Coarse-Grained%20Theory%20of%20Surface%20Nanostructure%20Formation

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Coarse-Grained Theory of Surface Nanostructure
Formation

• Dimitri D. Vvedensky
• The Blackett Laboratory, Imperial College London
• Christoph A. Haselwandter
• Department of Applied Physics, Caltech

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Imperial College London
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Outline

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

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Outline

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

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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)
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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).
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Multiscale Physics Critical Phenomena
2D Ising Model
J. D. Noh, Chungham National University, Korea
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Multiscale Physics Medical Implants
B. Kasemo, Surface Science 500, 656 (2002)
Time Scale
ns
µm
ms
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Outline

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

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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)
Direct analysis/solution
Continuum equation
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
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Lattice-to-Continuum Method
Atomistic Continuum Equation
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Continuum Equation for Random Deposition/Diffusion
Compare atomistic equation directly to computer
simulations?
Extract qualitative multiscale surface features
via RG analysis
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The Multiscale Paradigm
M. Scheffler, FHIBerlin
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Outline

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

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

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Outline

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

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Stable Unstable Fixed Points
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Initial Conditions Crossover
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Outline

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

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Regimes of Growth

• D/Fgtgt1. 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/Fltlt1. Growth dominated by shot noise.

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Growth on Patterned Substrates. 1.
H.-C. Kan et al., Phys. Rev. Lett. 92, 146101
(2004).
KPZ
cVLDS
VLDS
Mound
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Growth on Patterned Substrates. 2.
H.-C. Kan et al., Phys. Rev. Lett. 92, 146101
(2004).
Experiment
KPZ
cVLDS
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Analysis from Initial Conditions
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Outline

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

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The Submonolayer Regime
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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

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Ongoing and Future Work

• Coarse-graining magnetohydrodynamics
• Coarse-grained molecular dynamics