Solubility of Cr2O3 and Speciation of Chromium in Soda–Lime–Silicate Melts

Solubility of Cr2O3 and Speciation of Chromium in Soda–Lime–Silicate Melts

Hichem Khedim,z Tuti Katrina,z Renaud Podor,y Pierre-Jean Panteix,w,z Christophe Rapin,z

and Michel Vilasiz

zDepartement CP2S–Equipe 206, Institut Jean Lamour, Faculte des Sciences et Techniques, Nancy Universite,Boulevard des Aiguillettes, BP 70239 54506, Vandoeuvre les Nancy, Cedex, France

yInstitut de Chimie Separative de Marcoule, UMR 5257-ICSM Site de Marcoule, Batiment 426-Acces directpar le Visiatome, BP 17171 30207, Bagnols Sur Ceze, Cedex, France

Chromium oxide solubility was measured in soda–lime–silicatemelts using a thermochemical reactor allowing an independentcontrol of temperature, glass composition, and oxygen fugacityin a closed system. This investigation performed in the ternaryNa2O–CaO–xSiO2 (NCS) system showed that the physico-chemical and thermochemical models used for chromium chem-istry description in binary melts are applicable in the ternarysystem. The presence of Cr(II), Cr(III), and Cr(VI) has beenevidenced and their respective contributions in the total chro-mium content dissolved in the melt were determined. A new ap-proach based on optical basicity allowed the quantification ofthe basicity of the melt and consequently the free oxygen ionsactivity (aO2�). The treatment of the obtained results led to thedetermination of thermodynamical properties of the system. Thestandard enthalpies and entropies corresponding to the oxida-tion and reduction reactions were determined.

I. Introduction

THE dissolution processes of minerals and refractory materi-als in molten silicates are of major interest for geologists

(relict grains, xenoliths, magma assimilation) and chemists (cor-rosion of ceramics by molten glasses). It has been shown that thesolubility of elements in silicate melts strongly depends on glassbasicity (alkaline oxides content), temperature, and oxygen fu-gacity.1–4 This latter parameter influences the redox propertiesof the glass and yields to the stabilization of high or low oxida-tion states for the multivalent elements in the melt. Therefore,effects related to the action of both O2� (basic effect) and O2

(oxidizing effect) rule together the formation of the oxide poly-hedron, the well-known tetrahedra or octahedra, which stabilizethe metallic or semimetallic solute in the molten silicate liquid.Oxygen is one of the principal reactants in redox equilibria,which occur in molten glasses. The equilibrium state of the glassstrongly depends on its composition, which conditions the O2�

activity (i.e. the basicity). Thus, for glasses of fixed O2� activity,the measurement of dissolved oxygen can be used to controlsome processes, such as the control of the properties of the melt(viscosity, quality of refining) or the final state of the material(color, ageing y).5–8

Melts containing one or more multivalent elements are inequilibrium when all the components taking part in the redoxreactions assume a common value of the potential.9 Reactions

involving oxygen which are known to be generally slow around251C, are very fast at temperature higher than 10001C. In thiscase, free oxygen ions O2�, which are imposed by the glasscomposition,9–11 take part in redox reactions.

The redox reactions between oxygen and multivalent ele-ments in the glass melt are often described as follows:

MðmÞþ ,MðmþnÞþ þ ne�n

4O2 þ ne� , n

2O2�

MðmÞþ þ n

4O2 ,MðmþnÞþ þ n

2O2�

(1)

This reaction, in satisfying the equilibrium constant, allowsthe prediction of the influence of the state variables on thisequilibrium:

(1) For constant temperature and glass composition (aO2�),an increase in oxygen fugacity should increase the oxidized spe-cies (M(m1n)1) content.

(2) For constant temperature and oxygen fugacity ( fO2), anincrease in the O2� activity should increase the concentration ofthe reduced species (M(m)1).

