Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore
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This document summarizes research on using ab initio modeling and multiscale simulations to design new materials. It discusses how density functional theory can be used to calculate material properties from first principles and inform higher scale simulations. Examples are given of designing titanium alloys for biomedical implants, high strength steels, soft magnetic steels, magnesium alloys, and chitin composites by predicting properties like elastic modulus from the electronic structure of the materials.
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Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore
- 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 IHPC - Institute for High Performance Computing Singapore 1. Nov 2010 Dierk Raabe Using ab-initio based multiscale models and experiments for alloy design
- 2. 1 New materials for key technologies: Aero-space
- 3. 2 New materials for key technologies: mobility on land and water
- 4. 3 New materials for key technologies: Power plants
- 5. 4 New materials for key technologies: Green energy
- 6. 5 New materials for key technologies: infrastructure
- 7. 6 New materials for key technologies: Health
- 8. 7 New materials for key technologies: Information, energy, lighting
- 9. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
- 10. 9 Ab initio and crystal modeling Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69
- 11. 10www.mpie.de Replace empirical by knowledge-based alloy design
- 12. 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)
- 13. 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)
- 14. Adiabatic Born-Oppenheimer approximation Decoupling of core and electron dynamics Electrons Atomic cores Raabe: Adv. Mater. 14 (2002)
- 15. 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
- 16. 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
- 17. 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
- 18. 17 Ab initio: theoretical methods Hohenberg Kohn, Phys. Rev. 136 (1964) B864
- 19. 18 Ab initio: typical quantities of interest in materials mechanics Raabe: Adv. Mater. 14 (2002)
- 20. 19Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421 Theory and Simulation: Multiscale crystal mechanics
- 21. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
- 22. 21 115 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
- 23. 22 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, …
- 24. Construct binary alloys in the hexagonal phase Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475
- 25. Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475 Construct binary alloys in the cubic phase
- 26. 25 MECHANICAL INSTABILITY!! Ultra-sonic measurement exp. polycrystals bcc+hcp phases Ti-hex: 117 GPa theory: bcc polycrystals XRD DFT polycrystalYoung`smodulus(GPa) Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475 Elastic properties / Hershey homogenization hex bcc
- 27. 26 Ti-18.75at.%Nb Ti-25at.%Nb Ti-31.25at.%Nb Az=3.210 Az=2.418 Az=1.058 [001] [100] [010] Young‘s modulus surface plots Pure Nb Az=0.5027 Az= 2 C44/(C11 − C12) Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642 Hershey FEM FFT Ab initio alloy design: Elastic properties: Ti-Nb system
- 28. 27 More than one million hip implants per year: Take-home message elastically compliant Titanium-alloys can reduce surgery www.mpie.de
- 29. Overview Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
- 30. 29 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 Hickel, Dick, Neugebauer
- 31. 30www.mpie.de Ab-initio methods for the design of high strength steels C A B B C Hickel, Dick, Neugebauer
- 32. 31 twinning
- 33. 32 Microstructure hierarchy Dmitrieva et al., Acta Mater, 2010
- 34. 33 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 ? ?
- 35. M A Mn layer 1 Mn layer 2 34 Mn layer2 Mn layer 1 Mn iso-concentration surfaces at 18 at.% Thermo-Calc Phase equilibrium Mn-contents: 27 at. % Mn in austenite (A) 3 at. % Mn in ferrite (martensite) (M) 1D profile: step size 0.5 nm M A M depletion zone nominal 12 at.% Mn APT results: chemical profiles Dmitrieva et al., Acta Mater, in press 2010
- 36. 35 precipitates in a` no precipitates in 12MnPH after aging (48h 450°C) nmDtxDiff 302 nmxDiff 2 Raabe, Ponge, Dmitrieva, Sander: Adv. Eng. Mat. 11 (2009) 547
- 37. Mean diffusion path of Mn in austenite (aging 450°C/48h) 2 nm 36 M A Mn layer 1 Mn layer 2 nominal 12 at.% Thermo-Calc Phase equilibrium Mn content: 27 at. % in austenite 3 at. % in ferrite (martensite) 10 nm Ti, Si, Mo Mn-rich layer AM PB migration Mn diffusion phase boundary aging New austenite (formed during aging) DICTRA AM original position phase boundary final position phase boundary APT results and simulation: DICTRA/ThermoCalc Dmitrieva et al., Acta Mater, in press 2010
- 38. 37 Develop new materials via ab-initio methods www.mpie.de
- 39. 38 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
- 40. 39 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
- 41. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
- 42. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
- 43. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
- 44. Modeling: ab-initio, DFT / GGA, binding energies Fe-Si steel with Cu nano-precipitates
- 45. 44 Ab-initio, binding energies: Cu-Cu in Fe matrix Fe-Si steel with Cu nano-precipitates
- 46. 45 Ab-initio, binding energies: Si-Si in Fe matrix Fe-Si steel with Cu nano-precipitates
- 47. 46 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
- 48. 47 Ab-initio, use binding energies in kinetic Monte Carlo model
- 49. 48 Develop new materials via ab-initio methods www.mpie.de
- 50. 49 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
- 51. 50 Develop new materials via ab-initio methods www.mpie.de
- 52. 51 The materials science of chitin composites Fabritius, Sachs, Romano, Raabe : Adv. Mater. 21 (2009) 391
- 53. 52 Exocuticle Endocuticle Epicuticle Exocuticle and endocuticle have different stacking density of twisted plywood layers Cuticle hardened by mineralization with CaCO3
- 54. 53
- 56. 55 180° rotation of fiber planes
- 57. 56
- 59. 58
- 60. 59
- 61. 60
- 62. 61
- 63. 62
- 64. 63
- 65. 64Sachs, Fabritius, Raabe: Journal of Structural Biology 161 (2008) 120 Structure hierarchy of chitin-compounds Nikolov et al.: Adv. Mater. 22 (2010) p. 519; Al-Sawalmih et al.: Adv. Funct. Mater. 18 (2008) p. 3307 Fabritius et al.: Adv. Mater. 21 (2009) 391
- 66. 65 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 a-chitin? Nikolov et al. : Adv. Mater. 22 (2010), 519
- 67. 66 Hydrogen positions? H-bonding pattern ? two conformations of a-chitin 108 atoms / 52 unknown H-positions R. Minke and J. Blackwell, J. Mol. Biol. 120, (1978) What is a-chitin?
