ISSN 0012-5008, Doklady Chemistry, 2006, Vol. 408, Part 1, pp. 83–86. © Pleiades Publishing, Inc., 2006.Original Russian Text © V.Ya. Dashevskii, N.P. Lyakishev, 2006, published in Doklady Akademii Nauk, 2006, Vol. 408, No. 2, pp. 214–217.

83

Iron–cobalt alloys are widely used in advancedengineering. Oxygen contained in these alloys deterio-rates their performance properties. A physicochemicalinvestigation of oxygen solutions in iron–cobalt meltswill create a basis for optimizing the preparation ofthese alloys.

There are no experimental data on the compositionof an oxide phase in equilibrium with iron–cobalt meltsor on oxygen solubilities in these melts for a wide rangeof cobalt concentrations. Averin [1] experimentallystudied oxygen solubilities only in alloys containing25, 50, and 75% cobalt.

We can calculate the composition of an oxide phaseand estimate oxygen solubilities in melts from thermo-dynamic data for oxygen solutions in liquid iron [1–3]and cobalt [1, 2, 4] and in iron–cobalt melts [5].

Oxygen solutions in iron- and cobalt-based meltsshould be regarded as real solutions, whose formationis accompanied by a heat effect and a change in entropy.Equations describing the behavior of the components ofa real solution may be derived from equations for idealsolutions with activities instead of concentrations (

a

=

γ

X

). Interaction parameters serve to take into accountreciprocal effects of the components of the solution on

their thermodynamic parameters:

= [6]

.

The underlying idea of the approach is the Taylorexpansion of an excess thermodynamic function (

∆

G

i

,

∆

H

i

,

∆

S

i

). In most cases, the required accuracy is suchthat the expansion is confined to the zero- and first-order terms of the series:

εij-⎝

⎛ ∂ γ iln∂X j

-------------⎠⎞

γ iln γ i°ln Σ∂ γ iln∂X j

-------------X j+ γ i°ln Σεij X j.+= =

The metal–oxide equilibrium reaction for iron,

(1)

may be represented as the sum of the reactions

(2)

(3)

Here, is the activity coefficient and

M

i

is the molec-ular weight. For oxygen solutions in liquid iron at1873 K, = 0.0105 [7]. Therefore, at 1873 K,

∆

= 23905 J/mol and

K

(1)

= 0.2155. Oxygen solu-bilities in iron may be calculated from

At 1873 K, = –0.17 [3] and the oxygen solu-bility is accordingly 0.235%, which correlates withexperimental data in [1, 2].

The metal–oxide equilibrium reaction for cobalt,

(4)

may be represented as the sum of the reactions

(5)

(6)

FeO liq( ) Fe liq( ) O[ ]1% Fe( ),+=

K 1( ) aO O[ ] f O= =

FeO liq( ) Fe liq( ) 1/2O2,+=

∆G 2( )° 239987 49.57T , J/mol 2[ ],–=

1/2O2 gas( ) O[ ]1% Fe( ),=

∆G 3( )° RTγ O Fe( )° MFe

MO 100×-----------------------⎝ ⎠

⎛ ⎞ .ln=

γ i°

γ O Fe( )°G 1( )°

%O[ ]log Fe K 1( )log eO Fe( )O %O[ ]–=

= K 1( )log eO Fe( )O K 1( ).–

eO Fe( )O

CoO solid( ) Co liq( ) O[ ]1%(Co),+=

K 4( ) aO O[ ] f O⋅= =

CoO solid( ) Co liq( ) 1/2O2,+=

∆G 5( )° 261884 85.83T , J/mol 2[ ],–=

1/2O2 gas( ) O[ ]1% Co( ),=

∆G 6( )° RTγ O Co( )° MCo

MO 100×-----------------------⎝ ⎠

⎛ ⎞ .ln=

Thermodynamics of Oxygen Solutions in Iron–Cobalt MeltsV. Ya. Dashevskii and Academician N. P. Lyakishev

Received January 13, 2006

DOI: 10.1134/S0012500806050089

Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Leninskii pr. 49, Moscow, 119991 Russia

CHEMICAL TECHNOLOGY

84

DOKLADY CHEMISTRY Vol. 408 Part 1 2006

DASHEVSKII, LYAKISHEV

For oxygen solutions in liquid cobalt at 1873 K, = 0.169 [7]. Therefore, at 1873 K, ∆ =

22006 J/mol and K(4) = 0.2435. Oxygen solubilities incobalt may be calculated from

At 1873 K, = 0 [4] and the oxygen solubilityis accordingly 0.244%, which correlates with experi-mental data in [1].

