Vol48/04/2005def 549 ANNALS OF GEOPHYSICS, VOL. 48, N. 4/5, August/October 2005 Key words silicate melt – acid-base – oxide melt – thermodynamic properties 1. Introduction In extraction metallurgy, quasi-chemical (Toop and Samis, 1962a,b) and polymer models (Masson 1965, 1972) have been used with con- siderable success to express the variation with melt composition and temperature of metal ox- ide activities in silicate melts. The aim of such calculations is to interpret the thermodynamic properties of the melts and to allow modelling of the activities of oxide components so as to maximize refining efficiency by minimizing metal loss in slags and by optimizing the physi- co-chemical conditions required for smelting. In contrast, in the earth sciences, most prob- lems involving silicate liquids, at least in the outer part of the Earth, require knowledge of the behaviour, not of oxide constituents, but of the activities and chemical potentials of silicate species. The requirements are to provide a framework for understanding crystal-liquid equilibria over a wide range of pressure, tem- perature, gas and melt compositions and to in- clude accurate descriptions of other thermody- namic properties such as density, viscosity and surface tension, again over a wide range of P, T, X. These problems have been tackled until now mainly by fitting a large number of param- eters to empirical or semi-empirical thermody- namic models (e.g., Berman and Brown 1984; Ghiorso and Sack, 1995; Ghiorso et al., 2002). In these models, the excess free energy of mix- ing of components is usually expressed by a particular functional form, such as that of the regular solution model, and the coefficients of the variables are fitted using calorimetric and Mailing address: Dr. Donald G. Fraser, Department of Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, U.K.; e-mail: Donald.Fraser@earth.ox.ac.uk Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts Donald G. Fraser Department of Earth Sciences, University of Oxford, U.K. Abstract Phase equilibrium relationships in igneous systems can be estimated using empirical mathematical models based on multi-component regular solution formulae. Although these provide useable results within the fitted region, they can give very misleading values outside the compositional range of curve fitting. Moreover, they usually give poor esti- mates of the well-characterized melting relations of simple systems and do not relate to the large body of thermody- namic activity data available in the metallurgical literature, nor to spectroscopic, diffraction or computational mod- els of silicate melt properties. The aim of this paper is to extend previous acid-base models of silicate melts and to use a quasi-chemical model to calculate the activities of quasi-chemical silicate mixing units, or structons, from com- binations of the oxo-species used in quasi-chemical and polymer models to calculate oxide activities in metallurgy. 550 Donald G. Fraser phase equilibrium data for the compositional range of interest. Thus, in an n-component system, (1.1) where νi are the stoicheiometric coefficients. The various parameters must be fitted for each component i. This mathematical curve fitting approach can provide usable results within the range of compositions for which the parameters are fit- ted although inaccurate results are obtained for certain compositions, particular those rich in Na (e.g., Asimow et al., 2001). The calculated data agree particularly poorly with the basic bi- nary and ternary phase diagrams of igneous petrology for which so many primary measure- ments are available. An important and usually un-stated reason for the success of these poly- nomial curve-fits is that they deal with the lim- ited polymerised region of composition-space which is energetically rather homogeneous – that is, it excludes those basic compositions which show most of the high-energy interac- lnRT a+n=lnRT Xliq liq liq solid solidi i i i i n 0 1 0+o n c = ^ h7 A/ tions of MO and SiO2 (see fig. 1). Thus, al- though geologically useful, the models behave poorly in the very compositional region which is most sensitive to changes in the acid-base properties of the melts and which provides most fundamental information about their properties and