Oxidation state of iron in silicate glasses and melts: a thermochemical model

Chemical Geology 174 Ž2001. 157–179 www.elsevier.comrlocaterchemgeo

Oxidation state of iron in silicate glasses and melts: a thermochemical model Giulio Ottonello a,) , Roberto Moretti b, Luigi Marini a , Marino Vetuschi Zuccolini a a

Permanent Earth Sciences Technical ObserÕatory, c r o DIPTERIS UniÕersita` di GenoÕa, Corso Europa 26, 16132 GenoÕa, Italy b Dipartimento di Scienze della Terra, UniÕersita` di Pisa, Via S. Maria 53, 56123 Pisa, Italy Accepted 9 February 2000

Abstract The acid and base dissociation constants of FeO and Fe 2 O 3 components in silicate melts are defined in terms of observed relationships between atomistic properties of dissolved oxides Žnephelauxetic parameters, electronegativity, fractional ionic character of the bond. and polymerization constants in simple systems. These constants are obtained from the Toop–Samis model depicting the Gibbs free energy of mixing of binary MO–SiO 2 melts, which is coupled with the amphoteric treatment of altervalent dissolved oxides. Model parameterization is carried out on the basis of the extended set of data concerning thermodynamic activity of FeO in melts buffered by equilibrium with pure iron metal and a gaseous phase and on the various measurements of bulk redox state of iron in chemically complex melts at various T, f O 2 conditions. Dissociation . without any constants are related to thermodynamic parameters of the main dissolved species ŽO 2y, Fe 2q, Fe 3q, FeOy 2 significant error progression. As an ancillary result, thermochemical calculations allow to quantify to some extent the spectroscopy on quenched melts systematic errors in the Fe IIrFe III bulk redox ratio arising from the utilization of Mossbauer ¨ and glasses. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Melts; Glasses; Iron redox; Polymer model; Mossbauer ¨

1. Redox state, oxide reactivity and melt structure: introductory remarks The characteristic process of acid–base reactions in oxide systems is Athe transfer of an oxygen ion

from a state of polarization to anotherB ŽFlood and Forland, 1947.. This concept is particularly impor¨ tant in silicate melts and glasses where the polymerization reactions governing the size and distribution of polymeric units in the polyanion matrix may be considered as simple acid–base reactions involving three distinct polarization states of oxygen, i.e., in the Fincham–Richardson notation:

)

Corresponding author. Tel.: q39-10-3538136; fax: q39-10352169.

2Oym O 0 q O 2y

0009-2541r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 5 4 1 Ž 0 0 . 0 0 3 1 4 - 4

Ž 1.

158

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Although the Lux–Flood formulation formally difŽproton-based. exfers from a Bronsted–Lowry ¨ change, the two formulations are mutually consistent ŽFlood and Forland, 1947. and, with this proviso, the ¨ link between redox and acid–base exchanges is represented by the Anormal oxygen electrodeB equilibrium: 1 2

O 2 q 2eym O 2y

Ž 2.

It is well established that the Lux–Flood acid–base property of dissolved oxides markedly affects the extent of polymerization reaction by producing or consuming free oxygen ions ŽO 2y ., i.e., for a generic oxide MO ŽFraser, 1975a,b, 1977.: MO q O 2ym MO 22y

Ž 3-a .

MO m M 2qq O 2y

Ž 3-b.

Eqs. Ž3-a. and Ž3-b. being acidic and basic behavior, respectively. Although it is easy to envisage a direct relationship between the polymerization constant Ž K 1 . of reaction Ž1. and basicity of dissolved oxides in binary systems ŽToop and Samis, 1962a,b. the extension to multicomponent melts and glasses is not as immediate. Moreover, in the presence of altervalent elements such as Fe, the normal oxygen electrode reaction Ž2. and the dissociation equilibria ŽEqs. Ž3-a. and Ž3-b.. are coupled. The thermochemical implications of this coupling may be conveniently addressed by taking into account both the polymeric nature of the anion matrix, along the guidelines of the Toop–Samis model, and the Fraser’s amphotheric treatment of dissolved oxides. Although this study is devoted mainly to the comprehension of iron reactivity in melts and glasses and not to establish heuristic properties, the model here developed is of some help in deciphering conflicting experimental observations and systematic biases concerning the redox state of iron in chemically complex glasses and melts. As an ancillary result, the model has the property of predicting the equilibrium oxygen fugacity of a melt with virtually the same accuracy of well known empirical methods. Moreover, the observed

ferrous oxide content in melts of different composition equilibrated with a metallic phase is also reproduced with sufficient accuracy, regardless of the chemical composition of the investigated system, a fact of some interest in mantle–core equilibrium studies.

2. Thermodynamic model In a chemically complex melt or glass, the capability of transferring fractional electronic charges from the ligands to the central cation depends in a complex fashion on the melt or glass structure, which affects the polarization state of the ligand itself. Nevertheless, the mean polarization state of the various ligands Žmainly the oxide ions Oy and O 2y in natural silicate melts. and their ability to transfer fractional electronic charges to the central cation are conveniently represented by the Aoptical basicityB of the medium, i.e. the ratio hrh ) where h is the Jørgensen’s Ž1962. function of the ligand in the polarization state of interest and h ) is the same function relative to the ligand in an unpolarised state Žmainly free O 2y ions in an oxidic medium; Duffy and Ingram, 1971.:

Ls

1yb

h s h

)

s 1yb

)

n free y nglass n free y n )

Ž 4.

with n free s1 S 0 ™3 P1 absorption band of the free p-block cation; nglass s1 S 0 ™3 P1 absorption band measured in the glass; n ) s1 S 0 ™3 P1 absorption band in a free O 2y medium. The reciprocal of optical basicity L of a cation Ži.e. the Abasicity moderating parameterB g of Duffy and Ingram, 1973. represents the tendency of an oxide forming metal M to reduce the localized donor properties of oxide ions, and is related to the optical basicity of the medium by:

gMs

ZM = r M < ZO < = L MO

Ž 5.

where Z M s formal oxidation number of cation in MO; ZO s formal oxidation number of oxide ion in

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

MO; r M s stoichiometric ratio between number of cations and number of total oxide ions in the medium. Although g M reduces to Ly1 MO in a simple single oxide medium, it has the property to describe the Jorgensen’s h function in complex systems according to ŽDuffy and Ingram, 1976.:

h s h) 1 y

y

ZA = rA < ZO <

ZB = r B < ZO <

ž

1y

ž

1y 1

gB

/

1

gA

/

y...

with A, B, . . . oxide forming cations.

Ž 6.

159

Optical basicity of simple oxides appears to be related to atomistic properties of the intervening cations, such as the Pauling and Sanderson’s electronegativities ŽPauling, 1932, 1960, 1980; Sanderson, 1967; Duffy and Ingram, 1974a,b. or the free ion polarizability ŽYoung et al., 1992.. Some details on the nature of these relations are given in Appendix A. Discrete values of L and g for the various metals of interest in this study are listed in Table A1. It is of interest now to establish a formal link between the basicity moderating parameter of the dissolved oxides and the extent of the polymerization reaction Ž1.. As shown by Toop and Samis Ž1962a,b., the three forms of oxygen present in the melt Ži.e. O 2y,Oy and O 0 . are related to melt stoichiometry

Fig. 1. Gibbs free energy of mixing in MO–SiO 2 melts according to different experimental sources. Fincham–Richardson anionic mixing curves have been superimposed for comparative purposes Žsolid lines.. Numerals refer to the value of ln K 1 adopted in calculations ŽEq. 10..

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

160

and to the constant of the polymerization reaction Ž K 1 . by the following mass balance equations:

ŽO0 . s

4 NSiO 2 y Ž Oy .

Ž 7.

