An Effect of High Magnetic Field on Phase Transformation in Fe-C System

8/9/2019 An Effect of High Magnetic Field on Phase Transformation in Fe-C System

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May 2000

Ž .Materials Letters 43 2000 225–229

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An effect of high magnetic field on phase transformationin Fe–C system

H.D. Joo ), S.U. Kim, N.S. Shin, Y.M. Koo

Center for Aerospace Materials, Pohang UniÕersity of Science and Technology, Pohang 790-784, South Korea

Received 11 June 1999; accepted 5 October 1999

Abstract

The effect of a magnetic field on the Gibbs free energy of a material depends on its magnetization behaviors. To

investigate the change in the Fe–Fe C phase diagram caused by a high external magnetic field, the magnetic Gibbs free3

energies of the phases austenite, ferrite, and cementite are calculated on the basis of the molecular field theory. Using the

calculated Gibbs free energy as a function of weight percentage carbon and temperature at a particular magnetic field, a

phase diagram of the Fe–Fe C system is drawn. The phase diagram is shifted upwards so that the Ac and Ac temperatures3 1 3

increase as the magnetic field is applied, but the Ac temperature change is almost independent of applied magnetic fieldm

value. The increase of eutectoid temperature and composition and its application to microstructural control are discussed.

q2000 Elsevier Science B.V. All rights reserved.

PACS: 75.20.H; 75.50B; 81.30B

Keywords: Molecular field theory; Fe–C system; Phase diagram; High magnetic field

1. Introduction

Magnetic field is one of the important external

physical quantities that affect properties of materials.

In recent years, development of instruments produc-

ing magnetic fields as high as 100 kOe in consider-

able volume enables one to research various proper-

ties in materials. Many studies have been carried out

on the effect of magnetic field on phase transforma-w xtion in various ferrous alloys 1,2 . However, these

studies are not about the gra transformation, but the

martensitic transformation. Since discontinuity of

magnetic susceptibility between the g and a phases

)

Corresponding author.

exists at the transformation temperature, an external

magnetic field causes a difference in their Gibbs free

energies, namely, it causes the phase diagram to

change. In addition, it is supposed that high magnetic

field may affect grain refinement, and studies are in

progress. The calculations associated with the change

of phase diagram are very important because they

can be applied to control microstructure and mechan-ical properties from the viewpoint of kinetics as well

as thermodynamics.

In the present study, the Gibbs free energy change

of each phase in steel is determined on the basis of

molecular field theory when high magnetic field is

applied. The change of the Fe–Fe C phase diagram3by applied magnetic field is determined.

00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .P I I : S 0 1 6 7 - 5 7 7 X 9 9 0 0 2 6 3 - 3


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2. Theory

2.1. Magnetic moments of phases in Fe–C system

There are at least two divergent viewpoints in thew xferromagnetic model 3,4 . One is the Weiss model,

which is applicable to electrons that are localized

within the positive ions forming the lattice. The other

is the collective electron model, which deals with

almost free itinerant electrons. Although both theo-

ries have merits and demerits for describing the

magnetic properties of ferromagnetic materials, the

current consensus is that the collective electron model

is intrinsically closer to reality in most cases, but it

does not provide any simple model from which first

principle calculations can be made. Because of this

drawback, interpretations of magnetic properties are

still more often made on the basis of the Weiss

w xmodel 4 . Therefore, the theory of ferromagnetismin steel is developed on basis of the Weiss model.

In order to calculate the Gibbs free energy change

induced by the applied magnetic field, determination

of the magnetization vs. temperature diagram is the

first consideration. For the calculation of the mag-

netic moment in ferrite, we use the molecular fieldw xtheory 3 . Although disagreement of the magnetic

moment per atom, m , between paramagnetic andHferromagnetic regions exists, it is assumed that the

magnetic moment per atom in the ferromagnetic

region, m s 2.219m , is valid in the whole temper-H B

Fig. 1. The relative magnetization of pure iron calculated from

molecular field theory as a function of temperature and applied

magnetic field.

Fig. 2. Magnetization and inverse susceptibility curves below andŽ .above the Curie temperature of ferrite: a is the relative magneti-

Ž . Ž . Ž . Ž .zation when applied magnetic field is zero, b , c , d and e areŽ .susceptibility data; b is from the Curie–Weiss equation fitted

w x Ž . Ž . Ž . w xfrom other data 6 , c , d and e are experimental data 5,7 .

ature range and all data for pure iron can be applied

to the Fe–C system. Because the paramagnetic sus-

ceptibility of ferrite satisfies the Curie–Weiss law

only above 1150 K, the paramagnetic m s 1.82mH Bderived from the Curie constant cannot be used for

ferrite in most temperature ranges and it may bew xmore reasonable to use the ferromagnetic m 5 . AH

mapping of the M – H –T surface is calculated and it

is shown in Fig 1. This curve corresponds to the

shape of an experimental curve, such as reported byw xGorodestsky et al. 6 , for the weak ferromagnet

YFeO .3The Gibbs free energy of the paramagnetic region

can be determined by the susceptibility x , which is

the ratio of the induced magnetization to the induc-

ing field and roughly follows the Curie–Weiss law.