the true effects of different metal ions. They are certainly not based on the knowledge of the structures and properties of the liquids. The models are therefore unreliable for extrap- olation beyond the range for which they are fit- ted and, especially, provide little insight into the underlying properties and behaviour of silicate melts. The question of the acid-base properties of silicate melts (Duffy and Ingram, 1971) and of how to relate thermodynamic properties to structure (Fraser, 1977) has recently been revis- ited in an attempt to discover the factors which determine the values of the empirical coeffi- cients for components in CaO-MgO-Al2O3- SiO2 (Beckett, 2002). In addition there is re- newed interest in using acid-base properties to devise a predictive thermodynamic model properly grounded on a structural basis (Fraser 1977, 2003; Ottonello, 2001, 2005) and in ex- plaining the behaviour of altervalent elements in silicate melts (Fraser, 1975; Moretti and Ot- tonello, 2003). The aim of the present paper is to examine the extensive work on oxide activities which has been done on binary SiO2-MO melts of metallurgical interest and to relate these to the distributions of silicate species in melts. These distributions reflect the fundamental properties of silicate melts and provide insight into the chemical factors such as the acid-base proper- ties of oxides which influence crystal liquid equilibrium in igneous systems. 2. Oxide activity measurements in binary silicate melts The thermochemistry of melts and slags in divalent binary systems MO-SiO2 has been stud- ied extensively (e.g., Richardson, 1956; Cripps- Clark et al., 1974; Navrotsky, 1995). Mixing is usually highly non-ideal and significant devia- tions from ideality are observed (fig. 1). The variations of oxide activity with bulk composi- Fig. 1. Experimental measurements of oxide activ- ities in binary silicate melts. Also shown are curves calculated using a bi-functional linear polymer mod- el (see below). 551 Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts tion have the general form of titration curves in which each basic oxide can be considered to be titrated with the acidic oxide SiO2. The differing basicities of different oxides can be seen clearly. 3. Acid-base schemes Although the qualitative concept of acidic and basic oxides is familiar to geologists and dates back to Berzelius, a quantitative defini- tion of oxide acidity and basicity was proposed by Flood and Förland (1947) following the work of Lux (1939). In aqueous systems, acidic or basic behaviour is conveniently treated using the conjugate acid-base formulation of Brönst- ed and Lowry (3.1) e.g., (3.2) Alternatively, and relevant to silicate melts, a Lewis acid is simply an electron acceptor e.g., Al3+ so that the Lewis acidity may be related to the Pauling electronegativity. In non-protonic solvents like molten oxides and silicates, a different formalism is required. In the Lux-Flood system, oxide-ion, O2−, takes the place of protons in aqueous solutions. Thus, a basic oxide is a substance capable of furni- shing oxide ions, and an acidic oxide is one which reacts with O2−. Thus, (3.3) e.g., (3.4) Each acid or base is therefore characterized by a defined thermodynamic dissociation or equi- librium constant. The mixing properties of sili- cate melts may therefore be investigated by titrating melts with SiO2, just as protonic acid- base systems are investigated by pH titration. The interpretation of these deviations from ideality has been the subject of a family of mod- els, all of which express the non-ideality in terms of reaction between the mixing components. Measurements of the electrical conductivi- ties and transport properties of silicate melts .SiO SiO O3 2 2 2= +- - Base Acid O2= + - .H SO HSO H2 4 4= +- +- Acid Base H= + + (Bockris et al., 1952a,b; Waff and Weill, 1975; Stebbins et al., 1995) have shown that, with the exception of melts containing transition-metal ions in which significant charge transfer processes may operate, conduction in the melts is entirely ionic with Faraday’s Law being obeyed. Importantly, the conductance is unipo- lar (Bockris et al., 1952b; Bockris and Mellors, 1956) and occurs by the transport of relatively mobile cations while the anions remain