Transcript Document

Yuri Gornostyrev
Institute of quantum materials science
Institute of metal physics UB RAS
Ekaterinburg, http://www.iqms.ru
In collaboration with
O.I.Gorbatov, I.K. Razumov, S.V. Okatov, A.R. Kuznetsov
(IQMS), P.V. Korzhavyi, A.V. Ruban (KTH), A.I. Lichtenstein
(Hamburg Uni), M.I. Katsnelson (Radboud Uni) V.N. Urtsev,
A.V. Shmakov (RTC Ausferr)
MISiS, 20-10-2013
IQMS
IQMS
Problem of Fe. Effect of magnetism on
fundamental properties
• C. Zener (1952): the start
Fragment of phase diagram Fe-C
temperature of martensitic
transformation Ms ~ TC
• Experiment: Ms = 1020K
(C. Liu et al, J Mater. Proc.
Tech., 2001)
TC ~ Tg-a
C. Zener, 1952
L. Kaufman, E.V. Clougherty, R.J.
Weiss, Acta Metall., 11, 323 (1963)

Free energy of Fe with taking into
account magnetic fluctuations
L. Kaufman, et. al., 1963
M. Hillert, et. al., 1967
G. Inden, 1976
M. Hillert, et. al., 1978
T. Nishizawa, et. al., 1979
G. Inden, 1981
B. Jonsson, 1992, 1994, 1995
Y. Liu, et. al., 2009
Wei Xiong, et. al., 2012
H. Hasegava, D.G. Pettifor, PRL, 50,
130 (1983)
Magnetism play crucial role in phase equilibrium and
transformation kinetic
MISiS, 20-10-2013
2
IQMS
Selected problems initiated by the
metallurgical needs
Mechanism polymorphous g – a transformation in
steel
Transformation kinetic and microstructure formation
Effect of alloying elements on phase equilibrium
and transformation
Precipitation of alloying elements and carbonitride
in steels
Scheme of controlled rolling
low alloying pipe steel
Clustering of foreign atoms in maraging steels
Grain boundaries segregations
and more …
Thus, there is close relation between quantum mechanics and technology
MISiS, 20-10-2013
3
The purpose and methods of calculations
Motivation: elucidate the effect of magnetism on
thermodynamic of iron-based alloy
We employed the following methods and approximations
 Density Functional Theory, DFT1
 Coherent Potential Approximation, CPA2
 Korringa, Kohn, Rostoker - Green's Function Methods. KKR-GF
 Generalized Gradient Approximation, GGA4
 Locally Self-consistent Green's Function method, LSGF5
 Disordered Local Moment Model, DLM6
 VASP7
1. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133
(1965)
2. P. Soven, Phys. Rev. 156, 809 (1967)
3. J. Korringa. Physica 13, 392 (1947); W. Kohn and N. Rostoker. Phys. Rev. 94, 1111 (1954)
4. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
5. I.A. Abrikosov, A.M.N. Niklasson, S.I. Simak, B. Johansson, A.V. Ruban, H.L. Skriver. Phys. Rev. Lett. 76, 22,
4203 (1996); I.A. Abrikosov, S.I. Simak, B. Johansson, A.V. Ruban, H.L. Skriver. Phys. Rev. B 56, 15, 9319 (1997)
6. B.L. Gyorffy, A.J. Pindor, J.B. Stauton, G.M. Stocks, H. Winter, J Phys. F 15, 1337 (1985); J.B. Stauton, B.L.
Gyorffy, Phys. Rev. Lett. 69, 371 (1992)
7. G. Kresse and J. Furthmuller, Phys. Rev. B 54, P.11169 (1996); G. Kresse and J. Hafner, Journal Phys.
Condensed Matter, 6, 8245 (1994); G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999).
MISiS, 20-10-2013
4
IQMS
Play important role
in pipe steels and maraging steels
and use to control phase stability, transformation and
strengthening
MISiS, 20-10-2013
IQMS
Precipitation in steel. Important cases
1. Nb carbonitride precipitation Nb(CN) at T < 1100 C
to prevent austenite grain growth
2. Cu-reach nano-size precipitate at T < 700 C
Strength, plasticity and toughness.
This steel proposed in prof. M. Fine
group at NWU
Distribution of copper atoms in steel with 1.2 at.%
Cu after annealing [1].
3. Complex precipitation Ti-Al-Mn in maraging steels T < 500 C
High strength and plasticity
[1] D. Isheim, M. S. Gagliano, M. E. Fine, D. N. Seidman, Acta Materialia V. 54 p. 841 (2006).
KTH, 15-05-2013
6
IQMS
Thermodynamics and structure of alloys
from first principles
V(2)
CVS alloy energy
Electronic structure
and chemical bonding
Microstructure
formation
Interaction with
dislocation,
hardening
Effective cluster
interactions energy
properties
Experiment
(HREM, 3D AP)
MISiS, 20-10-2013
7
Ab-initio interaction energies between alloying elements
« + » is repulsion
« - » is attraction
local ordering
decomposition
• Interatomic interactions follow to the number of element in the periodic table
