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A thermodynamic assessment of the iron-oxygen system
Vo1.2, No.2, pp.147-167. 0 PergamonPress Limited,1978. Printedin Great Britain.
CALPHAD
A THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM P. J. Spencer and 0. Kubaschewski Lehrstuhl fiirMetallurgic der Kernbrennstoffe und Theoretische Hilttenkunde, Rheinisch-Westfglische Technische Hochschule Aachen, Germany
1. Introduction The iron-oxygen system has been and continues to be the subject of a very great number of experimental studies concerned with the precise definition of thermodynamic properties, including the phase boundaries, of the various solid and liquid phases of the system. Subsequent to the excellent thermodynamic analysis of iron oxide phase relations carried out by Darken and Gurry (1.2) some 30 years ago. a large amunt of experimental work has provided additional information for example for the solutions of oxygen 0) phase and for the equilibrium in liquid iron, for the solid wtistite (Fe between magnetite ('Fe3040 and hematite 1-y('Fe203'). A number of authors have carried out assessments of the published experimental data for one or other of the phases or phase-equilibria in the system, but it is evident that if the necessary consistency of thermodynamic values between all the phases is to be achieved, then the different equilibria must be considered not independently, but in a single over-all assessment of the iron-oxygen system. In the present assessment, solid wiistite has been chosen as the most suitable 'reference phase' for the entire system, since by far the greatest amount of experimental data is available for this phase. Figure 1 illustrates the complete phase diagram accepted here for the ironoxygen system and will be referred to frequently in the discussions which follow. 2. The Wiistite Phase Field The results of many of the experimental determinations of the wCistite phase boundaries are summarised in the compilations due to Hansen and Anderko, to Elliott and to Shunk (3). More recent experimental studies of wiistite have provided additional phase boundary information (4-8),and recent reviews of the thermodynamic properties of the phase made by Giddings and Gordon (9) and by Lbhberg and Stannek (10) also contain summarised information on the stability range of w(istite. There has been some controversy in the literature regarding the existence of three allotropic varieties of wiistite, & w W2* and W3 above 1184 K and three additional varieties W' Wi, and W' low this temperature. Care1 and Gavarri (11) have recently s!&marised thd structural evidence for varieties Wl, W2, and W3, while Giddings and Gordon (9) have discussed the experimental problems associated with some thermodynamic studies which, by demonstrating changes in measured properties, also appear to reveal structural changes in wUstite.
147
P. J. Spencerand 0. Kubaschewski
148
In the present assessment wUstite will be treated as a continuous single phase region, for it already seems clear from the conflicting evidence available, that precise definition of changes in equilibrium thermodynamic values corresponding to the boundaries of the various wtlstiteallotropes will probably require accuracies greater than those associated with currently available measurements for the phase. Figure 2 illustrates the results of a number of investigationsof the tistite phase boundaries. The phase limits tabulated by Darken and Gurry (1) have been accepted here since their studies were self-consistentboth with regard to their directly- observed phase boundaries and to the thermodynamic values determined as part of the same study. 2.1 The Equilibrium Reaction (1-y)Fe(s)+ 3 02 (4) = Fel_yO(s) Thermodynamic studies of the iron-oxygen-wUstiteequilibria reported in the literature may be seen in Table f. Experimental methods used include equilibration of specimens with CO/CO2 or H2/H20 gas mixtures, thermogravimetric techniques, and emf measurements using solid electrolytes. There is generally good agreement between the different sets of measurements, irrespectiveof the experimental method used, and most reported Gibbs free energies of formation for wfistiteof composition corresponding to that of the Fe-rich boundar of the phase lie within 2000 - 3000 J/m01 of each other at all temperatures between 833 and 1644 K. This ie illustrated in Figure 3, where a representative set of plots of AGB vs T/K are presented. The selected values for the Gibbs free energy of formation of wiistiteat its iron-rich boundary have not been based on these data alone, however, but after consideration also of reported values across the entire Mstite phase (see below). Table I Therraodynamic Studies of the Equilibrium Reaction (l-~)Fe(a) * f O,(g)
= Fe1_yO(s)
Authors
a
Schenck and Dingmann(l2) &mm&t and Schultz(l3) chipman and Marshall(l4) Darken and Gurry(1) Himmel, t&h1 and Birchenall (15) Hauffe and Pfeiffer(16) Edstrbm(l7) Marion(18) Kiukkola and Wagner(19) Peters and Mann(20) Koch(21) Mstsushita and Goto(22) Barbi(23) Vallet and Raccah(24)
1927 1930 1940 1945 1953 1953 1953 1955 1957 1958 1961 1963 1964 1964
1965 Gerlach, Probst and NeuschUtz(25) Steele and Alcock(26) 1965 Tretyakov and Schmalzried 1965 (27) Ackermann and Sandford(4) 1966 von Bogdandy and Engell(28) 1967
Method CO/CO equilibration H2/rr26equilibration H2/R20 equilibration CO/CO2 equilibration
Approx.Temp. Range (K) 873 - 1373 873 - 1273 1438 - 1644 1311 - 1638
H2/B20 equilibration 1073 Thermogravimstric 1173 CO/CO2 and H2/H20 equil. 873 H2/H20 equilibration 898 1073 emf emf 943 898 gas equilibration 773 emf emf 973 Thermograv.with 1073 co/co2 equilibration 1083 CO/CO2 equilibration emf emf CO/CO2 equilibration co/co2 and H2/H20 equil. review
-
1256 1273 1673 1498 1373 1523 1644 1179 1273 1523
- 1313
873 - 1373 1003 - 1503 972 - 1277 903 - 1675
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
149
1500
1250 --
,000
__
a-Fe+Wiistite
0.54
Fig.1:
The
iron-oxygen
phase
’
0.h
x0 --
0.h
diagram
200
t 5 16W
1200
800
6W
Fig.2
0150
0.52
0.54 x0 -_)
0.55
:qstite phase boundaries accordidg to different exp.investigations
Fig.3:
The Gibbs
free energy . rormation of Fe function
of tem&tuZ,"
of El
150
P. J. Spencerand 0. Kubaschewski
O/Fe-1.11
1.08
1.05
1.11
1.16
‘9 Yo-_
0.51
o d o X
Rim a Smith M.l Giddings tenI. Sockel a Schmotzried Lykosov et a,. temt.1 *cker”unn a Wtord
+
SuwJcp
v 0
Wet a Raccohllhermogm Marion IHp2OI
. 0
Bronsky Lahberg
awagner
0.52
0.53
0.54
0,ss
Iend ,WL
ICOKn21
a Hed tCOlC02l aStonnek
Ica/co2.a2/af3l
Fig.6: The relative partial entropy of solution of oxyg in the wtlstite phase
Fig.4: Experimental determinations of log PO2 across the wiistite phase
0.51
0.52
0.53
A4 e -
Morucca
Selected
el.o1,1348K values
-270 -
x0
Fig.5: The relative partial enthalpy of solution of oxygen in the wtistite phase
--)
Fig.7: ISO-p contours for the wUsti ?8 phase calculated fro the selected thermodynamic data
151
THERMODYNAMIC ASSESSMENTOF THE IRON-OXYGENSYSTEM
Table I (cont.) 8waroop and Wagner(5) Oharette and Flengas(29) Bransky and Hed(30) Socks1 and Schmalzried(31) Rizzo and Smith(32) Rizzo, Gordon and Cutler(8) Moriyama, Sato, Aaao and Kozuka(33) Fender and Riley(34) Riecke and Bohnenkamp(35) Lykasov et a1.(7) Fischer and Pateisky(36) Picard and Dode(37)
1967 1968 1968 1968 1968 1969 1969
1223 - 1523 co/co2 equilibration 903 - 1543 emf Thermograv. with co/co2eq. 1273 - 1573 1473 emf 1038 - 1238 emf 813 - 1473 emf 973 - 1373 emf
1969 1969 1969 1970 1970
Ariya and Yakovleva(38) Viktorovich, Lisovskii and Zhaglov(39) Su-I1 Pyun!40) Lljhberg and Stannek(l0)
1970 1972
emf co/co2 and H2/H20 equil. emf emf Thermograv.with CO/C02/H2 equilibration emf HZ/H20 equilibration
1173 - 1310 1346 - 1646
1975 1975
emf Hz/H20 equilibration
1073 - 1173 1173 - 1373
973 1073 973 803
- 1623 - 1373 - 1473 - 1643 1173
2.2 Thermodynamic Values across the Wiistite Phase There are many reported thermodynamic studies of wiistite across its range of composition (e.g. 1, 4, 5, 7, 8, 10, 15, 16, 18, 23, 24, 30-32, 34, 35, 37, 38, 41). Discrepancies which exist between the results of different authors are most noticeable in the case of emf measurements, and in particular for experimental temperatures below about 1173 K and for oxygen-rich compositions of the phase. In Figure 4, the results of a number of investigations of the wCistite phase are plotted as log p vs composition for a range of temperatures. These 02 using different experimental techniques, demonstrate results, obtained a general consistency both with regard to the actual values of log p at different temperatures and to the linear concentration dependence 02 of the log p. values at each temperature. (The symbols on the curves in most cases 2 do not represent experimental points but simply serve to indicate the curves obtained from the results of different workers.) The data shown in Figure 4 provide Gibbs free energy values for wllstite, whereas the calorimetric measurements carried out at 1348 K by Harucco, Gerdanian and Dode(41) enable the partial enthalpies of mixing of oxygen in Fe 0 to be directly determined. (The latter study supersedes earlier repohEXd measurements (42) by the same authors.) The partial enthalpy values due to Marucco et al.(see Figure 5) were combined with partial Gibbs energies of oxygen at 1348 K, obtained from the data shown in Figure 4, to calculate partial entropy values for oxygen by use of the equation AGO = AH - T AS-. The values-of AH and ASOat selected wilstite compositions s ere the R recombined (assumr -8g their temperature independence) to calculate AG values at various temperatures. It was found that agreement with the origi*Ral experimental partial Gibbs energies was poor (up to + 3000 - 3350 J/g-atom discrepancyi at temperatures 200 - 300 K away from 1348 K and that the introduction of a constant E-. value to express the temperature dependence of the partial enthalpies --Y and entropies did not improve the agreement. An analysis was therefore made of the partial enthalpies and entropies of oxygen obtained from a composite treatment of the different Gibbs energy investigations, and temperature-independent values of AH and AS were selected for compositions corresponding to values of O/Fe bet&en 1.06 %d 1.16. The selected values are shown in Figure 5 and 6 and listed in Table II.Using the selected data,
152
P. J. Spencer
and 0.
