Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore
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Transcript of Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore
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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]
IHPC - Institute for High Performance Computing Singapore 1. Nov 2010 Dierk Raabe
Using ab-initio based multiscale models and experiments for alloy design
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TitaniumAluminiumMagnesiumNickelSteelsIntermetallics
New materials for key technologies: Aero-space
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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
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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
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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)
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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
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11www.mpie.de
Replace empirical by knowledge-based alloy design
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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)
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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)
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Adiabatic Born-Oppenheimer approximation
Decoupling of core and electron dynamics
Electrons
Atomic cores
Raabe: Adv. Mater. 14 (2002)
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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
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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
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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)
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20Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421
Theory and Simulation: Multiscale crystal mechanics
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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, …
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Construct binary alloys in the hexagonal phase
Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475
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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
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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
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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
?
?
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M A
Mn layer 1Mn layer 2
35
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
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Mean diffusion path of Mn in austenite
(aging 450°C/48h) 2 nm
37
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
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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
![Page 39: Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore](https://reader038.fdocuments.net/reader038/viewer/2022103018/55893389d8b42add138b46a5/html5/thumbnails/39.jpg)
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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
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Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates
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Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates
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Modeling: ab-initio, DFT / GGA, binding energies
Fe-Si steel with Cu nano-precipitates
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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
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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
![Page 50: Ab initio simulation in materials science, Dierk Raabe, lecture at IHPC Singapore](https://reader038.fdocuments.net/reader038/viewer/2022103018/55893389d8b42add138b46a5/html5/thumbnails/50.jpg)
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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
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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
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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
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exocuticleexocuticle
endocuticleendocuticle
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180° rotation of fiber planes180° rotation of fiber planes
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Normal direction
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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
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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
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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
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Hierarchical modeling of stiffness starting from ab initio
Nikolov et al. : Adv. Mater. 22 (2010), 519
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Hierarchical modeling of stiffness starting from ab initio
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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
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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
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* DFT: density functional theory
Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475
From ab-initio to polycrystal mechanics
Gb, Gb2 , ...<E>