2

2y

Ž O . s Ž 1 y NSiO 2 . y y 2

quadratic Eq. Ž9. for different values of the polymerization constant K 1 , showed that the Fincham– Richardson assumption of a purely anionic contribution to the Gibbs free energy of mixing in a binary melt MO–SiO 2 Žwith MO completely dissociated basic oxide. holds true:

Ž Oy .

Ž 8.

2

DGmixing ' Gmixing ,anionic s

y

Ž Oy . 2

RT ln K 1

Ž 10 .

Ž O . Ž 4 K 1 y 1 . q Ž O . Ž 2 q 2 NSiO 2 . q 8 NSiO 2Ž NSiO 2 y 1 . s 0

Although Toop and Samis’ deductions were based on few experimental observations Žconcerning notably PbO–SiO 2 and CaO–SiO 2 melts., they still hold after more than three decades of research. The fact that the Toop and Samis model is not able to reproduce the observed solvi at high silica content in

Ž 9.

where NSiO 2 are the moles of SiO 2 and terms in parentheses refer to number of moles per unit mole of melt. Toop and Samis Ž1962a,b., solving the

Table 1 Toop–Samis polymerization constants in MO–SiO 2 melts at various T conditions, as inferred from Gibbs free energy of mixing curves and thermodynamic activity data. Values of the basicity moderating parameter of the network modifier are also listed. Bold values adopted in Fig. 2 MO

g M vq

K1

T Ž8C.

Refs.

Na 2 O

0.87

0.001 0.001

Ž1. Ž3.

K 2O

0.71

0.0005 0.001

Ž1. Ž2,3.

0.0020 0.0017 0.0020 0.0016 0.0021 0.0023

Ž1. Ž4. Ž5,3. Ž7,8. Ž11. Ž12.

CaO

MgO SnO

ZnO

1.00

1.28 2.09 a

1.72 a

0.0073 0.0085 0.318 0.331 0.057 0.06 0.017

; 1600 1500 1600

1100

Ž1. Ž6. Ž1. Ž6.

1300 1560

Ž1. Ž4. Ž6.

1600

MO MnO

CoO

FeO

g M vq 1.69

a

1.96 a

1.96

NiO

2.09 a

PbO

2.09 a

K1 0.049 0.04 0.05 0.174 0.10 0.141 0.174 0.050 0.17 0.188 0.10 0.18 0.318 0.35 0.1237 0.002–0.01 0.04 0.032 0.138

T Ž8C.

Refs.

1600

Ž1. Ž5,3. Ž6.

1450

Ž1. Ž5,3. Ž6.

1600 1600 1325 1960

1100 1000 727

Ž1. Ž5,3. Ž4. Ž6. Ž9. Ž10. Ž1. Ž5,3. Ž1. Ž3. Ž4. Ž6. Ž7.

Ž1. estimated via Eq. Ž29-II.; Ž2. Charles Ž1969.; Ž3. Hess Ž1971.; Ž4. Toop and Samis Ž1962a,b.; Ž5. Masson Ž1965, 1968.; Ž6. Reyes and Gaskell Ž1983.; Ž7. Navrotsky Ž1994.; Ž8. Masson et al. Ž1970.; Ž9. based on activity data of Schumann and Ensio Ž1951.; Ž10. based on activity data of Distin et al. Ž1971.; Ž11. based on activity data of Carter and MacFarlane Ž1957. and Sharma and Richardson Ž1962.; Ž12. based on activity data of Zou et al. Ž1982.. a Based on Pauling electronegativity.

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

simple systems implies the existence of additional excess Gibbs free energy of mixing contributions not accounted for by the model itself. As extensively discussed elsewhere ŽOttonello, 2000. and by analogy with recent findings on block copolymer melts ŽBates and Fredrickson, 1990, and references therein., these additional terms may be conceived as mechanical strain energy contributions arising from the relative arrangements of monomeric units in the polymer chains and are much smaller than the chemical interaction terms. The smallness of the contributions to the Gibbs free energy of mixing curves causing the opening of solvi at high silica content may be appreciated from the assessments of Taylor and Dinsdale Ž1990. concerning the CaO–SiO 2 system ŽIRSID cellular model; see particularly their Fig. 5. and of Pelton and Blander Ž1986. for the CaO–FeO–SiO 2 system Žmodified quasichemical model.. Discarding these minor contributions to the bulk Gibbs free energy of mixing, we may infer appropriate values of the polymerization constant K 1 for the various MO– SiO 2 binary systems with Eq. Ž10. and the existing Gibbs free energy of mixing, or measured thermodynamic activities ŽFig. 1, Table 1 and references therein.. Reflecting the reduced donor property of the ligand field, the difference between the basicity moderating parameters of the Anetwork modifierB g M vq and of the Anetwork formerB g Si 4q may be expected to affect the polymerization extent of the anion matrix in a simple fashion. Indeed, as we may see in Fig. 2, a simple exponential relationship links the polymerization reaction constant K 1,MO – SiO 2 in binary MO–SiO 2 melts with g M vq. The correlation coefficient of this relationship Žwhich is based on selected K 1 values among those listed in Table 1. is rather high Ž R 2 s 0.997. although T effects are neglected. Moreover, the slope of the linear relationship Ž4.662. is similar to the coefficient of the inverse relation between optical basicity and bond energies derived in Appendix A.1 Since, according to Eq. Ž6. the Jorgensen’s h function is a generalized additive property, the above

1

Note that the intercept term y1.1445 in Eq. Ž11. would eventually disappear if one adopts for Si 4q a basicity moderating parameter g Si4q s 2.34 instead of the currently accepted values 2.09–2.17.

161

Fig. 2. Relationship between polymerization constant of the Toop–Samis model in MO–SiO 2 melts and basicity moderating parameter of the network former M hq ŽTable 1..

discussed correlation implies that the extent of polymerization of chemically complex melts and glasses may be readily obtained by a simple mass balance involving oxide constituents and their specific g values:

žÝ g /

K 2,melt s exp 4.662 =

X M ivq g M ivq

i

y Ý X T jhq j

T jhq

y 1.1445

Ž 11 .

where X M ivq, g M ivq and X T jhq , g T jhq are respectively atom fraction and basicity moderating parameter of network modifiers and network formers in one mole of the multicomponent melt or slag. Let us now consider in more detail the anionic structure of the melt. In a simple fused-salt approach, such as the Temkin model ŽTemkin, 1945., the activity of a basic molten oxide in a MO–SiO 2 binary join is

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

162

determined by the molar fraction of O 2y ions over the anion matrix: 2

Ý anionss Ž O 2y . q Ý structons a MO s Ž O 2y . r Ž O 2y . q Ý structons

Ž 12 . Ž 13 .

In a multicomponent melt, we must know the acid– base behavior of each dissolved oxide Ži.e. the disproportionation between Anetwork formersB and Anetwork modifiersB .. The activity of MO will be now: a MO s

Ž M 2q .

Ý cations

=

tion of reference is sufficient and may be obtained by non-linear minimization techniques involving compositionally different systems and estimated versus observed Temkin model activity of the dissolved basic oxides Žsee later on.. On the basis of the above outlined considerations, we may now address the problem of reactivity of altervalent oxides on thermochemical basis. We recall that, as noted by Douglas et al. Ž1966., the altervalent equilibria in melts and glasses may be generalized as follows:

Ž O 2y . R Ž n . Oa q

Ž O 2y . q Ý structons

m 4

O2 m R Ž n q m . Ob

Ž 14 . q Ž a yb. q

2y

Since the number of moles of O in the melt is related to K 1 and NSiO 2 by mass balance ŽEqs. Ž7. – Ž9.., the evaluation of a MO rests solely on the estimate of the number of structons present in the anion matrix. Toop and Samis Ž1962a,b. thus proposed a Apolymerization pathB of general validity, based essentially on the viscosity data of Bockris et al. Ž1955. Žcf. Fig. 3 in Toop and Samis, 1962a.. As shown by Ottonello Ž1983., the polymerization path of the Toop–Samis model may be approximated by the simple power function: 1.95 Ý structonss NSi = P²y I:

Ž 15 .

where P²yI: is the proportion of singly bonded oxygen and is given by

Ž Oy . P²yI: s Ž O 0 . q Ž Oy . q NT

Ž 16 .