• The strongest effect of magnetism is for Cr, Mn, Ni, Cu, V
• The tendency to decomposition for Cu and Zn
O.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, PMM, 2013
MISiS, 20-10-2013
8
IQMS
Effective pair Cu-Cu interactions
Total effective pair interaction in bcc-Fe with 1
at.% Cu for different global magnetization
Vtot(2)  V (2)  Vd
chemical contribution
Dependence of the effective pair
interactions in the nn positions on square
of global magnetization
relaxation contribution
• Interactions depend on the temperature and the concentration of the alloy
• Dependence on the concentration is more pronounced in the ferromagnetic state
O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB in press
MISiS, 20-10-2013
9
IQMS
Solubility Cu in bcc Fe: results of Monte Carlo
modeling
1% Cu – isolated Cu atoms in pair
12.5% Cu – the nearest neighbor in
first coordination shell.
● - G. Salje and M. Feller-Knipmeier, J.
Appl.Phys. 48, 1833 (1977)
■ - M. Perez et. al, Philos. Mag. 85,
2197 (2005)
•Increase of copper concentration results in smoothing magnetic effect
•Concentration dependent Cu-Cu interactions with strained-induce interactions
give agreement with the experiment
MISiS, 20-10-2013
10
IQMS
Time-Temperature-Transformation (TTT) diagram
of decomposition of dilute Fe-Cu alloy
FM
PDLM
TTT diagram of decomposition
of dilute Fe-Cu alloy showed
the time needed to attain the
precipitation fraction equal 0.2
from maximal value at given
temperature.
Accounting of changes in
magnetic state is necessary
for correct description of the
transformation
• It is in a good agreement with experimental kinetics
O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban,
PRB, in press
MISiS, 20-10-2013
11
IQMS
SRO is responsible
for induced magnetic anisotropy in
Fe-Si, Fe-Al and for large
magnetostriction in Fe-Ga
MISiS, 20-10-2013
Effect of temperature on SRO in Fe-Si
Profiles of superstructure peak (300) and (003) of single crystal Fe(1-x)Six (x =
0.08) diffuse scattering [N.V. Ershov et al. 2008, 2009]
850°C
450°C
B2
B2
D03
D03
Different SRO appear in T > TC and T < TC regions
After cooling from 850°C SRO B2
type is dominate
Relative volume of D03 regions
increases after annealing at 450°C.
What is mechanism of SRO formation in Fe-Si alloys?
Why SRO change nearby Curie temperature?
MISiS, 20-10-2013
13
IQMS
Energy of effective pair interactions
Effective Si-Si interaction
energies for Fe – 8% Si alloy
Total interactions
Chemical interactions
1.
2.
3.
The interactions are mostly repulsion and short-ranged
Sensitive to magnetic state of iron
Interaction energy of 2-th neighbors significant decrease in PM state
MISiS, 20-10-2013
14
IQMS
Monte Carlo simulation of short-range order in Fe-Si
PnSiSi – the probability of finding an atom Β in the n-th
coordination sphere of another atom Β
Τ = 900 oC
Τ = 300 oC
B2
D03
- Metropolis Monte Carlo predicts B2 type SRO for T > TC and CSi  8%.
- D03 type SRO corresponds to T < TC.
MISiS, 20-10-2013
15
1. Short-ranged order formation in Fe-Si and Fe-Al has been
investigated by Monte Carlo with ab-initio calculated of interatomic
interaction energies.
2. We found essential effect of magnetism on SRO formation
- B2 type SRO form at T > TC, and It inherits during cooling down;
- D03 type SRO is preferable for temperatures T < TC and appears
after annealing of quenches samples;
3. The results support the model of the induced magnetic anisotropy
based on ordering Si-Si pairs. However, these pairs do not appear
during annealing below TC and rather quenched from paramagnetic
state
MISiS, 20-10-2013
16
IQMS
Give main contribution to microstructure
formation
The microscopic mechanism is still not
clear
MISiS, 20-10-2013
IQMS
What mechanism of martensitic
transformation?
Martensitic transformation appear at T < Ms as
results of lattice instability
But there is not soft modes in phonon
spectra of fcc Fe
Leonov, I., Poteryaev, A.I., Anisimov, V.I.
& Vollhardt, D., PRB, 2012
What reasons for lattice instability in fcc Fe ?
MISiS, 20-10-2013
18
IQMS
Bain path energetics. Importance of
magnetic short range order (MSRO).
The energy of Fe in dependence on tetragonal
distortions for different magnetic states