station- ary. Silicate melts are thus ionic liquids like other molten salts but have an immobile anion network. Interestingly, recent NMR data (Lee and Stebbins, 2003) indicate that the behaviour of cations may also be non-random and a pro- posal to extend the Temkin equation (Temkin, 1945) to express the different behaviour of cations of different charge is discussed below. The non-ideality observed in the mixing properties of silicate melts when expressed as oxide components is the observable. The diffi- culty in its interpretation is caused by the diffi- culty in expressing the excess free energy of mixing (the generally negative deviation from ideality) as a function of composition. 4. Quasi-chemical models – Temkin equation The regular solution model (Hildebrand and Scott, 1950) interprets the excess free energy of mixing of a solution entirely as an enthalpy of mixing and retains a purely configurational en- tropy of mixing. This treatment is successful for the description of mixing of similar compo- nents – e.g., cyclohexane and benzene and the mixing of some ionic solids when the anionic framework is fixed. However it becomes more difficult to express the excess functions for mixing components as the magnitude of the de- viations from ideality increases. In the case of silicates, the high energies associated with making and breaking Si-O-Si or Al-O-Si bonds make it unlikely that a simple regular solution model could succeed in systems of variable sto- icheiometry like melts. This is the reason for the inability of the polynomial regular solution models to deal adequately with simple systems. Quasi-chemical models are first-order re- finements of the regular solution treatment and 552 Donald G. Fraser use the excess free energy of mixing to form new species with mixing properties which are much closer to ideal (e.g., Guggenheim, 1952). The choice of quasi-chemical components in the case of silicate liquids is initially compli- cated by the presence of a large number of dif- ferent silicate anions. While silicate minerals are usually monodisperse, containing only a single type of anion (e.g., SiO44− in olivine), molten silicates contain a distribution of differ- ent polymeric silicate anions of different mo- lecular weights and are thus polydisperse sys- tems with statistical distributions of polymers of different molecular weight. Vibrational spectroscopic studies of melts and glasses provide broad information on the proportions of different bonds present among the silicate anions (e.g., Mysen, 1997). It is al- so possible to separate some of the different an- ionic species themselves using chromatograph- ic techniques (Lentz, 1964; Götz and Masson, 1970) and even simple orthosilicate composi- tions like Pb2SiO4 contain, in the glass, a distri- bution of condensed polymeric species (fig. 2). It is immediately clear from these data that even orthosilicate melts are composed not of M2+ and SiO44− ions, but rather of Pb2+ ions coordinat- ing a distribution of anions of different molecu- lar weight. Simple measures such as NBO/T, cal- culated from the overall stoicheiometry, al- though widely used in the geological literature, do not give this result and have been useful only because most igneous melts are more poly- merised than the metasilicate composition. Expression of the statistical nature of liquids and glasses and, in particular, the case of molten silicates, requires treatment of the energetics of all the simultaneous equilibria. Any successful treatment of the nature of silicate liquids must treat the polymerization equilibria responsible for the observed distribution of species in the melt. Similar problems exist in mixtures of or- ganic polymers (Flory, 1936, 1953) and experi- ence in the treatment of organic polmer melts and solutions has been of great value in develop- ing models of molten silicates. These models deal with the complex molecular weight distri- butions observed by making two assumptions: 1) polymerization equilibria (i.e. the reactivities of functional groups) are independent of molecular weight and 2) Temkin mixing. The Temkin mod- el of ionic salts (Temkin, 1945) considers the en- ergetics of substituting cations for anions and, (essentially following the quasi-chemical ap- proach) assumes