TitleTHERMODYNAMIC STUDIES ON THE EQUILIBRIUMDISTRIBUTION OF SOLUTE ELEMENTS BETWEEN SOLIDAND LIQUID PHASES IN IRON ALLOYS

Author(s) 田中, 敏宏

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Osaka University Knowledge Archive : OUKAOsaka University Knowledge Archive : OUKA

https://ir.library.osaka-u.ac.jp/

Osaka University

THERMODYNAMIC STVDIES ON THE EQUILIBRIUM DISTRIBUTION OF SOLVTE

ELEMENTS BETWEEN SOLID AND LIQUID PHASES IN IRON ALLOYS

( etafi ez fo' Gi 6 rsesit#o tutw eerp•ditf>bl et rs tr 6 ts rtG}le esli}?oftea )

1984

TOSHIHtRO TANAKA

Chapter 1.

Chapter 2.

Chapter 3.

Contents

General lntroduction.

1•1 lmportance of Equi1ibrium Distribution Coefficient in Metal1urgical Processes.

1.2 Surveys of Previous Studies.

1.3 Purpose and Arrangement of the Thesis.

1.4 References.

Equ"ibrium Distritwtion of Carbon between Solid and Liquid Phases in lron-Carbon Bimary Alloys.

2•1 lntroduction.

2.2 Experimenta1.

2.2.1 Abparatus for Quenched Specinens.

2.2.2 Sample and Holding Teifiperature.

2.2.3 deuilibration Tiipe•

2.2.4 -letallographic Structure ef Quenched SpeciueRs and lleasurement of ConceRtration Distribetion by EPMA.

2.2.5 Concentration Distribution.

2.3 Results and Discussien.

2.3.1 ExperiRienta1 Resu1bs.

2.3.2 Validity of the ExperiBK)ntal MethQd and Results.

2.3.3 Thernodynamica1 Ca1culation of the Equilibrium Distribetion of Carbon.

2.4 Conclusion.

2.5 References.

Equilibrium Distribution of So1ute E1ements between So1id and Liquid Phases in Iron-Carbon Base Ternary Alloys.

3.l tntroduction.

3.2 Experimental.

3•2.1 Procedure for making Quenched Specimens•

3•2.2 Sample and Holding Teanperature•

Page

1

1

4 13

15

17

17

17

17

18

19

oo

2za

22

25

ve

32

34

35

35

36

ss

36

3.2.3

3.2.4

3.3

3.4

3.4.1

3.4.2

3.4.3

3.5

3.6

Equi1ibration Time•

"Ietallographic Structure of Quenched Specimens and the Measurement of Concentration Distribution by EPMA.

drperimenta1 Resu1ts.

Discussion•

TherModynamic Treatment of Equilibrium Distribution Coefficient kXo and the Periodicity of kts of Solute X agaimst Atomic Number in lron Alloys.

Factors contro11ing Equi1ibrium Distribution Coeffi- cients of Solute Eleeients in Iron Base Binary Alloys•

Equi1ibrium Distribution Coefficient of the Third Element in Fe-C Base Ternary Alloys.

Conclusion.

References.

se

37

41

42

42

48

54

59

61

Chapter 4. Effects of Solute Interactiorts on the Equi"brium Distribetion ef Solute Eleipents between Solid and Liquid Phases in fron Base TerBary A1loys.

4.l tntroduction.

4•2 De.'rivation ef an dauation describing the Effect of Solute lfiteraction on the EÅítuiSibriu- Distribetion Coefficient.

4.3 Results and Discussion.

4.3.1 Effect of CarboR on the Equilibrium Distritwtion of Various Alloying Elements between Solid and Liquid Phases in Fe-C Base Ternary Alloys.

4•3.2 Effects of Various Alloying Elesitents on the EquilibriuN Distribution of Nitrogen and Hydrogen betsteen Solid and Liquid Phases in Fe-N, H Base Ternary Alloys.

4.3.3 Application of Distritution lnteractioR Coefficient to the Equilibrium Distribetion of P and S between sc1id and Liquid Phases in lron Base Ternary Alloys.

4.4 Cenclusion•

4.5 RefererN)es.

es

as

es

os

os

73

75

77

va

Chapter 5. Effects of Solute lnteractioRs on of Solute Eleipents between Solid meIti-co"iponent A11oys.

5•1 Introduction.

theand

Equi1ibriumLiquid Phases

Distribution in lron Base

80

80

Chapter 6.

Chapter 7.

5.2 Derivation of a Parameter describing the Effect of Solute Interactjon on the bouj1ibrium Distribetion Coefficient.

5.3 Experimental•

5.4 Resulbs and Discussion.

5•4.1 Effects of Solute lnteractions on the Equilibrium Distribetion of Solute Elegients betveen Solid and Liquid Phases in Fe-C Base Quarternary Alloys.

5•4•2 Effects of Varibus Solute Elemenbs on the Equilihrium Distribetion of N, H, P and S between Solid and Liquid Phases in lren Base Multi-coraponent Alloys.

5.5 Conclusion.

5.6 References.

Equj1ibrium Distrjbutjon Coefficient ef Phospborus in Iron A11oys.

6.1 Ifitroductien.

6.2 E)(periNents1.

6.3 Results and Oiswssien.

6.3.1 bouilibriu- Distribution Coefficient of P between a and Liquid Phases iR Fe-P BiBary Alloys.

6.3.2 Equi!ibrium Distribetien CoefficieBt ef P for r Phases and the Effects ef Carbon en kPo .

6•3.3 Change of the bouilibriun Distribution (oefficient and the fegregation Coefficient of P with the Concent- ration of Carbon. - 6•3.4 Thermodynamical Re1ation between Equilibrium Distri- betlon Coefficients of Various So!ute Eleraents for a Phase and those for r Phase•

6.4 Conclusion.'

6.5 References.

Equi1ibrium Distribution of Gaseous Elements between Solid and Liqu id Phases in F e, C o, N i and C u Base Al loys•

7.1 tntroductien.

7.2 Equations for Equilibrium Distribution Coefficient of N and H in lron Base Alloys.

7.3 Effects of Various Solute Elements on the bouilibrium Distribetion of N and H between Selid and Liquid Phases in Co, Ni and Cu Base Alloys.

eo

82

83

83

ew

93

94

95

95

95

ee

ee

ss

1oo

104

111

112

113

113

1l3

117

7.4

7.5

Conclusion•

References.

ln123

Chapter 8. Summary. 124

AckrK}w 1 edgeinent .

Pub1ications re1evant to the Thesis.

127

128

pmCht1Generaltlntrodkt,!!xUg!!cti .

1.1 lm ortance of uilibrium Distribution Coefficient in Mptt@u!,!.ng11 ical

Processes.

The micro-segregation of solute elements in engineering steels is known to

affect considerably the physico-chetfiical and mechanical properties of the mate-

rials, and so far a number of studies have been made to investigate the mecha-

nisms of the segregation of the solutes and to improve the quality of steels.

The micro-segregation of the solutes in steels is essentially caused by various

factors and its formation mechanisiii is very complicated. Hogever, the most dom-

imant factor is regarded to be the redistribution ef the solutes during solidi-

fication, which is caused by the difference between solidus and 1iquidus in the

phase diagram of the alloys. So, the ratio of the concentration of the solute

X distributed betseeen solid and liquid phases at the equi1ibrium state, that is

to say, the ratio of the concentration of the solute on solidus and that on

1iquidus as sbown in Fig.1-1 is considered to be very important factor for the

ruicro-segregation. Generally this ratio is given in Eq.(1-1) as kXo and called

equi1ibrium distribution coefficient, and also ( 1 -- kXe ) is termed the segre-

gation coefficient.

kXo =N,S /N" (1-l)where NxS and NA are the concentration of X in solid and liquid phases, res-

pectively.

m•P•

Liquidus o S SoEidus {p ---- -- --- -p "--- -- -- -p --- -- --- :- I I 2l i oI. t l-- i Fe N,S NS Concentration of X Fig.1-1 Solidus and 1iquidus near the melting point of iron.

-- 1-

Although ko shows the equi1ibrium distribution of the solute between solid

and liquid phases, sorae equations have been reported to indicate the redistritu-

tion of the solute also for the non-equi1ibrium state, in Nhich the solidifica-

tion proceeds at a finite rate. For example, the solute distribution along the

initial partion of the rod specimen to solidify is given as below by Burton et

al.1) or seith et ai.2) and so on• . For complete or partial mixing of liquid and no diffusion in solid,

NS. ke No ' k, + (1 --ko) exp (-Rd/D) . <Burton's equation) (1-2)

For mixing in 1iquid by diffusion and no diffusion in solid,

il: 'ti IF [1 "erfv!(R/2D)x+ (2ko-])exp{ -k,O-k,) i} x}e.fc{ (2ko-1;vi(R/D)X

(Sifiith's eeuation) (1-3)

IR all ef the equations described above, the terms of ke of the solute

eleipent are surely iRvolved. 'Hence, it is of comsiderable iMpartance to know

the vallles ef ko ef various eletpents in iron ailoys vhenever the problems,

which are ascribed to the redistribution of the so1ute during solidification,

are discussed. The values of ko described above are mainly for binary alloys.

There are inany kinds of iron and steels includiRg various alloying e;eBients

at a wide variety of compositions. Thus, the values of ko at various coRipo-

sitions in iron base multi-component alSoys should also be required to examine

the micro-segregation in such alloys because ko of the solute in tuulti-compo-

nent iron alloys, i•e. Fe-C base alloy which is one of the most fundamental

alloys, are considered to be different frorn that in binary alloys due to the

effects of their solute-interactions. However, ' the comprehensive studies about

ko not only in Fe-C base alloys but also in multi-component iron alloys

have been done neither experimentally nor theoretically.

With the above background, therefore, the experivaental and theoretical

' -2-

})

studies on ko in iron base multi-component systems are very

to raake clear the physico-chemical properties of iron alloys

the fundatnenta1 information to explain the various phenomena

concerning to the ndcro-segregation in $teels.

useful in order

and also to obtain

of so1idification

-3-

1.2pmtvfP Stdt. VaIues of the equi1ibrium distribution coefficients of various e1ements,

ke in iron alloys previously published by other investigators3'"15) are 1isted

in Table 1-1. It is obvious from this table that there exist noticeable dis-

crepancies a"tong these values of ko in each system. The methods obtaining

ko can almost be divided into the following three kinds, namely,

1) From liquidus an(l solidus of phase diagram.

2) From thermodynaniical calculation.

3) From direct deters"imation of ko by experiments, for example, the meas-

urenient of concentratjons in quenched specimens including soljd and iiquid coex-

isted phases or using furton's equationl) or smith's equation2), and so on.

As is seen from Table 1-1, most of the values of ko were determined by

means of the above mettxxis 1) and 2).

' In the uethod l), the accuracy of ko obtai#ed frota phase diagratns is de-

pendent upan that of phase diagne• ln general, it is said that the accuracy of

sotidus Might be less than that of liquidus. This is vhy the liquidus oan be

deterttiirx)d by a therii;al amalysis bet it is very diffioult to ob'tain the solidus

by such a nethod. Hence, the acctjracy of so!idus inflllences that of ko but

the phase diagraitts vbose solidus has been established are very few. Also, the

curvature of $olidus or 1iquidus makes the deterrnination of ko more difficult.

1'hus, the method 1), that is to say, to detertuine ko from phase diagrams is

considered unre1iab1e.

' ln the method 2), Hays et al.8) obtained ko for a dilute sorution thermo-

dynamically by using the folIowing equation.

zko =1- mAHm/RTm (1-4)

where R is gas constant, Tm and AHm are melting point and heat of fusion of

solvent metal respectively, and also m is the slope of 1iquidus at infinite

dilution of the solute.

-4-

Vhen ko is obtained by using bo•(1-4), the value m is required but it

nvst be deterrnined by ilteans of the phase diagram. Also, the calculation is very

sensitive bo the cboice of "quidus slope, and an addit'ional difficulty is that

'there is noticeable ourvature on the 1iquidus ourves.

Vada et al.9) also determined ko thermodynamically• They calculated the

free energy change aecoifipanied by transfer of alloying elements from one phase

to another using solidus, liquidus and phase boundary curves of a -- r phase

transformation in phase diagrams to obtain ko .

Consequently, values of ko having been decided thermodynamically in the

past are dependent upon the accuracy of phase diagram.

So, it is comsidered more appropriate bo deterreine ko experirnentally as

described in 3). Then, some of the experiuental procedure to ebtain keare

arranged as fotlows.

O l)avis;6) Fischer et al.7) and so on deterained kofroei the relation be-

tyteen the eoncentratien distribetioR of the solute and the distance in the rod

specirm so}idified uni-directiomaIly. For instance, provided that the mixing

in 1iquid is caused by enly diffusion and there is nc diffusion in sotid, the

solute distritution along the initial partion of the rod srxximen bo solidify is

given by smith et al.2) in bo.<1-s).

Iig: .i -IIi (i+erfvi(R/2D)x+(2ko-i)exp(-k,(i.k,)gx}erfc{(2kQ-i3,i(RlD)X})

-•-• (1-5)

where X is the distance frot" the start point of solidification, R the solidi-

fication velocity and D the diffusion constant of the solute in liquid. A set

of concentration-distance ourves are calculated for various values of ko , and

by coinparison of the curyes with an experimental one the correct ke can be se-

lected• Hovever, vhen the above equation is used, the condition, the nixing in

the liquid by only diffusion and no diffusion in the solid, must be satisfied.

Since the convection in the 1iquid should further be excluded, the experiment at

elevated teBiperature becoiiies much more difficult. AIso, the data of diffusion

-5-

constant of various elernents in 1iquid rnetals are needed but so far the reliable

data have scarcely been obtained•

tn this experimental method, a precise measurement for the concentration at

a solid-1iquid inberface can be done at a plane interface than an irregular one.

To achieve a plane solid-1iquid interface, high G/R values are needed where

G is a temperature gradient ahead of interface. However, as the morphology of

the interface depends on not only G/R but also the contents of alloying ele-

ments, this rnetbod ig used only for the alloys which contain small amounts of

solutes. For example, Davis16) obtained ko of Ag, sb, pb and so on in

S n alIoys by using Eq.(1-5), tut the. contents of those solute eleipents were

smaller than e.05 wtX.

In the case of eRgineering alloys wbose solute contents are conparatively

large, higher G/R value is required. So, virtuallya plain interface can oot

be obtaifted during solidifieatioR and the precise neasureuent of the concentra•-

tion distribetion is very difficult.

@ There is arK)ther experiuental precedure by using the rod specigien. The

$pecimeR is set in the furnace vith teraperature gradient. Solid and liquid

phases Åëoexist at the interface. The specimen is quenched vhen the plain inter-

face is obtained and also the equilibrium is achieved. Then, the concentrations

of the solute in both selid and 1iquid phases at the interface are measured to

obtain kQ. uiHeda et al.17,18) used this metbod to determine values of ko of

various solute elegtents in some kind of engineering steels. In this case, the

true equilibrium between solid and liquid phases can not be achieved because the

two phase region of solid and liquid coexisted is not taken inte account in this

metbod. "eRce, this experimental procedure can be applied te only the alloys of

which the tve phase region is very narrow. In other words, it is considerably

difficult to determine ko of solute elements in Fe-C and Fe-P base

altoys, which have vide two phase regions, by this method• Also, as the speci-

raen is large and it is quenched together vith the cel1, the coo1ing rate is so

smal1 that the equi1ibrium between solid and 1iquid phases at elevated tempera-

-6-

ture may not be well preserved.

@ Then, other method is described below• The solid and 1iquid phases are

equilibrated at a fixed tet"perature• After quenching fhe specimen, the concent-

rations of the solute eletnents are measured to determine ko . This experimen-

tal metbod has been used by Kirkveod et al.19,'20)okamoto et al.2,1,22)Takahashi et

al?3a)nd scndrmann et al.24'"26) to obtain ko in iron alloys•

However, in this methed sonie proble"ss are pointed out. For instance, the

disturhance of the cor}centration at the interface and that of the structures in

1iquid phase occur during quenching. And such problems have not been investi-

gated enough. For example, xirkwood et al.19) reparted the wrong values of ko

because of the insufficient metal!ographicat observation of the quenched speci-

lteris and then tbey corrected those values.20) HoiHever, this experimental metlx)d

seegrs to be iNest faithful to the definitien of kg. Tbes, if the experi-enta1

procedure are earefuSly checked, this uettx)d is cersidered sK)st suitable te de-

beriiRe ko •

In Table 1-1, described above, the valus of ko are mainly in iron base

bimary alloys. The equilibriu- distritwtion (Å~)efficient ke of a selute ele-

sbent in multi-coisponent systesis such as eagirK)erirrg altoys is coRsidered to be

different froi" ke in ircn base bimary alleys because of the solute-inter-

actions. In partioular, since the interactions between carbon and the alloying

elegrernt is fairly large in Fe-C base alloys, ko of the alloying element is

tbought to change with the eoncentration of carbon. For example, the micro-seg-

regation ratio of p27'28)and cr29) were reported to change with carbon

eontent in Fe-c base steeis. okamoto et al.21'22) showed that ko of si

and Cr change with the concentration of C in Fe-C alloys. However, even

in these fundamenta1 alloys, enough informatjon of the influences of C on ko

or the micro-segregation ratios of the alloying elements have hardly been ob-

'tairK)d.

Recently, Kirkwood et al.1,9t20) okamoto et al.21'22) and vmeda et al.17,18)

tueasured ko of various elements in multi•-component iron alloys• However they

-7-

reported only the values of ko at some compositions in a few kinds of iron

alloys. Thus, the comprehensive study concerning the relation between ko in

rnulti-component systems and the solute-interactions has not yet been established

both experimentally and theoretically. ' If the value of ko can strictly be calculated thermodynamically, the ef-

fects of the solute-interactions on ke may be clarified. Kirkwood et ai?O)and

okamoto et al.21,22,30) caloulated ko by using the therrnodynarnical data, but

they only corapared their experimental results with the calculated ones and did

not investigate the relations between ko and the solute-interactions enough.

1'herefore, it is expected that if the thermodynaraical and statistical knowledge

of the activity or the interaction paras#eter can be applied to solve the above

unknovn relatioRs, the useful results yould be surely ebtained.

FurtheriRore, if the factor controlIing ko of the solute element in iron

base bimary alleys are eiade clear theoretica1ly, it is very interestirig frou the

view peint of physical cheuiistry and also the prediction ef the value of ke in

the case ef nc measured values for the equi1ibrium distribution coefficients.

Bune-Rothery et al.31,32) stadied the change of the solidus and iiquidus in the

phase diagrams of various alloys, and they described that the differer)ce betveen

the partial excess free energy of the solute eleinent in 1iquid and that in solid,

which is obtained from the slope of 1iquidus and solidus in the various phase

djagrauis, ehanges periodically with the atomic number of the elemeRt. However,

the factors, upon vhich tbose differences of the excess free energy and thier

periodicity depend, have not been investigated enough.

As described above, there are a lot of problems, which have to be investi-

ga'ted experimentally and a1so theoretica1ly, about the equi1ibrium distribution

coefficient,ko , of various elements and the influences of the solute-interac'

tjons on ko in iron alloys. '

-8-

Tab1e 1-1 bouilibrium distribution coefficient in iron a1loys.

Element Composition kXo Method Ref.(wt.x)

O.6 E (3)Al (6) O.60 E (4)

O.92 A (5)

e.o3 E (4)(s) O.05. A (5)

O.11 A (6)B

O.04 A (5)(r) O.05 A (6)

O.oo9-O.023 O.llÅ}O.025 c (7)O.13 A (8)O.141 E (7)O.17 A <9)

O.44 O.18 E (10)(s) O.20 E (4)

O.20 A (6)e.25 E (3)

c o.os O.25 E (10)e.as-o.2s O.29 B (ll)

e.se A (6)e.34 A (9)O.35 E (4)

(r) e.M-3.79 O.35-C.46 D <12)O.51-4.sa e.3s-o.se E (10)

e.36 A (5)

O.89 A (9)e.e22-O.l5 e.94 c (7)

(6) O.95 A (5)O.97 E (4)

Cr 1.e E (7)

(r) O.85 A (5)O.87 A (9)

Method: A:

B:

c:

D:

E:

Frotn

From

From

Fromsolid

Froth

the rmodynasn i cs .

zoRe me1ting.

application of twrton's or Smith's equations.

measurenent of concentrations in quenched specinens and 1iquid phases.

phase diagram.

inc1uding

-9 --

Table 1-1 Contirrued•

Element Composition kXo Method Ref.(vt.x)

O.90 A (5)bo (6) O.94 A (6)

(r) O.95 A (5)

O.56 A (8)O.592 E (7)

(s) O.028-O.055 e.7o c (7)de O.90 A (6)

O.70 A (6)(r) O.88 A (5)

O.27 E (4)(6) O.2';r A (6)

H e.32 A (5)

(r) O.45 A (5)

O.I23 E (7)e.15 E (3)

o.6-e.7 E <13)O.68 E <14)

O.025-O.22 e.tsÅ}o.ca c (7)(6) e.3-1.o e.ts D (12)

O.76 A (9)tinln o.se-e.so E (4)

O.84 A (8)O.90 A (6)

O.75 A (6)(r) O.78 A (9)

O.95 A (5).O.7 E (3)O.70 E (5)

(6) O.74 A (9>O.80 A (5)

bo O.86 A- (6)

O.57 A (9)(r) O.6 A (5)

O.25 A (6)O.28 A (5)

(6) O.32 A (9>O.38 E (4>

N

O.48 A (6)(r) O.50 A (9)

O.M A (5)

--- 1 O-

Table 1-1 (ontinued•

Element 'Contposition kXo Method Ref•(wt.x)

O.030-O.035 O.549 E (7)O.75 c (7)

(6) O.76 A (9)O.80 A (5)

Ni O.83 A (6)

(r) O.85 A (9)O.95 A (5)

O.02 E (4)O.02 A (5)

(s) O.O12-O.096 O.022 B (11)o O.1 B (3)

O.10 A (8)

(r) O.02 A (5)e.o3 A (6)

e.13 A (8)e.14 A <9)

g.15-O.18 E <4)e.ols-o.og2 O.16Å}O.04 c (7)

(s) C.co4-O.211 e.17 B (11)e.2 E (3)

P C.2-O.5 B (15)e.or-o.2s O.23 D (12)

e.:n E (15)O.28 E (7)

(r) e.os A (5)e.es A (9)

O.oo2 E (3)O.02 A (5)

o.2o-o.4s o.oas D (12)O.04-O.05 E (4)

(6) O.047-O.25 O.04-O.os B <11)s O.05 A (8)

O.oo2-O.O09 O.052Å}O.Ol c (7)O.114 E (7)

(r) O.02e.os

AA (5)(6)

O.6 E (14)O.62 A (9)O.66 A (8)O.7' E (3)

si (6) o.nÅ}o.ca c (7>O.83 A (6)

O.4-1.0 O.84 D (12)O.84 E <4)O.912 E (7)

-- 1 1 --

Table 1-1 Continued.

E1ement Composition(wt.x)

kXe Method Ref.

si (r) O.5O.54

AA <5)(9)

Ti(6)

O.14O.40O.6O.60

AAEE (5)(6)(3)(4)

(r)O.07O.3

AA (5)(6)

(s) O.95 A (5)v

(r) O.5 A (5)

v (6) O.90O.96

AA (5)(6)

Zr (6) e.sO.50

EE (3)(4)

-- l2--

1.3!PmpmpndA ntftheThesis. Equilibrium djstributions of the solute elements between solid and 1iquid

phases in iron alloys have not been studied enough as described in this chapter '1.2. The purpose of this work is to discuss the equilibrium distribution of the

solute in iren base multi-component al1eys experimental1y and theoretica11y, and

to obtain fundamental knowledge to explain various phenomena during solidifica-

tion concerning to micro-segregation in iren alloys. In this thesis, these re-

sults are described jn the following eight chapters•

Chapter 1 of general introduction vil1 be followed by chapter 2 which

describes the equj1ibrum distribetion gf carbon between solid and 1iquid phases

in iron-carbon bimary alloys.

Subsequently, the factors control1ing the equilibrium distritwtion cceffi-

cient in iron alloys and also the equilibrium distribetion of the third eleesients

ifi Fe-C base termary alloys vill be diseti$sed experinenta1ly and theoreti-

eally in chapter 3.

In chapter 4, the effecbs ef solute-pinteractioms on the equilibrium distri-

betion ef solute ele-enbs between solid and liquid phases in iron base ternary

alloys vi!l be exaaiirK)d and the rxirv therisKxiyriamica1 coefficient 'to represent

such effects wi11 be derived. The Rext chapter vi11 describe the derivation of

the parameter indicating effects of solute-interactions on the equilibrium dis-

tribution of solute elements between solid and liquid phases in iron base multi-

component alloys and also the experimental results on the influences of S i, V

and Ce on the variation of ko of Sn and Cu vith carbon in Fe-C

hase quarternary alloys. The experimental results are compared vith the calcu-

lated oRes by using the parameter derived in this chapter.