Kubaschewski
it was found possible to reproduce the original experimental AG values to within + 850 J/g-atom for nearly all temperatures covered by thg experimental data shown in Figure 4. The partial enthalpies and entropies of oxygen have been used to derive iso-p. contours across the wUstite phase (Figure 7), and the intercepts of these 2 contours on the Fe-rich boundary of the phase define the temperature dependence of the Gibbs free energy of formation‘at the boundary according to the reaction specified at section 2.1. The intercept values of AG: are plotted in Figure 3. Partial Gibbs energies of solution of iron in wiistite were obtained by means of the Gibbs-Ouhem relation. The temperature coefficients of the AGPe data provided partial enthalpies and entropies of iron in wUstite. Integral thermodynamic values for the wUstite phase were finally calculated from the partial properties by use of the relation AZ = x0 AZ0 + xPe AZFe, where Z corresponds to G, Ii or S. A complete list of selected thermodynamic values for the wiistite phase of the iron-oxygen system is given in Table II.Temperature ranges for application of these data are also listed and have been obtained by reference to the wUstite phase boundaries shown in Figures 1 and 2. It can be seen from the iron-oxygen phase diagram that there are difficulties associated with expressing thermodynamic values for wtistite at room temperature, since under equilibrium conditions, w6stite dissociates into&-Fe and Fe 0 at temperatures below 833 K - the wiistite composition at the dissociat904 0 according to the present selected data. ~o~ve:3s",~:',u~~a~~~~g~~~~~~~ n t s are reported for tistite of composition Fe0 9470 at temperatues where the oxide is in reality metastable. Thus . Table II Selected Thermodynamic Values for the Solid WUstite Phase
o/Fe
1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16
"0
0.5146 0.5169 0.5192 0.5215 0.5238 0.5261 0.5283 0.5305 0.5327 0.5349 0.5370
‘se “Fe 'Rf "f AHO AsO (J/g-atom) (J/K* (J/g* (J/K. (J/g* (J/K* goatom ) atom) g *atom) atom) g -atom
-262460 -263800 -265100 -266270 -266815 -267025 -266940 -266690 -266270 -265770 -264930
-66.23 -69.54 -72.68 -75.73 -78.41 -80.96 -83.26 -85.44 -87.40 -89.29 -91.09
1445 2885 4150 5375 6505 7550 7930 7545 6570 5295 3450
3.81 7.32 10.75 14.18 17.57 20.92 23.68 26.11 28.16 30.04 31.46
-134360 -134965 -135645 -136285 -136660 -136900 -137285 -137940 -138770 -139695 -140670
-32.234 -32.405 -32.564 -32.706 -32.702 -32.677 -32.815 -33.066 -33.401 -33.786 -34.346
Temp.Range (K) 839 872 910 952 1000 1060 1126 1200 1274 1352 1433
-
1647 1650 1654 1658 1661 1664 1668 1672 1676 1679 1682
From the intercepts of the selected data at the Fe-rich boundary of w6stiter AGf(FeO .g530) - -261182 + 62.93 T or alternatively AGf(FeO . 488'0 . 512)
J/m01
- -133733 + 32.221 T
(1050 - 1550 K) J/g-atom
(1050 - 1550 K).
Todd and Ronnickson(43) have carried out C measurements in the range 52 to 298 K and from their results have derived g standard entropy value, STg8, for 0 of 59.41 + 0.84 J/K.mol. This figure included a calculated $ contributi& of 1.72 J/K-m01 due to completely random distribution of
153
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
the vacant iron spaces in the FsO.9470 lattice. Earlier low-temperatureC P (44) in the temperature range 70.7 - 279.8 A. Heat capacity values in the temperature range 298 - 1784 X (i.e. including data for liquid wlietitefhave been obtained from the heat content msaeuremnts made by Coughlin, King and ~nnickson(45). Their data for solid wiietiteof composition Fe0 *947 0 can be represented by the equation
nmauurenmnte ware made by Millar
Cp(J/X.mol) - 48.79 + 8.37*10-3T - 2 .80~105T-2
(298 - 1644 K)
(i.e. including the metaetable range between 298 and 833 K). The liquid has a constant heat capacity of 68.2 J/K.mol. 0, obtained from the The enthalpy of formation of wtietiteof composition Fe present analysis of experimsntal data msaeured in the edwrature range 1038 to 1573 X, is -26106O.J/m01. If the msan temperature of this range, 1305 X, is taken as the reference temperature for the AI-If value, then using the above C 0 within experiment& 0 (aesmrmd to be the mum for Fe equation for Fe error), togethe$!'%&h C data for Fe(46) and for 0xy&11~?47), a value of be calculated. The value so obtained is AH (298J/mol. x, for Fe0.9458AScan(29* K) for Fe 0 is similarly calculated to be -264005 with the standard entropies of -68.551 J/X-m&and this vafue, in =onjun=?i~~' iron and oxygen, produces a value of 59.79 J/K==1 for @ figure is in excellent agreement with the experimental va 0.8 J/K*mol reported by Todd and Bonnickson(43) for the almost identical composition Fe0 . 9470. It is recommended, therefore, that since the wUetite dissociation composition 0 is the equilibrium composition of wUstite stable to the lowest of Fe tempe&&%!e, it should be used as the reference composition for room temperature thermodynamic values for the phase. From the present selected data, these are calculated to bs A~~(298 K, Fe0 I94sO) = - 263005 J/la01 s~98(Fe0.9450) = 59.79 J/X'mol 3. The Wstite - Mxanetite Esuilibrium Phase boundary studies relevant to the wlfstite-magnetite equilibrium have been sunnnarieedby Hansen (3), whose selected values are based on the work of Darken and Gurry(2) and are shown in Pigure 1. Thermodynamic data for magnetite at the iron-rich boundary of the phase (i.e. at the etoichioamtric composition Fe 0 I have been calculated from the selected values for wUstite in the following ddner. Partial Gibbs energies of mixing of oxygen and of iron at the oxygen-rich boundary of wUstite(i.e. compositions of wiietitewhich are in equilibrium with magnetite) have been interpolated from the data given in Table II at one hundred degree intervals. Since these values of AG and AG are constant through the w8etite + magnetite two-phase region, they %e ale$ehe partial Gibbs energies of oxygen and iron respectively at the stoichiomatric composition Fe304. They can therefore be recombined using the expression AG = x AG + ~s~G~g~~~e~o =+~*~.57f~~dd~~v~,";rf8~:s~~do~f;ain Gibbs energies of'for&iatio Table III and illustrated in Figure 8. TO check the consistency of the selected data for wUstite and magnetite, the following condition was investigated.At the temperature of 833 K, wUetite of undergoes eutectoid decomposition into 'pure' iron ",~~~~~~~;t~8f4~a~8~rlfan Fe0.428600_5714. Hence the Gibbs energy change for the reaction 0.1948 Fe(e) + 1.75 Feo~428600~5714(e)= 1.9448 Fe0~485800~5142(e)
154
P. J. Spencerand 0. Kubaschewski
must be zero at 833 R. From the sslected data, AG for wfistiteof the eutectoid composition is equal to -107320 J/seato& at 833 K (see Figure 3). Since AGf for pure Fe is sero, then from the above equation ) must be -119265 J/g-atom at 833 K. From the plot of ~~f[~~004?8~~oT%l&own in Figure 8 this is found to be the case as clogely3a$ can be read from the graph. Table III Thermodynamic Values Relating to the Wtfstite-Magnetite Equilibrium Temp. wiistite boundary (K) (x0)
AG in 2-phase w@st.+magnet. (J/g-atom)
in Z-phase AGf of wtist. 40 of A%i t.+magnet. at O-rich Fb304 (J/g-atom) boundary (J/g.atom: (J/g.atom)
-3548 -203135 873 0.5170 -117590 -106735 -104685 -113530 -9966 -191210 973 0.5226 -15525 -179620 0.5265 -109285 1073 -101920 -22075 -105140 -167445 -99075 0.5297 1173 -29040 -155015 -101025 0.5327 -96150 1273 -36460 -142465 -97020 0.5354 -93220 1373 -44410 -129285 0.5381 -92870 1473 -90080 -54025 -114850 0.5412 -88780 1573 -86945 In the temperature range 800 - 1600 K the Gibbs energy of formation of Fe304 can be represented by the equation: Y/g*atom AGf - -153805 + 41.42 T or = -1076625 + 289.95 T J/mol AGf Experimental therrmdynamic data pertaining to the wiistite-magnetite equilibrium have been obtained, for example, by (4, 8, 12, 13, 23, 19, 31-34, 48, 49). However, it is not a straight forward matter to make a consistent comparison of the selected Gibbs energies of formation for Fe304 with data reported by the various investigators.Experimental msthode which provide values of AG for Fe304 in most cases involve studies of the equilibrium between Fe1 0 gnd Fe 0 as a function of temperature. Since there are considerable discrgpanciei besden the reported compositions of Fe 0 at the oxygen-rich boundary of wiistite,there are also likely to be si@ficant differences in the experimant; 0 with Fe 0 . Consequently, no Gibbs energies for the equilibrium of Fe serious attempt has been made hera to an&e all Id deported Gibbs energies of formation of magnetite, although it is observed that there is very good agreement between the present selected values and data reported by e.g.(1,9,391 (see Figure 8), for which studies there is also close agreement as to the position of the oxygen-rich boundary of wUetite. ht 298 R the composition of magnetite is well-defined at the stoichiomstric composition Fe 0 . Roth (50, 51) has made measurements of the enthalpy of formation of tAe4compound at 298 K using both bomb calorimetry and acid solution calorimetry. The values of AH he obtained were -1111.7 and -1115.9 kJ/mol,respectively.Humphrey, King and Kelley (52) have determined the enthalpy change for the reaction Fe0_g470(8) + 0.8215 Fe(s) + 0.6787 O2 (gl = 0.5895 Fe304(8) The average value of AH (298 K) obtained from two experimsntal determinations was -391.04 kJ/mol. If fihepresent assessed value of -263.01 kJ/mol for 0) is used in conjunction with the above equation, then AHf(Fe304) as -1109.6 kJ/mol. From the above values for the enthalpy of formation of Fe304, a figure of-1112.92 4.0 kJ/mol is selected.
