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Lecture 3

Study of Nanoscale

Phenomena by Magnetic

Properties Measurements

Dr. Javad Mola

Institute of Iron and Steel Technology (IEST)

Tel: 03731 39 2407

E-mail: mola@iest.tu-freiberg.de

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Introduction

This lecture demonstrates how quick and straightforward magnetic

measurements could be used to obtain information regarding nanoscale

phenomena such as the redistribution of alloying elements. Due to

occurrence over a small scale, such phenomena are otherwise difficult

to study directly since their direct examination requires access to

analytical tools with a high spatial resolution (e.g. Atom Probe

Tomography, Energy-Dispersive Spectroscopy in a Transmission

Electron Microscope, …). Even specimen preparation for such methods

could be difficult and timely.

After a brief review of ferromagnetism, the following case studies are

presented:

- Precise retained austenite quantification

- Redistribution of alloying elements between martensite and

tempering carbides

- Redistribution of Mn between martensite and austenite during

intercritical annealing of a high Mn steel

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Direct Observation of Elemental Partitioning

Low-alloy steel AISI 4340

Tempered 2 h at 325 °C Tempered 2 h at 450 °C

Martensitic Matrix

Martensitic Matrix

M3C

M3C

A.J. Clarke, M.K. Miller, R.D. Field, D.R. Coughlin, P.J. Gibbs, K.D. Clarke, D.J. Alexander, K.A. Powers, P.A. Papin, G. Krauss, Acta Mater. 77 (2014) 17–27.

Atom Probe Tomography (APT) investigations for the observation of nanoscale elemental redistribution phenomena

Advantage: very high resolutions achievable

Disadvantage: limited access, time-consuming and costly specimen preparation and measurements

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Direct Observation of Elemental PartitioningAtom probe tomography (APT) results for an Fe-9.66Mn-2.98C (at.%) steel after aging at

600 °C for 6 hferrite

austenite

M.M. Aranda, R. Rementeria, J. Poplawsky, E. Urones-Garrote, C. Capdevila, Scr. Mater. 104 (2015) 67–70.

austenite

cementite

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Direct Observation of Elemental Partitioning

0 10 20 30 400

2

4

6

8

10

12

14

16

18

Ma

ss

-% M

n

Position

γ

γ

Fe-7Mn-0.1C steel heat treated

at 600 °C (α + range)

A

B

BA

Bruno C. De Cooman, P. Gibbs, S. Lee, D.K. Matlock, Metall. Mater. Trans. A 44 (2013) 2563–2572.

TEM-EDS analysis (time-consuming specimen preparation, lower resolution compared to APT)

Partitioning of Mn between ferrite and austenite during intercritical annealing of medium Mn

steels. The Mn content of austenite influences its deformation-induced processes and

mechanical properties of the duplex ferritic-austenitic microstructure.

Energy-Dispersive Spectroscopy

(EDS) analysis in TEM

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Tensile engineering stress-strain curves for

Fe-7.1Mn steel annealed for 1 week at

various temperatures.

Evolution of retained austenite fraction

with strain for Fe-7.1Mn steel

Effect of Elemental Partitioning on Tensile Behavior

P.J. Gibbs, E.D. Moor, M.J. Merwin, B. Clausen, J.G. Speer, D.K. Matlock, Metall. Mater. Trans. A 42 (2011) 3691–3702.

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Indirect Investigation of Partitioning PhenomenaIf the partitioning of alloying elements is associated with variations in the magnetic

properties of phases, it can be studied indirectly by magnetic-based methods. To do this,

one needs to know how the magnetic properties of ferromagnetic phases present in the

microstructure of steels (ferrite, certain carbides and nitrides) are influenced by the

redistribution of alloying elements.

Phase 1

(Ferromagnetic)

Phase 2

(Ferromagnetic /

Paramagnetic)

Elemental

redistributionConsequences of

elemental redistribution

Changes in magnetic properties

and magnetization response of

ferromagnetic phase(s)

Example of magnetic properties

influenced by the chemical

composition are Curie

temperature, saturation

magnetization, magnetic

susceptibility, and magnetic

permeability.

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Magnetic Properties: Dia- and Para-MagnetismD

iam

ag

neti

sm

Pa

ram

ag

neti

sm

In the absence of an external field, no dipoles exist in a diamagnetic material; in the

presence of a field, dipoles are induced that are aligned opposite to the field direction.

