coarse-grained theory of surface nanostructure formation
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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 CollegeLondon
Outline
• Systems with many scales• The coarse-graining road map• Renormalization-group trajectories• Transient effects and crossover• Experimental realizations• Extension to the submonolayer regime
Outline
• Systems with many scales• The coarse-graining road map• Renormalization-group trajectories• Transient effects and crossover• Experimental realizations• Extension to the submonolayer regime
Multiscale Physics: Turbulence
C. H. K. Williamson, Cornell (Source: http://www.efluids.com)
• 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
Multiscale Physics: Fracture
F. F. Abraham, D. Brodbeck, R. A. Rafey, andW. E. Rudge, Phys. Rev. Lett. 73, 272 (1994).
• 2D simulation of 106- atom system• Bond-breaking at crack tip• Dislocation emission blunts crack tip• Feed-back between atomic and continuum modes
Multiscale Physics: Critical Phenomena2D Ising Model
J. D. Noh, Chungham National University, Korea
Multiscale “Physics”: Medical ImplantsB. Kasemo, Surface Science 500, 656 (2002)
Time Scale
ns
µm
ms
Outline
• Systems with many scales• The coarse-graining road map• Renormalization-group trajectories• Transient effects and crossover• Experimental realizations• Extension to the submonolayer regime
formulationMaster & Chapman-
Kolmogorov equations
Lattice Langevin equation
Hierarchy of equations
KMC simulations
Lattice model
Macroscopic equation
continuum variables
renormalization-group(crossover, scaling,self-organization)
analytic
stable
fixed point
Chua et al., PRE 72, 051103 (2005),C. A. H. & D. D. V., PRE 76, 041115 (2007)
Direct analysis/solution
C. A. H. & D. D. V. PRL, EPL, PRE (2007, 2008)
Coarse-Graining Road Map
Continuum equation
Lattice-to-Continuum Method
“Atomistic” Continuum Equation
Compare atomistic equation directly to computer simulations?
Extract qualitative multiscale surface features via RG analysis…
Continuum Equation for Random Deposition/Diffusion
The Multiscale Paradigm
M. Scheffler, FHI–Berlin
Outline
• The coarse-graining road map
• Renormalization-group trajectories
• Transient effects and crossover
• Experimental realizations
• Extension to the submonolayer regime
Renormalization Group Transformations
Real Space
MomentumSpace
Original System Coarse Graining Rescaling
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.
Outline
• The coarse-graining road map
• Renormalization-group trajectories
• Transient effects and crossover
• Experimental realizations
• Extension to the submonolayer regime
Stable & Unstable Fixed Points
Initial Conditions & Crossover
Outline
• The coarse-graining road map
• Renormalization-group trajectories
• Transient effects and crossover
• Experimental realizations
• Extension to the submonolayer regime
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 SolidFilms 517, 3408 (2009)).
• D/F<<1. Growth dominated by shot noise.
Growth on Patterned Substrates. 1.H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004).
KPZ
cVLDS
VLDS
Mound
Growth on Patterned Substrates. 2.H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004).
Experiment KPZ cVLDS
Analysis from Initial Conditions
Outline
• The coarse-graining road map
• Renormalization-group trajectories
• Transient effects and crossover
• Experimental realizations
• Extension to the submonolayer regime
The Submonolayer Regime
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
Ongoing and Future Work
• Coarse-graining magnetohydrodynamics• Coarse-grained molecular dynamics