THE~D~~IC
ASSESS~NT OF THE IRON-OVEN
SYSTEM
155
Low-temperature heat capacity amasuremants on Fe 0 have been carried out (90 - 295 K) and by by Millar(44) (60.5 - 299.7 K) , by Parks and KelR$(53) Westrum and Grenvold(54) (5 - 350 K) . The extrapolations involved in deriving standard entropy values from the first two mentioned studies are avoided by the lower temperature smasurements made by Westrum and Gronvold, whose value for Fe 0 is therefore considered to be tire reliable. The value of s d was la6?15 J/K.mol, but the authors indicated that a zero point obta entropy of 3.39 J/K-m01 may be associated with the compound. High-temperature heat content measurement on Fe 0 have been summarised by Coughlin, King and BonnicksonfQS), who themselves shade measurements in the range 298 - 1825 K.~!Phe heat content data for magnetite show a magnetic anomaly around 880 K which correspondsto a maximum in the heat capacity. The C date were therfore represented in two temperature ranges, (which does not i&ply a structural transformation), as given below: Cp(J/%.mol) = 91.55 + 0.202 T(+ 0.6 %) = 200.83(+ 0.2 %)
(298 - 900 K) (900 - 1825 K)
for Fe 0 (-1112.9 kJ/mol and 146.15 If the values of AH (298 K) and So values of Coughlin et J/K.mol respectively jf are combined2%th the &alpy al. to calculate AG (Fe 0 ) at higher temperatures, the values obtained in the range 800 - 1606 K ir& between approximately 0 and 775 J/g.atom less negative than those derived via the selected data for wtistite. However, if a possible 3.35 J/~.mol zero point entropy of Fe 0 (54) is added to the So value of 146.15 J/K.mol, then the calculated AG 3d%ta differ by an averag ;49* of about 165 J/g-atom only from the selected va fues in the range 800 - 1600 K. The selected value Of '398 for Fe304 is therefore 149.50 J/k.mol. 4. The Maqnetite Phase Field The variation of the partial pressure of oxygen across the magnetite phase field has been investigated by Darken and Gurry(2), by Greig et al.(SS) and by Smiltens(56), all of whom used a gas equilibration msthod, and by Sockel and Schmalsried(31) using a solid electrolyte emf technique. In addition, Schmalzried and Tretjakow(57) have calculated values of log p for different magnetite compositions on the basis of disorder models. There 02.is good general consistency between the different experimental results, and the latter are also in excellent agreement with the log p values at the composition Fe304 as obtained via the selected data for '2 wiistite. Nevertheless, the derivation of AH and AS0 values from the temperature coefficients of the log PO data is c8 nsidered to be too unreliable, in the case of magnetite, 2 warrant tabulation of the values obtained. However, it is observed to that AH appears to change in value from about -209200 J/g.atom at x = 0.572 to abou q -138100 J/g.atom at x0 = 0.577. At the same two composition P as0 has values of approximately -98.32 J,&.g.atom and -75.3 J/K-g.atom respectively. The log P, values at three different temperatures have been integrated, using the 2 Gibbs-Huhem relation, to obtain values of the partial Gibbs of iron in magnetite. values of AG , AG energy and AGf(= x0 AGO + xpe AGFe) at 1473 K, 1673 K and 1848 K are l%tedFfn Table Iv. 5. The Maqnetite-Hematite Equilibrium The phase boundaries corresponding to the equilibrium between the 'Fe30 ’ and ‘Fe20 ’ phases and to the stability range of Fe20 are shown in Figure f. There are c2 nsiderable differences with regard to the r;i ported range of homogeneity tf,;'e~G?: (3). For example, White, Graham and Hay(58) and Schm~l(59) report I rty of Fe in hematite of about 0.12 - 0.35 at% at 1573 K, increasing to about 0.53 at% at 1723 K. On the other hand, Greig et al.(55) have found the solubility of Fe to be less than 0.024 at% for all temperatures between
1.3343
1.3348
1.3359 1.3364
1.3474 1.3548
1.3585
1.3629 1.3708
0.5716
0.5717
0.5719 0.5720
0.5740 0.5753+
0.5760
0.5768 0.5782+
Phase boundary
1.3337
0.5715
+
O/Fe
xO
Values
composition
-45185 -38035
-63805 -61840
-86190
-101045
-9625
-17405
-26570
-43345 -41800
-47700
-50960
-69205
0
-3450
-12760
-26275 -25105
-29290
-31800
-35230
1848~
Phase
IV
-156270 -165995
-131450 -134065
-101615
-81840
-60180
-186215
-174885
-162040
-139340 -141400
-133535
-129180
-104870
K
-182160
-177140
-163865
-145275 -146860
-141230
-137870
-133295
1848
at 1473 K, 1673
%e (J/g-atom) 1473 K 1673 K
for the Magnetite
A00 (J/g-atom) K 1673~
-116860
1473
Thermodynamic
Table
-92510 -92380
-92765 -92750
-92795
-92820
-92845
1473
K
-84110
-84180
-84280
-84440 -84430
-84460
-84470
-84490
AGf (J/g-atom) K 1673 K
K and 1848
-77090
-77095
-77130
-77220 -77215
-77230
-77240
-77250
1848 K
F $ : z 1 E.
0 .
B *
a" B : 1
4 .
.cd
157
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
1473
K and 1723 K and Ruer and Nakato(60) report 'practically zero' eolubility of Fe in hematite between 1423 K and 1473 K. The boundaries illustrated in Figure 1 are based on the emf and static oxygen pressure msasuremnts
carried out by Komarov and Oleinikov(61).which produced the following values for the solubility of Fe in hematite: Fe
T(K) solubility(at%)
1173 0.014
1273 0.024
1526 0.054
1567 0.066
1611 0.086
1657 0.123
A number of thermodynamic studies of the magnetite-hematiteequilibrium are reported in the literature(c.g. 2, 29, 33, 59, 62-67). These investigations have provided values of the Gibbs energy change for the reaction 4 Fe304(s) + O,(g) = 6 Fe203(e) for tewratures between 573 K and 1730 K. The experimental data have been treated in the following way. Por the temperature8 below about 1250 K, the magnetite phase does not have a significant range of homgeneity and consequently its composition can ba considered to b8 stoichiometricFe 0 (see Figure 1). The expression given below Table 3 for the Gibbs energy of3f&mation of Fe 0 has therefore been used in combination with the AG values obtained fro& he different experimental Studies of the above equilibrium to calculate AGf (Fe203) as a function of temperature. The latter values are plotted in Figure 9.
For temp8ratures of 1473 K and 1673 K, values of the partial Gibbs energies of oxygen and iron at the oxygen-rich boundary of magnetite (see Table IV), which are constant through the magnetite + hematite Z-phase region, have bean recombined (using the relation AG = x p AGg + %e bGYg)at the composition of the iron-rich boundarv of hematite to D OVI e A cI va es for hematite at 1473 K and 1673 K, These-two values of A& are sh
antiferromagnetictransformatiog in the compound. Coughlin et al. observed a second C maximum at about 1050 K which is presumably also of magnetic origin. In ordefto fit their experimental data, Cpughlin et al. introduced an arbitrary enthalpy of transformationof 670 J/m& at 950 K, although this should not, of course, be considered to represent the with the magnetic transformation. The heat capacity of d-Fe203
total heat effect associated
may be expressed by the following equations
Cp(J/K-mo1) = 98.28 f 77.82.1d3T = 150.6 = 132.67 + 7.364*10-3T
- 14.85S105T-2
(298 - 950 K) (950 - 1050 K) (1050 - 1750 K)
158
P. J. Spencer and 0. Kubaschewski
It is found that there is very good agreemsnt between Gibbs energies of formation of Fe 0 calculated via the selected data for magnetite, asodescribe above, and calcul 2a ted using the calorimetric values for AH (298 K) C (298 - 1250 K), when a value of AH (298 K) of -823410 J/&o1 is f?gure is therefore selected as the gtandard enthalpy of formation of Fs203. 6. The Hematite Phase Field The equilibrium oxygen pressures over solid solutions based on hematite have been measured by Komarov and Olei~ikov(61) using both an emf technique (lo73 1273 K) and a static pressure measurement method (1526 - 1657 K). The values of AG calculated from their data at the Fe-rich boundary of hematite appear to be ?n reasonable agreement with the selected values of AG at the oxygenrich boundary of magnetite. In addition, their experimental m?asurements are in accord with the figure of 1730 K for the dissociation t8mperature of hematite, although the stoichiometriccomposition Fe203 is stable to about 1720 K only (see Figure 1). Because the hematite homogeneity range is very narrow, no partial thernwdynami values are tabulated here, but it is noted that Komarov and Oleinikov report that the partial enthalpy of solution of oxygen in hematite changes from about -246.9 kJ/g*atom at the Fe-rich boundary of the phase to about -154.8 kY/g.atc (The AH data were derived from the measured AGo at stoichiometricFe 0 - 1657 K) . values in the temper&&e range 1.873 The con8istency of tb8 selected data for magnetite and for hematite has final1 been checked using the fact that hematite of composition F8 dissociatss into magnetite of composition Fe0 .41g800.58o2 aRd401800.5982 oxygen at a temperature of 1730 K. Hence, for the reaction 0.9571 Feo.41g800e5802(d
+ 0.0215
o,(g)
- P80.4OlSOO_59S2(s)
AG must be zero at 1730 K. From the values of 6G for magnetite given in of 0 TabfeIV, an interpolated value of AG (1730 K) for Ff -81650 J/g.atom is obtained. Hence, dG (1730 X) for Re~~eQtl3*a8'~omposition = -78147 J/g*atom. From the must be equal to 0.957f ~f8t48f80~~5g03 T/K for hematite shown iz $z:," 9 , the valus of AGf at 1730 F is found tofbe -78157 J/g-atom. licnce,the selected thermodynamic date for magnetite and hematite are consistent. 7. The Liauid Oxide Phase Field Summ8rised phase boundary information relevant to the liquid oxide region of the phase diagram is contained in reference 3. 7.1 The equilibrium reaction 2(1-y) Fe(s) + 02(g) = 2 Fel_yO(l) The equilibrium between solid iron, oxygen and liquid wUstite has been studieC for example by Chipman and Marshall(14), using an H2&20 equilibration m&hod, by Darken and Gurry (2) using CO/CO2 equilibration,by Goto and ~tsushita(70) using an emf mthod and by Fischer and Patefsky(36) also using an emf techniqc The Gibbs free energies of formation of the liquid oxide at the iron-rich boundary of the base, ae obtained by (2. 14, 70), are in good agreement whereas values reported by (36) are about (withint 800 JBmol ‘Fee’), 2500 J/mol 'FeO' less exothermic in the temperature range 1644 - 1809 K. Selected data have been obtained by consideration also of values at higher oxygen concentrationsinthe liquid oxide phase field. 7.2 TheraPdynamicvalues across the liquid oxide phase Thermodynamic studies of the liquid oxide phase have been made by Darken and Gurry (2) and by White (71). In the present assessment, thermodynamic values for the liquid oxide have beer obtained in the following way.
159
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
x Selected doto bxed on wiistite l Viktorwich. L~~kii~Zh~to~ &Z/H$ &JR-13731) 0 6iddings a Eordm iRevie*) 18?3-l673 X1 o i&ken a Gurry LCDICOZ~ 113734673 K) + CatcutaLed via RI wzgfj as298 and heat contents 1298-1600K)
Richardsan and Idles Ehizhikov etat.f1030-12~~ Fmn setected d&o t m~etife phase J
Pig.8:
The Gibbs free energy of formation of magnetite as a function of tevrature
Fig.9: The Gibbs free energy of formation of hematite ae a function of temperature
2023Ks
I Tankins, Gakcen and Man 11823K. H?IHD equBb.1 * Schwerdtfke; 11873K. emf.) 0 Gatellier and Olette (1873K. e.m.f.1 l numbed Sanoll(lZfK, H2/H2B l
.
