583

ANNALS OF GEOPHYSICS, VOL. 48, N. 4/5, August/October 2005

Key words polymerisation – basicity – oxidationstate – water speciation – Temkin model

1. Introduction

During the last century many models havebeen proposed dealing with the thermodynamicproperties of silicate melts (or slags), especial-ly with the goal of understanding slag-melt par-titioning of elements for industrial reasons rele-vant to steelmaking. The heuristic capability ofa model assessing silicate melts energetics be-

comes particularly important when dealingwith the generalised problem of multicompo-nent, mutliphase equilibria, as shown by thethermochemical treatments presented in Ghior-so et al. (1983), Ghiorso and Sack (1994), Pel-ton (1998), Papale (1999) and Moretti et al.(2003). To model element solubility and speci-ation it is necessary to account fully for thecompositional variables of the system. Never-theless, compositional variables cannot be un-derstood without a comprehensive model ableto rescale measured concentrations in terms ofcomponent activities, which represent the obvi-ous control parameters of chemical reactionstaking place in the system. Therefore, thechoice of the model for component activitiesrepresents a crucial step in silicate melt thermo-dynamics. Here, I will show that ionic modelsaccounting for the variable degree of polymeri-

Polymerisation, basicity, oxidation stateand their role in ionic modelling

of silicate melts

Roberto MorettiIstituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Napoli, Italy

AbstractIn order to describe and quantify the reactivity of silicate melts, the ionic notation provided by the Temkin for-malism has been historically accepted, giving rise to the study of melt chemical equilibria in terms of complete-ly dissociated ionic species. Indeed, ionic modelling of melts works properly as long as the true extension of theanionic matrix is known. This information may be attained in the framework of the Toop-Samis (1962a,b) mod-el, through a parameterisation of the acid-base properties of the dissolved oxides. Moreover, by combining thepolymeric model of Toop and Samis with the «group basicity» concept of Duffy and Ingram (1973, 1974a,b,1976) the bulk optical basicity (Duffy and Ingram, 1971; Duffy, 1992) of molten silicates and glasses can be splitinto two distinct contributions, i.e. the basicity of the dissolved basic oxides and the basicity of the polymericunits. Application to practical cases, such as the assessment of the oxidation state of iron, require bridging of theenergetic gap between the standard state of completely dissociated component (Temkin standard state) and thestandard state of pure melt component at P and T of interest. On this basis it is possible to set up a preliminarymodel for iron speciation in both anhydrous and hydrous aluminosilicate melts. In the case of hydrous melts, Iintroduce both acidic and basic dissociation of the water component, requiring the combined occurrence of H+

cations, OH− free anions and, to a very minor extent, of T-OH groups. The amphoteric behaviour of water re-vealed by this study is therefore in line with the earlier prediction of Fraser (1975).

Mailing address: Dr. Roberto Moretti, Istituto Nazio-nale di Geofisica e Vulcanologia, Osservatorio Vesuviano,Via Diocleziano 328, 80124 Napoli, Italy; e-mail: moret-ti@ov.ingv.it

584

Roberto Moretti

sation represent suitable tools to model silicatemelt reactivity.

The earliest theories on the constitution ofsilicate slags were developed as a result of min-eralogical examination of the constituents ofsolidified melts and may be classified as molec-ular models. In 1923, Colclough (quoted inGaskell, 2000), perhaps anticipating Bowen(1928), pointed out that, as the phases occurringin the solid state are formed by selective crys-tallisation from the melt, mineralogical exami-nation cannot provide evidence that the com-pounds, observed in the solid state, had existedin the liquid. The concept of thermodynamicequilibrium was particularly stressed bySchenck (1945), who recognised that each reac-tion proceeds up to the achievement of equilib-rium, independently of the extension of the sys-tem. In molecular models it is assumed that mo-lecular complexes are formed in the melt inproportions dictated by the overall melt stoi-chiometry. Gaskell (2000) states that a commonfeature of molecular models is that «rather thanthe constitution of the slag being deduced fromthe observed behaviour, a set of arbitrary as-sumptions was manipulated to reproduce theobserved behaviour. Comparison among the ap-proaches shows that the degree of success ofany model in giving the required reproductionis not sensitive to the finer details of the as-sumed constitution or to the internal thermody-namic consistency of the model». This recallssomehow the normative deconvolution adoptedby Ghiorso et al. (1983) in their multicompo-nent free energy minimization procedure con-ducted in a regular solution approximation ofthe zeroth order. In fact this model does not ac-count for the true nature of silicate melts andthe choice of components reflects the topologyof the compositional space investigated by theauthors.

Most melts or slags are however «ionic»rather than «molecular» liquids. The existence ofions in the liquid state was already demonstratedin 1923 by Sauerwald and Neuendorff (quoted inGaskell, 2000) who successfully electrolysediron silicate melts, and in 1924 by Farup et al.(quoted in Gaskell, 2000) who measured theconductivity of melts in the systems CaO-SiO2

and CaO-Al2O3-SiO2.

Tamman (1931, quoted in Gaskell, 2000) al-ready assumed electrolytic dissociation of met-allurgical slags. A first application of an ionictheory of slags to the treatment of slag-metalequilibria was made by Herasymenko (1938)who assumed that slags were mixtures of Fe2+,Mn2+, Ca2+, Al3+ and SiO4

4-.The need for an ionic model of silicate

melts emerged clearly from the experimentaldeterminations on viscosity and electrical con-ductivity. Further electrical conductivity meas-urements carried out by various authors indi-cate an essentially ionic unipolar conductivity(Bockris et al., 1952a,b; Bockris and Mellors,1956; Waffe and Weill, 1975), where chargetransfer evidently operates by cations, with an-ions being essentially stationary. Transferenceof electronic charges (h- and n-type conductiv-ity) is observed only in melts enriched in tran-sition elements, where band conduction andelectron hopping phenomena are favoured. Iwill hereon dismiss the neutral molecular ap-proach and accept that silicate melts, like otherfused salts, are ionic liquids. In an ionic melt,coulombic forces acting between charges of op-posite sign lead to a relative short-distance or-dering of ions, with anions surrounded bycations and vice versa. The probability of find-ing a cation replacing an anion in such orderingis effectively zero and, from a statistical pointof view, the melt can be considered a quasi-lat-tice, with two distinct sites, usually defined as«anion matrix» and «cation matrix».

The distinction between these two matriceswas made by Temkin (1945), who consideredthat the electrostatic forces characterising ionicinteractions are sufficiently strong to make thearrangements of ions in the pure fused salts andin mixture of salts similar to those in the crys-talline state, implying co-ordination of cationsby anions.

In the Temkin approach to fused salts, theactivity of component AZ in the ideal mixtureof the two fused salts AZ and BY is expressedby the Temkin equation

(1.1)

A straight application of the Temkin model tosilicate melts is inadequate because the exten-

.a X X n n n nnn

,AZ melt A ZA B Z Y

ZA $= + +=

585

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

sion of the anion matrix varies in a complicatedfashion with composition. This complexity isreflected by activity-composition relationshipsdeviating from the ideal Temkin model behav-iour and may be fully accounted for by polymerchemistry.

2. The Toop-Samis model

In polymeric models of silicate melts, it ispostulated that, at each composition, for given P-T values, the melt is characterized by an equilib-rium distribution of several ionic species of oxy-gen, metal cations and ionic silicate polymers.

The charge balance of a polymerization re-action involving SiO4

4− monomers may be for-mally described by a homogenous reaction in-volving three forms of oxygen: singly bondedO-, doubly bonded O0 (or «bridging oxygen»),and free oxygen O2− (Fincham and Richardson,1954)

(2.1)

Polymer chemistry shows that the larger thevarious polymers are, the more their reactivityis independent of the length of polymer chains.This fact, known as the «principle of equal re-activity of co-condensing functional groups»,has been verified in fused polyphosphate sys-tems, which are analogous, in several respects,to silicate melts (cf. Fraser, 1977; Ottonello,1997).

Assuming this principle to be valid, theequilibrium constant of reaction (2.1) becomes

(2.2)

Terms in parentheses represent the number ofmoles in the melt, which can be used in place ofactivities since all three species of oxygen spe-ciate over the same matrix (anion matrix: thethree oxygen types either mix ideally or theiractivity coefficients cancel out ).

Toop and Samis (1962 a,b) showed that in abinary melt MO-SiO2 the total number of bondsper mole of melt is given by

(2.3)( ) ( ) N2 O O 4 SiO0

2+ =-

( )( )( )

.KO

O O.2 1 2

0 2

= -

-

.O O O2 2 2m m m0 2

, +- -

where NSiO2 are the moles of SiO2 in the MO-SiO2 melt. The Toop and Samis model assumesthe basic oxide MO to be completely dissociat-ed. The number of bridging oxygens in the meltis thus

(2.4)

Mass balance gives the number of moles of freeoxygen per unit mole of melt

(2.5)

where obviously 1−NSiO2 represents the numberof moles of basic oxide in the melt.

Combining the various equations one gets

(2.6)

which reduces to a quadratic equation in (O−)

(2.7)

Given NSiO2, eq. (2.7) may be solved.Since the number of oxygens which react

according to eq. (2.2) is (O−)/2 per mole of melt,the free energy of mixing per mole of melt is

(2.8)

The validity of this equation has been provedmany times (see for example Fraser, 1975; Ot-tonello, 1997; Ottonello et al., 2001).

3. Polymerisation and acid-base properties

It is evident that the reaction (2.1) betweenthe three oxygen species represents the character-istic process of an acid-base reaction in oxide sys-tems, which was defined by Flood and Förland(1947) as «the transfer of an oxygen ion from astate of polarisation to another». This acceptanceis particularly important in silicate melts andglasses where polymerisation reactions govern-ing extension and distribution of polymeric unitsmay be restated as (as already shown) simple

[( )/ ] .lnG RT KO 2 .mixing 2 1=∆ -

( ) ( ) ( )( )

( ) .

K N

N N

O 4 1 O 2 2

8 1 0

. iO

iO iO

22 1 S

S S

2

2 2

- + + +

+ - =

- -

( )[ ( )] [ ( )]

KN N

4 O4 O 2 2 O

.iO

2 1 2

SiOS 2 2=- - -

-

- -

( ) ( )( )

NO 12O

SiO2

2= - ---

( )( )

.N

O2

4 OSiO0 2=- -

586

Roberto Moretti

acid-base reactions involving three distinct polar-isation states of oxygen (see eq. (2.2)).

Although the Lux-Flood formulation for-mally differs from a Brönsted-Lowry (proton-based) exchange, the two formulations are mu-tually consistent (Flood and Förland, 1947)and, with this proviso, the link between redoxand acid-base exchanges in the Lux-Flood ac-ceptation is represented by the «normal oxygenelectrode» equilibrium

(3.1)

Thus in aprotic solvents O2− replaces H+. A ba-sic oxide is the one capable of furnishing oxy-gen ions and an acidic oxide is one that associ-ates oxygen ions

(3.2)

It is well established that the Lux-Flood acid-base property of dissolved oxides markedly af-fects the extent of polymerisation by producingor consuming free oxygen ions (O2−). Thus, fora generic oxide MO (Fraser, 1975, 1977):

(3.3)

(3.4)

with (3.3) and (3.4) showing acidic and basicbehaviours, respectively. Although it is concep-tually immediate to envisage directly a directrelationship between polymerisation constant(K2) and basicity of dissolved oxides in binarysystems (Toop and Samis, 1962,a,b), the exten-sion to multicomponent melts and glasses is notimmediate. Moreover, in the presence of alter-valent elements such as Fe, mutual interactionsare established between the normal oxygenelectrode reaction (3.1) and the dissociationequilibria ((3.3)-(3.4)). These may be addressedby taking into account both the polymeric na-ture of the anion matrix, along the guidelines ofthe Toop-Samis model, and Fraser’s am-photheric treatment of dissolved oxides.

