 Ry. energy cut-off with  point sampling in the irreducible Brillouin zone Forces converged till < 0.03 eV/ Å Used RISC/6000 and DEC alpha machines at UIUC

48. Self-organized Pt and PtRu nano-assemblies on carbon Nucleation and growth of bimetallic nanoparticles [PtRu5] n from the cluster precursors PtRu 5 C(CO) 5 as observed by EXAFS, occurring on C substrate. Pt atoms segregate from the core at 400-500 K to the surface at ~700 K. Ru Pt support

49. Embedded Atom Method (EAM) details Classical potential between atoms made up of a pair potential and an embedding function EAM analytical functional for fcc metals from R.A. Johnson, PRB 39,12554(1989) EAM potential is well fitted to cohesive energy, bulk modulus, vacancy formation energy and other properties Forces converged till < 0.03 eV/ Å The potential also yields good surface properties such as the diffusion barrier on Pt(111)

50. Three areas of my research Length scale: 100 nm Materials: metals, semiconductors, metal nitrides (Ag, Pt, Si, Ge, TiN) Phenomenon: Energetics, dynamics, fluctuations of steps, islands Techniques: Analytical, Numerical solutions to PDEs, Monte Carlo Length scale: 10 nm Materials: amorphous semiconductors, disordered metal alloys, silica, (a-Si, a-SiO 2, a-Al 92 Sm 8 ) Phenomenon: Structural properties, order-disorder transition, Techniques: Monte Carlo, Molecular dynamics, Image simulation Length scale: 1 nm Materials: Metals, semi-conductors (Ag, Pt, Si, Ge, Pt-Ru clusters, Graphite) Phenomenon: Energetics, structural and electronic properties Techniques: Ab initio, molecular dynamics, Image simulation

51. Density Functional Theory (DFT) Hohenberg Kohn Theorems (1964) (1)The external potential of a quantum many body system is uniquely determined by the  r), so the total energy is a unique functional of the particle density E = E  r)]. (2) The density that minimizes the energy is the ground state density and the energy is the ground state energy, Min{E  r)]} = E 0 Synonyms: DFT = Ab initio = First Principles

52. Kohn Sham Theory (1965) The ground state density of the interacting system of particles can be calculated as the ground state density of non-interacting particles moving in an effective potential v eff  r)]. Coulomb potential of nuclei Hartree electrostatic potential is universal! Exchange correlation potential

53. Practical Algorithm Effective Schrodinger equation for non-interactng electrons Implementation: 1.Guess an initial charge density for N electrons 2. Calculate all the contributions to the effective potential 3. Solve the Schrodinger equation and find N electron states 4. Fill the eigenstates with electrons starting from the bottom 5.Calculate the new charge density 6.Calculate all the contributions to the effective potential and iterate until the charge density and effective potential are self- consistent. 7.Then calculate total energy.

54. Value of ab initio method Powerful predictive tool to calculate properties of materials Fully first principles ==> –(1) no fitting parameters, use only fundamental constants (e, h, m e, c) as input –(2) Fully quantum mechanical for electrons Thousands of materials properties calculated to date Used by biochemists, drug designers, geologists, materials scientists, and even astrophysicists! Evolved into different varieties for ease of applications Awarded chemistry Nobel Prize to W. Kohn and H. Pople 1998

55. What is it good for? Pros Very good at predicting structural properties: (1) Lattice constant good to 1-10% (2) Bulk modulus good to 1-10% (3) Very robust relative energy ordering between structures (4) Good pressure induced phase changes Good band structures, electronic properties Good phonon spectra Good chemical reaction and bonding pathways Cons Computationally intensive, Si band gap is wrong Excited electronic states difficult

56. Schematic of FEM measurement

57. Long standing problem: Lack of a technique for direct measurement of Medium Range Order (MRO).  Diffraction is only sensitive to the 2- body correlation function g 2 (r 1,2 ).  3- and 4-body correlation functions, g 3 (r 12,r 13 ) and g 4 (r 12,r 13,r 14 ) carry MRO statistics. dihedral angle φ 1 2 3 4 FEM measures medium range order MRO

58. Basis for present work Keblinski et al. : Quench from the melt Paracrystallites give V(k) with peaks S. Nakhmanson et al. : Modified WWW dynamics Fit one data set for V(k) Studied structural, vibrational, and electronic properties. Review: N. Mousseau et al. : Phil. Mag. B 82, 171 (2002). _________________________________________________ Present work: Follow Nakhmanson et al. : make family of models.

