A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S

Volume 54 2009 Issue 3

M. KOPYTO∗ , W. PRZYBYŁO∗ , B. ONDERKA∗∗ , K. FITZNER∗∗

THERMODYNAMIC PROPERTIES OF Sb2O3-SiO2 AND PbO-Sb2O3-SiO2 LIQUID SOLUTIONS

WŁAŚCIWOŚCI TERMODYNAMICZNE CIEKŁYCH ROZTWORÓW Sb2O3-SiO2 I PbO-Sb2O3-SiO2

Thermodynamic properties of the liquid PbO-SiO2 and Sb2O3-SiO2 solutions were derived from the results of theelectrochemical studies by the use of solid oxide galvanic cells with YSZ electrolyte. Activities of PbO in silicate meltswere determined directly in the temperature range from 850 to 1025 K and for SiO2 mole fractions 0.2, 0.3, 0.4 and 0.5 frommeasured e.m.f.’s of the cell:

Pb,PbO − SiO2 | YSZ | Ni,NiO

relatively to Gibbs energy change of pure PbO formation.The thermodynamic properties of Sb2O3-SiO2 liquid solutions were derived indirectly from the measurements conducted withthe cell of the type:

Pb,PbO − Sb2O3 − SiO2 | YSZ | Ni,NiO

in ternary PbO-Sb2O3-SiO2 liquid solutions in the temperature range from 1070 to 1280 K.Two pseudobinary phase diagrams, namely, PbO-SiO2 and PbO-Sb2O3 were optimized, and next using the obtained results thediagram of Sb2O3-SiO2 system, and the liquidus in the pseudoternary PbO-Sb2O3-SiO2 were predicted.

Na podstawie badań elektrochemicznych z wykorzystaniem ogniw galwanicznych ze stałym elektrolitem cyrkonowymYSZ określono właściwości termodynamiczne ciekłych roztworów PbO-SiO2 i Sb2O3-SiO2. W zakresie temperatury od 850do 1025 K dla stężeń molowych SiO2 0.2, 0.3, 0.4 i 0.5 wyznaczono aktywności PbO w żużlu krzemionkowym w odniesieniudo energii swobodnej Gibbsa tworzenia czystego PbO. Obliczenia wykonano bezpośrednio ze zmierzonych doświadczalnie siłelektromotorycznych ogniwa o schemacie:

Pb,PbO − SiO2 | YSZ | Ni,NiO

Właściwości termodynamiczne ciekłych roztworów Sb2O3-SiO2 określono pośrednio z danych termodynamicznych otrzymanychz pomiarów dla ciekłych roztworów PbO-Sb2O3-SiO2. Zastosowane tu ogniwa typu:

Pb,PbO − Sb2O3 − SiO2 | YSZ | Ni,NiO

pracowały w zakresie temperatury 1070-1280 K.Zoptymalizowano dane termodynamiczne dla dwóch pseudopodwójnych układów fazowych PbO-SiO2 and PbO-Sb2O3 iwyznaczono ich diagram fazowe. Tak wyznaczone dane termodynamiczne zastosowano do oszacowania wykresu fazo-wego Sb2O3-SiO2 i określenia przewidywanego kształtu powierzchni likwidus w pseudopotrójnym układzie tlenkowymPbO-Sb2O3-SiO2.

1. Introduction

Silver production from anodic sledges which are leftafter electrorefining of copper is based on the so calledKaldo process, in which two subsequent stages of reduc-

tion and oxidation take place. After the second step, so-lutes from silver are transferred into the slag phase. In or-der to predict the distribution behavior of the impuritiesbetween metal (which is silver with traces of bismuth,lead and antimony as the most common) and the slag un-

∗ INSTITUTE OF METALLURGY AND MATERIALS SCIENCE, POLISH ACADEMY OF SCIENCES, 30-059 KRAKOW, 25 REYMONTA STR., POLAND∗∗ AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY, FACULTY OF NON-FERROUS METALS, LABORATORY OF PHYSICAL CHEMISTRY AND ELECTROCHEMISTRY, 30-059 KRAKOW,30 MICKIEWICZA AVE., POLAND

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der fixed temperature and partial oxygen pressure, ther-modynamic properties of both liquid solutions, name-ly, metallic phase and the slag phase must be known.Thus, thermodynamic properties of at least four compo-nent oxides solution: SiO2+Bi2O3+Sb2O3+PbO shouldbe known. The inspection of literature on this subjectindicates that no such information exists. Indeed, thissystem is not easy to work with, due to a high meltingpoint of SiO2 on the one hand, and the high vapourpressure of the rest of the oxides on the other. It seemsthat the only chance to work out a sensible solution tothis problem is to gather experimental information on allbinary systems which contribute to this particular qua-ternary solution (six of them altogether), and then addthem up according to a certain thermodynamic model inorder to predict behavior of this multicomponent oxidesolution.

