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Phase equilibria and thermodynamics in the Fe-Mo and Fe-Mo-O systems
Journal of the Less-Common
PHASE EQUILIBRIA Fe-MO-0 SYSTEMS
Metals, 81 (1981) 229 - 238
229
AND THERMODYNAMICS
IN THE Fe-MO AND
H. KLEYKAMP and V. SCHAUER Kernforschungszentrum Karlsruhe, Znstitut fir Material- und FestkZirperforschung, Postfach 3640, 7500 Karlsruhe (F.R.G.) (Received April 7,198l)
summary The Fe-MO-0 system was reinvestigated at 1173 and 1273 K on the metal-rich side of the FeO-Moos boundary. Two ternary oxides, FezMoO and FezMoaOs, were observed which coexist with a-Fe(Mo) at 1173 K and with FesMoz at 1273 K. Electromotive force measurements were made on galvanic cells with oxygen ion conducting solid electrolytes between 1190 and 1330 K for the determination of the Gibbs energies of formation of FesMoe, FezMoO and FeaMosOs. The results can be presented by the following relationships: f A G” (FesMos>
= +46.1 - 0.05332’ + 3.1 (kJ mol-‘)
f A G” (FesMoOl)
= -1081.7
+ 0.26672’+
2.6 (kJ moll)
f A G” (FeaMosOs)
= -2267.8
+ 0.61657’f
4.5 (kJ mol-‘)
The heat of formation and the standard entropy of FesMo, were calculated using the Gibbs energy of formation results and literature data of calorimetric measurements, which give ‘AH sss0(Fe3M02) = +15.0 kJ mol-’ and Ssas0(Fe3M02) = 177 J K-l mol-’ at 298 K. The Gibbs energy of formation of Fes,Moa can then be expressed by fAG”@‘esMos) = +1&O - 0.05362’ + 0.0000177Ts (kJ mol-‘) between 298 and 1500 K.
1. Introduction A review of the available thermodynamic data on metallic systems of the refractory metals and the iron group metals has shown that some of these data are incomplete and are in doubt in a few cases [ 11. The present study is part of a continuous programme for the investigation of phase equilibria and thermodynamic properties of these systems [2, 31 and we report on the results of the Fe-MO and Fe-MO-0 systems. Electromotive force (e.m.f.) measurements have been made on galvanic cells with oxygen ion conducting solid electrolytes for the determination of the Gibbs energies of formation of 0022-5088/81/0000-0000/$02.50
@ Elsevier Sequoia/Printed in The Netherlands
230
the intermetallic phase FesMos in the Fe-MO system and of the ternary oxides FezMoO and FesMosOs in the Fe-MO-O system. Knowledge of the phase equilibria in the latter system is required for the arrangement of appropriate galvanic cells for the e.m.f. measurements.
2. The FIYMO system Essential contributions to the Fe-MO phase diagram have been given in refs. 4 - 11: the three intermetallic phases R (FesMos), p (FesMos, Fe,W, type; R&a, rhombohedral; 39 - 43 at.% MO) [12 - 141 and u (FeMo) are well characterized, whereas the existence of the h phase ( FezMo) is still uncertain. R and u are high temperature phases; the p phase is formed peritectoidally at 1370 “c. The X phase has been detected by aging of alloys at low temperatures between 500 and 850 “C [ 15 - 171. In contrast, results of diffusion couples between 800 and 1400 “C did not confirm the existence of the X phase [6,11,18] nor did a A phase occur by annealing compacted powders for up to 1500 h between 800 and 900 “c [ 7,8]. However, the addition of silicon raised the rate of formation of this compound considerably [ 81. It was suggested that the X phase is formed peritectoidally at 950 “c [ 91. This phase exists possibly only by impurity stabilization. Our annealing experiments (900 “C, 912 h) with pellets of very pure iron and molybdenum powders (67at.%Fe-33at.%Mo) did not confirm the existence of the X phase FesMo. The p phase FeaMoz was prepared by annealing the pellets at 1000 “C. The lattice parameters were evaluated on the basis of a hexagonal indexing of the six most intense lines [ 191. These results and the literature values are summarized in Table 1.
3. The Fe-MO-0
system
Phase studies on the Fe-MO-0 system have been reported in refs. 20 28. In particular, on the FeOl +%-MOO, section the ternary oxides FeZMoO* and FezMosOs [23,27] or FezMoO and FeMoOs [21,24,26] have been observed between 800 and 1100 “c. A two-phase equilibrium FelMoOlFesMoz has been found at 900 “C [ 271, FesMo, being the only intermetallic phase at this temperature. The two-phase equilibria FeMoOs-FezMo and FeMoOs-FesMo, have been reported in ref. 28. Though FezMosOs has been well characterized by X-ray measurements in early papers [ 20,221, this phase has been ignored in the phase studies by Russian workers in later research [ 21,24,26,28]. The phases FesMosO and FeMoO have been stated to exist on the metal-rich side of the FeOi +x-MoOz section [ 291. As the available information on the phase relations in the ternary system is contradictory, it appeared to be advisable to re-examine the phase
231 TABLE 1 Lattice parameters of ,Uphase Feflog
a (nm)
c (nm)
Composition
Reference
0.4751a 0.4749 0.4698 0.47546 i: 5 0.4748 * 2b 0.4780 * 2b
2.568= 2.569 2.574 2.5716 * 3 2.570 * 2b 2.584 + 2b
Fe-rich boundary Fe-rich boundary Fe-rich boundary Fe-rich boundary MO-rich boundary
12,13 14 8 9 -
aThe original data were multiplied by 0.100202. bAnnealed at 1000 “C.