Then, the equi1ibrium distribution ef P in Fe-P and Fe--P--C

altoys vill be examined in chapter 6. Also, in this chapter, therrnodynamical

re1ation between equi1ibrium distribution coefficient of various e1ements for

a phase and that for r phase in iron alloys wj1I be discussed.

Furthermore, the equi1ibrium distribution of gaseous elements between solid

--13--

and 1iquid phases in Fe, Co, Ni and Cu base alSoys wi11 be

chapter 7.

Finally, conÅëIuding summary wi11 be given in chaptier 8.

examined in

-14--

Ll,-Euspt1maeS24Rf

1) J.A.twrton, R.C.Printtti and W•P•Slichter: J. Chein• Phys., gr (1953), i987

2) V.G.Si"ith, V.A.Tiller and J.W.Rutter: Can. j.Phys., &t (1955), 723

3) W.A.Ti1ler: JISI, l!Qt22 (1959>,338

4) F.eeters, K.Ruttiger, A.Dier}er and G•Zahs: Arch• EisenhUttenw., -t (1969) ,oo1

5) J.Chipnian: Physical Chemistry of Steelmaking Committee, Iron and Steel Division, AlME, Basic Open Hearth Steelittaking, The Anierican lnstitute of Mining and Metallurgical Engineering, (1951),632

6) 2iSi6iiSltSi5g Eiectrie Furnace Steeimaking, voi. 2, John wiiey & sons,

7) W.A.Fischer and H.Frye: Arch• E'isenndtterw•, ALt (1970), 293

8) A.Hays and J.ChipRtan: Trans. AIME, 135 (1938), 85

9) T.Vada and H.Vada: The Abstract for the 61st Lecture Meeting of Japan lmstitute ef "letals, JIM, Sendai , (1967), l74

10) 3.Tariaka: Tetsu-bo-Hagane, :!3, (1967), 1586

11) V.A.Fischer, H.Spilzer and M.gishinuma: Arch• EiseRbetterM,i•, ptt (196e), 365

!2) T.Takahashi, M.Kudo, X.tchikawa and J.TaBaka: Slolidification ef Iron and Steel, A Data B(x)k on the Solid{ficatien PheAoi#ema of tron and Steel, ed. by Selidification Coagg., joint Soc. IroR Steei Basic Research of tSIJ ISIJ, Tokyo, (1977). ( Appendix ).

13) W.A.Hume-Rothery and R.A.twckley: JtSI, 202 (1964), 534

14) E.T.'I'urkdogan: Trans. het. Soc. AME, 233 (1965), 21oo

15) R.L.SN3ith and J.L.Rutherford: J.Metals, Q (1957), 478

16) K.G.Davis: Met. Trans., 2 (1971), 3315 ' 17) S.Suzuki, T.tkpeda and Y.Kimura: The 19th Coigni. (Solidification), Japan Soc. Promotion Sci. (JSPS), Rep. No.l9-1025Ul, (May, 1980)

18) S.Suzuki, G•AsarK), T•lhiieda and Y.Kimura: Tetsu-bo-Hagane, pa (1980), S748

19) B.A.Rickinsen and D.H.Xirkwood: Metal Sci., L2 (!978), 138

' 20) A•J•W•Ogi1vy, A•Ostrowskii and D.H.Kirks"ood: Metal Sci., 1.5 (1981), 168

21) A.Kagawa and T•Okamoto: Metal Sci., Lt (1980), 519

22) A.Kagawa, S.Moriyama and T.Okamoto: J. Met. Sci., 2Z (1982), 135

23) 1'•Takahashi, M.Kudo, K.fchikawa and T.Tanaka: Solidification of lron and Steel, ed. by Solidification Comm., Joint Soc. Iron Steel Basic Research ef tSIJ, ISIJ, Tokye, (1977), 104

-15-

24)

25)

26)

27)

28)

29)

30)

31)

32)

E.Schifrmann and U. Hensgeu: Arch. EisenhUttenwes•, El. (1980), 1

E.SchUrtllann, H.P.Kaiser and U•Hensgeu: Arch. Eise.nhU'ttenwes., blt (1980>, 5

E.Schbrmann, H.P. Kaiser and U.Hensgeu: Arch. EisenhUttenwes., blt (1980),127

H.Misumi and K.Kitaniura: 1'etsu-bo-Hagane, St (l983), S964

T.Matsumiya, H.Kajioka, S.Mizoguchi, Y.Ueshima and H.Esaka:Tetsu-to-Hagane, Qt (1983), A217

T.Okamoto: Solidification of lron and Stee1, ed. by Solidification Comm.,Joint Soc. Iron Steel Basic Research of ISIJ, ISIJ, Tokyo, (1977)

A•Kagawa, K.lwata and T.Okaraobo: The Abstract for the 88th LectureMeeting of japan lnstitiite of Metals, JIM, Sendai, (1981) 274

R•A•3ucktey and W.Hume-Rothery: ' jlSl, 2el (1963>,227

A.K•Sinha, R.A.Buckley and V.Hume-Rothery: JlSt, 207 (1969), 36

-- 1 6--

pm!E-ui ibrium Dist itwtion of Carbon between Solid nd Li uid P

tt in lron-Carbon BinwwS tem.

2•1 lntroduction. ' Since the experimenta1 msethod, in whjch the 1iquid and solid phases coexist

at equi1ibrium state and concentratioms of the solutes in quenched specimens are

measured by EPMA, has been suggested to be most prornising procedure to de-

terinine ke in the previous chapter l.2, this procedure was used in this vork.

First of al1, the fundallientat investigation must be required for this experimen-

tal -ethod, for exa"iple, the disturhance of the concentration at interface be-

ween solid and liquid phases during quenching main;y caused by the diffusion of

the selute, which is one ef the most ixportant problems in this procedure.

So, in this verl(, this prcx)edure was applied bo Fe-C a!loys because

the diffusiyity of carbon in this systesi has beeR krx,wn te be large, and the

validity of the application of the experiueRta1 uethod to this alloy vas also

dlsctsssed. {}n the oti)er hand, there seeiRs to exist soiee discrepancies, partiou-

Iarly, atx)ut solidus iR this alloy and no detail discussion on this point in

the previous studies. Then, solidus and 1iquidus obtained experiittentally vere

compared with the curves given in other verks and also with the caloulated re-

su1ts using thermodynamical data.

2.2 Exeri tal.

2.2.1 A aratus for uenchedS iuiens.

The apparatus for preparing quenched specimens is sbown in Fig•2-1. A

sample veighing 7 g was placed into an aluraina crucible in parified argon

ataosphere. After melting down of the sample, it was coo1ed to a fixed tempe-

rature between 1423K and 1673K, at vhich austenite and fiquid phases coexist,

-17-

Argasttopyrorneter

fbrtemp.measurermt

cootingpipe.

toPIDfortemp.controlling

siliconitfurnace

thermocoup{

speCi

.speclmen

shooter

stopper

silicoritfurnec

crucibte

-Argas--i.

oit

Fig.2-1 Apparatus for quenching speci-ens.

and held at that teiiiperature for a given titae. Vhefi equiIibrium was achieved,

by witndrawing the stopper, the saseple fef1 through the hole at the bottoin of

the crucible and vas quenched into oil, to make speciesien including tve phases

having been 1iquid and solid before quenching.

As the vertical tube furmace used had a bot zone of 50 mta length and the

height of the sainple was within 10 ram, it is reasonable to expect that the solid

distribution in the sample was uniform.

2•2.2mutl dHldiTemperature. Compositions of samples used and their equilibrjum holding temperatures are

listed in Table 2-1. These samples were prepared in the high frequency induc-

tjon furnace from electrolytjc iron and pure graphite.

The equilibrium holding temperature was fixed to make the ratio of solid in

the specimens from 5 to 10 X.

-l8`--

Table 2-! Chemical compositions(wtX) aBd equi1ibration teillperatures (K) for F e-C specimens.

Ne. Temp. C si Mn P s Al(K)

1 1446 3.81 O.153 O.O05 O.O03 O.O05 O.1112 1521 3.30 O.164 O.O05 O.O03 O.O03 O.1643 1596 2.57 O.104 O.O05 O.O03 O.O04 O.0804 1632 2.41 O.109 O.OIO O.O03 O.oo4 O.0645 1672 1.ro O.065 O.O05 O.O03 O.O05 O.025

2.2.3pmtlbtiTime• To deteriEine the time required bo establish complete equiSibrium betseeen

the two phases, a series of experiinefits vere carried out on Fe-3.8 wtX C

alloys, in yhich speciuems were quenched after different bolding tiRies at

l446 K. The results of the analysis ef carbon from the central regioms of the

the solid p?iases are given in Fig.2-2. This figure stx)ws clearly that the equi-

1ibriuM vas achieved after bolding the srx)cinems for attout 30 llin. Corisequently,

the holding time was determined to be 1 hr.

'-'- cth!

o 20a.--f

sm.•di

1.0;'8

e8o

L=-o08-R--6---O---=L--;--o o

Fig.2-2

o o

O 30 60 90 120 Time [min]carbon doncentration in austenite of the

held at 1446K with equilibration time.

150 180

Fe-C alloy

-l9-

2.2.4 Met@11o ra hic Structu e of uenched S eci ens and Measurement of Concentration Distribu:tlLl.pm-tly-!b EPMA•

AIl the speeimens were sphericai, and the sotid phases were distributed

uniformty in each specimen. Photograph 2-1 shows the metallographic structures

of the quenched specimens, where ciroulars are sotid phases and the other part

is 1iquid one vhich had existed before quenching• ln these photographs, Nos. 1

and 5 are the specimens held at the lowest and highest temperature, respective-

ly. It is ebvious from these photographs that the quantities of dendrites which

crystal1ized in Iiquid phase during quenching increase as the holdjng tempera-

ture becomes higher and higher. Since the carbon centent of No. 1 specirnen is

approximate1y equal to the eutectic one, the quantities of crystal1ized auste-

nite are qui'te small during solidification as obvious from Photo.2-2 (A). On

the other hand, although the carbon content of No. 5 specjmen is less than the

suaximuM carbon solubility in austenite, i'ts structure coRsists of austenite

grains surrounded by cementite divorced froiu 1edeturite as shown in Photo.2-2(B).

As exhibited in Photo.2-1, the average diaueter of the solid phase is about

loo 'N•2X)() lim in the specitiren he1d at lower tets!perabere but about 3CM stm in

the specinen held at higher teiBperature becats$e the rate of coarsening of the

solid phase at higher tetttperature is'larger than at lower or}e.

Electron prcbe micro aRalysis was carried out by scaRniRg the focussed beam

over a region which included both solid and quenched liquid. Since the struc-

ture of the tiquid phase in the specimen vas not so uniform as that of the solid

phase, in the 1iquid phases a focussed beam was moved over the distance which

was 2 or 3 times of the diaraeter of the $olid phase, and tl)e concentrations at

the 1iquid region of each specirnen vere averaged. In this experiment, using

electrolytic iron, O.69 vtX C steel and 4•24 vtX C cast iron, the relation

between X--ray intensity and carbon content was established. The caron con-

centrations were determined by use of the calibration curve as shown in Fig.2-3.

-20-

t' ljieeffgl'ii['=fiz'

'iiv//',1?L/4'p•',•".,

iiiNs[SX/..-Sl.2...-.]

,.

kK'et "E'a't,i5, "•l. '•' .. .,.,.

T. Z.lt;t t-M:-t,• ,.,•

•'i.i•-IS.: •n•• ,l-///i/f.-!iil•?,/L•:\

,.: -. ' l' .: -'t.7' "i:

-t-

`,i ' lilfiIileet'"""'N..31

NUEtPl! i.,. t'1 lt;s;t-'.. th"if.: :`, -•-L{ISttti't '5.[i•S-'

-- s-)t•' "ii .v.

k•

'ISIt,rg.- '

-v ..eT -- -if' E+ 'x' i:!! "'

t

Pboto.2-1

"•:•i"i,•Nisi• ;kXiX,i,iii,l-l•iva

bes!!.'Et .-

't"fEitt.,.'X'trdi'.ii'i"ii,.i,,s

tt .t tl ' ' ?' C J}'. ee rl' .. .".r ;s '')t:2:ISde'sietij,ll

N 1oo ll an No• Equi1ibration temperature

1 1446 2 1521 3 1596 4 1632 5 1672

No.?

Åí,'sSviE",i

erP'

.

No.4i

(K)".l '-.t/tts'-

' No.51 Microstructures of quenched specimens.

Photo.2-2

H 100 ItmMicrostructures of quenched specimens,(A) No.1 and (B) No.5.

-21-

50 ;li

g 4o e g- 3o ut - a- ov ..- 20 •.ut.-

sC iO c 1. H • Oo•ito 2.0 3.0 4.0 '5.0

. Carbon,Weight Percent

Fig.2-3 The calibration curve for carbon in electron probe micro analysis.

2.2.5 CorK)entration Distribution. - Soige examples of the comentration distribetien i#easured by EPMA are

given in Fig.2-4. It is obvious fron this figure that in the specimen held at

higher tteniperature, the distarbarx)e of concentration distribution is regiarkab1e

because the quantity of dentrite crystallized in the 1iquid phases is large. tn

determimation of equilibrium carbon concentration in the solid phase, the values

at the center of the solid phase in which carbon concentration is unifornt as

illustrated in Fig.2-4, were used•

2.3 Results and Discussion.

2.3.1pmEx talRlt. Figure 2t•5 shows the measured carbon concentration in both solid and Iiquid

phases as a function of temperature in the Fe-C systet", and the solidus and

liquidus which were obtained by fitting the plots by curves. This figure also

1)indicates the liquidus by Buckley and Hume-Rothery , and the solidus by Benz

and Etliott,2) Adcock,3) and Honda and Endo.4) so far a number of studies

have been carried out on the 1iquidus except Buckley and Hume-Rothery, but al1

-22-

Equilibrationtempera ture ( K)

No. 1 1446

No.2 1521

pti

tiquid

'

i+l

i iJt

tiquid k

k '

sotid

II lt

sotid

tiqu'nt

No.3 1596

No.4 161Z

i,i,,, 1 li

,

li,

d

tiquid f solid

T

i

// tI

, ,

tiquid

No.5 1672

i:

1

Iiquid

•• ke

't

t' Izl !, "

si :i - sotid

'i

l

•i

Iiquid

'

"•i

I•'i ii'

solid

:1•

,

t

!

ii

Iiquid

li

'r'

d ti, J

t't t' ''

it

:xl, ! t

iF•------•--------l

100p

Fig.2-4 Carbon distribution in quenched specjmen.

-23--

these results coincide very we11 with that of Buckley and Nume-Rothery. So,

those results are not shown in this figure. On the other hand, there are some

types of solidus curves, for example, the curve convex downward by Honda and

Endo, the one slightly convex upward by Adcock and the straight 1ine by Benz and

Elliott. This fact means that the determination of soljdus is more difficult

than that of the 1iquidus. The liquidus obtained in this work corresponds to

that of Buckley and Hume-Rothery, and extrapolating the 1iquidus of this work

it reaches eutectic point which has already been established as most reliable.

Hs-th L7

•d)--

o LÅë

aEo-

1673

1573

14 73

-- >X,x l!orO\iN

X'X,x.,.X/'i"t,N

.,,. N'Xx .,. sVv ,i... Nclly

x"l"s " t"ts"t

t" "-- st" "- l- . s . s . It{

N

..

,

.

NX"'k••i(ii

X

NN•

Ns

liqutdus ----Buckley&HumeRother9)

solidus

NN

Ns(

---- Benz

----Adcock3)

"-'-'v Honcia & Endo4)

Present

/

NN

NN

& EEEioti2)

work•--- O-- experimental"--- co{cutated

/ /-

'

O 1.0- 2.0 ' 3.0- 4.0 Carbon Weight Percent'

Fig.2-5 Experimenta1 and ca1cu1ated resu1ts corresponding to the solidus and 1iquidus of austenite-1iquid iron in the Fe-C system.

The solidus obtained in the present work coincides comparatively wel1 vith that

of Benz and El1iott. The solidus calculated using thermodynamic data is also

sbovn in Fig.2-5. The detail of this calculation will be discussed later in the

section 2.3.3.

-24-

2.3.2

Vhen

carbon

even ln

tration '

of al1,

face and

tu re

interface

data of

diffusion

ence

sbown in

using the

content '

Ytaj-i"d-l-ty-Qf-the-{ildtfthExperirnental Method and Results.

this experimental method is applied to Fe-C system in which

diffusivity is known to be large, it is considered that carbon diffuses

the solid phase during quenching, and in some cases the carbon concen-

in solid after quenching may differ froma the equi1ibrium one. So first

considering the change of carbon concentration at the sotid-1iquid inter--

the change of carbon diffusivity in the solid phase with the ternpera-

during quenching, the diffusion distance of carbon from the liquid-solid

into the solid phase during quenching was calcuSated by use of the

coo1ing rates obtained in this vork.

First, supposing that these phenomena are based on one dimensional

of carbon, Fick's second Iaw in Eq.(2-1) is changed into the differ-

equation (2-2), and then the explicit metbod was used for this purpose as

Fig.2-6. The diffusivity of carbon in austenite measured at 1173 1673K

Fe-O.6 wtXC alley5) is asstjmed to be applicable to the carbon

in this verk.

ac == D ax2 at

Ci ,j- Ci-1 ,j C i-1 ,j-l - 2Ci-1 ,j + Ci-1 ,j+1

where,

D=

i

v

To

=D <Ax)2At

1.7s Å~ lo-2 exp ( - 27`llTX 103 )

i.7s Å~io-2 exp( - R(lig '-iv\AI9;•i)

, j: step nuraber of time on the vertiCal

abscissa, respectively, in Fig.2-6.

: cooling rate [K/Sec]

: equilibration temperature [K]

-25-

(2e2)

(2-3)

axis and distance on the

To -VAt.i: temperature at step i after start of quenching.

Also, initial and boundary conditiens are shown in Eqs•(2-4) and (2-5),

respectiveIy.

Ce,j = Co

'

c,,o = co+-li-zft•i

vhere,Ce : equi1ibrium concentration in the solid phase [ wt%]

m: gradient of the solidus [KlwtX]

iAt

o (i'1)At E F' 2At

6t ' O Ax 2Ax. (j-1]lax jAx (j+1)A

. Dlstatance . ' Fig.2-6 Explicit metbod.

' 6) Cooling rate V was calculated by using Eq•(2-6)

v = [ 340 Å~ (1/O/o Cz- l /4.3>O•3s ]i oom

vhere, Z: the secondary dendrite arm spacing [um], obtained from

graphs of microstructure of the quenched specimens in this

-26- -

(2-4)

(2-5)

(2-6)

photo-

work.

Figure 2-7 indicates the measured cooling rate. Since dendrite structures

could not clearly be observed in 1iquid phases in Nos• 1 and 5 specimens, the

extrapolated values obtained frem 1inear approximation of the relation between

the cooling rate and temperature of other specimens were adopted as the coo"ng

rates of these specimens.

3oo

T• .sttl' L

g 2oo L .O,

g

1OO

I673' 1573 1473 Equitibration temperature [Kl

' Fig.2-7 Change of cooling rates of the Fe-C alloy with equ"ibration temperature before cooling.

Thus, the change of concentration dist•ribution in the solid phase due to

carbon diffusion during quenching vere calculated by using Eq.(2-2). Sovae exam-

ples of the calouIated results are given in Fig.2-8, which shows the concentra-

tion distributions of carbon in the solid phase at the end of solidification

when it is assumecl that each specimen solidifies completely at temperature of

100 K under than eutectic one. It is obvious from Fig.2-8 that the diffusien

distance of carbon in even the specimen held at higher temperature is less than

IOO llm from so1id-1iquid interface. Comparing these diffusion distances with

-27-

the diameters of solid phases as shown in Photo•2-1, that is to say, about 100

•-- 200ptm of the specimen held at low ternperature and about 300um held at

high one, and also from Fig.2-8, which shows that the calculated diffusion dis-

tances of carbon into austenite during quenching are larger than the measured

values from the C K a intensity profiles in Fig.2-4 , it is supposed that

present experimental results were in the equilibrium state enough as far as the

carbon concentration at the center of the solid phase was used in the quenched

specimens obtained in this work•

2.4

2.2

p. 2.0$..c- 1.8

;t

2 1.6a"

s" 1.4'oa-

) 1.28AB IDU as

O.6

-

thu'vaixaSonternperature

1446 K

i521 K

1596' K

1632K

1672K

Fig.2-8

O 20 40 60 80 1oo 120 Dlstance from.solldA}qu'xi intertace ' [mp]

Carbon diffusion distances in the solid phase during quenching•

There taay exist the depression of temperature during quenching, namely,

until the specimen dropped into oil after withdrawing the stopper. In this re-

gard, it was found from the preliminary experiments that it took O.35 sec during

quenching and the depression of temperature was 15 K. Then, assuming that

the depression of temperature of the specimen is 15 K during quenching and

calculating the carbon diffusion distance in the same way as described above,

the results are found to be as same as in Fig.2-8. Thus, the depression of tem'

-28-

perature during quenching can be neglected.

2.3.3 Thermod namlca 1cu1ation of the E ui1ibrium Distribution of Carbon.

ln order to discuss therraodynamically the distribution of carbon between

solid and liquid phases, the solidus corresponding to the 1iquidus obtained in

this experiment vas oalculated using the thermodynamic data and conpared wjth

the experimenta1 resulbs.

Equi1ibriurn between 1iquid and solid phases in an Fe-C al;oy is

represented by Eqs.(2-7) to (2-9)

pt }

ptE

ptL

.1=" c

-s=llc

s=" c

+RT

+RT

inrL N

inr2 N

1

c

s

c

(2-7)

(2-8)

(2-9>

vhere,

From

cient

the

of

llc : chennical potentia; of carbon

."c : chemical potential of carbon in standard state

Nc : mole fraction of carbon

rc : activity coefficient of carbon

R : gas constant

T : absolute temperature

Superscripts 1 and s : liquid state and solid state

equi1ibrium condition Eq.(2-9), the equilibrium distribution

carbon kCo , is obtained as follows•

coeffi-

kC,-- Ng/N 1 =(rc

1

c/r,S)e xp { (ft} -.. a2 > /RT} (2-10>

-29-

lf the standard state of carbon in both liquid and solid phases is taken to

solid graphite, i.e.,

•1 •s Uc ="c (2-11)

Equation (2-10) ean be written as

kCo --- r: /r2 (2-i2)

Thus, substituting the values of activity coefficients rc , reported by

other investigators into the above equation (2-12), and also using the equilib-

rillm distribution coefficient obtained from Eq.(2-12), the so1idus correspending

to the 1iquidus obtained experimentally can be calculated.

Vhen the equi1ibriuM distribution coefficient kCo is calculated in

bo.(2-12), the thersK)dynaiNic data have bo be correct and reasonable• Then, the

data7'"13) previously obtaiRed on the actiyity of carbon in liquid iron and

austenife s?ere investigated• Mong these data, the values, which are applicable

to the tei#perature range (l423N1673K) in this york, and also are beiRg given as

a function of both temperature and cor}centration, were selected. Furtherniore,

in determination of the data used in the above calculation, the values, whose

degrees of the quotation and the convergency are high, were adopted. Figures

2•-9 and 2-le show soilte representative data of activity coefficients of carbon in

1iquid iron and austenite, respectively, at 1473, 1573 and 1673 K as a function

of Nc• From Fig•2-9, the agreeraent between the data of Chipman8) and that of

'Ueda et al.7) is very good. Rowever, since the data of Chjpman was calculated

from the activity in austenite using the equi1ibrium condition between solid and

liquid phases, it is thought to be uBsuitable for this discussion. On the other

hand, as the data of Ueda et al. was reported mohe recently that of Chipt"an,

and was obtained by measuring the rate of effusion of iron vapour, it is con-

sidered to be more suitable for this discussion than that of Chipman. 'l'hen, the

data of Ueda et al. was adopted as

-30-

O.8

O.6

O.4FO

m o.2 o " oA -- ----- ->B--------->c --=O:

7)- Veda et al--- J. Chipman 8) -

---- ARist and J.Chipman'-'--- H,Schenck et aln)

-i .t- d tt;" tt-

...

;;) 1

iZ ' ' ''

H -"

' ' .t.t

td.l-tt

't

;;" ;

' tt tt --e- -l- t 't. d. --- ' .-t'

'

'

. ' ' ' ' •v • 9) .-- . ed te "- -e- tet e-t t- . ..-. "" "'" .-2,27..--....•. e- X .....-' .;[;;• ig.- -.- .•-'..1;:.'.:

Il.Il.-.-.J-;.:ti-:--:'f':=i:":"';""'

..---'• A:1473K B:1573 K C:1673 K

.

Fig•2-9

o

Activity

O.O5

coefficient

O.1O

Nc

of carbon in

O.1 5

liquid iron.