Several studies confirm the first prediction,12–14 but secondwas rejected by many others.15–18 In this case, increasing basicityleads to an increase of the oxidized species concentration. Thisdisagreement is explained by taking account of the oxyacidcharacter of the cations, which interact with the free oxygenions. This leads to the formation of oxy-complexes which pres-ent different stabilities, charges, symmetries, and coordinationnumbers.19

By taking into account the combined effect of the redoxreaction and the oxy-acid–basicity, equilibrium described byEq. (1) can be expressed by the equation:

MOð2x�mÞ�x þ n

4O2 þ y� x� n

2

� �O2� ,MOð2y�m�nÞ�y (2)

In this equilibrium, the oxidized and reduced species are com-plexed by free oxygen ions, whereby the x and y indices are thecoordination numbers of resulting oxo-complex species. If thevalue of the stoichiometric coefficient (y–x–n/2) related to (O2�)is positive, an increase in the basicity stabilizes the highest ox-idation state. In the contrary case, the reverse occurs. The equi-librium constant of the reaction can be given by:

KðTÞ ¼a MOð2y�m�nÞ�y

� �aðO2�Þðx�yþn=2Þ

a MOð2x�mÞ�x

� �ð f O2Þn=4

(3)

where ai is the activity of the i element and fO2 is the oxygenfugacity.

J. Smialek—contributing editor

This work was financially supported by the ANR through the Actimelt project.wAuthor to whom correspondence should be addressed. e-mail: pierre-jean.pant

[email protected]

Manuscript No. 26476. Received July 20, 2009; approved December 4, 2009.

Journal

J. Am. Ceram. Soc., 93 [5] 1347–1354 (2010)

DOI: 10.1111/j.1551-2916.2009.03581.x

r 2010 The American Ceramic Society

1347

mailto:[email protected]

mailto:[email protected]

By replacing activities by the expression (ai 5 gi �Ci), the equi-librium constant can be written as:

KðTÞ ¼gMðmþnÞþ MOð2y�m�nÞ�y

h iaðO2�Þðx�yþn=2Þ

gMðmÞþ MOð2x�mÞ�x

h ið f O2Þn=4

(4)

where gi is the activity coefficient of the i component in the meltand [i] is the concentration of the i component in the melt.

Because the concentrations of the multivalent ions in meltsare generally low, applying Henry’s law, their activities can beequated to their concentrations.5,19 Consequently, the equilib-rium constant K(T) expression can be evaluated, using only theconcentrations of the multivalent elements, the oxygen fugacityand the activity of the free oxygen ions:

KðTÞ ¼MOð2y�m�nÞ�y

h iaðO2�Þðx�yþn=2Þ

MOð2x�mÞ�x

h ið f O2Þn=4

(5)

Consequently:

< ¼MOð2y�m�nÞ�y

h i

MOð2x�mÞ�x

h i

¼ KðTÞ½aðO2�Þ�ðx�y�n=2Þ½ f O2�n=4 (6)

with < as the redox ratio.Chromium can exist in various oxidation states. It is often

used in metallurgy for its properties of hardness and corrosionresistance. Much of the equipments used in the glass industryinvolves superalloys containing up to 30% chromium. The abil-ity of these alloys to resist corrosion is related to the chemicaldurability of the chromium oxide (Cr2O3) layer formed at thealloy/glass interface.20,21 In the ambient environments, chro-mium is primarily in the Cr(III) form, but also in the Cr(VI)form in some oxidizing environments close to the surface.22

Nevertheless, several studies showed the existence of Cr(II) insilicates melted under reducing conditions.23–27 The behavior ofchromium in the silicate melts is of interest not only in glassmanufacture,28 but also in many other areas such as nuclearwaste immobilization,29 slag recycling,28 and geochemistry.30

However, a good description of the chemistry of chromium insilicate melts passes inevitably by a good comprehension of thechemical equilibria (acid–bases, redox) taking place betweenchromium and the melt.

In a previous work,1 a chemical model describing chromiumchemistry in the Na2O–SiO2 binary melts was developed. A de-scription of the reactions occurring when chromium oxide is incontact with the glass melt is given in Fig. 1. The first reaction(Eq. (7)) is the direct dissolution of Cr2O3 into the melt as aCr(III) oxo-complex. This is an acid–base reaction which is in-dependent of the fO2.

1

2Cr2O3ðcrystalÞ , CrðIIIÞOð2x�3Þ�x ðmeltÞ þ 3

2� x

� �O2�ðmeltÞ

(7)

Cr(III) species can be oxidized to Cr(VI) species (Eq. (8)),under oxidizing conditions, or reduced to Cr(II) species(Eq. (9)), under reducing conditions

CrðIIIÞOð2x�3Þ�x ðmeltÞ þ 3

4O2ðgasÞ , CrðVIÞOð2y�6Þ�y ðmeltÞ

þ x� yþ 3

2

� �O2�ðmeltÞ ð8Þ

CrðIIIÞOð2x�3Þ�x ðmeltÞ þ z� xþ 1

2

� �O2�

, CrðVIÞOð2y�6Þ�y ðmeltÞ þ 3

4O2ðgasÞ

(9)

