Ab Initio Lecture Sidney University Oct 2010

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

Düsseldorf, [email protected]

Sydney Oct. 2010 Dierk Raabe

Combining ab-initio based multiscale models and experiments for structural alloy design

Ab initio in materials science: what for ?

Ab initio introduction

Multiscale crystal mechanical modeling

Examples of ab initio crystal mechanicsTitanium (ab initio and continuum)

Mn-steels (identify mechanisms)

Steel with Cu precipitates (atom scale experiments)

Mg-Li alloy design (ab initio property maps)

Nouvelle cuisine (ab initio and homogenization)

Conclusions and challenges

Overview

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

3

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

Overview











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


Adiabatic Born-Oppenheimer approximation

Decoupling of core and electron dynamics

Electrons

Atomic cores


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


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


11Hohenberg Kohn, Phys. Rev. 136 (1964) B864

Hohenberg-Kohn-Sham theorem

12

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


Overview











14

Ab initio: typical quantities of interest in materials mechanics

Lattice parameter (e.g. alloys, solute limits)

Ground state energy of phases

Elastic properties

Simple defect structures and formation energies, e.g.

vacancies, interstitials, dislocation cores

Energy landscapes for athermal transformations


15Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Theory and Simulation: Multiscale crystal plasticity

Overview











17

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

18

Design-task: reduce elastic stiffness


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



Construct binary alloys in the cubic phase

21

MECHANICALINSTABILITY!!

Ultra-sonic measurement

exp. polycrystals

bcc+hcp phases

Ti-hex: 117 GPa

theory: bcc polycrystals

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

22

XRDDFT

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

Elastic properties / Hershey homogenization

23Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

Discrete FFTs, stress and strain; different anisotropy

Ti: 115 GPa

Ti – 35 Nb - 7 Zr - 5 Ta: 59.9 GPa (elastic isotropic)

Overview











25

200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80

tota

l elo

ngatio

n to f

ract

ure

[%

]

ultimate tensile strength [MPa]

TRIP and complex phaseTRIP and complex phase

martensiticmartensitic

Maraging-TRIPand advanced QPMaraging-TRIPand advanced QP

dual phasedual phase

ferriticferritic

Motivation: TWIP, TRIP, maraging, and combinations

steels with very good formabilitysteels with very good formability steels with extreme strength and acceptable formabilitysteels with extreme strength and acceptable formability

austenitic stainlessaustenitic stainless

advanced TWIP and TRIP

advanced TWIP and TRIP

Raabe, Ponge, Dmitrieva, Sander: Scripta Mater. 60 (2009) 1141

26

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

Dick, Hickel, Neugebauer

27www.mpie.de

Ab-initio methods for the design of high strength steels

C AB

B

C

Dick, Hickel, Neugebauer

28

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

?

?

29

Develop new materials via ab-initio methods

www.mpie.de










30

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

31

Cu 2 wt.%

20 nm

120 min

20 nm

6000 minIso-concentration surfaces for Cu 11 at.%

Fe-Si-Cu, LEAP 3000X HR analysis


450°C aging

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


36

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


37

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


38

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


39

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

40


www.mpie.de










41

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

42


www.mpie.de










43

The materials science of chitin composites

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

44

Exocuticle

Endocuticle

Epicuticle

Exocuticle and endocuticle have different stacking density of twisted plywood layers

Cuticle hardened by mineralization with CaCO3

45

exocuticleexocuticle

endocuticleendocuticle

46

180° rotation of fiber planes180° rotation of fiber planes

47

Normal direction

52

R1

R2

R3

R4

Beam stop

DESY (BW5), l=0.196 Å.

very strong chitin texturesclusters of calcite

XRD wide angle diffraction, chitin, lobster

A. Al-Sawalmih at al. Advanced functional materials 18 (2008) 3307

53Sachs, Fabritius, Raabe: J Material Research 21 (2006) 1987

Mechanical properties (microscopic, nanoindentation)

54

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

55

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

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


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

57Nikolov et al. : Adv. Mater. 22 (2010), 519

58

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


Ab initio prediction of α-chitin elastic properties

59Nikolov et al. : Adv. Mater. 22 (2010), 519

60

Hierarchical modeling of stiffness starting from ab initio

61


www.mpie.de










62

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

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

Ab Initio Lecture Sidney University Oct 2010

Technology

Transcript of Ab Initio Lecture Sidney University Oct 2010