Yuri Gornostyrev Institute of quantum materials science

Institute of metal physics UB RAS Ekaterinburg, http://www.iqms.ru

IQMS

ROLE OF MAGNETISM IN PHASE STABILITY AND

KINETIC OF TRANSFORMATION IN IRON AND STEEL

MISiS, 20-10-2013

In collaboration withO.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)

Problem of Fe. Effect of magnetism on fundamental properties

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• C. Zener (1952): the start temperature of martensitic transformation Ms ~ TC

• Experiment: Ms = 1020K (C. Liu et al, J Mater. Proc. Tech., 2001)

Fragment of phase diagram Fe-C

H. Hasegava, D.G. Pettifor, PRL, 50, 130 (1983)

L. Kaufman, E.V. Clougherty, R.J. Weiss, Acta Metall., 11, 323 (1963)

Free energy of Fe with taking into account magnetic fluctuations

Magnetism play crucial role in phase equilibrium and transformation kinetic

C. Zener, 1952

TC ~ Tg-a

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L. Kaufman, et. al., 1963M. Hillert, et. al., 1967G. Inden, 1976 M. Hillert, et. al., 1978T. Nishizawa, et. al., 1979G. Inden, 1981B. Jonsson, 1992, 1994, 1995 Y. Liu, et. al., 2009Wei Xiong, et. al., 2012

IQMS Selected problems initiated by the metallurgical needs

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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

Clustering of foreign atoms in maraging steels Grain boundaries segregations

and more …

Scheme of controlled rolling low alloying pipe steel

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Thus, there is close relation between quantum mechanics and technology

The purpose and methods of calculations

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

Motivation: elucidate the effect of magnetism on thermodynamic of iron-based alloy

We employed the following methods and approximations

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).

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Play important role in pipe steels and maraging steels

and use to control phase stability, transformation and strengthening

EFFECTS OF MAGNETISM ON PRECIPITATION

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Precipitation in steel. Important cases

Distribution of copper atoms in steel with 1.2 at.% Cu after annealing [1].

Strength, plasticity and toughness.

This steel proposed in prof. M. Fine group at NWU

[1] D. Isheim, M. S. Gagliano, M. E. Fine, D. N. Seidman, Acta Materialia V. 54 p. 841 (2006).

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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

3. Complex precipitation Ti-Al-Mn in maraging steels T < 500 C

High strength and plasticity

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IQMS Thermodynamics and structure of alloys from first principles

Experiment (HREM, 3D AP)

properties

V(2)

Electronic structure and chemical bonding

CVS alloy energy

Microstructure formation

Interaction with dislocation, hardening

Effective cluster interactions energy

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Ab-initio interaction energies between alloying elements

• 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 ZnO.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, PMM, 2013

« + » is repulsion« - » is attraction

local ordering decomposition

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Total effective pair interaction in bcc-Fe with 1 at.% Cu for different global magnetization

Dependence of the effective pair interactions in the nn positions on square of global magnetization

O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB in press

Effective pair Cu-Cu interactions

• Interactions depend on the temperature and the concentration of the alloy• Dependence on the concentration is more pronounced in the ferromagnetic state

(2) (2)tot dV V V

chemical contribution relaxation contribution

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•Increase of copper concentration results in smoothing magnetic effect •Concentration dependent Cu-Cu interactions with strained-induce interactions give agreement with the experiment

1% Cu – isolated Cu atoms in pair

12.5% Cu – the nearest neighbor in first coordination shell.

Solubility Cu in bcc Fe: results of Monte Carlo modeling

● - G. Salje and M. Feller-Knipmeier, J. Appl.Phys. 48, 1833 (1977)■ - M. Perez et. al, Philos. Mag. 85, 2197 (2005)

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O.I. Gorbatov, I.K. Razumov, Yu.N. Gornostyrev, V.I. Razumovskiy, P.A. Korzhavyi, A.V. Ruban, PRB, in press

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

Time-Temperature-Transformation (TTT) diagram of decomposition of dilute Fe-Cu alloy

• It is in a good agreement with experimental kinetics

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PDLMFM

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SRO is responsible for induced magnetic anisotropy in

Fe-Si, Fe-Al and for large magnetostriction in Fe-Ga

EFFECTS OF MAGNETISM ON SHORT RANGE ORDER IN SOFT MAGNETIC

ALLOY FE-X (X=SI,AL,GA,GE)

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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]

After cooling from 850°C SRO B2 type is dominate

Relative volume of D03 regions increases after annealing at 450°C.

B2 D03

B2 D03

Effect of temperature on SRO in Fe-Si

850°C450°C

Different SRO appear in T > TC and T < TC regions

What is mechanism of SRO formation in Fe-Si alloys?Why SRO change nearby Curie temperature?

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Effective Si-Si interaction energies for Fe – 8% Si alloy

Energy of effective pair interactions

1. The interactions are mostly repulsion and short-ranged2. Sensitive to magnetic state of iron3. Interaction energy of 2-th neighbors significant decrease in PM state

Chemical interactions

Total interactions

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- Metropolis Monte Carlo predicts B2 type SRO for T > TC and CSi 8%.- D03 type SRO corresponds to T < TC.

