ATOMISTIC/CONTINUUM MULTISCALE COUPLING

Transcription

1 ATOMISTIC/CONTINUUM MULTISCALE COUPLING Michael Moseler Multiscale Modelling and Tribosimulation Fraunhofer Institute for Mechanics of Materials IWM

2 Multiscale Materials Modelling (MMM) Continuum models Coarse grained models Classical Molecular Dynamics Ab initio Molecular Dynamics

3 Accelerated Molecular Dynamics Continuum models Coarse grained models Classical Molecular Dynamics Ab initio Molecular Dynamics

4 Extending the continuum regime Continuum models Coarse grained models Classical Molecular Dynamics Ab initio Molecular Dynamics

5 Multiscale modeling 10 cm MACRO 10 µm Microscale: atomistics 10 nm tim e sc al es MICRO ge Constitutive equations Material parameters Boundary conditions Corrections (e.g. finite size) Validation Continuum equations Br id Bridge length and time scales Hierarchical atomistic/continuum coupling 10 Å Continuum equations MICRO

6 Classical transport and shape evolution in small systems Today CNT growth: ACS Nano 5, 686 (2011) Capillary impregantion: NJP, 10, (2008) Wear of surfaces: Nature Mat. 10, 34 (2011) DLC growth: Science 309, 1545 (2005) Rayleigh instability: Science 289, 1165 (2000)

7 Classical molecular dynamics of nanojet formation and breakup Nanojets Moseler & Landman, Science 289, 1165 (2000).

8 Rayleigh instability and the validity of hydrodynamics on the nanoscale? Lubrication equations: Jens Eggers, Rev. Mod. Phys. 69, 865,(1997) J. Eggers, E. Villermaux, Rep. Prog. Phys. 71, (2008) Intrinsic scales: Similarity solution : threads

9 Comparison of molecular dynamics with Navier-Stokes Taking into account stress fluctuations in small systems

10 Experimental validation? Stochastic terms dominate on length scales smaller than Thermal capillary length scales: Hennequin, et al., Phys. Rev. Lett (2006) Colloidal fluids:

11 Growth of carbon nanotubes and the shape evolution of catalyst particles Bamboo structure

12 Environmental TEM experiments: Shape dynamics of Ni catalyst particles T=750 K

13 Molecular dynamics of a solid Ni nanoparticle in a double wall carbon nanotube Moseler et al., A T=1160 K EAM Ni10561 interacting via Morse potentials with a static CNT ACS Nano 5, 686 (2011)

14 Transport mechanism: surface diffusion

15 Continuum transport model Two Reservoirs: Diffusive particle current: 2 µ r = γω r Dsedge ρ s µ J = 2πr kt z dl 4B = 2 dt Ledge r µ R = γω r 1 R ( L) 2 R Mullins B: WW Mullins, J.Appl.Phys (1957) γdsedge ρ s Ω 2 B= kt

16 r 1 R ( L) edge dl 4B dl = Use from MD and solve 2 dt dt t =0 Ledge r for D sedge

17 Comparison with experiment

18 CNT with Fe-Catalyst Tip growth of (15,0) tube catalysed by Fe561 Molecular dynamics simulation with reactive Bond-Order-Potential (Albe, Nordlund) Deposition rate C/s Growth at 600 K

19 Growth at 1200K

20 Cross section of the newly grown CNT Fe (green) is incorporated in CNT-walls

21 Deposition of AgN on Au(111) Effect of deposition energy 34 ev 340 ev Count Grönhagen, Järvi et al., to be published 6 8 Height [A] experiment simulation 15 Height [A] Height [A] count 3 ev

22 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 ev

23 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 Thank you for your attention!

24 Topography evolution during thin film growth

25 Capillary smoothing? C impinges on ta-c with 100 ev MD with Brenner BOP, D. W. Brenner, Phys. Rev. B 42, 8458 (1990) Casiraghi, Ferrari, Ohr, Flewitt, Chu, Robertson, PRL 91, (2003)

26 Atomistic simulation of film growth The smoothing of a rough DLC film 4000 C-atoms with 100 ev hit a film with an area 7.05nm x 2.35nm

27 Downhill currents h(x) G.Carter, PRB 54, (1996 ) M.Moseler et al. Comp. Mat. Sci. 10, 452 (1998) Particle current: j (x) = ν h(x) α

28 Mesoscale description Stochastic differential equation of motion j (x, t ) = ν h(x, t ) r: deposition rate, Ω : average atomic volume Stanley&Barabasi, Fractal concepts in Surface Growth

29 The Edwards-Wilkinson equation s~t h(x, s ) hk ( s ) FT Solution: Power spectral density

30 Evolution of the experimental power spectral density Moseler, Gumbsch, Casiraghi, Ferrari, Robertson The ultrasmoothness of diamond-like carbon, Science 309, 1545 (2005)

31 Nanocapillary pumps Applications in Lab-on-Chips Non wetted (Au) Nanotribology Printing Zimmermann et al., Lab Chip 7, 119 (2007) Wetted (Au/ML)

32 τ 0+τ 1 Meniscus relaxation: Establisment of Poiseuille flow: D. Quere, Europhys.Lett. 39, 533 (1997). Washburn s law Balance of capillary and Poiseuille pressure:

33 Steady state simulations U Capillary Number: ηu Ca = γ Au: Au/ML: J. Eggers, H. A. Stone, J. Fluid Mech. 505, 309 (2004)

34 U= Navier slip law:

35 The stress singularity : d τ τ L1 L2 L3

36 Continuum mechanical modelling z Velocity from lubrication approx.+ BCs Mass flux: h(x) U Steady state: : : x

37 x (nm)

38 Extended Washburn equation