59. 12 p-Si models + 1 CRN model % of c-Si atoms # of c-Si grains Total # of models 43%1 or 2 or 43 32%1 or 2 or 43 21%1 or 2 or 43 11%1 or 2 or 43 0%01(CRN) All models have similar pair-distribution function g 2 (r). All models have bond-angle distribution peaked at 109 o ±10 o. All models have double peaked dihedral angle distribution at 60 o and 180 o. All models made of exactly 1000 Si atoms

60. 43% of c-Si differing number of grains

61. 12% of c-Si differing number of grains

62. Single grain variance differing % of c-Si

63. Two grain variance differing % of c-Si data

64. Four grain variance differing % of c-Si

65. Effect of strain on CRN

66. Strain effect on single grain data

67. Strain effect on two grain data

68. Large length scale 100 nm Length scale: 100 nm Materials: Metals, semiconductors, metal nitrides (Ag, Pt, Si, Ge, TiN) Phenomenon: Energetics, dynamics, fluctuations of steps, islands Techniques: Analytical, Numerical solutions to PDEs, Monte Carlo Example Length scale: > 100 nm Materials: surface of TiN(111) Phenomenon: Dislocation driven surface dynamics Techniques: Analytical model

69. Low energy electron micrographs of decay of two dimensional (2D) TiN islands on TiN(111) 4x4  m 2 t real = 12 min t movie = 17 sec T a = 1280  C Rate of area change dA/dt ~ exp(-E a /kT), E a = activation energy for atom detachment from step to terrace

70. ~ eV Ea ~ 2.5 eV *S. Kodambaka, V. Petrova, S.V. Khare, D. Gall, A. Rockett, I. Petrov, and J.E. Greene, Phys. Rev. Lett. 89, 176102 (2002). * Measured E a is in agreement with detachment limited step-curvature driven surface transport* Rate island area change dA/dt vs. temperature T

71. field of view: 2.5  m t real = 90 s; t movie = 9 s Low energy electron micrographs of growth of spirals and loops of TiN on TiN(111) T = 1415 o C t real = 200 s; t movie = 21 s field of view: 1.0  m T = 1380 o C Spiral 2D Loop Not BCF growth structures T/T m ~ 0.5 2D Loop schematic

72. near-equilibrium shape-preserving  period =   ) ~  = (2  /  ) ~ exp(-E d /kT), is thermally-activated absenceapplied stressnet mass change by deposition/evaporation. absence of applied stress & net mass change by deposition/evaporation. t = 0 s 15 s 31 s 47 s  = 47 s TiN(111) spiral step growth T = 1415 o C

73. E d = 4.5  0.2 eV versus T for spirals  versus T for spirals Activation energy for island decay E a = 2.5 eV Activation energy for spiral or loop growth E d = 4.5 eV Activation energy for sublimation E evaporation ~ 10 eV E a << E d << E evaporation Spiralloop Spiral (& loop) nucleation and growth bulk mass transport MUST be due to bulk mass transport !!  (10 -2 rad/s)  is thermally-activated

74. Modeling dislocation-driven spiral growth Assumptions: driving force: bulk dislocation line energy minimization  surface spiral step formation via bulk point defect transport dislocation cores emit/absorb point defects at a rate R(T). r core r loop At steady state: B.C.s: C - point defect concentration (1/Å 2 ) D s - surface diffusivity (Å 2 /s) k s - attachment/detachment rate (Å/s)  - area/TiN (Å 2 ) Step velocity:  constant growth rate dA/dt

75. Modeling dislocation-driven spiral growth Analytical model, two key assumptions: (1) driving force: bulk dislocation line energy  minimization  surface spiral step formation via bulk point defect transport (2) dislocation cores emit/absorb point defects at a constant rate R(T). r core r loop Results of model consistent with observations: (1) Loop or spiral growth rate dA/dt and are constant (1) Loop or spiral growth rate dA/dt and  are constant (2) Both are thermally activated (3) Activation energy E d corresponds to facile point defect migration along bulk dislocation cores. R(T)

76. TiN(111) step dynamics and the effect of surface-terminated dislocations were studied using LEEM (1200-1500 o C). Spiral step growth kinetics: qualitatively & quantitatively different from 2D TiN(111) island decay. Mechanism: facile bulk point defect migration along the dislocations (E d = 4.5±0.2 eV). “Dislocation Driven Surface Dynamics on Solids”, S. Kodambaka, S. V. Khare, W. Sweich, K. Ohmori, I. Petrov, and J. E. Greene, Nature, 429, 49 (2004). Available at: http://www.physics.utoledo.edu/~khare/pubs/ Spirals Summary

77. Future theory for catalytic nano-clusters Obtain molecular orbital picture of the bonding. Study catalysis on Pt-Ru surfaces. Investigate other alloy systems which are being discovered such as ceria, tungsten oxide, alumina and others. Predict new useful catalytic materials.