Mass-Spectrometric and Electrochemical ... - Wiley Online Library

May 1981

Studies of Thermodynamic Properties of Liquid and Solid Phases in Ca0-A120,

of CoC12(g) a t the gas-solid interface being determined by the equilibrium between Co304(s) and the partial pressures of C12(g) and 02(g) in the corrosive gas mixture. At lower partial pressures of oxygen, the corrosion rate is controlled by mixed diffusion of C12(g) and CoCl,(g) through the gas boundary layer. Acknowledgments: The authors thank J. Bonini, C. T. Kang, and J. Oh for assistance in performing part of the experimental studies and B. A. Wilcox, DMRNSF, for his interest in this work.

References ID. W. McKee, D. A. Shores, and K. L. Luthra, “Effect of SO2 and NaCl on High Temperature Hot Corrosion,” J . Electrochem. Soc.. 125 [3] 41 1-19 (1978). 2W. W. Liang and K. H. Yun; pp. 60-72 in Proceedings of the Symposium on Corrosion-Erosion Behavior of Materials. Edited by K. Natesan. American Institute of Mechanical Engineers. Warrendale, Penn., 1980. ’W. W. Liang, K. H. Yun, and M. J. McNallan, “High Temperature Corrosion of Cobalt in Chlorine/Oxygen Environment”; unpublished work.

307

‘R. C. Hurst, J. B. Johnson, M. Davies. and P. Hancock; pp. 143-57 in Deposition and Corrosion in Gas Turbines. Edited by A. B. Hart and A. J. B. Cutler. Wiley-Interscience, New York, 1973. ’M. K. Hossain, A. C. Noke, and S. R. J. Saunders, “Oxidation of an Ni-CrAl Alloy at 850°C in Air Containing HCI Gas,” Oxid. M a . , 12 [ 5 ] 451-7 I (1978). 6M. K. Hossain and S. R. J. Saunders, “Microstructural Study of the Influence of NaCl Vapor on the Oxidation of an NiCr-Al Alloy at 850”C,” ibid., [I] 1-22. ’P. Hancock, R. C. Hurst, and A. R. Sollars, “Influence of Chloride Contamination of the Atmosphere on the Mechanism of Oxidation of Iron,” Chem. Metall. Iron Steel (Spec. Publ. Iron Steel Inst. (London)), 1973, p. 413. 8J. Krueger, A. Melin, and H. Winterhager, “Oxidation of Cobalt Between 800” and llOO°C,” Cobalt, 33, 176-86 (1966). 9W. R. Ott and D. T. Rankin. “Oxidation of Sintered Cobalt Oxide.” J. Am. Ceram. SOC..62 [3-41 203-205’(1979). ‘OG.H. Geiger and D. R. Pokier, Transport Phenomena in Metallurgy. AddisonWesley, Reading, Mass., 1973. “R. J. Fruehan and L. J. Martonik, “Rate of Chlorination of Metals and Oxides: 111.” Met. Trans.. 4 1121 2793-97 (19731. ”J. 0. Hirchfelder, C. F. Cirtiss, and R. B. Bird, Molecular Theory of Gases and Liquids. Wiley-Interscience, New York, 1954.

Mass-Spectrometric and Electrochemical Studies of Thermodynamic Properties of Liquid and Solid Phases in the System Ca0-A1203 MICHEL ALLIBERT and CHRISTIAN CHATILLON Laboratoire de Thermodynamique et Physico-Chimie Metallurgiques, E.N.S.E.E.G., Domaine Universitaire, B.P. 44, 38401 Saint Martin DHeres, France

K. T. JACOB* Department of Metallurgy and Materials Science, University of Toronto, Toronto, Canada M5S 1A4

ROGER LOURTAU Creusot Loire, Acieries d’Imphy, 58160 Imphy, France

The activities of CaO and Al2O3in lime-alumina melts were studied by Knudsen cell-mass spectrometry at 2060 K. Emf of solid state cells, with CaF2 as the electrolyte, was measured from 923 to 1223 K to obtain the free energies of formation of the interoxide compounds. The results are critically evaluated in the light of data reported in the literature on phase equilibria, activities in melts, and stabilities of compounds. A coherent set of data is presented, including the previously unknown free energy of formation of CaO. 6AI20, and the temperature dependence of activities in the liquid phase. I.

Introduction

T

phase diagram and the thermodynamic properties of the system CaO-A1201have been studied by several investigators because of their interest in steel, cement, and ceramic industries. Reviews by Chipman’ and Rein and Chipman2 summarize the thermodynamic data available up to 1965; the suggested phase diagrams are available from the American Ceramic Society.] References 1 and 2 identify two important sets of thermodynamic data: the heat capacity and heat of formation of CaO. 2Al2O1,CaO. Alz03, HE

Presented at the 82nd Annual Meeting, The American Ceramic Society, Chicago, Illinois, April 28, 1980 (Basic Science Division No. 45-8-80), Received May 21, 1980; revised copy received October 24, 1980. The work of K. T. Jacob was supported in part by the Natural Sciences and Engineering Research Council of Canada. The mass spectrometry measurements were made possible by partial financial assistance of the Delegation Generale al la Recherche Scientifique and by an Ugine Acier scholarship to R. Lourtau. *Member, the American Ceramic Society.

