MPI Metallforschung Stuttgart, Nov 2005
Materials modeling
from femtometer to centimeter
Barend Thijsse
Department of Materials Science and Engineering
Virtual Materials Lab
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Talk layout
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Our group and the Virtual Materials Lab
Why use computers to study materials?
The need for multiscale modeling
Examples and challenges
Outlook
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Our group: Art & Archaeology
Dr. Joris Dik
Si
Pb
Vermeer or not Vermeer ?
Young Woman at the Virginals
Delft, 1672
VML
optical
100mu
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Our group: Behavior of Thin Films
Dr. Amarante Böttger
0.04
Bulk iron value
60 nm film
127 nm film
189 nm film
312 nm film
300
Young modulus, GPa
0.03
Probability
250
0.02
200
150
0.01
(b)
0.00
-40
-20
0
height n( m)
20
Interface roughness & fracture energy
influence of roughness amplitude (w) and
lateral correlation (ξ) on fracture energy
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100
40
100
200
300
400
500
Annealing temperature, ºC
Nano-crystalline Fe layers
Coalescence of nano-voids and the effect
on state of stress and elastic behaviour.
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Our group: The Virtual Materials Lab
Dr. Marcel Sluiter, Prof. dr. Barend Thijsse
1 nm
Searching for materials
with new properties
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0.1 µm
Understanding how materials
change with time
10 cm
Optimizing fabrication
methods
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Why use computers to study materials?
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Predict, before doing expensive experiments
Explore conditions hard to realize in the lab
Not many theories for nonequilibrium
See what instruments cannot see
Focus on the effect of parameters one-by-one
Discover things beyond your imagination
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Contributors
 Master students
• Patricia Parlevliet, Willem van Dorp, Kees Bos
 PhD students
• Maria Timonova, Ivan Lazic, Peter Klaver,
Giannandrea Abbate, (Emmanuel Jannot)
 Postdocs
• Berk Hess
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Delft and Stuttgart
Radial distribution functions of a-Ni81B19
Experiment (neutron diffraction)
P. Lamparter, W. Sperl, S. Steeb, J. Blétry,
Z. Naturforschung 37a (1982) 1223
Simulation (RMC → MD)
B.J. Thijsse, L.D. van Ee, J. Sietsma
Mat. Res. Soc. Conf. Proc. 321 (1994) 65
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Materials: many lengths and times
10 days
15 min
↑ time
continuum
Dual Damascene (M2 Cu/SiLK) Module
1s
TaN barrier
thickness:
TaN barrier
Horizontal lines
25nm
milli
fields: mass, velocity, etc.
solid mechanics
fluid flow
250nmoxide
50nm SiC
400nm SiLK
70nm oxide
400nm SiLK
30nm SiC
150nmoxide
400nm SiLK
30nm SiC
Cu
400 nm 400 nm 400 nm
Vertical lines 8
nm
oxide
RH 15-05-02
W plugs
micro
micro
nano
nano
pico
quantum
femto
femto
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meso
electrons
pico
atoms
defects
surfaces
nano
grains
recrystallization
crack growth
dislocations
grain boundaries
thin films
micro
length →
milli
1m
1 km
1000 km
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Multiscale modeling
Quantum mechanics
Classical mechanics
Continuum mechanics
Schrödinger solver
Molecular Dynamics simulations
Monte Carlo simulations
Finite elements methods
Time and temperature:
Viscosity
Diffusion coefficients
Thermodynamic quantities
Nucleation kinetics
Dislocation dynamics
Interface structure
Hardness
Macroscopic behavior
Structure data
Energy data
Parameter fitting
Atomic force functions
(potentials)
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Quantum calculations
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Multiscale modeling
Quantum mechanics
Classical mechanics
Continuum mechanics
Schrödinger solver
Molecular Dynamics simulations
Monte Carlo simulations
Finite elements methods
Time and temperature:
Sticking coefficients
Diffusion coefficients
Thermodynamic quantities
Nucleation kinetics
Dislocation dynamics
Interface structure
Hardness
Macroscopic behavior
Structure data
Energy data
Parameter fitting
Atomic force functions
(potentials)
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From quantum data to potentials
Parameter fitting
Atomic force functions
(potentials)
Structure data
Energy data
Tersoff III
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Timonova+Thijsse, 2005
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From quantum data to potentials
Molecular Dynamics simulations
300 K
0 ps
2 ps
7 ps
Timonova+Thijsse, 2005
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The potentials bottleneck
Easy
Not available or unreliable
Noble gases
fcc, hcp and bcc metals
Semiconductors
C-H-Si-F-Cl
Oxides and nitrides
Other metals
Binary metal compounds
Metal-nonmetal combinations
III-V semiconductors
Biomolecules
Very difficult
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Multiscale modeling
Quantum mechanics
Classical mechanics
Continuum mechanics
Schrödinger solver
Molecular Dynamics simulations
Monte Carlo simulations
Finite elements methods
Time and temperature:
Sticking coefficients
Diffusion coefficients
Thermodynamic quantities
Nucleation kinetics
Dislocation dynamics
Interface structure
Hardness
Macroscopic behavior
Structure data
Energy data
Parameter fitting
Atomic force functions
(potentials)
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Molecular dynamics
t=0
initialize positions
Modeling at the atom level
initialize velocities
t=t+dt
i=1..N
calc F(i) from all r(i)
a(i)=F(i)/m(i)
v(i)=v(i)+dt*a(i)
r(i)=r(i)+dt*v(i)+dt^2*a(i)/2
Cu on Mo(110), 1000 K
next i
continue?