that the energy cost of wrongly substituting a cation for an anion is sufficiently high that the probability of mixing cations and anions is zero. The correct Temkin entropy of mixing is therefore obtained by mixing anions and cations independently on sites of the anion matrix and cation matrix respectively. Recent NMR data (Lee and Stebbins, 2003) show that this is true for Mg and Ca, for example, but seems not to be true for ions of different charge. Thus, whereas Mg and Ca ions mix close to ran- domly, Na and Ca ions occupy separate sites in the glasses studied. Fig. 2. Distribution of polymers in Pb2SiO4 glass obtained by trimethyl sliylation gas liquid chro- matography of quenched glass. Temperatures refer to chromatographic separation. Peaks 1-4 represent SiO4 momomers, Si2O7 dimers, Si3O9 rings and Si4O12 rings respectively (after Masson, 1972). 553 Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts It is proposed here that for multi-component melts, the simple Temkin assumption may need to be extended to allow for this behaviour by in- troducing sub-matrices. The simplest would be a matrix for each valence state M I, M II, M III and M IV. Treatment of the behaviour of P and As might require a further set of exclusive sites M V. Note that the sites M IV and M V are proba- bly the sites of network-forming ions and M III, at least, may be amphoteric as described below. This provides a continuity of treatment of met- al ions and network forming constituents for the first time. It is analogous to the independent treatment of the entropy of mixing on different sites in solids, e.g., in M II3 M III2 Si3O12 garnets. The unipolar electrical conductance is deter- mined by the very low diffusivity of highly charged ions in network-forming sites. This is supported by recent molecular dynamics calcu- lations using a modified BKS potential which show low diffusivity of SiIV (Gemmell et al., 2003). Moreover it allows treatment of the whole melt array as an inter-related network of metal ion potential energy wells in a back- ground of oxygen and other electronegative atoms, normally regarded as forming the «net- work-forming» sites. 5. Binary silicate melts In the case of binary silicate melts, the Temkin model and the extended model de- scribed above are identical. Oxide activity data have been obtained for many such systems for large parts of the composition range MO-SiO2. Methods used include equilibration with a pure metal (Richardson and Webb, 1956) extraction from phase diagrams and emf measurements using CaO/ZrO2 solid electrolytes. Activity-composition curves for three bina- ry systems are shown in fig 1. The form of these aMO versus XMO curves is determined by the titration of MO by added SiO2. Masson (1965) has shown that polymer models may be used to express the measured activity by writing sets of polymerization equi- libria of the form K1 (5.1)SiO SiO Si O O4 4 2 7 2+ + + - K2 (5.2) … Kn (5.3) where K1 = K2 = … Kn. For bifunctional (linear) polymerization, this leads to (5.4) and for branched chains (Masson, 1972) (5.5) Curves calculated from (5.1 to 5.3) above for lin- ear chains are also shown in fig. 1 and agree well with the experimental data for these systems. These models do not express self-condensa- tion to form ring or network structures and so are unsuitable, without extension to describe the behaviour of magmas considerably more SiO2-rich than the metasilicate composition. 5.1. The Toop and Samis (quasi-chemical) model An alternative to discrete polymerization re- actions is to express the excess free energy of mixing in terms of the formation, not of dis- crete anions, but of quasi-chemical or virtual species. The proportions of species will again reflect the magnitude of the non-ideality. This approach was introduced by Toop and Samis (1962) who considered the interaction of just three oxo-species (5.6) Where O2− represents a «free» oxide ion, not bound as part of the silicate network, O0 is an oxo-bridge Si-O-Si and O− a singly charged oxygen atom also bonded to the cations present. Allowing simple Temkin mixing, the pro- portions of the species are thus given by (5.7)( ) .K X X XO O O22 $= - -- .O O O22 0+ =- - [ / ])a K3 1-+/ (1 1-)a- ./ (3 1+2=/X1 MO MOSiO2 ])1-[ /a K1+/ (1 1-/ ( )a1 1 -+2=/X1 MO MOSiO2 SiO Si O Si O O4 3 1 1 3 4 2 n n n n+ + ++ + + - SiO Si O Si O O4 2 7 3 10 2+ + + - 554 Donald G. Fraser Applying charge and mass balance constraints (Fraser, 1977), ∆Gmix may be calculated for any bulk composition. Data for the systems PbO- SiO2 and CaO-SiO2 are shown in fig. 3. 