This parameter accounts for the presence of chargebalanced tetrahedrally coordinated cations other than Si Ž NT s NSi q NAl q NFe III q . . . ; see Ottonello Ž1983., for details.. Alternative formulations of the polymerization trend may be devised and it may be shown that a distinct polymerization trend is found for each system ŽOttonello, 2000.. However, for the purpose of this study, a general polymerization equa-

2

O 2y

Ž 17 .

For iron, setting b s Ž a q mr2. the equilibrium is written in the simple stoichiometric form Ži.e. no oxide ions involved.: FeO q

1 4

O 2 m FeO1.5

Ž 18 .

However, the above equation, written for macroscopic melt components, must be coupled with homogeneous speciation reactions defining the structural state of iron in melts and glasses, which is a complex function of bulk composition and P,T conditions, as shown by experimental evidence. Let us now assume with Fraser Ž1975a,b, 1977. that Fe 2 O 3 behaves as an amphoteric oxide in the Lux–Flood acid–base acception of the term. Its double dissociation in the melt Žor glass. may be expressed by the following homogeneous equilibria: 2y Fe 2 O 3 Žmelt. q OŽmelt. m 2FeOy 2 Žmelt.

Ž 19 .

3q 2y Fe 2 O 3 Žmelt. m 2FeŽmelt. q 3OŽmelt.

Ž 20 .

For ferrous iron, on the other hand, only a basic dissociation is plausible, i.e. 2q 2y q OŽmelt. FeOŽmelt. m FeŽmelt.

2 The anion matrix comprises simple anions, such as O 2y, and all sorts of polyanions, or AstructonsB in Fraser’s therminology ŽFraser, 1975a,b..

m

Ž 21 .

Adopting the Temkin model for ionic salts ŽEq. Ž14.. and assuming the cluster to mix ideally over the anion matrix and the Fe 3q, Fe 2q cations to mix

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

ideally over the cation matrix, the following equation is obtained: Fe II

ž / Fe

III

1 s

K 18 fO1r4 2 =

a1r2 O 2y K 21 Ý cations 1r2 2 1r2 K 19 aO 2y Ý anionsq K 20 Ý cations

Ž 22 . It is similar to Eq. Ž14. in Fraser Ž1975a., although here Ýanions replaces Ýstructons. Eq. Ž22. basically states that, due to disproportionation of trivalent iron between the cation and anion matrixes, we cannot expect the ratio of rational activity coefficients of FeO1.5 and FeO Žsecond term on the right. to be 1. Although apparently complex, Eq. Ž22. may be conveniently solved on thermochemical grounds, based on the plethora of experimental data concerning ferrous iron solubility and iron redox in melts Žandror glasses. equilibrated at known T, f O 2 conditions.

3. Solubility of ferrous iron in silicate melts: experimental evidences The number of experiments dealing with the solubility of ferrous iron in silicate melts is rather impressive and we cannot review all the experimental evidences produced in almost 5 decades of material science and earth science research. It is however of interest to recall that the experimental information covered progressively all degrees of chemical complexity: from the simple binary join FeO–SiO 2 ŽSchumann and Ensio, 1951; Bodsworth, 1959. to ternary FeO–Fe 2 O 3 –SiO 2 melts ŽTurkdogan and Bills, 1957; Turkdogan, 1962., ternary FeO–MO– SiO 2 melts ŽBell et al., 1952; Elliott, 1955; Richardson, 1956, 1958, 1974; Abraham and Richardson, 1961; Kojima and Sano, 1966; Meysson and Rist, 1969; Scimar, 1969., four component ŽTurkdogan and Bills, 1957; Bell, 1961, 1963. and multicomponent systems ŽRoeder, 1974; Doyle, 1983, 1988; Doyle and Naldrett, 1986; Holzheid and Palme, 1996; Holzheid et al., 1997..

163

Most experiments on multicomponent systems are based on the equilibrium between the melt and a metallic phase at known T, f O 2 . Moreover, the f O 2 operating conditions in most experiments are such that the amount of Fe 3q present in the system is negligible within experimental uncertainty. Finally, in the more recent experiments, the solubility of ferrous iron is interpreted in terms of deviations from an ideal macroscopic equivalence between the measured molar fraction of FeO in the system and the thermodynamic activity of FeO, based on the simple equilibrium: Fe metal q

1 2

O 2,gas m FeOmelt

Ž 23 .

Because FeO is a dissociable solute ŽEq. Ž21.., however, the possible nonideality described by the rational activity coefficient associated with equilibrium Ž23. Ži.e. g FeO s a FeO rX FeO . cannot be distinguished from the apparent nonideality arising from the choice of a reference state. In fact, in the absence of a method allowing one to determine the concentration of undissociated salts, it is customary Žand convenient. to adopt a reference state such that: ) a 2y a FeO s a Fe 2q me lt melt O melt

Ž 24 .

which Žcombined with a Temkin’s model activity of ionic constituents. is precisely the reference state implicit in the Toop–Samis model Žcf. Eq. Ž14... Indeed, the Toop–Samis model assumes a completely basic behavior for all the various non-SiO 2 molten components in mixture. The quadratic Eq. Ž9. in Oy allows the calculation of the anionic integral free energy of mixing. It is entirely based on mass and charge balance arguments involving complete dissociation of the MO oxide in a MO–SiO 2 system. The reference state for MO consistent with the Toop–Samis development is thus that one of a completely dissociated oxide in solution in which the ŽTemkin model. activity is one. However, the thermodynamic equilibrium a Fe 2q a 2y me lt O melt a FeO me lt

s K 21

Ž 25 .

demands that the reference state is such that K 21 reduces to one ŽLewis and Randall, 1970; chapter 22.. We may conceive this as an energy gap between

164 Table 2 Thermodynamic parameters adopted or derived in this study: H T0 r ,P r , D H fusion ŽkJrmol.; S T0 r ,P r , D S fusion ŽJrmol K .; V T0r ,P r ŽJrbar.; T r s 298.15 K for crystalline and gaseous components; T r s 1000 K for melt components; P r s 1 bar in all cases Component

Phase

H T0 r ,P r

S T0 r ,P r

V T0r ,P r

T fusion

D H fusion

D S fusion

Fe 2 O 3

hematite

3.0274 Ž1 . –

1895 Ž1 . –

103.47 Ž8 . –

54.601 Ž8 . –

Fe 2 O 3

melt

87.400 Ž1 . 87.446 Ž2 . 248.352 Ž10 . 279.713 Ž11 . 46.226 Ž7 . 207.105 Ž7 . 59.80 Ž1 . 60.75 Ž2 . 57.59 Ž9 . 131.117 Ž10 . 72.971 Ž12 . 85.902 Ž7 . 205.15 Ž1 . 205.04 Ž2 . 160.95 Ž2 . 63.636 Ž7 .

1.2000 Ž1 . – –

1652 Ž1 . 1650 Ž2 . –

22.185 Ž1 . 27.510 Ž2 . –

2478.92 – 2478.92 Ž3 .

