Solubility products for titanium-, vanadium-, and niobium-carbide in ferrite

ScriptaMetallurgica et Materialia, Vol. 32. No. 1, pp. 7-12. 1995 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0956-716X05 $9.50 + .OO

SOLUBlLlTY PRODUCTS FOR TITANIUM-, VANADIUM-, AND NIOBIUM-CARBIDE

IN FERRITE

K. A. Taylor Research Department Bethlehem Steel Corporation Bethlehem, Pennsylvania 18016 U.S.A.

(Received July 7, 1994)

Carbide- and nitride-forming elements, such as titanium, vanadium, and niobium, play important roles in the metallurgy of many modern steel products. These elements readily precipitate as stable carbides/nitrides during processing, even when present at relatively small levels. The precipitation of these alloy carbides/nitrides provides a means for controlling strength or hardness, grain size, the level of solute carbon, and other factors that affect properties and performance. Precipitation in austenite during hot deformation has received considerable attention and “solubility products” for many compounds have been published and used as alloy/processing development tools. The technologically important alloy nitrides generally exhibit relatively low austenite solubility. Alloy nitride solubilities in ferrite are even lower and, for practical purposes, can often be considered zero. In contrast, some alloy carbides exhibit substantial solubility in ferrite. However, thermochemical or solubility data on carbide/ferrite equilibria are sparse and, as a result, few experimental ferrite solubility relationships are available. A method is described herein for obtaining such a relationship from a known or assumed austenite solubility product using information on the activity coefficients of the solutes of interest. Solubility relationships for titanium-, vanadium-, and niobium-carbide in ferrite are then derived from published austenite solubility products and available thermodynamic information on binary Fe-Ti, Fe-V, and Fe-Nb solid-solutions.

Thermodvnamic

Formalism

Solubilitv Product The reaction between expressed as:

a carbide-forming

alloying element M and carbon to produce a carbide can be M +xC

=MC,.

(1)

The underlining indicates an element in solid-solution and x is a coefficient that defines the stolchiometnc proportions. At equilibrium the following relation is satisfied:

where K&

x is the solubility product for MC, in equilibrium with matrix phase 4, [Ml@and [Cl@are the matnx

8

SOLUBILITY

PRODUCTS

Vol. 32, No. 1

concentrations of M and C, respectively, AGO,, is the free energy change attending the formation of one mole of MC, from its constituent elements in Iherr standard states, R is the ideal gas constant (8 314 J/mole-DK), T is absolute temperature, and $, and yg are the activity coefficients for M and C In solidsolution, respectively. The standard states assumed here are graphite and the pure body-centered cubic metals. The solubility product, bc,, defines the locus of matrix compositions that would be in equilibnum with pure MC, at a given temperature. If AG& IS a linear function of temperature (reflecting that AG” = AH" - TAP) and activity coefficients are not strongly concentration-dependent, then Eq. 2 can be rewritten aslog,&,c,

=

~o~,,UMl,GJ,)“~s C,fl + C,,

(3)

where C, and C, are constants. (The subscript “e” indicates that [M] and [C] are equilibrium concentrations; this notation is dropped in subsequent sections.) While the thermodynamics of most systems are probably not strictly linear with temperature, Eq. 3 is nevertheless the form in which solubility products are often expressed. From Eq. 2, it follows that the solubility products for austenite (y) and ferrite (a) are related as follows.

or Wh~c, =log,J&, +log&:, where

log,OK$

s

(4b) (4c)

= log,0

The right-hand side of Eq. 4a containing activity coefficient terms IS the ratio of the ferrite and austenite solubility products. The logarithm of this solubility product ratio (Eq. 4c) IS added to the logarithm of the austenite solubility product to obtain a similar function for the ferrite solubillty product (Eq. 4b). That is, Ku can be determined knowing KYand the activity coefficients.

Carbon. Based on experimental results involving equilibration of Fe-C alloys with H&H, or CO/CO, gas mixtures, the following expressions for the activity coefficients for carbon In austenite and ferrite were derived by Ban-ya et al. (1) and Lobo and Geiger (2) respectively

m,*v:=y

+ 2.72log,,,T

- 10.525 (900% 5 T 5 1400°C)

5646 ” =log1oYc - 2.687 T

(680°C < T 2 845°C)

A ngorous descrrption of actrvrty coefficients should include consideratron of solute-carbon interaction effects (i.e , Ti-C, V-C, and Nb-C interactions). However, bulk concentrations of these solutes in many steels of Industrial importance are relatively low Hence, such interactions are often small and are not accounted for in the present treatment. Carbide Formers.