A thorough literature search showed that phasediagram of only PbO+SiO2 binary system is well known[1]. Despite high melting temperature of one of the con-stituent oxides it is characterized by a wide range ofliquid solutions – up to XSiO2 = 0.7 at 1273 K. In thesolid state silicates of nPbO·mSiO2 type appear, and twoof them, PbSiO3 and Pb2SiO4 melt congruently, at 1037and 1016 K, respectively. First activity measurements inPbO-SiO2 liquid solutions were carried out by Callow[2], Richardson and Webb [3] and Minenko and Ivanova[4]. Application of solid electrolytes on ZrO2 basis ingalvanic cells stimulated more activity studies of PbO inthis liquid solution. For example, works of Sridhar andJeffes [5], Kozuka and Samis [6], Charette and Flen-gas [7], and Kapoor and Frohberg [8] provided a lotof thermodynamic data of the liquid oxide phase. Also,partial enthalpies of mixing of PbO and SiO2 in liquidsolution were obtained by Østvold and Kleppa [9] whoused self-made drop calorimeter.

The other two systems: PbO+Bi2O3 and PbO+Sb2O3are not so well known. Phase diagram of the PbO+Bi2O3system was studied by Boivin and Tridot [10] as well asBiefeld and White [11]. The single study of Mehrotra,Frohberg and Kapoor [12] provides activity data for bothcomponents at 1173 K. These data have not been verifiedso far.

The PbO-Sb2O3 phase diagram is even less known.It was given first time by Maier and Hincke [13] in 1932.Barthel [14] and Pelzel [15] determined the liquidus inPbO-rich part of this system which agreed closely withMaier and Hincke’s data [13]. This study was later re-peated and Zunkel and Larson [16] by DTA analysisand metal-slag equilibration. Determination of the en-tire liquidus by Hennig and Kohlmayer [17] showed re-markable disagreement with the data mentioned above.It seems that only Sb2O3-rich part of the diagram can-

not be questioned. However, once the composition ofPbSb2O4 phase is reached and liquidus temperature rises,there are some doubts if PbO-rich part of this phase dia-gram can be trusted. None of the investigators mentionedabove reported any mutual solubility in the PbO-Sb2O3solid system. The existence of (PbO) terminal solutionsuggested by the only result of metal-slag equilibrationdone by Zunkel and Larson [16] is not certain and hasnot been taken into consideration in our work.

The activity of Sb2O3 in the liquid solution wasmeasured by Sugimoto et al. [18] and recently by Itoh etal. [19]. They both used electrochemical method employ-ing galvanic cells with solid electrolyte. The results ofboth studies showed negative deviation from the Raoult’sLaw, which is compatible with the existence of thePbSb2O4 solid phase in this system. Maier and Hincke[13] are the only investigators who made vapour-pressuremeasurements on liquid slags in the temperature rangeof interest but their data gave only one point in the de-sirable composition range. Their Sb2O3 activity resultobtained at 973 K agree reasonably well with the resultsof McClincy and Larson [20], who used gas saturationmethod.

There are three different studies which suggest thephase equilibria in the Bi2O3+Sb2O3 system: Tairi etal. [21], Turkoglu et al. [22] and Jingkui et al. [23].All these studies agree at one point: there exists, oneto one BiSbO3 solid phase with a high melting point,which divides the system into two parts. Bi2O3-rich partshows numerous phases with solid solutions betweenthem. Equilibrium with the liquid phase is not knownin this part of the system. According to Jingkui et al.[23] Sb2O3-rich part looks like the eutectic system. Toa certain extent it is similar to the system suggested byTshernogorenko et al. [24] who studied reciprocal re-actions in the Sb-Bi-O system. Two other studies [21]and [22] did not show the course of the liquidus line inthis range of concentrations. Instead, the existence of thesolid solutions is suggested. Recently, new informationabout thermodynamic properties of these liquid solutionswas given by Krzyżak and Fitzner [25].

The Bi2O3+SiO2 system, another binary constituentof the four component SiO2+Bi2O3+Sb2O3+PbO solu-tion has been recently reviewed in the work of Kopytoet al. [26]. Finally, no thermodynamic and phase diagramdata are known to exist for Sb2O3+SiO2 system.

This short literature survey indicates that it is notpossible at present to predict properties of the quater-nary slag solution. In order to gather more data on re-spective binary systems, attempts have been made in thisstudy to determine the thermodynamic properties of theliquid phase in Sb2O3-SiO2 system. In order to checkthe reliability of galvanic cell performance, activity de-

813

termination and the thermodynamic properties of liquidPbO-SiO2 phase were studied first.

2. Experimental

Materials

Pure antimony (99.9%), was obtained from FlukaAG (Switzerland). Lead was delivered by ZMR Skaw-ina (Poland) and it was 99.99% pure. The lead oxideand antimony sesquioxide of 99.9% purity were obtainedfrom Fluka AG and from International Enzymes Ltd.(UK), respectively. SiO2 powder was obtained from sili-ca glass, after grinding and boiling in nitro-hydrochloricacid. Dried in the next step and then annealed at 1250 K,finally, it was quickly quenched in the cold distilled wa-ter. After another drying, fine silica powder was obtainedwhich was next used in sample preparation.