- 68. 67 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
- 69. 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 68Nikolov et al. : Adv. Mater. 22 (2010), 519
- 70. 69 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
- 71. 70 Hierarchical modeling of stiffness starting from ab initio Nikolov et al. : Adv. Mater. 22 (2010), 519
- 72. 71 Hierarchical modeling of stiffness starting from ab initio
- 73. 72 Develop new materials via ab-initio methods www.mpie.de
- 74. 73D. Raabe: Advanced Materials 14 (2002) p. 639 Scales in computational crystal plasticity
- 75. 74 * DFT: density functional theory Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475 From ab-initio to polycrystal mechanics Gb, Gb2 , ... <E>
Editor's Notes
- Quantitative analysis of the chemical interfaces between austenite and martensite was performed using 1D concentration profiles computed over the region of interest (cylindrical units). We calculated the content of manganese averaged over the 0.5 nm thick cross sections of the cylinders (profile step size 0.5 nm). For both interfaces, strong increase of Mn content up to 26 at. % was observed. The content of the Mn on the austenitic side is about 12 at. %, whereas on the martensitic side a slight depletion of Mn down to 6 at. % can be observed. In order to avoid the contribution of the precipitates to the chemical profile within the martensitic area, we separately measured the 1D concentration profiles within the martensitic matrix after exclusion of the precipitates. These profiles are also plotted. In order to understand the reasons for the Mn accumulation on the phase boundary, we consider the measured Mn contents. Since the phase equilibrium concentration of Mn in the austenite is much higher than in the ferrite (martensite) as was calculated by using Thermo-Calc (26.7 vs. 3.3 at. %), we expect a redistribution of Mn atoms during aging: enrichment in the austenite and depletion in the martensite. However, the Mn content measured in the austenite remains the same as in the nominal alloy composition (about 12.2 at. %, see Table1). In the martensitic matrix, a slight Mn depletion down to 10.3 at. % was detected. The diffusion in the FCC lattice of austenite is widely suppressed. The martensitic matrix is depleted to 10.3 at. % which is mostly due to the enrichment of Mn in the precipitates. However, Mn content decreases continuously in the martensite toward the phase boundary and, just some nanometers before the Mn-rich layer starts, drops to about 5-6 at. %. The formation of such depletion zone indicates an enhanced diffusion behavior of Mn atoms from the martensite to the austenite. Due to the low diffusion in the austenite, Mn atoms accumulate in the phase boundary and built up a Mn-enriched layer. The Mn gradient obtained from the thermodynamic calculation using DICTRA provides nearly the same distribution of the Mn content on the austenite/martensite phase boundary (Fig. 4). Enrichment of Mn up to the content of 27 at. % is observed in the interface between austenite and ferrite. For the simulation of the diffusion of Mn in the martensite, we enhanced the mobility of the atoms given for ferrite by a factor of 45. (During time of annealing at given temperature in (α+γ) range, Mn moves from ferrite to austenite across interface surface between austenite and ferrite until equilibrium state of the chemical potentials of Mn in austenite and ferrite will be reached. The balance depends on temperature and time of annealing.)
- In order to understand the dynamics of the formation of the Mn-enriched layers on the phase boundaries, we consider the phase equilibrium contents of Mn. The averaged content of Mn measured for the Mn-enriched layers is about 26 at. %. This content corresponds to the phase equilibrium content of this element in the austenite which is 26.7 at. %. As known, local phase equilibrium can be easily reached on the grain/phase boundaries. Thus, right on the phase boundary, the equilibrium composition in austenite is reached, and a local phase transformation from martensite to austenite within the Mn-enriched layer can be expected. However, the With the growth of the Mn-enriched layer towards the martensitic grain, the material within the layer becomes austenitic and, thus, the phase boundary moves. The final thickness of the Mn-enriched layer is about 20 nm, thus, the phase boundary moved 20 nm during the aging treatment. The layer-to-austenite interface provides the information about the position of the original phase boundary between the retained austenite and the martensite before aging. Further diffusion of Mn into austenite during aging was suppressed just beyond the crystallographic BCC/FCC boundary. The martensite-to-layer interface, however, indicates the position of the final phase boundary when the Mn diffusion was stopped by the water quenching after the aging treatment. The Mn enriched area in-between these two layers therefore can be addressed as additional austenite formed during the aging. The growth of the austenite leads to an enhancement of austenite volume fraction during aging. This can be correlated to the growth of the existing austenite grains where the phase boundaries serve as nucleation seeds. We assumed an epitaxial formation of reverted austenite on the phase boundary of the retained austenite.
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