1. 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. Gleiter 1 and A. Mukherjee 2 1 Institut für Nanotechnologie, Forschungszentrum Karlsruhe 2 Department of Chem. Engrg. & Materials Science, UC Davis Beijing, Shenyang, June 2005

2. 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 Cluster Supercomputer Using Consumer Electronics Interfacial Materials Group - Materials Science Division

3. 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 Simulations and theory can provide the basic understanding and elucidate the criteria for the design of optimized microstructures

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

5. 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)

6. 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!

7. 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 r split = Kb 2 /(  i - bm  );  i = stacking-fault energy: Dislocation splitting increases with applied stress, . Two length scales in dislocation nucleation from the GBs: r split and d ! Consequence: for d ≤ r split, dislocation slip mechanism ceases.

8. Dislocation nucleation and slip deformation by glide (V. Yamakov et al., Acta mater. 49, 2713, 2001) columnar microstructure fully 3-d simulation 4 of 12 possible slip systems 4 grains 24 high-angle tilt GBs (30°, 60° and 90°) d = 20 - 100 nm  = 2.0 - 2.5 Gpa Al(EAM) potential

9. Dislocation nucleation: d = 30 nm  = 2.3 GPa

10. 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 (d=10 nm): Liao et al., APL 84, 592, 2004

11. Structural relaxation after unloading: d = 30 nm  = 2.3  0 GPa

12. Deformation to ~12% plastic strain: d = 45 nm  = 2.3 GPa

13. Formation of a new grain during deformation (V. Yamakov et al., Nature Mats. 1, 1-4, 2002)

14. Deformation twinning in nanocrystalline Al by three distinct mechanisms (V. Yamakov et al., Acta mater. 50, 5005, 2002) 1. Stacking-fault overlapping inside the grain 2. Coordinated nucleation of partials from the GBs 3. Grain-boundary decomposition 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.

15. 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  m

17. d = 32 nm;  = 2.0 GPa; T = 300 K Dislocation dynamics in fully 3d microstructure (V. Yamakov et al., Phil. Mag. Lett. 83, 385, 2003)

18. Crossover in the strain rate due to transition from dislocation to grain-boundary mediated processes GB-mediated creep Dislocation glide

19. ‘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)

20. 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

21. t=0 columnar microstructure 25 grains, d=15 nm,  min ~14.9  ~400,000 atoms t=7.2 ns 1.4 million MD time steps Pd (EAM) potential fully 3d physics Grain growth in nanocrystalline Pd by MD simulation (A. Haslam et al., Mat. Sci & Engin. A 318, 293, 2001) Grain growth on MD time scale (driving force ~ 1/d)!

22. Grain growth by curvature-driven grain-boundary migration

23. ‘T1 event’ completed ‘T2 event’ completed Energy (curvature) - driven grain-boundary migration

24. Grain growth by grain rotation-induced grain coalescence

25. Grain rotation-induced grain coalescence (A. Haslam et al., Mat. Sci & Enginrg. A 318, 293, 2001) Viscous, dissipative process:  i = M i  i

26.  = 0.6 GPa T = 1200K (T m ~1500 K)

27. Creep deformation speeds up the grain growth! 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! (A. Haslam et al., Acta mater. 51, 2097, 2003)

28. The onset of grain growth accelerates the creep! (A. Haslam et al., Acta mater. 52, 1971, 2004)

29. Grain growth during creep produces mobile dislocations: Triple-junction disintegration! (A. Haslam et al., Acta mater. 51, 2097, 2003)

30. 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

31. Atomic level Mesoscale Continuum level Newton’s Law Principle of virtual-power dissipation How to transfer atomic-level insights and parameters to the mesoscale? Continuum mechanics, Constitutive laws

32. Theory of diffusion accommodated grain rotation (D.Moldovan et. al., Acta mater. 49, 3521, 2001) “cumulative torque” diffusion accommodated viscous-like rotation Grain coalescence by grain rotation

