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Coarse-Grained Theory of Surface Nanostructure Formation

Coarse-Grained Theory of Surface Nanostructure Formation. Dimitri D. Vvedensky The Blackett Laboratory, Imperial College London Christoph A. Haselwandter Department of Applied Physics, Caltech. Imperial College London. Outline. Systems with many scales The coarse-graining road map

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Coarse-Grained Theory of Surface Nanostructure Formation

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  1. Coarse-Grained Theory of Surface Nanostructure Formation Dimitri D. Vvedensky The Blackett Laboratory, Imperial College London Christoph A. Haselwandter Department of Applied Physics, Caltech

  2. Imperial College London

  3. Outline • Systems with many scales • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  4. Outline • Systems with many scales • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  5. Multiscale Physics: Turbulence • Free gliding of delta-wing in water • Fluorescent dye illuminated by laser • Vortices in near field • Turbulence in far field • Both panels have same scale • Energy cascades from large to small scales C. H. K. Williamson, Cornell (Source: http://www.efluids.com)

  6. Multiscale Physics: Fracture • 2D simulation of 106- atom system • Bond-breaking at crack tip • Dislocation emission blunts crack tip • Feed-back between atomic and continuum modes F. F. Abraham, D. Brodbeck, R. A. Rafey, and W. E. Rudge, Phys. Rev. Lett. 73, 272 (1994).

  7. Multiscale Physics: Critical Phenomena 2D Ising Model J. D. Noh, Chungham National University, Korea

  8. Multiscale “Physics”: Medical Implants B. Kasemo, Surface Science500, 656 (2002) Time Scale ns µm ms

  9. Outline • Systems with many scales • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  10. Coarse-Graining Road Map stable Hierarchy of equations Macroscopic equation fixed point renormalization-group (crossover, scaling, self-organization) C. A. H. & D. D. V. PRL, EPL, PRE (2007, 2008) Continuum equation Direct analysis/solution Lattice Langevin equation KMC simulations continuum variables Chua et al., PRE 72, 051103 (2005), C. A. H. & D. D. V., PRE 76, 041115 (2007) analytic Master & Chapman- Kolmogorov equations Lattice model formulation

  11. Lattice-to-Continuum Method “Atomistic” Continuum Equation

  12. Continuum Equation for Random Deposition/Diffusion Compare atomistic equation directly to computer simulations? Extract qualitative multiscale surface features via RG analysis…

  13. The Multiscale Paradigm M. Scheffler, FHI–Berlin

  14. Outline • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  15. Renormalization Group Transformations Original System Coarse Graining Rescaling Real Space Momentum Space

  16. Renormalization-Group Equations • Points along RG trajectory constitute a hierarchy of equations. • RG “weeds out” terms that become irrelevant as the scale is increased, and absorbs their contributions into other terms.

  17. Outline • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  18. Stable & Unstable Fixed Points

  19. Initial Conditions & Crossover

  20. Outline • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  21. Regimes of Growth • D/F>>1. Typical MBE conditions. Initially, conserved Mullins-Herring. Submonolayer regime. • D/F ≈ 1. Diffusion noise diminished in importance. Initially, Mullins-Herring. Al on silicone oil (Fang et al., Thin Solid Films 517, 3408 (2009)). • D/F<<1. Growth dominated by shot noise.

  22. Growth on Patterned Substrates. 1. H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004). KPZ cVLDS VLDS Mound

  23. Growth on Patterned Substrates. 2. H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004). Experiment KPZ cVLDS

  24. Analysis from Initial Conditions

  25. Outline • The coarse-graining road map • Renormalization-group trajectories • Transient effects and crossover • Experimental realizations • Extension to the submonolayer regime

  26. The Submonolayer Regime

  27. Summary • Continuum formulation that retains connection to atomistic processes • Unifies a wide range of experimental scenarios • Extension to submonolayer regime • Large-scale morphologies on patterned substrates

  28. Ongoing and Future Work • Coarse-graining magnetohydrodynamics • Coarse-grained molecular dynamics

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