B2D03

Monte Carlo simulation of short-range order in Fe-Si

Τ = 900 oCΤ = 300 oC

SiSinP – the probability of finding an atom Β in the n-th

coordination sphere of another atom Β

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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

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Give main contribution to microstructure formation

The microscopic mechanism is still not clear

POLYMORPHIC TRANSFORMATION IN IRON

AND STEEL

MISiS, 20-10-2013

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IQMS What mechanism of martensitic transformation?

Martensitic transformation appear at T < Ms as results of lattice instability

What reasons for lattice instability in fcc Fe ?

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But there is not soft modes in phonon spectra of fcc Fe

Leonov, I., Poteryaev, A.I., Anisimov, V.I. & Vollhardt, D., PRB, 2012

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 200919

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IQMS Bain path in dependence on temperature

For description of BP at intermediate temperature the exchange interactions in dependence on deformation are nesessary

From Fe FM 0K calculation

(PM)

(FM)

Fe

From Fe DLM calculation

Intermidiate T?

Martensitic transformation

Nucleation and grows

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Spin lattice coupling in g-Fe.

Exchange energy appear big and comparable with T in distorted FCC Fe Follow expect strong spin lattice coupling

Exchange parameters from spin-spiral calculations (VASP)

--BZ

nnnji

jijiEXMNM EM

RJJJEEEEQ

QRQee )exp()(1)( ; ;,

,

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S.V. Okatov et al, PRB 2012 21MISiS, 20-10-2013

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IQMS Simple model of Bain path in dependence on temperature

-

jiji

jiPM JEE mm)ˆ()ˆ( , Energy )(~)ˆ(~)ˆ(),ˆ( TQJgTg PM -

/exp1

/exp1)(C

Cji TTk

kTTQ-

- mm 0.04eV ,2/)( tC JkT

-

---- a

a

1)/~exp(ln)1(~~),~(~),( 0

~

00

JJTsgJdTJQTsgTef PM

J

PMtt

Free energy magnetic contribution (Hellmann-Feynman)

Bain path energetics from ab-initio for FM and PM(DLM) states

MISiS, 20-10-2013

Kinetic equations of modelFor displacements

The solution this equation is determined thee new phase nucleation (with taking into account thermal fluctuations and microstructure formation

j

i

j

iji

tu

rtu 22

2

ij

ijF

cF

Mtc

2

TQExpMM /0 -

and composition evolution

xxcvvvcvxx

xx kcxxxcxvAd

dEF

222 221)(22 ---

yycvvvcvyy

yy kcxxxcxvAd

dEF

222 221)(22 ----

eAFe

xyxy

where

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IQMS Results of modeling

Martensitic transformation after fast (a)/slow(b) cooling at T < MS

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ИКМ Towards of consistent model of polymorphic transformation in steel

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

What we need to be happy ?

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IQMS Effect carbon on Bain path and critical points

Description of plastic relaxation is still open

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C=0% C=1%

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Thank you for attention

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Backup

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IQMS Transformation in Fe-c. Results of modeling

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)

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5E+04 7.5E+04 1E+05 6E+05 2E+06

1 1.37 1.5 15 7.5E+05

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

Effect of magnetism on solubility

•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

A.P. Miodownik, Bulletin of Alloy Phase Diagrams, Volume 2, Issue 4, March 1982, Pages 406-412

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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

O.I. Gorbatov, S.V. Okatov, Yu.N. Gornostyrev, P.A. Korzhavyi, A.V. Ruban, 2008

mR

y

Multiscale approach: Application to decomposition and hardening in Fe-Cu alloy

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( I ) Ab-initio calculation of the interaction energy between Cu atoms in bcc Fe

( II ) Monte-Carlo simulations of the alloys decomposition with ab-initio parameters

Prediction solubility Cu in Fe and phase diagramPrecipitate size and morphology vs. time and temperature annealing

( III ) Molecular dynamic modeling of the interaction between dislocation and Cu particles

( IV ) Determination of the shear resistance in dependence on composition and size Cu particles

Assessment strengthening Fe due to embedded Cu nano particles Prediction of treatment regimes to obtain high strength and plasticity

d=4.5nm Dislocation

energy

Dislocation locking

cr

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Effective cluster interactions from SGPM calculations

Precipitation kinetics in Fe-Cu-

Nb

Monte-Carlo modeling with first-principle parameterization

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IQMS Effect carbon on Bain path and critical points

Description of plastic relaxation is still open

0

0.05

0.1

0.15

0.2

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

a1/a2

)(g

0

0.05

0.1

0.15

0.2

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

a1/a2 0

0.05

0.1

0.15

0.2

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

a1/a2

)(g )(g

C=1%C=0% C=3% T,K1184

840

373

FS

BSMS

0 3.4 c, at.%

1000bcc+fcc fcc+Cem

fcc

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MPIE, 2-10-2012 35

ИКМ Towards of consistent model of polymorphic transformation in steel

-

--

rm

mm

r

dCCf

J

dcbaF

jijiji

2

,,

2642

)(),,(

)(

)(

deformation

magnetism

carbon

(FM)

(PM)

1300К

1200К

1100К

1000К (FM)

FeBain path energetics for FM and PM statesFinite T from effective Hamiltonian

The construction of effective Hamiltonian for finite T is nesessary