1.0

O.9

-v o.8

ao- O.7

O.6

-----

---

11)S.Banya et ct.J. Chipmani2)DR.Poirieri3}

/ ' t/ tv/ ... t ' 't ' / ''"" : t"' t ' ' 't- t Z: ttte: ttt- t ' t ' -r . 't'

' / t / ' ' t ' 't ; "'t ' t ' ' tttt

' e '

' //. t tt

'Zt tt ''

' -.'

' - '

/tt.•.;

t '

' / ' / tt / -ptt-tt t t tt te t/ tt t/ ettt ' ' ' te '-e A: B: c:

/-. tt .-:.-' t / ' //- - / ' /'t t/ "tt ' x '

1473 K -

1573K1673K

' /t-tt ' /t t ' t

•/ . t ' ' 't

}A

IB

]c

-

O.O2 O.O4 O.O6

NcO.O 8

Fig.2-10 Activity coefficient of 'carbon in austenite.

-- 3 1 --

log r6 = (5 3TOO +o.so7)1.'-7VNtin+( 6;4 -o.ss7) . <2-13)

About the data of activity of earbon in austenite in Fig.2-10 the value of

Ban-ya et al.11) approaches that of chipman12) at higher temperature range and

also that of poirier13) at Iower teraperature range. so, the data of Ban-ya et

at. vas adopted as

' iog 76 = (3 7T70 -io.s) + (o.43 + 3 9TOO)i -NNe e (2-i4)

- ' +2.72 !og T- log (l-.IVt) '"MT

SubstitutiRg Eqs•(2-l3) and (2-14) into Eq•(2-12) and also using the

relation N8 = kCo • Nt , the solidus correspondiRg to the liquidus obtain-

ed experimentally can be calculated. The result is shown in Fig.2-5. From this

figure, the calculated resutt is in coiiiparatively good agreement with the

experimental one. Tbos, present experimental results are thought to be appro-

priate a1so in the theriiK)clynamical starrdpoint.

2.4 Conclusion.

In order to investigate the validity of the experimental procedure for

equilibrium distribution coefficient and to obtain carbon distribution between

solid and 1iquid phases in Fe-C binary system, austenite-liquid phases

equilibrated in the temperature range from 1423 to 1673K vere quenched and the

carbon concentratjons in each phase were determined by EPMA•

The results obtained are surnmarized as follows.

@ Solidus and 1jquidus obtained Åëoincided wel1 with the curves gjven in other

'works.

@ Diffusion distance of C frorn liquid-solid jnterface into solid phase

during quenching was calculated. From the results of the calculation, it became

clear that carbon concentration in the center of solid phase was not influenced

-32-

by the carbon diffusion during quenching• Thus, this experimenta1 procedure

is considered 'to be vatid for even the Fe-C alloys including earbon whose

diffusivity is very Iarge•

@ Equilibrium distribution coefficient of C in Fe-C system was deter-

mined therraodynamicatly. Solidus corresponding to the 1iquidus obtained experi-

mentally was calculated by using the above coefficient and it was in good agree-

ment vith the experimentat one.

-33-

2.5

1)

2)

3)

4)

5)

6)

7)

8)

9)

IO)

11)

l2)

l3)

References.

R•A.Bucktey and W.Hume-Rothery: JtSt, 196 (1960),403.

M•G.Benz and J.F.E11iott: Trans.Met.Soc•AlME, 221 (1961),323.

F•Adcock: JlSl, 135 (1937),720.

K•Honda and H.Endo: Science Reports Tohoku Univ., 1-6 (1927),235.

D.F.Ka1inovich, t.I.Kovenskii and M.D.Smo1in: Izv. Vyssh• Ucheb. Zaved, Fiz,Q (1971),116.

T.Okamoto and H•hatsumoto: 39th lnternational Foundry Congress, AFS,Ph"ade1phia, l'lay 1972.

A•Ueda, K.Fujimura and T.Mori: Tetsu-to-Hagane, CL/ (1975), 42.

J•Chipifian: het. Trans., l (1970),2163.

A•Rist and J.Chipman: Rev• Met., S3 (1956),796•

H•Schenck, E.Steirttnetz ar}d M.Gloz: Arch. Eisenhutterw., lt (1971),307•

S•Ban-ya, J•F.EHiott and J.Chipman: Met• Trans., .! (1970), 313.

J•Chirmian: Trans. ISet. Soc. AIME, 239 (l{X}7>,2.

D.R.Poirier: Trans. t'tet. Soc. AIME,242 (l968>,685•

-34-

SCEHELa.l;L!LecL---hat 3

Eqg-U/fillbrium Distribution of Solute Eleraents between Solipmd and Li id Phases

in lron-Carbon Base Ternar Allo s.

3.1 lntroduction.

As described in chapter 1, the equiIibrium distribution coefficients of

solute ele"ients in multi-component systems are thought to be different from

tbose in binary systems since some intera6tions ainong solutes are expeÅëted to

exist in multi-component systems, but a comprehensive theory concerning this

problem has not yet been developed• .

Recent1y, some investigatorslN4) have measured the equi1ibrium distribution

coefficients of solute elements in various kinds of iron alloys and caloulated

thes" by using thermodyrtatnical data. However, in their vorks, mainly, they sbed-

ied if the experimental results vere valid or not in ceiEparison vith the calou-

late(S values, and did not discuss the mechanism of the equilibrium distribution

of selute and the effect ef sotute interaction on it.

The purpose of this chapter is to obtain the equi1ibrium distribution

coefficients fer C, Ni and V in Fe--C--•-Ni(up bo 4wtX C and l vtX

Ni)and Fe-C--V (up to 4 wtX C and 3wtX V) alloys and to disouss

the mechanisms of these solute distributions between solid and ;iquid phases.

In these systems, there are fev data for the equi1ibrium distribution coeffi-

cients of the selutes, especially in a wide temperature range. Since the ther-

modyrramic interaction between N iand C in iron alloy is known to be opposite

to that between V and C, it is also interesting from a therraodynamic stand-

point bo make clear the mechanisms of distributions of Ni and V. Moreover,

based on the results on these systeras,the factors which control the solute dis-

tributions between soiid and liquid phases in irbn base binary arroys and

iron-carbon hase ternary ones were discussed thermedynamically•

-35-

3.2 -Eww,'tl.3.2•1 Procedure for makin uenched S ecimens.

The apparatus for preparing quenched specimens is the sarne as sbown in Fig.

2-1• A sample weighing about 5 g was placed into an alumina crucible in purifi-

ed argon gas atmosphere. After the saraple melted down, it was cooled to a fixed

tetnperature between 1453 K and 1693 K, at whjch austenite and 1iquid phases coex-

isted,and held at that temperature for a given tinte. When the equilibriuM was

achieved, by withdrawing the stopper, the sample fet1 through the hole at the

bottoin of crucible and vas quenched in oi1 or 10 X KOH aqua, to make the

specimen including two phases of 1iquid and solid before quenching.

As the vertical tube furrtace had a bot zor}e ef 30 mra over which the temper-

ature s,zs constant vithin Å}2K and the height of the sample vas shorter than

IO Hm, it is reasoBable to expect that the tetHperature distribution in the sara-

ple was uniferm. The sample vas often stirred when it was held at a given testi-

perature so that the solids could distribete unifor"ily in the saruple.

3.2.2pmtlndHldTefiL!/petaeqttuere•

The coiiipositions of the samples used and their equitibriura bo1ding

teipperatures are listed in Table 3-1. These samples were prepared in a high

frequency induction furnace from electrolytic iron, pure graphite, nickel and

vanadium.

The equiljbrium temperature was fixed at ahout 20 K lower than the 1jquidus

temperature to make the ratio of solid to 1iquid in the specimen as smal1 as

possib1e.

3.2.3!tilq!,!l-!-ibpm-fu!MbrationTime.

To detertRine the time required for the establishment of the complete

equilibrium between the two phases, a series of experiraents were carried out on

the Fe --C-V alloys, in which the specjmens were quenched after different

bolding tienes at the same temperature. The results of the analysis of V from

-- 36-

Table 3-1 Chemica1 cornposition andfor Fe-C-Ni and

equilibratien temperatureFe-C-V alloys.

Wt06 C wt2 V wtg Ni Holding Temperature[ K ]

2.573.502.303.342.453.37l.622.773.282.7!3.84

1

l

o

o

2

2

.03

.06

.44

.44

.96

.80

O.39Oe48Oe591.03O.93

l543l468l6281536l622l543l673l573l526l605l473

l548l476l64315461632

l6831593l5561608l483

1653

16131490

the central regions of the solid plrases are given in Fig.

shews clear1y that the equilibrium has been achieyed after

the holding time was determined to be 3 to 4 hr.

3•2•4 ML!e:ttaj-IQggapbj-{;LSSruetL!ll h St t fl}genghLe!d;LSpesS nd

3•-l. Thisfigure

3 hr. Consequently,

the Measurement of

ConcentrationDistriLtt!ytign-byt b EPMA•

AI1 the speciraens were spherical, and the solid phases were distributed

uniformly in each specimen. Photograph 3-1 shows the microstructures of the

quenched specimens, vhere circulars and the rest are the solid and 1iquid phases,

respectively, which had coexisted before quenching.

Al1 the specimens quenched vere prepared for metallographic examinations by

potishing and etching in 10 X Nita1. Then, the parts of solid and 1iquid to be

microanalysed were marked out with microhardness impressions, and then repolish-

ed to remove the etching.

-37-

Eg o.32g6 O.2zo.

a•

r O.1•g-

)

A A//. /e /e

A

A

e

Ae

Fe-2.3oc-o.44v

Fe -3.34 C-O.44V

e

10 30 60 120

Time IBOtmin]

240 300

Fig.3-1 Vanadiurn concentration invith equi1ibration tinte.

atlstenite of Fe-C-V alloys

Fe--3. 84C-O.93Ni

Fe-3. 28C-O.59Ni

Photo.3-1 Microstructures of quenched spec1mens.

-38-

Electron probe microanalysis was carried out at an accelerating voltage of

20 KV by scanning the focussed beam at 50 ltra/min over the region which inclu-

ded both solid and 1iquid. Since, particularly, the structure of the part of

the 1iquid phase in the speciraen vas not so uniform as that of the solid phases,

in the part of the 1iquid phase a focussed beam was moved over the distance cor-

responding to 2 or 3 times of the diameter of the part of the solid phase, and

then the concentrations of the solutes at the liquid region of each specimen

were averaged.

The actual composition were obtained from the calibratjDn curye which was

previously estab"shed with the chemically analysed specimens of Fe-C-V

and Fe-C-Ni alloys, shown in Fig.3-2. The chemical composition of these

saraples used are listed in Table 3-2. Sorae examples of the concentration dis-

tribution measured by EPMA are given in Fig.3-3.

;."-3oo ee/"P --. --t O"Q2oo - e - ..pt.s

g loo :.

0 O.2 O.4 O.6 OB 1.0 1.2 WTel. Ni

v. ;. 150' -': u 'o'eth-. . .. gl oo . '•e':"-h' S 50 E- , - ' tt o ,a2 o.4 o.6 o.e ' ' ' WTV.V • x"L . V' 2oo • A . -- n O..the A.-s ' 't'-1OO./

e, c' --- • O 1.0 2.0 3.0 4.0 WTV. C

Fig•3-2 Calibration curves for Ni, V and C in electron prove micro ana1ysis.

-39-

Table 3-2 Chemica1 composition for standard

wt9. C WtO-o V WtO"e Ni

o

o

o

l

2

3

o

1

1

2

3

.

.

.

.

.

.

.

.

.

.

.

oo

71

9704

30

34

92

14

31

7184

o.ooO.44O.59O.41O.44O.44

o.oo

l

o

o

1

o

-•

.

.

.

.

2059

94

0393

speclmens.

( pure iron )

:iquid

pbase so!id phaseNi

c

seTid

c

solid

c

v

nickel and

,N,S-.,,V•

iiqAgl/;de

g/:Xl:quide

Ni wvtw"

1;quidphase

li

"vx,;Fe-l.62•C-O.39•Ni tTqu',gk- phase ,,.i;i

wiN Ni - ' Fe-3.84•C-O.93-Ni

ipiq,".i,d,F phase

Fig.3-3

Fe--3.so-c-1.o6•v

Carbon,quenched specimens•

-40-

a

vanadium distributions in

3•3 Epmt tlResults• Figure 3-4 shows the experimental results on a plot of the carbon

conce' ntration in both the austenite and 1iquid phases in Fe--C--Ni and

Fe--C-V systems tosether with the 1jquidus and solidus in Fe-C binary

system. It is obvious that the distribution of C between the solid and 1iquid

phases inFe-C-Ni and Fe-C-V alloys "ith 1 'v3wtX Ni and V

differs 1ittle from that in Fe-C binary system•

The variation of the equiIibrium distribution coefficjent of Ni, kNo" , in

F e •-- C -- N i system and that of V, kVe , in F e -- C -V system are given as

function of the carbon concentration of liquidus, respectively, in Figs.3-5 and

3-6• tn these figures, the calculated values of kNoi and kVo using thermo-

dynamic data are also shown. This caSculation wi1l be discussed in detail at

the later section• lt can be seen froa{ Figs.3-5 and 3-6 that kNo'` increases in

F e -- C -- Ni sys tem and kVo dec reases in F e-C --- V sys tem wi th the

increasing carbon content• The effects of Ni and V contents on kXi and

kVo in Figs.3-5 and 3-6 are seemingly negligible• Also the experimen'bal re-

sults are thought to be in reasonable agree}"ent vith the calculated ones.

1673

:.

'eLe 1573o"o•aE•o--

1473

bo,N

e,

)iN< .

NO •.N ssNON

ei

NOON v N eN

J`)bL

NN(D

NX

AAN AA

SN

NNeN

oiei

--- Fe--C binary system .

a.NAd,

o

Fle-C-O.5Ni fe -C-1 .0Ni fe<-O.5V Fe -c-1 .ov

Å~

NkAe NAON NNOO SN hNx .AA,

O.05 O.10 . 0A5 Mole fractton of carbon

Fig.3-4 Carbon distribution between austenite and 1iquid phases in Fe-C--Ni and Fe--C-V systerns.

-41-

K•t''

'vtu'

{8

c..9

s,p.

.L.,n

vE

.25.

,-:-.-

ts'

tt tt O.7 , •. s"L4 sl'/:'/t,r/..sg'111i..11il./11,1111ii'illi/ii/lilli;ii/iii//////il•>t-il"9'lii""i"//111111"./////l.i'•i-S:-iilNli'iiii}•(i"e;'i;'iiiillitiiiiiililii"""NN11111111iillllllE.11.Il,ili-,..t./L,

' O,08 O,10 O,12 O14' O.16 OD8' O.10 O.12 O,14 O.16 • Mote fraction of carbon on tlquldus . . Mole traction of carbon on.liquldus

Fig.3-5 Change of klSiof Ni in Fe-C Fig.3-6 Change of kY of V in Fe-C -Ni alloys vith carbon con- -V alloys yith carbon con- centratien on 1iquidus. centration on 1iquidus.

3.4 Discussion. ' ln this section, the equi1ibrium distribution ceefficient was djscussed

therenodyRaraiea11y in erder to c1arify the controlliRg factor of so1ute distribu-

tion between solid and liquid phases in iron alleys and the effects of carbon on

the equiIibrium distribution coefficients of the third eteMents in Fe--C

'base al1oys.

3•4•1 TLthlQc!gg!;!y!IQ!!Ll-{ermd m T tmentofEpmltb mDistributionCoefficipmtnt k and

the PeriodicitLy oustk ofSoluteXQILainst Atomic Number in lron

ALI !1-{}ys •

Equi1ibrium between 1iquid and solid phases

sented by Eqs•(3-1) to (3-3) as stated in chapter

'

ptl= nl + RTin( rl Nl)

": = rk: + RTin( rR N9 )

--42--

in an

2.

iron-rich a}loy ls repre-

(3-l)

(3-2)

ls Ux = "x

where,,ux : chemical potential of X

iLx : chemical potential of X in standard state

Nx : raole fraction of X

rx : activity coefficient of X

R : gas constant

T : absolute temperature

superscripts 1 and s: Iiquid state and solid state.

From Eq. (3-3) of the equi1ibrium condition, the equi1ibrium

efficient ef X, kXe , is derived as follovs.

koX --- N9 /Nl

=exp{(ftki -a9 )/RT} exp (!nrl --i

(3-3)

distribution co-

nr9) (3-4)

m.p.

9 2 9 x s F

Fjg.3-7

GeneraIly,

phase diagram, the

uidus at their

in Fig.3-7, is

.t -Cross polRt of liqu!dus and solidus .7 Tangents .;.",t of liquidus ' ..' 1 and solidus tt ttt

tl Sotidus IUquidus

Fe Ni Nk Concentration ot X Sketch of soljdus and liquidus near the melting point of iron.

when the equilibrium distribution coefficient is read from the

value obtained from the tangents of the solidus and the 1iq-

cross point, that is to say, the point NE xO'S-.O as sketched

regarded to be valid near the melting point of iron. Then, as

-43-

1orsNx -->O, Eq• (3-4) can be simplified to

"nkoX )Nx.o = (NR/Nl )NxÅÄo

=exp{(Rl-a:)/RT} exp (in71 -in7R) (3's)

vhere, 7x is the activity coefficient of eletnent X at the infinite dilution.

In Bragg-Wi11iams approximation, the actjvity coefficient of element X in

a binary system of Fe-$uhstitutioma1 element X is given by

lnr, = {WFe-x (1-Nx )} /RT (3-6)

and in systen of Fe-interstitiat element X binary one

lnrx =(WFe-x+2Nx xx)/RT (3-7)

vhere, W and x represent the interchange erergy between Fe ancS X,

and the binding energy of $olute X, respectively•

As Nx --->O in Eqs•(3-6) and (3-7), both these equatioms are expressed

as

(1nrx )Nx.o=1n7;x =WFe./RT (3-s)

Substituting Eq.(3-8) into Eq.(3-5) gives

( 1 n k5 )Nx.o " (N: /Nl )Nx.-o

=exp{(4 '-Ii:)/RT} exp{(WFI,.,-Wi,-,> /RT} (3'9)

lt is obvious froru Eq. (3-9> that the equi1'ibrium distribution coefficient

of solute eletnent X at the infinite dilution consists of the free energy of

fusion of element X and the difference between the interchaRge energies of

Fe-X in 1iquid phase and in solid one. Also these energies are dependent

-44-

upon only the properties of element X• Then, in order to examine the above re-

sults the change of equilibrium distribution coefficient of element X with its

atomic number is considered•

The equi1ibrium distribution coefficients of element X in iron alloys

7) are plotted against the atoraic number of thepublished by other investigators

element X in Fig.3-8. As exhibited in this figure, the equilibrium distribu-

tion coefficients of element X are thought to change periodicafly against

atomic number. Then, this periodicat change will be discussed through the com-

parison with the above equation (3-9).

First of alI, the catculated free energy of fusion of each element at the

rnelting point of iron is shown in Fig.3-9(A). It is obvious frora this figure

that the free energy of fusion changes periodically against the atomic number of

the e1eRtent.

1.0

"c.9..Vb'

-(i,

e8--=-

O.5p.-L.va

vE2-b."p"-

trri.t

o

A!

2I

,

5-B2g,iod t

l

L•8ii

.g

A9

,

!l

,l

Third Period

AX

2.a

8.

2A9RA

s

,

,

Fourth Per',od D•6-oXRo "2i AX6

'A o

AA A AA

A o o

AA A o

t

,

li

in r-iron

in 6-iron

1

H

fifth Period A/

2. A 8

AO

Fig.3-8

?l co 5 to 15 20 25 30 eC NO ASP T,VCr)li Fe CoM Cu b Atomic number

Change ef equi1ibrium distribution coefficients ina11oys with atoraic number.

Mo

lron

-- 45-

e? ' gXE 2

-1 •g.-.,

.--. .p o .l 9•-•2

o g, '3 ct -4

x i.O •g•

6o ' 6: O.5 oe 8A th U) hi .9 g-e ,

x O.6 ,g ,.,

.be .g. g o.4 e} o.3 68 8b 02 e'>' e=- g.?06i

Fig.3-9 and between

Generally, the

the differences in the atomic

(chemical factor). For

interchange energy between

WA-B =VM • (6A

where, VM : atomjc volume

6 : solubility

: ' : : : : : : : : : :

iol. , :

2nd : 3rdp,oerlod ' i,`-period

l

: ,l/o i/\ON ,• lioo ,9 t: P: Ol :

.-•

lr

iolr ,2'

il

IP

ll

p etrh

/od

.oPx .ObM

x

K

ll

IN

toto :o : : :

:}w/i'i<ool

i•:v

eo,

:s

/rD

X,

IX;/, eN

tol:;:,

NooO

Å~ o 1ooo

P

/

: p.t . II: X•j)!` Ns>,.. X //

t" t}1 t 5 !O rs 20 25 so A{omic pumber

Periodicity for free energy of fusion of element X djfference of atomic radius and e1eetronegativity Fe and X.

interchange energy is considered to be dependent upon both

size (size factor) and the chemical property

exarnple, Mott8) proposed the fo"owing equation as the

A and B elements.

-6B )2-23o6o n(xA -- xB S (3-le)

of the alloy

parameter

-46-

x : electronegativity

n : nlimber of A-B boding.

'rherefore, the differences of the atomic radius as the size factor and the

electronegativity as the chemical factor between F e and a solute element are

taken into account and plotted against the atomic number of the eleraent, respec-

tively, in Figs.3-9(B) and (C>. As exhibited in these figures, both the size

factor and the cheinical one also change periodically against the atomic number,

and this fact suggests the existence of a physical periodicity in interchange

energy.

Thus, from the foregojng Eq. (3-9) it is considered reasonable that the

equi1ibriura distritwtion coefficients of the solute elernent in iron base alloys

clvange periodically agairist the a'toinic number of the element.

Consequently, the free energy of fusion of element X and the difference of

interchange energy between Fe and element X are considered to be the funda-

mental factors contrelIing the equi1ibrium distribution of the ete"ient X in

iron a1loys.

-47-

3.4.2 F

Etements in lron Base Binar Allo s.

In the foregoing section, the quantity ( WFLex -WFS..x) vas obtained as

one of the factors centrolling ko and mainly the effect of it on the periodic-

ity of kXo was discussed. In this section, (We.-x -WFS..x) is discussed

furtheri"ore. In infinite dilution of the solute in iron alloy, the equilibrium

distribution coefficient of a solute eleinent X, kXe is written in the follow-

ing equation as described before.

x sl =(Nx /Nx )Nx+o ' (ko )NxÅÄo

exp {(Iil '- il:) /RT} exp { (WFI,-,-Wi,-.) /RT} (3-11)

'

( WFt..x-WfiS."x) Night be derived fron the therieodyrtamical properties of

the coiHponents. severa1 studies8Nll) have been reparted to derive the excess

energies in 1iquid alloys from the thermodynamical properties of their compo-

nents deductively. For exagiple, Mott gave the foregoing equation (3-10) and

described that the excess energy could be deterKined by the electronegativity

and solubi1ity paraseeter of the coBiponents. Also, Miedeima et al.11) recently

sbowed that the excess energy in liquid solution consists of the werk function

and the electron density at the boundary of Wigner-Seitz cel1.

About the excess energy in solid solution, Si"K}ji et allO)and Miedeena et al.

stated that there is an essential difference between solid and liquid solutions.

In solid solution, where atoms of different sizes have to occupy equivalent

lattice positions, an additional positjve contribution to the excess energy

arises, due to the elastic deforatations necessary to accommodate the size mis-

match. In 1iquid solution such a size mismatch energy makes a less dominant

contribution to the excess energy than in solid solution•

Hence, when the difference of the excess energy between solid and 1iquid

solution is disoussed, it is coRsidered that (We,-x-Wi..x) is nearly equal to

the size mismatch energy in solid solution. Namely,

-48-

tors control1in E ui1ibrium Distr'but'on Coeff'cient of So1ute

(WFIe-x-- W SFe-2

! -- ( the size mismatch energy in solid solution ) (3-12)

in vhich the size mismatch energy AEsizE can be estimated from the elastic

constants and the relative size difference of the two metals, using dshelby's

e1astic contiiNum theory.12)

2 AEslzE oc BVm XS , (3-13)

vhere B Vm is the average value of the product of bulk modulus and reolar volume,

and S is the relative size difference defined as

s. (vi13 -vi/3)/(vi13+vl13) (3'14>

Substi'tution ef Eqs.(3-12) and (3-13) into (3-11) gives

RTinko-(ftl-ft9 ) oc -BvmÅ~62 (3-ls)

Then, the relation in Eq.(3-15) is discussed vhen the solute elen;enbs are

the substitutioma1 transition elefnents in iron afloys. The results are illust-

ra ted in Fig.3- 10. tn th is fi gu re, a pl et of {R T InkXo -- ( ilak - ii fi ) } wi th

BVm Å~ S2 is shown for various elements. It is obvious from this figure that

transition eleinenbs are nearly satisfied with the relation in Eq.(3-15). Thus,

the size mismatch energy is considered as one of the factors governing the equi-

tibrium distribution coefficieRt of the solute in iron base binary alloys.