54.35 Ž1 . – –

0.444 Ž1 . – –

melt melt crystalline

FeO Fe Fe 2q O2

melt melt melt gas

O O 2y

gas melt

Component

Phase

C P s A q BT q CT y2 q DT 2 q ET y 1r2 q FT 1r2 q GT y 1

3q

Fe 2 O 3

hematite

Fe 2 O 3

melt

Fe 3q FeO y 2 FeO

melt melt crystalline

FeO

melt

Fe Fe 2q O2

liquid melt melt gas

O O 2y

gas melt

13.429 Ž1 . 14.581 Ž2 . –

– – –

– – –

A

B

C

D

E

F

G

y838.61 y1.0957e q 3 98.282 150.624 132.675 240.9 229.0 199.7 191.84 58.655 141.048 67.352 50.802 78.8 78.9 78.94 68.2 46.024 42.371 48.318 29.957 20.874 41.197

y2.3434 0.27267 7.7822e y 2 – 7.3638e y 3 – – – – – – 3.7580e y 3 8.6149e y 3 – – –

– y1.0239e q 8 y1.48532e q 6 – – – – – – – – 3.1570e q 5 y3.30954e q 5 – – –

6.0519e y 4 – – – – – – – – – – – – – – –

– 3.3960e q 4 – – – – – – – – – y3.8167e q 2 – – – –

86.525 – – – – – – – – – – – – – – –

2.7821e q 4 – – – – – – – – – – – – – – –

– – y6.9132e y 4 4.184e y 3 y5.0208e y 5 –

– – 4.9923e q 5 y1.6736e q 5 9.7487e q 4 –

– – – – – –

– – y4.2066e q 2 – – –

– – – – – –

– – – – –

T range

Refs.

298 – 950 950 – 1800 298 – 953 953 – 1053 1053 – 1730 – – – – 1000 – 2000 1000 – 2000 298 – 1652 298 – 1650 – – – 1650 – 3678 1809 – 3135 1000 – 2000 298 – 1800 298 – 3000 298 – 2000 1000 – 2000

Ž1 . Ž1 . Ž2 . Ž2 . Ž2 . Ž4 . Ž5 . Ž6 . Ž8 . Ž7 . Ž7 . Ž1 . Ž2 . Ž4 . Ž5 . Ž6 . Ž1,2 . Ž2. Ž7 . Ž1 . Ž2 . Ž2 . Ž7 .

Ž1 . Robie et al. Ž1978 .; Ž2 . Barin and Knacke Ž1973 ., Barin et al. Ž1977 .; Ž3 . ideal gas, assumed; this work; Ž4 . Lange and Navrotsky Ž1992 .; Ž5 . Stebbins et al. Ž1984 .; Ž6 . Richet and Bottinga Ž1985 .; Ž7 . estimated; this work; Ž8 . Ghiorso et al. Ž1983 .; Ž9 . Fei and Saxena Ž1986 .; Ž10 . estimated from data of Ž1 . and extrapolated Cp melt of Ž4 .; Ž11 . estimated from data of Ž1 . and extrapolated Cp melt of Ž9 .; Ž12 . estimated from data of Ž2 . and extrapolated Cp melt of Ž2 ..

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Fe FeO y 2 FeO

y824.640 Ž1 . y825.503 Ž2 . y702.373 Ž10 . y658.464 Ž11 . y45.735 Ž7 . y407.782 Ž7 . y272.043 Ž1 . y272.044 Ž2 . y267.270 Ž9 . y222.067 Ž10 . 35.702 Ž12 . y17.000 Ž7 . – – 249.17 Ž2 . y177.468 Ž7 .

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

the standard state of completely dissociated ŽTemkin model. oxide component FeO ) , for which:

m FeO ,melt s m )FeO ,melt q RT ln Ž aFe 2qP aO 2y . ,

Ž 26 .

and the true molten oxide component, for which

m FeO ,melt s m0FeO ,melt q RT ln aFeO ,melt

Ž 27 .

We have thus exp

ž

m )FeO ,melt y m0FeO ,melt RT

/

s

aFeO ,melt aFe 2qP aO 2y

s Ky1 24

Ž 28 . Eq. Ž28. is the only key on which solubility experiments based on the simple macroscopic notation ŽEq. Ž23.. may be compared with a detailed solubility model involving ionic fractions on structural sites. Indeed, as already noted by the Fraser Ž1977., in the absence of a correct evaluation of the various equilibria of the type ŽEq. Ž21.. for the various oxides present in the melt, a direct comparison of their model activities is meaningless Žcf. Fig. 12 in Fraser, 1977.. Before comparing the various experimental sources, moreover, major readjustments must be also introduced in terms of computed FeO activities. In fact, the standard reference state of the involved reactants and products are not identical in all cases, and the sources of the adopted thermodynamic data are also different. For example Roeder Ž1974. and Doyle Ž1988. adopt for FeO the standard state of ŽFe 0.947 O; Coughlin, 1954.. Doyle molten wustite ¨ and Naldrett Ž1986., on the other hand, prefer to use the thermodynamic data of Stull and Prophet Ž1971. for stoichiometric liquid FeO. Holzheid et al. Ž1997. adopt again molten wustite as reference state, with ¨ the thermodynamic data of Barin Ž1989.. However, adopting molten wustite as reference state of the ¨ dissolved ferrous iron component in the silicate melts implies that the stoichiometry of reactants cannot be that one of the macroscopic equilibrium ŽEq. Ž23... All these different approaches would introduce serious biases, if not accounted for, when comparative estimates are made on the basis of a unifying thermochemical model. Finally, the isobaric heat capacity of liquid FeO Ž68.2 Jrmol= K according to Robie et al., 1978 and Barin et al., 1977. is sensibly different from the partial molar heat capacity mea-

165

sured for FeO in silicate melts Ž78.8–78.94 JrŽmol = K., see Table 2 and references therein.. Thus, the enthalpy of solution of FeO crystals in silicate melts is not equal to the enthalpy of fusion at T s Tfusion , P s 1 bar. To derive the thermodynamic properties of FeO Žand Fe 2 O 3 as well, see later on. at reference state conditions, the most reasonable procedure is that one based on the equilibrium of potentials of pure components at the temperature of fusion ŽTf .: Hi0, P r ,T ,melt s Hi0, P r ,T r ,crystal q

Tf

HT C

P ,i ,crystal dT

r

q D Hi ,fusion q

T

HT C

P ,i ,melt dT

Ž 29 .

r

Si0, P r ,T ,melt s Si0, P r ,T r ,crystal q

dT

Tf

HT C

P ,i ,crystal

r

q D Si ,fusion q

dT

T

HT C

T

P ,i ,melt

r

T

Ž 30 .

Gi0, P ,T ,melt s Hi0, P r T ,melt y TSi0, P r ,T ,melt P

0 i , P ,T ,melt d P

HP V

q

Ž 31 .

r

In the above equations, the heat capacity of FeO melt is the partial molar heat capacity of the FeO component measured in silicate melts Žconstant, and not appreciably affected by composition, on the basis of the existing experimental observations.. Moreover, its range of validity is arbitrarily extrapolated downward to the low-T limit of interest in this study Ž1000 K.. Since we will retrieve experiments which are invariably carried out at 1 bar total pressure, we will disregard the volume integral in Eq. Ž31.. Among the various parameters listed in Table 2, the only relevant discrepancy concerns the estimates of the heat capacity of molten Fe 2 O 3 . This, as noted by Lange and Navrotsky Ž1992., is probably due to the inherent difficulty of accurately characterizing the redox state of iron in conventional drop calorimetry experiments. Therefore, in evaluating the Gibbs free energy change associated to reactions Ž18. and Ž23., we adopted for the Fe 2 O 3 and FeO melt components the heat capacity estimates of Lange and

