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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
Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
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
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
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
Hohenberg Kohn, Phys. Rev. 136 (1964) B864
Overview
Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
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
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
Raabe: Adv. Mater. 14 (2002)
15Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421
Theory and Simulation: Multiscale crystal plasticity
Overview
Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
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
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
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
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
Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Mater.58 (2010)
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
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
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
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
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
36
Ab-initio, binding energies: Cu-Cu in Fe matrix
Fe-Si steel with Cu nano-precipitates
37
Ab-initio, binding energies: Si-Si in Fe matrix
Fe-Si steel with Cu nano-precipitates
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
Fe-Si steel with Cu nano-precipitates
39
Ab-initio, use binding energies in kinetic Monte Carlo model
40
Develop new materials via ab-initio methods
www.mpie.de
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
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
Develop new materials via ab-initio methods
www.mpie.de
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
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
48
49
50
51
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
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
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
Nikolov et al. : Adv. Mater. 22 (2010), 519
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
Develop new materials via ab-initio methods
www.mpie.de
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
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