12Ca0. 7A120,, and 3 C a 0 . A1203reported by Koehler et aL4 and activity measurements of Sharma and Richardson5 in the liquid state, later confirmed and extended by Kor and Richardson6These two sets of data are not compatible2 for the composition corresponding to CaO. 2Al2O1 and CaO. Al2O1. As suggested by Rein and Chipman, the activities derived by Carter and Macfarlane’ were based on an incorrect assumption regarding the constancy of the activity coefficient of CaS in the melts. Measurements by Cameron et on sulfide solubilities are incompatible with those of Kor and Richardson and with thermochemical data4 on 12Ca0. 7Al2O1 and 3 C a 0 . AI20,. Thermochemical information is not available on the compound CaO. 6Al2O1. The most recent and complete phase diagram is that by Nurse et a1.,9 who showed that 12Ca0. 7Al2O1 is not stable in the pseudobinary system CaO-A1203.It appears that this phase is stabilized by the presence of moisture or halogens. However, Cockayne and Lentlo have grown single crystals of 12Ca0. 7Al2O1, several centimeters long, from melts. Although their observations suggest that it is a congruently melting compound, an infrared absorption band at 2.8 wm due to hydroxyl ions was visible in their sample. Since the absorption was unaffected by prolonged vacuum treatment of the melt, it is likely that OH- ions are present as an impurity rather than as a constituent. To resolve some of these discrepancies, activities in Ca0-AI2O3 melts were measured at 2060 K using Knudsen effusion-mass spectrometry. The selected temperature was -250 K higher than those used in earlier s t ~ d i e s , ~so- ~that reliable partial enthalpies could be evaluated by combining the present results with selected values

Journal of the American Ceramic Society-Allibert e t al.

308 Table I.

Ionic Species, Appearance Potentials, and Operating Conditions of the Spectrometer Appearance potential* (ev)

Operating potential (ev)

A120+

Al 0 A120

6.1 6 13.6 7.7

AIO+

A10

9.5

14 14 17 14 14

Ion

Ca Al+' O+ +

Pa re.n t species

Ca

Vol. 64, No. 5 effusion orifice

Typical ion intensities (arbitrary units)

580 2 1 0.1 0.1

*From Ref. 13.

at lower temperatures. The free energies of the solid compounds, including CaO. 6A120,, were measured by solid state electrochemical cells incorporating CaF, at 923 to 1223 K. A consistent set of data for the system Ca0-AI20, was then derived based on all available information. 11.

Mass-Spectrometric Measurements

( I ) Outline of Method The measurements were carried out using a mass spectrometer* with a special device for differential measurements; this device consisted of multiple effusion cells. The details of the apparatus are described elsewhere.Il Six effusion cells were drilled in a molybdenum block. Two contained the reference mixtures, a CaOsaturated melt and pure AI,O,, and the other four contained homogeneous melts of different compositions. The molybdenum block was held by movable supports which permit each effusion cell to be geometrically aligned with the spectrometer, one at a time. The gaseous species effusing from the melts were compared to those coming from the reference cells, all being ionized and analyzed by the mass spectrometer under exactly identical conditions. This direct comparison eliminates the need for estimating the various constants in equations relating the vapor pressures to their corresponding ion intensities. Although a general discussion of the requirements and applications of this technique has been published,I2 some specific details are given below. ( 2 ) Procedure Weighed amounts of dehydrated pure A1203and CaO (obtained from CaCO,) were placed in the effusion cells. The molybdenum block containing the effusion cells was placed in a medium-frequency induction furnace and heated above the melting point of AI20, under He for a minimum of 15 min. After cooling and reweighing to check for losses, the block was placed in the mass spectrometer and heated under vacuum to a temperature where some of the gaseous species effusing from the cells can be observed. This procedure permits proper tuning of the apparatus at a temperature a t which no significant weight loss can occur in several hours. The gaseous species observed in the spectrometer were Ca, 0, Al, AI20, and AIO. It was very difficult to make accurate measurements on A1043+because of the interference of Ca4,+; the intensity of the latter was approximately twice that of the former. Because of the presence of Fe5,+ (as an impurity), the ionic intensity of CaO+ could not be accurately monitered. A resolution ((m/ A m ) X ( l / A l ) ) of 1300 was used. At a resolution of ~ 2 0 0 0 ,the interference from Cad,+ and Fe5,+ could have been minimized. However, an increase in the resolution beyond 1300 resulted in a drastic decrease in sensitivity. The duration of the measurements at 2060 K was kept to a minimum so that the results were unaffected by the melt creeping out of the effusion cells. The short time available before this occurrence limited the measurements to Ca, Al, and 0 species. If longer periods had been available, it would have been possible to measure CaO+ intensity using an enriched isotope (Ca,,). Information on the ionic species seen in the spectrometer, their appearance potentials, parent species, and typical intensities at specific operating potentials are summarized in Table I. The molecular beam was defined using two cold diaphrams, one *90 HT, Nuclide Corp., AGV Div., North Acton, Mass