166

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Navrotsky Ž1992., based on step scanning calorimetry. The adopted thermodynamic data for crystalline Fe 2 O 3 Žhematite., stoichiometric FeO and gaseous oxygen are those of Robie et al. Ž1978.. The reaction constants were regressed against the reciprocal of absolute temperature obtaining the relationships listed in Table 3. Since the thermodynamic constants obtained in literature for equilibrium Ž23. have been regressed by most authors Žwith the notable exception of Holzheid et al., 1997. against the reciprocal of absolute temperature, with a functional form analogous to that one adopted here ŽTable 4., the shift from one reference state to another is straightforward. The FeO solubility data in multicomponent melts ŽRoeder, 1974; Doyle and Naldrett, 1986; Doyle, 1988. have been recast in terms of thermodynamic activity combining Eqs. Ž14. and Ž23. and expressed in terms of polymerization constant factors and FeO basic dissociation constant ŽTable 3.. The decision not to include the data of Holzheid and Palme Ž1996. and Holzheid et al. Ž1997. in the computational database was dictated by the fact that these authors adopted a metal alloy rather than pure Fe metal to buffer the FeO activity in the silicate melt. Inclusion of these data in our database could have induced uncertainties linked with the estimates of iron activity in the metal alloy in equilibrium with the melt and the buffered atmosphere in our calculations. The dataset of Doyle and Naldrett Ž1986. includes compositions close to high-TiO 2 mare basalts. Preliminary attempts to reproduce the activity of the ferrous oxide component in these samples assuming that Ti 4q behaves as a network former gave inconsistent results. Also, several attempts to partition Ti 4q be-

tween cation and anion matrixes, in line with the experimental evidences of Farges et al. Ž1996a,b. and Gan et al. Ž1996. were unsuccessful. The best results were obtained assuming that Ti 4q behaves chiefly as a network modifier in silicate melts, in agreement with the observations of Dickinson and Hess Ž1985. and with more recent findings based on quantum chemistry argumentations applied to glass clusters ŽKowada et al., 1995.. During the minimization step, the basicity moderating parameter of ferrous iron g Fe 2q needed refinement due to the conflicting literature estimates ŽTables 3 and A1.. Treating g Fe 2q as a adjustable variable does not appreciably affect the overall model precision. Nevertheless, the range in the literature values is rather wide and the value refined here is intermediate between those hitherto proposed. Computed versus observed FeO activities are shown in Fig. 3. The standard error on 392 estimates is 0.082, which is a satisfactory result, when compared to the state of art in this sort of measurements and considering that three distinct data sets have been regressed simultaneously. The greatest discrepancies occur in in the high activity set of measurements of Doyle Ž1988. ŽFig. 3., while the data sets of Roeder Ž1974. and Doyle and Naldrett Ž1986. are mutually consistent. Since the error distribution is normal and no significant correlation factors are observed with any chemical variable Žor T or f O 2 . the scatter of points in the dataset of Doyle Ž1988. is difficult to explain. Incidentally, we may note that the assumption of a AconstantB activity coefficient for FeO in silicate melts equilibrated with a metallic phase at temperatures of 1300–16008C postulated by Holzheid et al. Ž1997. on the basis of their own

Table 3 Computed reaction constants. K 18 , K 23 are based on selected thermodynamic data Žsee Table 2 and text.. K 21 is based on equality Ž14. applied to an experimental data set of 392 aFeO values in multicomponent melts equilibrated with a f O 2 buffered atmosphere and Fe metal at various T. K 19 , K 20 , are based on Eq. Ž22. applied to an experimental dataset of 488 iron redox ratios measured in melts equilibrated at a f O 2 buffered atmosphere and various T. Stepwise minimization procedure carried out with the computer package MINUIT ŽJames and Roos, 1977.. Regression statistics are also given. See text and Figs. 3 and 4 for references to experimental data Ž R 2 s 0.9981. Log K 18 s y2.8792 q 6364.8rT Ž R 2 s 0.9875. Log K 23 s y2.7523 q 13189rT ŽÝ x 2 . s 4.82 Log K 21 s 1.1529–1622.4rT n T s 2.8776 = Py1.7165 g Fe 2qs 1.3541 s y, x s 0.082 :y 1² ŽÝ x 2 . s 39.88 Log K 19 s 5.3392–3357.4rT Log K 20 s 1.8285–4100.2rT s y, x s 0.204 R 2 s 0.935 Ý x 2 s ÝŽŽ y y yestim . 2 r< yestim <.

s y, x s

(ŽÝŽ y y y

estim

.2 . rŽ N .

R 2 s ŽÝŽ yˆ linear y y . 2 .rŽÝŽ y y y . 2 . s Žw n Ý xy y Ý xÝ y x 2 .rŽw nÝ x 2 y ŽÝ x . 2 xw nÝ y 2 y ŽÝ y . 2 x.

R 2 s 0.894

Equilibrium

a

b

T-range

Refs.

Source of thermodynamic data

0.947Fe g q1r2O 2,gas m Fe 0.947 O liquid 0.947Fe g q1r2O 2,gas m Fe 0.947 O liquid 0.947Fe g,d,liquid q1r2O 2,gas mFe 0.947 O liquid

y5.380 y5.837 y7.632

27,739.6 28,719.2 31,571

1423–1579 1600 1000–2000

Roedder Ž1974. Doyle Ž1988. this study

Fe g q1r2O 2,gas mFeO liquid 0.947Fe g,d,liquid q1r2O 2,gas mFe 0.947 O liquid Fe a ,g,d,liquid q1r2O 2,gas mFeOmelt-component

y5.922 y5.503 y6.339

29,763.1 27,967 30,375

1600 1000–2000 1000–2000

Doyle and Naldrett Ž1986. Holzheid et al. Ž1997. this study

Fe 0.947 Owuestite qCOgas mFe g qCO 2,gas ¨ FeOme lt-component qCOgas m Fe a ,g,d,liquid qCO 2,gas

y4.966 y3.895

6878.7 3487.1

1538–1638 1000–2000

Bodsworth Ž1959. this study

Fe 0.947 Owuestite qH 2,gas m Fe g qH 2 Ogas ¨ FeOme lt-component qH 2,gas m Fe a ,g,d,liquid qH 2 Ogas

y1.835 y0.4304

2866.8 y210.7

1538–1638 1000–2000

Bodsworth Ž1959. this study

Schumann and Ensio Ž1951., Coughlin Ž1954. Coughlin Ž1954. Barin and Knacke Ž1973., Barin et al. Ž1977., Robie et al. Ž1978., Lange and Navrotsky Ž1992. Stull and Prophet Ž1971. Barin Ž1989. Barin and Knacke Ž1973., Barin et al. Ž1977., Robie et al. Ž1978., Lange and Navrotsky Ž1992. Darken and Gurry Ž1946. Barin and Knacke Ž1973., Barin et al. Ž1977., Robie et al. Ž1978., Lange and Navrotsky Ž1992. Darken and Gurry Ž1946., Natl. Bur. St. Ž1948. Barin and Knacke Ž1973., Barin et al. Ž1977., Robie et al. Ž1978., Lange and Navrotsky Ž1992.