Onslur ‘and Capon (extrap. to 20231, t$IH20 equitib.1 rb Schenck and Steinmetz 11898K, H2/lt$l equitib.1
-22oooo
c
---(
I
0,002
i
I
I
O#OS
Calc~&~edy!ues with sotubddy limit
I
0,olo
I
I
0.0’
*o
Fig.10:
The
iron at 1823
1923 R
2023
160
Partial
P. J. Spencer and 0. Kubaschewski
Gibbs energies of solution of oxygen in solid wtiatitswere calculated at the aolidua temperature for selected compositions using the data linted in Table II. These values of A0 are constant across the aolidua-liquiduagap and hence they define the va%es of AG in the liquid oxide at various liquidus compositions and temparaturea.'Theliquidua AG values have been combined, at the appropriate compositions,w ith the expe&nental AG values obtained from the results of Darken and Gurry at 1673 K, 1773 K and'1873 K, to enable calculation of the temperature dependence of AG . In this way, partial entropies of mixing of oxygen in the liquid oxide'were obtained. Then, using the relation AG 1:AE - T AS and assuming temperature independence of AH and AS , val8%a of0 AH wepi calculated for the liquid oxide at the relev8nt liqui8ua temperatures'andcompositions. From the experimental results of Darken and Gurry, an enthalpy of fusion of 0 of 30250 $ 2100 J/m01 is derived. This cowares very well with the ok% f 31340 J/mol obtained by Coughlin, King and Bonnickson(45) from high temperature enthalpy measurements on Fe 0. The latter value is preferred, but the concentration dependence of the'&% a1py of fusion of wiiatiteas reported by Darken and Gurry is retained in conjunction with the selected &Ifu at selected wiistitecompositions have value for Fe been ~o~ine~*~~~*~'*' e correspond Of AI%#d enthalpies of formation of Wstite to provide enthalpies of formation of liquid oxide. These values of AH for the liquid, in conjuction with the previoualy calculated AH0 data, provfde values of AI$~ in the liquid oxide( AHf = x0 AH0 + %e AI$~). Finally, since the liquidus-aoliduagap for the wiistitephase is very narrow, use has been made of the fact that the Gibbs energies of formation of solid an liquid wiiafiteof the same composition must have the same value (relativeto t same standard states) at the appropriate aolidus/liquiduatemperature. Thus, using the data in Table II,appropriate values of AGf have been calculated and combined with the dearivedAHf values for the liquid oxide to produce liquid AS, data. Values of A In the liquid oxide phase were then obtained from the calculated values o Sf and AS,. It is of interest to note that the partial enthalpies of mixing of oxygen in liquid oxide obtained from the temperature coefficients of the data measured by Whiteffl) in the composition range x = 0.569 to 0.580 approximately,lie very close (within 4 - 20 kJ/o.atom) to'the straiaht line drawn throuah the AH- values calculated in the-range-x = 0.515 to-O.537 approximately:Further extrapolation of the calculated data ?or the liquid to the composition Fe 0 produces an enthalpy of formation of -133930 J/g.atom approximately. If t&4 value is combined with the value of AHffFe 04) at the mslting point of the compound ( AH solid = -154495 J/g*atom), 2n enthalpy of fusion of Fe 0 of 20565 J/g.ato& results. This is in very good agreement with the figur3 ;4f 19730 + 1190 J/g-atom derived by Darken and Gurry(2) from an analysis of their experimental data. A complete listing of the thermodynamicproperties of the liquid oxide phase is given in Table V. 8. The Eauilibrium Between the Liquid Oxide Phase and Solutions of Oxygen in 6 and Liquid Iron It can be seen from Figure 1 that at temperatures between 1663 R and 1796 K th liquid oxide phase is in equilibrium with solutions of oxygen in &-Fe, and at temperatures above 1796 K liquid oxide is in equilibrium with solutions of oxygen in liquid Fe. Studies of the phase boundaries relevant to these equilibria are given in (3). A further summary of oxygen solubility data has been made by Sawamura and Sano(72) and, more recently, Distfn, Whiteway and Meaaon (73) have defined the oxygen solubility limit at temperatures up to 2230 K uai an experimental method involving levitation of the specimens. Their results ar incorporatad in Figure 1. The partial Gibbs energies of oxygen at the iron-rich boundary of the liquid oxide phase at specific temperatures define the partial Gibbs energies of
0.5146 0.5169
0.5192 0.5215
0.5238
0.5261
0.5283
0.5305
0.5327 0.5349
0.5370
1.08 1.09
1.10
1.11
1.12
1.13
1.14 1.15
1.16
x0
1.06 1.07
O/Fe
AHO
-280245
-284845 -282505
-287190
-289615
-292045
-294470
-299325 -296895
-304260 -301835
(J/g-atom)
ASO
-104.35
-102.63 -103.51
-101.75
-100.88
-100.04
-99.12
-97.32 -98.24
-95.52 -96.40
v
*‘Fe
52070
58810 55500
61870
64620
66750
68550
73250 70670
78640 76035
65.14
64.02 64.81
63.14
62.13
60.96
59.33
56.74 57.91
54.81 55.69
Oxide
Phaoe
-126380
-124255 -125300
-123305
-122525
-122010
-121600
-120190 -121020
-118400 -119285
-25.87
-24.76 -25.23
-24.33
-23.99
-23.75
-23.66
-23.24 -23.51
-22.56 -22.92
dHf AS, (J/g-atom) (J/K.g*atom)
for the Liquid
Table Values
(J/g-atom) (J/K.g*atom)
%e
Thermodynamic
(J/K.g.atom)
Selected
14290
14515 14395
14630
14760
14890
15060
15455 15265
15960 15675
AH fus (J/g-atom)
z C/Y F: s
8 z
?
;;r
8
8
% s K s 3
0
4 s
P. J. Spencer and 0. Kubaschewski
162
oxygen at the appropriate solubility limits in the &and liquid phases of iron from the selected data given in Table 5 and the phase boundaries shown in Figure 1, values of AG at the oxygen solubility limit in 6- and liquid F have been derived. The values are given in Table VI. Hence,
Table VI Partial Gibbs Energies of Oxygen Relevant to the Equilibrium Between Liquid Oxide and Solutionu of Oxygen in 6- and Liquid Iron Iron-rich boundary Solubility limit of Temperature AGO of liquid oxide 0 in& or liq. Fe K (J/g.atom) xO xO 1673 0.5082 0.00032(~) -155515 1723 0.5067 0.00053t6) -153505 1773 0.5053 O.C0085(&) -151230 1823 0.5042 0.0064 iliq) -148655 1873 0.5032 0.0079 (liq) -14.5955 1923 0.5022 0.0097 (liq) -143045 1973 0.5013 0.0118 (liq) -140095 2023 0.5004 0.0141 (liqf -137340 It is, of course, necessary to check the consistency of the value in Table VI with values obtained from experimental thermodynamic investigationsof the solutions of oxygen in 6 - and liquid Fe. There have been numerous such studies of solutions in liquid iron, mainly using equilibrationwith H2fi20 gas mixtures, but more recently also employing solid oxide electrolyte emf methods (e.g. 74 - 90). It is generally agreed that solutions of oxygen in liquid iron obey Henry's Law up to the solubility limit for temperatures between 1823 K and 1973 X. Use has been made of this behaviour to calculate partial Gibbs energies of oxygen in liquid iron at different compositions and temperatures using the values of AG at the solubility limits given in Table VI. The resulting data are plottea as AG vs x at three temperatures in Figure 10, together with experimental value8 obta!?nedfrom six reprssentative investigations.The calculated values are found to lie mostly within 2 1250 J/g*atom of the measured data at the same temperaturqand differences of this magnitude are alw observed between the different experimental studie for the sams temperature of investigation.Consequently, it is demonstrated that there is very good consistency between the selected AGO data for the liquid oxide phase and thermodynamic values for solutions of oxygen in liquid iron. Calculated partial and integral thermodynamic values for the solutions of oxygen in liquid iron are given in Table VII. Table VII Partial and Integral ThermodynamicValues for the Solutionsof Oxygen in Liquid Iron xO 0.0005 0.001 0.002 0.004 0.006 0.008
AH0 (J/g*atom) -130790 -130790 -130790 -130790 -130790 -130790
ASO (J/K-g-atom) 31.05 25.27 19.50 13.77 10.38 7.99
~J~g~~torn~ -67 -130 -264 -523 -787 -1046
(J/K$atom) 0.0197 0.0335 0.0556 0.0883 0.1121 0.1301
The solubility of oxygen in S-Fe has been determined by Tankins and Gokcen(9 from studies of the equilibrium with gaseous H /H 0 mixtures in the temperatu range 1693 - 1783 K. The authors summarise the2daQa obtained by previous
163
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
investigators and from their results derive the following equation to represent the oxygen solubility: log wt% = -12630/T + 5.51 The solubility boundary for oxygen in J-Fe shown in Figure 1 is based on this equation. The values obtained from Tenkins and Gokeen’s data for the partial Gibbs energy of solution of oxygen at the solubility limit in S-Fe at 1673 K, 1723 K and 1773 K are -156503, -154055 and -151670 J/g-atom respectively. These values differ by between 400 and 1000 J/g.atom only from the Values of AG for the 1iqUi.d discrepancies ar% within the oxide - &-Fe equilibrium given in TableVI.The experimental error limits and consequently consistency between selected Gibbs free energies for the liquid oxide phase and experimental values for solutions of oxygen in &Fe is demonstrated, Using the selected partial Gibbs energies of oxygen, the following expression has been derived to represent AGO in S-Fe: AGO
= 13661 - 34.23 T + RT In XC
J/g+atom
9. The Equilibrium Between Wstite and Solutions of Oxygen in b-Fe and d-Fe 0 The solubility of oxygen in both k-Fe and d-Fe is very uncertain and there are considerable discrepancies between the results obtained by many investigators (see(3)). It is apparent that even very small amounts of impurities, in particular silicon and aluminium, can give rise to formation of oxide particles and lead to experimental values for the solubility of oxygen which are too high. Consequently it has been found that the purer the iron sample used, the lower is the oxygen solubility determined.It is also a general finding that the solubility of oxygen in -Fe is 'much lower' than in d-Fe. k The very tentative (and somewhat arbitrary) solubilities selected here, based on the lowest reported solubiliizg values ind-Fe(92), are_ghe temperature invariant values of x0 = 2.4.10 in b-Fe and x0 = 2.4.10 in d-Fe. Wing the selected solubility values and the selected partial Gibbs energies of solution of oxygen at the iron-rich boundary of wtfstite, the following expressions have been derived to represent AG, in & -Fe and &-Fe solid solutions: 170.21 T + RT 3n x0
J/g.atom
AGo(in d-Fe) = -262609 + 153.13 T + RT In x0
J/g-atom
A~~(in k-Fe) = -260149
+
Acknowledqement The work described above has been carried out as part of a research programme on the metallurgical thermochemistry of iron and steel sponsored by the Commission of the European Communities, Division Steel.