Figure 3-11 indicates the variation of {RTInkXo - (t]Ek -ilR ) } with

BVm Å~62for the semi-metals and the noble rnetals as solute elements together

vith the results for traBsition metals as shown in Fig.3-10. As can be seen

from this figure, these metals except ttiansition ones are not satisfied with the

-49-

o 20

Bvm x 62

40 60 80 1OO

Cu -2000Aut x;=

s-.X•= -4000

•• i-•

X.e

sh -6000cr

cu de-cocr{gl Mg},

-8000

OTi

gMtt,,

oW

oNb oTa

Fig.3-10 Reration be tween RTln kXe -- (lil -- RR ) and B vm Å~ 62 forsubstitutiona1 tramsitiQn elements as so1ute in iron base al1oys.

o 50

Bvmx 62

100 150 2OO

zoe-amsi4 .

IAt

2Sb

"IoRTXxJx'vi

xtexs

"or..",ny-.,

-5

-10

-15

8ilezpt

Å~9 8Xs

MAs

o

o:transition metal

RSn

Fig.3-11 Relation between RT1nkXo -(Iik --IleR) and BVm Å~6Zfor semi-taetals and noble metals as solute in iron base alloys.

-50-

re!ation in Eq.(3-15). In other seords, it is considered that aBother excess

energy AE, which is represented in the folloving equation (3-16), is in-

fluenced on ko together with the size mismatch energy for the semi-rnetals and

nob1e meta1s.

RT1nkXo . = (il - aS ) + (W P,-,- WFS,p,) +AE

AE >O (3-!6) '

Hereupon, it should be necessary to refer to the excess energy AE in

Eq.(3-16>. According to Miedema et al.., an additieftal energy is requjred to

describe the excess energy between the semi metals or the noble metals and the

transition metals. That is to say,

'

WA-B ec {-P (AÅë)2+Q (An)?-R} (3-17)

where, Åë and n are the verk function and the electron demsity at the bounda-

ry of Vigner-Seitz celi of the components, respectively. P and Q are the

comstants to be deterigined expirically. R is required for the alloys vhich

consist of semi metals or nobte metals - transition metals but it is negligible

for transition metals - transition metals alloys. They also reported

ls (3-18) R <R

ln this case,

AE= (-Rl )-(---RS)>O (3-19)

which satisfies Eq.(3-16). However, Miedeina et al• have not described the phys-

ical meanings about the parameter R.

Consequently, the problems of AE are obviously related to the structure

and thertnodynamica1 properties of alloys in both sotid and 1iquid phases and

more detai1 studies are needed for further disoussion jn the near future.

The relation in Eq.(3-15) is discussed for the interstitial elements in

-51-

iron alloys. However, in this case, Eq•(3-14) must be rewritten for the these

elements because these elements dissolute into the interstitial sites and the

size mismatch is not due to the difference of the radius between solute and

solvent atoms. Then, the difference between half of the interatomic distance of

iron r and the radius of the interstitial atom, ro is used instead of 6 as

shown in Fig•3-12.

Figure 3-13 representsaplot of RTlnko with (r-ro) for B, C

and N. From this figure, the size rnismatch energy is considered to be the

irnportant factor to affect ko also for the interstitial elements.

Figures 3-14 and 3-15 show the variation of RTInkXo -- (ak -fitR ) with

BVm Å~62 for transition metals as solute elements in Ce and Ni base

alloys, respectively. Also in these alloys, the size mismatch energy is tbought

as the factor governing ko , as described in iron alloys.

SoluteFe l, l ete?)ent

l jl l ll te l II kr. -)I

l-ri"' t'et

Fe

o

-2

? -4 9 x x.e -6

is - or -8

-IO

4

(r -- r. )2x lo2

e IZ

IB c

I

IN

Fig.3-12 Relation between r and ro•

Fig.3- 13 Rekati on RT 1 n kXo and (r -- ro )Z.

-52-

2BVmx 6o

Ni

40 80 120

•- 2

nlo '-5--4utA

x.?

T.XY -6xx"

'!ii

-S5 -s

(il5

FeeCcr

. Mn

Cobalt Base A{loys

oTi

oMo

o Nb

Tao

Fig.3-14 Retation between R T 1 n kXo -substitutiorta1 transition meta1s

(ak -as,as solute

)in

and

CoBVmhase

Å~ 62 for

a1loys.

o 40Bvm x 62

80 120

neo-r=Xe-2

P..

JxaY-4'Sk'

s-.gl-6

Co9Y."

Cu ov

N;ckel Base Atloys

OTi

oMo

o Nb

oTa

Fig.3-l5 Relation be tween R T l n kXo -substitutiona1 transition metals

(fty -bRas solute

)in

andNi

BVmbase

Å~ bN2 for

al1oys.

-53-

3.4.3.

F e -- C Base Te rnar Al lo s.

The foregoing experimental results of this work showed that kNo" in Fe-

C -- N i sys tem inc reased and kVo in F e -- C - V sys tem dec reased wi th the

increasing carbon content. In this section let us examine these results therino-

dymamica11y.

Equation (3-4) can also be applied for the equi1ibrium distribution

coefficient of element X in Fe-C-X ternary system• ln this case, the

effect of carbon must be included in the activity coefficient 7'x of element

X in Eq•(3-4). Then, to consider the effect of C, the activity coefficient

of element X can be expressed in terms of the interaÅëtien parameter c as

fo11ows:

lnrx =1ndix +Åí: Nx +s: Nc (3-2e)

where, e: : self-interaction parauieter of element X

sCx : interactien paranieter of C on X

By substibeting lp.(3-20) and the relations NxS '-"tkXo .NN and N,S =ko .Ne

into Eq.(3-4), the equilibrium distribution coefficient of element X in

F e - C - X terna ry sys tem is rep resented by

inkXo "- (pt' ,1 -th9 )+infk /i9

+ (<,1- esk ,x) Nl + (.q,i- 8,S k8) N: (3-21)

Here, the first and the second terms show the fundamental factor control1-

ing kXe , the third and the fourth ter"ts denote the concentration dependences

of X and C, respectively, on kXo . Thus kXo can be calculated by sub-

stituting thermodynamical data into Eq.(3-21). The calculated ktj and kVo

are shovn in Figs.3-5 and 3-6 with the experimental ones. The thermodynamical

data used in the above calculation are given in Table 3-3.13N20)

-54-

Euilibrium Distribution Coefficient of he Third Elemethtt i

Now, let us call attention to the fourth term in the right-hand side of

Eq.(3-21). Mori and tchise24) proposed that there exists a 1inear relation of

Efi in solid and liquid phases, eCx'S =m.e9't , in iron-nitrogen-X systems.

The value m, which is not strictly equal to unity, is considered to be related

to the difference of the structure between solid and 1iquid phases. Then, this

treatment has been applied for Fe•-C--X systems. The relations of sorne

elements X between sE't in liquid phase13) and ecx•s in solid one13-'16•18,23)

are shown in Fjg.3-16. In this figure, it i$ obvious that a linear relation

holds approximately between sCx't and ÅíCx'S . This relation obtained by the

least square method is given as

Åíii,S= O.925•sCx•i (3--22)

Table 3-3 Thermodynamical data for calculating kXiand kVe .

Austentte Ref. Ltqutd Ref.

Ntckel

ln YNt

c:l

e:i

607 -2-O.386 (IS73K) , - T 12TOO

4640- - .- T. :.?'2{.-..-.-...--

(14)

ft1

(15)

-O•416 (ls73K) , . 7 I3 '2

i5,60

2•8s as73K) , 53T4o t2

(13)

tl

(13)

fikt ' "Kt ' 2L6•T + o.goxlo'3.T2'. 3. 2.T.lnT + 1257 ( Ref.(20) )

Vanadtum

t3

ln Yv

eU

,g

-3 •iO (1273K) a phase), - 39 TSO

79,OO

2340o lt2 -18.4 '(1273K) , - T

k2 k3 ' (22)

tl

(16)

336o k2-1.80' (1873K) , - T 60so ft2 3.23'(1873K)', T 301oo k2-!6.1 (i873K) , - T

(17)

(13).

(13)

"ll - ": - 4s.6•T . 1.29xlo-3.T2 - O.lxlo5.T-'i -- 6.45.T.lnT - 3935 ( Ref.(20> )

Carbonln Yc

E8

8680-

T + 2e72 lmT - 24.3

8980 + 3.00 T

(18)

(18)

2720 - 2.00 T7830 + 3.66 T

• (19)

(19)

tl

"3

estimated from the equatton E: =

The value of the term {("e} - ilYv

' {Cti,; -- "l) +RT'in Yil"U

tn liq. - T equilibrtutu

where the last term is equal to

-2

>+

}s

< RT

lnYx t2 Temperature' dependence !s estirnated in this work.

RT ln YeIVU } tn liq. - y phase eguiltbrium is calculated from the equation:

{ ( fi ,i - "g ) + RT• in "G / "e } + { os - "U ) + RT•in ye NU }

in ltq. - a equiltbrtum tn a - v equtlibrtum ln kY(a-\) s RT ln NU/Nav tn Fe-V btnary system )Nv.o n - O•577'T (Ref•(21)).

' ' '

-55-

er.ricxSnB/si

utts8e-6

.E4vutrt

2

F,,8•,`

bo

i

-le-16-K -rz-n -S-6

oMo

-4-2

Mn

46eEC,p n.varsm!'qu;diron(IB73K)

.Cr-6

-6C,austeniteEx'-p =

"u-va

/ov -rs

Fig.3-16 Relation between E9'i in liquid and Efi'Sin austenite.

substituting Eq.(3-22) into the fourth terui in the right-hand side of

Eq.(3-21) yie1ds

(eq,i- Åí",SkCo ) N: = (i ---o.g2s kCe ) Åíq,i N: (3-23)

As the equilibrium distribution coefficient of C, kCe , takes the value

smaller than unity,

(1 --O.g25 k8)>O (3-24)

It is obvious from Eqs.(3-21) and (3-23) that since ÅíCx is positive for the

elet:tent X with the repulsive effect against C, the value of the fourth term

in the right-hand side of Eq.(3-21) becomes positive and the kXo increases vith

the jncreasjng C content. On the other hand, since ÅícX is negative for the

element X with the attractive effect against C, the value of the fourth term

of Eq•(3-21) becomes negative aRd the kXo decreases with the jncreasing C

-- 56-

content•

Figure 3-17 shows plots of the present experimental results, kNo" and kVo

as a function of the carbon content, together with kXo for some kinds of ele-

ments published by other workers.1'"3'25'"30) As i"ustrated in this figure, in

Fe-C-'Ni,Fe-C--Si and Fe--C-•Co systeens, kNo",kSi' and kC8

increase with the increasing C content because these elements denote the re-

pulsive effect against C. While V, Mn and Cr indicate the attractive

effect in Fe-C base alloy systems, so kVo , kXn and kCo' decrease with

the increasing carbon content• Thus, the present experimental results could be

understood as described above•

Consequently, the fourth term in the right-hand side of Eq.(3-21) can be

expected as an important factor control"ng the variation of kXe as a func-

tion of the carbon content in Fe-C--X alleys.

Fig.3-17

t6

1.4E.!.V.

1,2,z:8 ..5 i.o,

.?

LU O,8'v'

E.2 O,6

Le-,

8 a4

O.2

o

M MrL'Urneda et al.:Vunin et aL a eo:v"nin et at : . n Si;Okarnoto et ot.:Umeda et oL O Cr:Okomoto etaL:Vmeda et al. ec.,xxi65:/,OO.d, e.",.a" ecu OMo:Suzuki et at, -::l.1' :r,m,e,,bR,oLhg[y,gtat• . .7.

'rV M /6I:A" i:l';;;);'•''#'""--"-"- "-"-'""'-'------

'nM-.e-M8Sgi.-!-/-.oo

'' •F P--h-xn -• Mn 's Cr -oM:i;----::rl:sL ....y. bM,

O,05 O.10 O.15 Mole fraetton of earbon

ChaRge of equilibriurn distribution coefficientswith carbon concentration in iron-carbon base

of some elementsa1loys.

-57-

Moreover, in order to investigate the fourth terrn of Eq.(3-21) the

influence of C on kXo is intended to be estimated quantitatively in terms

of free energy. Namely, multiplying each term in Eq•(3-21) by RT where R

is the gas constant and T is the absolute temperature, we derive

RT 1 nkXo = (nS - ptR ) +RT 1 n fa" /7xS

+RT (c:}t --- Åí<•S kXo) Nk (3-25) +RT (Åífi•i -efi•S kCo ) N6

Ve define the physjcal meaning of each term in this equation as foHows:

The ;eft-har}d term: the energy to let X distribute by the ratio kXe into

tiquid ar}d so"d phases.

The first and second terms of the right-hand side: the energy control1ing dis-

tribution of X fundaiRentally.

The third terra: the energy depending on the X content.

The forth term: the energy depending on the interaction of C en X.

,"

Fjg•3-18 Change of energy components concerning the distributjons of Ni and V between solid and 1iquid vith temperature.

-58-

Figure 3-18 depicts the variation of the calculated energies of each term

in Eq.(3-25) as a fu nction of tera pe ra tu re in F e -- C-N i and F e -- C -- V

systems, respectively. It is clear from this figure that the energy depending

on the interaction of C on Ni and V is the most dominant factor among these

ene rgies related to R T 1 n kXo .

3•5 Conclusion.

In order to investigate nickel and vanadiurn distribution between the solid

and 1iquid phases in Fe-C base ternary systems, austenite-1iquid phases

equ"ibrated in the temperature range from 1453 to 1693 K were quenched and the

nickel and vanadium and carbon concentrations in each phase were analysed by

EPMA to obtain the equi1ibrium distribution coefficients of these so1utese

Moreover, the factors vhich control the equi1ibrium distribetion between solid

and liquid phases in iron aSloys vere discussed therRiodynasnically. The results

obtaiged are sumi"arized as follows:

O The fundamenta1 factors control1ing the equi1ibrium distribution of

so!ute eletiient in iron aHoys are the free energy of fusion of the solute

element and the difference of the interchange energy of iron with the solute

element between the solid and liquid phases.

@ The difference of the interchange energy of iron with the solute element

between solid and 1iquld phases is dependent upon the size raismatch energy in

solid solution for transition metals and interstitial elements as solute element

but fer serai-metals and noble ones, the difference of another excess energy

between soljd and 1iquid phases js required together wjth the size mismatch

energy.

@ In iron base binary al1oys the equi1ibrium distribution coefficient of

the solute element changes periodically against the atomic number of the element

@ Particularly, in Fe-C base ternary alloys the most important factor

control1ing the equi1ibrium distribution of the 3rd element X is the interac-

tion energy between C and X.

-59-

@ tn Fe-C baseequi1ibriutu distribution

the repu1sive interaction

attractive one.

ternary altoys, with the increasing carbon content

coefficient of the 3rd eleraent X, kX6 increases

between C and X while kXo decreases for the

the

for

-60-

3.6

l)

2)

3)

4)

6)

7)

8)

9)

10)

11)

12)

13)

14)

15)

16)

17)

18)

19)

20)

21)

22)

23)

24)

25)

Re erences.

S.Suzuki, T.Utneda and Y.Kimura: The 19th Comma• (Solidification), Japan Soc. Promotion Sci. (JSPS), Rep. No• 19-10254, (May,1980).

A•Kagawa and T.Okanioto: Metal Sci., Lt (1980), 519.

A.J•V.Ogilvy, A.Ostrowskii and D.H.Kirkwood: Metal Sci•, l!l5 (1981), 168•

A•Kagawa, K.lwata and T.Okamoto: The Abstract for the 88th Lecture Meeting of Japan lnstitute of Metals, JIM, Sendai, (1981), 274.

H.Wada and T.Saito: J•Japan lnst. Metals: pa (1961), 159•

T.Takahashi, M.Kudo and K.gchikava: Solidification of lron and Steel, A hata Book on the Solidification Phenomena of lron and Steel, ed. by So1idification Comtii., joint Soc. Iron Steel Basic Research of lS1J, ISIJ, Tokyo, (1977). ( Appendix ).

B.V.Mott: PhH. Mag., 2 (1957), 259.

J•H•O.Varley: Phil. Mag., 45 (1954),887

M.Shimoji and K.Niva: Acta. "Set., 5 (1957), 496

A.R.Miedema, P.F• de Chatel and F.R. de Boer: Physica 100B (1980),1

D.J.fshelby: Solid State Physics 3, F.Seitz and D.Turnbe11, eds. (Aca[iemic Press, Nev York, l956), 79

G.K.Sigvorth and J.F.El1iott: Metal Sci., 8 (1974), 298•

E•J•Grinsey: J. CheRi• Thermo•, 9 (1979), 415.

T.Vada, H.Vada, J.F.EHiott and J.Chipman: Met• Trans., 2 (l971), 2199•

J•Chipman and 3.F.Elliott: Trans. Met. Soc. AIME, 242 (1968), 35•

T.Furukawa and E.Kato: Tetsu-to-Hagane, 61/. (1975), 3050.

S.Ban-ya, J.F.Elliott and j•Chipman: Met. Trans., 1 (1970), l313•

J.Chipvaan: Met. Trans.,3(1972), 55 ' O.Kubaschewski and C.B.Alcock: Meta11urgica1 Thermochemistry, 5th ed., Pergaruon Press, New York, (1979),336.

T•Nishizawa and M.Hasebe: Tetsu-bo-"agane, S7 (l981>, 2086•

R•Hultgren, P.D.besai, D.T."avkiRs, M.Gleiser and K•K•Kelley: Selected Values of the Thermodynamic Properties of Binary Alloys, ASI'I, Ohio, (l973).

'I'•Vada, H•Wada, J.F.Elliott and J.Chipman: Met• Trans•, 3 (l972), 2865.

T•Mori and E.lchise: J. Japan lnst• Metals, &2 (l968), 949.

K•Parasneswaran, K.Metz and A.Morris: Met• Trans•, 10.A- (1979), 1929.

-61-

26)

27)

28)

29)

30)

R.A.Buckley and W.Hume-Rothery: JISt, !Q7 (1es4), 895.

B.A•Rickjnson and D.H.Kirkwood: Met. Scj., .L2 (1978), 138.

K•P•Vunin and U.N.Taran: On the Structure of Cast lron,The New Japan Soc. Casting and Forging, Osaka, (1979)

A•Kagawa, S.Moriyatua and T.Okamoto: J.Mat•Sci•, Lt (1982), 135.

K.Suzuki, A.Taniguchj and K.Hirota: Tetsu-to-"agane, St (1978), S606.

-62-

-!C.uap!Ler-Lht4

Effects of Solute lnteractions on the Eq!,!Fi1ibriurn Distribution of Solute

Elements between Solid and Li uid Phases in lron Base Ternary-ALI !-gy:1 s.

4.1 lntroduction•

The equilibrium distribution coefficients of sorne elements in ternary sys-

tems are considered to be different freM those in binary systerns because of the

passible existence of solute interactions as described in the foregoing chapter,

but the enechanisms are so complicated that any detailed inforrnation has not yet

been obtained. So, it veuld be very useful if the effect of the addition of an

alloying eletuent on the distribution could be known by a simple equation vhich

indicates such effects.

The purpase of thjs chapter is bo derive an equatioB for the change of the

equilibriutu distribetion coefficients vith so1ute-interaction in iron base ter-

nary system and to discuss the influences of the sotute-interaction on the equi•-

1ibrium distributien of some elements in Fe--C, Fe-N, Fe--H, Fe-P

and F e - S base te rma ry sys tems .

4.2 Derivation of an uation describin the Effect of Solute lnteraction on

the Egy-i-1ibrium Distribut.ion Coefficien.t.

In this section, the equi1ibrium distribution coefficient is discussed

thermodynamically in tertNs of activity coefficients, interaction parameters as

described in the previous chapter. First of al1, the equi1ibrium distribution

coefficients of solute i in Fe-- i binary and Fe--• i --- j ternary system,

kb2 and kii3 are given by Eqs.(4-1) and (4-2), respectively•

inkio'2 = (kl• -k?• ) /RT+infl• /7?• + (Åíii•i-- ek•Skio'2) Nl• (4-1)

ln kio'3 = (bl• -ft ?• )/RT+infl• /7?• + (eii•i- ÅíiiSkio'3) Nl• (4-2)

+ (Åíj:i-- E9rS kj63) N1

ll J

-63-

where ,tLi is the chemical potential of solute i in standard state, 7;i the

activity coefficient of solute i at the infinite dilution, Åíl the self-

interaction parameter of solute is el• the interaction parameter of j on i,

and superscripts i and s show 1iquid and solid states, respectively.

The fourth terrn in the right-hand side of Eq•(4-2) indieates the effect of

alloying elei"ent j on the equilibrium distribution coefficient of solutei.

As the parts from the first term to the third one in the right-hand side of

Eq.(4-2) are equal to k'62 of Eq.(4-1), the following equations (4-3) and (4-4)

are derived.

i.ki,' ,3= i.ki,,2 +(4,i- g'i,sig',,3) N]. (4-3)

inki,' '3/ ki,' 2= (cj,rL Åíj;.Sigb3) N]. (4-4)

'l'he left-hand side of Eq.(4-4) shows the ratio of the equi1ibrium distribu-

tien coefficient of solute i in Fe-i-j terRary systern to that in Fe-

-- i binary $ystei" and this ratio is comsidered as a parameter indicating the

effect of the addition of the alloying element j on the equilibrium distribu-

tion coefficient of solutei. Then, the right-hand side of Eq.(4-4) is discuss-

ed furthert"ore. ' ln order to simplify the right•-hand side of Eq.(4-4), the correlation

between the interaction parameter of j on i in solid phase and that in 1iquid

one was investigated. Figures 4-1 (A),(B) and (C) show the relations between

el'S in soiid phase1N7) and Åíl•'t in 1iquid onel'6'7) in Fe-c base

(where i: C), Fe-H base (where i: H) and Fe-N base (where i:

N) ternary systems, respectively. It is obvious from these figures that a

--linear relation holds approximately betveen Åíl•'i ' and el,S in each ternary

system.

Mori et al.6'7) proposed that in Fe--N, Fe--H base ternary systems,

the gradients of these linear relations become unity as the ternperature of

-64-

Fig.4-1(A)

Fis.4-!(B)

Fig.4 •- 1(C)

Ay' 5re.n

J20'E

2B

o -5.c.-

-.oul -to

osi

Fe-C-jo

Co

'

oMo

Ocr-Mn

,

ov-15

Relation betweenin austenite in 20

--s

\Rz-oe'c-

-U ut o o

.c-

-20-zul

•-10 -5 O 5Ee in tiquid iron('J875K )

interaction parameterF e -- C -- j ternary

-40 -25 -20 -15 -10 -5 O ek in tiqu;d iron( ls75K',)

Relation between interaction paratneterin austeni te in F e -N •- j te rna ry

10

in 1iquidsys tern •

sig

Fe-N-j kis-`i5t9•,P'

ocu

Mneow

QcrOOMoo

ov

e'-.,

xoNJs'E

g -2o8

.c-

--=ul -4o

5ro in tiquidsystera.

Mos

S,"lilil9,Pe

-Pibo/ Cu

ovFe-H-j

OTi

oTa

-15 -10 -5 O• Els in tiquid iTon( ls73K )

Relation between interaction parameter in 1iquidin austeni te in F e --- H- j terna ry sys tem.

iron and

iron

iron

that

and that

and that

-65-

1iquid phase approaches that of solid one. They also suggested that these gradi-

ents are not strictly equal to unity because of the difference of the structure

in solid and ;iquid phases. Then, this relations are discussed here thermody-

naenica1ly•

Based on the zeroth approximation of the quasi-chemical rnodel, the activity

coefficient at the infinite dilution and Åíi• are derived as fo"ows:8)

ln fi (in Fe )= WF,-i/RT <4-5)

e?' =(Wi-j '--ZEf ,-i) /RT (4-6)

where Wi-j is the interchange energy. Atso, the equilibrium distribution

coefficient of solute i at the infinite dilution is represented by

(i nkio' )t,. i,Ni.,= (bl -- a? ) /RT+in 7,i / fai (4-7)

'

Coigbining these equations (4-5), (4-6) and (4-7), the difference between

the interaction para"}eter in liquid phase and that in solid one, As, is given

by Eq.(4-8).