Examples are water, wood, copper, mercury, gold, graphite, and bismuth.

In the absence of an external magnetic field, the orientation of atomic magnetic moments in a

paramagnetic material is random and there is no net macroscopic magnetization. These

atomic dipoles are free to rotate, and paramagnetism results when they preferentially align

with an external field. Examples are magnesium, aluminum, molybdenum, lithium, and

tantalum.

Weakly repelled by magnetic fields

Weakly attracted to magnetic fields

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetic Properties: Ferromagnetism

Certain metallic materials possess a permanent magnetic moment in the absence

of an external field, and manifest very large and permanent magnetizations. These

are the characteristics of ferromagnetism, and they are displayed by the

transition metals iron, cobalt, nickel, and some of the rare earth metals such as

gadolinium (Gd). Ferromagnets are noticeably attracted to magnetic fields.

Schematic illustration of the

mutual alignment of atomic

dipoles for a ferromagnetic

material, which will persist

even in the absence of an

external magnetic field.

Plot of saturation magnetization as a

function of temperature for iron and

Fe3O4.

TC

for p

ure

Fe

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetic Domains

Gradual change in magnetic dipole

orientation across a domain wall

Domains in a ferromagnetic material; arrows

represent atomic magnetic dipoles. Within each

domain, all dipoles are aligned, whereas the

direction of alignment varies from one domain to

another. The net macroscopic magnetization is

the average of all domains.

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetization Process

Domain configuration during several stages of magnetization of a ferromagnetic

material.

Growth of domains that are oriented in directions nearly parallel to applied magnetic field (H)

Domain rotation and alignment with the direction of applied magnetic field (H)

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetization Cycle and Hysteresis

The hysteresis loop is represented by the solid red curve; the dashed blue curve indicates

the initial magnetization. The area within a loop represents the magnetic energy loss per

unit volume of material per magnetization-demagnetization cycle; this energy loss is

manifested as heat that is generated within the magnetic specimen and is capable of

raising its temperature.

Remanence, Br

Coercive force, Hc

Soft magnet

(easily

magnetized-

demagnetized)Hard magnet

(high resistance to

demagnetization)William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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Magnetic (Magnetocrystalline) Anisotropy

111

100

110

<100>, easy magnetization direction

Iron

Nickel

<110>

<111>

Anisotropy of magnetization behavior in Fe and Ni single crystals with

their <100>, <110>, and <111> crystallographic axes parallel to the

external magnetic field (H) direction.

easy

magnetization

direction

William D. Callister. Materials Science and Engineering: An Introduction. 7th ed. New York: John Wiley & Sons; 2007.

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14J. Crangle, G.M. Goodman, Proc. R. Soc. Lond. Ser. Math. Phys. Sci. 321 (1971) 477–491.

(Saturation) Magnetization of Iron

Authors (year) at 293 K at 77 K at 0 or 4 K

Magnetic isothermals

for pure iron at

temperatures near

Curie temperature

indicating gradual

demagnetization of

iron

217.61

217.35

-

217.6

-

-

-

221.4

221.74

-

221.71

221.7

Weiss & Forrer (1929)

Danan (1958)

Danan, Herr & Meyer (1968)

Crangle & Goodman (1971)

Magnetization (), emu/g

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15H. Yamauchi, H. Watanabe, Y. Suzuki, H. Saito, Magnetization of α-Phase Fe-Mn Alloys, J. Phys. Soc. Jpn. 36 (1974) 971–974.

Magnetization of Fe-Mn Alloys

Magnetization curves for Fe-Mn

alloys at 4.2 K

Temperature-dependent

magnetization of Fe-Mn alloys at

the magnetic field of 6.05 kOe

159 K100 K

Reduced m

agnetiza

tion

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Magnetization of Fe-Mn Alloys

H. Yamauchi, H. Watanabe, Y. Suzuki, H. Saito, Magnetization of α-Phase Fe-Mn Alloys, J. Phys. Soc. Jpn. 36 (1974) 971–974.

Magnetization change as a function of Mn content.

Simple dilution (magnetic

moment of Mnatoms assumed to

be zero).

