SFB-761 “Stahl – ab initio” Sub-project A2 “ Ab initio thermodynamics and kinetics”

Department of Computational Materials DesignDüsseldorf, Germany

I. Bleskov, F. Körmann, T. Hickel, and J. Neugebauer

[email protected]

Impact of Magnetism on Thermodynamic Properties of Iron

SFB-761 “Stahl – ab initio”Sub-project A2 “Ab initio thermodynamics and kinetics”

FEST-VEK 2013 (MISIS), 21-22.10.2013, Moscow I. Bleskov et al., MPIE Düsseldorf 2

Contents

• Motivation• Methodology

– ANNNI model– Explicit approach– Structures

• Results– Magnetic phase diagram of iron– γ-surface– twins

• Summary


Motivation


Motivation

99% of the passenger cars have a steel body 60-70% of the car weight consist of steel or steel-based parts

Passive safety and Protection from Frontal crash Rear collision Side impact Roll over

Weight increasing

Decreasing of Engine efficiency and economy Environmental pollution

Steels with low weight density high Energy-absorbtion and strength Tend to be mutually exclusive


Motivation

Material should react only locally to failures induced by high external stress

On the atomic scale this means Changes in the atomic layers stacking sequence

under the stress and gradual twin formation (TWIP) during deformation (“dynamical” Hall-Petch effect)

B.C

. De

Coo

man

, Kw

ang-

geun

Chi

n, J

inky

ung

Kim

Strength + Plasticity


MotivationAtomic layers shear can take place only if the stacking fault energy (SFE), i.e. energy required to change the sequence in atomic layer stacking, lies in a specific range

A. Saeed-Akbari, et al., Meta. and Mater. Trans. A 40, 3076 (2009)

SFE is the crucial quantitative parameter that characterizes the type of plasticity mechanism in crystalline materials

The idea that changing the SFE one can tune the mechanical properties opens an attractive way to the design of new high-strength lightweight steels


Motivation

Figure from: J. Nakano and P. J. Jacques, CALPHAD 34 (2010) 167

SFE trends different influence of alloying

elements chemical and magnetic

disorder dependence of properties on

sample preparation and microstructure

Ab initio calculations allowindependent consideration of the influence of different factors on the SFE

High-Mn steels (austenitic fcc structure stabilized by Mn) exceptional mechanical properties relatively lightweight


MotivationLocal magnetism can influence different properties of a material

Magnetic contribution to SFE

Phonon spectrum in PM fcc Fe,F.Körmann (SFB-761)

Vibrational, electronic, and magnetic contributions to the heat capacity of FM bcc FeF.Körmann (SFB-761)But due to computational challenge, often the simpler NM calculation are performed.

Reliability may be questionable in this case.


Motivation

The impact of local magnetism on the SFE in pure iron is considered because Iron is a basis element in steels To avoid the influence of alloying elements

Magnetic ordering Computational details

Nonmagnetic (NM)

VASP code; PAW basis set; PBE exchange-correlation functional

Ferromagnetic (FM)

Antiferromagnetic (single-layer)

Antiferromagnetic (double-layer)

Paramagnetic EMTO + CPA code; disordered local moment (DLM) approximation (quasi-binary alloy); GGA exchange-correlation effects


Contents




• Summary


Methodology. ANNNI model

Advantages Disadvantages Results• Defect-free bulk

structures =>• Moderate computational

costs

• Neglect of local changes of atomic/electronic structure

• Loss of info on segregation effects

• Influence of Carbon on the ISFE in steels

• Magnetic contribution to ISFE in ternary and quarternary Fe-based alloys and steels…


Methodology. Explicit approach

Advantages Disadvantages Results• Atomic relaxation,• Changes in electronic

structure,• Segregation effects due to

SF formation• Energetic barriers to form

a particular stacking

• Big supercell =>• High computational costs

• Influence of C, H (A9) on the γ-surface in Fe-based alloys…

More general approach with the supercell explicitly containing the defect Shear of one part of the crystal with respect to another => concept of the

generalized stacking fault energy (γ-) surface, where ISF is a particular point (minimum)


Methodology. fcc = …ABCABC…

Construct the cell explicitly containing …ABCABC… stacking:Face centered cubic => hexagonal with 3 atoms per cell

A

B

C

A

B

C


Methodology. Supercell structuresNM, FM, PM AFMS AFMD

[111

]

[112]


Methodology. Supercell structuresNM, FM, PM AFMS AFMD

[111

]

[112]