Ac = eji? 1- egl ,S

=(lnkio' )F,-i,Ni.,- (1nk8 )j-i,Ni., (4'8)

'

As is obvious from Eq.(4-8), As can be obtained from the difference

between the equilibrium distribution coefficient of solute i in F e -- i

binary system and that in j-i binary one. Then, the relation between Åíl•A in

liqujd phase and Åíl•'S jn solid one vhjch is given by using AÅí in Eq.(4•-8),

i.e. cltS =Åíl,i --AÅí in iron-carbon base ternary systeras is obtained as

shown in Fig.4-2. This figure indjcates that a linear relation holds approxi-

mately between Åíl'i and Åíl'S . Also, the gradient of this line obtained

-66-

Fig•4-2

xoul < f-rtxcr Il

ut-

xUpt

77

5 Fe-c-x e

coo

Mn

-5 Mo Ti

W-10 $lope-of1.oo

~Xv:h"-15

ttn

v

-20 .-' Ta

/1

-25 1 Nb

-25

Re1ationthat in

-20 -15 -10 -5 O 5 E.E't in {iquid iron

between interaction parameter in Iiquid iron andsol id iron in F e -- C base terna ry sys tem

by the least square method is 1.03 and it is reasonable that the gradient of

jthis line is approximately equal to unity. Thus, the relation of Åíi between 'solid and liquid phases is shown by Eq.(4-9).

e9' '1; ÅíJ' 'S (4-9) 11

From Eqs.(4-4) and (4-9), the ratio of the equilibrium distribution

coefficient of the solute i in Fe-i-j ternary system to that in Fe--•- i

binary system is represented by the following sirnple equation (4-10).

inkj =-ink'o''/3 ki62= (i-kj6G3 ej:iNl <4-io) IJ 1

' ' ln Eq•(4-lo), the ratio of k;63 to kk2 , that is to say, the

parameter indicating the change of the equilibrium djstribution coefficient of

solute i with the addition of the a{loying element j, is defined as kll ,

-67-

named Distribution

rium distribution

obtained frorn this

known.

4.3 esults and

lnteraction

coefficient

coefficient

Discussion.

Coefficient (D I C).

of solute i in Fe- kll when that in

on the EqyU/-i-!brium

Furthermore,

i-j ternary

Fe-i binary

Distribution of Various

the equi1ib-

system can be

system is

4.3.1 Effect of Carbon

E1ementsbetwee!}-Stgljd-g!lptmUggmL!1dndLid Phases in Fe-C Base

AlILgy-iHng

TernewA11oys•

Effects of so1ute-jnteraction on the equi1ibrium distribution coefficients

in a fev kinds of iron alloys are discussed in this section by using the fore-

going coefficient DlC, kl .

First, the change of the coeffieient DIC of solute i with carbon con-

centration is discussed vhen the concentration of solute i is dilute in F e --

C-i terRary systeiu. Then, the equi1ibrium distribution coefficient of solute

i in Fe-C--- i teraary systeei is calculated from the DIC for the carbon

concentration range up to the eutectic point on the equi1ibrium between auste-

nite and liquid phases and also compared vith the experimental results.

The change ef the coefficient DIC of solute i with carbon

concentration is given by

lnkiC. =1nkio'3/ki62= <1-kCo'S ÅíCilN: (4'11)'

Since the concentration of solute i is considered to be dilute in this

work, the values of the equilibrium distribution coefficient of carbon in

Fe-C binary system can be used as kCo'3 in Eq.(4-11). Besides, the data

of Åí9•'t , being valid for the wide concentration range and at any temperature,

must be used, but nothing has been reported. Then, such values are obtained in

the fo1lowing way.

Using the interaction parameter e6' at the infinite djlution reported by

Sigvorth et al.1) ar}d that at the carbon-saturated state obtained by Neumann

-68L

et al.10) , and also assuming that e6' is proportional to carbon concent-

ration and the reciprocal of the absolute temperature, the value of e6 at

arbitraly carbon concentration and temperature can be obtained• ln this case,

as the interaction pararneter reported at the carbon-saturated state ig the in-

teraction parameter at constant carbon activity w6' , this parameter has to be

converted into the interaction parameter at constant concentration, c6 ,which

can be expanded at arbitraly concentration. When the concentration of solute i

is dilute in Fe-C base ternary system, the equation for the conversion of

the interaction parameter at constant activity to that at constant concentration

is shown by Eq.(4-12).11)

.(e ci)Nc = Na,! i=o = ( g ili l•l YC ) Nc . N&,Ni =o

=ii + ( g il2Yc ),,.,,,,.,&•Naj•( g i}\ !c )., ,.(g8.l2,),.,

. ' ln this equation, the left-hand side is the interaction parameter at ,constant concentration and the last term in the right-hand side is the interac-

tion parameter at cortstant activity. The second terrn in the parentheses of the

right hand side corresponds to the self-interaction parameter of carbon and this

term can be obtained from the change of the activity of carbon with its concen-

tration in Fe•--c binary systern reported by Ban-ya et al.12)

Finally, Åí6' obtained above has to be converted into Åí? . The equation

for this conversion is given by Eq.(4-13)13)

( Åí g• )Ni '-- ( e2 )Nc + ( cCFe )N F, (4-13)

'

ln the infinite dilution, ÅíF• is equal to sE . However, the last term

in the right-hand side of the equation is needed when this conversion is applied

at the arbitraly concentration. The last term shows the change of the activity

of F e with carbon concentration and can be obtained from the data byCh i prnan .1 4)

-69-

Thus, the interaction parameters e? at any temperature and carbon concen-

tration can be obtained. Figure 4-3 indicates the change of Åí(? of various

elements with the temperature and carbon concentration corresponding to the

1 iqu idus in F e •--• C bi na ry sys tem.

Using Eq.(4-11) and Åí? obtained above, the change of the coefficient

D I C of various elements with the temperature and carbon concentration corre-

sponding to the liquidus in Fe--C binary system can be calculated. The

results are shovn in Fig.4-4. As illustrated in this figure, the coefficient

DIC of Si, A1, Ni and so on having the repulsive effects against

carbon increase Nith increasing carbon concentratioR. On the other hand, the

DIC of Cr, V and so on having the attractive effect against carbon de-

crease vith increasing carbon concentration.

' Temperttture IK.j V68 1673 IS73 1473 o Weligr Petceni.oof Carbgn,o 4.o

ub--20'm'EeEsthut

sPthsi

= h.910e>coc

-

BAt.Cu

8s50t1E98g.b-lo9eE-20

-------------t----- ------------------------i--i

Ni

co

MnmoctwvTamo

O O.05 O.10 O.15 ..MtOiq".Id'.ag'IO."F2tCcagEnOa"ry system.

Fig.4-3 Change of interact,ion parameter of various elements with carbon concentration in Fe-C base ternary system.

-70-

1768Temperature [Kl 1673 IS73

o We;ght Percent of Carbon 1.0 z.o 30

1473i

,2.2

."-s.1•8 .n.X .x..

2 ! 1.4 .o

:.

'E l i.o o 9 " o

O.6

Fig.4-4 Change in F

Moreover, the

Fe-C base

equi1ibrium

1ated results are

as shown in

coefficients of

report by

assumed to be

adopted. In

perimenta1

results obtained

perimetal ones in

Thus, the

useful as the

4.0Sii

h At

Cu

Ni

=) r- '---------"'----'--co

Mn Mo Cr

v Ta

O O.05 O.10 O.15 Mgie Er.ac.t.ion of Carbon on L;qu;dus in Fe-C $ystem.

of DIC of various elements with carbon concentration e-C base termary systee;.

' equilibrium distribution coefficients of various elemenbs in

ternary systeifi are calculated from the coefficient DIC and the

distribution coefficient in iron base binary system, and the calcu-

compared vith the measured values by various investigators15"23)

Fig.4--5. Here, regarding the data of the equilibrium distribution

various elernents in iron base binary system, the values in the

Takahashi et al.24) about the equi1ibrium distribution coefficient are

approximately equal to the values in binary systera and then

Fig.4-5, the solid and dashed 1ines denote the calculated and ex-

resu1ts, respective1y. This figure indicates that the ca1culated

from the coefficient DIC are in good agreement with the ex-

each system.

coefficient DI C defined in this work is considered to be

parameter indicating the effects of solute-interaction on the

--71-

equi"brium distribution coefficient•

E•se

.y

=eoUc9sp.

-:.9

oE2".n.

==cr

al

'

1.2-- ---:Okamotoet

UmedaetaLaL

o.s't.si:CaL -N. ' O.6

ID

tO.8

.' O.4

1.4 -- A--:Hume Rothery et al. O.2

•-•- A-••-:Morita

CaL

etaL ..4..

-•-4-

O.6

1.2 ;

'Ni

O.4

1.0 A....

l-A..A.-A-•--

08 ... oo-oO'`-O-O-.O.O

1.4

:CaLN- .

Cr 1.2

Q6 'OsNN

t.

-- o--:Okamoto et aL NN 1.0Kirkwood et aL ss

o

Fig.4-5

i{-t"'--n -- ----.- Mn .--.. - -. -

NI"t'il-/t:.:Aj':"ii'lllafiliiii:,a:'i,..l.'."''}'""-":'"""--',gis-\s-'

.

--- o------ -o-- : Suz uki

-- a--:Vunin

-p - -t- -b- -. et al. "'"et aL

Mo--

ea

: Morris

:Vunin:Cat

et

et

aLaL Cu

e

Co a;-'-'"-""--"'-----"-"--'NN----4

O.05 O.10 O.15 O O.05 O.10 O.15Carbon Mote Fraction Carbon Mote Fraction Change of the equi1ibrium distribution coefficient of sorne elements vith carbon concentration in Fe--C base ternary system.

-72-

4.3.2 Effects of arious Allo in ElerneL!n}!s-ptumtso th Euillb.riumUstribution

Qt!US-ilpogen-fNit dH!d;!Åíggenpe!betweenSautlidandLiuidPhasesin e-N, HwwBaeT AIILQys•

lt is important to know the equi1ibrium distribution behaviours of gaseous

elements in relation to various phenomena during solidlfication of steels, but

Iittle information has been obtained so far concerning this problem. Then, the

purpose of this section is to disouss the effects of various alloying elements

on the equi1ibrium distributions of nitrogen and hydrogen between solid and

1iquid phases in iren hase ternary systex by using the foregoing DIC.

The variation of the DIC of nitrogen and hyclrogen with the concentra-

tion of various alloying elements in Fe--- i-X ternary system ( i: N or

H) is represented by Eq.(4-14).

ink5• =inkei '3/kd' '2 = (i - kX6 G5 ÅíXi'iNl (4-i4)

Since the solubilities of nitrogeR and hydrogen in solid and liquid alloys

are consideiably small, the effects of these gaseous elements on the distribu-

tion of the alloying element X between solid and 1iquid phases can be neglect--

ed. Then, in this work, the value of kXo'Z in Fe-X binary system was used as

kXe'3 in Fe-i-X ternary system in Eq.(4-14). Also the data of Sigvorth et

ai., lshii et ai .2 5' 26) and Mori ta et al .2 7) we re used as cl 't . Fi gu res 4'6

(A) and (B) sbow the variations of the coefficient DIC of nitrogen and hy-

drogen with the concentrations of various alloying elements in Fe-N and

F e --b H base ternary system, respectively. In these figures, solid 1ines are

the caloulatecl resuSts when a phase is assumed to crystallize out of liquid

solution and the values of kXo for a phase are used in Eq•(4-14). Similarly,

chain 1ines show the calculated results when the'primary crystals are presumed

to be 7' phase. It is obvious from these figures that C, Si and so on indi-

cating the repulsive effects against N and H increase the DIC of these

gaseous eleraents, and on the other hand Cr, Ti and so on showing the attrac-

-73-

tive effects against N and H decrease the DIC of these gaseous e1ements.

A

1 .2

N.2Rx 1.1

'c'

s 9 •.-.

z6

9 .-: 1.0 a

ct c ,C ,B BZs,'

/.l/'--- 7

/.Z7i

M7'

wY7

7t .-. ' -t- .-

:Å~:Silll;s

xxXsxxxexx-Å~ "Å~:wx. Mli;"r"b-

cu.si Ni-- or Co, Al

W Mn or Mo v•Cr

;

l

Fl

Fig.4-6(A)

B

O O.Ol O.02 O.03 O.04 Mo:e Fraction of Atloying

Cha nge of D I C of ni trogen vi thgf a1Ioying e1eiBenbs.

OD5 O.06Etement

the concentration

;'o2>K`

i'

:oa

bz'

6 9 " o

1.1

1.0

O.9

c .c or /---- T ./. /si // /' /' lt 7/ ,4/4?/!-/---"g,

tll -.r -!-Z' Al L--r== Co,Cr

Å~Å~

Å~. Å~

. Å~s Å~

N Å~fi

v

Ti

Fig.4-6(B>

O O.Ol O.02 O.03 Mole Fract;on of

Change of DIC of hydrogenof a1loying e1ements

Q04 O.05 OD6Attoying Elernent

with the concentration

-74-

4.3.3 pmt l t fDtributionInteractionCoefficienttothpatE librium

DistributionofPand Sbetween-wStg!j-!;La!]!;U,lg!,!-td2bases-ild dLi dPh nlronBase

' !rnar All .

Although the concentrations of P and S are dilute in steels generally,

these elements are knovn to play an important role in relation to the micro-

segregation. So, many studies have been carried out in order to make clear the

mechanisms of their segregations and also to improve thein. However, the influ-

ences of various aHoying elements on the equi1ibrium distributioms of P and

S have not yet been known quite well. In this section, these kinds of effects

are discussed by using the foregoing coefficient D I C when the concentrations

of P and S are dilute in Fe-i-X (i: P or S) termary system• The

change of D I C of P and S with the concentration of the alloying elements

in Fe-i-X termary systera (i: P or S ) is given by Eq•(4-15).

ink5• =inkoi'3/kio'2 =(i-kX65 ÅíXi'iNl (4-is)

As the cencentrations of P and S are censidered to be d"ute in this

mork, the equilibrium distribution coefficient ef the alloying element in iron

base binary systeig can be used as kXe'3 in Eq.(4-15), as described in the last

section• Also, the data of sigworth et al.1) and Ban-ya et al.28) were adopted

as Åíl't . The changes of the coefficients DIC of P and S "ith various

alloying elenients are shown in Figs.4-7(A) and 4-7(B) in Fe-P and Fe-S

base ternary systems respectively. In these figures, solid lines and chain ones

indicate the calculated results for a phase and r one, respectively. As can

be seen frorn these figures, the elements denoting the repulsive effects against

P and S, e.g. C, Si and so on, increase the DIC of P and S, while

the elements indicating the attractive effects against P and S,e.g. Cr,

V and so on, decrease those of P and S•

Thus, it is obvious that effects of solute-interaction on the equHibrium

distributions of N, H, P and S, which are intimately concerned with the

-75-

miero-segregation of stee1s, can be discussed' by using the coefficient DI C.

A

1.2

X'e:>)ef(•

x - 1.1g

6a8a`

5 9 1.0 E•

t--w- -. -

pt

T

' Cu 1/• •. ./.7'.. z,,,.z:B

/7 ,.-'ij'f .--i &i

llli{i'Illlliilll::llll:l:::!,,,=kt,

=F=:' :::.::-'-'--'------""----"--"---cr

Å~- - Å~- Å~- XCr

cc Si 7'/-'

Fig.4-7(A)

B

o O.Ol

Mote

Change ofof al1oying

1.1

O.02 O.03Fract;on of

DIC ofel esnents .

O.04 O.05 O.06Atloying Etef'nent

phospborus with the concentration

N.n.lyls{ut"":1.o

/r•

z'

El• o.g

a

B

tt1 7 ./I4;,1.-/

4/'

W./si

AI.W.-Mo

x

- '-m--.. ..

.

x.

x,

---- . ---.. .- ----- . .---. Ni"E;,7cS'M".

Jl Ng KMn Cu

ct

"` Co,Ni

x,

x' Ti Ti

---•--- T

Fig.4-7(B)

O O.Ol O.02 O.03 Mote Fraction of

Change of DIC of sulphurof a1loying e1ements.

O.04 O.05 O.06AIIoying Element

with the concentration

-76-

4.4 Conclusion.

The effects of solute interaction on the equiIibri'um distribution of solute

elements between solid and 1iquid phases in iron hase ternary system were studi-

ed thermodynamica11y.

'l'he results obtained are summarized as follews.

O Distribution Interaction Coefficient (DIC), kl ,which is defined

as the ratio of the equilibrium distribution coefficient of solute i in

F e - i - j te rna ry syste"t to that in F e - i bi na ry one, was derived as

shown in the following equation.

inkg• =ink8'3/kio'2= (i --kt"S cj;iN]. .

D I C is considered to be the para}neter indicating the change of the

equilibrium distribetion coefficient of solute i with the addition of j.

@ App;ying DIC for.the equilibrium distribution of element i in

Fe-C-- i termary systeg", the change of DIC of various elemeRts vith the

tei:iperature and carbon concentration corresponding to the liquidus in Fe--C

bimary systesi could be obtained. DIC of Si, Al, Ni and so en having

the repulsive effects against carbon increase with increasing carbon concentra-

tion. On the other hand, DIC of Cr, V and so en having the attractive

effect against carbon decrease with increasing carbon concentration.

The caloulated values of ko of various alloying elements in Fe-C

base ternary alloys frofn D I C are in good agreement with the experimental

ones. ' @ The effects of solute-interactjons on ko of N, H, P and S in iron

base ternary alloys could be estimated by the use of DIC • The eleraents

der}oting the repulsive effects agajnst N, H, P and S in iron alloys, e.g.,

C, Si and so on, increase DIC of N, H, P and S, vhile the elements

indicating the attractive effects against N, H, P and S in the alloys,

e•g• Cr, V and so on, decrease those of N, H, P and S•

-77-

4.5

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(1O)

(11)

(12)

(13)

(14)

(15)

(16)

(l7>

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

References•

'G• K. Sigworth and J. F. Elliott : Me'tal•Sci.,8 (1974),298

E• J• Grimsey : J. Chem. Thermo., 9rk (1979),415

T• Wada, H. Wada, J. F. Elliott and J. Chipman : Met• Trans.,2 (1971),2199

J• Chipman and J. F. Elliott : Trans. Met. Soc. AIME, 242 (1968),35

T• Wada, H. Wada, J. F. EIIiott and 3. Chipman : Met• Trans.,3 (1972),2865

T• lfori and E. Ichise : J. Japan lnst. Metal$, 3L2 (1968),949

A. Morooka and T. Mori : The reports of the Third Japan-USSR Joint Symposi-um of Physical Chemistry of Metallurgical Processes, (1971),141

H. Wada and T. Saito : J. Japan lnst. Metals, 3L5 (1961),l59

H• Wada, K.Gunji and T. Vada :J. Japan tnst. Metals, &t (1966),613

F• Neumann und H• Schenck:Arch. Eisenh{ittenw., at (1959),477

K• Fujimura, T. "IOri, T. Azuma and S. Urakawa : Tutsu-to-Hagane, fu9 (1973),

mS. Ban-ya, J. F. Elliott and J. Chipman : Met. Trans.,1 (1970),1313

T. Mori and A. Morooka : Tetsu-to-Hagane,5Lt (1966),947

J• ChipiEan : ISet. Trams., 1 (1970),2163

S. Suzuki, T. URieda and Y. Kimura : The 19th Comm. (Sotidification), JapanSoc. Promotion Sci. (3SPS), No.19-10254, (May, 1980)

A. Kagawa and T. Okamoto : Metal. Sci., :EL4 (1980),519

A• J• W• Ogilvy, A. Ostowskii and D. H. Kirkwood : Metal. Sci•,1in5 (1981),168

K. Parameswaran, K. Metz and A. Morris : Met. Trans.,ILqt (1979),1929

R. A. Buckiey and V. Hume-Rothery : JISI,197 (1964),895 '

B. A• Rickinson and D. H. Kirkwood : Met. Sci.,ILt (1978),l38

K. P. Vunin and U. N. Taran : "On the Structure of Cast lron", The new3apan Society for the Casting and Forging, (1979)

A. Kagawa, S. Moriyama and T• Okamoto : J. Mat. Sci.,1-7 (l982),135

X. Su2uki, A. Taniguchi and K• "jrota : Tetsu-to-Hagane, St (1978),S606

T. Takahashi et al.: "Solidification of lron and Steel" ( A Data Book onthe Solidificat•ion Phenomena of Iron and Steel ), (1977) Solidificationsubcomrnittee, Basic Research Cotumittee on lron and Steel, ISIJ.

F. tshii, S. Ban-ya and T• Fuwa : Tetsu-to-Hagane, b6-8 (1982),1551

-78-

(26)

(27)

(28)

F.

Z.Lt

s.

lshji and

lvtorita and(1978),648

Banya, N.

T. Fuva : Tetsu••to•-Hagane, 68.. (1982),1560

K. Kunisada : Tetsu-to-Hagane, St (1977),

Maruyama and S• Fujino : Tetsu-to-Hagane,

1663 : Trans.

6-9- (1983),921

ISIJ,

-79-

yCp-ad2mLer--uhat 5

Effec ts of So 1ute l nte ract ions en the Eutt i 1 i br i um i str i bu ILI.gn--ojLSo 1ute

El;ptmentsBetweenSolidandLsu/ dPh es lronBase"ulti-cQmponentLuAluQysll •

5•1 Introduction.

In the foregoing chapter 4, the effects of solute-interactions on the equi-

1ibrium distribution of solute elements in iron base ternary alloys could be

explained by the use of Distribution Interaction Coefficient ( D I C ) defined

in that chapter. In this chapter, DIC vas applied to the equitibrium dis-

tribution of solutes in iron base multi-component systems and the new parameter

was derived. Also, the influences of Si, V and Co on the variations of

ko of Sn and Cu vith carbon in Fe-C base quarternary alloys were

obtained experimentally and those results vere discussed by means of the new

paranieter• tn particular, Sn is one of the impurities which are diffioult to

be rerioved from steels and it shows unique therEKxSynaii!ical behaviour in Fe-C

base altoysl) Also, the equilibrium distribution coefficient of Sn in Fe-'-C

hase a!loys have oot been reported. So, it is comsidered very iraportant to

investigate ko and the effects of the solute interactiors on ko in Fe-C

al1oys.

5.2 Derivation of a Parameter describipan th Effect of SpLJ.!,Lte lnteraction on

th/!eJtilggj-ll!;![-jltb iura D.istribution Coefficient.

The equiiibrjum distribution coefficient of solute

system, k`b2, is given by Eq•(5-1)•

1nki62= (ti l• -b\• ) /RT+1n71• /r' Si + <Ehi '1

Assuraing that the effect$ of solute interactions on

-- 80-

i in Fe-i bi na ry

- .l' •5kl ) Nl• (s-i)

the solute i in

F e - i - p - q - r - -- - multi -cornponent sys tem are approximately describ-

ed by a simple terrn of Wagner's forraalism concerning the activity coefficient

of the solute in multi-component system, the equilibrium distribution coeffi-

cient of solute i in multi-component system can be derived in the following

equation (5-2)•

inkio"L (Rl• -j?•)/RT+in71• /7?• +(cii'i-eii'Skg)N1•

. (b?. ,1-,Pi,Sk,P ) N} + (8i,1-.qi,Skq, ) Na

+(e"i'1-- Eri'Sko) Nl. +•... (s-2)

Here, this vaulti-certiponent systei" is supposed to be the n-eoraponents systet"

and the equilibrium distribution coefficient of the solute i is indicated as

kis" . Vhen the concentration of the sotute i is very ditute, the parts fro"t

the first term to the third one in the rigth-hand side of Eq.(5-2) are nearly

equal to kie2 of Eq.(5-1). Then, the equation (5-3) can be ebtaint•

'

l .ki,, n/ kid2= (.pi,l- ,pi,sk ,p > NB + (Åíqi,l -- 8i,Skq, ) Na

+ (Er"- sr.,sk er> N1 +.... 1r 1 (5-3)

As described in the previous chapter, when the teinperature of 1iquid phase

is equal to that of solid one, the interaction parameter of j on i, cl• , in

1iquid phase may be assuraed to be approximately equal to that in solid phase,i.e

Åíji,l: Åígl ,s (s -- 4>

From Eqs.(5-3> and (5-4), the ratio of the equilibrium

cient of the solute i in jron base n-components'system to

binary system is represented by the simple equation (5-5)•

-81"

distribution coeffi-

that in Fe -- i

1nki,',n/ ki,, 2= (1-k:) ,P?INI + (1-k,q ) .q"N1 IP lq + (1-k,r ) Eri,INJ +••••

=6P NI +6g Nl +sr Nl +.... (5-5) lq 1 pr 1

6J iE (1-kg) .j ,1 (s-6) 11 . . Here, the parts of ( 1 -- k6 ).cl't in Eq•(5-5) for each solute eleraent p,

q, r and so on are defined as 6e' in Eq•(5-6) and called Distribution lnter-

action Parameter(DIP). The DIP ,6i• , is considered to be a parameter

indicating the effect of the alloying etement j on the equilibriurn distribution

of the so lu te i be tween sol id and liqu id phases in F e - i -- j terna ry sys tem.

That is to say, if 6ij is pasitive, the etement j has the tendency to in-

crease the equilibrium distribution coefficient of the solute i. On the other

hand, if 6ii is negative, the solute j decreases kio .