Assuming again that solute-carbon

Interaction effects are small, expressions

for the

SOLUBILTIY PRODUCIS

VoI. 32. No. 1

activity coefficients of Ti, V, and Nb in iron can be derived from free energy functions for binary Fe-Ti, Fe-V, In general, the activity coefficient of M is related to the excess free energres and Fe-Nb solid-solutions. of mixing according to: RTlny,

z GG = G&,

+ (1 -[M])-,

f3GE.,

WJJI

where GE is the partial excess molar free energy for M and G;“,.,,,is-the excess molar free energy of the Fe-M solution. The excess molar free energy is obtained from the integral molar free energy of mixing, AG;t*: G;“,., where

= AG;EM - AGm”,‘d = AG:zM - RT([M]In[M]

+ (1- [M])In(l -[MI)}.

(6)

AGm’x,idIS the ideal molar free energy of mixing.

Application of Eq. 6 to free-energy functions developed by Kaufman (3-5) to calculate phase diagrams results in the expressions for partial excess molar free energies given in Table 1. Functions for activity coefficients follow directly from these expressions (as indicated by Eq. 7) and allow ferrite solubility products to be derived from existing solubility products for austenite.

Results The following carbides are consrdered in the present analysis: TIC, VC,, and NbC,. All of these are MCtype monocarbides with the NaCl (rocksalt) crystal structure. The subscript x is used for vanadium- and niobium-carbide to indicate that these compounds can be carbon deficient (9,lO). The stoichiometry of vanadium carbide is often expressed as VC,_ while that for niobium carbide has been reported as close to NbC,,. Using Eqs. 5 and 6 and the information in Table 1, activity coefficients for C, Ti, V, and Nb were computed and substituted into Eq. 4a to calculate solubility product ratios (K*) over the temperature range 500°C 5 T 5 900°C’. Fig. 1 shows, for each carbide, the mathematically possible range of values for log,,K”” over the span of concentrations [C]a, [CIY, [M]“, [MIY from zero to one atomic percent’. Linear functions of the form C,TT+C, were fitted to mean values within these ranges; the resulting expressions for log&” are given in Table 2 and are also plotted in Fig. 1. The advantage of this procedure is that the resulting functions are mathematically simple (concentration dependences are removed) and of the same form in which austenite-solubility expressions are usually defined. The justification for this approach is that the activity coefficients are not strongly concentration-dependent, as indicated by the relatively small sizes of the ranges in Fig. 1. The expressions for log,,K”‘Y indicate that carbide solubilities in ferrite are considerably lower than in austenite, as expected. For example, at a temperature of 727°C (lOOO”K), values for log,,K”/Y range between about -0.6 and -7.5, indicating that alloy carbide solubilities in ferrite are between about l/6 and l/30 of those in austenite. Austenite solubility products published previously in Refs. 6-8 (Table 2) were used here to obtarn solubilrty products for ferrite, as prescribed by Eq. 4b. The resulting solubility product relationships, wrth the concentration variables expressed in weiaht percent, are given in Table 2 and plotted in Fig. 2. Solubility isotherms for each alloy carbide are plotted for temperatures between 600 and 900°C in Figs. 3-6. As is

‘Activity coefficient expressions were used over this entire temperature range, even though it actually extends beyond the applicable range of some of the present functions (e.g., those for y: and &) 2Bulk [C) and [Ml levels of most steels of industrial importance fall well within this range.

SOLUBILITY PRODUCTS

10

the case for austenite, solubility products for ferrite rank K&

x

Vol. 32, No. 1

<

Fig 2 compares solubility relationships for VC, and NbC, with previous determinations (10-13). For temperatures between about 800 and 9OO”C, the present solubility products for VC and VC,,, are in good agreement with that for VC obtained from internal friction data by Koyama et al. (11) and that for VC given by Todd and Li (12). However, the present values decrease more rapidly with decreasing temperature, especially the solubility product for VC. The solubility relationship for VC,,, derived previously by Sekine et al. (13) from internal friction measurements provides the highest vanadium carbide solubility products; differences between their relationship and those proposed here are relatively small at higher temperatures, but increase to more than a factor of 10 at temperatures below 600°C. Finally, solubility products for NbC are slightly smaller than those for NbC,,, as derived by Sharma et al. (10) using austenite solubility data.