Fig. 1. Profile of ion intensities obtained by displacement of effusion cell in front of ion source of mass spectrometer.

just beneath the electron beam in the ion source and the other immediately above the effusion holes (=I0 mm). With effusion holes 1.2 mm in diameter and proper alignments, these diaphrams allow only molecules coming from inside the effusion cell to reach the ionization chamber. This collimation decreases the usual observed intensity by a factor of 2 to 4 but eliminates corrections for differing orifice characteristics when comparing two effusion cells. Furthermore, such a design eliminates the parasitic contributions to the ion current due to surface diffusion or a vaporization-condensation process occurring near the effusion hole. The significance of the parasitic contributions can be seen by monitoring the ion intensities after gradual displacement of the effusion cell from the ideal alignment (Fig. 1). The displacement is obtained by moving the whole furnace assembly in front of the ion source. The profiles indicate that ionized Al and Ca can originate from cell walls or the radiation shield. If these atoms reach the spectrometer, incorrect densities are recorded.

(3) Analysis and Results The CaO and A1,0, activities were independently deduced from the ion intensities of 0+,Ca+, and Al+. The relation between the partial pressure (P,) and the ionic intensity (I,+) of the ith species can be written in the form: P,S,=I,+ T

(1)

If the geometric and electricql characteristics and temperature are maintained constant, the ratio of partial pressures over a melt and a reference material (denoted by subscript ( )o) is equal to the ratio of ion intensities: P,/(P,)O= I!+ /(I,+)o

(2)

By considering the dissociation reactions: A1203-2AI

CaO-Ca

+3 0 f O

(3)

(4)

the activities of A120, and CaO in homogeneous melts can be calculated relative to solid Al2O3and CaO as:

The reference for CaO, shown by subscript 1 in Eq. (7), was a mixture of CaO and A1203containing 20 wt% (12 mol%) A120,. From 18 10 to 2200 K, this composition falls in a two-phase region where solid CaO and a melt coexist. The reference for Al20,, indicated by subscript 2 in Eq. (8), was pure a-AI20,. Combining Eq. (2) with Eqs. (5) and (6) gives

Studies of Thermodynamic Properties of Liquid and Solid Phases in Ca0-A1203

May 1981

309

Table 11. Activity Data Obtained by Mass Spectrometry at 2060 K Composition of melt (mol%CaO)

64.5 57.8 54.8 49.5 43.8 41.4 35.2

ar.ni

0.040 0.025

+

CaO melt 80

1

“Activities are referred to solid standard states.

I

I

.2

I

1

I

1

X’AI2’03L

I

’

aAlZo1

0.02 .05 .06 .20 .4 1 .25 .50

0.42 0.20 0.14 0.082 0.048

_

_

,005 _

!*

Fig. 2. Activities in CaO-AI,O, melt at 2060 K relative to solid CaO and AI2O3as standard states.(*) Activity of CaO obtained by mass spectrometry; (0)activity of A120, obtained by mass spectrometry; (-) activity of A1203

obtained by Gibbs-Duhem integration.

,

The results obtained at 2060 K are summarized in Table I1 and plotted in Fig. 2. Various attempts have been made to find a representation of the experimental results, consistent with the GibbsDuhem relation, either giving equal weight to the measured activities of CaO and AI20, or taking into account only the CaO activities, which are less scattered than the A1203activities. The scatter in alumina activities arises from the experimental uncertainties in the ion intensities of 0 and Al, which are approximately five times the uncertainty in the intensity of Ca. A critical evaluation of these mass-spectrometric data in the light of emf measurements reported in the next section and the other data reported in the literature (Section IV) also indicate that the activities of CaO obtained in this study are more reliable than the values for A1,03. The curve for the activity of AI2O3 in Fig. 2 is obtained by Gibbs-Duhem integration of the smooth curve through all experimental points for CaO. Only two of the measured activities of A1203lie above the values from the Gibbs-Duhem relation; all other points for A1203 lie below the curve. 111. Solid State Electrochemical Measurements

( 1 ) Principle The use of solid electrochemical cells based on CaF, electrolyte for determining the Gibbs energies of formation of compounds containing CaO was initiated by Benz and Wagner.I4 Since the fluorine ions are the mobile species in CaF,, the emf is given by U”Fz

-nFE=

tF-d/.LF2

(9)

K’F 2

where pLIF2 and /.L’’~~are the chemical potentials of fluorine at the two electrodes, n is the number of electrons associated with the electrode reaction, F the Faraday constant, t F - the transport number of fluorine ions, and E the emf. The region in the temperaturefluorine potential space where tF- >0.99 is well establi~hed.’~ The experimental conditions used in this study fall within the electrolytic conduction domain (tF->0.99) for CaF,. Equation (9) can therefore be simplified as: - nFE =/.L’FZ -/.L”F2

(10)

Diagram of apparatus used for emf measurements. Fig. 3.