The appropriate amounts of silica and other oxideswere mixed and pelletized into small, cylindrical pellets.These pellets were inserted into electrolyte tubes andplaced on the top of the metal. After metal and oxidesheating and melting such a liquid system was used asa working electrode of the cell. Solid electrolyte tubesCSZ closed at one end (length 400 mm, φ = 8) and YSC(length 50 mm, φ = 6) were supplied by Yamari TradingCo., Japan.

Technique

Two types of e.m.f. cells were used in our ex-periments and they are shown in Figures 1a and 1b,respectively. The cell construction differs dependingon the investigated system and the type of the refer-ence electrode used during measurements. The first cell(Fig.1a) was employed during e.m.f. measurements inPb-PbO and Pb-(PbO+SiO2) liquid system, while theother one, was used to measure e.m.f.’s produced bythe Pb-(PbO+Sb2O3+SiO2) working electrode (Fig.1b).

In the first cell (Fig.1a), the tube of solid zirconiaelectrolyte contained about 2 g of metallic lead and thepellet of PbO or PbO-SiO2 oxide mixture of a chosencomposition. Dry air which acts as a reference electrodeflowed in the outer furnace compartment and was flush-ing the electrolyte tube from the outside. Platinum wirewas used as a connection to the outer part of the elec-trolyte tube’s bottom. The working electrode was flushedinside the electrolyte tube with purified argon. The leadsfrom the liquid electrode of the cell were made of a pieceof iridium wire electrically welded to Kanthal wire. Thewhole cell was put into a constant temperature zone ofthe vertical resistance furnace.

In the other cell (Fig. 1b) the reference electrode wasa mixture of Ni+NiO powders in the molar ratio 1.5:1.The investigated electrode contained, at first, antimonyand then lead together with the appropriate mixture ofoxides.

Fig. 1. The design of two types of e.m.f. cells: with air reference electrode (PO2 = 0.213 bar) (a) and with Ni/NiO reference electrode (b)

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The working electrode and reference electrode wereplaced in a crucible made of alumina, sealed with hightemperature cement and placed in a quartz tube closedat one end. Before experiments the whole system wasflushed with pure argon.

Once the temperature was raised, it was controlledby Eurotherm controller, and e.m.f. was measured byhigh-resistance Keithley 2000 multimeter. The course ofexperiment (data necessary to reach equilibrium by thesystem) was controlled by check of e.m.f. vs. time curveslope acquired by a computer program. The cell wasworking for about one week and the measurements weretaken at increasing and decreasing temperature.

3. Results

3.1. Thermodynamic properties of PbO-SiO2 liquidsolutions

At the beginning Gibbs energy of formation of solidPbO according to the reaction:

Pb(l) +1/2O2 => PbO(s) (1)

was determined by the use of a galvanic cell:

Pb(l),PbO(s) | O−2 | air (I)

in the temperature range 848-1123 K. It was calculatedfrom the following formula:

∆G0f,PbO = −2 · F · E0 + 0.5 · R · T ln PO2 , (2)

where: PO2 = 0.213 bar denotes oxygen partial pressureat the air reference electrode, E0 is an electromotive forceof the cell (I), F is a Faraday constant. Finally, T and Rare an absolute temperature and a gas constant, respec-tively.

Electromotive force values obtained in this workwere corrected with thermo e.m.f. of (Kanthal+Ir)-Ptjunction {E(Kanthal+Ir)−Pt (mV) = –0.2364 – 5.458 ·10−4· T+ 8.316 · 10−6· T2}.

Using corrected e.m.f. vs. T dependence in the form:

E(V) = 1.1181(±0.0013)− 53.33 · 10−5(±1.36 · 10−6) · T(3)

∆G0f,PbO for the formation of the solid lead oxide was

derived directly from equation (2) in the following form:

∆G0f,PbO(J ·mol−1) = −215771(±260) + 96.43(±0.3) · T

(4)

Fig. 2. The comparison of Gibbs energy of formation of solid β-PbO.All reviewed experimental data are bracketed by the lines represent-ing results of Iwase et al. [28, 29] and Mehrotra et al. [30] shownas shadowed stripe. The newest results of ∆G0

f ,PbO of solid PbO [31]were superimposed

The results of Gibbs energy of formation of solidβ-PbO (β-PbO, orthorhombic), ∆G0

f,PbO, as a function oftemperature are compared in Fig. 2 with earlier exper-imental data reviewed by Risold et al. [27]. The linerepresenting the obtained ∆G0

f,PbO values is bracketed inthe middle of the most extreme literature results [28,29] and [30]. It means that all other 12 sets of datalie1)

between them. Additionally, the newest results of Gibbsenergy of formation of solid β-PbO [31] were superim-posed (Fig. 2).