In a chemically complex melt or glass, thecapability of transferring fractional electroniccharges from the ligands to the central cationdepends in a complex fashion on the melt or

MO MO O2 2, + -+

MO O MO222

,+ - -

.Base Acid O2, + -

.21

O 2e O22

,+ - -

glass structure, which affects the polarisationstate of the ligand itself. The mean polarisationstate of the various ligands (mainly oxide ionsin natural silicate melts) and their ability totransfer fractional electronic charges to the cen-tral cation are nevertheless conveniently repre-sented by an experimentally observable param-eter which is an index of the basicity of themedium: the optical basicity (see Duffy, 1992for an exhaustive review of the subject). A for-mal link is thus needed between polymerisationconstant and optical basicity.

4. The «optical basicity» concept

As we have already seen there are strict mu-tual interconnections between the concepts of«oxidation state» and «basicity», whenever thislast term is referred to non-protonated systems.Following Jørgensen (1969) we may define ox-idation by means of four distinct formalisms:

– Formal oxidation number denoted byRoman numeral superscripts (including thenon-Roman notations 0, −I, ...) whenever thisdoes not imply an accurate description of thetrue nature of the complex (i.e. NiII for nickel inthe aqueous complex Ni(H2O)6

2+ or SVI in thesulphate complex SO4

2−).– Spectroscopic oxidation states derived

by experimentally observed excited levels, de-noted by on-line Roman numerals in parenthe-ses; i.e. Cr(III)O6, Ni(II)Cl6, etc.

– Conditional oxidation states derivedfrom electronic configuration; i.e. [Ar]3d 5 forMn2+, Fe2+, etc.

– Distributed oxidation states adjacentatoms bonded in the complex share the elec-trons equally; i.e. C⟨0⟩ and H⟨0⟩ in CH4; S⟨0⟩and O⟨-I⟩ in SiO4

4− etc. The usual notation with arabic numeral su-

perscripts (i.e. Li+, Mg2+, Cr3+, F-) which we willhereafter refer to « formal ionic charges» shouldbe reserved for cases in which «entities and mol-ecules are sufficiently separated and are eitherneutral or carry charges which are a positive ornegative integer multiplied by the protoniccharge» (Jørgensen, 1969).

In Brönsted’s formalism, redox reactionsare those involving exchange of electrons be-

587

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

tween the reactants and acid-base reactions arethose involving protons. The Brönsted acid-base function for protonated systems is usuallyrepresented as

(4.1)

The link joining redox and acid-base reactionsis the normal hydrogen electrode reaction

(4.2)

As in non-protonated systems the Brönsted-Lowry formalism is better replaced by the Lux-Flood acid-base definition (Flood and Förland,1947), three sorts of transitions are involved inacid-base equilibria:

i) Transitions accompanied by an alterationof the co-ordination number of oxygen, but nochange of distributed oxidation state, for atomswith a high ionisation energy, such as for exam-ple in

(4.3)

ii) Transitions which do not involve anychange in co-ordination number, but a changein distributed oxidation state, for medium ioni-sation energy atoms, such as in

(4.4)

iii) Transitions which involve both changein co-ordination number and in distributed oxi-dation state, leading to the formation of isolat-ed cations, such as occurring for low ionisationenergy atoms

(4.5)

In silicate melts we envisage simple acid-basereactions involving three distinct polarisationstates of oxygen, eq. (2.1), which in a distrib-uted oxidation state notation may be expressedas follows:

(4.6)

Although formally different, the Brönsted-Lowry and the Lux-Flood formulations are mu-

.O I O O2 0 2,- +- -

.CaO Ca O0 2, ++ -2

.O O OSi I Si 0 2 24

4

2, +- - -

.CO CO O0 03

2 22, +- -

.2e 2H H2,+- +

.Acid Base H, + +

tually consistent and, if we still accept theBrönsted definition of redox reactions, then itmay be readily seen that the link joining redoxand acid-base exchanges in the Lux-Flood ac-ceptation is now represented by the oxygenelectrode equilibrium.

The fact that reaction (3.1) could also re-semble an equilibrium between a Lewis acid(i.e. a substance acting as acceptor of a pair ofelectrons; O2 in our case) and a Lewis base (i.e.a substance acting as donor of a pair of elec-trons; O2− in our case), leading to a stable octetconfiguration, further emphasises the necessity ofdistinguishing a redox equilibrium, i.e. «a reac-tion involving free electrons (in the broad senseof the term) and resulting in a change of formaloxidation number» from an acid-base equilibri-um which, in the Brönsted-Lowry formalism isbasically «the transfer of an oxygen ion from astate of polarisation to another», as already noted.

Although we may conceive formal integercharges for isolated non-interacting (gaseous)ions (i.e. Li+, Mg2+, Fe3+, etc.) and (althoughmuch less evidently) for isolated complexes,this formalism cannot be readily transferred tothe formal oxidation state within a complexsince, in most cases, it is in contrast with boththe quantum-mechanical concept of «electrondensity» and with the notion of «fractional ion-ic character of a bond» (Pauling, 1932, 1960;Gordy, 1950; Hinze et al., 1963; Phillips, 1970,see below). Moreover, in a chemically complexmelt or glass the capability of transferring frac-tional electronic charges from the ligands to thecentral cation depends in a complex fashion onthe melt structure, which affects the polarisationstate of the ligand itself. The mean polarisationstate of the various ligands (mainly oxide ions innatural silicate melts) and their ability to trans-fer fractional electronic charges to the centralcation are nevertheless conveniently represent-ed by the «optical basicity» of the medium(Duffy and Ingram, 1971). The concept of opti-cal basicity arises primarily from the systematicstudy of the orbital expansion (or «nephe-laux-etic effect») induced by an increased localiseddonor pressure on p-block metals. Metal ionssuch as TlI (group III), PbII (group IV), BiIII

(group V) (i.e. oxidation number = group num-ber −2) have an electron pair in the outermost

588

Roberto Moretti

(6s) orbital. When trace concentrations of themetal are dissolved in melts and glasses, coordi-nation with the ligand field anions results in for-mation of Molecular Orbitals (MOs) which in-crease the electron density of the inner shells.The consequent shielding of nuclear charges af-fects the energy involved in the outermost6s→6p transitions which become lower themore the inner shell electron density is increased.Lowering of the 6s→6p transition energy is ex-perimentally observed as a dramatic red-wardshift of the 6s→6p UV absorption band when thep-block free ion is immersed in a ligand field.The spectroscopic shift of the 1S0→ 3P1 absorp-tion band experienced by Pb when passing froma free ion (Pb2+) condition to PbII in an O2- ligandfield is for instance 60700−29700=31000 cm−1

(Duffy and Ingram, 1971, 1974b, 1976). For BiIII

the analogous redward shift is 28.8 kK (1 kK =1000 cm−1) and is 18.3 kK for TlI.

This phenomenon is quantitatively under-stood in terms of ligand field theory by analogywith the behavior of 3d, 4d and 5f transitionions (Jørgensen, 1962, 1969; and referencestherein). In octahedral 3d chromophores for ex-ample, the energy splitting between anti bond-ing , MOs and the dxy, dxz, dyz AOs ofthe central atom (∆ cov-σ) is linearly affected bythe position of the ligand in the spectrochemi-cal series (represented by parameter f ) and by arepresentative parameter of the central cation(g), according to the simple relationship (Jør-gensen, 1969)

(4.7)

The precision achieved by this simple equationin describing ∆ cov-σ in 3d 3, 3d 6 and 3d 8 chro-mophores is remarkable (cf. table 5.8 in Jør-gensen, 1969). However, the energy shift in-duced by changes in f is not so marked as to al-low a basicity scale to be proposed on the basisof eq. (4.7) (cf. table 5.5. in Jørgensen, 1969).

Jørgensen (1962) pointed out that the ex-pansion of the radial function consequent onlowering of the effective nuclear charge (Zeff)results in three distinct nephelauxetic parame-ters (β). These are β ll for the interaction be-tween two electrons in the lower sub-shell, β lu.for the interaction between an electron in the

f ( ) ( )cov ligand cation=∆ -v g$ .

*x y2 2Ψ -

*z2Ψ

lower and an electron in the upper sub-shell andβ uu for the interaction between two electrons inthe upper sub-shell

(4.8)

(4.9)

(4.10)

Zeff* in the above equations is the effective nu-

clear charge of the free cation; a is related to themean radial distance of the orbital from the cen-tre of nuclear charges and β ll > β lu > β uu. Ac-cording to Duffy and Ingram (1971) the opticalbasicity, Λ, is represented by the ratio h/h*

where h is the Jørgensen’s (1962) function ofthe ligand in the polarisation state of interestand h* is the same function relative to the ligandin an unpolarised state (i.e. free O2− ions in anoxide medium)

(4.11)

with ν free= 1S0→ 3P1 absorption band of the freep-block cation; ν glass= 1S0→ 3P1 absorption bandmeasured in the glass; ν *= 1S0→ 3P1 absorptionband in a free O2− medium.

As we see in fig. 1, the optical basicity ofsimple oxides appears related to the atomisticproperties of the intervening cations, such asthe Pauling and Sanderson’s electronegativities(χP and χS respectively) or the free ion polariz-ability (Young et al., 1992).

Although Duffy and Ingram (1974a) sug-gest a simple linear dependency between the re-ciprocal of optical basicity Λ (or «basicity mod-erating parameter» γ ; see later) and Paulingelectronegativity χP (straight line in fig. 1), hereI focus attention on the fact that a strict connec-tion between optical basicity and bond ionicityshould exist. The true nature of this relationship(which we depict as a second order polynomialdependency in the same figure) can be envis-aged by equating the spectroscopic definition offractional ionic character of a bond (Phillips,

hh

1

1* * *

free

free glass= =

-

-=

--

bb

o oo o

Λ

aZZ

*uu u4

eff

eff=b

a aZZ

*lu l u2 2

eff

eff=b

aZZ

*ll l4

eff

eff=b

589

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

1970) with Pauling notation

(4.12)

where χO and χM are respectively the Paulingelectronegativity of oxygen and metal and

(4.13)

Ei in eq. (4.13) is the «ionic energy gap» and Eg

is the total energy gap between bonding and an-ti bonding orbitals (Ec corresponds to Eg for thenon-polar covalent bond in the same row of theperiodic table, with a correction for inter-atom-ic spacing)

(4.14)

with = plasma frequency for valence elec-trons; and ε∞ = optical dielectric constant.

The operational relationship between frac-tional ionic character of the bond in the oxideand optical basicity is the following:

(4.15)

( . .4 6242 4 6702-= f . .R 0 9517i1 =Λ - 2)

P'~

( )E

1g

P

21

'=

-f~

3

i cg2 2 2

1

( ) .E E E= +

( )expf

E EE

141

ii c

i2 2

2

O M=+

= - - -| |^ h: D

Based on eqs. (4.12) and (4.15) we get the fol-lowing approximation:

(4.16)

which suggests an optical basicity of 0.225 fora purely covalent non polar bond (see also eq.(4.13)). This value compares favourably withthe value 0.46 ÷ 0.48 indicated by Duffy andIngram (1974a) for SiO2 which has a fractionalionic character around 0.5 (0.516 according toPauling, 1960).

The reciprocal of optical basicity («basicitymoderating parameter» γ M, according to Duffyand Ingram, 1973) represents the tendency ofan oxide forming cation M to reduce the lo-calised donor properties of oxide ions. It is re-lated to the optical basicity of the medium by

(4.17)

where ZM = formal oxidation number of cationM in MO; ZO = formal oxidation number of ox-ide ion in MO; rM = stoichiometric ratio be-tween number of cations M and number of totaloxide ions in the medium.