The fluorine potential at each electrode is established by the reaction; C a F h ) +02(g)-+CaO(s)

+ F2(g)

(1 1)

If CaF, is present at unit activity a t the electrodes, dry oxygen gas at a pressure of I O S Pa is passed over the electrodes and the activity of CaO is fixed (either by having pure CaO or a mixture of adjacent phases in the system CaO-Al,O,); the fluorine potentials and emf are unambiguously defined. The emf can be related directly to the chemical potential of CaO; - nFE =Apcao

(12)

(2) Procedure The calcium aluminates were prepared by prolonged heating in dry inert gas at 1620 K of powdered stoichiometric mixtures of anhydrous A120, and CaO obtained by thermal decomposition of CaCO, in vacuum. The mixtures were initially heated for 50 h, then quenched, ground, repelletized, and heat-treated for an additional 100 h. X-ray diffraction (XRD) analysis of the pellets confirmed the formation of the required aluminates. The reference electrode pellet was prepared by heating a compacted mixture of 85% CaO and 15% CaF, a t 1280 K. The other electrodes were prepared in a similar manner by first taking an equimolar mixture of two neighboring phases in the system CaO-AI,O, and mixing it with 15% CaF,. An intimate mixing of the CaF, with the oxide phases at the electrode is required to generate the fluorine potential, according to Eq. (1 1). Without the addition of CaF, to the electrodes, the emf response is sluggish. A schematic diagram of the emf apparatus is shown in Fig. 3.

~

Journal of the American Ceramic Society-Allibert et al.

310

Vol. 64, No. 5

Table IV. Gibbs' Energies of Formation of Calcium Aluminates from Component Oxides Obtained from Emf Measurements Compound

AGO (J/mol)

CaO. 6A1203 CaO. 2A120, CaO. AI2O3 12Ca0.7A12O3

- I 7 430-37.2T(-t1350) -16 070-25.7T (rt800) - 18 120- 18.61T ( k 1800) -94 840-209.1 T ( 26000)

Pt, 02,CaO/CaF2/ 12Ca0. 7A120,+Ca0. A1,0,, OZrPt (IV) Pt, 02,CaO/CaF2/3Ca0. AI,O,+ 12Ca0. 7AI20,, O,, Pt (V) Pt, 02,CaO/CaF,/CaO+ 3 C a 0 . Al20,, 02,Pt

I

* I

I

900K

T-

1200K

Fig. 4. Temperature dependence of emf for cells I to VI.

The electrode pellets were spring-loaded on either side of a transparent single crystal of CaF, with a platinum gauze placed between the electrodes and the solid electrolyte. The platinum wires spotwelded to the platinum gauze provide electrical leads to a high impedance (10l6 0)voltmeter. The pellets are held together under pressure through a system consisting of springs, an alumina rod, and a flat-bottomed alumina tube with a section cut away parallel to its axis, as shown in the figure. Direct contact of the electrode pellets with the alumina rod or tube was prevented by inserting platinum foils between them. The cell was maintained under dry flowing oxygen at a pressure of lo5 Pa. In preliminary experiments, the transparent CaF, crystals became translucent during the run. Fine opaque precipitates appeared to have formed inside the CaF, crystal. These precipitates were identified as CaO by electron diffraction. They apparently formed by reaction of the crystal with residual moisture in the gas phase. CaF,(s)

+ H,O(g)-CaO(s) +2HF(g)

(13)

The CaO precipitation was minimized by degassing the alumina tubes and rods under vacuum and by using improved drying procedures for oxygen gas. The gas was first dried by two towers of anhydrous magnesium perchlorate and then over anhydrous phosphorus pentoxide. Since CaO, CaF,, and 0, gas must be in contact to fix the fluorine potential, the presence of a few internal precipitates of CaO in CaF, would not invalidate the emf results. It can be shown from thermodynamic considerations that CaF, will not react with dry oxygen to form CaO. The emf of the following cells were measured as a function of temperature in the range 923 to 1223 K: Pt, 02,CaO/CaF,/CaO. 6AI20,+Al2O3, 02,Pt

(1)

Pt, 02,CaO/CaF,/CaO. 2AI20, +CaO. 6AI2O3,02,Pt

(11)