A good agreement is found between literature da-ta and present results obtained for ∆G0

f,PbO because thespread of data is about 2.5% of measured value and incase of comprehensive review of Ganesan et al. [31]is less then 0.5%. Consequently, one can believe thatthe determination of thermodynamic properties of oxidesystems by the use of our experimental setup is accurateand reliable.

To determine PbO activity in the liquid slag thee.m.f. of the cell II:

Pb, {(PbO)x + (SiO2)(1−x)} | O−2 | Ni + NiO (II)

was measured in the temperature range from 1050 to1300 K. The scheme of the cell is written in such a waythat the right-hand electrode is a positive one.

In comparison with the cell I the reference electrodewas changed (Fig. 1b) in order to reduce measured e.m.f.and to increase the precision of measurements.

The overall cell I reaction is:

1) The thermochemical calorie was adopted in present calculations: 1 calth = 4.184 J

815

Pb(l) +1/2O2 => PbO(l) (5)

and for the reversible reaction (1) the change in Gibbsfree energy can be expressed as follows:

∆G = −2F · E = µPbO − µPb −1/2µO2 (6)

while

RT · lnaPbO = ∆G0NiO − ∆G0

PbO − ∆Gs−lPbO − 2F · E (7)

Electromotive force values E obtained in this workby the use of cell (II) and corrected with thermo e.m.f. of(Kanthal+Ir)-Pt junction are shown in Fig. 3. The resultsof e.m.f. measurements were treated by least-squaresanalysis and obtained equations are given in Table 1.

Thermodynamic data of formation of liquid PbO inreaction (5) was calculated taking into account ∆G0

PbOexpressed by equation (4) and the assessed by Risoldet al. [27] Gibbs energy of fusion of pure, β-PbO (or-thorhombic):

∆Gβ−lPbO(J/mol) = 26500 − 22.9 · T (8)

TABLE 1The experimental e.m.f. vs. temperature for different composition of

PbO-SiO2 liquid solutions

XPbO e.m.f., E(V) = A + B · T0.8 -0.2699 (±0.0143) + 10.661 · 10−5 (±1.19 · 10−5) · T0.7 -0.2522 (±0.0391) + 9.975 · 10−5 (±3.2 · 10−5) · T

0.667 -0.2460 (±0.0391) + 9.590 · 10−5 (±3.2 · 10−5) · T0.6 -0.2118 (±0.00392) + 9.590 · 10−5 (±3.24 · 10−6) · T0.5 -0.2904 (±0.00579) + 18.511 · 10−5 (±4.78 · 10−6) · T

1050 1100 1150 1200 1250 1300

T, K

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

e.m

.f.,

V

Least square fit

0.5

0.6

0.667

0.7

0.8

Fig. 3. Temperature dependence of e.m.f. of the cell II for differentXPbO concentration

The Gibbs energy of formation of solid NiO,

∆G0f,NiO, obtained from e.m.f. measurements by Kale and

Fray [32] was accepted in PbO activity calculations withthe use of equation 7. The activities of PbO in the liq-uid slag calculated directly from measured e.m.f.’s areshown in Fig. 4 as a function of PbO mole fraction atthe chosen temperature 1273 K. These results indicatelarge negative deviation from the Raoult’s Law, whichin fact is compatible with the existence of solid silicatesin this system.

0.0 0.2 0.4 0.6 0.8 1.0

XPbO

0.0

0.2

0.4

0.6

0.8

1.0

Activity

of

Pb

O

Richardson, Webb [3]

Sridhar, Jeffes [5]

Kozuka, Samis [6]

Charette, Flengas [7]

this work

Fig. 4. The activity of PbO in PbO-SiO2 liquid slag in the frame ofexperimental temperature range obtained at 1273 K

The PbO activity measurements together with theØstvold and Kleppa [9] enthalpies of solution data wereused for the optimization of thermodynamic parametersof PbO-SiO2 liquid slag by means of methods similar to[33, 34].

3.2. Thermodynamic properties of Sb2O3-SiO2liquid solutions

At first, the cell of the type:

Ni,NiO | O−2 | Sb(l), {(Sb2O3)x + (SiO2)(1−x)} (III)

was used to determine activity of Sb2O3 in the liq-uid phase. Since there is no information about theSb2O3-SiO2 phase diagram, it was assumed that becauseof substantial difference in melting points of pure com-ponent oxides, one may expect that the range of composi-tions available for experiments is located on Sb2O3-richside. Two compositions XSb2O3 = 0.6 and 0.7 were arbi-trarily chosen for investigations.