field distribution on the metal-rich side of the FeO, +x-MoOs section in the temperature range 900 - 1000 “C, which is relevant for the following e.m.f. measurements. The pellets made from FesOa, MoOz, iron and molybdenum in appropriate proportions were annealed at 900 and 1000 “C under argon of high purity and afterwards were analysed by chemical and X-ray methods. Only two ternary oxides, FezMoO, and FesMosOs, have been observed; in these compounds the chemical potentials of oxygen are very similar. These results and literature values are summarized in Table 2. The two-phase equilibrium FezMoaOs-FesMoz appears in the whole temperature range investigated. FezMoO, and FezMosOs are in equilibrium with a-Fe(Mo) at 900 “C and with FeaMo, at 1000 “C (Fig. 1). The change in the phase field distribution occurs at 916 “C (see Section 6). The existence of the metal-rich oxides FeaMosO and FeMoO reported in ref. 29 could not be confirmed in this study at 900 and 1000 “C. TABLE 2 Lattice parameters of ternary Fe-MO oxides Oxide
System
Second phase
= (=I
c @ml
Reference
FezMoO
Cubic
-
0.8501 0.845 0.849 03513s 0.850 t la 0.8506 + 3 0.8511 t 7
-
21 23 23 24 26 -
-_
-
0.5782 JZ5 0.579a 0.5783 + 5 0.5787 f 1
1.0046 * 10 1 .006a 1.007 * 4 1.008 t 3
20 22 -
Eeu.950 FeZMo30a Fe, Fe3M02 FegMosOa, FesMo, Fe&IosOa
Hexagonal
Fe2MoOq, FeaMog MoOg, MO
aThe original data were multiplied by 0.100202.
232
Fe
a- Fel MO)
MO F+iO,
(4
0
MO
(b) Fig. 1. Isothermal sections of the Fe-MO-0
system at (a) 1173 K and (b) 1273 K.
233
4. Electromotive
force measurements
From knowledge of the phase relations in the Fe-MO-0 system the unknown Gibbs energies of formation of FeaMoe, FezMoOd and FesMosOs were determined above 1189 K by the arrangement of three galvanic cells as follows: a-Fe1 -,Mo,,
FesMos,
FesMo2, FezMoOd, FesMos,
FezMoO
I FeQseO, Fe
FesMosOsIThOo~Y2031Feo.s50, IThOs - Y,03 IFeaseO,
MO, FezMosOs
The e.m.f. measurements the cells a-Fe1 _xMo,,
IThOs*YsOs
(I)
Fe
(II)
Fe
(III)
would have been possible below 1189 K by use of
FezMoOd,
a-Fe1 -xM~, , FesMos,
Fe,Mo,Os FesMosOs
IThOs*Y,Os
IFeasaO, Fe
IThOa- YsOs I FesssO,
(Ia)
Fe
(IIa)
and cell (III). The terminal solubility of molybdenum in the a-Fe(Mo) solid solution in equilibrium with FesMo, is given by xMO = -0.18 + 0.00620T within the temperature range of the e.m.f. measurements [ 111. The total reactions of the cells (I) - (III) for a virtual current from the right-hand electrode to the left-hand electrode, considering the FesMo, homogeneity range to be from 39 to 43 at.% MO [ 111, are given by 0.17 0.39 -x
Fel_,Mo,
1 - 3x + 0.39 -x Fe o.slMoo.39 + 4Feo.950
= FezMoOd + 3.8Fe
(1)
3.816Fe0.61Mo0.39 + 5.295FeQgs 0 = FezMoOd + 0.162FezMo30s
+
+ 5.030Fe 3.569Fe0.57Mo0.43 + 1.491Mo
(2)
+ 8Feo.g50 = FesMo30s
+ 7.6Fe
(3)
Anticipating the Gibbs energy of formation of Fe3Moz f y, the iron activities on the iron- and molybdenum-rich sides of the homogeneity range have been estimated to be 0.94 and 0.38 respectively at 1200 K. Assuming linearity of AG, in the homogeneity range, the integration of the Gibbs-Duhem equation results in a very small increase in the Gibbs energy of formation with increasing iron content in Fe3Moa + y which gives f AG”(Feo.61Mooss> ‘A G” (Feo.s,Moo.43) = +50 J mol-’ at 1200 K. Therefore, the homogeneity range of Fe,Mos f y can be neglected with respect to the change in the Gibbs energy of formation and eqns. (1) - (3) can be simplified to 1 ~ 2-5.x
1 - 3x Fe1 _xMox + -2 _ b FesMoa + 4Fee.ss 0 = FezMoO
4Fe,Mo,
+ 28Feo.gs0
= 5FesMo0,
+ Fe,Mo30s
2Fe3Mos
+ 5Mo + 24FeoSg50 = 3FezMo30s
+ 26.6Fe
+ 22.8Fe
+ 3.8Fe
(4) (5) (6)
234
The following relations are given for the Gibbs energies of reaction ‘AGi” of the cells (I) - (III): 1-3X rAG1o = -8FEI= fAG”(FesMoO,> - 2--5xfAGo (FesMos) 1 - 2-5X =AGfIo = -56FEn
fAG”Wel_,M~,)
= 5fAGo (FesMoOJ
- 4fAGo{Fe0S9sO~
(7)
+ ‘AGO(FesMosOs) -
- 4”AG” (Fe,Moa> - 28fAG0 (Fee.ssO>
“AGUI’= -4WEm
(3)
= 3fA G” (FesMosOs) - 2’A Go (FesMos) - 24fh G” (Fe,s50)
(9)
In these equations Eiis the e.m.f. measured in the cells (I) - (III), Fis Faraday’s constant and fAG,” are the Gibbs energies of formation of the phases given in the angular brackets. The rearrangement of the equations with respect to the Gibbs energies of formation of the three phases gives fAG” (FesMoa)
3 =l-x -
‘A Go (FezMoO,)
=-
‘AGo (Fe1 __,MoJ -
F(40E,- 56Err + 16&r,) 2
6-15x
(16)
5-5X
‘AG” (Fe1 _.-*MO,) + 4fAGo (FeessO> -
1-X
-
2-5X
1-3X
1-3X
l-x
5-5X
5-5X
--48FE~II--+168FE,, 16FEI------2
fAG” (FesMosOs) = 1-X
(11) “AGo(Fe1 _-xMO,) + 8fAGo~Fes.9s0~ 2-5X
2-5X
l-x
5-5X
+ 112FErr -16FE1------
-
3-5X
48FE,11 5-5x (1%
The two-phase equilibria Fe(Mo)-FesMoa and FesMos-Mo(Fe) and the phase FesMos have been formed by arc melting the elements and by subsequent annealing at 1373 K. The stoichiometric oxides FesMoOd and FesMosOs have been produced under an argon atmosphere by solid state reaction of the components iron, FesOs and MoOs at 1273 K. The electrodes have been made by mixing and sintering the initial products under argon at 1273 K.