The effects of the solute interactions on the equi1ibriura distribution co-

efficients of the solute eleinents in a fev kinds of iron base multi•-component

systems were discussed in this vork by using the parameter 6ij . First of all,

the change of the equitibrium distribution coefficients of some elements with

the carbon concentration in Fe-C base alloys were determined experimentally,

and the results were examined by the use of Sij .

5.3 gx.pe-r..ILmental•

ln order to investigate the equi1ibrium djstribution of some elements

between austenite and liquid phases in Fe-C base alloys, austenite-1iquid

coexisted samples were quenched and the concentrations of solutes in each phase

were determined by EPMA. 1'he apparatus for Preparing quenched specirnens is

shown in Fig.5-1. The experimenta1 procedure was almost the same as described

-82-

ih chapter 2 and 3. In this experirnent, however, the specimens were quenched on

the copper plate with argon gas blov in order to quench the specimens more rapid-

ly than by KOH aqua or oi} used at the experiments in chapter2and 3.

The equiiibration time was determined to be 2.5 or 3 heurs. Moreover, area

analysis by EPMA was performed to measure the concentration of the solute

elements, so that the error in the concentration analysis caused by rough

structures jn 1iquid phase part could be as small as possible.

Thermocoupte (iOo'Ili\iil.l!Mp.S,:...,) "i'"z "as

5.4

5.4.1

Tab1e

-- Cuc--sn

Resu1ts

Effects

and

of

TherTnocoupte to PIO ( 2lr,t eo't'rptin"g)

specimen

(7oas,

Fig.5ny-1

Discussion.

So1ute

Ar gas- noute ,Xgr,;.g)

Apparatus

speclmen shooterstopper

sicfurnac

for

on

e

Csvcible

Interactions

So1ute E1ements between Solid

quenched

the Eg!t,!rL!-Ulnl b ium

-Ar.H2 gas

?nfP/etr

speclraens.

P. i strlb-u ti on

and Lt/guid Rhases in F e --- C

of

Base

.QuarternmuAlILQyLs•

Compositions of the samples and the experimental results are listed in

5-1. Alloy systems investigated in this work are Fe--C-Sn, Fe-C

and Fe-C-Co for Fe-C base ternary systems, and also Fe-

wi th Si, V or Co and Fe-C-Cu wi th V or Co for

-83-

Table 5-1 Compositions of the samples (wtX), holding temperature (K) and the results of ko•

Fe-C--Sn Fe-C--Cu Fe-C-Co Tenp. c sn. kSo" Tenp. c cu kCo" Tenp. c co kCoO

1418 4.e2 1.66 O.84 1443 4.03 1.23 1.M 14ss 3.ce 1.ce 1.24 1485 3.58 1.10 O.63 1495 3.45 1.15 1.43 1548 3.16 2.06 1.16 1586 2.91 1.03 O.42 1563 3.09 1.08 1.25 1644'2.46 2.15 1.05 1613 2.42 1.M O.37 1636 2.19 O.96 1.14

Fe-C-Sn-Si Fe-C-Cu-V ., Tenp. C Sn Si kSe" kSi Tenp. C Cu V k? kVo 1426 3.9'2 1.01 1.45 O.ss 1.22 14B 3.n 1.37 1.45 1.as O.24 1484 3.54 1.53 1.49 O.46 1.20 1586 2.52 1.49 1.48 1.21 O.34 15ss 2.53 1.st 1.as O.su 1.os IM3 1.sc 1.eo 1.51 1.os O.40 1623 2.07 1.50 1.41 O.28 1.03

Fe-C-Sn--V Fe-C-Cu-Co Tenp. C Sn V kSo" kVo Tenp. C Cu Ce kCe" kte 1493 3.58 1.46 1.28 O.60 O.2Z 1485 3.50 1.47 l.as 1.55 1.21 1536 3.13 1.33 1.16 O.50 O.31 1580 2.68 1.23 1.30 1.l8 1.12 1613 2'11i.1::I9-ls'4.1-ce.'37 O'40 1643 2'05' 1'85 1'60 l'04 1'03

Tenp. C Sn Co k? kCeO 1483 3.55 1.43 1.41 O.57 1.18 1573 2.69 1.52 1.49 O.39 1.10 !613 2.43 1.46 1.30 O.36 O.96

[s•, A KagGwa et aL .{/.l'!.a.--l!C;'":,/li/IEIie,tff.lw;o'ik'7..,

8 m:./1 ;l- co oC l.2 7 '.-. a-c' B- 'L- S .- 2o.6 A . 2Å~ AA LS DÅ~ Ct' S= o.4 .Å~. . .U Å~ Å~- O.2 '"""-N•V Q08 O.10 Q12 Qva O.rs Cqcbon Mote Froctipn.

Fig.5-2 Change of the equi1ibrium distribution coefficients of various elements with the concentration of carbon in F e -- C base alloys.

-84 --

F e •- C base quarternary systems. In each alloy, carbon concentration were

changed from 2.0 to 3.8 wtX and the concentrations of all solute elements except

carbon were about 1.5wtX.

Figure 5-2 indicates the variation with carbon concentration of the equi-

1ibrium distribution coefficient of the third element in each Fe-C base

ternary system• ln this figure,k8' is the results obtained by Kagawa et al.2,'3)

and kNo'` and kVo are the results obtained in the previous chapter 3• As shown in

Fig.5-2, the magnitude of effects of carbon on the equi1ibrium distribution co-

efficients of various elenents becomes larger in orders of V, Cr, Co, Ni

and Cu. These experimental results are discussed by using the parameter 6

in Eq•(5-7), which shows the effects of carbon on the equilibriura distribution

of these elements between sorid and 1iquid phases in Fe•--i•-C ternary sys-

tem.

6I =(1-k8) .?l (s-7)

Since the concentration of the solute i is assumed to be dilute in this

work, the values of the equiIibrium distribution coefficient of carbon in F e --

C binary system ean be used as kCo in Eq.(5-7). Namely, 6,C• is considered to

be dependent only on ÅíE•:tt . Neumann et al.4) reported that Åít?,t changes

regutarly against atomic nutaber on each period of the periodic table, so that

the variations of the equilibrium distribution coefficients of various etements

vith carbon concentration in Fig•5-2 are thought to correspond to the regular

change of cEtt .

The effects of Si, V and Co on the change of the equi1ibrium distri-

bution coefficient of S n with carbon concentration are represented in Figs.5-3

(A),(B) and (C), respectively. In these figures, chain ljnes show the change of

the equilibrium distribution coefficients of Sn in Fe--C-Sn ternary

-85-

.- 1.2Le

O.8

O.6iv

O.4

cutex>ox

8ex

Sex

O.6

b.4

O.2

1.2

}.o

O.4

Fe-c-sn-si o cs'- Si

'/' Fe-C-Sn-./ .A / i/ /'sn li/ ' -d.i./!"-l-'

Fe-C-Sn-V ' Fe-C-Sr}--./q/ ;;Z'Å~N)BXs .7 -!. ' Fe-C-">"'-s-..-V

t•/Sn

Fe-C-Sn -Co

Fe -CrCO Ns.O-2i{;7-

S3V•S-O

'

-5/// ./.Fe -C-SrtN>/ Sn

/ .Z'

J'

ÅíCsi

6is;i

6Ss;n

Åígin

sg

eVSnÅí"

sn

6"sn

8CsO.

6sC.O

= 9•69, SCs." 19•l

= a-kCo )• Åíg, >o

= (1-kCo )• csC. >O= 10.5

= 7. 18

= (1' kSob•ÅíSs't. <O

=-1.72

= 5.35< O ( From phase diagrasn )

= (1- kVo )• ÅíVs. <O

= 2.09

= (1-kCoO )'eCs'.= --O.387

O.08 QIO O.12 Q14 Oj6 Carbon Mole Fraction

Fig.5-3 Change of the equiIibrium distribution coefficjeBts of Sn, Co, V and Si with the concentration of C in Fe-C-Sn base systems.

system and solid 1ines indicates the effects of the addition of Si, V and

C o. The equilibrium distribution coefficient of S n increases with carbon

concentration in Fe-C base alloys and the additions of Si decrease ko ascan be seen in Fig.5-3(A). Here, sSs'h is given as 7•18 5),positive and large

value. If onty cSs",is taken into account, Si is thought to increase the

equilibrium djstribution coefficient of S n as described in Fig.5-2. However,

-86-

as the equilibrium distribution coefficient of S i is larger than unity jn the

high carbon concentration range, the parameter 6Ss".is negative. So the decrease

of the equilibrium distribution coefficient of Sn with the addition of Si

can be explained by 6gh' . Also, as is illustrated in F'ig.5-3(B), the addition

of V hardly changes the value of kSon and the effecbs of C on kSo"is smaller

than those in Fe-C-Sn alloys. In this alloy, ÅíYs. is shown to be pasi-

tive, but it is known that there exist a few kinds of stable intermeta11ic com-

pounds in v-sn binary a"oys,6) so that the interaction betveen v and sn

is considered to be attractive. In this case, 6g. becomes negative and then

the experimental results can be understood by this negative 6Vsn. Moreover,

Fig•5'3(C) indicates that the effect of the addition of Co on kSo" of Sn is

smal1, in vhich the value of 629.is very smal1 because ÅígR is smaller than egl

li Fe-C-Cu-V 1 .6 / / 8.ei..4 -[E" eeV. = 2.os ./'k Fe - c- cu 6I`2lii7S]22E{{l4tt.-..'/,.-cO.., '. 6M'Ed-i.iso-kVo)'.e"cu>o

'2o.2 X"N..- 1 .6

1.48..e

8.o1.2

1 .o

Fe-C-Cu-Co

.7 -o

-9-;' S- '.fi k:' Fe-c-co

'

l

`s,,

/.•<Fe-C-Cu

'`f

ÅíEo. =-o.23

6CcO. = ( 1 - kCoO )• ECco.

= O.044

O.OS QIO O.12 Q14 O.16 Carbon Mote Fraction 'Fig.5-4 Change of the equi1ibrium distribution coefficients Cu, V and Co with the concentration of C in F e - C --- C u base systems•

-87-

of

and ÅíVs. , and the value of kCoO of Co is about unity• The experimental re-

sults are thought to correspond to this smaller value of 6CsO.. '

The experimental resu1ts of the equi1ibrium distribution coefficjent of

Cu in Fe--C•-Cu-V and Fe--C-Cu-Co alloys are shown in Figs.

5-4(A) and (B), respectively. These figures indicate that V increases the

equilibriura distribution coefficient of Cu and the effect of Co is very

smatI. These results can be interpreted by the use of 6Vc. and 6CcO. because 8E,

is positive and the value of 6g: is very smal1 as shown in Figs•5-4(A) and

(B).

In thjs discussion, the calculated values of Åíg. ,ÅíCsO. ,ÅíVc. and ÅíCcO.

obtained by the follewing equation (5-8)7)are used since the measured values of

these parameters have not been obt}air}ed.

C31' = (-WFe-j+Wi-j -WFe-i) /RT

Wi-j =Vm (6i •-- 6j )2-23o6o R (xi -- xj )2 (s-s)

vhere R is gas constant, Vm the atomic volume of the alloy,6 the solllbility

parameter,x the electronegativity and n the number of A--B bonding. The

nurnerical values8)used for the calculation of Eq.(5-8) are represented in

Table 5-2.

Thus, the S defined in this work js considered to be very useful as the

parameter indicating the effect of the solute interaction on the equilibrium

distribution coefficient of the solute elernent. By the way, the interaction

parameter in liquid was assumed to be equal to that in solid in Eq.(5-4). fn

the previous chapter, this relation vas proposed to be useful for mainly the

interstitiat element ( for exarnple N, H, C ), and DIC was used for the

interstitia1-interstitiat and the interstitia1-substitutiona1 so1ute-inter-

actions. However, it is obvious from the foregoing discusston in this work that

-88-

Eqs.(5-5) and (5-6),i.e.D I C

tiona1 so1ute interactions.

Table 5-2

are also usefu1 for the substitutjonal-substitu-

Values for calculating sl •

e1ement Co de Fe Sn v

solubi1ityparatnetere1ectronegativity

atomicvo1umevalence

1262.16.6

5.78

107•1.97.095.44 1172.0

7.105.78

651.7

16.32.44

5.4.2 Effects of Various Solute Elements on the ELggilibrium Distribution of

Nuabetween Solid andL!t.iggjL{id Phases in Iron Base Multi-

po.mRgpeqtu-gysAll.

tn this section, the influences of various alloying elements on the equi-

tibrium distributien of N, H, S and P between solid and liquid phases in

iron base multi-cotnponent systems, for exasnpIe, stain1ess stee1s and chroinium

steels were discussed by the use of the parameter 6I .The parameter 61 of

N, H, P and S caloulated froni the equilibrium distribution coefficients of

various eiernents9)and the interaction parameterslO"13) are shown in Tabie s-3.

First of al1, the change of the equi1ibrium distributjon coefficient of N

with the concentration of Cr and Ni in iron base alloys is represented in

Fig.5-5. In this figure, the change of the equi1ibrium distribution coefficient

of N is denoted as the ratio of the equi1ibrium distribution coefficient of N

in multi-component system to that in binary one. It is obvious from Fig.5-5 that

the equilibriura distribution coefficient of N increase with the increasing of

nickel concentration and decrease with the increasing of Åëhromium one. Also,

the addition of Mo does not change the dependence of Ni or Cr on the

equilibrium distrihution of N but it decrease t•he absolute value of kNo .

The changes of the equilibriurn distribution coefficients of S and P

-89-

with the concentration of C r and C in the chromium steel are shown in Fig.5

-6 and Fig.5-7(A),(B), respectively. As shown in Fig•5-6, the equilibriura

distribution coefficient of S decreases with the concentration of C r while

it increases vith carbon concentration. Also, kSo increases with the addition

of Si and it decreases with additing Mn. Figs•5-7(A) and (B) show that

kPo increases vith carbon concentration and decreases with chroanium one, and

also it increases vith the addition of S i in the region ef the high concent-

ration of C r .

Consequently, 6ij defined in this work is considered to be a very simple

parameter indicating the effects of the so{ute-interactions on the equ"ibrium

distribution coefficient of the solute elements in iron base multi-component

systems, and it is very useful {n some practical use$•

Table 5-3 Values of 6ii in iron alloys.

.. . . .k6s) Åík,t cAtts> Åí2s•t eg•i5) 6k 6A 6B 6js

Al 6O.ee 1.639) 1.96 3.57va) 4Al O.13 O.157 O.286 O.353B 6O.11 4.995) 3.03 1.4g14) 6.59 4.44 2.70 1.33 5.87

ro.os 4.74 2.88 1.42 6.26c SO.17 7.g9) 3.75 5.4314) 6.23 6.87 3.}1 4.51 5.17

rO.32 5.37 2.55 3.69 4.24Co 8O.94 2.615) O.38 ---t---"- O.58 O.157 O.023 ----"---- O.035

rO.95 O.131 O.O19 ----e""-" O.029Cr 6O.95 -1O.1iO) -O.4 -6.365) -2.29 -O.505 -O.02 -O.318 -o.115

rO.87 -1.31 -O.052 -O.827 -O.298cu 6O.70 2.225) -O.O07 6.Is5) -2.34 O.666 -O.O02 1.85 -O.702

rO.88 O.266 -O.OOI O.738 -O.281Mn SO.90 -4.469) -O.30 O.o5 -5.87 -- O.446 -O.03 o.oo -O.587

rO.95 -O.233 -O.O15 o.oo -O.294Mo 6O.86 -4.610) O.15 ---"---"- O.349 -O.644 O.021 --------- O.049

ro.6o3)

-1.84 O.06 ----i---- O.140Ni SO.83 2.79) -O.05 o.o -O.05 O.459 -O.O09 o.oo -O.O09

rO.95 O.135 -O.O03 o.oo -O.O03si 6O.91 7.89) 3.62 7.78 O.702 O.326 O.691 O.700

ro.so 3.90 1.81 3.84 3.89Ti SO.60

)3)-118.2

-3.61 "-------- -14.1 -47.3 -1.44 -e------- -5.64ro.3o

10)-82.7 -2.53 -------e- -9.87

v 6O.96 -21.2 -1.47 ----e-e-- -3.27 -O.848 -O.059 ------"-- -O.131v 6O.95 -4.610) 1.34 ---)---e- 5.05 -O.23 O.067 --------- O.253

ro.so5)

-2.3 O.67 -"}----i- 2.53Zr SO.50 -237 -3.94 --------- -20.2 -l19 -1.97 --------- -10.l

-90-

Fe-Cr-Ni-N system

ÅëV7a

1.0L

1.02

.oo

Cr

2.S'"

'iDo..?"'S"

ii + l/ ,i, IT

T

z- t-

i:-:u

li '- -

A

:::,

,

. -.2

:::'

:'

Ny..vkl•.p-

{

:

:::1

'

;::

:ioe

:

tL Fe-Cr•-Nlt:: .,- Fe-Cr-Nt-Moi (N M. = O, OLI)

il/

INi

Fig.5-5 Change ofCr, Ni

DIand

C of Mo

N in

with the concentration of stainless steels.

Fe --Cr-C-p S system

kLIS;;{r{S

k$..2

o. s

on2

1.4

1.2

aln

O,OR

5pas

Oni.

Cr

s

-tt-'zz

::,

: : :•l l t

N..."

t l l l l l l

- ;.-l

lN wui o.o6

i'

I

- Fe-Cr-C-Si e Fe-Cr-C -e-Fetr-C-MnIl'

Il

ollo

c

Fig.5-6 Change ofcr, c,

Ds

1

iC ofand

S wi thMn in

the concentration ofchromiura steels.

-91-

A o.es e.lo

Cr;

k;LP;lfS

kp2

Fe-Cr-C-P system

O.06

O.OL

:

;:t

O.02

t,

,I

l,

tt,

I

t

,

t

1.4

1.2

s .

It1,

1

,

t

,

l

t

1

't,

; :.o4. I .06

: l : l

: t : e : : :o.os : • olro

c

B

Fe-Cr--C-Si-P

2.0

16aNi-

utN i.6

ax'

14

1.2

1.0

,

:::

IiIliNc

.i,.fl.

I-

zo

le

t i t i i

!rIII; llli ll

l/i9'.jl' , l

lxl.Slgia

x I l lstNl A

2D

IB

1.6

1.4

12

1.0

Fig.5-7 ChangeCr,

si

ofC

O.08

DIand

Cs

O.06 O.04 k Nsi

of P with thei in chromiurn

o.oz Cr

concentration ofstee1s.

-92-

5.5 Conclusion.

In this chapter, so as to describe the effects of the solute interactions

on the equi1ibrium distribution of solute elements between solid and 1iquid

phases in iron base mu1tj•-component systems, Distribution lnteraction Coeffici-

ent defined in chapter 4 was extended to iron base multi-coraponent systems.

Also, the influences of Si, V and Co on the variation of ko of Sn and

C u with carbon concentration were obtained experiraentally•

The results obtained are summarized as follows•

@ Distribution lnteraction Pararneter(DIP),6ij was defined as

61 = (i -kjo )• sl•

This parameter shows the effect of the element j on kb of the element i in

F e - i - j terna ry system.

@ ko of Sn increases with the increasing of carbon concentration and the

addition of Si decreases kSo"of Sn at high carbon cencentration in Fe-

C base alloys. The addition of V decreases kSo"of Sn and the influence

of C o on kSo" is very small. These experimental results could be explained by

use of DIP.

@ ko 's of Cu and Co increase with the increasing of carbon in Fe--C

-t Cu and Fe-C-Co alloys, respectively. The addition of V increases

k(iY of Cu and that of Co doesn't change kgll of Cu sufficiently in Fe

-- C base alloys. These results could be also interpreted by means cf DIP.

@ Values of DIP of various ailoying elements for P, S, N and H were

determined• Using those parameters, the variation of kNe of N with the con-

centration of Cr and Ni jnstainless steels and the variation of ko of P

and S with the concentration of Cr and C in chromiurn steels were calculat-

ed•

-93-

5.6

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

ll)

12)

13)

References.

T.Mori, M.Fujimura, H.Okajima and A•Yamauchi: Tetsu•-to-Hagane, S4 (1968),321

A.Kagawa and T.Okamoto: Meta1• Scj., 1.4 (1980),5;9

B.A.Rickinson and D.fl.Kirkwood: Met.Sci., ILt (1978), 138

F.Neumann and H.Schenck: Arch. Eisenh'u'ttenw•, lt (1959), 321

G.K.Sigworth and J•F.Elliott: Met. Sci., 8- (1974), 298

M.Hansen: Constitution of Binary Alloys, McGraw-Hi11 Book Company,New York, (1958)

H.Wada and T.Saito: J. Japan lnst• Metals, 25 (1961), 159

T.Sugiyama and S.lnagaki: Denki Seiko, -3-4ny (1963), 469

T.Takahashi, M.Kudo and K.Ichikawa: Solidification of lroB and Steel,A Data Book on the Solidification Phenomena of lron and Steel, ed. bySolidification Comm., Joint SoÅë. Iron Stee1 Basic Research of ISIJ, lSl3,Tokyo, (1977)

F.Ishii, S.Ban-ya and ft.Fuwa: Tetsu-to-Hagane, 6Lt (1982), 1551

F.Ishii and H.Fuwa: Tetsu-te-Hagane, Qt (1982), 1560

Z.Mori'ba and K. Kunisada : Tetsu-to-Hagane, 6m3J (1977), 1663 : Trans• ISIJ,ILt (1978), M8

S.Ban-ya, N.Maruyama and S.Fujino: Tetsu-to-Hagane, 6th9 (1983), 921

-94 --

Chmut6 ' Egyi1ibriurn DistributiQn Coelficient of..m.P..hp-sp.horus in 1ron A!lhtgysl s.•

6•1 lntroduction.

The effects of solute-interactions on kPo of P were discussed thermo-

dynamically in the previous chapters 4 and 5. Furthermore, the absolute value

of kPo is necessary to examine the micro-segregation of P in steels.

In this chapter, the equilibrium distribution coefficients of P in Fe-

P binary and Fe-P-C ternary alloys were determined experimentally to give

value of kPo for a and r phases. Also, the effect of carbon on the equilib-

rium distribution of P between solid and 1iquid phases and the segregation of

P in Fe--C base steels were discussed. The relation between ko of vari-

ous elements for a phase and that for r phase was also studied thermodynami-

catly.

6.2 pmE m-ental.

Also in this chapter, so is to investjgate the equi1ibrium distribution of

P between solid and liquid phases in Fe-P base alloys, solid-1iquid

phases equilibrated were quenched and the phosphorus concentration jn each phase

was determined by EPMA . The apparatus for preparing quenched speciraens

is the same as shown in Fig.5-1. After melting down the sarnple, it was cooled

to a fixed temperature, at which a phase and 1iquid phase coexisted, and

held at that temperature for 30 or 45 minutes. When the equilibrium was

achieved, by withdrawing the stopper, the sample fell through the hole at the

bottom of the crucible and was quenched on the copper plate vith Argon gas blow

as described in 5.4.

Area analysis by EPMA were performed in this experiment so that the

error in the measurement of the concentration of P in the 1iquid phase could

be as small as possible.

-95-

6.3

6.3.1

The

used in

in Table

we re

solid

in both

al1oys

obvious

resu1ts

Resu.Sts and

EguiIibrium

Discussion.

DistributioB Coefficie.nt of'P between a and LL-i-quid Phases

inFe.=twtBin AllL-gys•

compositjons of P and the equi1ibration temperature of the sample

this experiment to obtain kPo in Fe--P binary alloys are listed

6-1. In this vork, five samples were used as shown in this table. The

temperature range vas from 1733 to 1405 K and the equilibration teraperatures

debermined to make the ratio of solid in the sarnples, which included both

and 1iquid phases in the elevated temperature, about 10 X.

Figure 6-1 indicates the experimental results of the concentration of P

sol id and liqu id phases at vari ous tem pe ra tu res in F e - P bi na ry

with the liquidus and solidus published by other investigators.1'"6) As

frem this figure, the present results are in good agreement vith the

by Schifrmann.6) ln this experiment, the solid phase equi1ibrat)ed with

No,

Tab1e 6-1 Cheraica1 composition and equi1ibration im pe ra tu re for F e -- P bi na ry al loys.