Simple dilution

ε-phase?ε-phase?

For dilute Fe-Mn steels: (emu/g) 𝜎𝐹𝑒−𝑀𝑛 = 𝜎𝐹𝑒 − 1.18 × 𝑚𝑎𝑠𝑠%𝑀𝑛

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17T.D. Yensen, J. Frankl. Inst. 199 (1925) 333–342.D.I. Bardos, J.L. Beeby, A.T. Aldred, Phys. Rev. 177 (1969) 878–881.

Magnetization of Fe-Ni Alloys

BCC range FCC range

0 5 10 15 20 25200

205

210

215

220

225

230

Extr

ap

ola

ted

ma

gn

etiza

tio

n a

t 0

K (

em

u/g

)

Ni content (at.%)

BCC range

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18A.T. Aldred, Phys. Rev. B 14 (1976) 219–227.

Magnetization of Fe-Cr Alloys

0 10 20 30 40 50 60 7040

60

80

100

120

140

160

180

200

220

Extr

ap

ola

ted

ma

gn

etiza

tion

at

0K

(e

mu

/g)

Cr content (at.%)

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19A.T. Aldred, J. Phys. C Solid State Phys. 1 (1968) 244.

Magnetization of Fe-Mo Alloys

0 5 10

180

200

220

Extr

ap

ola

ted

ma

gn

etiza

tion

at

0K

(e

mu

/g)

Mo content (at.%)

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20D. Parsons, W. Sucksmith, J.E. Thompson, Philos. Mag. 3 (1958) 1174–1184.

Magnetization of Fe-Mo Alloys

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Approximate Magnetization of Fe-X Binary Alloys

If the influence of alloying elements on the magnetization of ferrite/martensite is

known, magnetic measurements can be used for phase quantification in steels

with duplex (σ+γ) microstructures.

Linear approximation of the effect of alloying elements on the

magnetic moment (Bohr magneton per atom) of iron.

W. Pepperhoff, M. Acet, Constitution and Magnetism of Iron and Its Alloys, 1st ed., Springer, 2001.

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𝜎 =

𝑖=1

𝑛

𝜎𝑖𝑓𝑖

𝒇𝜸 = 𝟏 −𝝈𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅

𝝈𝜶

Rule of mixtures applied to ferritic-austenitic steels (similarly martensitic steels with

retained austenite):

𝝈𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 = 𝝈𝜶 × 𝒇𝜶 + 𝝈𝜸 × 𝒇𝜸

In order to determine the fraction of phases, the magnetization of ferrite/martensite

(𝝈𝜶) must be known. The magnetization of ferrite (martensite) depends on

temperature, magnetic field intensity, and chemical composition.

Phase Quantification by Magnetic Measurements

Magnetization of multiphase mixtures:

Due to the paramagnetism of austenite, 𝝈𝜸 can be set to zero, therefore:

Austenite fraction:

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Linear factors for the influence of Mn, Cr, Ni, Si, and Mo in small quantities

on the magnetization of binary low-alloy Fe-X steels (X: alloying element).

𝜎𝐹𝑒−𝑋 = 𝜎𝐹𝑒 + 𝑓𝑋 ×𝑚𝑎𝑠𝑠%𝑋

J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Tempering of Martensite and Subsequent Redistribution of Cr, Mn, Ni, Mo, and Si Between Cementite and Martensite Studied by Magnetic Measurements

Alloying element (X) Coefficient fX, emu/g

per 1 mass-%X

Cr -2.12

Mn -1.18

Si -2.00

Ni +0.45

Mo -1.98

Magnetization of Binary Low-Alloy Steels

Ma

gn

etiza

tio

n, 𝜎𝐹𝑒−𝑋

Mass-% XFe

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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60

10

20

30

40

50

60

70

80

90

100

Water + liquid nitrogen -196 oC

Water + ethanol -100 oC

Water + ethanol -50 oC

Water 0 oC

Water 20 oC

Water 60 oC_10min

Water 80 oC_1min

Water 80 oC_10min

Oil 150 oC_1min

Oil 150 oC_10min

Ma

rte

nsite

fra

ctio

n,

vo

l.%

Carbon concentration, mass-%

Quenching conditions after austenitization

Fe-1.5Mn-1.46C

Martensite fractions in quenched Fe-1.5Mn-xC steels determined by magnetic

measurements at RT under a field of nearly 4 kOe (𝜎𝑅𝑇,𝐹𝑒,4𝑘𝑂𝑒 = 213.5 emu/g)