The equilibrium constants for the dissolution, oxidation, andreduction reactions can be written as:

Kd ¼ a O2�� 32�xð Þ

a CrðIIIÞ½ � (10)

Kox ¼a CrðVIÞ½ �a O2�� x�yþ3

2ð Þ

a CrðIIIÞ½ � f O3=42

(11)

Kred ¼a CrðIIÞ½ � f O1=4

2

a CrðIIIÞ½ �a O2�� z�xþ12ð Þ (12)

Fig. 1. Chemical reactions occurring when Cr2O3 crystals are in contactwith the melt. The chromium oxide is dissolved to Cr(III) complexesfollowing an acid–base reaction (Eq. (7)). The obtained Cr(III) speciescan be oxidized to Cr(VI) (Eq. (8)) or reduced to Cr(II) complexes(Eq. (9)).

Table I. Composition of Glasses Used as Started Materials

Aimed glass composition Na2CO3 (wt%) SiO2 (wt%) CaCO3 (wt%) Na (at.%) EPMA Si (at.%) EPMA Ca (at.%) EPMA x

Na2O–1.5SiO2 69.68 59.25 — 25.95 (0.40) 20.17 (0.19) — 1.56 (0.04)Na2O—2SiO2 58.19 65.97 — 21.91 (0.44) 22.38 (0.22) — 2.04 (0.06)Na2O—2.5SiO2 49.95 70.79 — 19.22 (0.49) 23.72 (0.25) — 2.47 (0.09)Na2O—3SiO2 43.75 74.41 — 16.34 (0.22) 25.16 (0.11) — 3.08 (0.06)Na2O—3.5SiO2 38.93 77.24 — 15.00 (0.33) 25.83 (0.17) — 3.466 (0.10)Na2O—CaO—3SiO2 40.89 60.42 35.21 14.04 (0.25) 21.32 (0.15) 7.02 (0.09) 3.03 (0.06)Na2O—CaO—4SiO2 34.04 67.06 29.31 10.98 (0.16) 23.64 (0.12) 5.85 (0.10) 4.30 (0.08)Na2O—CaO—7SiO2 22.64 78.08 19.50 7.57 (0.27) 26.82 (0.14) 3.70 (0.08) 7.09 (0.17)

1348 Journal of the American Ceramic Society—Khedim et al. Vol. 93, No. 5

where ai 5 gi.. Xi and ai is the activity, gi the activity coefficient,and Xi the mole fraction of species i.

In glass melts, polyvalent ion contents are generally very low,and in conformity with Henry’s law, the activity can be equatedto the concentration, so that:

log CrðIIIÞ½ � ¼ logKdiss þ x� 3

2

� �aðO2�Þ (13)

logCrðVIÞ½ �CrðIIIÞ½ � ¼

3

4log fO2 � x� yþ 3

2

� �log a½O2��

þ logKox (14)

logCrðIIÞ½ �CrðIIIÞ½ � ¼ �

1

4log f O2 þ z� xþ 1

2

� �log a O2��

þ logKred

(15)

The model developed in our previous works1,31 allows thedetermination of the redox ratio (Cr(II)/Cr(III) and Cr(VI)/Cr(III)). In this work, this model has been extended to a ternarysystem in order to study Cr2O3 solubility in the Na2O–CaO–SiO2 system.

II. Experimental Procedure

Sodium silicate and soda–lime–silicate glasses with the generalcomposition of Na2O–CaO–xSiO2 (x5 3, 4, and 7) were pre-pared from reagent-grade SiO2 (99.9%, Chempur, Karlsruhe,Germany), Na2CO3 (99.5%, Chempur), and CaCaO3 (99%,Chempur). Appropriate amounts of the reagent powders wereweighed and mixed, introduced into a Pt–Au (95 wt% of plat-inum and 5 wt% of gold) crucible and heated in a mufflefurnace. This type of crucible presents the advantage of a lowwetability with the glass, compared with a pure platinumcrucible. In these conditions the glass does not adhere to thecrucible walls.

