ATOMISTIC AND MESOSCALE SIMULTION OF GRAIN GROWTH

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Thermo-mechanical Behavior of Nanostructured
Materials by Multiscale Computer
Simulation Dieter Wolf with A. J. Haslam, D.
Moldovan, P. Schelling, M. Sepliarski, V.
Yamakov, S. R. Phillpot Materials Science
Division, Argonne National Laboratory Special
thanks to H. Gleiter1 and A. Mukherjee2 1Institu
t für Nanotechnologie, Forschungszentrum
Karlsruhe 2Department of Chem. Engrg. Materials
Science, UC Davis Beijing, Shenyang, June 2005
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Cluster Supercomputer Using Consumer
Electronics Interfacial Materials Group -
Materials Science Division
Hardware Odin I Beowulf Cluster 36 nodes - 450MHz
Pentium III (9/1999) Upgraded to 1GHz PIII
(5/2001) Odin II Beowulf Cluster 100 nodes -
700MHz Pentium III (8/2000) Odin III Beowulf
Cluster 100 nodes - 2.6GHz Pentium IV
(7/2003) Software Linux (Red Hat 6.1,
Mandrake 7.1) MPI Pentium Group
Fortran Additional information www.msd.anl.gov/im
/ cluster/odin.html
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Scientific opportunity

• Microstructure is inherently difficult to
  characterize non-destructively
• More microstructural models exist than have been
  tested or physically explained
• Synchrotron techniques start to provide exciting
  opportunity for non-destructive characterization
• Microstructurally designed materials are
  important in many technologies
• High-temperature structural ceramics for
  aerospace applications
• Light-weight Al alloys for fuel-efficiency in
  automotive applications
• Thermal-barrier coatings for turbine engines
• Corrosion resistant Pb-acid battery electrodes,
• Microstructural control enables
• Processing of inherently brittle materials (e.g.,
  by superplastic forming)
• Tailoring of microstructure-sensitive materials
  properties

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Scientific Opportunity Hierarchical Multi-scale
Simulation of Polycrystalline Materials
Atomic level
Continuum level
Mesoscale
Newtons Law
Continuum mechanics, Constitutive laws
Principle of virtual-power
dissipation
Goal Continuum simulations based on fundamental
understanding of GB physics!
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Synergism

• Computational Materials Science Network
  (CMSN)
• Microstructural effects on the mechanics
  of materials
• Objective Integration of dislocation
  with grain-boundary simulations on
• polycrystalline
  materials
• Focus on crossover in the Hall-Petch effect

Existence of a strongest grain size in
nanostructured materials?
(T. G. Nieh and J. Wadsworth, Scripta Met. 25,
955, 1991)
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Outline

• Microstructure and deformation physics of
  nanostructured materials by MD simulation
• Dislocation and grain-boundary mechanisms of
  plasticity in
• nanocrystalline Al
• Grain growth in nanocrystalline Pd
• Critical for understanding relation between
  coarse-grained and nanostructured materials!
• However MD has critical time-scale limitations
• Multiscale simulation of polycrystalline
  materials
• Use grain growth as a case study
• Focus on the atomistic - mesoscale linkage
• Critical for seeing the big picture and
  for applications!

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Crossover from dislocation to GB based
low-temperature plasticity in nanocrystalline
Al (V. Yamakov et al., Acta mater. 49, 2713,
2001)

• Size of a Frank-Read source cannot exceed grain
  size, d i.e., for a nm
• grain size, these sources are not
  operational!
• Dislocations can be nucleated from the GBs

• rsplit Kb2/(Gi - bm s)
• Gi stacking-fault energy
• Dislocation splitting increases with applied
  stress, s.