235
5. Results The e.m.f.s of the ceIIs (I) - (III) as functions of temperature in Fig. 2. The least-squares method calculations result in E,
(kO.3) = 60.5 + 1.8 - (0.0420
are given
f 0.0014)T
(mV) 1180 - 1320 K En (kO.3) = 83.7 f: 2.9 - (0.0615 ?r 0.0023)T (mV) 1210 - 1320 K Em (10.6) = 117.7 + 3.5 - (0.0834 ? 0.0028)T (mV) 1180 - 1320 K
(13) (14) (15)
The Gibbs energies of formation of FesMoa, FezMoO and Fe,MosOs as formulated in eqns. (10) - (12) are then calculated with eqns. (13) - (15) and with the Gibbs energies of formation of Fee,ssO [ 301 and of e-Fe1 _,Mo,. The Gibbs energy of formation of o-Fe, _xMo, is evaluated on the basis of a regular solution model with an interaction parameter A = 17.78 kJ mol-l given in ref. 10: fAG” (Fe, _xMox) = +4055 - 4.43T (J mol-r )
1200 - 1300 K
(16)
xMO of molybdenum
in a-Fe is -0.18
fA G” (FeaMoe)
= +46.1 - 0.0533T
+ 3.1 (kJ mol-l)
fA
= -1081.7
+ 0.2667T
+ 2.6 (kJ mol-I)
(18)
= -2267.8
+ 0.6165T
-+ 4.5 (kJ mol-‘)
(19)
The termindt solubility [ 111. This results in
G” (FezMoOS
fA G” (FesMosOs)
+ 0.00020T (17)
within the temperature range 1180 - 1330 K. The Gibbs energy of formation of FesMoe determined in this paper is presented in Fig. 3 together with values from the literature.
6. Discussion Kirchner et al. [lo] and Kaufman and Nesor [ 311 have calculated the Gibbs energy of formation of FesMo, on the basis of a regular solution model by use of different interaction parameters. Spencer and Putland [32] have determined the heat of formation and the heat capacity of FesMo, with a high temperature adiabatic catorimeter (773 - 1573 K) and have evaluated the Gibbs energy of formation of FesMoa between 773 and 1600 K on the basis of one Gibbs energy of formation value at 1445 K calculated by Kirchner et al. [lo]. Niissler et al. 1331 have measured the heat of formation of FesMoa at 1450 K, using a newly designed high temperature “tandem” cdlorimeter. Rezukhina and Kashina [28] have determined the Gibbs energy of formation of FesMo, by e.m.f. measurements; however, they used an incorrect Fe-MO-0 phase diagram for the galvanic cell arrangements. These results are illustrated in Fig. 3.
236 T(K) 1100 15 \
-
1200 I
1300 I
!
-cQ \o
10
5-
900
850
900
950 tl'c)
T(K)
900
1050
1100
1300
950
1000 t(T)
T(K) 1200
1050
-
1200
850
1000
-
_
1300
Fig. 2. Electromotive forces as functions of temperature: (a) cell (I); (b) cell (II); (c) cell (III). 0, 0, *, ThO, - Y,Og;v , ZrO2 - CaO. The different symbols represent the results of various experiments (see text).
237
1
-
O’
-1
1
A oze Lx ,” ‘t “* -4
/
Rezukhma
-3-
and
-----
Kashrell978) ,
\I
-L
I
. -5-
Spencer
Putland
11975)
Nesorl1975)
talc.
-
emf
_,I=----------
-6-
Kwchner
.900
and
study,
t
calorimetry
-7
Kaufman
>qhis and
emf
et al
119731 calculated
I
I
/
I
I
I
1000
1100
1200
1300
IL00
1500
T
1600
I K I -,-----~__+L
Fig. 3. Gibbs energy of formation of FeaMo2 as a function of temperature.
