A thermodynamic assessment of the iron-oxygen system

CALPHAD Vo1.2, No.2, pp.147-167. 0 Pergamon Press Limited, 1978. Printed in Great Britain.

A THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM

P. J. Spencer and 0. Kubaschewski

Lehrstuhl fiir Metallurgic 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 in liquid iron, for the solid wtistite (Fe 0) phase and for the equilibrium 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 iron- oxygen 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 three additional varieties W' Wi, and W'

& W2* and W3 above 1184 K and 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, in wUstite.

also appear to reveal structural changes

147

148 P. J. Spencer and 0. Kubaschewski

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 wtlstite allotropes will probably require accuracies greater than those associated with currently available measurements for the phase.

Figure 2 illustrates the results of a number of investigations of the tistite phase boundaries. The phase limits tabulated by Darken and Gurry (1) have been accepted here since their studies were self-consistent both 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-wUstite equilibria 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, irrespective of the experimental method used, and most reported Gibbs free energies of formation for wfistite of 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 represent- ative set of plots of AGB vs T/K are presented. The selected values for the Gibbs free energy of formation of wiistite at 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

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)

a 1927 1930 1940 1945

1953 1953 1953 1955 1957 1958 1961 1963 1964 1964

Gerlach, Probst and NeuschUtz(25)

1965

Steele and Alcock(26) 1965 Tretyakov and Schmalzried 1965

(27) Ackermann and Sandford(4) 1966 von Bogdandy and Engell(28) 1967

Approx.Temp. Method Range (K)

CO/CO equilibration H2/rr26 equilibration

873 - 1373 873 - 1273

H2/R20 equilibration 1438 - 1644 CO/CO2 equilibration 1311 - 1638

H2/B20 equilibration 1073 - 1256 Thermogravimstric 1173 - 1273 CO/CO2 and H2/H20 equil. 873 - 1673 H2/H20 equilibration 898 - 1498 emf 1073 - 1373 emf 943 - 1523 gas equilibration 898 - 1644 emf 773 - 1179 emf 973 - 1273 Thermograv.with 1073 - 1523 co/co2 equilibration CO/CO2 equilibration 1083 - 1313

emf 873 - 1373 emf 1003 - 1503

CO/CO2 equilibration 972 - 1277 co/co2 and H2/H20 903 - 1675 equil. review

THERMODYNAMIC ASSESSMENT OF THE IRON-OXYGEN SYSTEM 149

1500

1250 --

,000 __ a-Fe+Wiistite

Fig.1: The iron-oxygen

0.54 ’ 0.h 0.h x0 --

phase diagram

200

t 5

16W

1200

800

6W 0150 0.52 0.54 0.55

x0 -_) Fig.3:

Fig.2 :qstite phase boundaries accord- idg to different exp.investigations

The Gibbs free energy of . rormation of Fe function of tem&tuZ," El


O/Fe -- 1.05 1.08 1.11 1.11 1.16

‘9

Rim a Smith M.l

o Giddings tenI.

d Sockel a Schmotzried Iend

o Lykosov et a,. temt.1

X *cker”unn a Wtord ,WL

+ SuwJcp awagner ICOKn21

v Wet a Raccohllhermogm

0 Marion IHp2OI

. Bronsky a Hed tCOlC02l

0 Lahberg aStonnek

Ica/co2.a2/af3l

Fig.4: Experimental determinations of log PO2 across the wiistite phase

0.51 0.52 0.53

A4 e Morucca el.o1,1348K - Selected values

-270 -

Fig.5: The relative partial enthalpy of solution of oxygen in the wtistite phase

0.51 0.52 0.53

Yo-_

0.54 0,ss

Fig.6: The relative partial tropy of solution of in the wtlstite phase

en- oxyg

Fig.7:

x0 --)

ISO-p ?

contours for the wUsti 8 phase calculated fro the selected thermodynamic data


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)

Ariya and Yakovleva(38) Viktorovich, Lisovskii and Zhaglov(39) Su-I1 Pyun!40) Lljhberg and Stannek(l0)

1967 co/co2 equilibration 1223 - 1523 1968 emf 903 - 1543 1968 Thermograv. with co/co2eq. 1273 - 1573 1968 emf 1473 1968 emf 1038 - 1238 1969 emf 813 - 1473 1969 emf 973 - 1373

1969 1969 1969 1970 1970

1970 1972

1975 1975

emf 973 - 1623 co/co2 and H2/H20 equil. 1073 - 1373 emf 973 - 1473 emf 803 - 1643 Thermograv.with CO/C02/H2 1173 equilibration emf 1173 - 1310 HZ/H20 equilibration 1346 - 1646

emf 1073 - 1173 Hz/H20 equilibration 1173 - 1373

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 results, obtained 02 using different experimental techniques, demonstrate a general consistency both with regard to the actual values of log p

02 at

different temperatures and to the linear concentration dependence 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 re- pohEXd 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 at selected wilstite compositions

- T AS-. The values-of AH and ASO- s R ere the recombined (assumr g their -8

temperature independence) to calculate AG values at various temperatures. It was found that agreement with the origi al *R 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-.