164
P. J. Spencer and 0. Kubaschewski
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92. Sifferlen, R., Compt. Rend. 247, 1608 (1958)
167
CALPHAD
A THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM P. J. Spencer and 0. Kubaschewski Lehrstuhl fiirMetallurgic der Kernbrennstoffe und Theoretische Hilttenkunde, Rheinisch-Westfglische Technische Hochschule Aachen, Germany
1. Introduction The iron-oxygen system has been and continues to be the subject of a very great number of experimental studies concerned with the precise definition of thermodynamic properties, including the phase boundaries, of the various solid and liquid phases of the system. Subsequent to the excellent thermodynamic analysis of iron oxide phase relations carried out by Darken and Gurry (1.2) some 30 years ago. a large amunt of experimental work has provided additional information for example for the solutions of oxygen 0) phase and for the equilibrium in liquid iron, for the solid wtistite (Fe between magnetite ('Fe3040 and hematite 1-y('Fe203'). A number of authors have carried out assessments of the published experimental data for one or other of the phases or phase-equilibria in the system, but it is evident that if the necessary consistency of thermodynamic values between all the phases is to be achieved, then the different equilibria must be considered not independently, but in a single over-all assessment of the iron-oxygen system. In the present assessment, solid wiistite has been chosen as the most suitable 'reference phase' for the entire system, since by far the greatest amount of experimental data is available for this phase. Figure 1 illustrates the complete phase diagram accepted here for the ironoxygen system and will be referred to frequently in the discussions which follow. 2. The Wiistite Phase Field The results of many of the experimental determinations of the wCistite phase boundaries are summarised in the compilations due to Hansen and Anderko, to Elliott and to Shunk (3). More recent experimental studies of wiistite have provided additional phase boundary information (4-8),and recent reviews of the thermodynamic properties of the phase made by Giddings and Gordon (9) and by Lbhberg and Stannek (10) also contain summarised information on the stability range of w(istite. There has been some controversy in the literature regarding the existence of three allotropic varieties of wiistite, & w W2* and W3 above 1184 K and three additional varieties W' Wi, and W' low this temperature. Care1 and Gavarri (11) have recently s!&marised thd structural evidence for varieties Wl, W2, and W3, while Giddings and Gordon (9) have discussed the experimental problems associated with some thermodynamic studies which, by demonstrating changes in measured properties, also appear to reveal structural changes in wUstite.
147
P. J. Spencerand 0. Kubaschewski
148
In the present assessment wUstite will be treated as a continuous single phase region, for it already seems clear from the conflicting evidence available, that precise definition of changes in equilibrium thermodynamic values corresponding to the boundaries of the various wtlstiteallotropes will probably require accuracies greater than those associated with currently available measurements for the phase. Figure 2 illustrates the results of a number of investigationsof the tistite phase boundaries. The phase limits tabulated by Darken and Gurry (1) have been accepted here since their studies were self-consistentboth with regard to their directly- observed phase boundaries and to the thermodynamic values determined as part of the same study. 2.1 The Equilibrium Reaction (1-y)Fe(s)+ 3 02 (4) = Fel_yO(s) Thermodynamic studies of the iron-oxygen-wUstiteequilibria reported in the literature may be seen in Table f. Experimental methods used include equilibration of specimens with CO/CO2 or H2/H20 gas mixtures, thermogravimetric techniques, and emf measurements using solid electrolytes. There is generally good agreement between the different sets of measurements, irrespectiveof the experimental method used, and most reported Gibbs free energies of formation for wfistiteof composition corresponding to that of the Fe-rich boundar of the phase lie within 2000 - 3000 J/m01 of each other at all temperatures between 833 and 1644 K. This ie illustrated in Figure 3, where a representative set of plots of AGB vs T/K are presented. The selected values for the Gibbs free energy of formation of wiistiteat its iron-rich boundary have not been based on these data alone, however, but after consideration also of reported values across the entire Mstite phase (see below). Table I Therraodynamic Studies of the Equilibrium Reaction (l-~)Fe(a) * f O,(g)
= Fe1_yO(s)
Authors
a
Schenck and Dingmann(l2) &mm&t and Schultz(l3) chipman and Marshall(l4) Darken and Gurry(1) Himmel, t&h1 and Birchenall (15) Hauffe and Pfeiffer(16) Edstrbm(l7) Marion(18) Kiukkola and Wagner(19) Peters and Mann(20) Koch(21) Mstsushita and Goto(22) Barbi(23) Vallet and Raccah(24)
1927 1930 1940 1945 1953 1953 1953 1955 1957 1958 1961 1963 1964 1964
1965 Gerlach, Probst and NeuschUtz(25) Steele and Alcock(26) 1965 Tretyakov and Schmalzried 1965 (27) Ackermann and Sandford(4) 1966 von Bogdandy and Engell(28) 1967
Method CO/CO equilibration H2/rr26equilibration H2/R20 equilibration CO/CO2 equilibration
Approx.Temp. Range (K) 873 - 1373 873 - 1273 1438 - 1644 1311 - 1638
H2/B20 equilibration 1073 Thermogravimstric 1173 CO/CO2 and H2/H20 equil. 873 H2/H20 equilibration 898 1073 emf emf 943 898 gas equilibration 773 emf emf 973 Thermograv.with 1073 co/co2 equilibration 1083 CO/CO2 equilibration emf emf CO/CO2 equilibration co/co2 and H2/H20 equil. review
-
1256 1273 1673 1498 1373 1523 1644 1179 1273 1523
- 1313
873 - 1373 1003 - 1503 972 - 1277 903 - 1675
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
149
1500
1250 --
,000
__
a-Fe+Wiistite
0.54
Fig.1:
The
iron-oxygen
phase
’
0.h
x0 --
0.h
diagram
200
t 5 16W
1200
800
6W
Fig.2
0150
0.52
0.54 x0 -_)
0.55
:qstite phase boundaries accordidg to different exp.investigations
Fig.3:
The Gibbs
free energy . rormation of Fe function
of tem&tuZ,"
of El
150
P. J. Spencerand 0. Kubaschewski
O/Fe-1.11
1.08
1.05
1.11
1.16
‘9 Yo-_
0.51
o d o X
Rim a Smith M.l Giddings tenI. Sockel a Schmotzried Lykosov et a,. temt.1 *cker”unn a Wtord
+
SuwJcp
v 0
Wet a Raccohllhermogm Marion IHp2OI
. 0
Bronsky Lahberg
awagner
0.52
0.53
0.54
0,ss
Iend ,WL
ICOKn21
a Hed tCOlC02l aStonnek
Ica/co2.a2/af3l
Fig.6: The relative partial entropy of solution of oxyg in the wtlstite phase
Fig.4: Experimental determinations of log PO2 across the wiistite phase
0.51
0.52
0.53
A4 e -
Morucca
Selected
el.o1,1348K values
-270 -
x0
Fig.5: The relative partial enthalpy of solution of oxygen in the wtistite phase
--)
Fig.7: ISO-p contours for the wUsti ?8 phase calculated fro the selected thermodynamic data
151
THERMODYNAMIC ASSESSMENTOF THE IRON-OXYGENSYSTEM
Table I (cont.) 8waroop and Wagner(5) Oharette and Flengas(29) Bransky and Hed(30) Socks1 and Schmalzried(31) Rizzo and Smith(32) Rizzo, Gordon and Cutler(8) Moriyama, Sato, Aaao and Kozuka(33) Fender and Riley(34) Riecke and Bohnenkamp(35) Lykasov et a1.(7) Fischer and Pateisky(36) Picard and Dode(37)
1967 1968 1968 1968 1968 1969 1969
1223 - 1523 co/co2 equilibration 903 - 1543 emf Thermograv. with co/co2eq. 1273 - 1573 1473 emf 1038 - 1238 emf 813 - 1473 emf 973 - 1373 emf
1969 1969 1969 1970 1970
Ariya and Yakovleva(38) Viktorovich, Lisovskii and Zhaglov(39) Su-I1 Pyun!40) Lljhberg and Stannek(l0)
1970 1972
emf co/co2 and H2/H20 equil. emf emf Thermograv.with CO/C02/H2 equilibration emf HZ/H20 equilibration
1173 - 1310 1346 - 1646
1975 1975
emf Hz/H20 equilibration
1073 - 1173 1173 - 1373
973 1073 973 803
- 1623 - 1373 - 1473 - 1643 1173
2.2 Thermodynamic Values across the Wiistite Phase There are many reported thermodynamic studies of wiistite across its range of composition (e.g. 1, 4, 5, 7, 8, 10, 15, 16, 18, 23, 24, 30-32, 34, 35, 37, 38, 41). Discrepancies which exist between the results of different authors are most noticeable in the case of emf measurements, and in particular for experimental temperatures below about 1173 K and for oxygen-rich compositions of the phase. In Figure 4, the results of a number of investigations of the wCistite phase are plotted as log p vs composition for a range of temperatures. These 02 using different experimental techniques, demonstrate results, obtained a general consistency both with regard to the actual values of log p at different temperatures and to the linear concentration dependence 02 of the log p. values at each temperature. (The symbols on the curves in most cases 2 do not represent experimental points but simply serve to indicate the curves obtained from the results of different workers.) The data shown in Figure 4 provide Gibbs free energy values for wllstite, whereas the calorimetric measurements carried out at 1348 K by Harucco, Gerdanian and Dode(41) enable the partial enthalpies of mixing of oxygen in Fe 0 to be directly determined. (The latter study supersedes earlier repohEXd measurements (42) by the same authors.) The partial enthalpy values due to Marucco et al.(see Figure 5) were combined with partial Gibbs energies of oxygen at 1348 K, obtained from the data shown in Figure 4, to calculate partial entropy values for oxygen by use of the equation AGO = AH - T AS-. The values-of AH and ASOat selected wilstite compositions s ere the R recombined (assumr -8g their temperature independence) to calculate AG values at various temperatures. It was found that agreement with the origi*Ral experimental partial Gibbs energies was poor (up to + 3000 - 3350 J/g-atom discrepancyi at temperatures 200 - 300 K away from 1348 K and that the introduction of a constant E-. value to express the temperature dependence of the partial enthalpies --Y and entropies did not improve the agreement. An analysis was therefore made of the partial enthalpies and entropies of oxygen obtained from a composite treatment of the different Gibbs energy investigations, and temperature-independent values of AH and AS were selected for compositions corresponding to values of O/Fe bet&en 1.06 %d 1.16. The selected values are shown in Figure 5 and 6 and listed in Table II.Using the selected data,
152
P. J. Spencer
and 0.