6. Amphoteric oxides The mixing properties of binary silicate melts can be expressed well by models which give real insight into the properties of the melts and which have robust predictive power. An as- sumption of these models is simple Temkin mix- ing with complete dissociation of the basic oxide into M2+ and O2− in its standard state. This cannot be universally true and this standard state prob- lem must be considered carefully when compar- ing different binaries or working in multicompo- nent systems (Fraser, 1977). This problem is par- ticularly severe in the case of oxides such as Al2O3, Fe2O3 or TiO2 which may contribute structural units to a greater or lesser extent to the «silicate» framework of the melt – as noted above, electrical conductivity measurements in- dicate that conductivity is ionic and monopolar. One approach is to allow for amphoteric properties of real oxides – i.e. in which a given oxide component has the ability to react both as a basic and an acidic oxide depending on the overall composition (Fraser, 1975). To express the real ability of oxides to behave as acidic or basic components, the Temkin model must be further extended. The Lux-Flood acid base sys- tem defines acid-base behaviour by the reactiv- ity with oxide ion. By extension, amphoteric behaviour is therefore easy to express as can be seen in the case of Al2O3 (6.1) (6.2) The net effect of adding Al2O3 to a multivariate melt will be either to consume O2− or to increase the O2− activity depending on the bulk compo- sition and the values of Ka and Kb. Similar cri- teria apply to Fe2O3 and other altervalent ox- ides. For example it is well known that at con- stant P, T and aO2, iron is more highly oxidized in «basic» melts (Fudali, 1965; Paul and Dou- glas, 1965a,b). The variation in the oxidation state of Fe with bulk melt composition at con- stant P, T and fO2 has important implication for its partitioning behaviour and for calculations of redox conditions in the Earth. In the case of FeO, the two amphoteric equi- libria are Kb (6.3) Ka (6.4) in which Ka is exceedingly small and can be neglected. In contrast, the two reactions for Fe2O3 are likely to be of more equal magnitude (6.5) (6.6) Thus increasing melt basicity indicated by addi- tion of basic oxides MO stabilizes FeO2− and hence FeIII relative to Fe2++ O2− and hence FeII. Similar criteria apply to other altervalent oxides and it has been shown that in the melts in the binary systems Mg, CaSiO3-CaAl2Si2O8 .Fe O O FeO22 3 2 2+ = - - Fe O Fe O2 32 3 3 2= ++ - FeO O FeO2 2 2+ =- - FeO Fe O2 2= ++ - .Al O O AlO22 3 2 2+ = - - Al O Al O2 32 3 3 2= ++ - Fig. 3. ∆Gmix for the systems CaO-SiO2 and PbO- SiO2. Data compared with theoretical curves calcu- lated using the Toop and Samis quasi-chemical mod- el (after Toop and Samis, 1962a). 555 Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts and (Mg,Ca)2SiO4-CaAl2Si2O8 constant T and fO 2, Eu III/EuII ratios increase with increasing MO-content (i.e. decreasing SiO2) as expected from the above. However importantly, they al- so increase with increasing Ca/Mg ratio. Since melt basicity has been related to Pauling elec- tronegativity (Duffy and Ingram, 1971), the model predicts that with CaO more basic than MgO, EuIII/EuII ratios in Ca-rich melts should be higher than in Mg-rich liquids at constant T, P, fO 2 and XSiO 2 as is observed experimentally (Morris and Haskin, 1974; Fraser, 1975). 