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Table 4 Energetics of gas-melt equilibria according to various sources. Reaction constants regressed according to the functional form ln K s aq br T

167

168

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Fig. 3. Computed vs. observed activity of the ferrous oxide components in melts equilibrated with metallic iron at various T, aO 2 conditions. Regression statistics are given in Table 3.

experiments, although rather rough, has some validity, since the thermochemical calculations developed here predict activity coefficients of FeO that average 1.86 Ž392 compositions, R 2 s 0.96. in a more restricted T range.3

4. Basicity and redox state of iron in glasses and melts: experimental evidences Although the number of experiments dealing with iron redox state in melts and glasses equilibrated at 3 The average activity coefficient postulated by Holzheid et al. Ž1997. is almost identical, within uncertainty, with wustite as ¨ standard state Ž1.70"0.22., but, apparently, much higher with stoichiometric ferrous oxide.

known T, f O 2 conditions is again rather high Žwe limit our collection to about 550 experimental observations. some experimental results are affected by systematic biases, mainly consisting in errors in the analytical determination of ferrous and ferric iron content and errors associated with incomplete equilibrium exchanges with the buffering atmosphere at low T or in hyperacidic systems. Concerning the first class of problems there is nowadays a general consensus Žat least in geochemical literature. on the fact that Mossbauer spec¨ troscopy tends to overestimate the Fe 3q amount in crystals and glasses unless corrections are made for variable absorption efficiencies in the various coordination states. This problem will be treated more extensively later on. Here we simply stress the fact that the Mossbauer data constitute a limited portion ¨

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

of the general iron redox database concerning quenched melts Žroughly 18%.. We further limited the utilization of Mossbauer data to two low-iron ¨ datasets ŽMysen et al., 1984; Dingwell and Brearley, 1988; about 7% of the bulk database. avoiding hyperferruginous samples whose Mossbauer redox esti¨ mates are apparently affected by large biases Žsee later.. A final, and subordinate, class of problems is linked to the complex phenomena taking place at the meltrglass transition zone. It has been shown by Dyar et al. Ž1987. that the coordination state of Fe 2q in glass is affected by the quenching rate, the highest cooling rates yielding the largest tetrahedral Fe 2q values. This is interpreted by Dyar et al. Ž1987. as the result of progressive densifications, which affect the number of nearest neighbors. Glasses at temperatures below the glass transition cannot be thus regarded as structural analogues of melts as far as Fe 2q site partitioning is concerned. In view of these problems, we cannot obtain precise values of the thermodynamic parameters of the reacting species from the experimental database.

169

Moreover, we must avoid overfitting problems which are always present when dealing with chemically complex systems and large databases Žbut especially when deconvolution is carried out on an empirical ground, which is not our case.. Basically, since the thermochemical properties of the melt components FeO and Fe 2 O 3 are known with sufficient accuracy Žsee the preceding discussion., and since the basic dissociation constant K 21 has already been constrained on the basis of the existing measurements of the thermodynamic activity of the ferrous oxide component in multicomponent melts at different T, f O 2 conditions, the problem reduces now to the evaluation of the basic and acidic dissociation constants of ferric oxide Ži.e. K 19 , K 20 . in the T range of interest.

5. Model results The reaction constants K 19 , K 20 were obtained through nonlinear minimization ŽJames and Roos, 1977. carried out on the same functional form

Fig. 4. Iron redox ratio in quenched melts and glasses equilibrated with a f O 2 buffered atmosphere at various T conditions. Observed values Žabscissa axis. are compared with model results. See Table 3 for regression statistics.

170

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

adopted for equilibria Ž18., Ž21. and Ž23. and on the basis of 488 selected data produced in 50 years of investigation on silicate melts and glasses. Calculations were made by equating the experimentally observed redox ratios to the right-hand side of Eq. Ž22., which involves the effects of partitioning of iron between cation and anion matrixes. The calculated thermodynamic constants are listed in Table 3 and regression statistics are also included. Calculated vs. reported Fe II rFe III ratios are shown in Fig. 4. The accuracy of model predictions is surprisingly good in view of the alleged level of uncertainty in the experimental data Žsee the preceding discussion.. The distribution of residuals of Log ŽFe II rFe III . bulk ratios is virtually normal and no significant correlation factors are observed between the residuals and any chemical or physical variable. The comparison of the results of the structural model developed here with estimates based on the empirical equation developed by Kilinc et al. Ž1983. indicates the same level of accuracy Žstandard deviation on 488 estimates s y, x s 0.204. although the independent regression variables here are 4 instead of 8. The virtual identity in the accuracy of the two Žbasically different. procedures suggests that the attained level of accuracy reflects the inherent precision of the experimental database. Model results are thus sufficiently sound to allow estimates of energetics of the molten species Fe 2q, 2y Fe 3q, FeOy . These were obtained from the 2, O calculated equilibrium constants K 19 , K 20 and K 21. We initially assumed the standard electrode potentials of the partial reactions y Fe 2q meltq 2e m Fe metal

Ž 32 .

y Fe 3q meltq 3e m Fe metal

Ž 33 .

to be independent of T and identical to those observed in aqueous solutions at T s 298.15 K Ži.e. y0.474 and y0.059 V, respectively.. Based on the existing thermodynamic data for Fe metal we obtained provisional values of G Fe 2q , G Fe 3q at the various T me lt melt of interest Ž1000–2000 K.. These values, coupled with the Žmodel generated. Gibbs free energies changes involved in the homogeneous reactions Ž20. and Ž21. lead to two distinct estimates of the Gibbs free energy of free oxygen ions GO 2y at each T of me lt interest which did not differ by more than 30 kJrmol

in the worst case. The mean value of GO 2y was then me lt selected as the true one at all T of interest and the provisional values of G Fe 2q , G Fe 3q were readjusted me lt melt to be consistent with the Gibbs free energy changes involved in reactions Ž20. and Ž21., respectively. Values of G FeO y2,melt were then obtained in an analogous fashion from the estimated GO 2y and from the me lt Gibbs free energy change involved in equilibrium Ž19.. From the calculated values of GO 2y , G Fe 2q , me lt melt G Fe 3q and G FeO y2,melt in the T-range of interest Ž1000– me lt

Fig. 5. f O 2 estimates based on thermochemical calculations ŽEq. Ž22.; part a. and on a reworked form of the empirical equation of Sack et al. Ž1980., Kilinc et al. Ž1983. ŽEq. Ž34.; part b.. The dataset is the same one utilized to constrain the dissociation constants of ferric oxide component Žequilibria Ž19. and Ž20...

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

171

Fig. 6. Comparison between f O 2 estimates of the thermochemical model ŽEq. Ž22.. and those of the reworked form of the empirical equation of Sack et al. Ž1980., Kilinc et al. Ž1983. ŽEq. Ž34... The dataset is the same one utilized to constrain the dissociation constants of ferric oxide component Žequilibria Ž19. and Ž20...

0 0 2000 K. STr,Pr , H Tr,Pr and the constant isobaric heat 4 capacity of the melt species were readily derived by the usual thermodynamic relations ŽTable 2.. To check further the internal consistency of the proposed values we performed again the calculations involving Eq. Ž22. expressing now the various constants in terms of molar Gibbs free energies of reactants and products. The standard error on the estimate remained equal to the initial value Ž s y, x s 0.204. indicating that the roundoff effects associated with the functional form initially adopted to constrain the T-dependence of the free energy change involved in the heterogeneous equilibrium Ž18. and the homogeneous speciation reactions Ž19. to Ž21. are unimportant.

4

The choice of a constant isobaric heat capacity for the molten species implies that the intercept term in functional forms of type ln K s aq br T cannot be expected to represent a Žconstant. D S of reaction, or, conversely, if we adopt a constant entropy change D S, we cannot expect the Cp of molten species to be constant in the whole T range of interest.

Obviously, knowing the iron redox ratio in a given sample, one may apply Eq. Ž22. as an oxygen fugacity probe, by simple rearrangement of the terms. Model predictions of oxygen fugacity ŽFig. 5a. are compared with estimates based on a reworked form of Sack’s et al. Ž1980. equation Log f O 2 s ln Ž X Fe 2 O 3,1 r X FeO 1 . y br T y cy

Ý d i Xi

2.303a

i

Ž 34 . in part b of the same figure. Coefficients a,b,c,d in Eq. Ž34. are empirical regression constants and X terms are the molar fractions of oxide components in melt Žsee Kilinc et al., 1983; for details.. Although Eq. Ž34. is somewhat less precise than the thermochemical calculations developed here in predicting f O 2 Ž s y, x s 0.932 against 0.815 for the same dataset adopted here to constrain the model; i.e. 488 samples., both methods provide concordant estimates ŽFig. 6..