Kubaschewski
it was found possible to reproduce the original experimental AG values to within + 850 J/g-atom for nearly all temperatures covered by thg experimental data shown in Figure 4. The partial enthalpies and entropies of oxygen have been used to derive iso-p. contours across the wUstite phase (Figure 7), and the intercepts of these 2 contours on the Fe-rich boundary of the phase define the temperature dependence of the Gibbs free energy of formation‘at the boundary according to the reaction specified at section 2.1. The intercept values of AG: are plotted in Figure 3. Partial Gibbs energies of solution of iron in wiistite were obtained by means of the Gibbs-Ouhem relation. The temperature coefficients of the AGPe data provided partial enthalpies and entropies of iron in wUstite. Integral thermodynamic values for the wUstite phase were finally calculated from the partial properties by use of the relation AZ = x0 AZ0 + xPe AZFe, where Z corresponds to G, Ii or S. A complete list of selected thermodynamic values for the wiistite phase of the iron-oxygen system is given in Table II.Temperature ranges for application of these data are also listed and have been obtained by reference to the wUstite phase boundaries shown in Figures 1 and 2. It can be seen from the iron-oxygen phase diagram that there are difficulties associated with expressing thermodynamic values for wtistite at room temperature, since under equilibrium conditions, w6stite dissociates into&-Fe and Fe 0 at temperatures below 833 K - the wiistite composition at the dissociat904 0 according to the present selected data. ~o~ve:3s",~:',u~~a~~~~g~~~~~~~ n t s are reported for tistite of composition Fe0 9470 at temperatues where the oxide is in reality metastable. Thus . Table II Selected Thermodynamic Values for the Solid WUstite Phase
o/Fe
1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16
"0
0.5146 0.5169 0.5192 0.5215 0.5238 0.5261 0.5283 0.5305 0.5327 0.5349 0.5370
‘se “Fe 'Rf "f AHO AsO (J/g-atom) (J/K* (J/g* (J/K. (J/g* (J/K* goatom ) atom) g *atom) atom) g -atom
-262460 -263800 -265100 -266270 -266815 -267025 -266940 -266690 -266270 -265770 -264930
-66.23 -69.54 -72.68 -75.73 -78.41 -80.96 -83.26 -85.44 -87.40 -89.29 -91.09
1445 2885 4150 5375 6505 7550 7930 7545 6570 5295 3450
3.81 7.32 10.75 14.18 17.57 20.92 23.68 26.11 28.16 30.04 31.46
-134360 -134965 -135645 -136285 -136660 -136900 -137285 -137940 -138770 -139695 -140670
-32.234 -32.405 -32.564 -32.706 -32.702 -32.677 -32.815 -33.066 -33.401 -33.786 -34.346
Temp.Range (K) 839 872 910 952 1000 1060 1126 1200 1274 1352 1433
-
1647 1650 1654 1658 1661 1664 1668 1672 1676 1679 1682
From the intercepts of the selected data at the Fe-rich boundary of w6stiter AGf(FeO .g530) - -261182 + 62.93 T or alternatively AGf(FeO . 488'0 . 512)
J/m01
- -133733 + 32.221 T
(1050 - 1550 K) J/g-atom
(1050 - 1550 K).
Todd and Ronnickson(43) have carried out C measurements in the range 52 to 298 K and from their results have derived g standard entropy value, STg8, for 0 of 59.41 + 0.84 J/K.mol. This figure included a calculated $ contributi& of 1.72 J/K-m01 due to completely random distribution of
153
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
the vacant iron spaces in the FsO.9470 lattice. Earlier low-temperatureC P (44) in the temperature range 70.7 - 279.8 A. Heat capacity values in the temperature range 298 - 1784 X (i.e. including data for liquid wlietitefhave been obtained from the heat content msaeuremnts made by Coughlin, King and ~nnickson(45). Their data for solid wiietiteof composition Fe0 *947 0 can be represented by the equation
nmauurenmnte ware made by Millar
Cp(J/X.mol) - 48.79 + 8.37*10-3T - 2 .80~105T-2
(298 - 1644 K)
(i.e. including the metaetable range between 298 and 833 K). The liquid has a constant heat capacity of 68.2 J/K.mol. 0, obtained from the The enthalpy of formation of wtietiteof composition Fe present analysis of experimsntal data msaeured in the edwrature range 1038 to 1573 X, is -26106O.J/m01. If the msan temperature of this range, 1305 X, is taken as the reference temperature for the AI-If value, then using the above C 0 within experiment& 0 (aesmrmd to be the mum for Fe equation for Fe error), togethe$!'%&h C data for Fe(46) and for 0xy&11~?47), a value of be calculated. The value so obtained is AH (298J/mol. x, for Fe0.9458AScan(29* K) for Fe 0 is similarly calculated to be -264005 with the standard entropies of -68.551 J/X-m&and this vafue, in =onjun=?i~~' iron and oxygen, produces a value of 59.79 J/K==1 for @ figure is in excellent agreement with the experimental va 0.8 J/K*mol reported by Todd and Bonnickson(43) for the almost identical composition Fe0 . 9470. It is recommended, therefore, that since the wUetite dissociation composition 0 is the equilibrium composition of wUstite stable to the lowest of Fe tempe&&%!e, it should be used as the reference composition for room temperature thermodynamic values for the phase. From the present selected data, these are calculated to bs A~~(298 K, Fe0 I94sO) = - 263005 J/la01 s~98(Fe0.9450) = 59.79 J/X'mol 3. The Wstite - Mxanetite Esuilibrium Phase boundary studies relevant to the wlfstite-magnetite equilibrium have been sunnnarieedby Hansen (3), whose selected values are based on the work of Darken and Gurry(2) and are shown in Pigure 1. Thermodynamic data for magnetite at the iron-rich boundary of the phase (i.e. at the etoichioamtric composition Fe 0 I have been calculated from the selected values for wUstite in the following ddner. Partial Gibbs energies of mixing of oxygen and of iron at the oxygen-rich boundary of wUstite(i.e. compositions of wiietitewhich are in equilibrium with magnetite) have been interpolated from the data given in Table II at one hundred degree intervals. Since these values of AG and AG are constant through the w8etite + magnetite two-phase region, they %e ale$ehe partial Gibbs energies of oxygen and iron respectively at the stoichiomatric composition Fe304. They can therefore be recombined using the expression AG = x AG + ~s~G~g~~~e~o =+~*~.57f~~dd~~v~,";rf8~:s~~do~f;ain Gibbs energies of'for&iatio Table III and illustrated in Figure 8. TO check the consistency of the selected data for wUstite and magnetite, the following condition was investigated.At the temperature of 833 K, wUetite of undergoes eutectoid decomposition into 'pure' iron ",~~~~~~~;t~8f4~a~8~rlfan Fe0.428600_5714. Hence the Gibbs energy change for the reaction 0.1948 Fe(e) + 1.75 Feo~428600~5714(e)= 1.9448 Fe0~485800~5142(e)
154
P. J. Spencerand 0. Kubaschewski
must be zero at 833 R. From the sslected data, AG for wfistiteof the eutectoid composition is equal to -107320 J/seato& at 833 K (see Figure 3). Since AGf for pure Fe is sero, then from the above equation ) must be -119265 J/g-atom at 833 K. From the plot of ~~f[~~004?8~~oT%l&own in Figure 8 this is found to be the case as clogely3a$ can be read from the graph. Table III Thermodynamic Values Relating to the Wtfstite-Magnetite Equilibrium Temp. wiistite boundary (K) (x0)
AG in 2-phase w@st.+magnet. (J/g-atom)
in Z-phase AGf of wtist. 40 of A%i t.+magnet. at O-rich Fb304 (J/g-atom) boundary (J/g.atom: (J/g.atom)
-3548 -203135 873 0.5170 -117590 -106735 -104685 -113530 -9966 -191210 973 0.5226 -15525 -179620 0.5265 -109285 1073 -101920 -22075 -105140 -167445 -99075 0.5297 1173 -29040 -155015 -101025 0.5327 -96150 1273 -36460 -142465 -97020 0.5354 -93220 1373 -44410 -129285 0.5381 -92870 1473 -90080 -54025 -114850 0.5412 -88780 1573 -86945 In the temperature range 800 - 1600 K the Gibbs energy of formation of Fe304 can be represented by the equation: Y/g*atom AGf - -153805 + 41.42 T or = -1076625 + 289.95 T J/mol AGf Experimental therrmdynamic data pertaining to the wiistite-magnetite equilibrium have been obtained, for example, by (4, 8, 12, 13, 23, 19, 31-34, 48, 49). However, it is not a straight forward matter to make a consistent comparison of the selected Gibbs energies of formation for Fe304 with data reported by the various investigators.Experimental msthode which provide values of AG for Fe304 in most cases involve studies of the equilibrium between Fe1 0 gnd Fe 0 as a function of temperature. Since there are considerable discrgpanciei besden the reported compositions of Fe 0 at the oxygen-rich boundary of wiistite,there are also likely to be si@ficant differences in the experimant; 0 with Fe 0 . Consequently, no Gibbs energies for the equilibrium of Fe serious attempt has been made hera to an&e all Id deported Gibbs energies of formation of magnetite, although it is observed that there is very good agreement between the present selected values and data reported by e.g.(1,9,391 (see Figure 8), for which studies there is also close agreement as to the position of the oxygen-rich boundary of wUetite. ht 298 R the composition of magnetite is well-defined at the stoichiomstric composition Fe 0 . Roth (50, 51) has made measurements of the enthalpy of formation of tAe4compound at 298 K using both bomb calorimetry and acid solution calorimetry. The values of AH he obtained were -1111.7 and -1115.9 kJ/mol,respectively.Humphrey, King and Kelley (52) have determined the enthalpy change for the reaction Fe0_g470(8) + 0.8215 Fe(s) + 0.6787 O2 (gl = 0.5895 Fe304(8) The average value of AH (298 K) obtained from two experimsntal determinations was -391.04 kJ/mol. If fihepresent assessed value of -263.01 kJ/mol for 0) is used in conjunction with the above equation, then AHf(Fe304) as -1109.6 kJ/mol. From the above values for the enthalpy of formation of Fe304, a figure of-1112.92 4.0 kJ/mol is selected.