The average value of the heat of formation of FeaMo, from ref. 33 gives -9385 J (mol Fe,Mo,)-’ at 1450 K. The heat of formation at lower temperatures can then be calculated by use of the enthalpies of iron [ 341, molybdenum 1351 and Fe,Mo, [ 32,351, which results in -10390 J (mol Fe,Mo2)-’ at 1250 K and +14980 J (mol Fe,Mo&’ at 298 K. The Gibbs energy of formation of Fe,Mo, at 1250 K from this study as well as the heat of formation of Fe,Moz and the standard entropies of iron [34] and molybdenum [ 351 at the same temperature and the temperature dependence of the heat capacity of Fe,Moz f35] can then be taken to calculate the standard entropy of FesMo, at 298 K which gives 177 J K-l (mol Fe,Mo,)-l. From these results an averaged three-term expression can be calculated for the Gibbs energy of formation of Fe,Mo, between 298 and 1500 K, giving
fAG” (Fe,Mo,> = +1&O - 0.05352’ + 0.0000177T2
(kJ mol-’ )
(20)
with an error of +4.0 kJ mol-‘. Consequently, Fe,Mo2 should become unstable below 400 K. The Gibbs energy of formation of FezMoO, is -768.9 + 2.6 kJ mol ml at 1173 K (eqn. (18)) and is about 5 kJ mol-’ more negative than the value which can be deduced from the reaction 2Fe + MO + 4C02 = FezMoOd + 2C0 investigated by Schmahl and Dillenburg [ 271 at the same temperature. The Gibbs energies of formation of FesMoz, FezMoO, and FezMoaOs, determined in the present study, may be used to predict the change in the phase field distribution of the Fe-MO-0 system between 1173 and 1273 K on the metal-rich side of the wustite-Moo2 boundary. The Gibbs energy of the reaction (4 - l~)Fe~MoO*
+ (1 +x)FesMo,
= (2 - 5x)Fe2MosOs + 7FeI _XMoX (21)
gives ‘AG”= -199400
+ 167.7T (J (mol of reaction)-l)
(22)
238
between 1180 and 1330 K. The condition rAG” = 0 in eqn. (22) is fulfilled at a temperature T = 1189 K for the four-phase equilibrium in eqn. (21). The thermodynamic data in eqns. (16) - (19) are in accordance with the twophase equilibria in Fig. 1: the Fe(Mo)-FesMosOs equilibrium observed at 1173 K changes to the FesMos-FeaMoO, equilibrium observed at 1273 K at a predicted temperature of 1189 K. Acknowledgment The authors wish to thank Mr. W. Laumer for conducting the experiments. References 1 H. KIeykamp, Rep. KfK-Ext. 6/75-2,1975, p. 38 (Kernforschungszentrum Karlsruhe). 2 H. KIeykamp,J. Less-Common Met., 71 (1980) 127. 3 H. Kleykamp, V. Schauer and W. Laumer, Rep. KfK 2993 B, 1980, p. 138 (Kernforschungszentrum Karlsruhe). 4 W. P. Sykes, Trans. Am. Sot. Steel Treat., 10 (1926) 839; 16 (1929) 358. 5 T. Takei and T. Murakami, Sci. Rep.Tohoku Univ. Ser. 1, 18 (1929) 135. 6 S. R. BaenandP. Duwez,J. Met., 3 (1951) 331. 7 J. W. Putman, R. D. Potter and N. J. Grant, Trans. Am. Sot. Met., 43 (195 1) 824. 8 R. V. Skolozdra and E. I. Gladyshevskii, Inorg. Mater. (U.S.S.R.), 2 (1966) 1237. 9 A. K. Shina, R. A. Buckley and W. Hume-Rothery, J. Iron Steel Inst., London, 205 (1967) 191. 10 G. Kirchner, H. Harvig and B. Uhrenius, Metall. Trans., 4 (1973) 1059. 11 C. P. Heijwegen and G. D. Rieck, J. Less-Common Met., 37 (1974) 115. 12 H. Arnfeldt and A. Westgren, Jernkontorets Ann., 119 (1935) 185. 13 A. Westgren, Sci. Rep. Tohuku Univ. Ser. 1, K. Honda Anniversary Vol., (1936) 852. 14 C. J. Bechtoldt and H. C. Vacher, J. Res. Natl. Bur. Stand., 58 (1957) 7. 15 T. Miyazaki, S. Takagishi, H. Mori and T. Kozakai, Acta Metall., 28 (1980) 1143. 16 R. P. Zaletaeva, N. F. Lashko, M. D. Nesterova and S. A. Yuganova, Dokl. Akad. Nauk S.S.S.R., 81 (1951) 415. 17 J. Higgins and P. Wilkes, Philos. Mag., 25 (1972) 599. 18 R. D. Rawlings and C. W. A. Newey, J. Iron Steel Inst., London, 206 (1968) 723. 19 A. Raman, 2. Metallkd., 57 (1966) 301. 20 W. H. McCarroll, L. Katz and R. Ward, J. Am. Chem. Sot., 79 (1957) 5410. 21 Yu. D. Kozmanov and T. A. Ugolnikova, Russ. J. Znorg. Chem., 3 (1958) 284. 22 G. Monnier, Bull. Sot. Chem. Fr., (1959) 298; (1959) 1252. 23 W. Jiger, A. Rahmel and K. Becker, Arch. Eisenhiittenwes., 30 (1959) 435. 24 Yu. D. Kozmanov, Russ. J. Inorg. Chem., 5 (1960) 996. 25 W. Kunnmann, D. B. Rogers and A. Weld, J. Phys. Chem. Solids, 24 (1963) 1535. 26 L. N. Rusakov, I. A. Novokhatskii, L. M. Lenev and A. A. Savinskaja, Dokl. Akad. Nauk S.S.S.R., 161 (1965) 410. 27 N. G. Schmahl and H. Dillenburg, 2. Phys. Chem., N.F., 77 (1972) 113. 28 T. N. Rezukhina and T. A. Kashina, J. Chem. Thermodyn., 10 (1978) 279. 29 N. Schonberg, Acta Chem. Stand., 8 (1954) 630,932. 30 C. B. Alcock and S. Zador, Electrochim. Acta, 12 (1967) 673. 31 L. Kaufman and H. Nesor, Metall. Trans. A,6 (1975) 2123. 32 P. J. Spencer and F. H. Putland, J. Chem. Thermodyn., 7 (1975) 531. 33 H. D. Niissler, T. Hoster and 0. Kubaschewski, 2. Metatlkd., 71 (1980) 396. 34 JANAF thermochemical tables, Natl. Stand. Ref. Data Ser., NBS, 1971 (U.S. National Bureau of Standards). 35 L. Brewer and R. H. Lamoreaux, At. Energy Rev., Spec. Issue, 7 (1980) 11.