Pt, 02,CaO/CaF2/Ca0.A120,+Ca0.2A1203,02,Pt

(111)

The time required to attain steady emf's varied from 5-20 h at the lower temperatures to 5 at intermediate temperatures and 2 at the highest temperatures used in this study. The reversibility of the cells was checked by passing small currents (x10 PA) in either direction through the cell and verifying that the emf returned to the steady value before each titration. The emf was also independent of the flow rate of oxygen through the cell in the range of 50 to 300 mL min-I. The flow rate during emf measurements was maintained at 100 to 200 mL min-'. After each emf run the electrode pellets were examined by XRD. No significant changes in the composition of the electrodes were noted. Because of the rather high scanning speeds used, small changes in the lattice parameter due to solid solution formation could not be detected. The technique is also insensitive to small amounts (x5to 10%) of any new phase that might have formed.

(3) Results and Analysis The emf's obtained with the six cells are plotted in Fig. 4; they vary linearly with temperature. The equations representing the emf's and the corresponding chemical potentials of CaO are summarized in Table 111. The Gibbs energies of formation of the aluminates from their component oxides, derived from these chemical potentials or partial free energies of mixing, are given in Table IV. The emf of cell VI should be zero since CaO at unit activity is present at each electrode, in agreement with experiment. However, the emf of cell V was approximately zero, suggesting that 3CaO.AIzO, is unstable with respect to CaO and 12Ca0.7A120, in the temperature range of this study. This result is in apparent conflict with the diffraction patterns, which clearly showed 3Ca0.A120, as one component of the electrode pellet before and after emf studies, and with thermal data on this c ~ m p o u n d . ~ Many months after the emf results were completed, the authors became aware of a phase diagram for the ternary system CaOAI20,-CaF2at 1373 K, proposed by Brisi and RolandoI6 and shown in Fig. 5 . This diagram indicates that the I2Ca0.7AI20, phase will dissolve CaF, to form a solid solution which extends to the composition 1 1 C a O . 7AI2O3.CaF,. An equimolar mixture of 3Ca0.A120, and 12Ca0. 7AI2O3will, on reaction with CaF,, enter a three-phase field containing CaO, 3Ca0.A120,, and a solid solution l l CaO. 7A1203.(CaO,CaF,). If the reaction proceeded as shown in Fig. 5 , the emf of cell V would be zero, since a small amount of CaO a t unity activity would then be present a t the right electrode. This interpretation, however, is based on the assumption that the phase relations in this segment of the ternary sytem CaOAI,03-CaF2 at the lower temperatures corresponding to the emf

Table 111. Emf's of Solid-State Cells and Corresponding Chemical Potentials of CaO Composition of working electrode

Cell

I I1 I11 IV V VI

+

Emf (mV)

AI2O3 CaO .6A1203 90.3 +0.193T( k 7) CaO. 6AI20,+CaO. 2A120, 79.7+0.103T( k 5 ) 104.5 +0.06T( +. 3) CaO 2Al,O3+CaO. AI2O3 Ca0.A1,0,+12Ca0.7A120, -33.2+0.082T(15) O( f 5 ) 1 2 C a 0 7AI20,+ 3 C a 0 . AI20, 3 C a 0 . AI,O, CaO O( t- 5)

-

+

Apca0= -nFE(J/mol)

- 17 430-37.2T( f 1350) - 15 390- 19.9T( +. 1000) -20 170- 1 1.5 1T( f600) 6 400-15.77T(i 1000) O( f 1000) O( +. 10001

+

(VI)

May 1981

311

Studies of Thermodynamic Properties of Liquid and Solid Phases in CaO-A1203 Ca F2

Fig. 5. Phase diagram of the system Ca0-AI20,-CaF2 at 1373 K suggested in Ref. 16.

study are at least qualitatively similar to those determined at 1373 K. The ternary phase diagram (Fig. 5 ) also indicates the formation of another ternary compound, 3 C a 0 . 3AI2O3.CaF,, at 1373 K. Jacques17 measured the heat of formation of this compound from CaO. AI2O3and CaF, as 335 ( ? 16) kJ mol-' by low-temperature solution calorimetry; Brisi and Rolando16 found a value of +30.5 ( f 16) kJ mol-I. Although these values differ substantially, both studies suggest that the heat of formation is positive. The compound is therefore stable only above a yet-undetermined critical temperature. Because of the large positive heat of formation it is conceivable that the compound is unstable or only marginally stable in the temperature range covered by the emf measurements. If the compound is only marginally stable, the driving force and hence the rate of reaction would be low. Thus, significant amounts of this compound may not have formed during the emf studies. This interpretation is supported by the values for the emf of cell 111 and the Gibbs energy of formation of C a O . A1203derived from it. As shown in Fig. 13, these values are in excellent agreement with those obtained from thermal data4 and from the thermodynamic properties of melts and the phase diagram. If the ternary compound had formed, the oxide mixture containing CaO. A1203and CaO. 2A1203 would not be in equilibrium with CaF,, as assumed in the interpretation of the results. Both Nafzigeri8 and Chatterjee and Zhmoidin19 studied the liquidus region of the CaO-A1,O3-CaF, phase diagram. Although Chatterjee and Zhmoidin found evidence for the existence of 3 C a 0 . 3A1,O3. CaF2, Nafziger could not identify this compound at the higher temperatures, where the compound is expected to be stable. Even in the absence of the compound 3Ca0.3A120,. CaF,, the emf of cell IV would not give reliable Gibbs energy of formation of l2Ca0.7Al20,, because of the solid solubility of CaF2 in this compound. The Gibbs energy derived from the emf of cell IV should be more negative because the compound is present as a component of the solid solution at an activity less than unity in the electrode. The electrochemical studies on C a O . 6A120, and CaO .2AI20, are unaffected by the ternary-phase relations.