Ferromagnetic FCC Fe is unstable.
Paramagnetic (DLM) FCC Fe is stable,
however g - a transition do not lead to
energy gain.
Paramagnetic BCC Fe stabilize by
MSRO
Energy barrier connected with
magnetic structure SS – FM transition.

There is magnetic instability in FM FCC Fe.

Cooling down to T < TC (FM curve) lead to high driving force and small energy
barrier E << kT – martensitic mechanism; for T > TC – nucleation and grows.
S.V. Okatov et al, PRB 2009
MISiS, 20-10-2013
19
IQMS
Bain path in dependence on temperature
From Fe DLM calculation
Nucleation and grows
Fe
(PM)
Intermidiate T?
Martensitic transformation
(FM)
From Fe FM 0K calculation
For description of BP at intermediate temperature the exchange
interactions in dependence on deformation are nesessary
MISiS, 20-10-2013
20
IQMS
Spin lattice coupling in g-Fe.
Exchange parameters from spin-spiral calculations (VASP)
1
E  ENM  EM ; EEX   J i , j ei e j ; J n  J ( Rn )  E (Q) exp( -QR n )

M Q BZ
i, j
Exchange energy appear big and comparable with T in distorted FCC Fe
Follow expect strong spin lattice coupling
S.V. Okatov et al, PRB 2012
MISiS, 20-10-2013
21
IQMS
Energy
Simple model of Bain path in
dependence on temperature
E  E PM (ˆ) -  J i , j (ˆ)  mi m j 
i j
Q(T )  mi  m j 
1  exp- kTC /  
1  expk T - TC  /  
~ ~
g (ˆ,T )  g PM (ˆ) - J (ˆ)Q(T )
kTC  J ( t ) / 2,   0.04eV
Free energy magnetic contribution (Hellmann-Feynman)
~
~
~
J
~ ~
J  (1 -  )    exp(aJ /  ) 
~

f t (et , T )  g PM - Ts0 -  Q( J , T )dJ   g PM - Ts0 - 
ln


a
1 


0
Bain path energetics from ab-initio for FM and PM(DLM) states
MISiS, 20-10-2013
22
IQMS
Kinetic equations of model
For displacements
 ij
 2 ui
u
 2 
  2 i
t
t
j r j
 ij 
F
 ij
and composition evolution
c
F
 M 2
t
c
M  M 0 Exp- Q / T 
where
F dE( )