33. 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 Newton’s law! Terms are additive! v =   /r  i = M i  i ; M i ~d -5 ;  i ~d -4 ; (D. Moldovan et al., Acta mater. 49, 3521 2001) Velocity Monte-Carlo or FEM Simulation (F. Cleri, Physica 282, 339, 2000; Cocks, 1992) Triple-point equilibrium condition (Herring relation) not enforced a priori.  m ( v; k, ,  ) GB velocity Local GB curvature GB energy GB mobility  r (  ; , M) Angular velocity Torque Rotational mobility 

34. Validation of mesoscale approach against MD simulations (D. Moldovan et al., Phil. Mag. 83, 3643, 2003) Distinct processes enter as additive terms in the power functional: dislocations, GBs,... Ability to deconvolute interplay between distinct processes and driving forces! MD: t = 2.89 ns meso with grain rotation: t = 2.47 ns meso without grain rotation: t = 2.64 ns Newton’s laws for atoms Dissipative dynamics for GBs based on virtual power dissipation

35. No grain rotation With grain rotation

36. Growth law Asymptotic power law at large times: A(t) ~ t  isotropic  = 1.00 ± 0.02 anisotropic  = 0.70 ± 0.02 anisotropic+grain rotation:  = 0.98 ± 0.02

37. Grain-size distribution function Rotation leads to a narrower grain-size distribution function

38. Atomic level Mesoscale Continuum level Newton’s Law 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 Effects of Stress: connection with continuum level Continuum mechanics, Constitutive laws

39. 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

40. 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,… –Alloy oxidation

41. Perovskite oxides, ABO 3 PbTiO 3 - ferroelectric PbZrO 3 - antiferroelectric BaTiO 3 - ferroelectric SrTiO 3 - antiferrodistortive KNbO 3 - ferroelectric KTaO 3 - incipient ferroelectric

42. Phase diagram of pure KNbO 3 and of KTa 0.5 Nb 0.5 O 3 random solid solution correctly reproduced! Interatomic potentials for the KNbO 3 /KTaO 3 system (M. Sepliarski et al., Appl. Phys. Lett. 76, 3986, 2000) KNbO 3 KTa 0.5 Nb 0.5 O 3 cubic tetrag. orthorh. rhomboh.

43. Dieletric and piezoelectric constants of KNbO 3

44. Hysteresis Loops of KNbO 3 /KTaO 3 Superlattices: ‘Induced ferroelectricity’ (M. Sepliarski et al., J. Appl. Phys. 90, 4509, 2001) KNO (  =6) KTO (  =6) KNO KTO

45. 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. Gleiter 1 and A. Mukherjee 2 1 Institut für Nanotechnologie, Forschungszentrum Karlsruhe 2 Department of Chem. Engrg. & Materials Science, UC Davis UC Davis - 2/23/04

46. ELECTRONIC LEVEL ATOMIC LEVEL MESOSCALE CONTINUUM Potential of Mean Force Hydrodynamics input parameters Interatomic Potential MD Acceleration Algorithms Advanced Optimization Algorithms Variational Methods & Genetic Algorithms Pattern Recognition / Visualization Hydrodynamics Treatment ‘VIRTUAL FAB LAB’ for nanostructure assembly Advanced Optimization Algorithms Numerical Solution of Coupled PDEs

47. 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-ZrO 2 Displacive cubic-to-tetragonal phase transition in pure ZrO 2 Cubic-phase stabilization by yttria addition

49. Grain-boundary based deformation mechanism for d < d c ? (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!

50. Grain-size dependence of GB diffusion creep (V. Yamakov et al., Acta mater. 50, 61, 2002) Large grain size (d >>  ): creep rate ~ d -3 (Coble!) Small grain size: (d ≈  ): creep rate ~ d -2 (Nabarro-Herring!)

51. Intrinsically brittle materials should become ductile if the grain size is only small enough No strain hardening Very high strain rates (> 10 7 s -1 ) accessible byMD! Grain-boundary diffusion creep Gleiter, 1989: nc materials should deform via Coble creep, even at rather low temperatures (‘RT ductility’)