THE~D~~IC
ASSESS~NT OF THE IRON-OVEN
SYSTEM
155
Low-temperature heat capacity amasuremants on Fe 0 have been carried out (90 - 295 K) and by by Millar(44) (60.5 - 299.7 K) , by Parks and KelR$(53) Westrum and Grenvold(54) (5 - 350 K) . The extrapolations involved in deriving standard entropy values from the first two mentioned studies are avoided by the lower temperature smasurements made by Westrum and Gronvold, whose value for Fe 0 is therefore considered to be tire reliable. The value of s d was la6?15 J/K.mol, but the authors indicated that a zero point obta entropy of 3.39 J/K-m01 may be associated with the compound. High-temperature heat content measurement on Fe 0 have been summarised by Coughlin, King and BonnicksonfQS), who themselves shade measurements in the range 298 - 1825 K.~!Phe heat content data for magnetite show a magnetic anomaly around 880 K which correspondsto a maximum in the heat capacity. The C date were therfore represented in two temperature ranges, (which does not i&ply a structural transformation), as given below: Cp(J/%.mol) = 91.55 + 0.202 T(+ 0.6 %) = 200.83(+ 0.2 %)
(298 - 900 K) (900 - 1825 K)
for Fe 0 (-1112.9 kJ/mol and 146.15 If the values of AH (298 K) and So values of Coughlin et J/K.mol respectively jf are combined2%th the &alpy al. to calculate AG (Fe 0 ) at higher temperatures, the values obtained in the range 800 - 1606 K ir& between approximately 0 and 775 J/g.atom less negative than those derived via the selected data for wtistite. However, if a possible 3.35 J/~.mol zero point entropy of Fe 0 (54) is added to the So value of 146.15 J/K.mol, then the calculated AG 3d%ta differ by an averag ;49* of about 165 J/g-atom only from the selected va fues in the range 800 - 1600 K. The selected value Of '398 for Fe304 is therefore 149.50 J/k.mol. 4. The Maqnetite Phase Field The variation of the partial pressure of oxygen across the magnetite phase field has been investigated by Darken and Gurry(2), by Greig et al.(SS) and by Smiltens(56), all of whom used a gas equilibration msthod, and by Sockel and Schmalsried(31) using a solid electrolyte emf technique. In addition, Schmalzried and Tretjakow(57) have calculated values of log p for different magnetite compositions on the basis of disorder models. There 02.is good general consistency between the different experimental results, and the latter are also in excellent agreement with the log p values at the composition Fe304 as obtained via the selected data for '2 wiistite. Nevertheless, the derivation of AH and AS0 values from the temperature coefficients of the log PO data is c8 nsidered to be too unreliable, in the case of magnetite, 2 warrant tabulation of the values obtained. However, it is observed to that AH appears to change in value from about -209200 J/g.atom at x = 0.572 to abou q -138100 J/g.atom at x0 = 0.577. At the same two composition P as0 has values of approximately -98.32 J,&.g.atom and -75.3 J/K-g.atom respectively. The log P, values at three different temperatures have been integrated, using the 2 Gibbs-Huhem relation, to obtain values of the partial Gibbs of iron in magnetite. values of AG , AG energy and AGf(= x0 AGO + xpe AGFe) at 1473 K, 1673 K and 1848 K are l%tedFfn Table Iv. 5. The Maqnetite-Hematite Equilibrium The phase boundaries corresponding to the equilibrium between the 'Fe30 ’ and ‘Fe20 ’ phases and to the stability range of Fe20 are shown in Figure f. There are c2 nsiderable differences with regard to the r;i ported range of homogeneity tf,;'e~G?: (3). For example, White, Graham and Hay(58) and Schm~l(59) report I rty of Fe in hematite of about 0.12 - 0.35 at% at 1573 K, increasing to about 0.53 at% at 1723 K. On the other hand, Greig et al.(55) have found the solubility of Fe to be less than 0.024 at% for all temperatures between
1.3343
1.3348
1.3359 1.3364
1.3474 1.3548
1.3585
1.3629 1.3708
0.5716
0.5717
0.5719 0.5720
0.5740 0.5753+
0.5760
0.5768 0.5782+
Phase boundary
1.3337
0.5715
+
O/Fe
xO
Values
composition
-45185 -38035
-63805 -61840
-86190
-101045
-9625
-17405
-26570
-43345 -41800
-47700
-50960
-69205
0
-3450
-12760
-26275 -25105
-29290
-31800
-35230
1848~
Phase
IV
-156270 -165995
-131450 -134065
-101615
-81840
-60180
-186215
-174885
-162040
-139340 -141400
-133535
-129180
-104870
K
-182160
-177140
-163865
-145275 -146860
-141230
-137870
-133295
1848
at 1473 K, 1673
%e (J/g-atom) 1473 K 1673 K
for the Magnetite
A00 (J/g-atom) K 1673~
-116860
1473
Thermodynamic
Table
-92510 -92380
-92765 -92750
-92795
-92820
-92845
1473
K
-84110
-84180
-84280
-84440 -84430
-84460
-84470
-84490
AGf (J/g-atom) K 1673 K
K and 1848
-77090
-77095
-77130
-77220 -77215
-77230
-77240
-77250
1848 K
F $ : z 1 E.
0 .
B *
a" B : 1
4 .
.cd
157
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
1473
K and 1723 K and Ruer and Nakato(60) report 'practically zero' eolubility of Fe in hematite between 1423 K and 1473 K. The boundaries illustrated in Figure 1 are based on the emf and static oxygen pressure msasuremnts
carried out by Komarov and Oleinikov(61).which produced the following values for the solubility of Fe in hematite: Fe
T(K) solubility(at%)
1173 0.014
1273 0.024
1526 0.054
1567 0.066
1611 0.086
1657 0.123
A number of thermodynamic studies of the magnetite-hematiteequilibrium are reported in the literature(c.g. 2, 29, 33, 59, 62-67). These investigations have provided values of the Gibbs energy change for the reaction 4 Fe304(s) + O,(g) = 6 Fe203(e) for tewratures between 573 K and 1730 K. The experimental data have been treated in the following way. Por the temperature8 below about 1250 K, the magnetite phase does not have a significant range of homgeneity and consequently its composition can ba considered to b8 stoichiometricFe 0 (see Figure 1). The expression given below Table 3 for the Gibbs energy of3f&mation of Fe 0 has therefore been used in combination with the AG values obtained fro& he different experimental Studies of the above equilibrium to calculate AGf (Fe203) as a function of temperature. The latter values are plotted in Figure 9.
For temp8ratures of 1473 K and 1673 K, values of the partial Gibbs energies of oxygen and iron at the oxygen-rich boundary of magnetite (see Table IV), which are constant through the magnetite + hematite Z-phase region, have bean recombined (using the relation AG = x p AGg + %e bGYg)at the composition of the iron-rich boundarv of hematite to D OVI e A cI va es for hematite at 1473 K and 1673 K, These-two values of A& are sh
antiferromagnetictransformatiog in the compound. Coughlin et al. observed a second C maximum at about 1050 K which is presumably also of magnetic origin. In ordefto fit their experimental data, Cpughlin et al. introduced an arbitrary enthalpy of transformationof 670 J/m& at 950 K, although this should not, of course, be considered to represent the with the magnetic transformation. The heat capacity of d-Fe203
total heat effect associated
may be expressed by the following equations
Cp(J/K-mo1) = 98.28 f 77.82.1d3T = 150.6 = 132.67 + 7.364*10-3T
- 14.85S105T-2
(298 - 950 K) (950 - 1050 K) (1050 - 1750 K)
158
P. J. Spencer and 0. Kubaschewski
It is found that there is very good agreemsnt between Gibbs energies of formation of Fe 0 calculated via the selected data for magnetite, asodescribe above, and calcul 2a ted using the calorimetric values for AH (298 K) C (298 - 1250 K), when a value of AH (298 K) of -823410 J/&o1 is f?gure is therefore selected as the gtandard enthalpy of formation of Fs203. 6. The Hematite Phase Field The equilibrium oxygen pressures over solid solutions based on hematite have been measured by Komarov and Olei~ikov(61) using both an emf technique (lo73 1273 K) and a static pressure measurement method (1526 - 1657 K). The values of AG calculated from their data at the Fe-rich boundary of hematite appear to be ?n reasonable agreement with the selected values of AG at the oxygenrich boundary of magnetite. In addition, their experimental m?asurements are in accord with the figure of 1730 K for the dissociation t8mperature of hematite, although the stoichiometriccomposition Fe203 is stable to about 1720 K only (see Figure 1). Because the hematite homogeneity range is very narrow, no partial thernwdynami values are tabulated here, but it is noted that Komarov and Oleinikov report that the partial enthalpy of solution of oxygen in hematite changes from about -246.9 kJ/g*atom at the Fe-rich boundary of the phase to about -154.8 kY/g.atc (The AH data were derived from the measured AGo at stoichiometricFe 0 - 1657 K) . values in the temper&&e range 1.873 The con8istency of tb8 selected data for magnetite and for hematite has final1 been checked using the fact that hematite of composition F8 dissociatss into magnetite of composition Fe0 .41g800.58o2 aRd401800.5982 oxygen at a temperature of 1730 K. Hence, for the reaction 0.9571 Feo.41g800e5802(d
+ 0.0215
o,(g)
- P80.4OlSOO_59S2(s)
AG must be zero at 1730 K. From the values of 6G for magnetite given in of 0 TabfeIV, an interpolated value of AG (1730 K) for Ff -81650 J/g.atom is obtained. Hence, dG (1730 X) for Re~~eQtl3*a8'~omposition = -78147 J/g*atom. From the must be equal to 0.957f ~f8t48f80~~5g03 T/K for hematite shown iz $z:," 9 , the valus of AGf at 1730 F is found tofbe -78157 J/g-atom. licnce,the selected thermodynamic date for magnetite and hematite are consistent. 7. The Liauid Oxide Phase Field Summ8rised phase boundary information relevant to the liquid oxide region of the phase diagram is contained in reference 3. 7.1 The equilibrium reaction 2(1-y) Fe(s) + 02(g) = 2 Fel_yO(l) The equilibrium between solid iron, oxygen and liquid wUstite has been studieC for example by Chipman and Marshall(14), using an H2&20 equilibration m&hod, by Darken and Gurry (2) using CO/CO2 equilibration,by Goto and ~tsushita(70) using an emf mthod and by Fischer and Patefsky(36) also using an emf techniqc The Gibbs free energies of formation of the liquid oxide at the iron-rich boundary of the base, ae obtained by (2. 14, 70), are in good agreement whereas values reported by (36) are about (withint 800 JBmol ‘Fee’), 2500 J/mol 'FeO' less exothermic in the temperature range 1644 - 1809 K. Selected data have been obtained by consideration also of values at higher oxygen concentrationsinthe liquid oxide phase field. 7.2 TheraPdynamicvalues across the liquid oxide phase Thermodynamic studies of the liquid oxide phase have been made by Darken and Gurry (2) and by White (71). In the present assessment, thermodynamic values for the liquid oxide have beer obtained in the following way.
159
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
x Selected doto bxed on wiistite l Viktorwich. L~~kii~Zh~to~ &Z/H$ &JR-13731) 0 6iddings a Eordm iRevie*) 18?3-l673 X1 o i&ken a Gurry LCDICOZ~ 113734673 K) + CatcutaLed via RI wzgfj as298 and heat contents 1298-1600K)
Richardsan and Idles Ehizhikov etat.f1030-12~~ Fmn setected d&o t m~etife phase J
Pig.8:
The Gibbs free energy of formation of magnetite as a function of tevrature
Fig.9: The Gibbs free energy of formation of hematite ae a function of temperature
2023Ks
I Tankins, Gakcen and Man 11823K. H?IHD equBb.1 * Schwerdtfke; 11873K. emf.) 0 Gatellier and Olette (1873K. e.m.f.1 l numbed Sanoll(lZfK, H2/H2B l
.