--Y value to express the temperature dependence of the partial enthalpies 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,


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. these 2

contours across the wUstite phase (Figure 7), and the intercepts of 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. plotted in Figure 3.

The intercept values of AG: are

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 - at904

the wiistite composition at the dissoci-

~o~ve:3s",~:',u~~a~~~~g~~~~~~~ t 0 according to the present selected data. n 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 "0

1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16

0.5146 0.5169 0.5192 0.5215 0.5238 0.5261 0.5283 0.5305 0.5327 0.5349 0.5370

AHO AsO ‘se “Fe 'Rf "f Temp.Range

(J/g-atom) (J/K* (J/g* (J/K. (J/g* (J/K* (K) goatom ) atom) g *atom) atom) g -atom

-262460 -66.23 1445 3.81 -134360 -32.234 839 - 1647 -263800 -69.54 2885 7.32 -134965 -32.405 872 - 1650 -265100 -72.68 4150 10.75 -135645 -32.564 910 - 1654 -266270 -75.73 5375 14.18 -136285 -32.706 952 - 1658 -266815 -78.41 6505 17.57 -136660 -32.702 1000 - 1661 -267025 -80.96 7550 20.92 -136900 -32.677 1060 - 1664 -266940 -83.26 7930 23.68 -137285 -32.815 1126 - 1668 -266690 -85.44 7545 26.11 -137940 -33.066 1200 - 1672 -266270 -87.40 6570 28.16 -138770 -33.401 1274 - 1676 -265770 -89.29 5295 30.04 -139695 -33.786 1352 - 1679 -264930 -91.09 3450 31.46 -140670 -34.346 1433 - 1682

From the intercepts of the selected data at the Fe-rich boundary of w6stiter

AGf(FeO g530) - -261182 + 62.93 T J/m01 (1050 - 1550 K) .

or alternatively

AGf(FeO 488'0 512) - -133733 + 32.221 T 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


the vacant iron spaces in the FsO.947 0 lattice. Earlier low-temperature C nmauurenmnte ware made by Millar (44) in the temperature range P

70.7 - 279.8 A. Heat capacity values in the temperature range 298 - 1784 X (i.e. including data for liquid wlietitef have been obtained from the heat content msaeuremnts made by Coughlin, King and ~nnickson(45). Their data for solid wiietite of composition Fe0 947 0 can be represented by the equation *

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.

The enthalpy of formation of wtietite of composition Fe 0, obtained from the 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 equation for Fe 0 (aesmrmd to be the mum for Fe 0 within experiment& error), togethe$!'%&h C data for Fe(46) and for 0xy&11~?47), a value of

-264005 J/mol. AH (298 x, for Fe0.945 AS 8 can be calculated. The value so obtained is

-68.551 J/X-m&and this va ue, f

(29* K) for Fe

in =onjun=?i~~' 0 is similarly calculated to be with the standard entropies of

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 of Fe 0 is the equilibrium composition of wUstite stable to the lowest 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 94sO) = - 263005 J/la01 I

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 sunnnarieed by 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 wiietite which 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

Gibbs energies of'for&iatio expression AG = x AG + ~s~G~g~~~e~o =+~*~.57f ~~dd~~v~,";rf8~:s~~do~f;ain

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. for the reaction

Hence the Gibbs energy change

0.1948 Fe(e) + 1.75 Feo~428600~5714(e) = 1.9448 Fe0~485800~5142(e)


must be zero at 833 R. From the sslected data, AG for wfistite of the eutectoid composition is equal to Since AGf for pure Fe is sero,

-107320 J/seato& at 833 K (see Figure 3). then from the above equation

~~f[~~004?8~~oT%l&own in Figure 8 ) must be -119265 J/g-atom at 833 K. From the plot of

clogely3a$ can be read from the graph. this is found to be the case as

Table III

Thermodynamic Values Relating to the Wtfstite-Magnetite Equilibrium

Temp. wiistite AG in 2-phase (K) boundary w@st.+magnet. A%i

in Z-phase AGf of wtist. 40 of at O-rich

(x0) (J/g-atom) t.+magnet.

