1. 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
Sydney Oct. 2010 Dierk Raabe
Combining ab-initio based multiscale models and
experiments for structural alloy design

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

3. 2
Ab initio and crystal modeling
Counts, Friák, Raabe, Neugebauer: Acta Mater. 57 (2009) 69






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

5. 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)

6. 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)

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

8. 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

9. 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

10. 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
i
i rrn  
Calculate T(n) without consideration of interactions
      rdr
m2
rnT 2
i
i
2
2
*
i  







Determine optimal basis set by variational principle
  
 
0
r
rnE
i




Hohenberg Kohn, Phys. Rev. 136 (1964) B864

11. 10Hohenberg Kohn, Phys. Rev. 136 (1964) B864
Hohenberg-Kohn-Sham theorem

12. 11
Ab initio: theoretical methods
Hohenberg Kohn, Phys. Rev. 136 (1964) B864

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

14. 13
Ab initio: typical quantities of interest in materials mechanics
Raabe: Adv. Mater. 14 (2002)

15. 14Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421
Theory and Simulation: Multiscale crystal plasticity

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

17. 16
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

18. 17
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, …

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

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

21. 20
MECHANICAL
INSTABILITY!!
Ultra-sonic measurement
exp. polycrystals
bcc+hcp phases
Ti-hex: 117 GPa
theory: bcc
polycrystals
polycrystalYoung`smodulus(GPa)
Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475
Elastic properties / Hershey homogenization
hex
bcc

22. 21
XRD
DFT
Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475
Elastic properties / Hershey homogenization

23. 22Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642
Discrete FFTs, stress and strain; different anisotropy

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

25. 24
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600
0
10
20
30
40
50
60
70
80
totalelongationtofracture[%]
ultimate tensile strength [MPa]
TRIP and
complex phase
martensitic
Maraging-TRIP
and advanced QP
dual phase
ferritic
Motivation: TWIP, TRIP, maraging, and combinations
austenitic
stainless
advanced
TWIP and
TRIP
Raabe, Ponge, Dmitrieva, Sander: Scripta Mater. 60 (2009) 1141

26. 25
Stresss[MPa]
1000
800
600
400
200
0
0 20 40 60 80 100
Strain e [%]
TRIP
steel
TWIP steel
Ab-initio methods for the design of high strength steels
www.mpie.de
martensite
formation
twin formation
Dick, Hickel, Neugebauer

27. 26www.mpie.de
Ab-initio methods for the design of high strength steels
C A
B
B
C
Dick, Hickel, Neugebauer

28. 27
Mn atoms
Ni atoms
Mn iso-concentration surfaces at 18 at.%
APT results: Atomic map (12MnPH aged 450°C/48h)
70 million ions
Laser mode
(0.4nJ, 54K)
Dmitrieva et al., Acta Mater, in press 2010
Martensite decorated by precipitations
Austenite
?
?

29. 28
Develop new materials via ab-initio methods
www.mpie.de

30. 29
Nano-precipitates in soft magnetic steels
size Cu precipitates (nm)
{JP 2004 339603}
15 nm
magneticloss(W/kg)
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. 30
Cu 2 wt.%
20 nm
120 min
20 nm
6000 min
Iso-concentration
surfaces for
Cu 11 at.%
Fe-Si-Cu, LEAP 3000X HR analysis
Fe-Si steel with Cu nano-precipitates
450°C aging

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

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

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

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

36. 35
Ab-initio, binding energies: Cu-Cu in Fe matrix
Fe-Si steel with Cu nano-precipitates

37. 36
Ab-initio, binding energies: Si-Si in Fe matrix
Fe-Si steel with Cu nano-precipitates

38. 37
For neighbor interaction energy take
difference (in eV)
(repulsive) = 0.390
(attractive) = -0.124
(attractive) = -0.245
E SiSi
bin
E S iCu
bin
E CuCu
bin
Ab-initio, binding energies
Fe-Si steel with Cu nano-precipitates

39. 38
Ab-initio, use binding energies in kinetic Monte Carlo model

40. 39
Develop new materials via ab-initio methods
www.mpie.de

41. 40
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 modulus
r: mass density
B: compressive modulus
G: shear modulus
Weak under
normal load
Weak under
shear load

42. 41
Develop new materials via ab-initio methods
www.mpie.de

43. 42
The materials science of chitin composites
Fabritius, Sachs, Romano, Raabe : Adv. Mater. 21 (2009) 391

44. 43
Exocuticle
Endocuticle
Epicuticle
Exocuticle and
endocuticle have
different stacking
density of twisted
plywood layers
Cuticle hardened
by mineralization
with CaCO3

45. 44
exocuticle
endocuticle

46. 45
180° rotation
of fiber planes

47. 46
Normal
direction

48. 47

49. 48

50. 49

51. 50

52. 51
R1
R2
R3
R4
Beam stop
DESY (BW5), l=0.196 Å.
very strong chitin textures
clusters of calcite
XRD wide angle diffraction, chitin, lobster
A. Al-Sawalmih at al. Advanced functional materials 18 (2008) 3307

53. 52Sachs, Fabritius, Raabe: J Material Research 21 (2006) 1987
Mechanical properties (microscopic, nanoindentation)

54. 53
P218.96 35.64 19.50 90˚α-Chitin
Space group
Unit cell dimensions (Bohrradius)
a b c γ
Polymer
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 group
Unit cell dimensions (Bohrradius)
a b c γ
Polymer
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. 54
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. 55
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

57. rmax = 3.5Å
max = 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
c
b
H
C
O
N
DFT ground state structure
56Nikolov et al. : Adv. Mater. 22 (2010), 519

58. 57
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 [%]
EnergyE-E0[kcal/mol]
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

59. 58Nikolov et al. : Adv. Mater. 22 (2010), 519

60. 59
Hierarchical modeling of stiffness starting from ab initio

61. 60
Develop new materials via ab-initio methods
www.mpie.de

62. 61
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. 62
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