Although γM reduces to in a simple single ox-ide medium, it has the property to describe theadditive Jorgensen’s h function in chemicallycomplex media (with A, B, ... oxide formingcations) according to (Duffy and Ingram, 1973):

(4.18)

Moreover, based on eqs. (4.16) and (4.17) the op-tical basicity of the medium may be expressed as

. (4.19)

Direct estimates of the basicity moderating pa-rameter of the central cation may then be ob-tained from electronegativies (fig. 1) by appli-

Z r Z r2 2A

A A

B

B B# #f= + +c cΛ

.

h hZ

Z rZ

Z r1 1

1

11

*

O A O

B

A A B B# #$

$ f

= - - -

- -

c

c

c

c

m

m

<

F

ZZ r

MM M

M M

##

=c Λ O

.E E

E4 6 1

1

i c

i2 2

2.-

+

Λc m

Fig. 1. Pauling and Sanderson electronegativitiesand basicity moderating parameter. The straight lineis the intepolation of Duffy and Ingram (1974),γ=1.36 × ( χP− 0.26).

590

Roberto Moretti

cation of the second order polynomials

(4.20)

(4.21)

. ) .0 96=(R.0 1880|+.0 0193|S-.0 7398= S2c 2

.0 97)=(R.0 7404|+.0 6703|- P.0 8969= P2c 2

Equation (4.20), although conceptually less ob-vious than (4.16), is operationally more accu-rate and has been adopted by Ottonello et al.(2001) to evaluate basicity parameters, when-ever literature values were controversial orlacking.

Table I summarises the functional relation-ships among the previously discussed parameters.

Table I. Optical basicity Λ and basicity moderating parameter of the central cation γ according to varioussources. Pauling’s and Sanderson’s electronegativities (Pauling, 1932, 1960; Sanderson, 1967) are also listed. Λ,γ, χS: adimensional; χP: eV (from Ottonello et al., 2001).

Oxide Λ γ χP χ S

(1) (2) (3) (4) (5) (6) (6) (7)

H2O 0.40 0.39 2.56 2.50 2.15 3.55Li2O 1.00 1.00 1.0 0.74B2O3 0.42 0.42 2.38 2.0 2.84Na2O 1.15 1.15 1.15 1.15 1.15 0.87 0.87 0.9 0.70MgO 0.78 0.78 0.78 0.78 0.78 0.78 1.28 1.28 1.2 1.99Al2O3 0.60 0.60 0.60 0.61 0.59 0.59 1.69 1.67 1.5 2.25SiO2 0.48 0.46 0.48 0.48 0.48 0.48 2.09 2.09 1.8 2.62P2O5 0.40 0.40 0.33 0.8 0.40 0.40 2.50 2.50 2.1 3.34SO3 0.33 0.25 0.33 3.03 3.03 2.5 4.11K2O 1.40 1.4 1.40 1.40 1.36 0.74 0.71 0.8 0.41CaO 1.00 1.00 1.00 1.00 1.00 0.99 1.00 1.00 1.0 1.22TiO2 0.65 0.61 0.61 0.58 1.72 1.54 1.6 1.60Cr2O3 0.70 0.58 1.72 1.6 1.88MnO 0.94-1.03 0.98 0.90 0.59 0.59 1.69 1.69 1.5 2.07FeO 0.86-1.08 1.03 1.00 1.03 0.51 0.48 2.09 1.354 1.8 2.10

Fe2O3 0.73-0.81 0.77 1.21 0.48 0.48 2.09 2.09 1.8 2.10CoO 0.51 1.96 1.96 1.7 2.10NiO 0.48 2.09 2.09 1.8 2.10Cu2O 0.43 2.30 2.30 1.9 2.60ZnO 0.82-0.98 0.58 1.72 1.72 1.6 2.84SrO 1.10 1.03 0.97 1.0 1.00SnO 0.48 2.09 2.09 1.8 3.10BaO 1.15 1.15 1.15 1.15 1.12 0.89 0.9 0.78PbO 0.48 2.09 2.09 1.8 3.08

(1) Duffy (1992); (2) Young et al. (1992); (3) Duffy and Ingram (1974a,b); (4) Sosinsky and Sommerville(1986); (5) Gaskell (1982); (6) Ottonello et al. (2001); eq. (4.19) (note that Λ=γ −1); (7) Ottonello et al. (2001);obtained by non linear minimization of FeO thermodynamic activity data in multicomponent melts.

591

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

4.1. Group basicity

Since we have established that the experi-mentally derived concept of optical basicity is re-lated to atomistic properties and first principlessuch as Pauling’s electronegativity and fractionalionic character of a bond (or «bond order») (seeeqs. (4.12), (4.15) and (4.16)) we may tentativelyextend the concept to formal entities such as thesilica polymers (or «structons» in the sense ofFraser, 1975, 1977) within binary joins and thento complex melts. To address the problem wemay still use eq. (4.19) but now the cation to ox-ide ratio represents the local coordination presentin the structon (Duffy and Ingram, 1976). For in-stance, for a monomer SiO4

4− rA=M/O⟨−I⟩=1/4,for a dimer Si2O7

6− (or Si⟨0⟩2Ο⟨0⟩Ο⟨−I⟩66− in dis-

tributed oxidation state notation) rA=1/3, and soon. Group basicities of the most important poly-mer units present in silicate melts are listed intable II. We may note that, with the increase of

polymerisation, the group basicity of polymerchains progressively decreases due to the de-crease of the ratio O⟨−I⟩/O⟨0⟩. We may also notethat the presence of foreign cations (i.e. AlIII,FeIII) in the polymer units changes the group ba-sicity in a linear fashion with respect to the groupstoichiometry.

We may now inquire if, based on this newconcept, the basicity of a complex medium suchas a silicate melt or glass may be expected to varylinearly with composition along a binary join.

For this purpose the three forms of oxygenpresent in the melt (i.e. O2−, O⟨−I⟩ and O⟨0⟩)(Toop and Samis, 1962a,b) are related to meltstoichiometry and to the polymerisation reac-tion constant K2 by mass balance (eqs. (2.4),(2.5), (2.7)).

Along the polymerisation path (frommonomers SiO4

4− to silica), the group basicityof the polyanion (or structon) matrix, Λ«structons»,may be expressed as a linear function of the ra-tio between singly bonded oxygen and totaloxygen within the structons (see also table II)

(4.22)

where , are respectively the groupbasicity of the SiO4

4– monomer and of the SiO2

tectosilicate. The bulk basicity of the mediumresults expressed as

(4.23)

where

(4.24)

and ΛΜΟ is the basicity of the oxide in the bina-ry join MO-SiO2.

By combining eq. (4.23) with the mass bal-ances (2.4), (2.5) and (2.7) we may evaluatewhich part of the bulk basicity of the mediummay be ascribed to the effect of the structon ma-

O O I O O0 2= - + + -^ ^ ]h h g/

+( )1- -Λ Λ

Λ

=

+2

( ) .

O

O

O

O I

O

O I

O

O I O

0 5

10

medium MO MO

SiO SiO

2

44

# -

+-

-- +

Λ

Λ

-

-

^

^^

^ ^

h

hh

h h

/ /

/ /

SiO2ΛSiO44Λ -

Λ+=O I O

O I1

0structons SiO SiO44 2

-

--

+Λ Λ -

^ ^

^^

h h

hhTable II. Basicities of «structons» along the poly-

merisation path.

Group Group basicity

SiO44− 0.50000 0.73923

AlO45− 0.37500 0.85227

FeO45− 0.37500 0.80443

Si2O76− 0.57143 0.70198

Al2O711− 0.42857 0.83117

Fe2O711− 0.42857 0.77649

SiAlO77− - 0.76658

SiFeO77− - 0.73924

Si3O108− 0.60000 0.68707

Si4O1310− 0.61538 0.67906

SiO32−; Si2O6

4−; Si3O96−; 0.66667 0.65231

Si4O128−; Si5O15

10−; 1-ringSi2O5

2−; Si4O104−; Si6O15

6−; 0.80000 0.58278Si8O20

8−; Si10O2510−; 2-rings

Si3O72−; Si9O21

6−; Si12O289−; 0.85714 0.55297

3-ringsSiO2 1.00000 0.47847Al2O3 1.00000 0.60606Fe2O3 1.00000 0.47847

Z r2

A A#

592

Roberto Moretti

trix (third and fourth terms on the right in eq.(4.23)).

In fig. 2 see how the basicity of the structonmatrix is affected by the value of the polymeri-sation constant, which dictates the structonscontribution to the basicity of the medium.

Moles of quasi-chemical species of oxygen arealso shown for comparison.

Table III lists structural details along the joinCaO-SiO2, calculated adopting K2 .1=0.0017(Toop and Samis, 1962a) and ΛMO=1.00 (Duffyand Ingram, 1974b). We may note that the bulkoptical basicity of the medium is identical tothat obtainable through direct application of eq.(4.19). However, note also that the bulk basici-ty of the medium may be entirely ascribed tothe structon matrix over most part of the com-positional join (for XSiO2 >1/3). The basicitycontrol operated by the structon matrix is themore extended the more the dissolved oxide inthe binary MO-SiO2 system is basic (in theLux-Flood acceptation of the term) and thelower the polymerisation constant K2.1.

We have seen that in solving the various massbalances for different values of the polymerisa-tion constant, Toop and Samis (1962a,b) showedthat the Fincham and Richardson assumption of apurely anionic contribution to the Gibbs free en-ergy of mixing in binaries MO-SiO2 (with MOcompletely dissociated basic oxide) holds true.

It must be noted that the Toop-Samis modelaccounts for (negative) chemical interactions on-ly and is not able to reproduce the experimental-ly observed solvi at high silica content even insimple systems. This implies additional excessGibbs free energy terms of mixing which are not

Fig. 2. Basicity of the medium and of the structonmatrix (ordinate right-axis) calculated along the binaryjoin CaO-SiO2 assuming ΛCaO=1 and K2.1=0.0017(Toop and Samis, 1962a) and K2.1=1 (guess value putfor comparison). Abundances of quasi-chemicalspecies of oxygen (ordinate left-axis) are shown as afunction of the molar fraction of SiO2.

Table III. Basicity of structons and basicity of the medium in the MO-SiO2 binary (MO is CaO). ΛMO=1,Kp=0.0017.

NSiO2 O ⟨0⟩ O ⟨−I⟩ O2− Λstructons Λmedium

0.000 0.000 0.000 1.000 0.739 1.0000.100 0.000 0.399 0.700 0.739 0.9050.200 0.003 0.795 0.403 0.738 0.8260.300 0.019 1.162 0.119 0.735 0.7590.400 0.211 1.178 0.011 0.700 0.7020.500 0.503 0.993 0.003 0.652 0.6520.600 0.801 0.797 0.001 0.609 0.6090.700 1.101 0.599 0.001 0.570 0.5710.800 1.400 0.400 0.000 0.536 0.5360.900 1.700 0.200 0.000 0.506 0.5061.000 2.000 0.000 0.000 0.478 0.478

593

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

accounted by the model itself, as shown by Ot-tonello (2001). These additional terms (mechan-ical strain) are much smaller than chemical inter-action, but are sufficient to open solvi at high sil-ica content (Ottonello, 2001, 2005; Ottonelloand Moretti, 2004). Nevertheless, the mechani-cal strain energy contribution is so low that eqs.(2.1) and (2.8) may be used by Ottonello et al.(2001) to infer appropriate values of the poly-merisation constant K2.1 in MO-SiO2 systemsfrom measured thermodynamic activities orGibbs free energy of mixing (fig. 3 and Ottonel-lo and Moretti, 2004).

A simple T-independent exponential rela-tionship linking the polymerisation constant K2

and the basicity moderating parameter of thedissolved cation, based on the estimates ofToop and Samis (1962a,b), Hess (1971), Reyesand Gaskell (1983), Masson et al. (1970) on bi-nary MO-SiO2 melts has been proposed by Ot-tonello et al. (2001)

(4.25)

M M ..

( . )ln K

R4 662

1 14450 997.2 1

v v= ++

=c c+ +2

(4.26)

Since, according to eq. (4.18), the Jorgensen hfunction is a generalised property, acceptingthe validity of the above discussed relationshipwhich links ∆γ and K2.1 in simple systems, theextent of polymerisation of chemically com-plex melts and glasses may be readily obtainedby a simple mass balance involving oxide con-stituents and their specific γ values (Ottonelloet al., 2001)

(4.27)

where and are respectivelyatom fraction and basicity moderating parameterof network modifiers and network formers inone mole of the multicomponent melt or slag.