(J/g-atom) boundary Fb304

(J/g.atom) (J/g.atom:

873 0.5170 -203135 -3548 -106735 -117590 973 0.5226 -191210 -9966 -104685 -113530 1073 0.5265 -179620 -15525 -101920 -109285 1173 0.5297 -167445 -22075 -99075 -105140 1273 0.5327 -155015 -29040 -96150 -101025 1373 0.5354 -142465 -36460 -93220 -97020 1473 0.5381 -129285 -44410 -90080 -92870 1573 0.5412 -114850 -54025 -86945 -88780

In the temperature range 800 - 1600 K the Gibbs energy of formation of Fe304 can be represented by the equation:

AGf - -153805 + 41.42 T Y/g*atom or

AGf = -1076625 + 289.95 T J/mol

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. for Fe304 in most cases

Experimental msthode which provide values of AG 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; Gibbs energies for the equilibrium of Fe 0 with Fe 0 . Consequently, no 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 an d 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 fihe present 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 by Millar(44) (60.5 - 299.7 K) , by Parks and KelR$(53) (90 - 295 K) and by 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 of s for Fe 0 is therefore considered to be tire reliable. The value obta d was la6?15 J/K.mol, but the authors indicated that a zero point 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 %) (298 - 900 K)

= 200.83(+ 0.2 %) (900 - 1825 K)

If the values of AH (298 K) and So for Fe 0 (-1112.9 kJ/mol and 146.15 J/K.mol respectively jf are combined2%th the &alpy values of Coughlin et 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 of about 165 J/g-atom only from the selected va ues f

3d%ta differ by an averag ;49* 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

02. for different

magnetite compositions on the basis of disorder models. There is good general consistency between the different experimental results, and the latter are also in excellent agreement with the log p as obtained via the selected data for '2 wiistite. Nevertheless, the

values at the composition Fe304

derivation of AH and log PO

AS0 values from the temperature coefficients of the

to data is c nsidered to be too unreliable, in the case of magnetite, 8

2 warrant tabulation of the values obtained. However, it is observed that AH to abou q

appears to change in value from about -209200 J/g.atom at x = 0.572 -138100 J/g.atom at x0 =

has values of approximately 0.577. At the same two composition P as0

respectively. -98.32 J,&.g.atom and -75.3 J/K-g.atom

The log P, using the

values at three different temperatures have been integrated, 2 Gibbs-Huhem relation, to obtain values of the partial Gibbs

energy of iron in magnetite. values of AG , AG 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 c 2 nsiderable differences with regard to the r ported ;i tf,;'e~G?: (3). For example, White, Graham and Hay(58)

range of homogeneity

I rty of Fe in hematite of about 0.12 - and Schm~l(59) report

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

Table

IV

Thermodynamic

Values

for the Magnetite

Phase at 1473 K, 1673 K and 1848 K

A00

%e

AGf

(J/g-atom)

(J/g-atom)

(J/g-atom)

xO

O/Fe

1473 K

1673~

1848~

1473 K

1673

K

1848

K

1473 K

1673

K

1848

K

. cd 4

0.5715

1.3337

-116860

-69205

-35230

-60180

-104870

-133295

-92845

-84490

-77250

.

0.5716

1.3343

-101045

-50960

-31800

-81840

-129180

-137870

-92820

-84470

-77240

a"

B

0.5717

1.3348

-86190

-47700

-29290

-101615

-133535

-141230

-92795

-84460

-77230

: 1

0.5719

1.3359

-63805

-43345

-26275

-131450

-139340

-145275

-92765

-84440

-77220

B

0.5720

1.3364

-61840

-41800

-25105

-134065

-141400

-146860

-92750

-84430

-77215

*

0

0.5740

1.3474

-45185

-26570

-12760

-156270

-162040

-163865

-92510

-84280

-77130

.

0.5753+

1.3548

-38035

-165995

-92380

F

$

0.5760

1.3585

-17405

-3450

-174885

-177140

-84180

-77095

:

0.5768

1.3629

0

-182160

-77090

z

0.5782+

1

1.3708

-9625

-186215

-84110

E.