Two length scales in dislocation nucleation from
the GBs rsplit and d ! Consequence for d
rsplit, dislocation slip mechanism ceases.
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Dislocation nucleation and slip deformation by
glide (V. Yamakov et al., Acta mater. 49, 2713,
2001)

• lt110gt columnar
• microstructure
• fully 3-d simulation
• 4 of 12 possible slip systems
• 4 grains
• 24 lt110gt high-angle
• tilt GBs (30, 60 and 90)
• d 20 - 100 nm
• ? 2.0 - 2.5 Gpa
• Al(EAM) potential

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Dislocation nucleation d 30 nm ? 2.3 GPa
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Two Length Scales in Dislocation Nucleation (V.
Yamakov et al., Acta mater. 49, 2713, 2001)
Recent experimental observation of partial
dislocation slip in nc Cu (d10 nm) Liao et
al., APL 84, 592, 2004
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Structural relaxation after unloading d 30
nm ? 2.3 ? 0 GPa
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Deformation to 12 plastic strain d 45
nm ? 2.3 GPa
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Formation of a new grain during deformation (V.
Yamakov et al., Nature Mats. 1, 1-4, 2002)
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Deformation twinning in nanocrystalline Al by
three distinct mechanisms (V. Yamakov et al.,
Acta mater. 50, 5005, 2002)
2. Coordinated nucleation of partials from the
GBs 3. Grain-boundary decomposition
1. Stacking-fault overlapping inside the grain
Recent experimental confirmations Al Chen et
al. , Science 300, 1275, 2003 (PVD) Al Liao et
al., APL 83, 632, 2003 83, 5062, 2003
(cryogenic ball milling) Cu Liao et al., APL 84,
592 2004.
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Dislocation-twin network interactions Mechanism
for Hall-Petch hardening in nanocrystalline fcc
metals? (V. Yamakov et al., Acta mater. 51, 4135,
2003)
d 0.1 mm
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Dislocation dynamics in fully 3d
microstructure (V. Yamakov et al., Phil. Mag.
Lett. 83, 385, 2003)
d 32 nm ? 2.0 GPa T 300 K
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Crossover in the strain rate due to transition
from dislocation to grain-boundary mediated
processes
Dislocation glide
GB-mediated creep
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The Strongest Size
GB-mediated Dislocation slip
(Nieh Wadsworth, Scripta Met. 25, 955, 1991)
(V. Yamakov et al., Phil. Mag. Lett. 83, 385,
2003)

• The strongest size depends on
• types of GBs in microstructure
• level of applied stress
• stacking-fault energy

(Schioetz Jacobsen, Science 301, 1357, 2003)
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Outline

• Microstructure and deformation physics of
  nanostructured materials
• by MD simulation
• Dislocation and GB mechanisms of plasticity in
  nanocrystalline Al
• Grain boundaries act as sources and sinks for
  dislocations
• Length-scale competition between dislocation
  splitting distance and grain size
• Existence of a strongest grain size due to
  change in deformation mechanism with decreasing
  grain size
• Extensive deformation twinning predicted and
  confirmed experimentally
• Hall-Petch hardening probably due to dislocation
  pile-ups against twins
• Deformation physics of nanostructured materials
  is much richer
• than that of coarse-grained materials!
• Grain growth in nanocrystalline Pd

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Grain growth in nanocrystalline Pd by MD
simulation (A. Haslam et al., Mat. Sci Engin. A
318, 293, 2001)
t0 lt100gt columnar microstructure 25 grains, d15
nm, Qmin 14.9?, 400,000 atoms
t7.2 ns 1.4 million MD time steps Pd (EAM)
potential fully 3d physics
Grain growth on MD time scale (driving force
1/d)!
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Grain growth by curvature-driven grain-boundary
migration
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Energy (curvature) - driven grain-boundary
migration
T1 event completed
T2 event completed
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Grain growth by grain rotation-induced grain
coalescence
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Grain rotation-induced grain coalescence (A.
Haslam et al., Mat. Sci Enginrg. A 318, 293,
2001)
Viscous, dissipative process wi Mi ti
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• s 0.6 GPa
• T 1200K
• (Tm1500 K)