Mole Fraction Welght Percent Holding of Phosphorus of Phosphorus Temperature/K

1

2

3

45

O , Ot,l 1

O,053O,089O,l314

O,l51

2,315,025,l27,888,99

17331695160514781405

-96-

1qoo

"z-16002e9Åë

aEth

p 1'400

1200

!'--'-"-"'-----------"----'---'in----'-N'--"'----1 O E.Vaehtel, G.Brbain0963) . U B.SaklatwaU" ogoe}e'vo eM.Kanstantionov ogto) .'v.re. gE,:G.".r,k.e,`,i9,2:,'

olo "" ;iONN bo, e E.schfirrnamz oseo) ii"/ eti. :Noo)irtt.;,x O Present work

6 'oa s,t., '"'.N"NNerN'N

o "cp eNs. "N;rX...,,6' .-' k --."-.-.--...---1. )'-N/

't/

tt

-t t.L ' t l l 1 I t

-"-' t-'-'rt l l l l l

t

Fig.6-1

O 'oo5 O.10 Q15 O.20 O.25 NpExperimental results of phosphorus concentrations inand 1iquid phases in Fe--P biRary alloys.

solid

tiquid one is a phase. Then, using the concentrations of P in both a and

1iquid phase, the equilibrium distribution coefficient, of P for a phase, kPo'ct

were obtained. The tesnperature dependence of the equilibrium distribution

coefficient of P is shovn in Fig.6•-2. As obvious from this figure, the value

of kflo'ctchaRges from O•16 to O•26 in the range of temperature and concentration

of P measured iR this work. Also, kRo'ct increases as the temperature de-

creases, in other vords, the concentration of P increases. Furthermore, the

1inear relation holds between the equi1ibriurn distribution coefficientt of P,

kfblor, and temperature,T within the experimental error as shown in Fig•6-2. tf

the temperature dependence of kRo'or is regressed approximat' ely by an order of

temperature T, the following equation can be derived•

P. ctko = O.72 - 3.2Å~lo'4T (6-1)

When

pure iron,

the equi1ibrium

that is to say,

distribution coefficint of P at the

18e9K, is calculated using the above

me1ting point of

equation, kPo'ct

-97-

Np O.3

R•. o.2

.x

O.1

Fig.6•-2

can be

kPo'or at

amount of

Tab1e

and r phases

gether with

result of

the results

6.3.2

the

As can

for r phase

by Nakamura

ln order

o O.05 O.10 O.15

!i.o/

1609K ;

• i/i/l-

ke•or=O.72 --3.2 •10-"T

' 1800 1600 l400 Temperature [Kl

Temperature dependence of l{e of P in Fe-P binary alloys.

obtained as O.14. kPe'" at that teraperature corresponds practically to

infinite di1ution of P in engjneering stee1s which contajn quite smaH

phospborus.

6--2 gives the equi1jbrium distribution coefficeint of P for both a

equilibrated with 1iquid one pubtished by other workers 7"17)to-

the present results. In this table, the present experimental

kRo'"shows O.14 at infinite dilution for a phase and it coincides with

by chipman7)and wada et ai.8)

Egu!'rmttbmurLupmJDistribution Coeff.icie.nt Qf P fo"r Phase and

Effect of Carbon Qn kLgB •

be seen in Table 6-2, the equilibrium distribution coefficient

was reported as o•o6 by chipman}5) o.os by wada et al.8) and

et al!6) GeneraVly these values are smaller than those for a

to obtain the equiIibrium distribution coefficient of P for

-98-

of P

O.13

phase.

Table 6••2 EquiIibrium distribution coefficient of P for both a and r phases in Iron Alloys.

Phase Composition k?

O.13 Hays&Chipman{1938)O.14 WBdaetal.(1967)

O.15-O.18 2e2,eF,g?Y8g,iyer•Diener

O.O15-O.092{wtX) O.16+O.04 Fischer&Frye(1970)o.2o4-e.211(wtx) O.17 Fischer,Spilzer

&Hishimuma(1960)

a O.2 liller(1959)

O.2-O.5 Smith&Rutherferd(1957)

O.07-O.28(wtX) O.23 Takahashietal.(1977)O.27 Smith&Rutherford

(1957)

O.28 Fischer&Frye{1970)O.23 Nakamuraetal.(1981)O.29 Suzukietal.(l981)

O.04-O.15-{molefrac.)

O.14O.16-O.26 Pfesentwork(1984)

O.06 Chipman<1951)Y '

O.08 Wadaetal.(l967)O.13 Nqkamuraetal.(1981)

r phase, the equilibrium distribution coefficients of P between 1iquid and 7'

phases in F e -- C -- P ternary alloys, vhich contain about O.5 wt% of P, are

measured at the mole fraction of carbon between O.09 and O.16.

The experimental }nethod is the same as described in previous section. The

results are represented ln Fig.6-3. It is obvious from this figure that the

equi1ibrium distribution coefficient of P indicates about e.09 and the effect

of carbon on kPoX can not be seen remarkably in the concentration of carbon

raeasured in the experiment. However,if the equilibrium distribution coefficient

of P for r phase in Fe-P binary system is assumed to be O.06 and the

effect of carbon on kPo'r is taken into account using the Distribution lnterac-

tion Coefficient of C on P, the calculated result given by the chain 1ine in

Fig•6-3 is in good agreement with the experjmental one. Consequently, it is

supposed that the equilibrium distrjbution coeffjcient of P for r phase is

about e.06 and it increases to about O•09 at the high carbon concentration.

-99 -'

t.N th :•.-

csggaox

O.15

O.1O

O.05

e '9 9--g-v` .- .....-.--o'-

t . -.-

o

ogCatcutated vatue

(k?=O.06 by ch;pman)

Present work

By

cient of

6.3.3

ln

is

the

with the

reaction

tion

point of

The

the

O.08 QIO O.12 Q14 O.16 ' Mole Fraction of Carbon Fig.6-3 Change of kPo't of P with the concentration of C in F e -•- C base terna ry al loys.

the vay, the value O.06 assumed as the equi1ibrium distribution coeffi-

P for r phase is consistent with the result by chipman15)

Chan e of the uilibrium Distribution Coefficient and the+>Seglzegaltion

Coefficient of P vith the Concentration of Carbon.

this section, the effect of earbon on the segregation of P in steels

discussed using the results obtained above. Figure 6-il shows the change of

equiIibrium distribution coefficient of P, kPo ,(Fig.6-4(B)) and the

segregation cofficient of P, 1-k6 ,(Fig.6-4(C)) for both a and r phases

concentration of carbon in the range which includes the peritectic

of Fe--C binary system. In these figures, the equHibrium distribu-

coefficient of P can be estimated to be O•14 for a phase at the meltjng

pure iron and O.06 for r phase at the infinite dilution respectively•

effect of carbon on the phosphorus distribution can be also evaluated using

Distribution lnteraction Coefficient. Since the equ"ibriura distribution

coefficient of P in the peritectic reaction region may possibly change between

-- lOO-

<e1809L

O.9O.53A

g dO]7"oaES1667 T

O.15 ; BNt.a"'xliqNNN.,SNN1f-Iiq.

O.05it1

il c0925 'i

/i T-Iiq.1

'O.900ax't"O.875

/'cte/peritectic

liq //S".a.C.tiOn

:tl

: .

,

O.85OOO.2O.4O.6 O.8 1.0

Fig.6-4

Weight Percent of Carbon

Change of the equi1ibrium distribution coefficientand the segregation coefficient of P vith theconcentration of C in Fe-C base alloys.

-101-

kPo for a phase and that for r phase, then the variation of kPo for that

region is hypothetically indicated as straight line in Fig.6-4. As exhibited in

Fig•6-4(B), the equiIibrium distribution coefficjent of P gives about O.14 for

a phase and about O.06 for r phase and it increases slightly with the increas-

ing of the concentration of carbon for both a and r phases. Fig.6-4(C) shows

that the segregation coefficient of P increases as the solid phase equilibrated

with 1iquid one changes from a phase to r one, and it decreases with the in-

creasing of the concentration of carbon in each phase.

The change of the segregation coefficient of P with carbon content is com-

pared with the experimental results of the segregation of P in $teels previous-

ly published by other investigators. Figure 6-5(A) represents the variation of

the segregation coefficient of P shown in Fig.6-4(C) with the concentratien of

carbon up to O.2 wtX• Fig.6-5(B) denotes the change of the concentration of P

in 1iquid phase with that of carbon when the solidification ratio of uni-Adirec-

tional solidified steels is regarded as O.9983, reported by Matsumiya et al)S)

Misueni et al.19) reported the effect of carbon content oB the area where the

segregation ratio of P at the center of the eontinuously cast slab is larger

than 10 X as illustrated in Fig.6-5(C). Fig.6-5(d) gives the experimental re-

sults by lchikawa et al?O) about the influence of carbon on the maximum segrega-

tien ratio of P in the coRtinuously cast slab. All of these figures indicate

that the carbon content dependence of the segregation of P and the segregation

ratio of P increases with the concentration of carbon• Compared with the re-

sults of this work in Fig.6-5(A), it is suggested that the effect of carbon on

the segregation of P in steels depends strongly on the variation of the segre-

gat,ion coefficient of P accompanied with the change of the solid phase equi1ib-

rated with 1iquid one from a phase to r one due to the peritectic reaction.

-1O2--

Aa.x l

'v

O.88

O.87

-c"oo..EeOgep.ut.`aU'5v =a' gzO-sst::,g•

c .9 BU?e6sg$?02a'.5;Na

6 e".9:-SE

aG•Xx

8tl

Fig.6-5

o

8

6

4

2

o,

1 .0

O.8

O.6

e.4

O.2

40

30

20

10

oo

,

Mote fraction of O.O05 '

CarbonO.OIO

6-liq. iPe,' .it .e ,Ctt ii oC

nzone

:

Matumiyaetat..

ocoOrN-o-8.%a.-siLtt

Ichikawaetal.-!o.t''''/'o

Or'-'--

-' g"6--

Change ofthe concentration

O.05 QIO O.15 O.20Weight Percent ot carbonthe segregation coefficient of P with of C in Fe-C base alloys.

-- 1O3-

6.3.4 ThLe!t:!ngdyp@!!d!mdmlRelation between

of Various Solute Elements for

Eg!,!-L!l-LIb r i um Q i st r. .i bu t i on Coeff i c i ents

aPhawwseandthosefor Phase.

As is seen in the previous section, in order to discuss the segregation of

solute elements in F e •- C base steels, it is very irnportant to know the equi-

librium distribution coefficients of these elements for both a phase and r

one.

The purpose of thjs section is to derive the relation between the equi1ib-

rium distribution coefficients of various elements for a phase and those for

?' one thermodynamically and to discuss the validity of this relation compared

with the experirnental resutts. Also, the changes of the equi1ibrium distrjbu-

tion coefficients and the segregation coefficients of vari,ous elements with the

concentration of carbon are studied in F e -- C base steels.

At the infinite dilution of solute element X in iron alloy, the equi1ibri•-

um distribution coefficients ef the sotute element for the equi1ibrium of 1iquid

- a phases and liquid -7' phases, kXo'a and kXo'i, are gjven in the following

equations (6-2) and (6-3), respectively.

RTIn k46a= (aY -Rg ) +RTIn 7, /7,ct (6-2)

RT1nkX6X= (rkk -- rk{)+RT1n7x /7x' (6-3)

The following equation (6-4) is obtained from Eqs.(6-2) and (6-3)•

RTlnkXo'"/ kXo" :(al -ut )+RT1n 7xr /7,pl (6-4)

In Eq•(6-il), the right hand side is equal to Ferrite 1 Austenite Stabilizing

Parameter AGsc'T defined as the the free energy change accompanied by transfer

21)of one mole of each alloying element from ferrite to austenite. That is to say,

1n kXo•"/ kXo" =A G"i'/ RT (6-5)

-104-

lt is clear from Eq.(6-5) that AGxpl'T gives the thermodynamjcal relation bet-

ween k)F6"for the equi1ibrium of liquid - a phase and lel6Tfor that of 1iquid -

r phase. Values of AGff"T of various elements have been reported by many

investigators. particularly, tshida et al.21) reported the temperature depend-

ence of AGg'T of various elements as shown in Fig.6-6• The ratio of kXo'ct/kXoX

can be calculated in Eq.(6-5) by using AGxor'T obtained from the results of

lshjda et al. at 1768K, the temperature of the peritectic reaction in Fe-C

binary alloy. The results are shovn in Table 6-3. As is obvious from this

tab1e, for ferrite stabi1izing elements:

kXdct >kXo•r (6-6)for anstenite stabi1izing e1ements:

kx,•ct <kx,•r (6-7) The relations iR Eqs.(6-5), (6-6) and (6-7) are compared to the experimen-

=oExU•:

,-

nxe(

2000

o

-2000

-4ooo

-6ooO

At9t2i3bo

Nb Si

----`}

.YCLO

vl nyffi

c/'

./xlil/

Ll'(Mn

I

=.aF--.A- '

+ AlA COA Cro Cux Mne Mo•o Nbv Nie SiO Ti

evvW

'

2B 773 1273 17n Teraperature (K)

Fig.6-6 Temperature dependence of Ferrite/Austenite Stabilizing Parameter AG:'r of various elements in iron alloys•

-105-

Table 6-3 Ratio of kXo'ct/kXo'V of various elements in iron alloys.

Element AG"iT(cal) kx,•ct/kx,•r

Ti 1450 L51Nb 1350 1.47Mo 1170 1.40

Ferrite W 1070 1.36Stabi1izing v 900 1.29Elernents Al 760 1.24

si 550 1.17Cr 220 1.06•P 2200 1.87

Austenite co -- 5O O.99Stabi1izing Mn -70 O.98Elements Cu -170 O.95

Ni -360 O.90

tat results of sottie elements14)in Figs.6-7"v6-14 . tn these figures, the rela-

tions for Mo, Ni, Cr, Cu obtained from Eq.(6-5) are in good agreement

vith the experimental or)es. For Mn, the relation in Eq.(6-5) is almost sat-

isfied except the result by Fischer et allO) for a phase.

For P , some reported Åíhat• the equilibriuwt distribution coefficient kRo'"

is O•13 "v O•15 for a phase and about O.06 for r one, others showed kPe'ras O.2

-- O.23 for a phase and about O.13 for r one. However, the vatues reported by

each group are satisfied with the relation in Eq.(6-5) as shown in Fig.6-l4• So,

it seems questionable, for instance, to use the equi1ibrium distribution coeffi-

cient of P as about O.2 for a phase and about O.6 for r phase•

The equilibrium distribution coefficients of V and A1 for r phase

have not been reported, but they can be estimated from those for a phase by

using Eq.(6-5). The results are indicated in Fig.6-15. It is obvious frorn this

figure that kV6r= O.7 -- O.75 for V and kAot'T = O.48-- O.75 for A1• By the

way, it has been already descrived in chapter 4 that the calculated result of

the equjIibrium distribution of V for r phase in Fe-C-V system agreed

-106-

10

o'i` :- -'--"-'-"-- ""- -m,

B

eso' O.5

Ex'

Slope of 1.40

o

Fig.6-t7

O.5kl 4o.T

,

::::::1

::::

E,l!t,

Comparison of calculatedkMoO•"lkMoOtT of Mo withthe experimental results.

1.0-

,.o e"----'

b O.5ti .

N

o

Slope of 1.06

;::::1

::::::::'

v

o

Fig.6-8

O.5k9r, f

Comparison of calculatedkCor•a/k(iSiT of cr withthe experimental resu1ts.

o l.O

.5.

zx'

1.0

O.5

B`"'-o(----

e SIope

o

l-- -.. . 1 ll ll Ilof 090 l l Il lt l Il ll i l•

8--8O.5k.N i.T

1 .0

u. O.52C

.x

[i'

?&--?m

DNs,.

Slope of O.98

Fischer et aE;

;;:::::::

les

:

1.0 o Q5klytn.T

: :

.1 l

l l l I I I

l l l

51.0

Fig.6-9 Cornparison of ca1cu1atedk"eL"lkNo"' of Ni withthe experimenta1 resu1ts.

Fig.6-10 Comparison of ca1culatedkln-orlkMon•r of Mn withthe experiraefital results•

-- 1O7-

Vs

=v.x

1 .0

ot--'-----"-"'---'-

Dr-"'-'---"'--"---B

O.5

SEopeof O.95

o

Fig.6-11

O.5k9u,T

i11

li8

::::::::::::5

Comparison of calcu1atedkCe"'"/kUeV" of Cu Viththe experimenta1 resu1ts.

1.0

1 .o

e. O.5mx•

*--------------- -- -- --l

nu

'

omR<e -.- -- -. -- .. --

Slope of 1.17

t

I

tt

l

l

l

1

1I1ll1ll

oo5

,

't

1

t

'

,

'

'

'lt

l

t

I

l

l

t

1t

,

e

1

1,

l

Fig.6-12

O.5k?i.T

Comparison of ca1culatedkSd •or /kS6•T of s i wi th

the experimenta1 resu1ts.

1.0

6.F'.x

1 .0

lk------------

os l [ k- -----

[i(-

o

, t t s 1 l l l tl tl lloUo

S[ope ot 1.51

t l t l ' 1 t 1 l 1 t l , 1 ''t

O.5kli,t

1.0

b.

a-x

O.3

E I

o.26

6 i EF--

O.1

Fig.6-13 Coraparison of calcu1atedkT6'"lkT6" of Ti withthe experimenta1 results.

Slope of 1.87

o(-•- -•------

o

1

t

l

l

t

1

t1

l

lt

l

;

t

1

}

l

1

1

t

:t

l

1

,

t

t

I

o-6-L 6 O.1

Fig.6-14

k?.TO.2 O.3

Cornparison of ca1cu1atedkPo'"/kPo'T of Pwi'ththe experimenta1 resu1ts.

-108-

U>.ex

IP 1 .0 lk- -- -- -- ------- -- •- ------- , D,Ei-------"- '"-'- -' -" --'- l i lk -' ---- "'--- -' --"--- 'O'B st.p. .f li • O•s glolp2e4 ir//f.; /29 ,)lljl' ,{'•:oli40`--"-'-"---"',//11' 'li

-' bhs- . O.f8' o.?s O O.2 O.4 O.6 O.8 1.0 O O.2 O.4 O.6 Q8 -. kY" k."t" Fig•6-15 Estimation of kVo'X and kAoLTfrorn kXo'ct/kXo•T.

with the experiraental one vell when the value O.76 was used as kVdr.

Figure 6-16 shows the variation of the segregation coefficjents of varieus

alloying eleinents with the change of solid phase equilibrated with "quid one

from a phase to r one due to the peritectic reaction in Fe---C base

steels. In this figure, the abscissas indicates the concentration of carbon up

to O•8 wt% where the peritectic reaction is included. As is seen from Fig•6-16,

the segregation coefficients of the ferrite stabi1izing elements increase with

the increasing of the concentration of carbon, on the other hand, those of the

austenite stabi1izing elements decrease.

Fjgure 6--1'7 represents the experimental result,s of the variations of the

segregatioR ratios for cr and Ni vith carbon contents.22) fn Figs.6-s and

6-17, P and C r are ferrite stabilizing element and their segregation ratios

increase with carbon content, while N i is austenite stabilizing element and

the segregation ratio of Ni decreases. Consequently, the calculated results

from Eqs•(6-5),(6-6) and (6-7) are in good agreeraent with the experiwtental ones

-- 1O9--

.

1.0

Fig•6-16

1.0

Per;,tect':c(ct •-x-- reaction zone -- x-----7-

O.8

-'ie- o.65o

2..o...o.4

g99ut O.2

o

- --

"--

-- -- p

-- -

P..--"- - .. Nb .."-' .... -.'

t-t x ' tt Ti ..-' e---tv tt tt -dt Mo.-". ... -- ;;.t '.:... -C.u. .. .-.-. -. .. -.- - nt .-

-- t ...v.s...Ni Si -`'"' xv-e-' .--""M'E "Ns -. Cr .-: -.;v .t -.-.ta s=t== :" 7 --:.- ==pts co

O O.2 O.4 O.6 Carbon Weight PercentVariation of the segregatjon coefficien'bs ofwith carbon content in Fe-C base alleys•

O.8

varlous elements

5

9.0

4'9'

..C-3g9o2

utÅë

IBo

Ez-.--m to I

m

Doi?

D

z?5o=O.- g•

'gg

aq

1 .4

Q2 Q4 Carbon

Q6Weight

O.8Percent

1.0

1.2

1.0

o O.1

CarbonO.2

WeightQ3 O.4 Percent

O.5

Fig•6-l7 Variation of the segregationcarbon content in steels•

ratios of Cr and Ni with

-- 11 o-

6.4 Conclusion.

In this chapter,the equi1ibrium distribution coefficients of P in Fe--P

binary and Fe-P-C ternary systems were obtained experimentally and the

carbon content dependence of the equi1ibrium distribution coefficient of P was

discussed using Distribution lnteraction Coefficient. A1so, the re1ation bet-

ween kRo'crfor a phase and that for r one was derived thermodynamieally.

The results obtained are summarized as fotlows.

O Temperature dependence of kPo'or for a phase in Fe-P binary alloy is

given by

kRo' ct = o. 72 - 3.2Å~ io'` T

For the above equation, kPo'" at infinite dilution of P is O.14.

@ kPo'Tfor r phase at high concentratjen of carbon from O.09NO•16 is about

o.e9. kPo'r increases vith the concentration of carbon and kPd'at infinite

dilution is O.(}6.

@ The increase of the segregation ratio of P with carbon content in steels

is dependent on the change ef the equilibrium distribution coefficient of P

accompanied vith the transformation of the solid phase equi1ibrated with Iiquid

one due to the peritectic reaction.

@ The equilibrium distribution coefficients of solute element X, kXo'or,for

a phase and iefdrfor r phase are related te Ferrite / Austenite Stabi1izing

Parameter AGoriT as shown in the following equation.

1 n kXo'or/ kXo'T = A GR"/ R T

The ratio of kXo'cr/kXo'T can be caFculated from AGsc" .

@ For ferrite stabilizing elements: kXo'ct >kXo'T

and for austenite stabilizing elements: kXo'" <kXo•T.

@ ln Fe-C base steels, as the solid phase equi1ibrated with liquid one

changes from a phase to 7' phase with the incr'easeing of the concentration of

carbon due to the peritectic reaction, the segregation coefficients of ferrite

stabilizing e1ements increase whiIe those of austenite stabj1jzing elements

decrease.

-- 111-

6.5

1)

2)

3>

4)

5)

6>

7)

8)

9)

10)

11)

l2)

l3)

l4)

15)

16)

l7)

18)

19)

20)

21)

22)

References.

E.Wachtel, G.Urbain und E•Ubelacker: C•R•hebd. Seances, Acad. Sci. 257(1963) S.2470

B•Saklatwafla: Meta11urg., -5. (1908), S•331 u.S.711

W•Konstantinov: Stahl u. Eisen, at (1910), S.1120

E•Gerke: Metallurg., 5 (1908), S.604

R.Vogei: Arch. Eisenhuttenwes., 3 (1929/30), S•369

E•Schurmann und H.P.Keizer: Arch. Eisenhijttenwes., Sl. (1980), 325

A•Hays and J.Chipman: Trans. AIME, !at (1939>, 85

T.Wada and H.Wada: The Abstract for the 61st Lecture Meeting of Japanlnstitute of Metals, JIM, Sendai, (1967), 174

?i8g$;Sg15•RUttiger, A•Diener and G•Zahs: Arch. Eisenh'u'ttenwes., ooo

W.A.Fi$cher and H.Frye: Arch. Eisenh'u'ttenwes., AL/ (1970>, 293

V.A.Fischer, ".Spilzer and M.Hishimura: Arch. Eisenh'u'ttenwes.,31 (1960),365

W.A.Ti1ler: jtSl, .!IX2 (1959), 338

R.L.Smith and J.L.Rutherford: J.Meta1s, 9 (1957),478

T.Takahashi, M.Kudo and K.Ichikawa: Solidification of lron and Steet,A Oata Book on the Solidification Phenomena of lron and Steel, ed. bySolidification Comm., Joint Soc. Iron SteeL Basic Research of ISIJ, ISIJ,Tokyo, (1977)

J•Chjpman: Physical Chemistry of Steelmaking Committee, Iron and SteelDivision, AIME, Basic Open Hearth Steelmaking, The American Institute ofMining and Meta11urgica1 Engineerjng, <1951), 632

T.Nakaraura and H.Esaka: Tetsu•-to--Hagane, 6LZ (1981), S140

S.Suzuki, T.Umeda and Y.Kimura: Tetsu-to-Hagane, -6Z (l981), S142

T.Matsumiya, H.Kajioka, S•Mizoguchi, Y.Ueshima and H.Esaka:Tetsu-to-Bagane, 69 (1983), A217

H•Misumi and K.Kitamura: Tetsu-to-Hagane, St (1983), S964

H•Ichikawa, M•Kawasaki, T.Watanabe, M.Toyota and Y•Sugitani:Tetsu-to-Hagane, 6.9 (1983), A213 'K•Ishida and T•Nishizawa: J. Japan Inst. Metals, +3.6. (19t72), 270

T•Okamoto: Solidification of lron and Stee1, ed• by Solidification Comm.,Joint Soc• lron Steel Basic Research of IStJ, ISIJ, Tokyo,(1977).

'

-- 112-

!E;g!y i1.i briura Distribution

.sC.Ln-a-p!L!h tr7

of Gaseous Elernents between Solid and Liguict Phases

i/nmE-e.-Cm{nFeCoL.-ltYLaj)iand CuBase=fA!-L!Qyslt •

7.1 tntroduction.