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Multiscale modeling
Quantum mechanics
Classical mechanics
Continuum mechanics
Schrödinger solver
Molecular Dynamics simulations
Monte Carlo simulations
Finite elements methods
Time and temperature:
Sticking coefficients
Diffusion coefficients
Thermodynamic quantities
Nucleation kinetics
Dislocation dynamics
Interface structure
Hardness
Macroscopic behavior
Structure data
Energy data
Parameter fitting
Atomic force functions
(potentials)
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Simple examples for metals
500 eV Ar+ on Cu(110)
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Au wire
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bcc-fcc transformation in Fe
fcc
bcc
before
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fcc
bcc
after
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bcc-fcc transformation in Fe
bcc
fcc
bcc
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A million-atom example
Can be used as input for
↓
discrete dislocation dynamics
↓
continuum mechanics
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Shock wave on Cu crack
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One-monolayer terrace on Ta,
to study the effect of steps of
different orientations
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Cu deposition on Ta(100)
1.7 million atoms
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All •••••••• are vertical
edge dislocations split
into Shockley partials
Cu film structure
Cu 2
Cu 3
Cu 4
Cu 5
8x
epitaxial, bcc (100)
complex
fcc + hcp
+ stripes
fcc + GB
fcc + GB
Color = local crystallographic symmetry of each atom (green=fcc)
Color = height
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Top view
After 1000 K anneal
Experiment
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The time bottleneck
Q
1
Time to first
" = e Q /kT
jump occurrence:
#0
Simulation time
for 10000 atoms
(one cpu)
Real time
Surface
10 d
15 min
! Bulk
↑ time to first occurrence
300 K
↑ factor 30000
1s
750 K
1 ms
3000 y
1 µs
3y
↑ factor 30
1 ns
1 ps
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1 fs
0
1000 K
1d
Activation energy Q →
0.5
1
1.5 eV
1 min
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Ways to beat the time bottleneck
 Use many fast computers
 Focus on non-activated processes
• Bombardment, shock waves, plasticity
 Focus on low-activation energy processes
• Surfaces
 Live with it
 Develop smarter methods
• Statistics, Monte Carlo
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The computing machinery at VML
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Other ongoing and recent work
 AlCu precipitation in Al
• with Prof. Gottstein, RWTH Aachen
 Expanding plasma deposition of optical films
• with Prof. Kleijn, TU Delft
 Self healing Al2O3 coatings for high-T applications
• with Dr. Sloof, TU Delft
 Amorphous Magnetic Tunnel Junction multilayers
• with In Silico, Inc., Aix-en-Provence
 Semiconductor nanowires
• with Philips
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Recommended book:
Rob Phillips, Crystals, Defects and Microstructures
(Cambridge UP, 2001)
Outlook
 The Quantum→Classical→Continuum series still has
some serious problems and gaps
 Quantum level (electrons)
• Reliable but small systems only
 Classical level (atoms)
• Molecular Dynamics: Potential and Time problems
• Monte Carlo: Difficult for nonequilibrium
 Continuum level (fields)
• Detailed data needed: defects, nonequilibrium
 Yet: Active field with lots of progress
• Modeling gets faster, systems get smaller (nanofabrication)
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