Carbon Solubility and Mass Action Concentrations of Fe-Cr-C Melts

Carbon Solubility and Mass Action Concentrations of Fe-Cr-C Melts

Zhang Jian

Metallurgical Engineering School, University of Science and Technology Beijing Beijing 100083, China

ABSTRACT

According to the experimental data from literature sources, an empirical equation of carbon solubility in Fe-Cr-C melts has been regressed. Based on the coexistence theory of metallic melts involving compound formation, the phase diagram of Cr-C system as well as thermodynamic data of Fe-Cr-C melts a calculating model of mass action concentrations for these melts has been formulated . According to this model , the standard free energies of formation for CrC and Cr3C2 have been obtained. Satisfactory agreement between calculated and measured values shows that the model can reflect the structural characteristics of Fe-Cr-C melts.

KEY WORDS Activity, coexistence theory , mass action concentrations, saturated state

Fe-Cr-C melts are the key melts which the production of ferrochrome depends on. They also give direction to the manufacturing of stainless steel, bearing steel and steels containing chromium.

This leads to wide attention of metallurgists to study them. Research on the phase diagram of Cr-C results in relatively consistent conclusionE^1-4J, The solubility of carbon in Fe-Cr-C melts have been investigated by different scholars , though their results are inconsistent yet[s-7J. In regard to the activities of these melts, which also have been studied by several scholars[s-uJ, and useful empirical equations for calculation of activities have been obtained. However, theoretical models based

literature. The aim of this paper is to formulate the empirical equation for carbon solubility and the calculating model of mass action concentrations for Fe-Cr-C melts on the basis of aforementioned experimental results

theory of metallic compound formation.

as well as the coexistence melts structure involving

1 Empirical equation of carbon solubility in Fe-Cr-C melts

In literature[sJ there are experimental data of carbon solubility in Fe-Cr-C melts at temperatures ranged from 1550 to 1800'C, chromium content ranged from 0 to 85. 4

%

and carbon content ranged from 5. 36 to 11. 81

% .

In literature[izJ there are also experimental data of carbon solubility in Fe-Cr-C melts at 1500'C. But in both cases there isn't any empirical equation of carbon solubility in these melts yet. So it is worthwhile to treat these experimental data by regression. In so doing, an empirical relationship of carbon solubility with temperature and chromium content has been obtained as follows:

[%C]=12. 62923-13133. 9/T+o. 063996[%Cr]

(R=O. 995936, F=2446. 605)

Fig. 1 shows this relation. It is seen from the figure that carbon solubility increases with the increase of temperature and chromium content, as increasing in chromium content promotes the formation of greater amount of chromium carbides, which fix

facilitates the solution of chromium carbides in the melts. According to this empirical equation, the

l~

11

,..--,

9 u

~

7

• 1873k

(t 1973

20 40

[%Cr]

60

•

80

Fig. 1 Relationship between carbon solubility and temperature as well as[%Cr]

2 Mass action concentrations 2. 1 Structural units

100

According to the literatureC13J, there are me.tastable carbides FeC, Fe 2C, Fe 3C and FeC2 in Fe-C melts, where it also gives the relationships between the standard free energies of formation ,0.G0and temperature for these carbides.

It can be seen from Fig. 2 C)Jthat there are chromium carbides Cr 3C2, Cr⁷C 3 and Cr23C6 in the Cr-C melts, from which Cr7C 3 has congruent melting point, while Cr3C2 and Cr 23C6 are peritectoids. In addition it is also shown that Cr3C and probably CrC exists in Cr-C binary system.

Literature C2- 4J not only shows the existence of FeCr, CrC, Cr 3C2, Cr1C3 , Cr 3C and Cr23 C6 in Fe-Cr-C melts, but also give us their pertinent thermodynamic parameters.

From the above mentioned, the structural units can be determined as FeCr, FeC, CrC, Cr 3C2, Fe 2C, Cr1C3,Fe3C,Cr 3C,Cr 23C6 and FeC2.

):..>

CJ h

carbon solubility for Fe-Cr melts with different chromium content can be easily predicted.

Atonnc Percent Carbon

2000

or-~,10~~,2,0~~~3~0~~~~4o=---~~~~⁵~⁰~ 1863

1800 L

/ /

'13. 3 1811

±

lo·c

3 1600

(I:

h

"'

c.

