Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Ab Initio Lecture Sidney University Oct 2010

1,023 views

Published on

Published in: Technology
  • Be the first to comment

  • Be the first to like this

Ab Initio Lecture Sidney University Oct 2010

  1. 1. D. Raabe, F. Roters, P. Eisenlohr, H. Fabritius, S. Nikolov, M. Petrov O. Dmitrieva, T. Hickel, M. Friak, D. Ma, J. Neugebauer Düsseldorf, Germany WWW.MPIE.DE d.raabe@mpie.de Sydney Oct. 2010 Dierk Raabe Combining ab-initio based multiscale models and experiments for structural alloy design
  2. 2. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
  3. 3. 2 Ab initio and crystal modeling Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69     
  4. 4. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
  5. 5. Time-independent Schrödinger equation h/(2p) Many particles (stationary formulation) Square |y(r)|2 of wave function y(r) of a particle at given position r = (x,y,z) is a measure of probability to observe it there Raabe: Adv. Mater. 14 (2002)
  6. 6. i electrons: mass me ; charge qe = -e ; coordinates rei j atomic cores:mass mn ; charge qn = ze ; coordinates rnj Time-independent Schrödinger equation for many particles Raabe: Adv. Mater. 14 (2002)
  7. 7. Adiabatic Born-Oppenheimer approximation Decoupling of core and electron dynamics Electrons Atomic cores Raabe: Adv. Mater. 14 (2002)
  8. 8. Hohenberg-Kohn-Sham theorem: Ground state energy of a many body system definite function of its particle density Functional E(n(r)) has minimum with respect to variation in particle position at equilibrium density n0(r) Chemistry Nobelprice 1998 Hohenberg Kohn, Phys. Rev. 136 (1964) B864
  9. 9. Total energy functional T(n) kinetic energy EH(n) Hartree energy (electron-electron repulsion) Exc(n) Exchange and correlation energy U(r) external potential Exact form of T(n) and Exc(n) unknown Hohenberg Kohn, Phys. Rev. 136 (1964) B864
  10. 10. Local density approximation – Kohn-Sham theory Parametrization of particle density by a set of ‘One-electron-orbitals‘ These form a non-interacting reference system (basis functions)     2 i i rrn   Calculate T(n) without consideration of interactions       rdr m2 rnT 2 i i 2 2 * i          Determine optimal basis set by variational principle      0 r rnE i     Hohenberg Kohn, Phys. Rev. 136 (1964) B864
  11. 11. 10Hohenberg Kohn, Phys. Rev. 136 (1964) B864 Hohenberg-Kohn-Sham theorem
  12. 12. 11 Ab initio: theoretical methods Hohenberg Kohn, Phys. Rev. 136 (1964) B864
  13. 13. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
  14. 14. 13 Ab initio: typical quantities of interest in materials mechanics Raabe: Adv. Mater. 14 (2002)
  15. 15. 14Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421 Theory and Simulation: Multiscale crystal plasticity
  16. 16. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
  17. 17. 16 115 GPa 20-25 GPa Stress shielding Elastic Mismatch: Bone degeneration, abrasion, infection Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475 BCC Ti biomaterials design
  18. 18. 17 Design-task: reduce elastic stiffness Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475 M. Niinomi, Mater. Sci. Eng. 1998 Bio-compatible elements BCC Ti biomaterials design From hex to BCC structure: Ti-Nb, …
  19. 19. Construct binary alloys in the hexagonal phase Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475
  20. 20. Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475 Construct binary alloys in the cubic phase
  21. 21. 20 MECHANICAL INSTABILITY!! Ultra-sonic measurement exp. polycrystals bcc+hcp phases Ti-hex: 117 GPa theory: bcc polycrystals polycrystalYoung`smodulus(GPa) Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475 Elastic properties / Hershey homogenization hex bcc
  22. 22. 21 XRD DFT Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475 Elastic properties / Hershey homogenization
  23. 23. 22Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642 Discrete FFTs, stress and strain; different anisotropy
  24. 24. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
  25. 25. 24 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 0 10 20 30 40 50 60 70 80 totalelongationtofracture[%] ultimate tensile strength [MPa] TRIP and complex phase martensitic Maraging-TRIP and advanced QP dual phase ferritic Motivation: TWIP, TRIP, maraging, and combinations austenitic stainless advanced TWIP and TRIP Raabe, Ponge, Dmitrieva, Sander: Scripta Mater. 60 (2009) 1141
  26. 26. 25 Stresss[MPa] 1000 800 600 400 200 0 0 20 40 60 80 100 Strain e [%] TRIP steel TWIP steel Ab-initio methods for the design of high strength steels www.mpie.de martensite formation twin formation Dick, Hickel, Neugebauer
  27. 27. 26www.mpie.de Ab-initio methods for the design of high strength steels C A B B C Dick, Hickel, Neugebauer
  28. 28. 27 Mn atoms Ni atoms Mn iso-concentration surfaces at 18 at.% APT results: Atomic map (12MnPH aged 450°C/48h) 70 million ions Laser mode (0.4nJ, 54K) Dmitrieva et al., Acta Mater, in press 2010 Martensite decorated by precipitations Austenite ? ?