Informations on solubi1ities of gaseous elements in iroB base alloys are

necessarily iraportant for understanding of their physico-cheinical behaviour in

steels and also for developing high quality of steels• ln general the solubili••

ties of N and H in 1iquid iron alloys seera to have fairly been established.

Besides that, the detail information about the behaviour of gaseous elements in

alloys during solidification is necessary to discuss the generation of bubbles

during solidjfication, the influences of gaseous elements on physical and me-

chanical properties of alloys and so on.

In this chapter a simple equation of the equilibrium distribution coeffi-

cients of N and H between solid and 1iquid phases in iron alloys was derived

thermodynamical1y. Also, Distribution Interaction Coefficient (D I C) and

Distribution fnteraction Parameter (D I P) vere applied to the evaluation of

ko of N and H in Co, Ni and Cu base ternary alloys and the effects

of various alloying elements on the equi1ibrium distribution of these gaseous

elements between solid and 1iquid phases in these alloys were presumed.

7.2 Eguations foi[Etgg-L!-tibriupt Distributign Coefficient of wwin Iron

B!t$.e--iA!ugysll•

As stated in the

of elemeRt i( i=N

in k8 ' (Rl• -

+ ( ,ll •i-

Since it is well

previous chapter, the equilibrium distribution coefficient

or H) in Fe-i-X ternary system can be shown by

th ?. ) /RT+ 1 n fa l• /7?•

El•'Skj) Nl• + (e5• '1-- Eli'Sk5) Nl (7-1)

known that the dissolution of nitrogen or hydrogen in pure

-113--

iron, either in the 1iquid state or in the solid one, obeys Sievert's law, the

self-interaction pararneters of nitrogen or hydrogen in iron are shown as

ei• #O (7-2)

As a;ready mentioned, Mori and lchisel) proposed that a linear relation

bolds approximately between e of some eleinents X in ljqujd phase and Åí in

austenite and the gradient of this straight 1ine becomes unity as the ternpera-

ture of the 1iquid phase approaches that of solid one. So, the following equa-

tion can be assumed at the temperatures at which the 1iquid and the solid

coexist.

c\•'1* c5•'S (7'3)

Substituting Eqs.(7-2) aRd (7-3> into Eq.(7--1) yields

ink3 = (a l• -Åë• ) /RT+ in fa l• /7 ?•

+(1 --k,X) .l. ,I NI (7-4)

The above equation describes that the equilibrium distribution coefficient

consists of the terms (a1• --B?• )/RT+1nfa l• /fa ?• being dependent on the

property of nitrogen or hydrogen and the term (1 -- kXo ) e5• 'INlshowing the

the effect of the alloying .element X on ko•

On the other hand, as the same way described in Eq.(7-1) , the equi1ibrium

distribution coefficient of the alloying element X, ko is given by

1nkoX --- (thl -- ti:) /RT+in71 /f9

+ (g ,l-<,skE ) Nl + (gl,1--• Egl,sk ,i) Nl. (7-s)

As the fourth term of the right-hand side of the above equation shows

the effect of element i on ko but the i is gaseous elernent and its solubitity

-- l 14-

is quite smal1, this term can be neglected. The third term of the right-hand

side of Eq.(7-5) indicates the dependence of ko on the concentration of X.

The contribution of this terrn to ko is known to be much smaSler than that of

the first and second terms of the right-hand side of Eq•(7-5)• So this term can

be ignored, too• Thus, ko depends on only the first and the second terms

(al - a9 ) /RT+in 71 /7R

and it can be considered to be constant at a given temperature.

Consequently,ko can be calculated by substituting the thermodynaraic data

into Eq.(7-4). Also, the effects of various alloying elements X on ko can be

discussed.

It is obvious from Eq.(7-4) that the fundamental factor control1ing ko of

nitrogen and hydrogen,

(thl• --b?• )/RT+in71• /f?•

is equal to ko of these gaseous elements in Fe-N and Fe-H binary

systems. Nainely:

(al• -- b? ) /RT+ i n di l• /f\

= 1nkg (Fe-'i binary system)

ln order to,obtain the fundamental factor control1ing ko in F e -=- 'i --X

ternary systera, ko 's of nitrogen and hydrogen in Fe--N and Fe-H

binary systems are estimated as follows. Figure 7-1 shows the temperature de-

pendence of the solubilities of nitrogen and hydrogen in Fe-N and Fe-Hbinary systems.2) ln this figure, extrapolating the solubility curves, we can

obtain the solubi1ities of nitrogen and hydrogen in both the solid and the

1iquid phases at a given temperature and subsequently ko . Thus, the factor

(al• --a?•)/RT+inA• /f?•

can be estimated as shown in Table 7•-l.

Also, the second term of the right-hand side of Eq.(7-4) indicates the

effects of various alloying elements on ko of these gaseous elements, but

this term is equal to DIC and it was already stated in detail in chapter 4•

--115-

20

15

"o'z"iO

z

5

O.37

o

FerN

ct

9.84

system

'

17.Btiql }5.6

''

''t

'''

't-'t

t

r lellK,

8.45 -"------.

1667K65K

6t -----4.46

1.42

-"e.d- .-

" 3.73

-"

1000 1200 1400 1600 IBOO 2000Temperatvre {K]

Fig.7-1 Solubilities of

20

15

"9"=lo

z

5

O.37

o

Fe-H system17.2

ti'

,14.0

'

1611K

5.5.4""'

--e-'t'

1e"v2.77 -ee-'

'3.69

11B5Kd' 1.18

1000

nitrogen and

t200 1400 1600 Temperature tK]

hydrogen in iron.

IBOO 2000 •

Table 7-1 EquHibrium distribution ceefficients of nitrogen and hydrogen.

TemP.[K] [Oc]

NN.10"sol. Iiq.

Nke Nsol

.10"H. Iiq.

kH o

15QO 1227

i600 1327

i700 l427

1800 1527

y8.90 11.862.90y8.60 13.163.40y8.30 14.263.90y8.00 15.464.40

O.7S y4O.24 62O.65 y5O.26 63O.58 y5O.27 63O.52 y6O.28 64

.

.

.

.

.

.

.

.

6e 8.70 O.5380 O.3220 10.4 O.503S O.3275 12.1 O.4780 O.3130 13.8 O.4630 O.31

-11 6-

7.3

Nmbd between Solid. and Liguid Phases in==CL,---,o Ni and Cu

Base ALILgys•

Mukai3)showed that there exist the distinct correlations between the inter-

action parameters of alloying elements on nitrogen or hydrogen and the number of

effectiv' e free electron in 1iquid iron alloys. He also represented the same

correlations for 1iquid cobatt, nickel and copper alloys. So, the interactions

of nitrogen or hydrogen and various alloying elements in these nonferrous alloys

are considered to be caused by the same mechanism of the interaction in iron

altoys. Kato et al.4'5) also represented that the correlation holds between the

interactions of alloying elements on hydrogen in iron base alloys and those in

copper base ones. Then, the relations between the interaction parameters of

alloying elements en N and H in iron base alloys and those in cobalt, nickel

and copper base alloys are given in Figs.7-2--- 7-m6.4"18) }t is obvious from these

figures that the distinct correlations exist particularly in Figs.7•-2 -v 7-4.

Consequently, it is thought that as the interactions of alloying elements

on gaseous elements in cobalt, nickel and copper base alloys are seemingly based

on the same mechanism in jron base alloys, DIC and DIP can be applied to

these nonferreus alloy systems.

In the definition of DIC and DIP, the equilibrium djstribution coef-

ficient of the alloying elements, kXo , is stric"y that in ternary alloys.

Since, however, the solubjljty of gaseous elements in alloys is very smalt, the

effects of these gaseous elements on the equilibrium distribution coefficient of

the alloying etements is negljgibly smal1. Thus, it is assumed that the equi-

librium distribution coefficient of the alloyiRg element in binary alloys can be

used as kXo in DIC and DIP.

The data of the equi1ibrium distribution coefficient of the altoying ele-

ment obtained from the phase diagrams by "ultgren et al.19) and Hansen20)are

applied to the eqvi1ibrium distribution coefficient of the altoying element in

the definition of D I P. The calculated results of Distribution tnteraction

-117--

Effects of Various Solute Ele.ments op. .the ELqgit/lbbriurn Distrlbution of

8 .F

xzo

10

o

-10

-20

oSI

ONi-OAtOFe'

8".o ocu

ocr

oib

OTaov

-- 20 -lo

ek h Fe

o

`

8 2 •!

x=o

o

ow sO."i

OMO// OFe tocr

OB

os;

/

ONb ONiOlMn OCu

-2 oeXH ',n Fe

2 4

Fjg.7-2 Relation between Åírsin liquidCo alloys and Åí<in tiquidF e al loys.

Fig.7-3 Relatjon between eXHin liquidC o alloys and cit in 1iquidF e al loys.

E sxzo

o

-lo

-20

oor

ow/

OMo

OAt / oceOFe

-}o •- 5

ek }n Fe

o

6

4

2' .gxz 2o

o

ow

OMoos

ov

OAt

Fe

ocooor

ocu

-2 oell ;n Fe

2 4

Fig.7-4 Relation between Åí<in 1iquidNi alloys and skin 1iquidF e al loys.

Fig.7-5 Relation between Åíain IiquidNi alloys and ÅíXHin 1iquidF e al loys.

-118-

8 sx=-o

10

5

o

-5

opos

osn

OAI

os;

OMn

FO. OCo

lON;

Parameter of various

indicated in Tab1e

N 7-11 represent

tion of the alloying

ures that the alloying

and hydrogen have

e1eraent indicating

crease tho$e coefficients

of various a11oying

change in almost similar

O 2 4 ea in F.

Fig.7-6 Relation between Eain liquid C u alloys and eA in liquid Fe alloys.

elements on gaseous eletaents,65 = (1-kXo ) Åíestt,are

7-2 wjth the data4"17,19,20)used in the calculatjon• Fjgs•7-7

the variation of DIC 's of N and H with the eoncentra-

elevaents in various alloys. It is obvious from these fig-

elements denoting the repulsive effects against nitrogen

the tendency to increase DIC 's of N and H, while the

the attractive effects against these gaseous elements de-

of N and H. Also, it can be seen that DIC 's

elements on N or H in cobalt, nickel and copper alloys

' ' tendency for each element and in each atloy.

-119-

Table 7-2 Data of Åíl" Nlin Co,

,kXo

and and calculatedC u al loys.

results of 65 = ( 1-kXo ) ' Åílc,t

'Cohaitalloy Nickelalloy Copperal1oy

Nitrogen,kX,i9•20)e:J-,6)6:'

Hydrogene:jt7)6a

NitrogenkX,,9,20)c:J6k

HydrogeníAJ6A

ydrogenkX,i9,20).:J6:

ldgAuboCrdeFeMnboNbNiS

bsiS

nTaTivZn

.ss3.71.7O

.80-8.8-1.8O

.49-2.2-1.1O

.952.8O.14O

.64-2.4-O.86O

.47-14.7-7.8O

.955.5O.za'O.4512.66.9O

.13O

.25-18.4-•13.8O

.47-84.3-44.7O

.36-20.0-12.8

.0O.9o

.oo.o-O.85-O.43O.31O.02-

O.68-O.36O.90O.32o.oo.o-

O.46-O.022

.81.M2

.01.74

.84O.O'O)O.OO

.25O

.g5-1.249)-o.o6O

.80-26.6e)-5.3O

.54O

.80-3.3e-O.66O

.80-15.8iO)-3.2O

.51I

o)O.71-41.1-12.0o

.so

.glS)o.so3

.5H)2.6o

.7314)o.o4o

.s13)o.10o

.33t4)O.l51.2i4)O.243

.4M)O.os3

.oi3)1.sl

5}2.5O.25

.6o3.6i6)1.4O

.24-o.47i7)-o.36O

.58-1.917)-o.soO

.60-1.15)-o.44O

.1513.05)11.1O

.494.84)2.4e

.ls6.o4)4.gO

.826.s5)1.2

1 2O --

1.4

v'

sC-12g-.

<6

t-•

1.0

se

Sn

si

A:Zn

A9MnAu

o Mole

Fig.7-7

1.2

8e-

.C

:.zx•

AX1.0Vnz.:

O.B

si

Ta Y Nb

O.02 O.04 O06Fraction of AIIoying Element

Change of DIC of H in Cu alloys vith varieusalloying elements•

Al

NiFe

MoCuCr

o

Fig.7-8

OD2 O.04 O.05Mole Froc!ion of Atloying EIement

Change of DIC of N in C o al loys wi th vari ous alloying e1ements.

1.lo

81.osAC

9-.

AX-

\.ts

1.00

sSi

Al

Mo

FeNi

MnCu

o

1.0

2' c.:4- O. B9'-'

2-}

t

O.6

'

Fig.7-9

AlCoFe

Mo

Cr

Ti

O02 OD4 O.06Mole Froc{ion of AIIoying Eternent

Change of DIC of H in Co alloys with various alloying elements.

o

Fig.7-10

O.02 O.04 O.06Mole Fraction ot Attoying Element

Change of DIC of N in Ni alloys with various al1oying eteraents.

-- 121-

Au

1.10 si

i

Al rev tt Cu 1.oo Co o o.o2 ao4 o.o6 Mote Froction of Atloying Element

Fig.7•- 11 Change of D I C of H in N i al loys wi th vari ous a1loying e1ements.

7.4 Conclusion.

in this chapter, the equilibrium distribution of N and H between solid

and liquid phases in iron, cobalt, nicket and copper base atloys were discussed

thermodynamically. The resuVts obtained are summarized as folIovts.

@ The simp1e equation describing the equHibrium distribution coefficients

of nitrogen and hydrogen, kNo and kHo , in iron alloys were derived thermodynam-

ica11y in the following equation.

1n k5 = (ft1 •-• a7 ) /RT+1n (7it / fa7 )

+ (1 -- kXo )• el L•Nft

@ The effects of various alloying elements on the equilibrium distribution of

nitrogen and hydrogen between solid and liquid phases in nickel, cobalt and

copper base alloys were calculated by means of DIC and DIP.

-122-

7.5

1)

2)

3)

4)

5)

6)

7)

8>

9)

10)

11)

12)

l3)

14)

15)

l6)

17)

18)

19)

20)

References.

T.Mori and H.Ichise: j•Japan inst• Metals, Lt 0968), 949

Basic Open Hearth Steelmaking, ed. by Physical Chemistry of SteelmaingComm•, The Metallurgical Soc. of AIME, New York, (1964), 646

K•Mukai: J.Japan lnst. Metals, at (1974), 271

E.Kato and T.Orimo : J.Japan Inst. Metals, &t (1969), 1165

E.Kato and H.Ueno: J.Japan Inst. Metals, &t (l969), 1161

R.G.Blossey and R.D.Pehlke: Trans. Met. Soc. AIME, 236 (1966), 28

F.E.Voolley and R.D.Pehlke: Trans. Met. Soc. AIME, -2-33 (1965), 1454

J.C.Humbert and 3.F.Et"ott: Trans. Met. Soc. AIME, 218 (1960), 1076

R.G.Blossey and R.D.Pehlke: Trans. Met. Soc. AIME, -2m36.ny (1965), 566

V.V.Averin, A•V.Reviakin, V.S.FedorcheRko and L•N•M.Kozina:Nitrogen in Metals, The New Japan Soc. Casting and Forging, Osaka,(1979)69 and 80

K.W.Lange und H.Schenck: Z. Metallk., St (1969), 639

K.W.Lange und H.Schenck: Z. Metallk., m6.Q (1969), 63

H.Schenck uBd K.W.Lange: Arch. Eisenchtittenw., 39 (1968), 673

".Schenck und K.W.Lange: Arch. Eisenchtittenw., .3.r7h (1966), 739

T.Bagshaw and A.Mitchelt: J.Iron Steel Inst. (London), rZ-Om4. (1966), 87

P.Rontgen und W.Moller: Metal Wirtschaft, Lt (1934), 97

A.Sieverts und W.Krumbhaar: Ber. Deutsch. Chem. Ges., v4-3 (1910),893

G.K.Sigworth and J.F.El1iott: Met. Trans., 8 (1974),288

R.Huttgren, P•D.Desai, D.T.Hawkings, M.G:eiser and K.K•Kelley:Selected Vatues of the Thermodynamic Properties of Binary Alloys, ASM,ehio, (1973)

M.Hansen: Constitution of Binary A1loys, McGraw-Hi11 Book Company,New York, (1958)

'

-- 123-

ghLma.pÅ}e r r8-

S-u..pm.a-cy

ln this work, in order to explain the mechanisms of the equiIibrium distri-

butions of the solute elements between solid and 1iquid phases in iron alloys,

which are closely related not only to the miÅëro-segregation of the soiute but

a1so to various phenomena during so1idification, the physico-chemical character-

istics of the equilibrium distribtition coefficients and the influences of the

so1ute interactions on the equi1ibrium distributions of the solute e1ement

between sotid and liquid phases in iron alloys were discussed experimentally and

theoretically.

In chapter 1, the metallurgical significance of the studies on the equi1ib-

rium distribution of the solute eleraents between solid and liquid phases in iron

alIoys was described. Also, the surveys and problems of the studies published

by the other investigators were pointed out.

The experimental procedures to obtain k{!} were discussed in chapter 2.

In this method, the solid-liquid coexisted phases were quenched and the concent-

rations of the solute elements in both solid and Iiquid phases were measured by

EPMA to determine ko . The diffusion of the solute at the interface bet-

ween solid and liquid phases during quenching, which js one of the serious

problems in this experiment, was discussed. Consequently, the results showed

that this method was valid for even the F e - C alloys including carbon whose

diffusivity is very 1arge.

The influences of carbon on kXo of the solute elements in Fe-C base

ternary alloys were s'tudied experimentally and theoretically in chapter 3. Also,

the factors governing kXo of the solute element were discussed• The fundamental

factors to determine kXo are thought to be both the free energy of fusion of 'the solute element X and the difference of the interchange energies of iron

with X between solid and liquid phases which is mainly based on the size mis-

match energy in solid solution. Furthermore, the equi1ibrium distribution coef-

--124--

ficient of the solute element seems to change periodicalIy against the atomic

nuanber of the element in iron base binary alloys• Particularly, in Fe-C

base ternary alloys, it is considered that the most important factor control1ing

ko of the third eleraent X is the interaction energy between C and X , and

with the increase of carbon content, the equi1ibrium djstribution coefficient of

the third elernent X, kXo ,increases for the repulsive interaction between C

and X while kXo decreases for the attractive one•

ln chapter 4, the effects of the solute-interactions on kXo of the solute

element X in iron base ternary alloys were discussed thermodynarnically and

Distribution lnteraction Coefficient (DIC), which is the ratio of kXo in

ternary system to that in binary one, was defined. This coefficient is the

siraple pararneter giving the variation of kXe with the addition of other alloy-

ing element. Also, the changes of kXe of some third elements with carbon con-

centration in Fe-C base ternary systerns calculated by means of D I C were

in good agreement with the experimental results. Furthermore, the variation of

ko of N, H, P and S with the additions of various alloying elements were

predicted by using the above DIC.

The Distribution lnteraction Coefficient in iron base ternary systerns

defined in the foregoing chapter was extended to iron base multi•-component sys-

tems and Distribution lnteraction Parameter ( DIP), 61 , vas defined in

chapter 5• This parameter Sl• shows the effect of the element j on kio of

the element i. Also, in this chapter, the influences of Si, V and Co on

the variation of ko of Sn with carbon and the influences of V and Co

on the variation of ke of Cu with carbon were obtained experiraentally, and

those results could be explained by using DIP. Furthermore, the DIP 's of

various alloying elements for P, S, N and H were determined• Using those

parameters the variation of ko o{ N with the concentration of Cr and Ni

in stainless steels and the variation of ko of P and S with the concentra-

bion of Cr and C in chromium steels were calculated.

In order to reveal the mechanisms of the micro-segregation of P in engi-

--125-

neering steels, the temperature and concentration dependence of kPo of P and

the effects of carbon on kPo were obtained experimentally in chapter 6. The

result showed that kPo for a phase at infinite dilution of P was O•14 and

that for ?' phase was O.06. Also, the effect of carbon on the segregation of

in F e -- C base steels was djscussed. Thus, it has become clear that the in-

crease of segregation ratio of P with carbon content in Fe-C ba$e steels

is dependent on the change of the equi1ibrium distribution coefficient of P

accompanied with the variation of the solid phase equi1ibrated with 1iquid one

due to the peritectic reaction. Hence, in order to discuss the segregation of

the solute elernents in Fe-C base steels, it is very important to know kXo

for both a and ?' phases. Then, the relation between kXo for a phase and

that for r one was derived therinodynamically. It was found from the relation

derived above that kX6or was larger than kXdT for the ferrite stabilizing ele-

ments while kXo'ct was srnaller than kXo'X for the austenite stabi1izing elements,

and also the segregation coefficjent for the former etements increases and that

for the latter elements decreases accompanied with the chaRge ef the solid phase

frora a to r phases due to the peritectic reaction in Fe--C base steels.

In chapter 7, the equilibrium distributions of N and H between so"d and

1jquid phases were discussed thermodynamically and the sirnple equation to deter-

mine ko 's of N and H in iron alloys was derived. Also, the influences of

various alloying elements on ko of N and H in Co, Ni and Cu base

alloys could be estimated by the use of DIC and DIP.

The micro-segregation of the solute elements is one of the most important

problems in the metallurgical processes. So, it is considered that the system-

atical results obtained in this work about the equi1ibrium distribution of the

solute elements between solid and liquid phases in iron alloys would give the

useful information to solve those problems fundamentalry and also they would

contrjbute to more comprehensive understanding of various phenomena during soli-

dification of a1ioys in meta11urgical processes.

-- 126-

ACKNOWLEDGEMENTS

The auther is greatly indebted to Professor Z. Morita of the Department of

Meta11urgical Engineering, Osaka University for his constant help and

constructive discussion throughout the present studies.

The auther would 1ike to express his appreciation to Professor T. Okamoto

of the lnsti'tute of Scjentific and lndustrial Research, Osaka Universjty and

Professor T• Fukusako of the Department of Metallurgical Engineering, Osaka

University for their useful advice and the preliminary examination of this

thesis.

The auther wishes to thank Dr. T• lida, Mr. Y. Kita, Mr. M• Ueda and

Mr. A. Kagawa of Osaka University for their censtant help and useful advice

to the present studies.

-127--

tLub1ications Relevant to the. The..s..1.$•

and

The

some

major part of the present

parts have been revised.

thesis is based on the fol1owing pub1ications

(1)

:

:

:

Partition of Carbon between Solid and

T. ekamoto, Z. Morita, A. Kagawa and T

Trans• ISlJ, 2lh3 (1983),266

Tetsu-to-Hagane, 68. (1982),244

The 19th Comm.(So1idirfication), SapanRep. No.19-10319 (Feb.,1981)

Liquid in F

. Tanaka

Soc.

e-C

Prornotion

Binary

Sci.(JSPS),

System.

(2)

:

:

:

:

Thermodynamics of Solute Distribution between Solid and Liquid Phases inlron- base Ternary Alloys.

Z. Morita and T. Tanaka

Trans. ISIJ, 23- (1983), 824

Tetsu-to-Hagane, ZLt (1984), 1575

Proceedings of the Second japaB-U.S. Seminar on Advances in Science ofiron-and Steelmaking, May (1983), P.37, in Kyoto.

The 19th Comra.(Solidification), japan Soc. Proraotion Sci.(jSPS),Rep. No.19-10429 (Oct.,1982)

(3)

:

:

:

Effects of Solute-interaction onbetveen Solid and Liquid Phases

Z. Morita and T. Tanaka

Trans. ISIJ, -2ny4 (1984),206

Tetsu-to-Hagane, u7-O (l984), 1583

The 19th Comm.(So1idification),Rep. No.19-10521 (0ct.,1983)

the Equilibrium Distribution ofin tron Base Ternary System.

japan Soc. Promotion Sci.(JSPS),

So1ute

-1 2' 8-

(4) Effectsbetween

of SoluteSolid and

lnteraction onLiquid Phases

the Equi1ibrium Distributionin lron Base Multi-component

of SoluteSystem.

Z. Morita and T. Tanaka

: The Rep.

19th Comm.(So1idification), No.19-10535 (Feb.,1984)

Japan Soc. Promotion Sci.(JSPS),

(5) Equi1ibrium Distribution Coefficient of Phosphorus in jron A}loys.

Z. Morita and T. TaRaka

: The Rep.

19th Comm.(Solidification), No.19-10556 (May, 1984)

Japan Soc• Promotion Sci.(JSPS),

(6) Effects of Variousof Gaseous ElementsNi and Cu Baseand Hydrogen ).

A11oying between A11oys

Elements Solid andcontaining

on the Equi1ibrium Liquid Phases in Gaseous Elements

Distribution Fe, Co!( O>cygen, Nttrogen

Z. Morita and T. Tanaka

: The Rep.

19th Comm.(So1idification), No.19-10563 (May, 1984)

Japan Soc. Promotion Scj.(JSPS),

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