γ O Fe( )° G 4( )°

%O[ ]log Co K 4( )log eO Co( )O %O[ ]–=

= K 4( )log eO Co( )O K 4( ).–

eO Co( )O

The oxide phase above iron–cobalt melts containsFeO and CoO. The metal–oxide equilibrium reaction

(CoO) + [Fe]Fe–Co = (FeO) + [Co]Fe–Co (7)

may be represented as the sum of reactions (2) and

(8)

From this,

At 1873 K, ∆ = –46936 J/mol and K(7) = 20.352.

Using the perfect solution approximation for theoxide phase of oxygen solutions in iron–cobalt melts,we may write

Since XFeO + XCoO = 1,

(9)

The compositions of the oxide phase of the Fe–Co–O system calculated from Eq. (9) are displayed inTable 1 and Fig. 1. One can see that FeO is the majorcomponent of the oxide phase; the CoO concentrationin the oxide phase increases abruptly only when thecobalt mole fraction in the melt is higher than 0.8. Thisis because iron has a higher oxygen affinity than cobalt:∆ (FeO) = –147142 kJ/mol, and ∆ (CoO) =–101 124 kJ/mol [2]. Compositions of the oxidephase for Fe–Ni–O melts borrowed from [8] arealso plotted in Fig. 1. The cobalt mole fraction inthe melt at which CoO concentrations in the oxidephase are noticeable is lower than the nickel molefraction that provides the appearance of noticeableNiO concentrations in the oxide phase since cobalt hasa higher oxygen affinity than nickel: ∆ (NiO) =−75 451 kJ/mol [2].

Reaction (1) for iron–cobalt melts, which is

(10)

may be represented as the sum of reactions (2) and

(11)

The molecular weights of iron–cobalt melts werecalculated from [8]

MFe–Co = MFeXFe + MCoXCo,

CoO liq( ) Co liq( ) 1/2O2,+=

∆G 8( )° 253 511 81.85T , J/mol 2[ ].–=

∆G 7( )° 13 524 32.28T , J/mol.–=

G 7( )°

K 7( )XFeOXCoγ Co

XCoOXFeγ Fe---------------------------.=

XFeO

K 7( )XFeγ Fe

K 7( )XFeγ Fe XCoγ Co+------------------------------------------------.=

G1873 K° G1873 K°

G1873 K°

FeO( ) Fe[ ]Fe–Co O[ ]1%(Fe–Co),+=

K 10( )XFeγ Fe O[ ] f O

XFeO-------------------------------=

1/2O2 gas( ) O[ ]1%(Fe–Co),=

∆G 11( )° RTγ O(Fe–Co)° MFe–Co

MO 100×----------------------------------⎝ ⎠

⎛ ⎞ .ln=

1

2

3

4

1.0

0.8

0

0.6

0.4

0.2

0.2 0.4 0.6 0.8 1.0XCo, XNi

XFeO, XCoO, XNiO

Fig. 1. Composition of the oxide phase in equilibriumwith (1, 3) iron–cobalt–oxygen melts and (2, 4) iron–nickel–oxygen melts [8] vs. alloy composition at 1873 K:(1, 2) XFeO, (3) XCoO, and (4) XNiO.

Table 1. Composition of oxide phases of iron–cobalt–oxy-gen melts at 1873 K

XFe γFe [5] XCo γCo [5] XFeO XCoO

1.0 1.0 0 1.051 1.0 0

0.9 0.996 0.1 1.136 0.9938 0.0062

0.8 0.987 0.2 1.199 0.9853 0.0147

0.7 0.979 0.3 1.230 0.9742 0.0258

0.6 0.981 0.4 1.226 0.9607 0.0393

0.5 1.035 0.5 1.151 0.9482 0.0518

0.4 1.095 0.6 1.097 0.9312 0.0688

0.3 1.183 0.7 1.051 0.9076 0.0924

0.2 1.282 0.8 1.024 0.8643 0.1357

0.1 1.416 0.9 1.006 0.7609 0.2381

0 1.590 1.0 1.0 0 1.0

DOKLADY CHEMISTRY Vol. 408 Part 1 2006

THERMODYNAMICS OF OXYGEN SOLUTIONS IN IRON–COBALT MELTS 85

and the activity coefficients were calculatedfrom [9]

For oxygen solutions in liquid iron and cobalt,

= 0.0105 [7], = 0.169 [7], = 1.9 [3],

and = –4.1 [4]. The values calculated for MFe–Co,

, and the equilibrium constants of reaction (10)are listed in Table 2.