Martensite/RA in Hardened Fe-1.5Mn-xC Steels

M. Ren, Diplomarbeit, TU Bergakademie Freiberg, 2017.

𝝈𝜶(𝑭𝒆−𝟏.𝟓𝑴𝒏) = 𝟐𝟏𝟏. 𝟕 𝒆𝒎𝒖/𝒈

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Alloy ID C Cr Mn Si Ni Mo FeσRT ,

emu/g

σRT,αʹ ,

emu/gfγ,

vol.%

2Cr 0.68 2.10 - - - - Bal. 198.5 209.0 5.0

2Mn 0.70 - 2.37 - - - Bal. 198.0 210.7 6.0

2Si 0.69 - - 2.00 - - Bal. 198.0 209.5 5.5

2Ni 0.71 - - - 2.04 - Bal. 204.2 214.4 4.8

2Mo 0.71 - - - - 1.95 Bal. 198.4 209.6 5.4

Measured room temperature magnetizations (σRT) and retained austenite

contents in hardened ternary steels calculated based on magnetization of the

martensitic constituent (σRT,αʹ)

J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Martensite/RA in Hardened Steels

Hardening treatment: quenching from 1000 °C in a brine+ice mixture

followed by immediate transfer to a tank of liquid nitrogen at -196 °C.

𝒇𝜸 = 𝟏 −𝝈𝑹𝑻 (𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅)

𝝈𝑹𝑻,𝜶′Austenite fraction:

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26L.J.E. Hofer, Nature of the Carbides of Iron, U.S. Government Printing Office, 1966.

Magnetic Properties of Carbides of Iron

Curie temperatures

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27T. Shigematsu, J. Phys. Soc. Jpn. 37 (1974) 940–945.A. Kagawa, T. Okamoto, Trans. Jpn. Inst. Met. 20 (1979) 659–666.

Magnetic Properties of Impure Cementite

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28B.A. Apaev, Magnetic phase analysis of alloys, Moscow Steel, Moscow, 1976.

Thermomagnetic Measurements

In thermomagnetic measurements, magnetization is measured during

continuous heating.

Ce

me

ntite

fra

ctio

n, % 12

10

8

6

4

2

0

14

0 0.2 0.4 0.6 0.8

%C

1

2

3

45

6

6

5

4

3

2

1

Thermomagnetic measurements

for steels with various cementite

fractions.

Curie

temperature of

Fe3C

Incre

ased

Fe

3 C fra

ctio

n

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29V.G. Gavriljuk, Mater. Sci. Eng. A 345 (2003) 81–89.

Thermomagnetic Measurements

Thermomagnetic curves for pearlitic Fe-0.7C

steels cold rolled by 80%

Fine pearlite Coarse pearlite Advantage:

The method can be used

to determine Curie

temperature.

Disadvantage:

Quantitative analysis of

results requires that the

temperature dependence

of magnetization for

phases is known.

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Magnetic Measurements at Room Temperature

Time

Tem

pera

ture

Cycle 1 Cycle 2 Cycle n-1 Cycle n

Prior heating temperature

Ma

gn

eti

zati

on

at

RT

T1

T2

Tn-1

Tn

: Measurement

points (at RT)

T1 T2 TnTn-1

Reference

value

(before

heating)

In contrast to

thermomagnetic

measurements

where

magnetization is

measured

continuously as

the temperature

is varied,

magnetic

measurements

could be

performed at a

constant

temperature (for

instance room

temperature)

after exposure

to various

temperatures.

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31J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Magnetic Measurements at Room Temperature

Magnetic measurements at room

temperature after exposure to various

temperatures

Advantage: Quantitative analysis of results

does not require the knowledge of the

temperature dependence of magnetization for

phases.

Disadvantage: The method cannot be used to

determine Curie temperature.