The overall cell III reaction is:

Sb2O3 + 3Ni => 2Sb + 3NiO (9)

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and since for such a reaction the Gibbs free energychange is:

∆G = −6 · F · E = 2µSb + 3µNiO − µSb2O3 − 3µNi (10)

it is easy to show that for pure, liquid Sb2O3 (aSb2O3 = 1)standard Gibbs energy of formation of liquid antimonysesquioxide can be obtained from the measured e.m.f. ofcell III, E0:

∆G0f,Sb2O3

= −6F · E0 + 3∆G0f,NiO. (11)

The results of our measurements are shown in Fig-ure 5 and 6, respectively and are gathered in Table 2.Gibbs free energy change of the reaction of formationof pure liquid antimony sesquioxide (Tm = 929 K) wascalculated from equation (11) in the form:

∆G0f,Sb2O3

, J/mol = −679376(±780) + 233.17(±0.77) · T,(12)

TABLE 2Dependence of e.m.f. vs. temperature for particular composition of

Sb2O3-SiO2 liquid solution

XSb2O3 e.m.f., E(V) = A + B · T1 -0.04625 (±0.001347) + 4.233 · 10−5 (±1.34 · 10−6) · T

0.6 -0.03921 (±0.01477) + 3.826 · 10−5 (±1.19 · 10−5) · T0.7 -0.03636 (±0.00178) + 3.440 · 10−5 (±1.74 · 10−6) · T

and shown in Fig. 5 together with the results of Sugimotoet al. [18] and Isecke [35], the most extreme literatureresults. It means that all other 8 sets of data [36-38]fall within the narrow shadowed area and additionally,most of the experimental data lies between the resultsof Sugimoto et al. [18] and the present data. The spreadof the data is less than 2.2 % of the measured value.This excellent agreement between literature data and thepresent results of ∆ G0

f,Sb2O3can be treated as a proof of

reliability of galvanic cell III performance.Next, the activity of Sb2O3 in the liquid solution

(Sb2O3)x+(SiO2)(1−x) (0 < x < 1) can be obtained fromthe relation:

ln aSb2O3 =6FRT· (E0 − E), (13)

where measured E values are given in Table 2 in theform of A + BT equations.

Fig. 5. The comparison of Gibbs energy of formation of liquid Sb2O3

with the literature data. All reviewed experimental data are bracketedby the lines representing results of Sugimoto et al. [18] and Isecke[35] shown as shadowed area

950 1000 1050 1100

T, K

0.000

0.002

0.004

0.006

0.008

e.m

.f.,

V

XSb2O3

1.0

0.7

0.6

Fig. 6. Temperature dependence of e.m.f. of the cell III for pure liquidSb2O3 and for different XSb2O3 concentrations of Sb2O3-SiO2 liquidsolution

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0.0 0.2 0.4 0.6 0.8 1.0

XSiO2

0.0

0.2

0.4

0.6

0.8

1.0

Activity

of

Sb

2O

3a

nd

SiO

2

this work

calcul. 1073 K

Liquid +Tridym.

aSb2O3

aSiO2

Fig. 7. The estimated activity of Sb2O3 and SiO2 in Sb2O3-SiO2

liquid slag

It was found that the measured e.m.f.’s are very smalland do not differ much from the result obtained for pureSb2O3. Calculated Sb2O3 activity values at 1073 K forXSb2O3 = 0.6 and 0.7 are found to be 0.84 and 0.91,respectively. Considering experimental uncertainty thisis in fact constant value. It may indicate that there existsa two phase field on Sb2O3–rich side.

Activities are shown in Fig. 7 but taking into accountvery small values of measured e.m.f.’s the results arevery uncertain. Therefore, another attempt was made toestimate the properties of the considered binary system.

3.3. Thermodynamic properties of PbO-Sb2O3-SiO2liquid solutions

Activity of PbO in the liquid PbO-Sb2O3-SiO2ternary solution was measured using the cell of typeIV:

Ni,NiO | O−2 | Pb(l), (PbO(x) + Sb2O3(y) + SiO2(1−x−y)).(IV)

Measurements were carried out along thecross-section of the ternary system with XPbO/XSiO2 = 2,and for the slag compositions XSb2O3 = 0.1, 0.2, 0.3 and0.4. On the basis of the literature information about thethermodynamic properties of PbO-SiO2 and PbO-Sb2O3liquid solutions it was hoped that from the results ob-tained for the ternary system the interaction parameterscharacteristic of the binary Sb2O3-SiO2 solution may bederived.

The net cell IV reaction can be expressed in theform:

Pb + NiO => PbO + Ni (14)

which is analogous to net reaction of cell II. So, the cal-culation of the activity of liquid PbO in the slag phasefollows the previously described procedure and is de-scribed by the expression (7) where E is measured e.m.f.of cell IV.