To minimize the sodium losses by volatilization,32,33 noto200 g of glass were melted and the following thermal cyclewas used: 12001C for 2 h, 14001C for 2 h, and then 11001C for24 h. The melts were then quenched and finely crushed. Glasscompositions were systematically checked by electron probemicroanalysis: the intended and attained glass compositionsare reported in Table I. Ten grams of each resulting glasscomposition was mixed with 5 wt% Cr2O3, finely groundedand melted at 12001C for 5 min in a platinum crucible. Theprocess was performed three times to ensure a regular distri-bution of the Cr2O3 grains in the glass network. A mixedCr2O3-glass quantity (100 mg) was taken from the mixture,put in a carbon crucible, heated at 12001C for 1 min andremoved from the furnace to be quenched in air. Because ofthe poor wetability between the melt and the carbon crucible,the sample forms a glass ball.

The Cr2O3 solubility limit in the investigated melts was per-formed using the reactor described in our previous works.1,31,34

It allows the independent control of oxygen fugacity, tempera-ture and alkali volatilization in the silicate melt. The cell is con-stituted by a sealed silica tube of around 25–30 cm3 (Øext5 22mm, h�120 mm) containing several components that imposethe thermochemical parameters of the system. The Na2O partialvapor pressure is imposed by around 5 g of Na2O–CaO-xSiO2

Fig. 2. Variation of Cr (at.%) content as function of log fO2: (~)Na2O–CaO–3SiO2 12001C, (m) Na2O–CaO–3SiO2 12501C, (�) Na2O–CaO–7SiO2 12501C.

Fig. 3. Logarithmic plot of: (~) log[Cr(II)/Cr(III]) and (m) log[Cr(VI)/Cr(III]) as a function of logfO2 for Na2O–CaO–3SiO2 melt compositionat 12501C:

logCrðIIÞCrðIIIÞ

� ¼ �0:248 log f O2 � 2:773 ðR2 ¼ 0:994Þ

logCrðVIÞCrðIIIÞ

� ¼ 0:747 log f O2 þ 1:139 ðR2 ¼ 0:998Þ

Fig. 4. Variation of log[Cr(II)/Cr(III)] (A) and log[Cr(VI)/Cr(III)] (B) vs log(fO2) for three compositions of glass of system Na2O–CaO–xSiO2 (notedNCxS), T5 12501C.

May 2010 Solubility of Cr2O3 and Speciation of Chromium in Soda–Lime–Silicate Melts 1349

source melt (with 1oxo7) and located in a platinum crucible(Øext5 18 mm, h5 20 mm), shut by a platinum lid. The studiedglass balls (samples) are suspended in the reactor from the lid.The Pt crucible hosting the source and the sample constitutethe reactor of the cell. The oxygen fugacity in the device iscontrolled by a solid M/MxOy buffer (M 5metallic element;Fe/FeO, FeO/Fe3O4, Co/CoO, Ni/NiO, and Fe3O4/Fe2O3)incorporated below the reference reservoir either at the bot-tom of the silica tube or in an alumina crucible in order toprevent reactions with the silica tube and to avoid alloyingbetween the solid buffer and the platinum crucible. The silicatube is then evacuated and directly sealed under secondaryvacuum. Direct measurements show that the residual pres-sures inside the thermochemical cell never exceed Ptotal o10�6 bar at room temperature.

When prepared, the silica tubes are introduced in a mufflefurnace directly at the experimental temperature on an aluminasupport for a vertical maintain of the cell. After the heat treat-ment, the silica tubes are removed from the furnace and directlyquenched into cold water. The presence of both metal and oxidephases in the solid buffer after each run is systematically checkedby optical microscopy observation and X-ray diffraction.

Determinations of the total amount of dissolved chromiumand of the final glass composition were performed using aCameca SX100 Electron Microprobe (Gennevilliers, France).The analyses conditions were normalized to an accelerationvoltage of 25 kV and a 6 nA beam current. The electron beamwas defocalized to a 15 mm diameter, to perform the analysisin a relatively large volume of the material, and to limit Navolatilization.

III. Results and Discussions

To understand the effect of the partial substitution of alkalineoxide (Na2O) by the oxide (CaO) on the chromia solubility, thisone will be studied in the Na2O–CaO–xSiO2 system (notedNCS) for the three following melt compositions: x5 3, 4, and7, as a function of temperature and oxygen fugacity. The liq-

uidus temperatures in the NCS system are higher than in theNa2O–SiO2 system; therefore, the selected temperature range laybetween 12001 and 13001C.

Figure 2 shows three characteristic curves of chromium oxidesolubility in the NCS system. These three curves show the vari-ation of the dissolved total chromium content with the oxygenfugacity, and illustrate the influence of the three experimentalparameters: oxygen fugacity, temperature, and liquid composi-tion. The obtained results show that:

(1) Regardless of oxygen fugacity, chromium oxide solubil-ity increases with the temperature for a given liquid composition.