+

3 CaO;AI203

CaO. At2 0 3

Ca0.6h203

measurements at 2060 K, partial enthalpies of mixing must first be evaluated. This is done by combining activities obtained by mass spectrometry at 2060 K with those of Sharma and Richardson5 at 1773 K, as shown in Fig. 6. The partial enthalpies calculated from the slopes of the lines in these figures are plotted as a function of

h

Y h .r

* * r Y

.36 .38 .40 i .42

IV. Discussion For an evaluation of thermodynamic data on the system CaOAl2O3,the Gibbs energies of formation of solid compounds are compared with activities in the liquid phase using the phase diagram. To obtain activities a t the liquidus temperatures from the

Fig. 6. Variation of logarithm of activity of ( A ) CaO and ( B ) A1203with reciprocal absolute temperature.

Vol. 64, No. 5

Journal of the American Ceramic Society-Allibert et al.

312 I

I

1

1

I

1

I

1

r

.-0tn

50

3

rc

I

0

-50

CaO /mole

4 I

0

I

XA1203

-

100

A G A1203 kJ/mol

Fig. 8. Integral heat of mixing in the system CaO-AI,OI

1 41203

-

1

Fig. 7. Composition dependence of partial enthalpy of ( A ) CaO relative to solid CaO and ( B ) AI,03 relative to solid Al20, in CaO-AI,O, melts.

composition in Fig. 7. Since these partial enthalpies are with respect to solid CaO and Al,03 as standard states, their values at XAIzo,= 0 and X,,l,o,= I must equal the heats of fusion of CaO and AI,O,, respectively. Although a smooth curve can be drawn through the experimental points for CaO (Fig. 7(A)), two of the experimental points for A1203deviate significantly from the smooth curve in Fig. 7(B). The values for these two compositions have been altered to fall on the curve by adjusting activities at 1773 K for these compositions (Fig. 6(B)). The activities of A120, were obtained by Gibbs-Duhem integration a t both 2060 and 1773 K from measured activities of CaO. The integration is more accurate at 2060 K because the CaO activity is well defined across the whole composition range of the liquid phase, whereas at 1773 K the CaO activity has been measured only over a limited range and must be extrapolated at both ends to hypothetical saturation points.s Consequently, A120, activities at 2060 K are more reliable than those at 1773 K. The partial enthalpies are combined to produce the integral molar enthalpy of mixing of the liquid phase relative to solid CaO and A120, as standard states. The values, plotted in Fig. 8, are positive and the curve has an atypical convex curvature. However, by corit is seen that recting for the heats of fusion of CaO and A1203,20 the heat of mixing with respect to liquid CaO and A1203is negative with a minimum at XA,,,,=O.34. This composition is near that corresponding to the lowest liquidus temperature. The thermodynamic properties of solid compounds in the system

Table V. Temp. fKi

Ca0-A1,03 can be calculated from information on activities in the liquid phase evaluated in this study and the phase diagram. The activities of CaO and A1203are the same in all phases i n equilibrium. As indicated (Section I), the main controversial aspect of the phase diagram given by Nurse et aL9 is the melting behavior of 12Ca0.7AI,03. In calculating the Gibbs energy of the solid compounds, both the diagram of Nurse et a / . and Fig. 2295 (Ref. 3), showing congruent melting behavior for l 2 C a 0 . 7AI20,, were used. The latter indicates a melting point of 1665 K for 12Ca0.7AI,03 and shows two eutectics a t 1633 K on either side of this compound at XA],,,=0.351 and XAl,o,=0.38. For brevity, the results of the calculations are given in Table V for temperatures corresponding to three-phase equilibrium. The compositions and temperatures are more accurately known at these reaction isotherms than in other regions of the diagram. Calculations based on the melting temperatures of the compounds and compositions corresponding to twophase equilibria give similar results. The Gibbs energies of formation of the compounds are plotted as a function of temperature in Figs. 9 to 13. (1) CaO.6AI2O3 The Gibbs energies of formation of this compound from component oxides obtained from different sources are compared in Fig. 9. The results of the present emf measurements, extrapolated to higher temperatures, are in good agreement with values calculated from activities in the liquid phase and the phase diagram. Popov