  29. 29. 28 Develop new materials via ab-initio methods www.mpie.de
  30. 30. 29 Nano-precipitates in soft magnetic steels size Cu precipitates (nm) {JP 2004 339603} 15 nm magneticloss(W/kg) Fe-Si steel with Cu nano-precipitates nanoparticles too small for Bloch-wall interaction but effective as dislocation obstacles mechanically very strong soft magnets for motors
  31. 31. 30 Cu 2 wt.% 20 nm 120 min 20 nm 6000 min Iso-concentration surfaces for Cu 11 at.% Fe-Si-Cu, LEAP 3000X HR analysis Fe-Si steel with Cu nano-precipitates 450°C aging
  32. 32. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
  33. 33. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
  34. 34. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
  35. 35. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
  36. 36. 35 Ab-initio, binding energies: Cu-Cu in Fe matrix Fe-Si steel with Cu nano-precipitates
  37. 37. 36 Ab-initio, binding energies: Si-Si in Fe matrix Fe-Si steel with Cu nano-precipitates
  38. 38. 37 For neighbor interaction energy take difference (in eV) (repulsive) = 0.390 (attractive) = -0.124 (attractive) = -0.245 E SiSi bin E S iCu bin E CuCu bin Ab-initio, binding energies Fe-Si steel with Cu nano-precipitates
  39. 39. 38 Ab-initio, use binding energies in kinetic Monte Carlo model
  40. 40. 39 Develop new materials via ab-initio methods www.mpie.de
  41. 41. 40 Counts et al.: phys. stat. sol. B 245 (2008) 2630 Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69 Ab-initio design of Mg-Li alloys Y: Young‘s modulus r: mass density B: compressive modulus G: shear modulus Weak under normal load Weak under shear load
  42. 42. 41 Develop new materials via ab-initio methods www.mpie.de
  43. 43. 42 The materials science of chitin composites Fabritius, Sachs, Romano, Raabe : Adv. Mater. 21 (2009) 391
  44. 44. 43 Exocuticle Endocuticle Epicuticle Exocuticle and endocuticle have different stacking density of twisted plywood layers Cuticle hardened by mineralization with CaCO3
  45. 45. 44 exocuticle endocuticle
  46. 46. 45 180° rotation of fiber planes
  47. 47. 46 Normal direction
  48. 48. 47
  49. 49. 48
  50. 50. 49
  51. 51. 50
  52. 52. 51 R1 R2 R3 R4 Beam stop DESY (BW5), l=0.196 Å. very strong chitin textures clusters of calcite XRD wide angle diffraction, chitin, lobster A. Al-Sawalmih at al. Advanced functional materials 18 (2008) 3307
  53. 53. 52Sachs, Fabritius, Raabe: J Material Research 21 (2006) 1987 Mechanical properties (microscopic, nanoindentation)
  54. 54. 53 P218.96 35.64 19.50 90˚α-Chitin Space group Unit cell dimensions (Bohrradius) a b c γ Polymer Carlstrom, D. The crystal structure of α -chitin J. Biochem Biophys. Cytol., 1957, 3, 669 - 683. P218.96 35.64 19.50 90˚α-Chitin Space group Unit cell dimensions (Bohrradius) a b c γ Polymer Carlstrom, D. The crystal structure of α -chitin J. Biochem Biophys. Cytol., 1957, 3, 669 - 683. What is -chitin? Nikolov et al. : Adv. Mater. 22 (2010), 519
  55. 55. 54 Hydrogen positions? H-bonding pattern ? two conformations of -chitin 108 atoms / 52 unknown H-positions R. Minke and J. Blackwell, J. Mol. Biol. 120, (1978) What is -chitin?
  56. 56. 55 CPU time Accuracy •Empirical Potentials Geometry optimization Molecular Dynamics (universal force field) ~10 min High Low ~10000 min ~500 min Medium Resulting structures ~103 ~102 ~101 •Tight Binding (SCC-DFTB) Geometry optimization (SPHIngX) •DFT (PWs, PBE-GGA) Geometry Optimization (SPHIngX) Hierarchy of theoretical methods Nikolov et al. : Adv. Mater. 22 (2010), 519 C, C N H
  57. 57. rmax = 3.5Å max = 30° Hydrogen bond geometric definition ground state conformation 1 3 2 4 a [Å] b [Å] c [Å] PBE - GGA 4.98 19.32 10.45 Exp. [1] 4.74 18.86 10.32 meta-stable conformation 1 3 2 4 5 c b H C O N DFT ground state structure 56Nikolov et al. : Adv. Mater. 22 (2010), 519
  58. 58. 57 0.00 0.20 0.40 0.60 0.80 1.00 1.20 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 Lattice elongation [%] EnergyE-E0[kcal/mol] a_Lattice b_Lattice c_Lattice c b C, C N H Nikolov et al. : Adv. Mater. 22 (2010), 519 Ab initio prediction of α-chitin elastic properties
  59. 59. 58Nikolov et al. : Adv. Mater. 22 (2010), 519
  60. 60. 59 Hierarchical modeling of stiffness starting from ab initio
  61. 61. 60 Develop new materials via ab-initio methods www.mpie.de
  62. 62. 61 Summary  Ab-initio thermodynamics: structure, properties, phases  Ab-initio kinetics: QM and MC; use structure TD data in dislocation models  Coupling with atomic-scale experiments: just beginning  Engineering application feasible (handshaking)
  63. 63. 62 Outlook and Challenges  Design of complex alloys  Non-0K ab initio, larger supercells  Large scale QM for lattice defects  Transitions between particle and continuum theories  High throughput experimental screening of structural materials missing  Atomic-resolution experimentation Mpie.de

×