(2) Under oxidizing atmosphere, the solubility increaseswith the basicity (alkaline oxide content) of the glass.

(3) Under a reducing atmosphere, the solubility decreaseswhen the basicity increases.

(4) Independently of the temperature or composition of theglass, the general shapes of the curves remain unchanged. Theyalways comprise three distinct fields of solubility which arecharacteristic of the presence of the three chromium valences:Cr(II), Cr(III), and Cr(VI).

The model developed in our previous works1,31 was appliedto the experimental results obtained for the NCS system to de-termine the speciation of the chromium species as well as theredox parameters in the ternary system. When equilibrium isreached, the total chromium dissolved in the glass (Cr(tot)) is thesum of all chromium species:

CrðtotÞ ¼ CrðIIÞ þ CrðIIIÞ þ CrðVIÞ (16)

Using the same assumption as in the Na2O–SiO2 system, weconsider that the Cr(III) content in the melt remains constant asa function of ( fO2) for a given temperature.1,25 The minimum ofchromium content in the glass corresponds to the Cr(III) con-tribution. Therefore, under oxidizing conditions, Cr(II) contentcan be neglected compared with Cr(III) and Cr(VI). In the sameway, under reducing conditions, Cr(VI) can be neglected com-pared with Cr(III) and Cr(II). With these considerations, it canbe written:

Under oxidizing conditions

CrðtotÞ ¼ CrðIIIÞ þ CrðVIÞ (17)

Fig. 5. Variation of log[Cr(II)/Cr(III)] (A) and log[Cr(VI)/C (III)] (B) vs log(fO2) for Na2O–CaO–3SiO2 at three different temperatures (12001, 12501,and 13001C).

Table II. Log[aNa2O] Values in NCS and Na2O–SiO2

Systems Measured at T5 12501C

Na2O–SiO2 system49 Na2O–CaO–SiO2 (NCS) system45

Composition Log[aNa2O] Composition Log[aNa2O]

Na2O–1.5SiO2 �7.66 Na2O–CaO–3SiO2 �8.78Na2O–2SiO2 �8.24 Na2O–CaO–4SiO2 �9.69Na2O–2.5SiO2 �8.77 Na2O–CaO–7SiO2 �10.28Na2O–3SiO2 �9.35Na2O–3.5SiO2 �9.62Na2O–4SiO2 �9.43

Table III. Optical Basicity Values Calculated for theBinary End Ternary Systems According to Duffy and

Ingram Model 51–53

x (Na2O–xSiO2) 1.5 2 2.5 3

Optical basicity 0.748 0.703 0.663 0.648x (NC–xS) 3 4 7Optical basicity 0.718 0.678 0.612


Under reducing conditions

CrðtotÞ ¼ CrðIIÞ þ CrðIIIÞ (18)

Using this formalism, log(Cr(II)/Cr(III)) and log(Cr(VI)/Cr(III)) were plotted as a function of log( fO2) for the Na2O–CaO–3SiO2 system and reported on Fig. 3. The obtained resultsshow clearly that the two parameters are linearly dependent.The slope values obtained under reducing and oxidizing condi-tions are, respectively, �0.24 and 0.74. These are in good agree-ment with the theoretical values of the expected slopes (Eqs. (14)and (15)).

Variations of log(Cr(II)/Cr(III)) and log(Cr(VI)/Cr(III)) arereported as a function of log(fO2) at T5 12501C for three dif-ferent glass compositions (NC3S, NC4S, and NC7S) in Fig. 4.The results show that log(Cr(II)/Cr(III)) decreases with increas-ing basicity of the melt (Fig. 4(A)), although this variation isweak. On the contrary, log(Cr(VI)/Cr(III)) increases with in-creasing melt basicity. Therefore, an increase in the basicity ofthe glass (alkaline oxides content) leads to stabilize the oxidizedforms. This behavior is identical to that described in the Na2O–SiO2 system.1 These results are consistent with those obtainedby other authors for various systems and various multivalentelements.2,35,36

The influence of the temperature on the redox parameters wasstudied for the NC3S liquid composition. Values of log(Cr(II)/Cr(III)) and log(Cr(VI)/Cr(III)) are plotted as a function oflog( fO2) in Fig. 5 for three different temperatures (12001, 12501,and 13001C). The results reveal that whatever the imposed ox-ygen fugacity is, the redox ratio increases with increasing melttemperature. This same behavior was also observed in theNa2O–SiO2 system

1 and in several studies treating of the solu-bility of the multivalent species in silicate melts.20,37,38

The treatment of the whole set of data should lead to the de-termination of formulas for chromium complexes formed in theNCS system, as well as the thermodynamic properties related todissolution, oxidation, and reduction processes of chromia.However, the determination of these properties cannot be real-ized without knowing the values of the aO2� in the given liquid.This parameter is essential for a complete and consistent exploi-tation of the results. The following development permits a de-termination of the activity of the oxide ions aO2�.