7. Behaviour of H2O and CO2 The amphoteric behaviour of oxides also has implications for the solubility of H2O water in melts. Ignoring unreacted molecular water, the relevant reactions are Kb (7.1) Ka . (7.2) In acid melts, most water will be absorbed to depolymerize the network, forming OH groups bonded to silicate anions. However in basic compositions, water should dissolve by a dif- ferent mechanism such as (7.2). In this, H2O re- acts with oxide ion as an acidic oxide to pro- duce free hydroxyl ions. This mechanism, (Fraser, 1977), has recently been observed by careful MAS NMR observations of quenched CaMgSi2O6 glasses (Xue and Kanzaki, 2003). The overall solubility will depend on the over- all basicity, the values of Ka and Kb and the sta- bility of the free hydroxide species Ca(OH)2 and Mg(OH)2. The solubility of S also depends on similar reactions involving S2−/SO4 equilib- ria (Fincham and Richardson, 1954; Holzheid and Grove, 2002; O’Neill and Mavrogenes, 2002). Similarly CO2 behaves dominantly as an acidic oxide by the reaction (7.3) Note that H2O, CO2 and sulphur all interact with the oxo-species equilibria in molten silicates. Thus, for example, wet melting, or melting in the .OCO CO2 2 3 2+ =- - H O O OH22 2+ =- - H O O OH22 0+ = presence of differing amounts of CO2 or sulphur will not only involve the dissolution of the volatile component, but will perturb the balance of oxo-, and hence silicate, structural species in the silicate melt which are in equilibrium with solid phases on the liquidus. To maintain crystal liquid equilibrium, the effects of the dissolved volatile component must be offset, most usually by the addition of more or less silica. Thus, in moderately acidic melts, H2O dissolution occurs dominantly by (7.1) above. Wet melting thus re- quires addition of O0 (i.e. SiO2) to restore the O−/O0 equilibrium according to eq. (5.6) and wet melting leads to an expansion of the olivine pri- mary phase volume towards silica-rich (an- desitic) compositions as will be described below. CO2 has the opposite effect. 8. Implications of acid-base reactions for silicate crystal-melt phase equilibria The acid-base properties of oxides de- scribed above may be used to bridge the gap be- tween the experimental and theoretical work which has led to detailed understanding of ox- ide activities in metallurgical slags on the one hand, and the need for a similar conceptual framework for considering silicate activities and equilibiria on the other. The results of MAS NMR spectra obtained from silicate glasses and also from high temper- ature melts allow the identification in low pres- sure melts and glasses of species with half-lives long in comparison with the measurement tech- nique. Thus, SiO4 tetrahedra can be identified with different linkage states, Q (e.g., Stebbins, 1987). Olivine-like Q0 species are isolated tetra- hedral groups with no cross links, Q2 species are middle groups with pyroxene-like linkages and Q4 species are three dimensionally cross-linked. Successful application of the quasi-chemical model utilizes the excess free energy of mixing to form quasi-chemical species which then mix ide- ally. This can be applied to relate the NMR data to the oxide activity thermodynamic data by ex- tending the quasi-chemical model of Toop and Samis introduced above. In an early paper, Hug- gins (1954) referred to basic structural units as «structons» and we can express the compositions 556 Donald G. Fraser of silicate structons by an extension of the Q-for- malism used to interpret NMR spectra. Let each quasi-chemical constituent be represented by Siij where i is the number of singly bonded oxy- gens and j the number of bridging oxygens, then the set of five tetrahedral structons for Si is 40Si, 31Si, 22Si, 13Si and 04Si. The first is an isolated tetrahedron as in olivine and the last a fully cross- linked unit as in quartz. The Toop and Samis model considers the excess free energy of mixing to arise, as shown above, from the reaction (8.1) The quasi-chemical species, O− and O0 of this model may be used to construct silicate species or structons by considering the probability of forming each. These probabilities Pij are thus Within the quasi-chemical model, the structons mix ideally and their proportions can be calcu- lated directly from the proportions of Toop and Samis oxo-species. These are determined by the polymerisation equilibrium constant char- acteristic of each oxide. Basic oxides like CaO have a very low value of K (e.g., K = 0.003 in fig. 1) and less basic oxides such as NiO, high- er values (K = 46 in fig. 1). The relationship of these values to electronegativity will be consid- ered elsewhere (Fraser, in prep.). Silicate crystal-liquid phase equilibrium can be expressed simply using this model. For example the crystallization of enstatite from a melt is defined by the equilibrium and ( ) ( ) RT RT liq xtal 0 0 MgSiO MgSiO MgSiO MgSiO 3 3 3 3 + + n n ln ln ( ) ( ) . a a liq xtal = ( ) ( )liq xtalMgSiO MgSiO3 3=n n . . . . . . !