PHASE EQUILIBRIA Fe-MO-0 SYSTEMS
Metals, 81 (1981) 229 - 238
229
AND THERMODYNAMICS
IN THE Fe-MO AND
H. KLEYKAMP and V. SCHAUER Kernforschungszentrum Karlsruhe, Znstitut fir Material- und FestkZirperforschung, Postfach 3640, 7500 Karlsruhe (F.R.G.) (Received April 7,198l)
summary The Fe-MO-0 system was reinvestigated at 1173 and 1273 K on the metal-rich side of the FeO-Moos boundary. Two ternary oxides, FezMoO and FezMoaOs, were observed which coexist with a-Fe(Mo) at 1173 K and with FesMoz at 1273 K. Electromotive force measurements were made on galvanic cells with oxygen ion conducting solid electrolytes between 1190 and 1330 K for the determination of the Gibbs energies of formation of FesMoe, FezMoO and FeaMosOs. The results can be presented by the following relationships: f A G” (FesMos>
= +46.1 - 0.05332’ + 3.1 (kJ mol-‘)
f A G” (FesMoOl)
= -1081.7
+ 0.26672’+
2.6 (kJ moll)
f A G” (FeaMosOs)
= -2267.8
+ 0.61657’f
4.5 (kJ mol-‘)
The heat of formation and the standard entropy of FesMo, were calculated using the Gibbs energy of formation results and literature data of calorimetric measurements, which give ‘AH sss0(Fe3M02) = +15.0 kJ mol-’ and Ssas0(Fe3M02) = 177 J K-l mol-’ at 298 K. The Gibbs energy of formation of Fes,Moa can then be expressed by fAG”@‘esMos) = +1&O - 0.05362’ + 0.0000177Ts (kJ mol-‘) between 298 and 1500 K.
1. Introduction A review of the available thermodynamic data on metallic systems of the refractory metals and the iron group metals has shown that some of these data are incomplete and are in doubt in a few cases [ 11. The present study is part of a continuous programme for the investigation of phase equilibria and thermodynamic properties of these systems [2, 31 and we report on the results of the Fe-MO and Fe-MO-0 systems. Electromotive force (e.m.f.) measurements have been made on galvanic cells with oxygen ion conducting solid electrolytes for the determination of the Gibbs energies of formation of 0022-5088/81/0000-0000/$02.50
@ Elsevier Sequoia/Printed in The Netherlands
230
the intermetallic phase FesMos in the Fe-MO system and of the ternary oxides FezMoO and FesMosOs in the Fe-MO-O system. Knowledge of the phase equilibria in the latter system is required for the arrangement of appropriate galvanic cells for the e.m.f. measurements.
2. The FIYMO system Essential contributions to the Fe-MO phase diagram have been given in refs. 4 - 11: the three intermetallic phases R (FesMos), p (FesMos, Fe,W, type; R&a, rhombohedral; 39 - 43 at.% MO) [12 - 141 and u (FeMo) are well characterized, whereas the existence of the h phase ( FezMo) is still uncertain. R and u are high temperature phases; the p phase is formed peritectoidally at 1370 “c. The X phase has been detected by aging of alloys at low temperatures between 500 and 850 “C [ 15 - 171. In contrast, results of diffusion couples between 800 and 1400 “C did not confirm the existence of the X phase [6,11,18] nor did a A phase occur by annealing compacted powders for up to 1500 h between 800 and 900 “c [ 7,8]. However, the addition of silicon raised the rate of formation of this compound considerably [ 81. It was suggested that the X phase is formed peritectoidally at 950 “c [ 91. This phase exists possibly only by impurity stabilization. Our annealing experiments (900 “C, 912 h) with pellets of very pure iron and molybdenum powders (67at.%Fe-33at.%Mo) did not confirm the existence of the X phase FesMo. The p phase FeaMoz was prepared by annealing the pellets at 1000 “C. The lattice parameters were evaluated on the basis of a hexagonal indexing of the six most intense lines [ 191. These results and the literature values are summarized in Table 1.
3. The Fe-MO-0
system
Phase studies on the Fe-MO-0 system have been reported in refs. 20 28. In particular, on the FeOl +%-MOO, section the ternary oxides FeZMoO* and FezMosOs [23,27] or FezMoO and FeMoOs [21,24,26] have been observed between 800 and 1100 “c. A two-phase equilibrium FelMoOlFesMoz has been found at 900 “C [ 271, FesMo, being the only intermetallic phase at this temperature. The two-phase equilibria FeMoOs-FezMo and FeMoOs-FesMo, have been reported in ref. 28. Though FezMosOs has been well characterized by X-ray measurements in early papers [ 20,221, this phase has been ignored in the phase studies by Russian workers in later research [ 21,24,26,28]. The phases FesMosO and FeMoO have been stated to exist on the metal-rich side of the FeOi +x-MoOz section [ 291. As the available information on the phase relations in the ternary system is contradictory, it appeared to be advisable to re-examine the phase
231 TABLE 1 Lattice parameters of ,Uphase Feflog
a (nm)
c (nm)
Composition
Reference
0.4751a 0.4749 0.4698 0.47546 i: 5 0.4748 * 2b 0.4780 * 2b
2.568= 2.569 2.574 2.5716 * 3 2.570 * 2b 2.584 + 2b
Fe-rich boundary Fe-rich boundary Fe-rich boundary Fe-rich boundary MO-rich boundary
12,13 14 8 9 -
aThe original data were multiplied by 0.100202. bAnnealed at 1000 “C.
