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© Fraunhofer-Institut für Werkstoffmechanik IWM ATOMISTIC/CONTINUUM MULTISCALE COUPLING Michael Moseler Multiscale Modelling and Tribosimulation Fraunhofer Institute for Mechanics of Materials IWM

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Page 1: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

ATOMISTIC/CONTINUUM MULTISCALE COUPLINGMichael Moseler

Multiscale Modelling and Tribosimulation

Fraunhofer Institute for Mechanics of Materials IWM

Page 2: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Ab initio MolecularDynamics

Classical Molecular Dynamics

Coarse grained models

Continuum models

Multiscale Materials Modelling (MMM)

Page 3: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Ab initio MolecularDynamics

Classical Molecular Dynamics

Coarse grained models

Continuum models

Accelerated Molecular Dynamics

Page 4: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Ab initio MolecularDynamics

Classical Molecular Dynamics

Coarse grained models

Continuum models

Extending the continuum regime

Page 5: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Continuum equations

Microscale:atomistics

10 nm

10 µm

10 cm

Multiscale modelingHierarchical atomistic/continuum coupling

10 Å

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

MACRO

MICROContinuum equations

MICRO

Bridge

time

scale

sBrid

ge le

ngth

and

tim

e sc

ales

Page 6: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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)

Today

Page 7: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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

Classical molecular dynamics of nanojet formation and breakup

Page 8: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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?

Page 9: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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

Page 10: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Colloidal fluids:

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

Experimental validation?

Stochastic terms dominateon length scales smaller thanThermal capillary length scales:

Page 11: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Bamboo structure

Growth of carbon nanotubes and the shape evolution of catalyst particles

Page 12: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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

T=750 K

Page 13: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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)

Page 14: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Transport mechanism: surface diffusion

Page 15: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Two Reservoirs:

Diffusive particle current:

z

µ

kT

DrJ s

edges

∂∂−= ρπ2

−−=

)(1

42 LR

r

rL

B

dt

dL

edge

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

kT

DB s

edges

2Ω= ργ

r

2µr Ω= γ

R

2µR Ω= γ

Continuum transport model

Page 16: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

−−=

)(1

42 LR

r

rL

B

dt

dL

edge

Use from MD and solve for Dsedge

0=tdt

dL

edge

Page 17: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Comparison with experiment

Page 18: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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

Page 19: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

Growth at 1200K

Page 20: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Cross section of the newly grown CNT

Fe (green) is incorporated in CNT-walls

Page 21: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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

0 2 4 6 8 10 12 140

5

10

15

20

25

30

Height [A]

0

20

40

60

80

100

120

0 2 4 6 8 10 12 140

5

10

15

20

25

Co

unt

Height [A]

0

60

120

180

240

300

0 2 4 6 8 10 12 140

5

10

15

20

25

30

Height [A]

0

60

120

180

240

300

360

cou

nt

3 eV 34 eV 340 eV

experimentsimulation

Grönhagen, Järvi et al., to be published

Page 22: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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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

Page 23: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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

Page 24: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Topography evolution during thin film growth

Page 25: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM

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?

Page 26: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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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

Page 27: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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α

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

h(h(xx))

)()( xxj h∇−= νParticle current:

Page 28: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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r: deposition rate, Ω : average atomic volume

Stochastic differential equation of motion

Mesoscale description

Stanley&Barabasi, Fractal concepts in Surface Growth

),(),( tht xxj ∇−= ν

Page 29: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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The Edwards-Wilkinson equation

Solution: Power spectral density

)(),( k shshFT→←x

s ~ t

Page 30: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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

Evolution of theexperimental power spectral density

Page 31: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Nanocapillary pumps

Applications in

• Lab-on-Chips

• Nanotribology

• Printing

Non wetted (Au)

Wetted (Au/ML)

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

Page 32: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Washburn‘s law

Balance of capillary and Poiseuillepressure:

τ 0+

τ 1

Meniscus relaxation:

Establisment of Poiseuille flow:

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

Page 33: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Steady state simulations

γηU

Ca =Capillary Number:

U

Au:

Au/ML:

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

Page 34: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

© Fraunhofer-Institut für Werkstoffmechanik IWM Navier slip law:

U=

Page 35: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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The „stress singularity“:

L1

L2

L3

τ

τd

Page 36: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Continuum mechanical modelling

x

z

h(x)Velocity from lubrication approx.+ BCs

UMass flux:

Steady state:

:

:

Page 37: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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x (nm)

Page 38: ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM MULTISCALE COUPLING ... ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10

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Extended Washburn equation