+ Phase boundary

composition


1473 K and 1723 K and Ruer and Nakato(60) report 'practically zero' eolubi- lity 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:

T(K) 1173 1273 1526 1567 1611 1657

Fe solubility(at%) 0.014 0.024 0.054 0.066 0.086 0.123

A number of thermodynamic studies of the magnetite-hematite equilibrium 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 stoichiometric Fe 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 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&

p AGg + %e bGYg)at the composition

are sh<wf by crosses in Figure 9 and can be seen to join smoothly with the f ower-temperature obtained via references 29, 33, 64, 66, 67.

date for Fe203

The room-temperature enthalpy of formation of Fe20 has been measured by Roth using both bomb calorimeatry(50) and acid solution &loriamtry(Sl) . The former study yielded a value of ARf(298 K) of -826.8 kJ/mol and the latter a value of -816.3 kJ/mol.

Low-temperature heat capacities for the compound have been measured by Parks and Kelley(53) (88 - 289 K) and by Griinvold and Westrum(68) (5.58 - 345.42 K), !rhese measurements provide a standard entropy of Fe203 of 87.45 + 0.4 J/K*mol.

Earlier high-temperature enthalpy data for Fe 0 have been summarised by Coughlin, King and Ronnickson(45) who themsel$ea made measurements in the temperature range 298 - 1757 K. More recently,Reznitskii and Filippova(69) havemade measurements in the range 298 - loo0 K. Enthalpy values obtained from the latter two studies agree to w&thin 1 % at temperatures up to 1000 K and produce a maximum in the C curve at about 940 - 950 K which is due to the antiferromagnetic transformatiog 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 transformation of 670 J/m& at 950 K, although this should not, of course, be considered to represent the total heat effect associated with the magnetic transformation.

The heat capacity of d-Fe203 may be expressed by the following equations

Cp(J/K-mo1) = 98.28 f 77.82.1d3T - 14.85S105T-2 (298 - 950 K)

= 150.6 (950 - 1050 K)

= 132.67 + 7.364*10-3T (1050 - 1750 K)


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 C (298 - 1250 K),

ted using the calorimetric values for AH (298 K) when a value of AH (298 K) of -823410 J/&o1 is

f?gure is therefore selected as the g tandard 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 oxygen- rich 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 stoichiometric composition 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 at stoichiometric Fe 0 values in the temper&&e range 1.873

(The AH data were derived from the measured AGo - 1657 K) .

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 TabfeIV, an interpolated value of AG (1730 K) for Ff 0 -81650 J/g.atom is obtained. Hence, dG

of

f (1730 X) for Re~~eQtl3*a8'~omposition

must be equal to 0.957 = -78147 J/g*atom. From the ~f8t48f80~~5g03 T/K for hematite shown iz $z:," 9 is found tofbe -78157 J/g-atom. licnce,

, the valus of AGf at 1730 F 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 Fe l_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 (within t 800 J mol ‘Fee’), B whereas values reported by (36) are about 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 concentrationsin the liquid oxide phase field.

7.2 TheraPdynamic values 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.


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)

Pig.8: The Gibbs free energy of formation of magnetite as a function of tevrature

Fig.9:

Richardsan and Idles Ehizhikov etat.f1030-12~~

Fmn setected d&o t m~etife phase

J

The Gibbs free energy of formation of hematite ae a function of temperature

2023Ks

l Tankins, Gakcen and Man 11823K. H?IHD equBb.1

*

0 l

.

rb

Schwerdtfke; 11873K. emf.) Gatellier and Olette (1873K. e.m.f.1 numbed Sanoll(lZfK, H2/H2B

Onslur ‘and Capon (extrap. to 20231, t$IH20 equitib.1

Schenck and Steinmetz 11898K, H2/lt$l equitib.1

c -22oooo

---( Calc~&~ed y!ues with sotubddy limit

I

I i I I I I I

0,002 O#OS 0,olo 0.0’

*o

Fig.10: The iron at 1823 1923 R 2023


Partial Gibbs energies of solution of oxygen in solid wtiatits were calculated at the aolidua temperature for selected compositions using the data linted in Table II. These values of A0 are constant across the aolidua-liquidua gap and hence they define the va%es of AG in the liquid oxide at various liquidus compositions and temparaturea.'The liquidua 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 dence of AH

8 and AS ,

and assuming temperature indepen-

at the relev nt liqui8ua val %a of0 AH wepi calculated for the liquid oxide 8 temperatures'and compositions.