field distribution on the metal-rich side of the FeO, +x-MoOs section in the temperature range 900 - 1000 “C, which is relevant for the following e.m.f. measurements. The pellets made from FesOa, MoOz, iron and molybdenum in appropriate proportions were annealed at 900 and 1000 “C under argon of high purity and afterwards were analysed by chemical and X-ray methods. Only two ternary oxides, FezMoO, and FesMosOs, have been observed; in these compounds the chemical potentials of oxygen are very similar. These results and literature values are summarized in Table 2. The two-phase equilibrium FezMoaOs-FesMoz appears in the whole temperature range investigated. FezMoO, and FezMosOs are in equilibrium with a-Fe(Mo) at 900 “C and with FeaMo, at 1000 “C (Fig. 1). The change in the phase field distribution occurs at 916 “C (see Section 6). The existence of the metal-rich oxides FeaMosO and FeMoO reported in ref. 29 could not be confirmed in this study at 900 and 1000 “C. TABLE 2 Lattice parameters of ternary Fe-MO oxides Oxide
System
Second phase
= (=I
c @ml
Reference
FezMoO
Cubic
-
0.8501 0.845 0.849 03513s 0.850 t la 0.8506 + 3 0.8511 t 7
-
21 23 23 24 26 -
-_
-
0.5782 JZ5 0.579a 0.5783 + 5 0.5787 f 1
1.0046 * 10 1 .006a 1.007 * 4 1.008 t 3
20 22 -
Eeu.950 FeZMo30a Fe, Fe3M02 FegMosOa, FesMo, Fe&IosOa
Hexagonal
Fe2MoOq, FeaMog MoOg, MO
aThe original data were multiplied by 0.100202.
232
Fe
a- Fel MO)
MO F+iO,
(4
0
MO
(b) Fig. 1. Isothermal sections of the Fe-MO-0
system at (a) 1173 K and (b) 1273 K.
233
4. Electromotive
force measurements
From knowledge of the phase relations in the Fe-MO-0 system the unknown Gibbs energies of formation of FeaMoe, FezMoOd and FesMosOs were determined above 1189 K by the arrangement of three galvanic cells as follows: a-Fe1 -,Mo,,
FesMos,
FesMo2, FezMoOd, FesMos,
FezMoO
I FeQseO, Fe
FesMosOsIThOo~Y2031Feo.s50, IThOs - Y,03 IFeaseO,
MO, FezMosOs
The e.m.f. measurements the cells a-Fe1 _xMo,,
IThOs*YsOs
(I)
Fe
(II)
Fe
(III)
would have been possible below 1189 K by use of
FezMoOd,
a-Fe1 -xM~, , FesMos,
Fe,Mo,Os FesMosOs
IThOs*Y,Os
IFeasaO, Fe
IThOa- YsOs I FesssO,
(Ia)
Fe
(IIa)
and cell (III). The terminal solubility of molybdenum in the a-Fe(Mo) solid solution in equilibrium with FesMo, is given by xMO = -0.18 + 0.00620T within the temperature range of the e.m.f. measurements [ 111. The total reactions of the cells (I) - (III) for a virtual current from the right-hand electrode to the left-hand electrode, considering the FesMo, homogeneity range to be from 39 to 43 at.% MO [ 111, are given by 0.17 0.39 -x
Fel_,Mo,
1 - 3x + 0.39 -x Fe o.slMoo.39 + 4Feo.950
= FezMoOd + 3.8Fe
(1)
3.816Fe0.61Mo0.39 + 5.295FeQgs 0 = FezMoOd + 0.162FezMo30s
+
+ 5.030Fe 3.569Fe0.57Mo0.43 + 1.491Mo
(2)
+ 8Feo.g50 = FesMo30s
+ 7.6Fe
(3)
Anticipating the Gibbs energy of formation of Fe3Moz f y, the iron activities on the iron- and molybdenum-rich sides of the homogeneity range have been estimated to be 0.94 and 0.38 respectively at 1200 K. Assuming linearity of AG, in the homogeneity range, the integration of the Gibbs-Duhem equation results in a very small increase in the Gibbs energy of formation with increasing iron content in Fe3Moa + y which gives f AG”(Feo.61Mooss> ‘A G” (Feo.s,Moo.43) = +50 J mol-’ at 1200 K. Therefore, the homogeneity range of Fe,Mos f y can be neglected with respect to the change in the Gibbs energy of formation and eqns. (1) - (3) can be simplified to 1 ~ 2-5.x
1 - 3x Fe1 _xMox + -2 _ b FesMoa + 4Fee.ss 0 = FezMoO
4Fe,Mo,
+ 28Feo.gs0
= 5FesMo0,
+ Fe,Mo30s
2Fe3Mos
+ 5Mo + 24FeoSg50 = 3FezMo30s
+ 26.6Fe
+ 22.8Fe
+ 3.8Fe
(4) (5) (6)
234
The following relations are given for the Gibbs energies of reaction ‘AGi” of the cells (I) - (III): 1-3X rAG1o = -8FEI= fAG”(FesMoO,> - 2--5xfAGo (FesMos) 1 - 2-5X =AGfIo = -56FEn
fAG”Wel_,M~,)
= 5fAGo (FesMoOJ
- 4fAGo{Fe0S9sO~
(7)
+ ‘AGO(FesMosOs) -
- 4”AG” (Fe,Moa> - 28fAG0 (Fee.ssO>
“AGUI’= -4WEm
(3)
= 3fA G” (FesMosOs) - 2’A Go (FesMos) - 24fh G” (Fe,s50)
(9)
In these equations Eiis the e.m.f. measured in the cells (I) - (III), Fis Faraday’s constant and fAG,” are the Gibbs energies of formation of the phases given in the angular brackets. The rearrangement of the equations with respect to the Gibbs energies of formation of the three phases gives fAG” (FesMoa)
3 =l-x -
‘A Go (FezMoO,)
=-
‘AGo (Fe1 __,MoJ -
F(40E,- 56Err + 16&r,) 2
6-15x
(16)
5-5X
‘AG” (Fe1 _.-*MO,) + 4fAGo (FeessO> -
1-X
-
2-5X
1-3X
1-3X
l-x
5-5X
5-5X
--48FE~II--+168FE,, 16FEI------2
fAG” (FesMosOs) = 1-X
(11) “AGo(Fe1 _-xMO,) + 8fAGo~Fes.9s0~ 2-5X
2-5X
l-x
5-5X
+ 112FErr -16FE1------
-
3-5X
48FE,11 5-5x (1%
The two-phase equilibria Fe(Mo)-FesMoa and FesMos-Mo(Fe) and the phase FesMos have been formed by arc melting the elements and by subsequent annealing at 1373 K. The stoichiometric oxides FesMoOd and FesMosOs have been produced under an argon atmosphere by solid state reaction of the components iron, FesOs and MoOs at 1273 K. The electrodes have been made by mixing and sintering the initial products under argon at 1273 K.