E '1)

1400

10 cJ' ,.;

u

Weight Percent Carbon

Fig. 2 Phase diagram for Cr-C system

2. 2 Calculating model

20

Assuming composition of the reactants b1 = LXFe, b2

= (xc,, a= Lxc; composition of products x1 = XFe, x2

=xc,,y=xc, Z1=XFeCr• z2= XFeC• Z3=XcrC• u=Xcr,C,•

w=xF.,c, v=xc,,c, ,g1 =xF•,C• g2 =xc,,c, r =xc,,.c, ,s = XFec,; mass action concentrations of the melts (~ole fractions of the melts after nor-malization Ni= xi/

Lx)N1 =NFe' N2 =Ncr 'N3 =Ne' N4 = NFeCr 'Ns = NFeC' N6 = NcrC• N1 = Nc,,c,, Ns = NFe,C• N9 = Nc,,c,, N10 = NF.,c,N11 =Nc,,c,N12=Nc,,.c,, N13=NF.c,; Lx= sum of equilibrium mole fractions. Then it gives

chemical equilibria:

[Fe]+[Cr]=[FeCr] K1=N,/N 1N2' N,=K1N1N2,

z1=K 1x1x2/2:x ⁽¹⁾

6G⁰=-14550+6. 65T, J/mol[2^l

[Fe]+[C]=[FeC] K2=N5/N1N3,N⁵=K 2N1N3,

z2=K2x1y/2:x (2)

6G⁰=-97043+1l. 63T ,J/mol ^[i3_J

[Cr]+[C]=[CrC] K3=N,/N2N3, N,=K 3N2N3,

z3=K3x2y/2:x (3)

6G⁰=-90526-25. 9l16T, J/moJC2^l

3 [ Cr] + 2 [ C] = [ Cr3C2] K _ N, _ 3 2

, - N3Nzt N, - K,N2N3,

2 3

thermodynamic data reasonable and in conformity with practice, Eqs ( 11), (15) and Cl 6) have been

u=Ku-K,2 v=K41-K,3

Equations ( 11) ', ( 15) ' and ( 16) ' are different expressions of K₄(= CKc,₃c_{2 ).} Having Eqs. (11)' ~

(16)' and (21), K4 in conformity with practice can be evaluated in condition of known Nc,=ac,.

where ac, is calculated by Dresler's equation as follows:

ae, = Exp[ln Cxe,)-5 71/T + 786xe,

/T-215xUT+ ClO. 267-27675/T)xe+9. 164-33610/T)x~+

(-2. 808+15543/T)xexe,J (22)

Using calculated results of equation ( 21), the correctness of the aforementioned model can also be judged to a certain extent.

2. 3 Calculated results and discussions

In the course of calculating the mass action

0. 2

0. 1

0 0. I 0. 2

Fig. 3 Comparison of calculated Ncr with measured ac, for carbon saturated Fe-Cr-C melts

transformed to the following form :

(ll)'

(15)' (16)'

(21)

concentrations with the aforementioned model, it was found that K3(=Kcre) was still too big to make agreement between Ne, and ac,. In order to solve this problem, try and error method was us~d , putting

K3C=Kere)=Exp((90526+25. 9l16T)

/ 4. 575/ 4. 1868/T) /e (23)

changing c from 1 to 8. 6, it was found that when c

= 4, it made Re,= ae./Ne, = 0. 94253 for these carbon saturated melts and gave

6G~.eom-2013K>=-RTlnK3=-90526-14. 3794T ,J/mol (24) substituting this value into Eqs. (11)', 05)', 06)' and (21), it gave

()

'~

0. ~ ~ I

() !87:l

0 1973

• 207:l

I e

i /·~"'

o.:ii-

.~

..

I / •

I ~ o•

l_

./oe•

0. L

i er.

^e-

1

~~o

0.1 , ~<>"'

_ _ L _ _ ~

••

•

0

l(}Jl~

^I

0. I 0. 2 0. :1 0. ~ 0. Ci Her

Fig. 4 Comparison of calculated Ncr with measured ac, for both carbon saturated

and unsaturated Fe-Cr-C melts

,6.G~,3cma23-2onK> = - RTlnK4=-749672.11+231. 3989T,J/mol (25)

Substitution of Eqs. (24) and (25) into the model of mass action concentrations not only made Re,= 1.

014583, but also Re= 1. 002952, hence it satisfied the agreement of both Ne, and N'C with practice.

Fig. 3 shows the comparison of Ne, with measured ae, for carbon saturated Fe-Cr-C melts at different temperatures. It is seen in the figure that the agreement between Ne, and ae, is well.