Temperatures and Compositions Corresponding to Three-Phase Equilibria in System Ca0-AI2O3and Gibbs’ Energies of Formation of Compounds Derived from Activities in Liquid Phase Phase diagram consulted

2103 2035

Ref. 9 Ref. 9

1875

Ref. 9

1812 1633

Ref. 9 Ref. 9

1633

Fig. 2295 of Ref. 3

1633

Fig. 2295 of Ref. 3

Phases in eouilibrium

+

Melt (X~1,0,=0.74)+A1203 CaO. 6A1203 Melt (XAIzo,=0.66)+ CaO. 6AI2O3+Ca0.2AI2O3 Melt (XA1,O, =0.494) CaO . 2AI2O3 CaO. A1203 Melt (XAl,0,=0.29)+CaO+3Ca0.A1,0, Melt (X~l,,,=o.36)+ 3 C a 0 . Al20, CaO .Al,03 Melt (XAl,o,= 0.38) 1 2 C a 0 . 7Al2o3 CaO. A120, Melt (XAl,0,=0.35)+ 12Ca0. 7AI2O7+3 C a 0 . AI,Ol

+

+ +

+

+

Gibbs’ energy of formation of interoxide compounds from binary oxides IkJ Imol)

CaO. 6A1203,AGO = -94.7 Ca0.6Al2O3, AGO= -92.3 CaO.2AI20,, AGO= -73.6 CaO. 2A1203,AGO = - 69 .O CaO. A120,, AGO = - 54.0 3Ca0.A1203, AGO= -73.0 3 C a 0 . Alz03,AGO = -72.0 CaO.AI,O,, AGO= -46.7 12Ca0. 7AI2O3,AGO = - 396 CaO. A120,, AGO = -45.1 12Ca0.7Alz0,, AGO= -393 3 C a 0 . A1,O1, AGO = - 70.6

May 1981

Studies of Thermodynamic Properties of Liquid and Solid Phases in CaO-Al,O,

t

I

kq

'

313 I

1

I

-201

CA

-80

""I

Emf, this study

I

I

-120L l d O O K

I

2000 K

1000 K

2000 K

Fig. 11. Temperature dependence of Gibbs energy of formation of CaO.AI,O, (in kJ mol) ( 0 ) Values calculatcd from the phase diagram of Ref! 9; (0) value calculated from phase diagram No. 2295 in Ref. 3, showing 12Ca0. 7AI20, as a congruently melting compound and activities in liquid phase; R denotes the recommended equation and Th the thermochemical value (Ref. 4), which are almost identical.

Fig. 9. Variation of Gibbs energy of formation of CaO. 6A120, (in kJ/mol) with temperature. ( 0 )Values calculated from thermodynamic data evaluated for the liquid phase and the phase diagram (Ref. 9); R represents value recommended in the present study; (-) emf from present study; ( . . . ) e m f from Ref. 21.

12/7AG0 C12A7 kJ1

-201 -40

-80

I- -

I

I

I

I

1000 K

t

I

1

2000 K

I

Emf,this study 18

I

1000 K

I

I

2000 K

Fig. 12. Gibbs energy of formation of "/, Ca0.A120, (in kJ/mol). ( 0 )Values calculated from the phase diagram of Ref. 9; ( 0 )Values calculated from activities in liquid phase and phase diagram No. 2295 in Ref. 3; R denotes the recommended value and Th the thermochemical data (Ref. 4).

Fig. 10. Temperature dependence of Gibbs energy of formation or Ca0.2A120, (in kJ/mol). ( 0 )Values calculated

from properties of the liquid phase and the phase diagram (Ref. 9); Th represents the thermochemical data (Ref. 4) and R the recommended value; results of Ref. 6; (*) results of Ref. 2; (-) emf from present study.

(@I)

~

u I . reported ~~ emf measurements on this compound using a technique similar to that used in this study. Their cell operated with a CaF, electrolyte at 1260 to 1400 K using a mixture of 8 3 and CaZrO, under oxygen gas as the reference elecCa, ,1Zro830, trode. The activity of C a O in the reference electrode was determined by Levitskii et ~ 1 . 2in~ separate experiments with galvanic cells. I n this study the CaF, single crystals were found to soften at > 1275 K, thus impairing the mechanical stability of the cell assembly. The Gibbs energies of formation obtained from the present emf measurements are in good agreement with those of Popov et al. (Fig. 9). However, the temperature dependence of the Gibbs energy or the entropy of formation obtained in the two studies show significant differences, which cannot be resolved in the absence of complete thermal data. The values obtained from the present electrochemical measurements are probably more accurate because of the larger temperature range of measurement, the use of pure C a O as the reference electrode, and the good agreement with data on the liquid phase. The recommended equation for the Gibbs energy of formation is

et

AG"=-l7

430-33.2T(-t1500)

J/mol

(14)

phase diag.