We thus have a formal link between acid-base properties of the medium (expressed as a«contrast» between formers and modifier basic-ities) and polymerisation constants.

This equation represents a high T approxi-mation, polymerisation constants on single bi-naries being defined at a unique T for each bi-nary (see table 1 in Ottonello et al., 2001).More precise formulations in the multicompo-nent space are in progress, based on new T-de-pendent parameterisations of polymerisation inbinary joins (Ottonello and Moretti, 2004).

Let us furnish now more details about thecalculation of the anionic structure of the melt.

To estimate K2.1 for the various binaries,Hess (1971) adopted Temkin’s model for fusedsalts, which ascribes the thermodynamic activi-ty of the molten oxide to the activity product ofionic fractions over cationic and anionic ma-trixes, i.e.

(4.28)

where terms in brackets denote activities andterms in parentheses number of moles.

MM

M [ ] [ ]( ) ( )

a Ocations anions

OO

2v 2

v #= =+ -+ -

/ /

TXT j j+ +h hcM MX

iiv vc+ +

exp= # M

X

M.

.

K X4 662

1 1445

. , melt

i

j

T

2 1 i

j

i

j

vv +

- -

c+ +

+ +h hTc

a

l

:

E

/

/

MM ( . )

( . ) .

expK

R

4 10 3 8452

0 926

. , SiOO2 15

2v#=

=

c--

+

2

Fig. 3. Linear relationship between logarithm ofthe constant of polymerization reaction (2.1) in MO-SiO2 melts and basicity moderating parameter of thenetwork modifier Mν+. ∆γ=γMν+−γSi4+ .

594

Roberto Moretti

Since in a MO-SiO2 melt

(4.29)

and since the number of moles of O2− in themelt is related to K2.1 and NSiO2 by mass balance(eqs. (2.4), (2.5) and (2.8)), the evaluation ofaMO rests solely on the estimate of the numberof structons present in the anion matrix

(4.30)

. (4.31)

To evaluate Σstructons, Hess (1971) followedthe method devised by Flory (1953)

(4.32)

where NSi are the moles of silicon in the melt,is the number of silicon atoms in the struc-

ton of and P⟨0⟩ is the fraction of silicon bondsthat link to doubly bonded oxygens, i.e.

(4.33)

Being dependent on composition in a com-plex fashion, eq. (4.32) cannot be easily adapt-ed to multicomponent melts.

To address the problem quantitatively wemust know the acid-base behavior of each dis-solved oxide (i.e. the disproportionation between«network formers» and «network modifiers») inorder to consider the effect of mixing of bothcationic and anionic constituents over the twosulblattices of interest (the activity of the gener-ic oxide MO being now the bulk of eq. (4.27)).

To solve the problem Toop and Samis(1962a,b) proposed a «polymerisation path» ofgeneral validity, based essentially on the vis-cosity data of Bockris et al. (1955). As shownby Ottonello (1983), the polymerization path ofthe Toop-Samis model may be reconducted to

or

.PI2 O 0 O

2 O 00 =

+ -^ ^

^

h h

h

7 A

or

$=

!

structons

( ) !( ) !

NP

P P P1 1

2 24 3

x

n

Si

x x

Si

Si

0

02

0 02

1

$

- -

+o oo

=

r rr

^ ^h h<

<

F

F

/ /

M( )

( )a

O structons

O2

2

=+-

-

O

7 A/

anions O onsstruct2= +-] g/ /

M( ) cationsv /+ /

the simple form

(4.34)

where the simple power function

(4.35)

accounts for the mean number of tetrahedrallycoordinated cation per structon, P⟨−Ι⟩ is the pro-portion of singly bonded oxygen

(4.36)

and accounts for the presence of charge-bal-anced tetrahedrally coordinated cations otherthan Si (see Ottonello, 1983, for details), i.e.NT =NSi+NAl+NFeIII.

Equations (4.32) and (4.34) lead to consis-tent results, in terms of K2.1 when applied toMO-SiO2 melts. However it has been shown byOttonello (1983) that the polymerisation path inchemically complex immiscible liquid portions(Watson, 1976; Ryerson and Hess, 1978, 1980)is better represented by the exponential form

(4.37)

The amount of experimental data is at present-day large enough to allow a re-estimation of theabove parameters. Through non linear minimi-sation techniques we obtained

(4.38)

Such a form allows us to define the extension ofthe anion matrix in the Toop-Samis frameworkalong a unique polymerisation path.

The generalisations made for complex meltsthrough eqs. (4.27), (4.28), (4.34), (4.36) and(4.38), together with eq. (4.17) and the Toop-Samis equations constitute the polymeric model.

Deconvolution of the investigated systemsinto network formers and network modifiers wascarried out by (Ottonello et al., 2001) assumingamphotheric behaviour for Al2O3 and Fe2O3: i.e.Al3+ and Fe3+ are considered to have a partlyacidic behaviour. They are network formers ifcounterbalanced by basic oxides such as H2O,

( . ) .exp P2 8776 ( )#=o -.1 7165-

. )2 67-( .exp ln P5 I= -o lr

NP

O 0 O I

O I

TI =

+ - +

--

^ ^

^

h h

h

7 A

P .I

1 95=o --r

Nstructons T=

or/

595

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

Na2O, K2O and CaO, to form complexes of thetype MAl4+, MFe4+or M0.5Al4+, M0.5Fe4+ whichpolymerise as SiO4

4+ does. A completely acidicbehaviour was assigned to P5+ while Ti4+ is treat-ed as a network modifier, in agreement with newexperimental observations (see later on) and withfindings based on quantum chemistry argumen-tation applied to glass clusters (Kowada et al.,1995). A more precise definition of the Lux-Flood character of the various oxides was laterachieved by Ottonello and Moretti (2004) basedon the conversion of the Pelton and Blander(1986) quasi-chemical parameterisation of bina-ry MO-SiO2 interactions to the Hybrid Polymer-ic Model. The new classification does not sub-stantially alter the preceding observations.

On the basis of the above considerations, wemay now address the problem of reactivity ofaltervalent oxides (i.e. those oxides which dodisproportionate into different valent states andhave potentially distinct structural roles) on athermochemical basis.

5. Factors controlling the FeII/FeIII ratio in silicate melts

Since iron is the main redox buffer in natu-ral silicate melts, the treatment is specificallydeveloped for this element. Equilibrium amongdissolved iron in glasses or melts, the anion ma-trix and the gaseous phase is usually written inthe form (Johnston, 1964; Duffy, 1996)

(5.1)

However, based on what was previously stated,this form is misleading since it confuses formaloxidation numbers with formal ionic charges.Let us assume that we have spectroscopic evi-dence that ferric iron is only present in polyan-ionic complexes, and that the octahedral coordi-nation of Fe2+ observed in melts is the result ofionic couplings dictated by simple coulomb in-teractions. We will have in this case the bulkhomogeneous equilibrium

(5.2)

+Fe,e+O+( )Fe III O

O O

27

0

721

( ) ( ) ( )

( ) ( )

melt melt melt

melt melt

45 2

2+ +

- +

- -

-

.O4+Fe4,O4+Fe4 ( ) ( ) ( ) ( )melt melt melt gas3 2 2

2+ - +

obtained summing up the partial equilibria

(5.3)

(5.4)

(5.5)

(5.6)

and the corresponding heterogeneous reaction

(5.7)

Adopting the usual polymeric notation it maybe easily seen that iron reduction induces de-polymerisation of the melt structure

(5.8)

(5.9)

Let us now imagine that we have the spectro-scopic evidence that ferrous iron form in themelt or glass true octahedral complexes (in thesense of Pauling, 1960). We could write the fol-lowing homogeneous equilibria:

(5.10)

(5.11)

(5.12)

6O e ,++

+

( )

( )

Fe III O I

Fe II O O O3 0

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

45

610 2

,

-

+

- -

- -

O5 e ,++

+

( )

( )

Fe III O I

Fe II O O O25

021

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

45

610 2

,

-

+

- -

- -

O4 e ,++

+

( )

( )

Fe III O I

Fe II O O2 0

( ) ( )

( ) ( )

melt melt

melt melt

45

610

,

-- -

-

+Fe,Si O

2 .O

+

+

( )Fe III O

SiO

27

721

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

45

2 76 2

44+

- - +

-

+Fe,e+Si O

O

+

+

( )Fe III O

SiO

27

721

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

45

2 76 2

44 2+

- - - +

- -

( )Fe III O O Fe

O O

27

0

741

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

45 2

2

,+ +

+

- +

-

Fe Fee( ) ( )melt melt3 2

,++ - +

O O O27

27

0 7( ) ( ) ( )melt melt melt2

,+- -

O O21

e41

( ) ( )melt gas2

2, +- -

( )Fe III O Fe O4( ) ( ) ( )melt melt melt45 3 2

, +- + -

596

Roberto Moretti

or the corresponding heterogeneous reactions

(5.13)

(5.14)

(5.15)

The above notations emphasise the fact that wemust now produce additional free oxygen ionsO2− by polymerisation steps

(5.16)

(5.17)

The iron reduction may be regarded as an inter-nally buffered auto catalytic reaction: produc-tion of free electrons through the normal oxy-gen electrode favours decomposition of ferriciron clusters, making iron ions available to re-duction by free electrons. This is true regardlessof the fact that octahedral iron clusters may bepresent as simple ionic couplings (eqs. (5.2) to(5.4)) or as true complexes (eqs. (5.11) to(5.17)). In both instances, the whole process isbuffered by the availability of free oxygen inthe melt, which ceases at a critical acidity lim-it, due to polymeric equilibria.

The fact that nominal O2− may appear eitheras reactants or products stresses how mislead-ing it could be to conceive the Le Chatelierprinciple in terms of the simple mass action ef-fect of oxide ions. As noted by Douglas et al.(1966) the altervalent equilibria in melts and

.O+O2+ Si( )Fe II O

+ ,

,

( )Fe III O SiO5

41

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

45

44

610

76

2

- -

- -2

O+OSi+

+

( )Fe II O

,

,

( )Fe III O SiO5 e

25

21

( ) ( )

( ) ( ) ( )

melt melt

melt melt melt

45

44

610

76 2

+- - -

- - -2

+( )Fe II O,O6+

O+

( )

.

Fe III O I

21

041

( ) ( ) ( )

( ) ( )

melt melt melt

melt gas

45

610

2

-

+

- -

O3+2-O

O5 ,+

+

( )

( )

Fe III O I

Fe II O O O25

041

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

45

610

2,

-

+

-

-

4O ,++

+

( )

( )

Fe III O I O

Fe II O O O

21

2 014

( ) ( )

( ) ( ) ( )

melt melt

melt melt gas

45 2

610

2,

-

+

- -

-

glasses may be generalised as follows:

(5.18)

Equilibria such as those proposed by Johnston(1964); or Duffy (1996), (eq. (4.38)) and appar-ently violating the Le Chatelier principle de-mand . If , suchas in the Holmquist (1966) formulation

(5.19)

there is no paradox, and when the equilibrium is written in a simple stoichio-metric form (i.e. no oxide ions involved)

(5.20)

In the above equations it is assumed that ferriciron behaves essentially as a network former,although we know that in chemically complexmelts or glasses the structural behavior of FeIII

is a complex function of both bulk compositionand FeIII concentration.