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Creep deformation speeds up the grain growth!
(A. Haslam et al., Acta mater. 51, 2097, 2003)
Time to the disappearance of grain 23 by GB
migration
Coupled rotations of grains 8 and 14
Stress speeds up GB migration!
Stress speeds up grain rotations!
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The onset of grain growth accelerates the creep!
(A. Haslam et al., Acta mater. 52, 1971, 2004)
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Grain growth during creep produces mobile
dislocationsTriple-junction disintegration!
(A. Haslam et al., Acta mater. 51, 2097, 2003)
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Outline

• Microstructure and deformation physics of
  nanostructured materials
• by MD simulation
• Grain growth in nanocrystalline Pd
• Two growth mechanisms
• Different topological discontinuities for the two
  mechanisms
• GB disappearance generates dislocations
• Information on energies and mobilities of the
  grain boundaries
• Physics of grain growth in nanostructured
  materials is considerably richer
• than that in coarse-grained materials!
• Multiscale simulation of polycrystalline
  materials
• Use grain growth as a case study
• Focus on the atomistic - mesoscale linkage

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How to transfer atomic-level insights and
parameters to the mesoscale?
Atomic level
Continuum level
Mesoscale
Continuum mechanics, Constitutive laws
Newtons Law
Principle of virtual-power
dissipation
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Theory of diffusion accommodated grain
rotation (D.Moldovan et. al., Acta mater. 49,
3521, 2001)
viscous-like rotation
cumulative torque
diffusion accommodated
Grain coalescence by grain rotation
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Mesoscale Simulations (2d) (D. Moldovan et. al.,
Phil. Mag. A 82, 1271, 2002)

• Discretized GBs
• Variational functional for dissipated power
  (Cocks 1992, Needleman Rice 1980,
• see also Ziegler, Introduction to
  Thermomechanics, 1977)
• Viscous force laws Replaces Newtons law!
  Terms are additive!
• v m g/r wi Mi ti Mid-5 wi
  d-4 (D. Moldovan et al., Acta mater. 49,
  3521 2001)

Pm ( v k, g, m )
Pr ( w t, M)
GB velocity
GB mobility
Angular velocity
Rotational mobility
Local GB curvature
GB energy
Torque
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Validation of mesoscale approach against MD
simulations (D. Moldovan et al., Phil. Mag. 83,
3643, 2003)
meso with grain rotation t 2.47 ns
meso without grain rotation t 2.64 ns
MD t 2.89 ns
Dissipative dynamics for GBs based on virtual
power dissipation
Newtons laws for atoms

• Distinct processes enter as additive terms in
  the power functional dislocations, GBs,...
• Ability to deconvolute interplay between distinct
  processes and driving forces!

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With grain rotation
No grain rotation
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Growth law

• Asymptotic power law at large times A(t) ta
• isotropic a
  1.00 0.02
• anisotropic a
  0.70 0.02
• anisotropicgrain rotation a 0.98
  0.02

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Grain-size distribution function




Rotation leads to a narrower grain-size
distribution function
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Effects of Stress connection with continuum
level
Atomic level
Continuum level
Mesoscale
Newtons Law
Continuum mechanics, Constitutive laws
Principle of virtual-power
dissipation
Ultimate goal Dynamical FEM-type mesoscale
simulations with input based on fundamental
understanding of the structure and properties of
the microstructural elements
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Outline

• Microstructure and deformation physics of
  nanostructured materials
• by MD simulation
• Dislocation and grain-boundary mechanisms of
  plasticity in nanocrystalline Al
• Grain growth in nanocrystalline Pd
• Multiscale simulation of polycrystalline
  materials
• Use grain growth as a case study
• Focus on the atomistic - mesoscale linkage
• Outlook on hierarchical multiscale approach
• Complex-oxide ceramics

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The next forefront?