TABLE 3Dependence of e.m.f. vs. temperature for particular concentration of

PbO-SiO2-Sb2O3 liquid slag

XSb2O3 e.m.f., E(V) = A + B · T0.1 -0.19627 (±0.0112) + 8.900 · 10−5 (±9.58 · 10−6) · T0.2 -0.13967 (±0.0143) + 5.557 · 10−5 (±1.21 · 10−5) · T0.3 -0.14848 (±0.0092) + 7.006 · 10−5 (±7.95 · 10−6) · T0.4 -0.16643 (±0.0123) + 9.9304 · 10−5 (1.05±10−5) · T

The results produced by cell IV are shown in Fig. 8and are also gathered in Table 3. In our case experimentsfor higher Sb2O3 concentrations were not possible sincefor the sample of XSb2O3 = 0.4 microprobe detected an-timony in the lead used in the working electrode of cellIV. This speaks for the side reaction between the slagphase and the metal for higher Sb2O3 content, whichmakes experiments for higher Sb2O3 concentrations im-possible.

The calculated PbO activities for the ratio PbO/SiO2= 2 are shown in Fig. 9 as a function of X Sb2O3 at 973and 1173 K, respectively. In the same Figure activitiesof Sb2O3 determined at 973 K by McClincy and Larson[20] from vapor pressure measurements are also shown.Despite different techniques both sets of the data agreereasonably well.

1050 1100 1150 1200 1250 1300

T, K

-0.18

-0.15

-0.12

-0.09

-0.06

-0.03

0

0.03

0.06

e.m

.f,

V

Pb/PbO(l)

0.1 - XSb2O3

0.2

0.3

0.4

XPbO/XSiO2= 2

PbOSb2O3

SiO2

Pb/PbO(l)

Fig. 8. Temperature dependence of e.m.f. of the cell IV for differentXPbO concentration

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0.0 0.2 0.4 0.6 0.8 1.0

XSb2O3

0.0

0.2

0.4

0.6

0.8

1.0

Activity

of

PbO

an

dS

b2O

3

experimental

[20]

this work

calculated

973 K

1173 K

Liquid +

β-PbO

aSb2O3

aPbO

Fig. 9. The comparison of calculated and measured activity of Sb2O3

[20] and PbO in PbO-Sb2O3-SiO2 liquid slag for PbO/SiO2 = 2 at973 K and 1173 K, respectively

4. Thermodynamic assessment and phase diagramsestimation

A quasi-regular solution model was applied to de-scribe the binary liquid phase. The molar Gibbs energyof solution phase is expressed by the equation:

Gm = x0AGA + x0

BGB + RT(xA · lnxA + xB · lnxB) +ex Gm.(15)

The parameter 0Gi is the Gibbs energy of pure oxidespecies i, i.e. PbO, Sb2O3 and SiO2. Their values weretaken from [27], [39] and [40], respectively,The excess free energy is expressed as quasi-regular so-lution [44] by formula:

exGm = xAxB ·∑i=0

(xA − xB)i ·i LA,B, (16)

where iLA,B interaction parameters are temperature de-pendent and given in J·mole−1. When thermodynamicdata for terminal solutions are not available an assump-tion was made that the mutual solid solubility of SiO2,PbO or/and Sb2O3 is negligible.

The thermodynamic evaluation was carried out bythe optimization and calculation program, TCCR (Ther-moCalc AB Stockholm) [42] and Pandat 7.0, developedby Computherm LLC (USA) [43]. Using the obtainedactivity values, the thermodynamic properties of the liq-uid solutions were described with Redlich-Kister formu-la (16).

4.1. PbO+SiO2 system

PbO+SiO2 system was modeled using the obtainedactivity values and the data published in the literature[3, 5-7], the liquidus data [45-50] and the enthalpies ofsolution of liquid lead oxide in PbO-SiO2 melts at 1173K [9]. The parameters of excess Gibbs free energy ac-cording to the formalism (16) were collected in Table 4.The comparison between calculated and experimentallyobtained thermodynamic data are shown in Fig. 10 and11.

From this equation all thermodynamic functionsfor the liquid solutions can be determined. ParametersiLPbO,SiO2 are linearly dependent on temperature and aregiven in J·mole−1.

The Gibbs energy of the stoichiometric phases wasgiven relatively to the Gibbs energy of pure oxide species0Gi by the equation:

G(p,q) = p0GA + q0GB + ∆0Gf ,(p,q), (17)

where ∆0Gf ,(p,q) is a Gibbs energy of formation of ApBqcompound and p, q are the stoichiometric coefficients.∆0Gf ,(p,q) can be expressed as a sum of enthalpy andentropy terms in (J·mole−1):

∆0Gf ,(p,q) = ∆0H(p,q) − T · ∆0S9p,q) (18)

TABLE 4Optimized model parameters of the PbO-SiO2 phases

ParameterValue and linear dependence on temperature,

J·mole−1

Liquid phase Substitutional model0LPbO,SiO2 -33605.1 + 2.3701 · T1LPbO,SiO2 -13551.2 - 7.7051 · T2LPbO,SiO2 19293.2 - 2.4049 T

Phase Pb4SiO6 Linear compound

∆0Gf ,Pb4SiO6 -28837 - 5.5883 · TPhase Pb2SiO4 Linear compound

∆0Gf ,Pb4SiO4 -29859 - 1.7761 · TPhase PbSiO3 Linear compound

∆0Gf ,PbSiO3 -16850 - 5.0982 · T

Using this thermodynamic description of the liq-uid phase, Gibbs free energy of formation of both sili-cates, and available data on phase equilibria, the bina-ry PbO+SiO2 system was calculated and is shown inFig. 12.