In glass networks, the aO2� was introduced as a basicity in-dicator.39,40 Nevertheless, no standard state can be defined forthis ion. Moreover, this basicity depends on the bond strengthbetween the alkali and oxygen ion. When the size of the alkaliion increases, the bond strength decreases. As a consequence themobility of the oxide ions is higher.5,41 Furthermore, it is gen-erally agreed, in binary melts, to equate the activity of the oxideions (aO2�) to the activity of the sodium oxide (aNa2O).

In the case of binary melts (Na2O–SiO2 in this study), aO2� isequated to the Na2O activity.42–44 In the case of ternary glasses,the situation is more complex. One of the key points is toestablish where aO2� can still be equated to Na2O activity whenadding another modifying oxide (CaO) to the Na2O–SiO2 net-work. In this case, there is competition between the two basicspecies Na2O and CaO. From this, two assumptions can beproposed.

(i) If Na2O is much more basic than CaO, the aO2� could beequated to the Na2O activity. Then the contribution ofcalcium oxide on the acid–base properties can be neglected.Several studies have determined the Na2O activity in binaryNa2O–xSiO2 and ternary NCS system.45–50 The values appliedin this work are those measured by Neudorf and Elliott49

and Abdelouhab et al.45 (Table II). In this case, basicity isgiven by the value of log[aNa2O]. By comparing the two seriesof data, aNa2O values in NC3S and NC4S are the same as inthe Na2O–2.5SiO2 and Na2O–3.5SiO2 melts, respectively(Table II). Thus, these glasses have equivalent basicities. How-ever, the NC7S composition does not have an equivalent in thebinary melt.

(ii) If Na2O and CaO basicities are close, aO2� cannot beequated to the aNa2O. Initially, we propose, in the binary sys-tem, to equate the O2� activity (aO2�5 aNa2O in binary sys-tem) to the calculated optical basicity. Optical basicity values(Table III) were calculated according to the Duffy and Ingrammodel.51–53 The dependance of log[aO2�] at T5 12501C on theoptical basicity is plotted in Fig. 6.

For comparison, the optical basicity values of the ternarymelts (Table III) are reported in Fig. 6. This interpolation high-lights that O2� activities in ternary Na2O–CaO–x (3 and 4) SiO2

glasses are comparable to O2� activities in binary Na2O- � (1.7and 2.15) SiO2 glasses, respectively.

The oxide ions activities aO2� obtained from the optical basi-cities interpolation are inconsistent with the Na2O activitiesmeasured by Abdelouhad et al.45 (Table II). To validate oneof these two assumptions, we compare results concerning chro-

Fig. 6. Log a(O2)� in binary melts at 12501C as a function of calculatedoptical basicity. Dotted lines correspond to the extrapolation of a(O2�)in ternary melts from their optical basicity values.

Fig. 7. Log[Cr(VI)/Cr(III)] as a function of log( fO2) at T5 12501C, inthe ternary Na2O–CaO–3SiO2 composition compared with differentcompositions of binary glasses.

Fig. 8. Log[Cr(VI)/Cr(III)] as a function of log( fO2) at T512501C, inthe ternary Na2O–CaO–4SiO2 composition compared with differentcompositions of binary glasses.


mia solubility in the two vitreous systems Na2O–SiO231 and

NCS. According to the equations Eqs. (13), (14), and (15), redoxratios are expressed as a function of oxygen fugacity and O2�

activity. In these equations, for a given temperature and oxygenfugacity, only aO2� has an effect on redox parameters. Thismeans that for a given temperature and oxygen fugacity,the redox ratios should be the same for two glasses with thesame aO2�.