Acknowledaments The author gratefully acknowledges helpful discussions with J. G. Speer and S. S. Hansen, as well as assistance provided by J. L. Clarke with computations and statistical analyses.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

S. Ban-ya, J. F. Elliott, and J. Chipman, Metall. Trans. 1 (1970), 1313-1320. J. A. Lobo and G. H. Geiger, Metall. Trans. A 7A (1976) 1347-1357. L. Kaufman, CALPHAD 1 (1977) 28. L. Kaufman and H. Nesor, CALPHAD 2 (1978) 55-80. L. Kaufman, in User Applications of Allov Phase Diaorams, L. Kaufman, ed., ASM International, Materials Park, OH, 1987, 59-96. K. J. Irvine, F. B. Pickering, and T. Gladman, J. Iron Steel Inst. 205 (1967), 161-182. K. Narita and S. Koyama, Tetsu-to-Haaane 52 (1966), 788-791. B. Aaronsson, Steel-Strenothenino Mechanisms (papers presented at Zurich during May 5-6, 1969), Climax Molybdenum Special Publication (1970), 77-87. J. H. Woodhead, Vanadium ‘79 (papers presented at Chicago during November 7, 1979) Vanadium International Technical Committee, Al-A14. R. C. Sharma, V. K. Lakshmanan, and J. S Kirkaldy, Metall. Trans. A 15A (1984) 545-553. S. Koyama, T. Ishii, and K. Narita, J. Jon. Inst. Metals 37 (1973), 191-196. J. A. Todd and P. Li, Metall. Trans. A 17A (1986), 1191-1202. H. Sekine, T. Inoue, and M. Ogasawara, Trans. Iron Steel Inst. Jon. 8 (1968), 101-102.

TABLE 1 Solute, i

Phase’ ’ Y

(1 - [Ti])‘(-33472 (1 -

a Y

V

a -

‘Concentratrons

Applicable Range (“C)

G:,; (= RTln?)*

(Y or a)

Ti

Nb

Expressions for Partial Excess Molar Free Energies (J/mole) (Refs. 3-5)

(1 (1 -

+ 46024[Ti]) + (-1004 + 3.7656T)

725
[Ti])*(-46024 + 46024[Ti])

[V])*(-17405 + 1.159T) + (8996 + 3.556T)

325
[V])*(-15958 + 7.029T) + [V](-32082 - 10.04T)

25 5 T 5 2025

a

are in atom fraction

525 5 T 5 1525

8996 + 3.556T

Y (1 -

525
[Nb])*(8786 + 15900[Nb])

and temperature

in degrees

Kelvin.

SOLUBILITY PRODUCTS

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TABLE 2. Solubility Expressions* for TIC, VC,, and NbC, in Austenite (y) and Ferrite (o) Carbide

K

Iog,,Ka”

Iog,,KY (Ref.)

log,oKn (Ref.)

TIC

(PWl)

-2575/T + 1.65

-7000/T + 2.75 (6)

-9575/-T + 4.40

-2765/T + 1.33

-9500/T + 6.72 (7)

-12265/T + 8.05

MCI)

-6080/T + 2.72 (11) -83OOrT + 4.55 (12)

VC, -1975/T + 0.98

vw3

-7045/T + 4.24 (13) -3160/T + 1.64

([Nbl[CI)

NbC,

-9975lT + 6.34

-8000/T + 5.36 (8)

‘7

-9930/T + 3.90

-6770/T + 2.26 (6)

-10045/T + 4.45 (10)

VW1°.87) *Concentrations

are in weight percent and temperature

in degrees Kelvin

900°C -0.5

600°C

700%

5( 1°C

600°C

-1

-1

-6

-8---c -

3

-2.5

0.6

0.9

VC0.n VCo.75 (13) NbC NbCom(10)

1

1000/l

1.1

1.2

1.3

(OK-‘)

FIG. 1. Solubility ratio relationships for titanium-, vanadium-, and niobium-carbide. Hatching indicates ranges of mathematically-possible values for 0 2 [CY, [Cly, [My, [Ml’ I 0.01. Heavy lines represent functions for log,,Kti given in Table 2.

0.6

0.9

1

1000/T

1.1

1.2

(“K-l)

FIG. 2. Solubility relationships for titanium-, vanadium-, and niobium-carbide in ferrite. Hatching indicates ranges of the relationships for vanadiumand niobium-carbide. Heavy lines represent the predicted relationships from this work.

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0.02

0.004

.

1

Jw,Kc = -12265/l

+ 8.05

0.016

. 0.012

0.003

G

z

G

P

G -

G 0.002

-0.006

0.001

0.004

c

I

800"( /\

i

0.02

0.04

0.06

0.08

Oh

FIG. 3. Computed ferrite.

solubility

isotherms for TIC in

FIG. 4. Computed ferrite.

0.002

0.005

o.i5

solubility

012

0.25

3

pet.

isotherms

for VC in

&&K =-9930/T +3.90

0.004

0.016

. 0.003

. 0.012 5

z

;

T

G -

0:1

[Vl,wt.

[Ti], wt. pet.

O.ooB

0" - 0.002

0.004

0.001

E 0

PI,

wt.pet

FIG. 5. Computed solubility isotherms for VC,,,5 in ferrite

0.005

0.01

[Nb], wt.

0.015

0.02

'5

pet.

FIG 6. Computed solubility isotherms for NbC In ferrite.