This simply means that the above equation,written for macroscopic melt components, mustbe coupled with homogeneous speciation reac-tions defining the structural state of iron inmelts and glasses (which is a function of bulkcomposition and P, T conditions, as shown byexperimental evidence). Mössbauer observa-tions on quenched melts (Mysen, 1990, and ref-erences therein) indicate that when FeIII exceedsFeII (FeIII/ΣFe≥0.3) ferric iron is only present intetrahedral clusters; for 0.5≥FeIII/ΣFe≥0.3 bothtetrahedrally and octahedrally coordinated FeIII

is present and for FeIII/ΣFe≤0.5 tetrahedralclusters are absent. Virgo and Mysen (1985) onthe basis of spectroscopic and magnetic datasuggested that coexistence of FeIII and FeII leadsto formation of units stoichiometrically resem-bling Fe3O4 and composed of 0.33 tetrahedrallycoordinated FeIII, 0.33 octahedrally coordinatedFeIII and 0.33 octahedrally coordinated FeII (Vir-go and Mysen, 1985). Experimental data on melt

.FeO O FeO41

.2 1 5,+

( / )b a m 2+=

( )Fe III O I Fe O

O

4 4 6( ) ( ) ( )

( )

melt melt melt

gas

22 2

2

,- + +

+

- + -

( / )b a m 22 +( / )b a m 21 +

( ) ( )

( )

R nm

R n m

a bm

O4

O O

2O

ba 2

2

,+ + +

+ - + -: D

597

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

densities at various T, f O2 conditions seem toconfirm that FeIII is essentially present in tetrahe-dral coordination, although some discrepanciesin the partial molar volumes of molten Fe2O3

based on various experiments could be ascribedto the limited presence of a higher coordinationstate in some of the investigated materials (seeBottinga et al., 1983; Dingwell et al., 1988, andreferences therein).

The fact that FeIII could partly exist in octa-hedral coordination with oxygen may be as-cribed to the partial reaction

(5.21)

The above equilibria show us that the nature ofbonding between central cations and ligandsmust be attentively evaluated before reachingunwarranted conclusions.

Although the compositional effect differs inthe various investigated systems ( f O2 beingheld constant), Duffy (1992, 1996) has shownthat the basicity effect is identical for all binarysystems whenever optical basicity is introducedfor the compositional axis. Duffy (1992) pro-posed, at T=1400°C, the following semiloga-rithmic relationship between the observed re-dox mass ratio of iron and optical basicity

(5.22)

Although this relationship disregards the effectof temperature on the extent of the polymerisa-tion reaction, it is sufficiently accurate to allowcomparative estimates on widely differing sys-tems.

Nevertheless, this kind of equation cannotbe usefully employed on an empirical basis, notbecause of the chosen parametric scale (i.e. op-tical basicity) but rather because of the adoptedfunctional form. Figure 4 shows that Duffy’s re-worked expression (see figure) does not reach agood accuracy in reproducing the 1400°C dataavailable from the literature.

Following Fraser (1975, 1977), Ottonello et al. (2001) assumed that Fe2O3 behaves as anamphoteric oxide in the Lux-Flood acid-base

. . .oglFeFe

3 2 6 5III

II

= - Λb l

( ) ( )

.

Fe III O O I Fe III O

O O

5

25

021

( ) ( )

( ) ( )

melt melt

melt melt

45

69

2

,+ - +

+ +

- -

-

acceptation. Its double dissociation in the melt(or glass) may be reconducted to the followinghomogeneous reactions:

(5.23)

(5.24)

For ferrous iron on the other hand only a basicdissociation is plausible, i.e.

(5.25)

Adopting the Temkin model for ionic salts(Temkin, 1945) and assuming the Fe(III)O⟨−I⟩2

clusters to mix ideally over the structon matrixand the Fe3+, Fe2+ cations to mix ideally over thecation matrix, after some passages one arrivesat (Ottonello et al., 2001)

(5.26)

which is analogous to eq. (14) in Fraser (1975),

K a

K a K

a K

FeFe 1

anions cations

cations

./

./

./

/.

III

II

O

O

O

5 201 4

5 231 2 2

5 241 2

1 25 25

2

2

2

#

#

=

+-

-

b l

/ //

.FeO Fe O( ) ( ) ( )melt melt melt2 2

, ++ -

.Fe O Fe O2 3( ) ( ) ( )melt melt melt2 33 2

, ++ -

( )Fe O O Fe III O I2( ) ( ) ( )melt melt melt2 32

2,+ --

Fig. 4. Experimental ferrous to ferric iron ratio ver-sus summation of oxide optical basicities. Data fromvarious sources, also included in the database of Ot-tonello et al. (2001), show the need for a more rigor-ous approach to the functional form based on opticalbasicity.

598

Roberto Moretti

although here Σanions replaces, more correctly,Σstructons, since free anions such as O2−, CO3

2−,S2−, SO4

2− etc., are present in the anionic matrix,besides polymeric species.

Equation (5.26) implies that, due to dispro-portionation of trivalent iron between thecationic and anionic matrixes, we cannot expectthe ratio of rational activity coefficients ofFeO1.5 and FeO (second term on the right) to be1. In fact the first term on the right side of eq.(5.26) represents aFeO/aFeO1.5 (see eq. (5.20)),whereas the second term represents γFeO1.5/γFeO.

If we compare eq. (5.26) with the function-al form (5.22) we would deduce that the inter-cept term in the equation of Duffy (1992) corre-sponds to the first term on the right in eq.(5.26), whilst the slope coefficient embodies theremaining structural parameters.

Since the polymeric model allows the calcu-lation of the extension of the structon and thecation matrixes, Ottonello et al. (2001) conve-niently solved eq. (5.26) on thermochemicalgrounds, based on the plethora of experimentaldata concerning ferrous iron solubility and ironredox ratios in melts (and/or glasses) equilibrat-ed at known T and f O2 conditions. Neverthe-less, this was done only for nominally anhy-drous melts synthesised at 1 bar pressure. Onthis basis we can also investigate the depend-ence of iron oxidation state under hydrous con-ditions and therefore at higher pressure. It may

be here anticipated that the way iron dispropor-tionates also depends on water speciation inmelts, as a consequence of the effect that watercarries on polymerisation and then basicity interms of free oxygen ions activity.

6. Iron oxidation state in hydrous alumino-silicate melts: a preliminary modelextension

Water is commonly perceived as the mostbasic oxide: its presence in the natural systemsundergoing melting dramatically affects thesolidus temperature and the composition of theincipient melting liquid. Nevertheless, its basic-ity (in the Lux-Flood sense of the term) seemsto be over rated, ΛH2O being very close to ΛSiO2

(table I). Therefore, it is of primary interest totest the model reproducibility at pressure andinvestigate how both polymerisation and theferric to ferrous iron ratio in melts are affected.The still few data at present available in litera-ture also involve the presence of water. Here Ipresent an exploratory extension of the 1-baranhydrous model of Ottonello et al. (2001).

First of all, it is necessary to introduce theeffect of pressure on the equilibrium constantsfor reactions (5.20) and ((5.23) to (5.25)). Thisis easily done by accounting for volume termsof both ionic species and macroscopic compo-

Table IV. Molar volumes employed for macroscopic and ionic species involved in reactions (5.20), ((5.23) to(5.25)), (6.3) and (6.12). For ionic species I also listed the the adopted ionic radius.

Molar Volume @ 298.15 K Ionic radius Reference298.15 K (cc/mol) (Å)

FeO 9.64 - Lange (1994)Fe2O3 29.63 - Lange (1994)Fe2+ 0.90 0.78 Shannon (1976)Fe3+ 0.51 0.645 Shannon (1976)O2− 6.92 1.40 Shannon (1976)

FeO2− 75.99 (*) 3.29 (**) Shannon (1976)

OH− 6.92 1.40 Shannon (1976)OH 6.92 1.40 Shannon (1976)H+ 0 0 This work

(*) See text for details.(**) The value here adopted represents the summation of the radius of four-folded ferric iron (0.49 Å) and thediameter of an oxide ion O2−.

599

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

nents. This procedure is consistent with theTemkin approach inherent in the Toop-Samismodel, which demands scaling of the activitiesof liquid components from the standard state ofpure melt components at P and T of interest tothe standard state of completely dissociatedionic component.

The equilibrium constant for reaction(5.20), involving the macroscopic oxides FeOand FeO1.5 is then recomputed as

(6.1)

where

Molar volumes of melt phases, as well asisothermal compressibilities and isobaric ther-mal expansivities have been taken by Lange(1994).

For reactions (5.23) to (5.25) I still considerthe Lange (1994) data for macroscopic oxidesFe2O3 and FeO, whereas volume of ionicspecies are calculated on the basis of ionic radiiof Shannon (1976) assuming that the ‘effectivemolar volume’ of each ionic species equals thatof a mole of spherical molecules each charac-terised by its appropriate Shannon radius. Notethat for FeO2

− species I calculated the molarvolume from that of a sphere of radius

. Since the spherical volumeassociated with this radius should represent, at afirst approximation, the ‘effective volume’ of theFeIIIO4

5− complex, I subtracted the volume of twooxide ions O2− in order to obtain the ‘effectivevolume’ of the FeO2

− compound. This means thatI assume the volume change reaction for the as-sociation reaction to bezero.

Values of employed volumes are listed intable IV.

In our calculation the ionic radius for eachionic species is fixed for all temperatures (i.e.

FeO 2O FeO22

45

,+- - -

( / )r r1 2 ( )O Fe IV2 3+- +

( ) .V dP V V dP, ,melt

P

FeO melt FeO melt

P

1 1

.1 5= -∆ c c c# #

+ln K -

,O gas

= V dPmelt∆

+

ln KRT

RTV dP

1

41

. ( , ) . ( , )P T T

P

P

5 20 5 20 1

1

1

2

c

c

#

#

thermal expansivity is zero), therefore I recal-culated the thermal expansivity of macroscopicoxides at 298.15 K, obtaining that the variationin the reaction volume change is a constant atany temperature.

The model is now ready to investigate therole played by water in the ferric to ferrous ironratio of melts. Data in the literature disclosesome controversies about the oxidation state ofiron under hydrous conditions. FollowingMoore et al. (1995), water does not affect theferric to ferrous iron ratio, which is a record ofother processes having imposed the oxygen fu-gacity.

According to Baker and Rutherford (1996)and Gaillard et al. (2001) water does affect theferric to ferrous ratio. In some region of the P-T-f O2 space it may cause either a decrease or anincrease of oxidation. For example water-bear-ing rhyolitic melts have higher ferric to ferrousratio than anhydrous melts of the same compo-sition (Baker and Rutherford, 1996). The sameoccurs in metaluminous melts, but at highertemperatures (T>900°C) and around NNO,whereas in peralkaline melts such an increase isobserved at high T (Baker and Rutherford,1996). Gaillard et al. (2001) generalise this per-spective, observing an increase in the ferric toferrous ratio of iron in hydrous melts at log f O2<<NNO+1.5 for all studies compositions, meta-luminous and rhyolitic melts and natural pera-luminous and peralkaline obsidians. Howeverthey find that above NNO+1.5 water does nolonger affects the ferric to ferrous iron ratio,controlled by the anhydrous composition inagreement with Moore et al. (1995). Finally,Wilke et al. (2002) investigated tonalitic meltsat 850°C, whose ferric to ferrous iron ratioshowed a marked decrease with respect to thevalues computed through the Kress andCarmichael (1991) and then based on the anhy-drous composition. Nevertheless, this effect ismainly ascribed to the inaccurate calibration ofthe Kress-Carmichael equation at low T ratherthan to the water content of melts.

It is important to remark that Wilke et al.(2002) and Gaillard et al. (2001) did not ob-serve any effect of the quench rate on the ferricto ferrous ratio of investigated melts. This con-clusion cannot be obviously extended to the re-

600

Roberto Moretti

maining data here discussed, so quench-rate ef-fects may still represent an important source ofuncertainty.

Moreover, the dependencies of the ferric toferrous iron ration on water amount are con-trasting: Baker and Rutherford (1996) find dif-ferent explanations about the role of hydroxylgroups (Baker and Rutherford, 1996), whosecomplexity is enriched by the T dependency ofwater speciation (between OH− and H2O for allthe authors observing change on the iron oxida-tion state with the water content).

