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Ab initio in materials science: what for ?

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Presentation on theme: "Ab initio in materials science: what for ?"— Presentation transcript:

0 Using ab-initio based multiscale models and experiments for alloy design
D. Raabe, F. Roters, P. Eisenlohr, H. Fabritius, S. Nikolov, M. Petrov O. Dmitrieva, T. Hickel, M. Friak, D. Ma, J. Neugebauer Düsseldorf, Germany IHPC - Institute for High Performance Computing Singapore Nov Dierk Raabe

1 Ab initio in materials science: what for ?
Overview Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

2 Most exact known materials theory
Ab initio and crystal modeling Most exact known materials theory Combine to atomic scale experiments Obtain data not accessible otherwise Can be used at continuum scale Electronic rules for alloy design: Add electrons rather than atoms Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69

3 h/(2p) Time-independent Schrödinger equation
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 Many particles (stationary formulation) Raabe: Adv. Mater. 14 (2002)

4 Time-independent Schrödinger equation for many particles
i electrons: mass me ; charge qe = -e ; coordinates rei j atomic cores: mass mn ; charge qn = ze ; coordinates rnj Raabe: Adv. Mater. 14 (2002)

5 Adiabatic Born-Oppenheimer approximation
Decoupling of core and electron dynamics Electrons Atomic cores Raabe: Adv. Mater. 14 (2002)

6 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

7 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

8 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) Calculate T(n) without consideration of interactions Determine optimal basis set by variational principle Hohenberg Kohn, Phys. Rev. 136 (1964) B864

9 Entropy: non-0K, dynamical matrix, configuational analytical
Ab initio: theoretical methods Density functional theory (DFT), generalized gradient approximation (GGA); also LDA Vienna ab-initio simulation package (VASP) code or SPHINX; different pseudo-potentials, Brillouin zone sampling, supercell sizes, and cut-off energies, different exchange-correlation functions, M.-fit Entropy: non-0K, dynamical matrix, configuational analytical Hohenberg Kohn, Phys. Rev. 136 (1964) B864

10 Lattice structures (e.g. Polymers, carbides, Laves)
Ab initio: typical quantities of interest in materials mechanics Lattice structures (e.g. Polymers, carbides, Laves) Lattice parameter (e.g. alloys, solute limits) Ground state energies of phases, free energies Elastic properties Simple defect structures and formation energies, e.g. vacancies, interstitials, dislocation cores Energy landscapes for athermal transformations Raabe: Adv. Mater. 14 (2002)

11 Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421
Theory and Simulation: Multiscale crystal mechanics Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

12 Ab initio in materials science: what for ?
Overview Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

13 BCC Ti biomaterials design
115 GPa 20-25 GPa Stress shielding Elastic Mismatch: Bone degeneration, abrasion, infection Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

14 BCC Ti biomaterials design
Design-task: reduce elastic stiffness M. Niinomi, Mater. Sci. Eng Bio-compatible elements From hex to BCC structure: Ti-Nb, … Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

15 Construct binary alloys in the hexagonal phase
Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

16 Construct binary alloys in the cubic phase
Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

17 Elastic properties / Hershey homogenization
XRD DFT hex bcc Ti-hex: 117 GPa Ultra-sonic measurement exp. polycrystals bcc+hcp phases theory: bcc polycrystals polycrystal Young`s modulus (GPa) MECHANICAL INSTABILITY!! Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475

18 Ab initio alloy design: Elastic properties: Ti-Nb system
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) Hershey FEM FFT Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

19 Take-home message More than one million hip implants per year:
elastically compliant Titanium-alloys can reduce surgery

20 Ab initio in materials science: what for ?
Overview Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

21 Hickel, Dick, Neugebauer
Ab-initio methods for the design of high strength steels martensite formation twin formation 1000 800 600 400 200 TRIP steel Stress s [MPa] TWIP steel Strain e [%] Hickel, Dick, Neugebauer

22 Hickel, Dick, Neugebauer
Ab-initio methods for the design of high strength steels C A B Hickel, Dick, Neugebauer

23 Ab initio in materials science: what for ?
Develop new materials via ab-initio methods Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges

24 size Cu precipitates (nm)
Nano-precipitates in soft magnetic steels magnetic loss (W/kg) 15 nm size Cu precipitates (nm) {JP } nanoparticles too small for Bloch-wall interaction but effective as dislocation obstacles mechanically very strong soft magnets for motors Fe-Si steel with Cu nano-precipitates

25 Fe-Si-Cu, LEAP 3000X HR analysis
Cu 2 wt.% 120 min 450°C aging 20 nm 6000 min Iso-concentration surfaces for Cu 11 at.% 20 nm Fe-Si steel with Cu nano-precipitates

26 Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates 26

27 Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates 27

28 Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates 28

29 Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates 29

30 Ab-initio, binding energies: Cu-Cu in Fe matrix
Fe-Si steel with Cu nano-precipitates

31 Ab-initio, binding energies: Si-Si in Fe matrix
Fe-Si steel with Cu nano-precipitates

32 For neighbor interaction energy take difference (in eV)‏
Ab-initio, binding energies For neighbor interaction energy take difference (in eV)‏ (repulsive) = 0.390 (attractive) = (attractive) = Fe-Si steel with Cu nano-precipitates

33 Ab-initio, use binding energies in kinetic Monte Carlo model

34 Ab initio in materials science: what for ?
Develop new materials via ab-initio methods Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges

35 Ab-initio design of Mg-Li alloys
Weak under normal load Weak under shear load Y: Young‘s modulus r: mass density B: compressive modulus G: shear modulus Counts et al.: phys. stat. sol. B 245 (2008) 2630 Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69

36 Ab initio in materials science: what for ?
Develop new materials via ab-initio methods Ab initio in materials science: what for ? Ab initio to continuum models (mechanics) Titanium (ab initio and continuum) Mn-steels (identify mechanisms) Steel with Cu precipitates (atom scale experiments) Mg-Li alloy design (ab initio property maps) Singapore crab (ab initio and homogenization) Conclusions and challenges

37 Crystals and anisotropy
Scales in computational crystal plasticity Length [m] Boundary conditions 100 Crystals and anisotropy Kinetics of defects 10-3 Structure of defects Structure of matter 10-6 10-9 Time [s] 10-15 10-9 10-3 103 D. Raabe: Advanced Materials 14 (2002) p. 639

38 Gb, Gb2 , ... From ab-initio to polycrystal mechanics <E>
* DFT: density functional theory Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

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