The paramagnetic susceptibilities of g and a phasesw xhave been measured by Arajs and Miller 7 . Their

susceptibility data also satisfy the Curie–Weiss law

and the susceptibility can be determined by fitting

the susceptibility data to the Curie–Weiss equation.

1.23y1 y1w xx s emu mol Oe 1Ž .a

T y 1093

7.31y1 y1w xx s emu mol Oe 2Ž .g

T q 3370

where x and x are the magnetic susceptibilitiesa gfor a-Fe and g-Fe, respectively. It is known that the


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( ) H.D. Joo et al. r Materials Letters 43 2000 225– 229 227

w x Ž .Neel temperature of g-Fe is 44 K 8 , but Eq. 2 is

appropriate for describing the paramagnetic suscepti-

bility of g-Fe in this temperature region. Fig. 2

shows the magnetization and inverse susceptibility

curve below and above the Curie temperature drawnw xfrom the experimental data of Refs. 5,7,8 .

Next, the susceptibility of cementite, Fe C, must3be determined. Cementite is ferromagnetic like a-Fe.

Cementite satisfies the Curie–Weiss relation, whichŽ . w xis given by Eq. 3 9 .

1.95y1 y1w xx s emu mol Oe 3Ž .Fe C3 T y 506

where x is the magnetic susceptibility for Fe C.Fe C 33This has been measured below 575 K, but we as-

sume that the equation holds at high temperatures up

to 1400 K.

2.2. Gibbs free energy change by magnetic field

When magnetic field is applied, the resulting free

energy changes are classified into two terms; theŽ .thermal Gibbs free energy, G T , X , and the mag-T

Ž .netic Gibbs free energy, DG T , H .M

G T , X s G T , X q DG T , H 4Ž . Ž . Ž . Ž .total T M

The thermal Gibbs free energies of austenite and

ferrite are derived on the basis of the KRC model byw xShiflet et al. 10 .

Gg T , X s 1 y X Gg T Ž . Ž . Ž .T Fe

X q RTX ln

1 y X 14 y 12exp yW r RT Ž .gg XS ,gq X D H y T DS Ž .c

1q 1 y X RT Ž .

13 y 12exp yW r RT g

1 y X 14 y 12exp yW r RT Ž g=ln 5Ž .

1 y X

Ga T , X s 1 y X Ga T Ž . Ž . Ž .T Fe

q X 112 000y 51.4T RT X ln X Ž .

q 1 y X ln 1 y X 6Ž . Ž . Ž .a Ž .where X is the mole fraction of carbon, G T andFe

g Ž .G T are the Gibbs free energies of pure a-Fe andFeg XS ,gg-Fe at temperature T , and D H , DS are thec

partial molar enthalpy and the partial molar noncon-

figurational entropy of solution in austenite, respec-y1 gtively. We take W s 5880 J mol , D H s 444 000g c

y1 XS ,g y1 y1J mol and DS s 17.2 J mol K fromw x a Ž .Shiflet et al. 10 . G T can be obtained fromFe

w xSGTE DATA 11 .Ž .The magnetic Gibbs free energy, DG T , H , canM

be written in terms of an extensive variable, M , andan intensive variable, H .

dG T , H s H d M 7Ž . Ž .MGenerally, the paramagnetic Gibbs free energy

change by a magnetic field is given by

1para 2DG T , H s y x H . 8Ž . Ž .M 2

Since the magnetic moment of ferrite is not linear

and the magnetic susceptibilities from the Curie–

Weiss equation disagree with experimental data at

near the Curie point in Figs. 1 and 2, it is more

reasonable to use the magnetization determined bythe Weiss theory rather than the susceptibility to

calculate the Gibbs free energy of ferrite. IntegrationŽ .of Eq. 7 from the previous M – H curves in Fig. 1 is

carried out at each temperature to yield the magnetic

Gibbs free energy of ferrite as a function of applied

magnetic field. These are fitted as functions of tem-

perature at the magnetic fields of 120, 200 and 500Ž . Ž .kOe, and are described by Eqs. 9 – 11 , respec-

tively.a Ž .DG T ,12T sy1200q3.00T M

2y0.00173T at T -1043Ka Ž .DG T ,12T s5.18M

T y1045q36.1exp y at T )1043K

67.3

9Ž .a Ž .DG T ,20T sy1200q3.28T M

2y0.00197T at T -1043Ka Ž .DG T ,20T s11.5M

T y1045q69.3exp y at T )1043K

88.7

10Ž .a Ž .DG T ,50T sy890q3.64T M

2y0.00243T at T -1043Ka Ž .DG T ,50T s39.1 .M

T y1045q227exp y at T )1043K

162

11Ž .


