ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM...

ATOMISTIC/CONTINUUM MULTISCALE COUPLINGMichael Moseler

Multiscale Modelling and Tribosimulation

Fraunhofer Institute for Mechanics of Materials IWM

Ab initio MolecularDynamics

Classical Molecular Dynamics

Coarse grained models

Continuum models

Multiscale Materials Modelling (MMM)

Continuum models

Accelerated Molecular Dynamics

Continuum models

Extending the continuum regime

Continuum equations

Microscale:atomistics

10 µm

Multiscale modelingHierarchical atomistic/continuum coupling

Constitutive equations Material parametersBoundary conditionsCorrections (e.g. finite size)Validation

MICROContinuum equations

Bridge

Classical transport and shape evolution in small systems

Rayleigh instability: Science 289, 1165 (2000)

DLC growth: Science 309, 1545 (2005)

CNT growth: ACS Nano 5, 686 (2011) Capillary impregantion:

NJP, 10, 113022 (2008)

Wear of surfaces:Nature Mat. 10, 34 (2011)

NanojetsMoseler & Landman, Science 289, 1165 (2000).

Classical molecular dynamics of nanojet formation and breakup

Jens Eggers, Rev. Mod. Phys. 69, 865,(1997) J. Eggers, E. Villermaux, Rep. Prog. Phys. 71 , 036601 (2008)

Lubrication equations:

Intrinsic scales:

Similarity solution : threads

Rayleigh instability and the validity of hydrodynamics on the nanoscale?

Comparison of molecular dynamics with Navier-StokesTaking into account stress fluctuations in small systems

Colloidal fluids:

Hennequin, et al., Phys. Rev. Lett. 97 244503 (2006)

Experimental validation?

Stochastic terms dominateon length scales smaller thanThermal capillary length scales:

Bamboo structure

Growth of carbon nanotubes and the shape evolution of catalyst particles

Environmental TEM experiments:Environmental TEM experiments:Shape dynamics of Ni catalyst particlesShape dynamics of Ni catalyst particles

T=750 K

Molecular dynamics of a solid Ni nanoparticle in a double wall carbon nanotube

A T=1160 K EAM Ni10561 interacting via Morse potentials with a static CNT

Moseler et al., ACS Nano 5, 686 (2011)

Transport mechanism: surface diffusion

Two Reservoirs:

Diffusive particle current:

∂∂−= ρπ2

−−=

Mullins B:WW Mullins, J.Appl.Phys. 28 333 (1957)

2Ω= ργ

2µr Ω= γ

2µR Ω= γ

Continuum transport model

−−=

Use from MD and solve for Dsedge

Comparison with experiment

CNT with Fe-CatalystTip growth of (15,0) tube catalysed by Fe561

Molecular dynamics simulation with reactive Bond-Order-Potential (Albe, Nordlund)

Deposition rate 2⋅ 1010 C/s

Growth at 600 K

Growth at 1200K

Cross section of the newly grown CNT

Fe (green) is incorporated in CNT-walls

Deposition of AgN on Au(111)Effect of deposition energy

0 2 4 6 8 10 12 140

Height [A]

0 2 4 6 8 10 12 140

Height [A]

0 2 4 6 8 10 12 140

Height [A]

3 eV 34 eV 340 eV

experimentsimulation

Grönhagen, Järvi et al., to be published

Decay mechanism

Decay of top monolayer

Non-local effect of surface on cluster Barrier from ca. 0.4 to 0.2 eV

Barrier inferred from experiment at 77 K: ca. 0.25 eV

Thank you for your attention!

Summary

A hierarchical atomistic/continuum modelling is quite usefull for a quantitative understanding of complex shape dynamics in nanoscale systems.

Acknowledgement:

Uzi Landman, Georgia Institute of Technology

Andreas Klemenz, Fraunhofer IWM

F. Cervantes-Sodi, S.Hofmann, G. Czanyi, A. Ferrari, Cambridge Univ.

Tommi Järvi, Fraunhofer IWM

Topography evolution during thin film growth

Casiraghi, Ferrari, Ohr, Flewitt, Chu, Robertson, PRL 91, 226104 (2003)

C impinges on ta-C with 100 eV

MD with Brenner BOP, D. W. Brenner, Phys. Rev. B 42, 8458 (1990)

Capillary smoothing?

Atomistic simulation of film growth

The smoothing of a rough DLC film4000 C-atoms with 100 eV hit a filmwith an area 7.05nm x 2.35nm

Downhill currentsG.Carter, PRB 54, 17647 (1996 )M.Moseler et al. Comp. Mat. Sci. 10,452 (1998)

h(h(xx))

)()( xxj h∇−= νParticle current:

r: deposition rate, Ω : average atomic volume

Stochastic differential equation of motion

Mesoscale description

Stanley&Barabasi, Fractal concepts in Surface Growth

),(),( tht xxj ∇−= ν

The Edwards-Wilkinson equation

Solution: Power spectral density

)(),( k shshFT→←x

Moseler, Gumbsch, Casiraghi, Ferrari, Robertson„The ultrasmoothness of diamond-like carbon“, Science 309, 1545 (2005)

Evolution of theexperimental power spectral density

Nanocapillary pumps

Applications in

• Lab-on-Chips

• Nanotribology

• Printing

Non wetted (Au)

Wetted (Au/ML)

Zimmermann et al.,Lab Chip 7, 119 (2007)

Washburn‘s law

Balance of capillary and Poiseuillepressure:

Meniscus relaxation:

Establisment of Poiseuille flow:

D. Quere, Europhys.Lett. 39, 533 (1997).

Steady state simulations

Ca =Capillary Number:

Au/ML:

J. Eggers, H. A. Stone, J. Fluid Mech. 505, 309 (2004)

The „stress singularity“:

Continuum mechanical modelling

h(x)Velocity from lubrication approx.+ BCs

UMass flux:

Steady state:

x (nm)

Extended Washburn equation

ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM...

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