• Microstructure and deformation physics of
  complex oxides
• Charge and mass transport behavior, sintering,
  grain growth, deformation, fracture,
• Thermal transport
• Impurity segregation, off-stoichiometry
  accommodation, space-charge effects
• Oxygen-potential gradients chemical relaxation
• Multiscale simulation of oxide ceramics
• Fuel-cell materials, thermal-barrier coatings,
  high-k dielectrics, structural materials,

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Perovskite oxides, ABO3
PbTiO3 - ferroelectric PbZrO3 -
antiferroelectric BaTiO3 - ferroelectric SrTiO3
- antiferrodistortive KNbO3 - ferroelectric KTaO3
- incipient ferroelectric
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Interatomic potentials for the KNbO3/KTaO3
system (M. Sepliarski et al., Appl. Phys. Lett.
76, 3986, 2000)
KNbO3
KTa0.5Nb0.5O3
cubic
tetrag.
orthorh.
rhomboh.
Phase diagram of pure KNbO3 and of KTa0.5Nb0.5O3
random solid solution correctly reproduced!
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Dieletric and piezoelectric constants of KNbO3
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Hysteresis Loops of KNbO3/KTaO3 Superlattices
Induced ferroelectricity (M. Sepliarski et al.,
J. Appl. Phys. 90, 4509, 2001)
KNO (L6)
KNO
KTO (L6)
KTO
KNO
KTO
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Thermo-mechanical Behavior of Nanocrystalline
Materials by Multi-scale Computer
Simulation Dieter Wolf with A. J. Haslam, D.
Moldovan, P. Schelling, M. Sepliarski, V.
Yamakov, S. R. Phillpot Materials Science
Division, Argonne National Laboratory Special
thanks to H. Gleiter1 and A. Mukherjee2 1Institu
t für Nanotechnologie, Forschungszentrum
Karlsruhe 2Department of Chem. Engrg. Materials
Science, UC Davis UC Davis - 2/23/04
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VIRTUAL FAB LAB for nanostructure assembly
ELECTRONIC LEVEL
Advanced Optimization Algorithms
Interatomic Potential
MD Acceleration Algorithms
ATOMIC LEVEL
Variational Methods Genetic Algorithms
Potential of Mean Force
Pattern Recognition / Visualization
MESOSCALE
Numerical Solution of Coupled PDEs
Hydrodynamics input parameters
Hydrodynamics Treatment
Advanced Optimization Algorithms
CONTINUUM
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Phase Stability and Thermal Conductivity in
Zirconia and YSZ(P. Schelling et al., J. Am.
Ceram. Soc. 84, 1609, 2001)

• Interatomic potentials capture
• Ferroelastic Distortion in t-ZrO2
• Displacive cubic-to-tetragonal phase transition
• in pure ZrO2
• Cubic-phase stabilization by yttria addition

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Grain-boundary based deformation mechanism for d
lt dc ? (V. Yamakov et al., Acta mater. 50, 61,
2002)
Idea Design microstructure that is
stable against grain growth!

• 16 grains of identical shape and size
• arranged periodically on a bcc lattice
• Grain size d 3.8 - 15.2 nm
• Stress below dislocation-nucleation
• threshold!
• Unique capability of simulations to design
  idealized microstructures to deconvolute
  interplay between distinct GB processes and
  driving forces!

Steady-state GB diffusion creep under uniform
tensile stress!
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Grain-size dependence of GB diffusion creep (V.
Yamakov et al., Acta mater. 50, 61, 2002)
Large grain size (d gtgt d) creep rate d-3
(Coble!) Small grain size (d d) creep rate
d-2 (Nabarro-Herring!)
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Grain-boundary diffusion creep
Gleiter, 1989 nc materials should deform via
Coble creep, even at rather low temperatures (RT
ductility)

• Intrinsically brittle materials should become
  ductile if the grain size is only small enough
• No strain hardening
• Very high strain rates (gt 107 s-1) accessible
  byMD!