AG"C3A

1000 K

kJ

2000 K

Fig. 13. Gibbs energy of formation of 3Ca0.A1203(in kJ/ mol). ( 0 )Values calculated using the phase diagram in Ref. 9; (0). value calculated from hase diagram in Ref. 3 and activities in the liquid phase; results of Ref. 2; Th stands for the thermochemical values (Ref. 4) and R the values recommended in the present study.

(g)

Journal of the American Ceramic Society-Allibert et al.

314 corresponding to the reaction

+

CaO(s) 6A1203(s)-Ca0. 6A1203(s) (15) (2) CaO.2Al2O, The results of the emf measurements extrapolated to higher temperatures are in excellent agreement with values suggested by Kor and Richardson6 and Rein and Chipman.2 The values calculated in this study from activities in melts are x5 kJ more negative, as indicated in Fig. 10. The recommended equation for the Gibbs energy of formation of this compound is therefore weighted between these data. For the reaction

+

CaO(s) 2A1203(s)-Ca0. 2A1203(s) AGo=-16

400-26.8T(+2500)

J/mol

(16) (17)

The Gibbs energies calculated from thermochemical data4 are x 17 kJ more positive. The error probably resides in the value for the heat of formation obtained by hydrofluoric acid-solution calorimetry.

(3) CaO .A120, The thermochemical data4 for this compound are in excellent agreement with the results of the emf measurements and the values calculated from activities in the melt and phase diagram (Fig. 1 I). The values calculated using different phase diagrams3e4are in good agreement. Unlike the case of Ca0.6AI2O3 and CaO.2AI2O3,the emf results for CaO. A1203can be interpreted unambiguously only if the compound 3 C a 0 . 3A1203.CaF, is unstable or did not form, as discussed earlier in the analysis of electrochemical measurements. For the reaction CaO(s) -I-AI2O3(s)-Ca0. A1203(s)

(18)

AG0=-18

(19)

120-l8.62T(f1500) J/mol

( 4 ) 1 2 c a 0 . 7Al2oJ As shown in Fig. 12, the Gibbs energy of formation of this compound, calculated from thermochemical data: lies between the values obtained from emf and calculated from the properties of the liquid phase. The recommended equation is based on thermochemical data.4 For the reaction

I2/,CaO(s)

+ A1203(s)-+’Z/7Ca0.A1203(s)

(20)

AGo=-12

300-29.3T(+.2500) J/mol

(21)

As discussed previously, the because of the dissolution of calculated from activities in this compound agree closely,

emf results are probably unreliable CaFz in 12Ca0.7AI,03. The values two eutectic melts on either side of as shown in the figure.

(5) 3Ca0.A120, Quantitative information on the stability of this compound cannot be derived from emf measurements. The values calculated from the thermodynamic data of the liquid phase evaluated in this study using two phase are in good agreement with the earlier evaluation of Rein and Chipman2As shown in Fig. 13, these values are x8 kJ/mol more negative than those calculated from thermochemical data.4 This discrepancy is probably due to an error in the heat of formation of this compound obtained by acid-solution calorimetry. The recommended equation is based on the Gibbs energies calculated from the properties of the liquid phase with an entropy term compatible with heat-capacity data. For the reaction 3CaO(s) 4- A1203(s)-3CaO- A1203 AGo=-17

000-32.0T(+ 1500) J/mol

(22) (23)

V. Summary ( I ) Activities in CaO-A1203 melts at 2060 K were measured using a high-temperature mass spectrometer equipped with a multiple Knudsen cell assembly. Accurate values for the activities of CaO were obtained by this technique. The values for the activity of A1203 showed some scatter. A more consistent set of alumina

Vol. 64, No. 5

activities was obtained by Gibbs-Duhem integration of lime activities. (2) By combining the results of this study at 2060 K with those of Sharma and Richardson5a t 1773 K, the temperature dependence of activities or the partial heats of mixing in the liquid phase were calculated. (3) The Gibbs free energies of formation of solid calcium aluminates from their component oxides were measured with solid state galvanic cells using single-crystal CaF, as the electrolyte. The emf’s can be related unambiguously to thermodynamic data for the compounds CaO. 6A1203,CaO. 2AI2O3,and, perhaps, CaO. AI2O3. Due to the solid solubility of CaF, in 12Ca0.7A1203, the data obtained by the emf technique indicate enhanced stability (i.e. more negative Gibbs energies) for this compound. (4) The information on activities in melts was coupled with the phase diagram to derive the Gibbs energy of formation of the solid compounds. From a comparison of these values with those deduced from the emf measurements and other data reported in the literature,’,2