172

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Fig. 7. Best fit model temperatures compared with T of experiment. The dataset is the same one utilized to constrain the dissociation constants of ferric oxide component Žequilibria Ž19. and Ž20...

Fig. 7 finally shows the thermometric properties of the model. Calculations were conducted by varying iteratively the T conditions of each sample in the dataset, keeping constant the buffering f O 2 and the measured iron redox ratio. Best-fit temperatures are again clustered along the identity line. The standard deviation on T estimates is 958C and the maximum observed bias is 4828C.

6. Mossbauer vs. wet chemistry estimates of iron ¨ redox state: thermochemical constraints As already noted in the introductory remarks, there is nowadays a general consensus on the fact that Mossbauer spectroscopy tends to overestimate ¨ the Fe 3q amount in crystals and glasses unless corrections are made for variable absorption efficiencies in the various coordination states. Although such corrections are possible in mineralogical applications where the coordination state of ferrous and ferric

ions is assessed by complementary XRD investigation, for glasses the same information is obtainable only through synchrotron assisted EXAFS or micro XANES studies. Indeed, such studies also point out that the common Mossbauer assumption of a mainly ¨ VI-fold coordinated Fe 2q Že.g. Mysen et al., 1980. is wrong ŽMosbah et al., 1998; Waychunas et al., 1988.. According to Dyar et al. Ž1987., however, the analytical uncertainties associated with Fe 3q values obtained from Mossbauer spectroscopy, although rele¨ vant Žabsolute error of f 3%, in their comparative study. are not as high as those associated with wet chemical methods Žabsolute error of 8%; accuracy of individual measurements f 6% relative; see, however, Wilson Ž1960. and Whipple Ž1974. for an extended discussion on the accuracy of microcolorimetric procedures. and, within these analytical limits the two methods are comparable Žcf. Table 2 in Dyar et al., 1987.. This view is however not shared by Lange and Carmichael Ž1989. who, reanalyzing the comparative database of Mysen et al. Ž1985. point

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

Fig. 8. Statistics of residuals for the Mossbauer and wet chemistry ¨ iron redox data subsets. The distribution of residuals for the wet chemistry subset is normal, centered on x sy0.0003. The distribution of residuals for the Mossbauer subset is non-normal, ¨ centered on x sy0.2254.

out the existence of a systematic bias Žwhich, by the way, increases with the increase of total iron, and not with its decrease as suggested by Dyar et al., 1987. associated to 3–5% 1 s errors on the Fe 3qrÝFe Mossbauer determinations. According to Lange and ¨

173

Carmichael Ž1989., this systematic bias results in estimates of FeO affected by much larger errors than for wet chemistry data Ž2 s f 21% on wet chemical analyses; Table 1 in Lange and Carmichael, 1989.. Fig. 8 summarizes model statistics concerning all Ž100 the wet chemistry Ž452 values. and Mossbauer ¨ values. iron redox subsets. While the distribution of residuals is normal, with a Gaussian shape almost centered on zero for the wet chemistry iron redox estimates, the Mossbauer subset has a non-normal ¨ distribution substantially shifted toward reducing conditions. Fig. 9 is a quantile–quantile Žq–q. representation of calculated and observed FeO and Fe 2 O 3 abundances in the two subsets Žwet chemistry and Mossbauer, respectively; univariate statistics are ¨ shown in Table 5.. Switching from the relative estimates to Fe II rFe III wet chemical or Mossbauer ¨ weight percent amounts in the melt implies knowledge of the bulk iron content in the phase, which is usually obtained by XRF analyses or ICP-AES or other complementary techniques, not appreciably affected by systematic biases. In the q–q representation of Fig. 9 we see that calculated and observed wet chemistry FeO and Fe 2 O 3 abundances are roughly aligned along a 1:1 distribution while the

Fig. 9. Quantile–quantile representation of the observed vs. calculated FeO and Fe 2 O 3 weight percent amounts ŽMossbauer data subset: ¨ Mysen et al., 1984, 1985; Dingwell and Brearley, 1988; Dingwell et al., 1988; Wet chemistry data subset: Kennedy, 1948; Fudali, 1965; Paul and Douglas, 1965; Shibata, 1967; Thornber et al., 1980; Mo et al., 1982; Kilinc et al., 1983; Dyar et al., 1987; Kress and Carmichael, 1988, 1989, 1991; Lange and Carmichael, 1987.. Univariate statistics are given in Table 5.

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

174

Table 5 Univariate statistics of calculated and observed distributions Fe 2 O 3 Mean Standard deviation Coeff. of variation Maximum Upper quartile Median Lower quartile Minimum

FeO

Calculated

Wet chem.

Mossbauer ¨

Calculated

Wet chem.

Mossbauer ¨

10.17 17.56 10.27 14.08 1.01 0.80 39.90 49.68 17.53 30.27 5.54 15.71 2.09 3.40 0.16 0.15

10.25 – 10.61 – 1.04 – 40.75 – 17.26 – 5.22 – 2.01 – 0.35 –

– 19.74 – 16.47 – 0.83 – 55.00 – 33.97 – 17.70 – 3.20 – 0.01

5.77 5.18 4.10 4.02 0.71 0.78 24.55 20.48 9.38 6.72 5.22 3.95 2.27 2.51 0.05 0.94

5.70 – 3.99 – 0.70 – 27.26 – 9.11 – 5.28 – 2.29 – 0.03 –

– 3.21 – 2.67 – 0.83 – 13.76 – 4.00 – 2.54 – 1.40 – 0.30

FeO and Fe 2 O 3 Mossbauer abundances are respec¨ tively understimated and overestimated with respect to the calculated values. Since the q–q calculated vs. Mossbauer plot have nevertheless linear shapes, the ¨ bias is systematic Ždifferent mean and different spread.. The Mossbauer overestimation of the Fe 2 O 3 ¨ may be roughly evaluated in 14% of the true value. Unfortunately, as already noted by Lange and Carmichael Ž1989. this systematic bias results in much larger errors affecting the estimates of FeO. In summary, the model seems to confirm that Mossbauer ¨ spectroscopy is not a suitable procedure to assess the redox state of iron in melts or glasses, in the absence of precise structural constraints concerning the various iron species. Acknowledgements This work was carried out with the financial support of the CNR-GNV grant 98.00690.PF62. Appendix A The concept of optical basicity arises primarily from the systematic study of the expansion of or-

bitals Žor Anephelauxetic effectB . induced by an increased localized donor pressure on p-block metals. Metal ions such as Tl l Žgroup III., Pb II Žgroup IV., Bi III Žgroup V. Ži.e. oxidation numbers group number y 2. have an electron pair in the outermost Ž6s. orbital. When trace concentrations of the metal are dissolved in melts and glasses, coordination with the ligand field anions results in formation of Molecular Orbitals ŽMOs. which increase the electron density of the inner shells. The consequent shielding of nuclear charges affects the energy involved in the outermost 6s ™ 6p transitions which becomes smaller when the inner shell electron density is increased. Lowering of the 6s ™ 6p transition energy is experimentally observed as a dramatic red-ward shift of the 6s ™ 6p UV absorption band when the p-block free ion is immersed in a ligand field. The spectroscopic shift of the 1 S 0 ™3 P1 absorption band experienced by Pb when passing from a free ion ŽPb 2q . condition to Pb II in an O 2y ligand field is for instance 60,700–29,700 s 31,000 cmy1 ŽDuffy and Ingram, 1971,1976.. For Bi III the analogous redward shift is 28.8 kK Ž1 kK s 1000 cmy1 . and is 18.3 kK for Tl I. This phenomenon is quantitatively understood in terms of ligand field theory by analogy with the behavior of 3d, 4d and 5f transition ions ŽJørgensen,

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

1962, 1969; and references therein.. In octahedral 3d chromophores for example, the energy splitting between anti bonding Cz )2 , Cx)2yy 2 MOs and the d x y , d x z , d y z AOs of the central atom Ž Dcov- s . is linearly related to the position of the ligand in the spectrochemical series Žrepresented by parameter f . and to the representative parameter of the central cation Ž g ., according to the simple relationship ŽJørgensen, 1969.