These experimental results are likely toshow only apparent controversies. I then con-sidered the database generated by these authors(119 compositions) in order to expand the mod-el of Ottonello et al. (2001). It is clear that theparameterisation of the ferric to ferrous ratiomust consider the «impact» of water on meltacid-base properties and then polymerisation.In order to match this goal in the widest avail-able P-T-X range, I also considered thirty-seven1 bar compositions (from Fudali, 1965; andShibata, 1967) showing some water content (upto 0.66 wt%) and which were already account-ed for by Ottonello et al. (2001).

Consistent with the Temkin formalism ofcomplete dissociation of component oxides andon the basis of that «common perception»which requires water to behave as a strongmodifier (being a strong basic oxide in the Lux-Flood notation), I first considered water as un-dergoing uniquely a basic dissociation

(6.2)

Let us recall that this kind of dissociation is ac-companied by other homogeneous reactions inthe melt phase (Fraser, 1975; Ottonello, 1997),i.e. the association to NBOs’ originating stronghydrogen bonding, and the polymerisation re-action (6.4)

(6.3)

(6.4)

The summation of eqs. (6.2), (6.3) and (6.4) gives

(6.5)H O O 2OH20,+

.O O O22 0,+- -

H O OH2 2 2,++ -

.H O H O222

, ++ -

which well displays the depolymerising effectof water and which has been first discussed byFraser (1975, 1977).

According to the Temkin notation of com-plete dissociation, implicit in the Toop-Samisapproach, all the protons were considered tocontribute in defining the basicity of modifiers(i.e. the basicity of the cationic matrix). Thepolymeric constant and then initial (O−) valueswere computed assuming only the occurrenceof reaction (6.2), without any concomitant equi-librium (i.e. eq. (6.3)) leading to bonding withNBO’s. The latter mechanism was consideredas a subsequent step involving depletion of bothinitial O− and H+ to form OH. The followingmass balances must be satisfied:

(6.6)

(6.7)

The equilibrium constant for reaction (6.3) maybe expressed as

(6.8)

With some passages, substitution of eqs. (6.6)and ((6.7) to (6.8)) gives the following quadrat-ic equation:

(6.9)

The equation above has two possible roots, butonly the following one provides solutionsfalling between initial O− and initial H+, andthen physically meaningful

(6.10)

(O2−), (O0), Σstructons were then recalculatedon the basis of the new O− values. The numberof newly formed OH groups, nOH, was then in-cluded in the quantity Σanions.

n$n$K4 $-

nK n K n

K

K n K n

cations

2

cations

/ /

/

/ /

. .

.

. . .

OH

1 2HIN 1 2

OIN

1 2

1 2HIN 1 2

OIN 2

HIN

OIN

6 3 6 3

6 3

6 3 6 3 6 3

$ $

$ $

=+ + +

- + +

+ -

+ - + -_ i

/

/

.

K n K n K n

n K n n

cations

0

/ / /

/

. . .

.

1 2OH2 1 2

HIN 1 2

OIN

OH1 2

HIN

OIN

6 3 6 3 6 3

6 3

$ $ $ $

$ $ $

- + +

+ =

+ -

+ -

_ i/

.K nn

ncations

/.

1 2

O

OH

H6 3 $=

- +

/

.n n nH HIN

OH= -+ +

n n nO OHOIN= -- -

601

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

Furthermore, we should also consider thatthe theory, based on the Lux-Flood formalism,gives us an alternative to be evaluated: the am-photeric behavior of water, i.e. the existence ofan acidic dissociation, as testified by its rela-tively low value of optical basicity. The follow-ing reaction:

(6.11)

was first proposed by Fraser (1975). Moreoverthe existence of free OH− has recently been re-ported by Xue and Kanzaky (2003). Reaction(6.11) is actually that normally invoked in liter-ature to explain water dissolution in aluminosil-icate melts. Nevertheless, in the literature it isnot regarded as an acidic dissolution mecha-nism, neglecting the fact that it leads to meltpolymerisation because of the consumption offree oxygens.

I then introduced in the model the differencebetween reaction (6.11) and reaction (6.2), i.e.

(6.12)

whose equilibrium constant may be written as

(6.13)

This equation simply recognises the existenceof two dissolved species of water in melts, i.e.OH− and H+, consistently with the Temkin for-malism and the Lux-Flood notation for oxidesolvents.

I therefore by-pass the problem of determin-ing the activity of water in melts as well as inthe fluid phase, a problem which would beposed by solving eqs. (6.2) and (6.11) separate-ly or by solving their algebraic sum. The systemof equations is simply solved through addition-al mass balance on water

(6.14)

and the equilibrium constant for water specia-tion reaction (6.12). Equation (6.10) partitionsthe initial water amount, so that K2.1, polymerisation

is no more defined on the total analytical watercontent.

n n n2HIN

OH H O2$+ =+ -

.K nn

n n

cations. TOT

O

OH

H OH6 12

2$=

--

-

+ -

/

H O OH2,++ - -

H O O OH222,+ - -

Regression on available experimental datais performed through non-linear minimisationtechniques based on steepest descent and gradi-ent migration methods (James and Roos, 1977)on both K6.3

1/2 and K6.12. Equilibrium constantsvalues and statistics for the extended iron mod-el are given in table V, whereas reproducibilitymay be appreciated in fig. 5. It is worth remark-ing that the T dependence obtained for equilib-rium (6.12) shows that this reaction becomesmore important at higher T. On the other hand,reaction (6.3) is independent of temperature(the entropic term of the arrhenian dependence

Fig. 5. Reproduciblity (calculated versus experi-mental) of the extended iron oxidation state model.Anhydrous and hydrous datasets are distinguished.The whole database consists of 608 compositions.

Table V. Equilibrium constants for water speciationmechanisms and model statistics.

logK6.12 1.835 – 1304.65/T1/2(logK6.3) –1.335Number of hydrous 120compositionsNumber of all compositions 608(anhydrous+hydrous)Mean error (hydrous dataset) 0.277Standard error 0.357(hydrous dataset)Mean error (whole dataset) 0.187Standard error (whole dataset) 0.264

602

Roberto Moretti

describes the equilibrium constant) and left-ward shifted.

The effect of pressure was neglected for re-actions involving water species as the volumeassociated with H+ was assumed to be zero, sothat VO2−=VOH−=VOH.

The comparatively low precision of the hy-drous dataset with respect to the anhydrous oneprobably reflects model approximations, similar-ly to what was described for sulphur speciation inMoretti and Ottonello (2003a). In particular, amore general model based on the assessment ofwater solubility and speciation should require theFlood-Grjotheim treatment (Flood and Gr-jotheim, 1952) opportunely implemented and al-ready used for sulphur species (Moretti, 2002;Moretti and Ottonello, 2003b). Moreover, moreaccurate data for molar partial volumes are need-ed, in particular for iron oxides. In principle, wecould improve the precision of our model by re-fining on volume reactions, but I prefer to em-ploy independent experimental volume data. Apossible source of error is also related to the T-in-dependent computation of the polymeric exten-sion of the anionic matrix: a more general, i.e. T-dependent (Ottonello and Moretti, 2004, andwork in progress) polymerisation equation wouldrepresent a step forward in the continuos attemptto ameliorate model results and applications.

Figure 6a,b shows a comparison between: i)equation (5.26), accounting for water specia-tion and volume terms; ii) equation (5.26) un-der the 1 bar approximation and without con-sidering eqs. (6.3) and (6.12); and iii) the Kressand Carmichael (1991) empirical model.

It is evident that both eq. (5.26) under the 1bar approximation and the Kress-Carmichael al-gorithm do not work well in reproducing the ob-served FeII/FeIII ratio, which is largely underes-timated in the first case.

It is important to remark that the fact that we«identify» three water-derived species in melts(H+ cations, OH− free anions and, to a very mi-nor extent, OH groups terminating polymericunits, which can be then ascribed to T-OH link-ages) is quite consistent with NMR findings(Kohn et al., 1989; Schmidt, 2001; Xue andKanzaki, 2003). Intuitively, it would seem thattheir combination reproduces the water specia-tion – and solubility – observed in melts, simi-

larly to what was argued by Liu et al. (2002).Nevertheless these arguments cannot be pushedfurther and are purely qualitative: the modelhere developed is not aimed at reproducing thespeciation observed via FTIR or NMR sincemodel computations are based on a particularstandard state (that of completely dissociatedcomponent) which is introduced to describe theacid-base properties of melts and not the struc-tural units detected by spectroscopic tools. Forexample, the existence of equilibrium (6.2) and(6.11) (and hence equilibrium (6.12)) implies in-complete dissociation of the water component

Fig. 6a,b. Model reproducibility of the hydrousdatasets following different approaches (see text). Inpart a) of the figures data from various sources havebeen distinguished. H2O-unsaturated data from Bak-er and Rutherford (1996) were not considered.

a

b

603

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

and therefore the presence of molecular water.The existence of this species is not ruled out bythe present model, but calculations need nottreat it to solve chemical interactions of interestwhenever the Temkin standard state is applied.

Model generated distributions of (O−), (O0).(O2−), nOH, nOH−, nH+ are plotted in fig. 7a,b forthe system Na5-4xAlxSi3x (Al/Si =1/3) contain-ing an arbitrary amount of water (6 wt% in thewhole compositional range) at 900°C. We seethat H+ and OH− are always the predominantwater derived species in melts, whereas OH aresubordinated. In particular, abundances of OH−

anions and H+ cations are inversely related, ob-taining similar values at both low and high alu-mina contents. The abundance of T-OH groupsfollows the same trend of H+ cations, althoughmuch more smoothed. A slight increase in theconcentration of free oxygen (O2−) is computedfor compositions with alumina content largerthan that of albite (X=1).

Finally, it is worth remarking that the appre-ciable occurrence of both eqs. (6.2) and (6.11)suggests a strong similarity with water behav-iour in aqueous phase.

7. Conclusions and perspectives

The superiority of polymeric models in de-picting silicte melts and slags reactivity with re-

spect to other conceptual approaches is linkedto the following facts:

i) It is well recognised that «regular mix-ture» models fail to reproduce the Gibbs freeenergy of mixing of silicate melts. Minima inthe Gibbs free energy of mixing are badly allo-cated and badly conformed in the chemicalspace of interest. For heterogeneous equilibria(solid-liquid or liquid-gas in multicomponentsystems) this problem is almost ineffectivesince internal consistency is achieved with ex-tended databases encompassing model devia-tions through adjustable interaction parameters.

ii) The arbitrary deconvolution of chemi-cally complex melts into fictive components isa path-dependent process eventually complicat-ed by charge-balance considerations wheneveramphotheric oxides are involved (this applies toiron and other transitional elements in slags andnatural melts).

iii) Preliminary attempts to parameterise thebulk polymerisation proved satisfactory in de-ciphering the complex effect of the bulk Lux-Flood acidity of the system on the oxidationstate of iron in multicomponent melts andglasses (Ottonello et al., 2001). The Gibbs freeenergy of mixing of simple binaries MO-SiO2

and of ternary systems (CaO-FeO-SiO2) wassuccessfully simulated (Ottonello, 2001).

iv) Polymeric models carry a minimal set ofstructural information which can be employed

a b

Fig. 7a,b. Relative proportions of oxygens of the Fincham-Richardson (1954) notation (a) plotted against thecompositional parameter in the binary join Na5-4xAlxSi3xO8. Water-derived species dissolved in the same com-positional range have been plotted in b). Note the comparable amount of OH and OH− for the albitic composi-tion (x=1).

604

Roberto Moretti

for the study of partitioning of elements, vis-cosity and – plausibly – other transport proper-ties of silicate melts such as thermal and electri-cal conductivity.

The adopted polymeric parameterisation isbased on three main previous observations:

1) The basicity of a complex aprotic medi-um such as a silicate melt or glass is conve-niently represented by the «optical basicity»,arising from the nephelauxetic effect inducedon p-block metals by the ligand field (Duffyand Ingram, 1971, 1973, 1974a,b, 1976; Duffyand Grant, 1975).