235
5. Results The e.m.f.s of the ceIIs (I) - (III) as functions of temperature in Fig. 2. The least-squares method calculations result in E,
(kO.3) = 60.5 + 1.8 - (0.0420
are given
f 0.0014)T
(mV) 1180 - 1320 K En (kO.3) = 83.7 f: 2.9 - (0.0615 ?r 0.0023)T (mV) 1210 - 1320 K Em (10.6) = 117.7 + 3.5 - (0.0834 ? 0.0028)T (mV) 1180 - 1320 K
(13) (14) (15)
The Gibbs energies of formation of FesMoa, FezMoO and Fe,MosOs as formulated in eqns. (10) - (12) are then calculated with eqns. (13) - (15) and with the Gibbs energies of formation of Fee,ssO [ 301 and of e-Fe1 _,Mo,. The Gibbs energy of formation of o-Fe, _xMo, is evaluated on the basis of a regular solution model with an interaction parameter A = 17.78 kJ mol-l given in ref. 10: fAG” (Fe, _xMox) = +4055 - 4.43T (J mol-r )
1200 - 1300 K
(16)
xMO of molybdenum
in a-Fe is -0.18
fA G” (FeaMoe)
= +46.1 - 0.0533T
+ 3.1 (kJ mol-l)
fA
= -1081.7
+ 0.2667T
+ 2.6 (kJ mol-I)
(18)
= -2267.8
+ 0.6165T
-+ 4.5 (kJ mol-‘)
(19)
The termindt solubility [ 111. This results in
G” (FezMoOS
fA G” (FesMosOs)
+ 0.00020T (17)
within the temperature range 1180 - 1330 K. The Gibbs energy of formation of FesMoe determined in this paper is presented in Fig. 3 together with values from the literature.
6. Discussion Kirchner et al. [lo] and Kaufman and Nesor [ 311 have calculated the Gibbs energy of formation of FesMo, on the basis of a regular solution model by use of different interaction parameters. Spencer and Putland [32] have determined the heat of formation and the heat capacity of FesMo, with a high temperature adiabatic catorimeter (773 - 1573 K) and have evaluated the Gibbs energy of formation of FesMoa between 773 and 1600 K on the basis of one Gibbs energy of formation value at 1445 K calculated by Kirchner et al. [lo]. Niissler et al. 1331 have measured the heat of formation of FesMoa at 1450 K, using a newly designed high temperature “tandem” cdlorimeter. Rezukhina and Kashina [28] have determined the Gibbs energy of formation of FesMo, by e.m.f. measurements; however, they used an incorrect Fe-MO-0 phase diagram for the galvanic cell arrangements. These results are illustrated in Fig. 3.
236 T(K) 1100 15 \
-
1200 I
1300 I
!
-cQ \o
10
5-
900
850
900
950 tl'c)
T(K)
900
1050
1100
1300
950
1000 t(T)
T(K) 1200
1050
-
1200
850
1000
-
_
1300
Fig. 2. Electromotive forces as functions of temperature: (a) cell (I); (b) cell (II); (c) cell (III). 0, 0, *, ThO, - Y,Og;v , ZrO2 - CaO. The different symbols represent the results of various experiments (see text).
237
1
-
O’
-1
1
A oze Lx ,” ‘t “* -4
/
Rezukhma
-3-
and
-----
Kashrell978) ,
\I
-L
I
. -5-
Spencer
Putland
11975)
Nesorl1975)
talc.
-
emf
_,I=----------
-6-
Kwchner
.900
and
study,
t
calorimetry
-7
Kaufman
>qhis and
emf
et al
119731 calculated
I
I
/
I
I
I
1000
1100
1200
1300
IL00
1500
T
1600
I K I -,-----~__+L
Fig. 3. Gibbs energy of formation of FeaMo2 as a function of temperature.