 Av v - xvcc  xv 2 1 - 2 xv   2 xc c 2 - k  2 xx
 xx
d
F
dE( )
2 yy  2
 Av v - xvcc  xv 2 1  2 xv  - 2 xc c 2 - k 2 yy
 yy
d
F
 xy 
 Ae e
2 xx  2
 xy
The solution this equation is determined thee new phase nucleation (with
taking into account thermal fluctuations and microstructure formation
MISiS, 20-10-2013
23
IQMS
Results of modeling
Martensitic transformation after fast (a)/slow(b) cooling at T < MS
MISiS, 20-10-2013
24
ИКМ
Towards of consistent model of polymorphic
transformation in steel
What we need to be happy ?
1. Effective Hamiltonian (free energy) parameterization
from ab-inito
2. Taking into account effect of carbon on BP energetics
and phase equilibrium
3. Taking into account mechanism of plastic relaxation of
internal stress associated with transformation
MISiS, 20-10-2013
25
IQMS
Effect carbon on Bain path and critical
points
C=0%
C=1%
Description of plastic relaxation is still open
MISiS, 20-10-2013
26
Thank you for attention
MISiS, 20-10-2013
27
Backup
MISiS, 20-10-2013
28
IQMS
5E+04
1
Transformation in Fe-c. Results of modeling
7.5E+04
1.37
1E+05
1.5
6E+05
15
2E+06
7.5E+05
Ferrite transformation in Fe-2%C
at T=1100K with taking into
account carbon distribution (2-nd
row) and plastic relaxation
(black and white – ferrite two
orientations, gray – austenite)
Bainite transformation in Fe-2%C
at T=900K with taking into account
carbon distribution (2-nd row) and
plastic relaxation
(black and white – ferrite two
orientations, gray – austenite)
Proposed model catch main observed features of polymorphic transformation
MISiS, 20-10-2013
29
Effect of magnetism on solubility
A.P. Miodownik, Bulletin of
Alloy Phase Diagrams,
Volume 2, Issue 4, March
1982, Pages 406-412
•Magnetic state of the host (iron) exerts an influence
•Solubility anomaly in Fe-Cu and Fe-Zn at the Curie temperature is
the most pronounced effect
KTH, 15-05-2013
30
mRy
Solubility of 3d elements in bcc iron
•The strongest effect of magnetism is for Cr, Ni, Cu, V, Ti
•Sc has the largest relaxation contribution
31
O.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, 2008
IQMS
Multiscale approach: Application to
decomposition and hardening in Fe-Cu alloy
Prediction solubility Cu in Fe
and phase diagram
( I ) Ab-initio calculation of the
( II ) Monte-Carlo simulations of
interaction energy between Cu
atoms in bcc Fe
the alloys decomposition with abinitio parameters
Precipitate size and morphology
vs. time and temperature
annealing
( III ) Molecular dynamic
( IV ) Determination of the shear
modeling of the interaction
between dislocation and Cu
particles
resistance in dependence on
composition and size Cu particles
Assessment strengthening Fe
due to embedded Cu nano
particles
Dislocation
locking
d=4.5nm
Prediction of treatment regimes
to obtain high strength and
plasticity
cr
Dislocation energy
MISiS, 20-10-2013
32
IQMS
Monte-Carlo modeling with first-principle
parameterization
Precipitation kinetics
in Fe-Cu-Nb
Effective cluster
interactions from
SGPM calculations
KTH, 15-05-2013
33
IQMS
Effect carbon on Bain path and critical
points
0.2
g ( )
g ( )
g ( )
C=0%
0.2
C=1%
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
a1/a2
0
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
a1/a2
0
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
C=3%
a1/a2
0
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
T,K
1184
1000
fcc
FS
fcc+Cem
bcc+fcc
840
BS
MS
373
0
at.%
3.4
c,
Description of plastic relaxation is still open
MISiS, 20-10-2013
34
ИКМ
Towards of consistent model of polymorphic
transformation in steel
Bain path energetics
for FM and PM states
Fe
(PM)
1300К
Finite T from effective
Hamiltonian
1200К
1100К
1000К (FM)


F   a 2 - b 4  c 6  ( )2 dr -  J i , j ( )mim j 
i, j
(FM)

deformation
magnetism

  f (C ,  , m)  (C )2 dr
carbon
The construction of effective Hamiltonian for
finite T is nesessary
MPIE, 2-10-2012
35