The comparison of log(Cr(VI)/Cr(III)) vs log(fO2) of the ter-nary glass NC3S with the redox ratio of various binary sys-tems31 is plotted in Fig. 7. This plot clearly shows that for givenfO2 and temperature, the redox ratio obtained in the ternaryglass NC3S is closest to the characteristic redox ratio of N2.5S.In accordance with Eq. (6), it can thus be assumed that thebasicities (i.e. O2� activity) of NC3S and N2.5S are equivalent.In the same way, Fig. 8 exhibits that the NC4S ternary glasspresents a basicity, which is close to the basicity of N3.5S andN3S binary glasses. It although seems to be a bit closer to thebasicity of N3.5S glass. Regarding the results reported on TableIV, it can be considered that aNa2O5 aO2�.

The determination of O2� activities permit the characteriza-tion of the physicochemical properties of chromium in the NCSsystem:

(1) the identification of chromium complexes formed inNCS system,

(2) the determination of the thermodynamic properties fordissolution, oxidation, and reduction of the chromiumspecies in NCS melts, according to the physico-chemicalmodel suggested by our previous works.1,31

Determination of the chromium complexes formed in NCSsystems at 12501C was achieved by plotting the logarithms of(Cr(III), Cr(II)/Cr(III), and Cr(VI)/Cr(III)) as a function of O2�

activities in the system (Fig. 9). According to Eqs. (13), (14), and(15), the slopes of the straight lines are directly correlated to the(x–3/2), (x–y13/2), and (z–x11/2) parameters for a given tem-perature and f(O2).

Results concerning log[Cr(III)] and log[Cr(II)/Cr(III)] varia-tions, as a function aO2�, cannot be directly exploited to calcu-

late the x, y, and z parameters necessary for the identification ofthe formulas for the chromium complexes. Indeed, the variationof log[Cr(III)] as well as log[Cr(II)/Cr(III)] present a very lowvariation with aO2�. This makes impossible the determinationof the (3/2–x) and (z–x11/2) parameters. Nevertheless, resultsconcerning log[Cr(VI)/Cr(III)] can be exploited. The slope of theobtained straight line is equal to 0.514 (R25 0.99). This allows acalculation of the (x–y) value which is equal to 2. Some of themost stable Cr(VI) formulas are dichromate or chromate,36

(Cr2O7)2� or (CrO4)

2�, respectively. Considering these two pos-sible Cr(VI) formulas, Cr(III) formulas would be Cr2O3 or(CrO2)

�. However, the Cr2O3 formula for the Cr(III) complexcannot be considered: we assume that the Cr2O3 species is a solidprecipitate in the melt.

At this stage, it is only possible to formulate assumptionsconcerning the nature of the chromium complexes formed in theNa2O–CaO–SiO2 system. The whole of the experimental datarelated to this system must be supplemented by complementarysolubility measurements, covering a broader range of glass com-positions.

The thermochemical model, developed in previous works,1,31

is based on the knowledge of the nature of the Cr(II), Cr(III),and Cr(VI) complexes through the determination of the valuesof the x, y, and z parameters. As these latter parameters havenot been obtained for this system, only an approximate calcu-lation of the thermodynamic properties can be proposed. Thedevelopment consists in simplified equations which do not takeinto account the nature of the chromium complexes37,54:

1

2Cr2O3 ,

KTdiss

Cr3þ þ 3

2O2� (19)

Table IV. Log[aO2�] as Well as the Composition of the Binary Equivalent With the Ternary Na2O–CaO–xSiO2

for Each Studied Case

Melt composition Na2O–CaO–3SiO2 Na2O–CaO–4SiO2 Na2O–CaO–7SiO2

aNa2O Log[aNa2O] �8.75 �9.66 �10.42Equivalent binary system Na2O–2.5SiO2 Na2O—3.3SiO2 –

aO2 Log[aO2�] �7.97 �8.60 �10.24Equivalent binary system Na2O–1.7SiO2 Na2O–2.2SiO2 Na2O–4SiO2

Fig. 9. Variation as a function of log[a(O2�)] at T5 12501C of:(~) log[Cr(III)]5 –0.03log[a(Na2O)]�0.89 (R2 5 0.95), (m) log[Cr(II)/Cr(III)]5�0.07log[a(Na2O)]�0.92 (R25 0.95). (J) log[Cr(VI)/Cr(III)]5 0.5 log[a(Na2O)]14.86 (R2 50.99).