Dcov - s s fŽligand . P gŽcation .

175

not large enough to allow a basicity scale to be proposed on the basis of Eq. ŽA-1. Žcf. Table 5.5. in Jørgensen, 1969.. Nevertheless, as already discussed, the spectroscopic shift induced by the nephelauxetic effect on p-block metals by the ligand field is much more pronounced. Empirical relationships between observed Žor inferred. optical basicity of simple oxides ŽTable A1. and atomistic properties of the intervening cations, such as the Pauling and Sanderson’s electronegativities Ž x P and x S respectively in the same table. or the free ion polarizability have already been proposed ŽDuffy and Ingram, 1974a; Young et al., 1992.. Here we focus the attention on the fact that a strict connection between optical basicity and bond ionicity may be envisaged by equating the spectroscopic definition of fractional

Ž A-1.

The precision achieved by this simple equation in describing Dcov- s in 3d 3 , 3d 6 and 3d 8 chromophores is remarkable Žcf. Table 5.8 in Jørgensen, 1969.. However, the energy shift induced by changes in f is

Table A1 Optical basicity L and basicity moderating parameter of the central cation g according to various sources. Pauling’s and Sanderson’s electronegativities ŽPauling, 1932, 1960, 1980; Sanderson, 1967. are also listed. L, g , x S : adimensional; x P : eV Oxide

L Ž1.

H 2O Li 2 O B2 O3 Na 2 O MgO Al 2 O 3 SiO 2 P2 O5 SO 3 K 2O CaO TiO 2 Cr2 O 3 MnO FeO Fe 2 O 3 CoO NiO Cu 2 O ZnO SrO SnO BaO PbO

g Ž2.

Ž3.

Ž4.

Ž5.

0.40

0.78 0.60 0.48 0.40 0.33 1.00 0.70 0.94–1.03 0.86–1.08 0.73–0.81

1.15 0.78 0.60 0.46 0.40 1.40 1.00 0.65 0.98 1.03 0.77

0.42 1.15 0.78 0.60 0.48 0.33 0.25 1.4 1.00

1.00

1.15 0.78 0.61 0.48 0.8

1.15 0.78 0.59 0.48 0.40

1.40 1.00 0.61

1.40 1.00 0.61

0.90 1.03 1.21

0.59 0.51 0.48

1.15

1.15

0.82–0.98 1.10 1.15

1.15

Ž6.

Ž6.

Ž7.

0.39 1.00 0.42 1.15 0.78 0.59 0.48 0.40 0.33 1.36 0.99 0.58 0.58 0.59 0.48 0.48 0.51 0.48 0.43 0.58 1.03 0.48 1.12 0.48

2.56 1.00 2.38 0.87 1.28 1.69 2.09 2.50 3.03 0.74 1.00 1.72 1.72 1.69 2.09 2.09 1.96 2.09 2.30 1.72 0.97 2.09 0.89 2.09

2.50

0.87 1.28 1.67 2.09 2.50 3.03 0.71 1.00 1.54 1.69 1.354 a 2.09 1.96 2.09 2.30 1.72 2.09 2.09

xP

xS

2.15 1.0 2.0 0.9 1.2 1.5 1.8 2.1 2.5 0.8 1.0 1.6 1.6 1.5 1.8 1.8 1.7 1.8 1.9 1.6 1.0 1.8 0.9 1.8

3.55 0.74 2.84 0.70 1.99 2.25 2.62 3.34 4.11 0.41 1.22 1.60 1.88 2.07 2.10 2.10 2.10 2.10 2.60 2.84 1.00 3.10 0.78 3.08

Ž1. Duffy Ž1989,1990.; Ž2. Young et al. Ž1992.; Ž3. Duffy and Ingram Ž1974a.; Ž4. Sosinsky and Sommerville Ž1986.; Ž5. Gaskell Ž1982.; Ž6. this work; Eq. ŽA-7. Žnote that L s gy1 .; Ž7. value adopted in this study. a Obtained by non linear minimization of FeO thermodynamic activity data in multicomponent melts.

G. Ottonello et al.r Chemical Geology 174 (2001) 157–179

176

ionic character of a bond ŽPhillips, 1970. with Pauling’s relation: f i s Ei2r

Ž

Ei2 q Ec2

. s 1 y exp

1 y 4

Ž xO y x M .

2

Ž A-2. where x O and x M are the Pauling electronegativity of oxygen and metal, respectively, and Ei s Ž Eg2 y Ec2 .

1r2

Ž A-3.

Ei in Eq. ŽA-3. is the Aionic energy gapB and Eg is the total energy gap between bonding and anti bonding orbitals Ž Ec corresponds to Eg for the non-polar covalent bond in the same row of the periodic table, with a correction for inter-atomic spacing.: Eg s " v Pr Ž ´` y 1 .

1r2

Ž A-4.

with " v P s plasma frequency for valence electrons; ´` s optic dielectric constant. Based on the L values of the various oxides listed in Table A1 and the corresponding f i values calculated from Pauling’s electronegativities, the following operational relationship may be proposed:

L s Ž 4.6242 y 4.6702 f i .

y1

Ž R 2 s 0.95 .

1

ž

4.6 1 y

Ei2 Ei2 q Ec2

g s 0.8969 y 0.6703 x P q 0.7404 x P2

Ž R 2 s 0.97 . Ž A-7.

g s 0.7398 y 0.0193 x S q 0.1880 x S2

Ž R 2 s 0.96 . Ž A-8.

Eq. ŽA-7., although conceptually less obvious than Eq. ŽA-5., is operationally more accurate and has been adopted here to evaluate L,g values whenever literature values were controversial or lacking. In the case of Fe 2q, we noted large discrepancies between the L value proposed by Duffy and Ingram Ž1974a., Sosinsky and Sommerville Ž1986., Young et al. Ž1992., and the value postulated by Gaskell Ž1982. which is more appropriate from an atomistic point of view. We thus adopted initially for Fe 2q the L,g values derived by application of Eq. ŽA-7. Žvery akin to Gaskell’s indications; cf. Table A1. with the aim of establishing a simple link between basicity moderating parameter and polymerization constant Žsee text and Fig. 2. and refined then the g value of Fe 2q in a non-linear minimization procedure involving 392 FeO activity data in multicomponent melts. The resonance Žredundancy. of the procedure is quite limited and the results indicate for g of Fe 2q an intermediate value respect to those hitherto proposed ŽTable A1..

Ž A-5.

On the basis of equality ŽEq. ŽA-2.. we then get the following approximation:

Lf

from Pauling’s or Sanderson’s electronegativities by application of the second order polynomials

Ž A-6.

/

which suggests an optical basicity of 0.225 for a purely covalent nonpolar bond. This value compares favorably with the value attributed L f 0.46 q 0.48 to SiO 2 which has a fractional ionic character around 0.5 Ž0.516 according to Pauling, 1980.. Direct estimates of the basicity moderating parameter of the central cation may be also obtained

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