Constructing constrained invariant sets in multiscale continuum
ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM...
Transcript of ATOMISTIC/CONTINUUM MULTISCALE COUPLINGbemod12/Slides/Moseler_Bemod12.pdf · ATOMISTIC/CONTINUUM...
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ATOMISTIC/CONTINUUM MULTISCALE COUPLINGMichael Moseler
Multiscale Modelling and Tribosimulation
Fraunhofer Institute for Mechanics of Materials IWM
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Ab initio MolecularDynamics
Classical Molecular Dynamics
Coarse grained models
Continuum models
Multiscale Materials Modelling (MMM)
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Ab initio MolecularDynamics
Classical Molecular Dynamics
Coarse grained models
Continuum models
Accelerated Molecular Dynamics
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Ab initio MolecularDynamics
Classical Molecular Dynamics
Coarse grained models
Continuum models
Extending the continuum regime
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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
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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
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NanojetsMoseler & Landman, Science 289, 1165 (2000).
Classical molecular dynamics of nanojet formation and breakup
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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?
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Comparison of molecular dynamics with Navier-StokesTaking into account stress fluctuations in small systems
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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:
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Bamboo structure
Growth of carbon nanotubes and the shape evolution of catalyst particles
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Environmental TEM experiments:Environmental TEM experiments:Shape dynamics of Ni catalyst particlesShape dynamics of Ni catalyst particles
T=750 K
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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)
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Transport mechanism: surface diffusion
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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
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−−=
)(1
42 LR
r
rL
B
dt
dL
edge
Use from MD and solve for Dsedge
0=tdt
dL
edge
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Comparison with experiment
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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
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Growth at 1200K
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Cross section of the newly grown CNT
Fe (green) is incorporated in CNT-walls
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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
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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
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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
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Topography evolution during thin film growth
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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?
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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
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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:
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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
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The Edwards-Wilkinson equation
Solution: Power spectral density
)(),( k shshFT→←x
s ~ t
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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
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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)
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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).
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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)
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U=
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The „stress singularity“:
L1
L2
L3
τ
τd
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Continuum mechanical modelling
x
z
h(x)Velocity from lubrication approx.+ BCs
UMass flux:
Steady state:
:
:
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x (nm)
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Extended Washburn equation