Oxygen solubilities in iron–cobalt melts may be cal-culated from

(12)

The interaction parameter was calculatedfrom [8]

The oxygen concentrations calculated usingEq. (12) are listed in Table 2 and are displayed in Fig. 2.One can see that cobalt added to iron noticeablyreduces the oxygen saturation concentration. Thisreduction is due to the fact that cobalt increases the

oxygen activity coefficient in iron ( = 1.9 [3]),thus reducing the oxygen solubility. The oxygen con-centration starts to increase (first slowly, then abruptly)only when the cobalt mole fraction in the melt is about0.8. Figure 2 displays experimental data borrowed from[1]. There is a correlation between the results of the cal-

γ O(Fe–Co)°

γ O(Fe–Co)°ln XFe γ O(Fe)°ln XCo γ O(Co)°ln+=

+ XFeXCo XCo γ O(Co)°ln γ O(Fe)°ln εO Co( )Fe+–( )[

+ XFe γ O(Fe)°ln γ O(Co)°ln εO Fe( )Co+–( ) ].

γ O(Fe)° γ O(Co)° εO Fe( )Co

εO Co( )Fe

γ O(Fe–Co)°

%O[ ]log Fe–Co K 10( )log XFeOlog XFelog– γ Felog–+=

–eO Fe–Co( )O %O[ ] = K10log XFeOlog XFelog– γ Felog–+

– eO Fe–Co( )O K 10( )XFeO/XFeγ Fe.

eO Fe–Co( )O

εO Fe–Co( )O εO Fe( )

O XFe εO Co( )O XCo.+=

εO Fe( )O

culations and the data from [1]. The results of the cal-culations of oxygen solubilities in iron–nickel meltsborrowed from [8] are displayed in Fig. 2 for compari-son. The oxygen solubilities in iron–cobalt melts arelower than in iron–nickel melts over the entire range ofalloy compositions.

In summary, having performed a thermodynamicanalysis, we for the first time determined the composi-tion of the oxide phase and the equilibrium oxygen con-

1

3

XCo, XNi

2

0 0.2 0.4 0.6 0.8 1.0

1.0

0.8

0.6

0.4

0.2

[O], %

Table 2. Oxygen solubilities in iron–cobalt–oxygen melts at 1873 K

XCo MFe–Co , J/mol logK(10) [O], %

0 55.847 0.0105 23905 –0.6665 –0.170 0.2350.1 56.156 0.0127 27015 –0.7532 –0.1538 0.2100.2 56.464 0.0157 30303 –0.8449 –0.1375 0.1890.3 56.773 0.0195 33820 –0.9429 –0.1210 0.1700.4 57.081 0.0247 37596 –1.0482 –0.1043 0.1510.5 57.390 0.0423 41683 –1.1621 –0.0874 0.1290.6 57.699 0.0572 46107 –1.2855 –0.0703 0.1120.7 58.007 0.0797 50916 –1.4195 –0.0530 0.0980.8 58.316 0.1142 56146 –1.5654 –0.0355 0.0920.9 58.625 0.1383 61835 –1.7240 –0.0178 0.1021.0 58.933 0.169 22006 –0.6135 0 0.244

γ O° ∆G 10( )° eOO

Fig. 2. Oxygen solubilities in (1, 2) iron–cobalt melts(determined in this work) and (3) iron–nickel melts (bor-rowed from [8]) vs. alloy composition at 1873 K: (1) calcu-lated in this work, (2) borrowed from [1], and (3) calculatedin [8].

86

DOKLADY CHEMISTRY Vol. 408 Part 1 2006

DASHEVSKII, LYAKISHEV

centrations in iron–cobalt melts over a wide range ofalloy compositions.

ACKNOWLEDGMENTS

This work was supported by the presidential pro-gram “Leading Scientific Schools” (project no.NSh-4165.2006.3).

REFERENCES

1. Averin, V.V., Extended Abstract of Cand. Sci. (Techn.)Dissertation, Moscow: IMET AN SSSR, 1958.

2. Kulikov, I.S., Raskislenie splavov (Deoxidation ofAlloys), Moscow: Metallurgiya, 1975.

3. Steelmaking Data Sourcebook, New York:; Tokyo: Gor-don&Breach, 1988.

4. Sigworth, G.K. and Elliott, J.F., Can. Met. Quart., 1976,vol. 15, no. 2, pp. 123–127.

5. Hultgren, R., Desai, P.D., Hawkins, D.T., et al., SelectedValues of the Thermodynamic Properties of BinaryAlloys, Metals Park: Am. Soc. Met., 1435.

6. Wagner, C., Thermodynamics of Alloys, Reading: Addi-son–Wesley, 1952.

7. Chiang, T. and Chang, Y.A., Metal. Trans. B, 1976,vol. 7, pp. 453–457.

8. Dashevskii, V.Ya., Makarova, N.N., Grigorovich, K.V.,and Kashin, V.I., Dokl. Akad. Nauk, 1997, vol. 357,no. 6, pp. 789–791.

9. Frohberg, M.G. and Wang, M., Ztschr. Metallk., 1990,vol. 81, no. 7, pp. 513–518.