Onslur ‘and Capon (extrap. to 20231, t$IH20 equitib.1 rb Schenck and Steinmetz 11898K, H2/lt$l equitib.1
-22oooo
c
---(
I
0,002
i
I
I
O#OS
Calc~&~edy!ues with sotubddy limit
I
0,olo
I
I
0.0’
*o
Fig.10:
The
iron at 1823
1923 R
2023
160
Partial
P. J. Spencer and 0. Kubaschewski
Gibbs energies of solution of oxygen in solid wtiatitswere calculated at the aolidua temperature for selected compositions using the data linted in Table II. These values of A0 are constant across the aolidua-liquiduagap and hence they define the va%es of AG in the liquid oxide at various liquidus compositions and temparaturea.'Theliquidua AG values have been combined, at the appropriate compositions,w ith the expe&nental AG values obtained from the results of Darken and Gurry at 1673 K, 1773 K and'1873 K, to enable calculation of the temperature dependence of AG . In this way, partial entropies of mixing of oxygen in the liquid oxide'were obtained. Then, using the relation AG 1:AE - T AS and assuming temperature independence of AH and AS , val8%a of0 AH wepi calculated for the liquid oxide at the relev8nt liqui8ua temperatures'andcompositions. From the experimental results of Darken and Gurry, an enthalpy of fusion of 0 of 30250 $ 2100 J/m01 is derived. This cowares very well with the ok% f 31340 J/mol obtained by Coughlin, King and Bonnickson(45) from high temperature enthalpy measurements on Fe 0. The latter value is preferred, but the concentration dependence of the'&% a1py of fusion of wiiatiteas reported by Darken and Gurry is retained in conjunction with the selected &Ifu at selected wiistitecompositions have value for Fe been ~o~ine~*~~~*~'*' e correspond Of AI%#d enthalpies of formation of Wstite to provide enthalpies of formation of liquid oxide. These values of AH for the liquid, in conjuction with the previoualy calculated AH0 data, provfde values of AI$~ in the liquid oxide( AHf = x0 AH0 + %e AI$~). Finally, since the liquidus-aoliduagap for the wiistitephase is very narrow, use has been made of the fact that the Gibbs energies of formation of solid an liquid wiiafiteof the same composition must have the same value (relativeto t same standard states) at the appropriate aolidus/liquiduatemperature. Thus, using the data in Table II,appropriate values of AGf have been calculated and combined with the dearivedAHf values for the liquid oxide to produce liquid AS, data. Values of A In the liquid oxide phase were then obtained from the calculated values o Sf and AS,. It is of interest to note that the partial enthalpies of mixing of oxygen in liquid oxide obtained from the temperature coefficients of the data measured by Whiteffl) in the composition range x = 0.569 to 0.580 approximately,lie very close (within 4 - 20 kJ/o.atom) to'the straiaht line drawn throuah the AH- values calculated in the-range-x = 0.515 to-O.537 approximately:Further extrapolation of the calculated data ?or the liquid to the composition Fe 0 produces an enthalpy of formation of -133930 J/g.atom approximately. If t&4 value is combined with the value of AHffFe 04) at the mslting point of the compound ( AH solid = -154495 J/g*atom), 2n enthalpy of fusion of Fe 0 of 20565 J/g.ato& results. This is in very good agreement with the figur3 ;4f 19730 + 1190 J/g-atom derived by Darken and Gurry(2) from an analysis of their experimental data. A complete listing of the thermodynamicproperties of the liquid oxide phase is given in Table V. 8. The Eauilibrium Between the Liquid Oxide Phase and Solutions of Oxygen in 6 and Liquid Iron It can be seen from Figure 1 that at temperatures between 1663 R and 1796 K th liquid oxide phase is in equilibrium with solutions of oxygen in &-Fe, and at temperatures above 1796 K liquid oxide is in equilibrium with solutions of oxygen in liquid Fe. Studies of the phase boundaries relevant to these equilibria are given in (3). A further summary of oxygen solubility data has been made by Sawamura and Sano(72) and, more recently, Distfn, Whiteway and Meaaon (73) have defined the oxygen solubility limit at temperatures up to 2230 K uai an experimental method involving levitation of the specimens. Their results ar incorporatad in Figure 1. The partial Gibbs energies of oxygen at the iron-rich boundary of the liquid oxide phase at specific temperatures define the partial Gibbs energies of
0.5146 0.5169
0.5192 0.5215
0.5238
0.5261
0.5283
0.5305
0.5327 0.5349
0.5370
1.08 1.09
1.10
1.11
1.12
1.13
1.14 1.15
1.16
x0
1.06 1.07
O/Fe
AHO
-280245
-284845 -282505
-287190
-289615
-292045
-294470
-299325 -296895
-304260 -301835
(J/g-atom)
ASO
-104.35
-102.63 -103.51
-101.75
-100.88
-100.04
-99.12
-97.32 -98.24
-95.52 -96.40
v
*‘Fe
52070
58810 55500
61870
64620
66750
68550
73250 70670
78640 76035
65.14
64.02 64.81
63.14
62.13
60.96
59.33
56.74 57.91
54.81 55.69
Oxide
Phaoe
-126380
-124255 -125300
-123305
-122525
-122010
-121600
-120190 -121020
-118400 -119285
-25.87
-24.76 -25.23
-24.33
-23.99
-23.75
-23.66
-23.24 -23.51
-22.56 -22.92
dHf AS, (J/g-atom) (J/K.g*atom)
for the Liquid
Table Values
(J/g-atom) (J/K.g*atom)
%e
Thermodynamic
(J/K.g.atom)
Selected
14290
14515 14395
14630
14760
14890
15060
15455 15265
15960 15675
AH fus (J/g-atom)
z C/Y F: s
8 z
?
;;r
8
8
% s K s 3
0
4 s
P. J. Spencer and 0. Kubaschewski
162
oxygen at the appropriate solubility limits in the &and liquid phases of iron from the selected data given in Table 5 and the phase boundaries shown in Figure 1, values of AG at the oxygen solubility limit in 6- and liquid F have been derived. The values are given in Table VI. Hence,
Table VI Partial Gibbs Energies of Oxygen Relevant to the Equilibrium Between Liquid Oxide and Solutionu of Oxygen in 6- and Liquid Iron Iron-rich boundary Solubility limit of Temperature AGO of liquid oxide 0 in& or liq. Fe K (J/g.atom) xO xO 1673 0.5082 0.00032(~) -155515 1723 0.5067 0.00053t6) -153505 1773 0.5053 O.C0085(&) -151230 1823 0.5042 0.0064 iliq) -148655 1873 0.5032 0.0079 (liq) -14.5955 1923 0.5022 0.0097 (liq) -143045 1973 0.5013 0.0118 (liq) -140095 2023 0.5004 0.0141 (liqf -137340 It is, of course, necessary to check the consistency of the value in Table VI with values obtained from experimental thermodynamic investigationsof the solutions of oxygen in 6 - and liquid Fe. There have been numerous such studies of solutions in liquid iron, mainly using equilibrationwith H2fi20 gas mixtures, but more recently also employing solid oxide electrolyte emf methods (e.g. 74 - 90). It is generally agreed that solutions of oxygen in liquid iron obey Henry's Law up to the solubility limit for temperatures between 1823 K and 1973 X. Use has been made of this behaviour to calculate partial Gibbs energies of oxygen in liquid iron at different compositions and temperatures using the values of AG at the solubility limits given in Table VI. The resulting data are plottea as AG vs x at three temperatures in Figure 10, together with experimental value8 obta!?nedfrom six reprssentative investigations.The calculated values are found to lie mostly within 2 1250 J/g*atom of the measured data at the same temperaturqand differences of this magnitude are alw observed between the different experimental studie for the sams temperature of investigation.Consequently, it is demonstrated that there is very good consistency between the selected AGO data for the liquid oxide phase and thermodynamic values for solutions of oxygen in liquid iron. Calculated partial and integral thermodynamic values for the solutions of oxygen in liquid iron are given in Table VII. Table VII Partial and Integral ThermodynamicValues for the Solutionsof Oxygen in Liquid Iron xO 0.0005 0.001 0.002 0.004 0.006 0.008
AH0 (J/g*atom) -130790 -130790 -130790 -130790 -130790 -130790
ASO (J/K-g-atom) 31.05 25.27 19.50 13.77 10.38 7.99
~J~g~~torn~ -67 -130 -264 -523 -787 -1046
(J/K$atom) 0.0197 0.0335 0.0556 0.0883 0.1121 0.1301
The solubility of oxygen in S-Fe has been determined by Tankins and Gokcen(9 from studies of the equilibrium with gaseous H /H 0 mixtures in the temperatu range 1693 - 1783 K. The authors summarise the2daQa obtained by previous
163
THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM
investigators and from their results derive the following equation to represent the oxygen solubility: log wt% = -12630/T + 5.51 The solubility boundary for oxygen in J-Fe shown in Figure 1 is based on this equation. The values obtained from Tenkins and Gokeen’s data for the partial Gibbs energy of solution of oxygen at the solubility limit in S-Fe at 1673 K, 1723 K and 1773 K are -156503, -154055 and -151670 J/g-atom respectively. These values differ by between 400 and 1000 J/g.atom only from the Values of AG for the 1iqUi.d discrepancies ar% within the oxide - &-Fe equilibrium given in TableVI.The experimental error limits and consequently consistency between selected Gibbs free energies for the liquid oxide phase and experimental values for solutions of oxygen in &Fe is demonstrated, Using the selected partial Gibbs energies of oxygen, the following expression has been derived to represent AGO in S-Fe: AGO
= 13661 - 34.23 T + RT In XC
J/g+atom
9. The Equilibrium Between Wstite and Solutions of Oxygen in b-Fe and d-Fe 0 The solubility of oxygen in both k-Fe and d-Fe is very uncertain and there are considerable discrepancies between the results obtained by many investigators (see(3)). It is apparent that even very small amounts of impurities, in particular silicon and aluminium, can give rise to formation of oxide particles and lead to experimental values for the solubility of oxygen which are too high. Consequently it has been found that the purer the iron sample used, the lower is the oxygen solubility determined.It is also a general finding that the solubility of oxygen in -Fe is 'much lower' than in d-Fe. k The very tentative (and somewhat arbitrary) solubilities selected here, based on the lowest reported solubiliizg values ind-Fe(92), are_ghe temperature invariant values of x0 = 2.4.10 in b-Fe and x0 = 2.4.10 in d-Fe. Wing the selected solubility values and the selected partial Gibbs energies of solution of oxygen at the iron-rich boundary of wtfstite, the following expressions have been derived to represent AG, in & -Fe and &-Fe solid solutions: 170.21 T + RT 3n x0
J/g.atom
AGo(in d-Fe) = -262609 + 153.13 T + RT In x0
J/g-atom
A~~(in k-Fe) = -260149
+
Acknowledqement The work described above has been carried out as part of a research programme on the metallurgical thermochemistry of iron and steel sponsored by the Commission of the European Communities, Division Steel.
164
P. J. Spencer and 0. Kubaschewski
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167