From the experimental results of Darken and Gurry, an enthalpy of fusion of

ok% 0 of 30250 $ 2100 J/m01 is derived. This cowares very well with the f 31340 J/mol obtained by Coughlin, King and Bonnickson(45) from high

temperature enthalpy measurements on Fe but the concentration dependence of

0. The latter value is preferred, the'&% 1 a py of fusion of wiiatite as

reported by Darken and Gurry is retained in conjunction with the selected &Ifu value for Fe been ~o~ine~*~~~*~'*' Of AI%

at selected wiistite compositions have e correspond #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-aolidua gap for the wiistite phase is very narrow, use has been made of the fact that the Gibbs energies of formation of solid an liquid wiiafite of the same composition must have the same value (relative to t same standard states) at the appropriate aolidus/liquidua temperature. Thus, using the data in Table II,appropriate values of AGf have been calculated and combined with the dearived AHf AS, data. Values of A

values for the liquid oxide to produce liquid 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 very close (within 4 -

= 0.569 to 0.580 approximately, lie 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) compound ( AH solid = -154495 J/g*atom), 2

at the mslting point of the

20565 J/g.ato& results. n enthalpy of fusion of Fe 0 of

This is in very good agreement with the figur 3 ;4f 19730 + 1190 J/g-atom derived by Darken and Gurry(2) from an analysis of their experimental data.

A complete listing of the thermodynamic properties 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

Table v

Selected

Thermodynamic

Values

for the Liquid

Oxide Phaoe

4

s

O/F

e x0

A

HO

A

SO

%

e *‘

Fe

dHf

AS,

AH fus

(J/g-atom)

(J/K.g.atom) (J/g-atom) (J/K.g*atom) (J/g-atom) (J/K.g*atom)

(J/g-atom)

0

1.06

0.5146

-304260

-95.52

78640

54.81

-118400

-22.56

15960

%

1.07

0.5169

-301835

-96.40

76035

55.69

-119285

-22.92

15675

s K

1.08

0.5192

-299325

-97.32

73250

56.74

-120190

-23.24

15455

s

1.09

0.5215

-296895

-98.24

70670

57.91

-121020

-23.51

15265

3

1.10

0.5238

-294470

-99.12

68550

59.33

-121600

-23.66

15060

8

1.11

0.5261

-292045

-100.04

66750

60.96

-122010

-23.75

14890

8

1.12

0.5283

-289615

-100.88

64620

62.13

-122525

-23.99

14760

;;r

1.13

0.5305

-287190

-101.75

61870

63.14

-123305

-24.33

14630

?

1.14

0.5327

-284845

-102.63

58810

64.02

-124255

-24.76

14515

8

1.15

0.5349

-282505

-103.51

55500

64.81

-125300

-25.23

14395

z

1.16

0.5370

-280245

-104.35

52070

65.14

-126380

-25.87

14290

z

C/Y

F:

s


oxygen at the appropriate solubility limits in the &and liquid phases of iron Hence, 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.

Table VI

Partial Gibbs Energies of Oxygen Relevant to the Equilibrium Between Liquid Oxide and Solutionu of Oxygen in 6- and Liquid Iron

Temperature Iron-rich boundary Solubility limit of AGO K of liquid oxide 0 in& or liq. Fe

xO xO (J/g.atom)

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 investigations of the solutions of oxygen in 6 - and liquid Fe. There have been numerous such studies of solutions in liquid iron , mainly using equilibration with 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!?ned from six reprssent- ative 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 Thermodynamic Values for the Solutionsof Oxygen in Liquid Iron

xO AH0 (J/g*atom) ASO

(J/K-g-atom) ~J~g~~torn~ (J/K$atom)

0.0005 -130790 31.05 -67 0.0197 0.001 -130790 25.27 -130 0.0335 0.002 -130790 19.50 -264 0.0556 0.004 -130790 13.77 -523 0.0883 0.006 -130790 10.38 -787 0.1121 0.008 -130790 7.99 -1046 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 the 2 Q da a obtained by previous


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 oxide - &-Fe equilibrium given in TableVI.The discrepancies ar% within 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, has been derived to represent AGO in S-Fe:

the following expression

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

k -Fe is 'much lower' than in d-Fe.

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:

A~~(in k-Fe) = -260149 + 170.21 T

AGo(in d-Fe) = -262609 + 153.13 T

Acknowledqement

The work described above has been carried out as on the metallurgical thermochemistry of iron and Commission of the European Communities, Division

+ RT 3n x0 J/g.atom

+ RT In x0 J/g-atom

part of a research programme steel sponsored by the Steel.


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A thermodynamic assessment of the iron-oxygen system

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