Fig. 10. Representation of log(K0Tdiss), log(K0Tred), and log(K0Tox) as a

function of (1/T) for glass NC3S:

ð~Þ logK 0Tdiss ¼ 1:381� 1724

TðR2 ¼ 0:980Þ

ð}Þ logK 0Tred ¼ 3:138� 8989

TðR2 ¼ 0:934Þ

ð}Þ logK 0Tox ¼ 2:828� 2619

TðR2 ¼ 0:973Þ


Cr3þ þ 1

2O2� ,

KTred

Cr2þ þ 1

4O2 (20)

Cr3þ þ 3

4O2 ,

KTox

Cr6þ þ 3

2O2� (21)

The related equilibrium constants are written as follows:

KTdiss ¼ aCr3þðaO2�Þ3=2 (22)

KTred ¼aCr2þ

aCr3þðaO2�Þ1=2ð f O2Þ1=4 (23)

KTox ¼aCr6þ

aCr3þð f O2Þ3=4ðaO2�Þ3=2 (24)

As mentioned previously, the O2� activity is related to theglass composition. The concentration of the multivalent elementis considered to be relatively low compared with the concentra-tion of the free oxygen ions, so that for a given temperature andglass composition, O2� activity is not affected during a redoxreaction and remains constant.10,11 It is thus advantageous todefine equilibrium constants KT

0 freed from the O2� activityterm as follows:

K 0Tdiss ¼ aCr3þ (25)

K 0Tred ¼aCr2þ

aCr3þð f O2Þ1=4 (26)

K 0Tox ¼aCr6þ

aCr3þð f O2Þ3=4(27)

with

K 0Tdiss ¼KTdiss

ðaO2�Þ3=2(28)

K 0Tred ¼ KTredðaO2�Þ1=2 (29)

K 0Tred ¼KTred

ðaO2�Þ3=2(30)

Logarithmic equations for the three constants can be pro-posed where the activity a(Crn1) has been replaced by the con-centration [Crn1]

log½Cr3þ� ¼ logK 0Tdiss (31)

log½Cr2þ�½Cr3þ�

¼ � 1

4log f O2 þ logK 0Tred (32)

logCr6þ� �Cr3þ� � ¼ 3

4log f O2 þ logK 0Tox (33)

The y-axis intercept obtained by plotting log[Cr(II)/Cr(III)]and log[Cr(VI)/Cr(III)] vs logfO2 for the different temperatures

(Figs. 5 (A) and (B)), correspond to logK0Tred and logK0Tox val-ues, respectively (Eqs. (29) and (30)). Values of logK0Tdiss areexactly equal to the log[Cr(III)] values. These three sets of dataare reported on Fig. 10 as a function of (1/T). The results showthat logK0T is linearly correlated to (1/T), according to thefollowing expression:

logK ¼ aþ bT

(34)

The slopes and the y-axis intercepts of each straight line arerelated to the standard enthalpies and entropies for each reac-tion, in accordance with the following equation:

logK ¼ �DH0

2:3R

1

T

� �þ DS0

2:3R(35)

By identification, the general formula expressing the standardentropies DS0 and standard enthalpies DH0 of the reactions canbe written as:

DS 0 ¼ 2:3Ra (36)

DH0diss ¼ �2:3Rb (37)

The values concerning the standard enthalpies and entropiesof dissolution, oxidation, and reduction of the chromia in NC3Sglass system are given in Table V.

IV. Conclusion

Several important points of the chemistry of chromium in thesilicate melts have been highlighted in this study:

(1) The model previously developed for binary Na2O–xSiO2

1,31 has been successfully applied to the ternary Na2O–CaO–xSiO2 system.

(2) The solubility of Cr2O3 has been determined as functionof temperature, glass composition, and oxygen fugacity.

(3) Cr2O3 is dissolved as Cr(II), Cr(III), and Cr(VI) species.The speciation of chromium ions has been determined as afunction of oxygen fugacity and glass composition. The log[Cr(II)/Cr(III)] and log[Cr(VI)/Cr(III)] ratios vary with –1/4log( fO2) and 3/4 log( fO2), respectively, independently of themelt composition and temperature.

(4) The (DH1diss, DS1diss), (DH1red, DS1red), and (DH1ox,DS1ox) have been estimated for Cr(III) - Cr(VI), and Cr(III)- Cr(II) redox reactions.

Acknowledgments

The authors are grateful to J. Ravaux and S. Mathieu for performing EPMA(Service Commun d’Analyses par Microsonde Electronique de Nancy).

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Documents

Solubility of Cr2O3 and Speciation of Chromium in Soda–Lime–Silicate Melts