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Fig. 3. The Gibbs free energy difference between g and a phase

of pure iron as a function of temperature for various magnetic

fields.

Ž .Eq. 8 may also be applied to the magnetic Gibbs

free energy change of austenite as the Neel tempera-

ture of austenite is very low.

In contrast to ferrite and austenite, the thermal

Gibbs free energy of cementite is difficult to calcu-

late. Thus, the thermal Gibbs free energy is calcu-

lated reversely from the experimental phase diagram

of the Fe–C system. This method is quite simple

because the cementite austenite equilibrium tempera-

ture, Ac , in the phase diagram is almost a straightm

line and the composition of cementite is constant.The thermal Gibbs free energy of cementite deter-

mined in this way is given as follows.

GFe 3C T s 16 700 y 43.4T 12Ž . Ž .T

Thus, the magnetic Gibbs free energy of cementiteŽ .can be evaluated from Eq. 8 because it is formed at

a much higher temperature than its Curie tempera-

ture.

The Gibbs free energy change of the gra trans-

formation in pure iron is given as follows.

DGg™a T , H Ž .total1

g™a a 2s DG T , H y G T , H y x H Ž . Ž .T M gž /213Ž .

Fig. 3 shows the Gibbs free energy change of the

gra transformation vs. temperature diagram at a

particular magnetic field in pure iron. Since Ac is1equal to Ac in pure iron, the temperature at which3

g™a Ž .DG T , H s 0 is simply determined as the trans-totalformation temperature, which increases 10 K at 120

kOe.

3. Results and discussions

The Gibbs free energy calculated in the previous

section is used to determine the change of the gra

phase diagram. Fig. 4 shows the phase diagram

associated with the gra and grFe C transforma-3tions as a function of weight percentage carbon. Ac 3increases as magnetic field is applied, but the Ac mtemperature hardly moves so that both the eutectic

temperature and composition increase. Eutectoid

temperature, eutectoid composition and the gra

transformation temperature are determined from Fig.

4, which is summarized in Table 1.Considering kinetics, the change of phase trans-

formation temperature can be affected by many fac-

tors such as heatingrcooling rates and strain energy

per unit volume. The Ac temperatures have been3measured at various heating rates by Abiko and

w xSadamori 12 . As the heating rate is increased from

1 to 20 to 50 Krs, the Ac temperature increases3from 1180 to 1187 to 1198 K, respectively. The

increase in the Ac temperature at a heating rate of 350 Krs is similar to the change of transformation

temperature at 120 kOe. Also, the strain energy dueto dislocation accumulation causes a metastable phase

Fig. 4. Fe–C phase diagram associated with the g ra and g rFe C3transformation for various applied magnetic fields.


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Table 1

Eutectoid temperature, eutectoid composition and the gra transformation temperature determined from the calculated phase diagram

Applied magnetic field Eutectoid composition Eutectoid temperature gra TransformationŽ . Ž . Ž .T wt.% 8K temperature in pure iron

Ž .8K

Calculated data 0 0.76 1000 1184

12 0.795 1012 1194

20 0.818 1019 120950 0.914 1051 1306

w xtransformation 13 . These factors have been widely

used for controlling microstructure. For example,

accelerated cooling and recrystallization-controlled

rolling are applied to grain refinement. Similarly, the

change of transformation temperature by high mag-

netic field can be applied to microstructural control.

Dynamical applications such as imposing magnetic

cycles at a particular temperature gives additional

driving force for phase transformation; therefore, it

can be applied to microstructural control, too.

In addition, the possibility of improving mechani-

cal properties may be realized from the eutectoid

composition shift. Increased carbon content is associ-

ated with strengthening and hardening, but hypereu-

tectoid primary cementite decreases ductility. Since

external magnetic field enables us to increase carbon

content without hypereutectoid transformation, it may

improve mechanical properties. Tensile strength in-

creases by 6% and Brinell hardness and yield strength

also increase without producing primary cementitew xwhen a 120-kOe magnetic field is applied 14 .

Acknowledgements

This work was supported by Pohang Steel and the

Ministry of Commerce, Industry and Energy of the

Republic of Korea, and the authors wish to express

appreciation for the financial support.

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An Effect of High Magnetic Field on Phase Transformation in Fe-C System