2) Optical basicity is related to atomisticproperties of the dissolved oxide components inthe melts or glass, such as the Pauling andSanderson electronegativities (Pauling, 1960;Sanderson, 1967) and the fractional ionic charac-ter of the bond (Pauling, 1960; Phillips, 1970).

3) Bulk optical basicity of molten silicates,or glasses can be split into two distinct contri-butions, the basicity of the dissolved basic ox-ides and the basicity of the polymeric units (or«structon matrix» in the sense of Fraser,1975a,b, 1977). While the optical basicity ef-fect induced by the dissolved oxides varieswidely with the type of oxide component, theoptical basicity effect ascribable to the structonmatrix is virtually unaffected by composition,at parity of silica content in the system, and isdominant at high silica contents.

An exploratory application to the modellingof the oxidation state of iron shows that it ispossible to extend the model of Ottonello et al.(2001) to hydrous aluminosilicate melts. Thisrequires the introduction of volume terms forboth ionic species and macroscopic compo-nents, together with equilibria relevant to waterspeciation. These preliminary results are quitesatisfactory and promising, especially consider-ing that the polymerisation constant employedrepresents the high-T approximation (Ottonelloand Moretti, 2004) and that I adopted experi-mental values for molar volumes, whereasmore accurate partial molar volumes should beemployed. In particular, data are well explainedas long as both basic and acidic dissociations ofwater are considered.

A further slight amelioration to model preci-sion may be introduced by accounting for a sub-

sequent process of association to NBO’s, thatmay be seen at first approximation as character-istic of strongly hydrogen-bonded T-OH groups.The fact that water also undergoes an acidic dis-sociation, originating free anions OH−, agreeswith the recent findings of Xue and Kanzaki(2001, 2003), based on density functional theory,inferring the existence of NaOH groups in alka-line silicate glasses and confirms the predictionof Fraser (Fraser, 1975, 2003; and this issue).

It is worth stressing that the reliability ofcalibrated equilibrium constants involving ion-ic species of water and iron is subjected to i) thequality and P-T-X extension of the referencedatabase; and to ii) accurate estimates of reac-tion volumes of iron species and of reactions inwhich they are involved. Moreover, it must beclear that the present modelling does not haveany straight implication about the geometry ofcoordination polyhedra in silicate melts, not re-quired for the purposes of understanding poly-merisation and the acid-base behaviour of in-vestigated species. Therefore, ionic species de-picted by the model are not necessarily relatedto structural units that can be identified bymeans of current spectroscopic tools.

In the light of these results, some future ac-tivity may be here planned, both experimentaland theoretical. Some research lines may beproposed and followed contemporaneously tosolve accurately, the mixing properties of sili-cate melts:

i) Experimental – in situ measurement ofoptical basicity (nephelaxeutic parameter) at Tand P.

ii) Experimental – XPS measurement offree oxygen (O2−) in silicate melts coupled tothe Toop-Samis modelling of silicate melts (seenext point).

iii) Theoretical – application of the hybridmodel of Ottonello (2001) to the conformationof liquidus in multicomponent systems, follow-ing the guidelines of the Flood and Grjotheimtreatment for the calculation of chemical inter-actions coupled to strain energy modelling.

iv) Theoretical – by applying quantum-me-chanical codes to simple binaries and ternaries;in order to better assess the nature of nephelaux-etic effect in ligand field-related spectroscopicobservations.

605

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

The first task has the objective of improvingthe Toop-Samis model, by translating the T de-pendence of nephelaxeutic parameters intopolymerisation constants of the type of eq.(4.27). As required by the second task, this mayalso be done through XPS measurements ofoxygen species, which coupled to predictionsof the Fincham-Richardson approach allow athorough assessment of polymerisation in melts(Park and Rhee, 2001). The third task has theobjective of deciphering the contribution givenby the dissociation of every component inchemical systems of increasing complexity.First we should reconstruct the binary SiO2-Al2O3 and then study ternary fields MO-Al2O3-SiO2. With the introduction of alumina it is im-portant to investigate the effect of entropic ef-fects, because of the similitude of acid-baseproperties with silica. Navrotsky (1994) point-ed out that in this binary the Al3+ cation isforced to occupy the octahedral site. Entropicterms, arising from a «competitive» effect ofAl2O3 and SiO2 upon the polymerisation arethen expected to come out. Entropic termsshould also be much more evident in the pres-ence of alkalies in the system, mainly becauseof the charge compensation of the tetrahedralaluminum. The effects of non-random mixingof some network modifier oxides like Na2O andK2O must be carefully evaluated. Moreover, asystematic comparison, while creating the ther-modynamic database, will allow us to furtherrefine nephelauxetic parameters and their de-pendence upon intensive variables, especiallyin terms of temperature. Finally, we should alsoconsider the mechanical strain energy contribu-tion to the bulk free energy of mixing, sincesuch a term explains the observed solvi experi-mentally determined in SiO2 rich ranges of bi-nary systems. As shown by Ottonello andMoretti (2004) the plethora of thermodynamicdata emerging from the metallurgical commu-nity is, to this purpose, of invaluable help.Some queries may be addressed to experimen-talists, such as coupling optical basicity meas-urements with spectroscopic measurements onthe Rydberg’s and electron transfer emissionlines of 3d chromophores. This would allow usto assess better the differential nephelauxeticeffects and the structural state of complexes.

The fourth research line is devoted to a bettercomprehension of model clusters and complex-es which characterise the speciation state of sil-icate melts. A feasibility study for the adoptionof parallel computing techniques has to be car-ried out. Semi-empirical methods, such asHuckel-MO, have to be ruled out as they needa large amount of experimental data, the consis-tency of which is often doubtful.

All the considerations here reported are pre-liminary to the set-up of an ambitious generalthermochemical simulator able to depict theevolution of a complex (but essentially aprotic)system. Given such a general polymeric model,we can promote on its grounds thorough studiesof water solubility (as well as any othervolatile), through recalculation of equilibriumconstants for both eqs. (6.2) and (6.11).

For our scientific community final applica-tions will concern the study of the degassing ofactive volcanoes, the dynamics of magma flowand eruption, the interpretation of glass inclusionand plume composition analyses. Results will bealso valuable for material scientists devoted tothe physical chemistry of oxide systems.

Acknowledgements

I wish to thank Giulio Ottonello for hishelpful comments to a preliminary version ofthis paper, and also for his continuous encour-agement during recent years. The manuscriptbenefited of reviews by Don Fraser and MaxWilke. Mike Carroll is acknowledged for edito-rial handling. This work was carried out withthe financial support of Regione Campania,L.R. 5/2002 grant for basic research.

REFERENCES

BAKER, L.L. and M.J. RUTHERFORD (1996): The effect ofdissolved water on the oxidation of silicic melts,Geochim. Cosmochim. Acta, 60, 2179-2187.

BOCKRIS, J.O’M. and G.W. MELLORS (1956): Electric con-ductance in liquid lead silicates and borates, J. Phys.Chem., 60, 1321-1328.

BOCKRIS J.O’M., J.A. KITCHENER and A.E. DAVIES (1952a):Electric transport in liquid silicates, Trans. FaradaySoc., 48, 536-548.

606

Roberto Moretti

BOCKRIS, J.O’M., J.A. KITCHENER, S. IGNATOWIVZ and J.W.TOMLINSON (1952b): The electrical condctivity of sili-cate melts: systems containing Ca, Mn, Al, Discuss.Faraday Soc., 4, 281-286.

BOCKRIS, J.O’M., J.D. MACKENZIE and J.A. KITCHENER

(1955): Viscous flow in SiO2 and binary liquid sili-cates, Trans. Faraday Soc., 51, 1734-1748.

BOTTINGA, Y., P. RICHET and D. WEILL (1983): Calculationof the density and thermal expansion coefficient of sil-icate liquids, Bull. Mineral., 106, 129-138.

BOWEN, N.L. (1928): The Evolution of Igneous Rocks(Princeton University Press).

DINGWELL, D.B. and M. BREARLEY (1988): Melt densitiesin the CaO-FeO-Fe2O3-SiO2 system and the composi-tional dependence of the partial molar volume of ferriciron in silicate melts, Geoochim. Cosmochim. Acta, 52,2815-2825.

DINGWELL, D.B., M. BREARLEY and J.E. Jr. DICKINSON

(1988): Melt densities in the Na2O-FeO-Fe2O3-SiO2 sys-tem and the partial molar volume of tetrahedrally-coor-dinated ferric iron in silicate melts, Geochim. Cos-mochim. Acta, 52, 2467-2475.

DOUGLAS, R.W., P. NATH and A. PAUL (1966): Authors’ re-ply to the above comments, Phys. Chem. Glasses, 7,213-215.

DUFFY, J.A. (1992): A review of optical basicity and its ap-plications to oxidic systems, Geochim. Cosmochim.Acta, 57, 3961-3970.

DUFFY, J.A. (1996): Redox equilibria in glass, J. Non-Cryst.Solids, 196, 45-50.

DUFFY, J.A. and R.J. GRANT (1975): Effect of temperatureon optical basicity in the sodium oxide-boric oxideglass system, J. Phys. Chem., 79, 2780-2784.

DUFFY, J.A. and M.D. INGRAM (1971): Establishment of anoptical scale for Lewis basicity in inorganic oxiacids,molten salts and glasses, J. Am. Ceram. Soc., 93, 6448-6454.

DUFFY, J.A. and M.D. INGRAM (1973): Nephelauxetic effectand Pauling electronegativity, J. Chem. Soc. Chem.Comm., 17, 635-636.

DUFFY, J.A. and M.D. INGRAM (1974a): Optical basicity-IV:Influence of electronegativity on the Lewis basicityand solvent properties of molten oxianion salts andglasses, J. Inorg. Nucl. Chem., 17, 1203-1206.

DUFFY, J.A. and M.D. INGRAM (1974b): Ultraviolet spectraof Pb2+ and Bi3+ in glasses, Phys. Chem. Glasses, 15,34-35.

DUFFY, J.A. and M.D. INGRAM (1976): An interpretation ofglass chemistry in terms of the optical basicity concept,J. Non-Cryst. Solids, 21, 373-410.

FINCHAM, C.J.B. and F.D. RICHARDSON (1954): The behav-iour of sulphur in silicate and aluminate melts, Proc. R.Soc. London, Ser. A, 223, 40-62.

FLOOD, H. and T. FÖRLAND (1947): The acidic and basicproperties of oxides. Acta Chem. Scand., 1, 952-1005.

FLOOD, H. and T. GRJOTHEIM (1952): Thermodynamic calcu-lation of slag equilibria, J. Iron Steel Inst., 171, 64-80.

FLORY, P.J. (1953): Principles of Polymer Chemistry (Cor-nell University Press, Ithaca-New York).

FRASER, D.G. (1975): Activities of trace elements in silicatemelts. Geochim. Cosmochim. Acta, 39, 1525-1530.

FRASER, D.G. (1977): Thermodynamic properties of silicatemelts, in Thermodynamics in Geology, edited by F.G.

FRASER (D. Reidel Pub. Co., Dortrecht-Holland). FRASER, D.G. (2003): Acid-base properties, structons and the

thermodynamic properties of silicate melts, Geochim.Cosmochim. Acta, 67 (suppl. to no. 18), abstr. 103.

FUDALI, R.F. (1965): Oxygen fugacities of basaltic and an-desitic magmas, Geochim. Cosmochim. Acta, 29, 1063-1075.

GAILLARD, F., B. SCAILLET, M. PICHAVANT and J.-M. BÉNY

(2001): The effect of water and fO2 on the ferric-fer-rous ratio of silicic melts, Chem. Geol., 174, 255-273.

GASKELL, D.R. (1982): On the correlation between the dis-tribution of phosphorous between slag metal and thetheoretical optical basicity of the slag, Trans. Iron SteelInst. Jpn., 22, 997-1000.

GASKELL, D.R. (2000): Early model of the thermodynamicbehavior of slags and salts, in Proceedings of the SixthInternational Conference on «Molten slags, fluxes andsalts», Stockholm, Sweden – Helsinki, Finland, editedby S. SEETHARAMAN and DU SICHEN, Paper 004.