Contents




• Summary


Phase diagram of iron

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB

NMFMAFMSAFMDDLMNM@hcp

High

-Mn

stee

ls



3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB




3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB




3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB




3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB




3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB


>0


Contents




• Summary


γ-surface of fcc Fe

0 1-0.2-0.10.00.10.20.30.40.50.60.70.8

Fde

f - F

idea

l, eV

/cel

l



0 1-0.2-0.10.00.10.20.30.40.50.60.70.8

Fde

f - F

idea

l, eV

/cel

l

FMLS

FMHS



0 1-0.2-0.10.00.10.20.30.40.50.60.70.8

Fde

f - F

idea

l, eV

/cel

l

FMLS

FMHS

AFMS



0 1-0.2-0.10.00.10.20.30.40.50.60.70.8

Fde

f - F

idea

l, eV

/cel

l

FMLS

FMHS

AFMD

AFMS



0 1-0.2-0.10.00.10.20.30.40.50.60.70.8

Fde

f - F

idea

l, eV

/cel

l

FMLS

FMHS

AFMD

AFMSDLM

The GSFE surface topology as well as the ISFE are affected by magnetism

Magnetism changes the ISF energetic barrier


ISF Energy

NM FMLS FMHS AFMS AFMD DLM

-600

-400

-200

0

200

400

600

2TwinSFE

γISF

, mJ/

m2

Absolute value of the ISFE changes considerably in magnetic phases


Contents




• Summary


Twin Structure ( + magnetic mirror symmetry)NM, FM, DLM AFMS AFMD

[111

]

[112]


ISF and Twin Energy

NM FMLS FMHS AFMS AFMD DLM

-600

-400

-200

0

200

400

600

2TwinSFE

γISF

, mJ/

m2

The general rule that SFE = 2Twin is fulfilled.The difference is mainly due to the decreasing of the distance between defects in the same size supercell


Magnetism vs. Chemical trends of SFE (carbon)

0 0.1 0.2 0.3 0.4

-20

0

20

40

60

80

100

Non-magnetic

AFMD phase

C content in supercell [wt.%]

Ab in

itio

SFEW

ith C

- SF

EC fr

ee [m

J/m

2]

T. Hickel, S. Sandlöbes, R.K.W. Marceau, A. Dick, I. Bleskov, J. Neugebauer, and D. Raabe, Acta Materialia, SUBMITTED

The influence of magnetism on the SFE is not relevant for chemical trends


34

B

2.2 Å

1.8 Å

(002)

(-111)

Atomic planes mismatch on the twin boundary


Twin in fcc

[111

]

[112]


Twin γ-surface

[111

]

[112]


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8NMFMLSFMHSAFMSmAFMDmDLM

Fde

f - F

twin

, eV

/cel

l


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Fde

f - F

twin

, eV

/cel

l


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Fde

f - F

twin

, eV

/cel

l


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Fde

f - F

twin

, eV

/cel

l


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Fde

f - F

twin

, eV

/cel

l


Twin γ-surface

0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8NMFMLSFMHSAFMSmAFMDm

Fde

f - F

twin

, eV

/cel

l

Twin γ-surface is not strongly affected by local magnetism except FMHS phase, where the minimum exists.

“Agreement” with exp. => local ordering near the twin boundary


Twin FMHS local magnetic moments

0 12.45

2.50

2.55

2.60

2.65

2.70lo

cal m

ag. m

omen

t, μB

Only local magnetic moments of the atoms lying in the vicinity of the defect are affected


Twin γ-surface[1

11]

[112]


AB’ stacking

[111

][1-21]


3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB

AB’ stacking

FMFM@AB’


AB’ stacking

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0

1

2

3

4

5

6

7

8

9

V1/3, A/atom

ΔE, e

V/a

tom

local mag. m

oment, μB

FMFM@AB’


Contents




• Summary


Summary

• Detailed magnetic phase diagram for different structures in pure Fe (fcc, hcp, AB’) => PM/AFM magnetic phase is relevant for TWIP-steels

• Topology of GSFE surface strongly depends on local magnetic structure

• Magnetism strongly influences the SFE and twin energy in pure Fe

• Topology of twin γ-surface doesn’t suffer strong changes subject to local magnetism changes but

• discovers an unexpected minimum corresponding to AB’ stacking sequence which can shad a light to atomic planes mismatch in twin and matrix observed experimentally


Thank you for your attention!


0 1-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Fde

f - F

idea

l, eV

/cel

l

Documents

SFB-761 “Stahl – ab initio” Sub-project A2 “ Ab initio thermodynamics and kinetics”