0 100 200 300 400 500 600

194

196

198

200

202

Mas

s m

ag

neti

zati

on

, em

u/g

Temperature, oC

III

III

0 100 200 300 400 500 600

-0.05

0.00

0.05

0.10

0.15 +0.2 oC/s

Ap

pre

nt

CT

E,

10

-4 o

C-1

Temperature, oC

III

I

II

Dilatometry

Magnetic

measurements at RT

As-quenched Fe-2Mn-0.7C steel

I: transition carbides/C segregation to

defects

II: decomposition of retained austenite

III: cementite formation

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32J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Magnetic Measurements at Room Temperature

0 100 200 300 400 500 600

194

196

198

200

202

Ma

ss

ma

gn

eti

za

tio

n,

em

u/g

Temperature, oC

III

III

0 100 200 300 400 500 600

194

196

198

200

202

Ma

ss

ma

gn

eti

za

tio

n,

em

u/g

Temperature, oC

As-quenched Fe-2Mn-0.7C and Fe-2Cr-0.7C steels

I: transition carbides/C

segregation to defects

II: decomposition of retained

austenite

III: cementite formation

IV: ?

2Mn

2Cr

IV

IV

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33J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Magnetic Measurements at Room Temperature

2 4 6 8 10 12

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Cr in cementite, mass-%

Cr

in m

art

en

sit

e, m

ass

-%

0

40

80

120

190

195

200

208

210

212

RT,

RT

RT,'

Mag

neti

zati

on

, em

u/g

Cr in '

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34J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Magnetic Measurements at Room Temperature

0 100 200 300 400 500 600

194

196

198

200

202

Ma

ss

ma

gn

eti

za

tio

n,

em

u/g

Temperature, oC

As-quenched Fe-2Cr-0.7C steel

IV: Cr partitioning into

cementite and gradual

demagnetization of

cementite

θαʹ

R.A.E.

αʹθαʹ: martensite

θ: cementite

IV

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35J. Mola, G. Luan, D. Brochnow, O. Volkova, J. Wu, Metall. Mater. Trans. A 48 (2017) 5805–5812.

Magnetic Measurements at Room Temperature

0 100 200 300 400 500 600 700

196

198

200

202

204 2Si

Mas

s m

ag

neti

zati

on

at

RT

, em

u/g

Temperature, oC

IIII

II

0 100 200 300 400 500 600 700200

202

204

206

208

210

2Ni

Ma

ss

ma

gn

eti

za

tio

n a

t R

T,

em

u/g

Temperature, oC

III

I

II

0 100 200 300 400 500 600 700

196

198

200

202

204 2Mo

Ma

ss

ma

gn

eti

za

tio

n a

t R

T,

em

u/g

Temperature, oC

III

I

II

0 100 200 300 400 500 600

-0.1

0.0

0.1

0.2

0.3

0.4

III2Si

III

I

+0.2 oC/s Curves are

displaced

vertically

for clarity

2Ni

2Mo

2Cr

2Si

2Mn

CT

Ea, 1

0-4 o

C-1

Temperature, oC

As-quenched Fe-2X-0.7C steels

Delayed decomposition

of retained

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100 200 300 400 500 600

0.985

0.990

0.995

1.000

X45Cr13

Re

lati

ve C

ha

ng

e in

Mag

ne

tizati

on

Temperature, oC

X31Cr13

100 200 300 400 500 6000.06

0.08

0.10

0.12

0.14

X45Cr13

X31Cr13

Insta

nta

ne

ou

s C

TE

, 1

x 1

0-4 o

C-1

Temperature, oC

+20 oC/s

Temper stage IIITemper stage I

1: Decrease in magnetization due to

the formation of paramagnetic

cementite (cementite containing

13%Cr)

2: Unexplained mechanism, possibly

reduction in the solute Cr content of

the martensitic matrix

Magnetic Measurements at Room Temperature

1 2

As-quenched stainless steels

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0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

90

100

Dila

tom

ete

r in

du

cto

r p

ow

er,

%

Temperature, oC

Curie Temperature of Iron

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

L

/L0,

m/c

m

Temperature, oC

Tc

A3

TcFe

Paramagnetic

Fe

Ferromagnetic

Fe

The paramagnetic α is more difficult to heat inductively than ferromagnetic

α. Therefore, the power of the high-frequency generator shows an abrupt

increase at the Curie temperature.