Fig. 4 shows the comparison of Ne, with measured ae, for carbon sa.turated and unsaturated Fe-Cr-C melts. Though Ne, is a little less than ae,, but the

1. 0 (a) (b)

1873k l 97:lk

difference between them is so little , as to interfere with the preliminary evaluation of the mass action concentration of chromium Ne, for carbon unsaturated Fe-Cr \

I C

melts by using of the calculating model of mass action concentrations deduced in condition of carbon saturated Fe-Cr-C melts, because the calculating model was for mulated according to the mass action law, and its results should be independent of the composi tion of the melts (carbon saturated or unsaturated).

Fig. 5 shows the comparison of the calculated mass action concentration of carbon N'C with

(c) 2073k

0.8 1 l. 45%Cr 1 18. il%Cr

/{

54. l %Cr

2 13.01 2 :n. 6 2 68. 5

3 18. 6 :i 54 2 3 4

:i 78. 2 4

---

^{4 60.5} 4 67. I

o!(j

^{4 85.4}

0 0.6 ro"

I:

- <) 0. 4

z ^{0. 2}

_J,£~0 f ^If

~ ·

0 0. 1 0. 2 0. 3 0. 4 0 0. I 0. 2 0. 3 0. 4 () 0. I 0. 2 0. 3 0.4

xc x,. xc

Fig. 5 Comparison of calculated N'c with measured ac at different temperatures measured ae at different temperatures and chromium

content, except the 4'h curve at 1873 K, where it gives some difference between N 'e and ae, the rest of N'e have good agreement with ac. As the calculated N'e can meet carbon saturated and unsaturated conditions, so the agreement between N' e and ae as well as between Ne, and ae, confirms that the . aforementioned calculating model 1s applicable to different conditions ( temperature, chromium and carbon content), and it can reflect the structural reality of Fe-Cr-C melts.

Why Le varies with temperature, chromium and carbon content ( In order to clarify this problem, a multivariable regression of Le with temperature and

the mass action concentrations of carbides has been carried out, and it gives

Lc=-8153. 38+16477928/T+2706. 363Np,c,-3064. 54NF,c+

515. 4522Nc,c+l058. 687Nc,3C2+23722. 16

Np,2c-l. 1 X lO'Nc,ic3-3548. 38NF<Jc + 4187. 141Nc,3c-9. 1X10¹³ Nc,23c6+4. 58Xl0¹³NF,c2CR=O. 91260, F=27.17629)

(26) From this equation, it can be seen that temperature and various carbides have different effect on the carbon solubility of the melts, raising temperature has the effect of increasing the carbon solubility in the melts, so it makes Le decrease; FeCr, CrC, Cr3C2, Fe2C and Cr₃C have the effect of decreasing

the carbon solubility, so they make Le increase;

FeC,Fe3C,FeC₂₁ Cr1C3 and Cr 23C⁶ have the effect of increasing the carbon solubility in the melts, so they make Le decrease.

Fig. 6 shows the variation of NFe with car-bon and chromium content at 1873 K, It is seenfrom the figure, that NF. decreases with the mcrease of carbon content, however, with the increase of

I 1. 0

0.8

0.6

0.4

1873k

l l. 45%Cr 2 13.0l 3 18. 6 4 60. 5

~

0. 2

~0----;;:--'-:---~L_

^{_ _ __J_ _ __}

_J

0. 1 0. 2 0. 3 0. 4

Fig. 6 Effect of carbon and chromium . content on NF,

chromium content, the tendency of NF. decreasing slows down. The slowing down of the tendency of NF. decreasing with the inc-rease of carbon arises from the consumptionof iron with the formation of iron carbides; while the slowing down of the tendency of NF. decreasing with increasing of chromium contentis caused by reduction of the absolute amount of. iron. The situation of NF.

variation at other temperatures is similar as in Fig. 6

3 Conclusions

0) An empirical equation of carbon solubility in Fe- Cr-C melts based on the experimental data from literature sources has been formulated, which shows that the carbon solubility increaseswith the increase of temperature and chromium content.

( 2 ) A calculating model of mass action concentrations for Fe-Cr-C melts has been deduced.

Based on this model the standard free energies of formation for CrC and Cr 3C2 in conformity with practice have been determined as: LGtcom-2o73 K> =-

RTlnK3 = -90526-14. 3794T, J /mol; LGg,3cmm-201JK> =-

RTlnK,=-749672. 11 +231. 3989T, J/mol.

(3) The calculated results agree well with practice, this in turn shows that the model deduced can reflect the structural reality of Fe~Cr-C melts.

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