ab initio simulation in materials science, dierk raabe, lecture at ihpc singapore

D. Raabe, F. Roters, P. Eisenlohr, H. Fabritius, S. Nikolov, M. PetrovO. Dmitrieva, T. Hickel, M. Friak, D. Ma, J. Neugebauer

Düsseldorf, GermanyWWW.MPIE.DEd.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

TitaniumAluminiumMagnesiumNickelSteelsIntermetallics

New materials for key technologies: Aero-space

3

New materials for key technologies: mobility on land and water

SteelsMagnesiumAluminiumTitanium

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New materials for key technologies: Power plants

SteelsNickelIntermetallics

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New materials for key technologies: Green energy

SteelsCu(In,Ga)Se2

CdTe

6

New materials for key technologies: infrastructure

Steels

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New materials for key technologies: Health

TITANIUMMAGNESIUMPOYLMERSBONE

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New materials for key technologies: Information, energy, lighting

GoldCopperIII-V semiconductors

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

Overview

Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

10

Ab initio and crystal modeling

Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69

ELECTRONIC RULES FOR ALLOY DESIGN: ADD ELECTRONS RATHER THAN ATOMS

OBTAIN DATA NOT ACCESSIBLE OTHERWISE

COMBINE TO ATOMIC SCALE EXPERIMENTS

MOST EXACT KNOWN MATERIALS THEORY

CAN BE USED AT CONTINUUM SCALE

11www.mpie.de

Replace empirical by knowledge-based alloy design

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)

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)

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 energyEH(n) Hartree energy (electron-electron repulsion)Exc(n) Exchange and correlation energyU(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)

2

ii rrn

Calculate T(n) without consideration of interactions

rdrm2

rnT 2i

i

22

*i

Determine optimal basis set by variational principle

0rrnE

i

Hohenberg Kohn, Phys. Rev. 136 (1964) B864

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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

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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)

20Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Theory and Simulation: Multiscale crystal mechanics

Overview

Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

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

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115 GPa

20-25 GPa

Stress shieldingElastic Mismatch: Bone degeneration, abrasion, infection

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

BCC Ti biomaterials design

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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, …

Construct binary alloys in the hexagonal phase

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

Construct binary alloys in the cubic phase

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MECHANICALINSTABILITY!!

Ultra-sonic measurement

exp. polycrystals

bcc+hcp phases

Ti-hex: 117 GPa

theory: bcc polycrystals

XRDDFT

po

lycr

ysta

l Yo

un

g`s

mo

du

lus

(G

Pa)

Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475

Elastic properties / Hershey homogenization

hexbcc

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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

HersheyFEMFFT

HersheyFEMFFT

Ab initio alloy design: Elastic properties: Ti-Nb system

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More than one million hip implants per year:

Take-home message

elastically compliant Titanium-alloys can reduce surgery

www.mpie.de

Overview

Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)

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

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Str

ess

s [M

Pa]

1000

800

600

400

200

0

0 20 40 60 80 100Strain e [%]

TRIPsteel

TWIP steel

Ab-initio methods for the design of high strength steels

www.mpie.de

martensite formation

twin formation

Hickel, Dick, Neugebauer

31www.mpie.de

Ab-initio methods for the design of high strength steels

C AB

B

C

Hickel, Dick, Neugebauer

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twinning

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Microstructure hierarchy

Dmitrieva et al., Acta Mater, 2010

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Mn atomsNi atomsMn iso-concentration surfaces at 18 at.%

APT results: Atomic map (12MnPH aged 450°C/48h)

70 million ionsLaser mode (0.4nJ, 54K)

Dmitrieva et al., Acta Mater, in press 2010

Martensite decorated by precipitations

Austenite

?

?

M A

Mn layer 1Mn layer 2

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Mn layer2Mn 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 zonenominal 12 at.% Mn

APT results: chemical profiles

Dmitrieva et al., Acta Mater, in press 2010

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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

Mean diffusion path of Mn in austenite

(aging 450°C/48h) 2 nm

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M A

Mn layer 1Mn 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

AMPB migration

Mn diffusion

phase boundary

aging

Newaustenite

(formed during aging)

DICTRA

AM

original positionphase boundary

final positionphase boundary

APT results and simulation: DICTRA/ThermoCalc

Dmitrieva et al., Acta Mater, in press 2010

38

Develop new materials via ab-initio methods

www.mpie.de

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

39

Nano-precipitates in soft magnetic steels

size Cu precipitates (nm)

{JP 2004 339603}

15 nm

magneti

c lo

ss (

W/k

g)

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

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Cu 2 wt.%

20 nm

120 min

20 nm

6000 minIso-concentration surfaces for Cu 11 at.%

Fe-Si-Cu, LEAP 3000X HR analysis

Fe-Si steel with Cu nano-precipitates

450°C aging

Modeling: ab-initio, DFT / GGA, binding energies

Fe-Si steel with Cu nano-precipitates

Modeling: ab-initio, DFT / GGA, binding energies

Fe-Si steel with Cu nano-precipitates

Modeling: ab-initio, DFT / GGA, binding energies

Fe-Si steel with Cu nano-precipitates

Modeling: ab-initio, DFT / GGA, binding energies

Fe-Si steel with Cu nano-precipitates

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Ab-initio, binding energies: Cu-Cu in Fe matrix

Fe-Si steel with Cu nano-precipitates

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Ab-initio, binding energies: Si-Si in Fe matrix

Fe-Si steel with Cu nano-precipitates

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For neighbor interaction energy take difference (in eV)

(repulsive) = 0.390 (attractive) = -0.124 (attractive) = -0.245

ESiSibin

ESiCubin

E CuCubin

Ab-initio, binding energies

Fe-Si steel with Cu nano-precipitates

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

49

Develop new materials via ab-initio methods

www.mpie.de

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

50

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 modulusr: mass densityB: compressive modulusG: shear modulus

Weak under normal load

Weak under shear load

51

Develop new materials via ab-initio methods

www.mpie.de

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

52

The materials science of chitin composites

Fabritius, Sachs, Romano, Raabe : Adv. Mater. 21 (2009) 391

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Exocuticle

Endocuticle

Epicuticle

Exocuticle and endocuticle have different stacking density of twisted plywood layers

Cuticle hardened by mineralization with CaCO3

54

55

exocuticleexocuticle

endocuticleendocuticle

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180° rotation of fiber planes180° rotation of fiber planes

57

58

Normal direction

59

60

61

62

63

64

65Sachs, 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

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P218.96 35.64 19.50 90˚α-Chitin

Space groupUnit cell dimensions (Bohrradius)

a b c γPolymer

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 groupUnit cell dimensions (Bohrradius)

a b c γPolymer

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

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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?

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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

rmax = 3.5Åmax = 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

cb

H

C

O

N

DFT ground state structure

69Nikolov et al. : Adv. Mater. 22 (2010), 519

70

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 [%]

En

erg

y E

- E

0 [k

ca

l/mo

l]

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

Hierarchical modeling of stiffness starting from ab initio

Nikolov et al. : Adv. Mater. 22 (2010), 519

72

Hierarchical modeling of stiffness starting from ab initio

73

Develop new materials via ab-initio methods

www.mpie.de

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

74

Length [m]

10-9

10-6

10-3

100

10-15 10-9 10-3 103 Time [s]

Boundary conditions

Crystals and anisotropy

Kinetics of defects

Structure of defects

Structure of matter

D. Raabe: Advanced Materials 14 (2002) p. 639

Scales in computational crystal plasticity

75

* DFT: density functional theory

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

From ab-initio to polycrystal mechanics

Gb, Gb2 , ...<E>