819

0.0 0.2 0.4 0.6 0.8 1.0

XPbO

0.0

0.2

0.4

0.6

0.8

1.0A

ctivity

ofP

bO

and

SiO

2[3]

[5]

[6]

[7]

this work

calculated

Liquid +Tridymite

Fig. 10. The activity of PbO and SiO2 in PbO-SiO2 liquid slag cal-culated at 1273 K. The experimental data [3, 5-7] are superimposed

0.0 0.2 0.4 0.6 0.8

XSiO2

-20.0

-15.0

-10.0

-5.0

0.0

5.0

∆HP

bO,kJ·m

ol-1

Østvold, Kleppa [9]

calculated

Liquid +Tridymite

Fig. 11. Optimized partial enthalpies of solution of liquid lead oxidein PbO-SiO2 melts at 1173 K

0.0 0.2 0.4 0.6 0.8 1.0

XSiO2

800

1000

1200

1400

1600

1800

2000

T,

K

[45]

[46]

[47]

[47]

[48]

[49]

[50]

calculated

L + Tridymite

L + Quartz

Liquid

PbSiO3 + Quartz

PbS

iO3

Pb

4S

iO6

Pb

2S

iO4

β-PbO+L

L + Cristobalite

α-PbO+Pb4SiO

6

1143

1744

1017 1034

997, 0.21989, 0.25 996, 0.41

996, 0.60

Fig. 12. Optimized PbO-SiO2 phase diagram. Experimental data[45-50] are superimposed

The assessment of PbO-SiO2 system published byJak et al. [51], despite a good thermodynamic model-

ing, was not adopted in the present analysis because theassociate solution model used in it for liquid solution istoo complicated for our estimation of the activity in thePbO-Sb2O3-SiO2 system.

4.2. PbO+Sb2O3 system

The description of the thermodynamic properties ofanother binary system, namely PbO-Sb2O3, is based onthe phase diagram experimental data found in literature[13,16-18] and the data of Sb2O3 activity in the liq-uid oxide phase at temperatures range 973-1223 K [13,18-20]. The obtained excess Gibbs free energy parame-ters used in our calculations are gathered in Table 5.

The compound PbSb2O4 presented in Fig. 13 is ten-tative but still it is hard to agree that its congruent melt-ing temperature (1653 K) reported in [52] is realistic.The interpretation of the onset temperature in DTA mea-surements is a well known problem, especially, in vis-cous slag forming systems. In this case the experimentalerror can be substantial.

Consequently, for the equimolar compoundPbSb2O4, melting temperature at 843 K [53] is probablyclose to reality.

TABLE 5Optimized model parameters of the PbO-Sb2O3 phases

ParameterValue and linear dependence on temperature,

J·mole−1

Liquid Substitutional model0LPbO,Sb2O3 -63759.3 + 35.0117 · T1LPbO,Sb2O3 -579.6

Phase PbSb2O4 Linear compound

∆0Gf ,PbSb2O4 -107079 + 103.3 · T

0.0 0.2 0.4 0.6 0.8 1.0

XSb2O3

700

800

900

1000

1100

1200

T,

K

[13] DTA

[13] estimated

[16] slag-metal

[16] DTA

[17] DTA

[17] estimated

[18] slag-metal

calculated

L + β-Sb2O3

Liquid

PbSb2O4+α-Sb2O3

PbS

b2O

4

β-PbO+L

α-PbO+PbSb2O4

879.0872

762

851, 0.308854, 0.697

β-PbO+PbSb2O4

L + α-Sb2O3

Fig. 13. Optimized PbO-Sb2O3 phase diagram. Experimental data[13, 16-18] were superimposed

820

0.0 0.2 0.4 0.6 0.8 1.0

XSb2O3

0.0

0.2

0.4

0.6

0.8

1.0A

ctivity

of

PbO

and

Sb

2O

3

experimental

[13]

[18]

[19]

[20]

calculated

973 K

1023 K

1223 K

Liquid +

β-PbO

Fig. 14. The activity of PbO and Sb2O3 in PbO-Sb2O3 liquid slagcalculated at 973 K, 1023 K and 1223 K. The experimental data [13,18-20] were superimposed

4.3. Sb2O3+SiO2 and PbO-Sb2O3-SiO2 systems

In the case of Sb2O3+SiO2 system the adopted pro-cedure of calculations was slightly different. Having theactivity of lead and antimony oxides determined alongthe vertical cross-section of the PbO-Sb2O3-SiO2 sys-tem, and the activity of Sb2O3 in the binary system,one can use Redlich-Kister-Muggianu model [41, 54]to derive interaction parameters for binary Sb2O3-SiO2liquid solution. Because there is no thermodynamic in-formation about this system, the term describing ternaryinteractions were not taken into account. The obtainedmodel parameters are gathered in Table 6. Calculatedactivities in the binary system are shown in Fig. 7 andcompared at 1073 K with measured our values.

