Ab initio in materials science: what for ?

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Presentation transcript:

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 WWW.MPIE.DE d.raabe@mpie.de IHPC - Institute for High Performance Computing Singapore 1. Nov 2010 Dierk Raabe

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)

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

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)

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)

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

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

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

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

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

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)

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

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)

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

BCC Ti biomaterials design Design-task: reduce elastic stiffness M. Niinomi, Mater. Sci. Eng. 1998 Bio-compatible elements From hex to BCC structure: Ti-Nb, … Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

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

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

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

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

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

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)

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 0 20 40 60 80 100 Strain e [%] Hickel, Dick, Neugebauer www.mpie.de

Hickel, Dick, Neugebauer Ab-initio methods for the design of high strength steels C A B Hickel, Dick, Neugebauer www.mpie.de

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 www.mpie.de

size Cu precipitates (nm) Nano-precipitates in soft magnetic steels magnetic loss (W/kg) 15 nm size Cu precipitates (nm) {JP 2004 339603} 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

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

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

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

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

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

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

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

For neighbor interaction energy take difference (in eV)‏ Ab-initio, binding energies For neighbor interaction energy take difference (in eV)‏ (repulsive) = 0.390 (attractive) = -0.124 (attractive) = -0.245 Fe-Si steel with Cu nano-precipitates

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

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 www.mpie.de

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

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 www.mpie.de

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

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