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0 200 400 600 800 1000 1200

20

40

60

80

100

Dila

tom

ete

r in

du

cto

r p

ow

er,

%

Temperature, oC

Curie Temperature Shift with Alloying Elements

TcFe-18Cr Tc

Fe

Fe-18Cr

Fe

18%

Cr

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39S. Arajs, Phys. Status Solidi B 11 (1965) 121–126.

Effect of Alloying Elements on Tc of Iron

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40D. Parsons, W. Sucksmith, J.E. Thompson, Philos. Mag. 3 (1958) 1174–1184.

Effect of Alloying Elements on Tc of Iron

Al effect Si effect

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5 µm

2 µm

0.5 µm

γαʹ

γ + αʹ

As cold-rolled, 43 vol.% αʹ

RD

TD

Austenitic high Mn Fe−18Mn−2Al−2Si−0.04C steel after 80% cold-

rolling reduction at RT to induce nearly 43 vol.%αʹ

Partitioning of Mn between αʹ and

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Partitioning of Mn between αʹ and

200 300 400 500 600 700 800

0.20

0.22

0.24

0.26' reversion to

Tc

CT

Ea, 1

0-4 o

C-1

Temperature, oC

50 °C/s

200 300 400 500 600 700 800 900

10

20

30

40

50

60

Ind

uc

tor

po

we

r, %

Temperature, oC

Tc

20 550 600 650 700 750 800 850

Temperature, oC

10

20

30

40

Cooling rate: 50 oC/s

Holding time: 0 s

f ', v

ol.%

As c

old

-rolle

d

Heating rate: 50 oC/s

(475 °C)

(475 °C)

Chemical composition of

deformation-induced

martensite is the same as

the nominal composition,

namely it is

Fe−18Mn−2Al−2Si−0.04C

Curie temperature

corresponds to the

cold-rolled

condition (no

partitioning of

alloying elements)

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Partitioning of Mn between αʹ and

450 500 550 600

20

40

60

80

50 °C/s

Tprior

,

oC

Ind

uc

tor

po

we

r, %

Temperature, oC

1 N/A

2 540

3 560

4 580

5 600

6 620

8 660

10 700

12 740

13 760

14 780

Cycle

no.

Change in the Tc of martensite

after each heating cycle,

indicating the partitioning of

alloying elements between

martensite and austenite

Time

Tem

pera

ture

Cycle 1 Cycle 2 Cycle 13 Cycle 14

560 C

800 C

720 C680 C640 C600 C

760 C780 C

540 C

740 C700 C660 C620 C580 C

Flash heating cycles

500 550 600 650 700 750460

480

500

520

540

560

580

600

Heating rate: 50 oC/s

(flash heating)

Heating rate: 1 oC/s

Tc,

oC

Prior heating temperature, oC

Cycle 1 (as cold-rolled)

1 h 540 oC

0 2 4 6 8 10 12 14

Cycle no.

(cold-rolled, 475 °C)

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Partitioning of Mn between αʹ and

500 550 600 650 700 750460

480

500

520

540

560

580

600

Heating rate: 50 oC/s

(flash heating)

Heating rate: 1 oC/s

Tc,

oC

Prior heating temperature, oC

Cycle 1 (as cold-rolled)

1 h 540 oC

0 2 4 6 8 10 12 14

Cycle no.

500 550 600 650 700 7504

6

8

10

12

14

16

18

1 h 540 oC

Heating rate: 50 oC/s

(flash heating)

Heating rate: 1 oC/s

Estimated

from Tc

Nominal (as cold-rolled)

Mn

co

ncen

trati

on

in

', m

as

s-%

Temperature (°C)

Equilibrium

(Thermo-Calc)

Slower heating (1 °C/s) or isothermal holding at low temperatures (1 h 540

°C) leads to a more pronounced partitioning of Mn.

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Partitioning of Mn between αʹ and

0 10 20 30 40 50 60 70 800

2

4

6

8

10

12

14

16

18

20

'

Si

Al

Mn

co

nc

en

tra

tio

n,

ma

ss

-%

Distance, nm

Mn

γγ

αʹ

γ

αʹ

1 µm

Cold-rolled, heated to 650 °C at 50 °C/s, and

immediately cooled to RT at 50 °C/s

Confirmation of

the partitioning

of Mn between

martensite and

austenite by

TEM-EDS

analysis

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