Using the obtained model parameters the phase dia-gram for Sb2O3+SiO2 system was predicted and is shownin Fig. 15. It indicates the existence of a small miscibil-ity gap. This is contrary to PbO-SiO2 and Bi2O3+SiO2systems, where solid silicate phases are present, andthe liquid solutions exhibit negative deviations from theRaoult’s Law. Finally, the model calculations were ex-tended upon the ternary system. Activities of Sb2O3 de-termined at 973 K from vapor pressure measurements byMcClincy and Larson [20] are shown and compared withthe results of calculations in Fig. 9. Also, aPbO obtainedfrom our e.m.f. measurements are shown in the sameFigure. Considering the uncertainty in the description ofbinary systems the overall agreement is good. The pre-dicted liquidus in the ternary PbO-Sb2O3-SiO2 systemis shown in Fig. 16. Respective invariant reactions forboth unknown binary and ternary systems are gatheredin Table 7.

TABLE 6Optimized model parameters of the Sb2O3-SiO2 phases

Parameter Value, J·mole−1

Liquid Substitutional model0LSb2O3SiO2 -2314.81LSb2O3SiO2 16483.6

Fig. 15. Estimated Sb2O3-SiO2 system

Fig. 16. Estimated liquidus in pseudoternary PbO-Sb2O3-SiO2 system

821

TABLE 7Binary and ternary invariant reactions in PbO-Sb2O3-SiO2 pseudoternary system

Invariant Reaction T, K XPbO XSb2O3 XSiO2

U1 Liquid + Pb2SiO4 → PbSb2O4 + Pb4SiO6 845.7 0.6569 0.2437 0.0994E1 Liquid → PbSb2O4 + Pb4SiO6 + β-PbO 844.1 0.6839 0.2499 0.0662U2 Liquid + Pb2SiO4 → PbSb2O4 + PbSiO3 833.7 0.4632 0.2236 0.3132E2 Liquid → Quartz + PbSb2O4 + PbSiO3 777.5 0.2382 0.2016 0.5602E3 Liquid → α-Sb2O3 + Quartz + PbSb2O4 761.0 0.0204 0.2372 0.7424e1 Liquid → Pb4SiO6 + Pb2SiO4 989 0.75 – 0.25e2 Liquid → Pb2SiO4 + PbSiO3 996 0.59 – 0.41e3 Liquid → PbSiO3 + Quartz 996 0.4 – 0.60e4 Liquid → α-Sb2O3 + Quartz 765 – 0.232 0.768e5 Liquid → β-PbO + PbSb2O4 851 0.692 0.308 –e6 Liquid → α-Sb2O3 + PbSb2O4 854 0.303 0.697 –p1 Liquid + β-PbO → Pb4SiO6 997 0.79 – 0.21m Liquid1 → Liquid2 + α-Sb2O3 921 – 0.917 0.083

5. Conclusions

In this study the predicted ternary PbO-Sb2O3-SiO2oxide phase diagram has been suggested. Attempts havealso been made to determine the thermodynamic prop-erties of the liquid phase in Sb2O3-SiO2 system as wellas to calculate this pseudobinary phase diagram. Thoughthe predicted diagrams are probably not exact they maybe not far from reality for the following reasons:– Gibbs free energy of formation of pure oxides PbO

and Sb2O3 determined from our e.m.f. measurementsis in good agreement with the data taken from liter-ature. This speaks for the precision of our measure-ments and reversible cell operation.

– Thermodynamic properties of the liquid PbO-SiO2solutions represented by measured activities are alsoin reasonable agreement with the literature data. Thisfact demonstrates that the side reactions in the celldue to aggressive liquid phase were under control.

– Using available thermochemical and phase diagramdata calculations of two binary oxide systems, name-ly PbO-SiO2 and PbO-Sb2O3 were carried out andgood agreement was found between the calculatedand experimentally determined phase diagrams. Cal-culations were performed under the assumption thatthere are no associates in binary melts. Because ofthe lack of sufficient data the ternary interaction inthe liquid slag was omitted.

– CALPHAD method proved to be successful in pre-dicting unknown phase diagrams with the aid of min-imal amount of the experimental data. The thermody-namic description of Sb2O3-SiO2 system is tentativebut coherent. Attempts to estimate the temperaturedependence of liquid phase parameters were not suc-cessful.

– Finally, gathered parameters for the liquid phase

existing in respective binary systems are the founda-tion of the database built with the purpose of describ-ing the thermodynamic properties of Kaldo processslags. This work should be continued for other oxidesystems.

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Received: 20 February 2009.