GHIORSO, M.S. and R.O. SACK (1994): Chemical masstransfer in magmatic processes, IV. A revised internal-ly consistent thermodynamic model for the interpola-tion and extrapolation of liquid-solid equilibria in mag-matic systems at elevated temperatures and pressures,Contrib. Mineral. Petrol., 119, 197-212.

GHIORSO, M.S., I.S.E. CARMICHAEL, M.L. RIVERS and R.O.SACK (1983): The Gibbs free energy of natural silicateliquids; an expanded regular solution approximationfor the calculation of magmatic intensive variables,Contrib. Mineral. Petrol., 84, 107-145.

GORDY, W. (1950): Interpretation of nuclear quadrupolecouplings in molecules, J. Chem. Phys., 19, 792-793.

HERASYMENKO, P. (1938): Electrochemical theory of slag-metal equilibria, Part I. Reactions of manganese andsilicon in acid open-heart furnace, Trans. Farad. Soc.,34, 1245-1254.

HESS, P.C. (1971): Polymer models of silicate melts,Geochim. Cosmochim. Acta, 35, 289-306.

HINZE, J.A., M.A. WHITEHEAD and H.H. JAFFE (1963): Elec-tronegativity, II. Bond and orbital electronegativity, J.Inorg.Chem., 38, 983-984.

HOLMQUIST, S. (1966): Ionic formulation of redox equilib-ria in glass melts, J. Am. Ceram. Soc., 49, 228-229.

JAMES, F. and M. ROOS (1977): MINUIT: a System forFunction Minimisation and Analysis of Parameter Er-rors and Correlations (CERN Computer Center Gene-va, Switzerland).

JOHNSTON, W.D. (1964): Oxidation-reduction equilibria iniron-containing glass, J. Am. Ceram. Soc., 47, 198-201.

JØRGENSEN, C.K. (1962): Absorption Spectra and ChemicalBonding in Complexes (Pergamon Press, Oxford).

JØRGENSEN, C.K. (1969): Oxidation Numbers and OxidationStates (Springer-Verlag, Berlin-Heidelberg-New York).

KOHN, S.C., R. DUPREE and M.E. SMITH (1989): A multinu-clear magnetic resonance study of the structure of hy-drous albite glasses, Geochim. Cosmochim. Acta, 53,2925-2935.

KOWADA, Y., H. ADACHI, M. TATSUMISAGO and T. MINAMI

(1995): Electronic states of transition metal ions in sil-icate glasses, J. Non-Cryst. Solids, 192, 316-320.

KRESS, V.C. and I.S.E. CARMICHAEL (1991): The compress-ibility of silicate liquids containing Fe2O3 and the ef-fect of composition, temperature, oxygen fugacity and

607

Polymerisation, basicity, oxidation state and their role in ionic modelling of silicate melts

pressure on their redox states, Contrib. Mineral.Petrol., 108, 82-92.

LANGE, R.A. (1994): The effect of H2O, CO2 and F on thedensity and viscosity of silicate melts, in Volatiles inMagmas, edited by M.R. CARROLL and J.R. HOLLOWAY,Rev. Mineral., 30, 331-369.

LANGE, R.A. and I.S.E. CARMICHAEL (1989): Ferric-ferrousequilibria in Na2O-FeO-Fe2O3-SiO2 melts: effects ofanalytical techniques on derived partial molar volumes,Geochim. Cosmochim. Acta, 53, 2195-2204.

LIU, Y., H. NEKVASIL and H. LONG (2002): Water dissolutionin albite melts: constraints from ab initio NMR calcu-lations, Geochim. Cosmochim. Acta, 66, 4149-4163.

MASSON, C.R. (1965): An approach to the problem of ionicdistribution in liquid silicates, Proc. R. Soc. London,A287, 201-221.

MASSON, C.R., I.B. SMITH and S.G. WHITEWAY (1970): Ac-tivities and ionic distributions in liquid silicates: applica-tion of polymer theory, Can. J. Chem., 48, 1456-1464.

MO, X., I.S.E. CARMICHAEL, M. RIVERS and J. STEBBINS

(1982): The partial molar volume of Fe2O3 in multicom-ponent silicate liquids and the pressure dependence ofoxygen fugacity in magmas, Min. Mag., 45, 237-245.

MOORE, G., K. RIGHTER and I.S.E. CARMICHAEL (1995):The effect of dissolved water on the oxidation state ofiron in natural silicate liquids, Contrib. Mineral.Petrol., 120, 170-179.

MORETTI, R. (2002): Volatile solubility in silicate meltswith particular regard to sulphur species: theoreticalaspects and application to etnean volcanics, Ph.D. The-sis (Università degli Studi di Pisa), (in English).

MORETTI, R. and G. OTTONELLO (2003a): Polymerizationand disproportionation of iron and sulfur in silicatemelts: insights from an optical basicity-based ap-proach, J. Non-Cryst. Solids, 323, 111-119.

MORETTI, R. and G. OTTONELLO (2003b): A polymeric ap-proach to the sulfide capacity of silicate slags andmelts, Metall. Mat. Trans. B, 34B, 399-410.

MORETTI, R., P. PAPALE and G. OTTONELLO (2003): A mod-el for the saturation of C-H-O-S fluids in silicate melts,in Volcanic Degassing, edited by C. OPPENHEIMER,D.M. PYLE and J. BARCLAY, Geol. Soc. London Spec.Publ. 213, 81-101.

MYSEN, B.O., I.S.E. CARMICHAEL and D. VIRGO (1985): Acomparison of iron redox ratios in silicate glasses de-termined by wet-chemical and 57Fe Mössbauer reso-nant absorption methods, Contrib. Mineral. Petrol., 90,101-106.

NAVROTSKY, A. (1994): Physics and chemistry of Earth ma-terials (Cambridge University Press, Cambridge, U.K.).

OTTONELLO, G. (1983): Trace elements as monitors of mag-matic processes (1) limits imposed by Henry’s Lawproblem and (2) compositional effect of silicate liquid,in The Significance of Trace Elements in Solving Pet-rogenetic Problems and Controversies, edited by S.AUGUSTHITIS (Theophrastus Publications, Athens).

OTTONELLO, G. (1997): Principles of Geochemistry (Colum-bia University Press, New York-Chicester-West Sussex).

OTTONELLO, G. (2001): Thermodynamic constraints arisingfrom the polymeric approach to silicate slags: the sys-tem CaO-FeO-SiO2 as an example, J. Non Cryst.Solids, 282, 72-85.

OTTONELLO, G. (2005): Chemical interactions and configu-

rational disorder in silicate melts, Ann. Geophysics, 48(4/5), 561-581 (this volume).

OTTONELLO, G. and R. MORETTI (2004): Lux-Flood basiciyof binary silicate melts, J. Phys. Chem. Solids, 65,1609-1614.

OTTONELLO, G., R. MORETTI, L. MARINI and M. VETUSCHI

ZUCCOLINI (2001): On the oxidation state of iron in sil-icate melts and glasses: a thermochemical model,Chem. Geol., 174, 157-179.

PAPALE, P. (1999): Modeling of the solubility of a two-com-ponent H2O+CO2 fluid in silicate liquid, Am. Mineral.,84, 477-492.

PARK, J. and P.C. RHEE (2001): Ionic properties of oxygenin slags, J. Non-Cryst. Solids, 282, 7-14.

PAUL, A. and R.W. DOUGLAS (1965): Ferrous-ferric equilib-rium in binary alkali silicate glasses, Phys. Chem.Glasses, 6, 207-211.

PAULING, L. (1932): Nature of the chemical bond, IV. Theenergy of single bonds and the relative electronegativ-ity of atoms, J. Am. Chem. Soc., 54, 3570-3582.

PAULING, L. (1960): The Nature of the Chemical Bond (Cor-nell University Press, Ithaca-New York).

PELTON, A.D. (1998): Thermodynamic calculations ofchemical solubilities of gases in oxide melts and glass-es, Glastech. Ber. Glass Sci. Technol., 72 (7), 214-226.

PELTON, A.D. and M. BLANDER (1986): Thermodynamicanalysis of ordered liquid solutions by a modified qua-sichemical approach-application to silicate slags, Met-all. Trans. B, 17B, 805-815.

PHILLIPS, J.C. (1970): Ionicity of the chemical bond in crys-tals, Rev. Mod. Phys., 42 (3), 317.

REYES, R.A. and D.R. GASKELL (1983): The thermodynam-ic activity of ZnO in silicate melts, Metall. Trans. B,14B, 725-731.

RYERSON, F.J. and P.C. HESS (1978): Implications of liquiddistribution coefficients to mineral-liquid partitioning,Geochim. Cosmochim. Acta, 42, 921-932.

RYERSON, F.J. and P.C. HESS (1980): The role of P2O5 in sil-icate melts, Geochim. Cosmochim. Acta, 44, 611-624.

SANDERSON, R.T. (1967): Inorganic Chemistry (ReinholdPubl. Co., New York).

SCHENCK, H. (1945): Introduction to the Physical Chem-istry of Steelmaking (BISRA, London, U.K.).

SCHMIDT, B.C., T. RIEMER, S.C. KOHN, F. HOLTZ and R.DUPREE (2001): Structural implications of water disso-lution in haplogranitic glasses from NMR spectroscopy:influence of total water content and mixed alkali effect,Geochim. Cosmochim. Acta, 65, 2949-2964.

SHANNON, R.D. (1976): Revised effective ionic radii andsystematic studies of interatomic distances in haliedsand chalcogenides, Acta Cryst., A32, 751-767.

SHIBATA, K. (1967): The oxygen partial pressure of themagma from Mihara volcano, O-sima, Japan, Bull.Chem. Soc. Jpn., 40, 830-834.

SOSINSKY, D.J. and I.D. SOMMERVILLE (1986): The composi-tion and temperature dependence of the sulfide capacityof metallurgical slags, Metall. Trans. B, 17B, 331-337.

TEMKIN, M. (1945): Mixtures of fused salts as ionic solu-tions, Acta Phys. Chim. URSS, 20, 411-420.

TOOP, G.W. and C.S. SAMIS (1962a): Some new ionic con-cepts of silicate slags, Can. Met. Quart., 1, 129-152.

TOOP, G.W. and C.S. SAMIS (1962b): Activities of ions insilicate melts, Trans. Met. Soc. AIME, 224, 878-887.

608

Roberto Moretti

VIRGO, D. and B.O. MYSEN (1985): The structural state ofiron in oxidized versus reduced glasses at 1 atm: a 57FeMössbauer study, Phys. Chem. Miner., 12, 65-76.

WAFFE, H.S. and D.F. WEILL (1975): Electrical conductivi-ty of magmatic liquid effects of temperatures, oxygenfugacity and composition, Earth Planet. Sci. Lett., 28,254-260.

WATSON, E.B. (1976): Two-liquid partition coefficients: ex-perimental data and geochemical implications, Con-trib. Mineral. Petrol., 56, 119-134

WILKE, M., H. BEHRENS, D.M.J. BURKHARD and S. ROSSANO

(2002): The oxidation state of iron in silicic melt at 500Mpa water pressure, Chem. Geol., 189, 55-67.

XUE, X. and M. KANZAKI (2001): Ab initio calculation ofthe 17O and 1H NMR parameters for various OHgroups: implications to the speciation and dynamics ofdissolved water in silicate glasses, J. Phys. Chem. B,105, 3422-3434.

XUE, X. and M. KANZAKI (2003): The dissolution mecha-nism of water in alkaline earth silicate and aluminosil-icate melts: one view from 1H MAS NMR, Geochim.Cosmochim. Acta, 67 (suppl. to no. 18), abstr. 543.

YOUNG, R.W., J.A. DUFFY, G.J. HASSALL and Z. XU (1992):Use of optical basicity concept for determining phos-phorous and sulphur slag-metal partitions, IronmakingSteelmaking, 19, 201-219.