The average value of the heat of formation of FeaMo, from ref. 33 gives -9385 J (mol Fe,Mo,)-’ at 1450 K. The heat of formation at lower temperatures can then be calculated by use of the enthalpies of iron [ 341, molybdenum 1351 and Fe,Mo, [ 32,351, which results in -10390 J (mol Fe,Mo2)-’ at 1250 K and +14980 J (mol Fe,Mo&’ at 298 K. The Gibbs energy of formation of Fe,Mo, at 1250 K from this study as well as the heat of formation of Fe,Moz and the standard entropies of iron [34] and molybdenum [ 351 at the same temperature and the temperature dependence of the heat capacity of Fe,Moz f35] can then be taken to calculate the standard entropy of FesMo, at 298 K which gives 177 J K-l (mol Fe,Mo,)-l. From these results an averaged three-term expression can be calculated for the Gibbs energy of formation of Fe,Mo, between 298 and 1500 K, giving
fAG” (Fe,Mo,> = +1&O - 0.05352’ + 0.0000177T2
(kJ mol-’ )
(20)
with an error of +4.0 kJ mol-‘. Consequently, Fe,Mo2 should become unstable below 400 K. The Gibbs energy of formation of FezMoO, is -768.9 + 2.6 kJ mol ml at 1173 K (eqn. (18)) and is about 5 kJ mol-’ more negative than the value which can be deduced from the reaction 2Fe + MO + 4C02 = FezMoOd + 2C0 investigated by Schmahl and Dillenburg [ 271 at the same temperature. The Gibbs energies of formation of FesMoz, FezMoO, and FezMoaOs, determined in the present study, may be used to predict the change in the phase field distribution of the Fe-MO-0 system between 1173 and 1273 K on the metal-rich side of the wustite-Moo2 boundary. The Gibbs energy of the reaction (4 - l~)Fe~MoO*
+ (1 +x)FesMo,
= (2 - 5x)Fe2MosOs + 7FeI _XMoX (21)
gives ‘AG”= -199400
+ 167.7T (J (mol of reaction)-l)
(22)
238
between 1180 and 1330 K. The condition rAG” = 0 in eqn. (22) is fulfilled at a temperature T = 1189 K for the four-phase equilibrium in eqn. (21). The thermodynamic data in eqns. (16) - (19) are in accordance with the twophase equilibria in Fig. 1: the Fe(Mo)-FesMosOs equilibrium observed at 1173 K changes to the FesMos-FeaMoO, equilibrium observed at 1273 K at a predicted temperature of 1189 K. Acknowledgment The authors wish to thank Mr. W. Laumer for conducting the experiments. References 1 H. KIeykamp, Rep. KfK-Ext. 6/75-2,1975, p. 38 (Kernforschungszentrum Karlsruhe). 2 H. KIeykamp,J. Less-Common Met., 71 (1980) 127. 3 H. Kleykamp, V. Schauer and W. Laumer, Rep. KfK 2993 B, 1980, p. 138 (Kernforschungszentrum Karlsruhe). 4 W. P. Sykes, Trans. Am. Sot. Steel Treat., 10 (1926) 839; 16 (1929) 358. 5 T. Takei and T. Murakami, Sci. Rep.Tohoku Univ. Ser. 1, 18 (1929) 135. 6 S. R. BaenandP. Duwez,J. Met., 3 (1951) 331. 7 J. W. Putman, R. D. Potter and N. J. Grant, Trans. Am. Sot. Met., 43 (195 1) 824. 8 R. V. Skolozdra and E. I. Gladyshevskii, Inorg. Mater. (U.S.S.R.), 2 (1966) 1237. 9 A. K. Shina, R. A. Buckley and W. Hume-Rothery, J. Iron Steel Inst., London, 205 (1967) 191. 10 G. Kirchner, H. Harvig and B. Uhrenius, Metall. Trans., 4 (1973) 1059. 11 C. P. Heijwegen and G. D. Rieck, J. Less-Common Met., 37 (1974) 115. 12 H. Arnfeldt and A. Westgren, Jernkontorets Ann., 119 (1935) 185. 13 A. Westgren, Sci. Rep. Tohuku Univ. Ser. 1, K. Honda Anniversary Vol., (1936) 852. 14 C. J. Bechtoldt and H. C. Vacher, J. Res. Natl. Bur. Stand., 58 (1957) 7. 15 T. Miyazaki, S. Takagishi, H. Mori and T. Kozakai, Acta Metall., 28 (1980) 1143. 16 R. P. Zaletaeva, N. F. Lashko, M. D. Nesterova and S. A. Yuganova, Dokl. Akad. Nauk S.S.S.R., 81 (1951) 415. 17 J. Higgins and P. Wilkes, Philos. Mag., 25 (1972) 599. 18 R. D. Rawlings and C. W. A. Newey, J. Iron Steel Inst., London, 206 (1968) 723. 19 A. Raman, 2. Metallkd., 57 (1966) 301. 20 W. H. McCarroll, L. Katz and R. Ward, J. Am. Chem. Sot., 79 (1957) 5410. 21 Yu. D. Kozmanov and T. A. Ugolnikova, Russ. J. Znorg. Chem., 3 (1958) 284. 22 G. Monnier, Bull. Sot. Chem. Fr., (1959) 298; (1959) 1252. 23 W. Jiger, A. Rahmel and K. Becker, Arch. Eisenhiittenwes., 30 (1959) 435. 24 Yu. D. Kozmanov, Russ. J. Inorg. Chem., 5 (1960) 996. 25 W. Kunnmann, D. B. Rogers and A. Weld, J. Phys. Chem. Solids, 24 (1963) 1535. 26 L. N. Rusakov, I. A. Novokhatskii, L. M. Lenev and A. A. Savinskaja, Dokl. Akad. Nauk S.S.S.R., 161 (1965) 410. 27 N. G. Schmahl and H. Dillenburg, 2. Phys. Chem., N.F., 77 (1972) 113. 28 T. N. Rezukhina and T. A. Kashina, J. Chem. Thermodyn., 10 (1978) 279. 29 N. Schonberg, Acta Chem. Stand., 8 (1954) 630,932. 30 C. B. Alcock and S. Zador, Electrochim. Acta, 12 (1967) 673. 31 L. Kaufman and H. Nesor, Metall. Trans. A,6 (1975) 2123. 32 P. J. Spencer and F. H. Putland, J. Chem. Thermodyn., 7 (1975) 531. 33 H. D. Niissler, T. Hoster and 0. Kubaschewski, 2. Metatlkd., 71 (1980) 396. 34 JANAF thermochemical tables, Natl. Stand. Ref. Data Ser., NBS, 1971 (U.S. National Bureau of Standards). 35 L. Brewer and R. H. Lamoreaux, At. Energy Rev., Spec. Issue, 7 (1980) 11.