/ !. ! !/ !. ! !/ !. ! . P X X P X X X X P X X X X P X X X X P X X 1 4 3 1 4 4 2 2 6 4 1 3 4 1 O O O O O O O O O O O O O O O O 40 4 4 31 3 0 3 0 22 2 2 0 2 0 13 3 0 3 0 04 4 0 4 0 ) ) ) ) ) = = = = = = = = = = - - - - - - - - .O O O22 0+ =- - For true quasi-chemical mixing in the melt, the structon model predicts that ideal mixing of quasi-chemical species should obtain. Thus the activity in the melt is defined as aMgSiO3(liq)= = XMgCM.X 22Si = 6X 2O−X 2O0. Note that X MgCM refers to mixing in the divalent cation matrix. As not- ed above, the recent NMR data of Lee and Steb- bins (2003) suggest that it may be necessary to extend the simple Temkin model to consider the mixing of different types of cation in silicate melts and glasses in a more sophisticated way than hitherto. A first approach may be to con- sider the mixing of cations of different charge separately in different matrices. A test of this model is available if appropri- ate values of K are available for a system. Val- ues of the temperature dependence of K are available for the system FeO-SiO2 (Distin et al., 1971; Masson, 1972). A plot of LnK versus 1/T yields a value of 0.574 at the eutectic tempera- ture of 1455 K. Using this value, the activity of 40Si (i.e. SiO4) structons in the melt can be cal- culated at each temperature. For the eutectic composition at 1455 K, the value is 0.893. This compares well with the value of aFe2SiO4 cal- culated from the depression of freezing point of 0.882 (Fraser, 1977). 9. Multi-component systems The above model provides a means of relat- ing metallurgical oxide activity measurements to silicate element partitioning and phase equi- librium data. In the earth sciences an outstand- ing problem is to predict the effects of changing composition or volatile content. The effects of adding third components to a univariant equilibrium in the system MgO-SiO2 have been described by Kushiro (1973) for the forsterite-enstatite-liquid equilibrium and the effects of different oxides on this equilibrium are shown in fig. 4. This equilibrium is expressed in terms of the structon model by the two simultaneous equations ( ) ( ) RT RT liq xtal 0 0 Mg SiO Mg SiO Mg SiO Mg SiO 2 4 2 4 2 4 2 4 + + n n ln ln ( )liq = ( ) a a xtal 557 Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts The activities of the melt components are giv- en by The effect of adding basic or acidic oxides will shift the balance of the forsterite-enstatite-melt equilibrium according to the proportions of 40Si and 22Si structons in the melt. Thus addition of a basic oxide such as K2O will increase the pro- portion of 40Si relative to 22Si. Equilibrium is on- ly maintained by a balancing shift towards SiO2- rich compositions. Conversely addition of an acidic oxide such as P2O5 will have the opposite effect and move the position of the equilibrium to SiO2 poor values. The effect of added water in this diagram is basic, but less so than for Na2O or K2O. H2O dis- solves in silicate melts with at least two chemical mechanisms in addition to dissolution as molec- . . .. ( ) ( ) . a X X X X a X X X X X liq liq 6 Mg CM Si Mg CM O Mg CM Si Mg CM O O 2 40 2 4 22 2 2 0 Mg SiO MgSiO 2 4 3 = = = = - - ( ) ( ) RT RT liq xtal 0 0 MgSiO MgSiO MgSiO MgSiO 3 3 3 3 + + n n ln ln ( ) ( ) . a a liq xtal = ular H2O, as discussed above. The net effect for these compositions seems to be somewhat basic of neutral so that the forsterite-enstatite equilibri- um is shifted to SiO2-rich compositions. This be- haviour, with the expansion of the forsterite pri- mary phase volume to SiO2-rich compositions during wet melting is well known as is shown in fig. 5 for the system Di-fo-SiO2. Whereas wet melting leads to silica-rich melt compositions, melting in the presence of CO2 has the opposite effect implying that CO2 is an acidic oxide, consuming O2− dominantly by the formation of CO32−. The structon model provides a framework within which a range of properties of silicate melts may be considered. These include redox behaviour, volatile solubili- ty, physical properties and crystal-liquid equilib- rium in igneous systems. In order for quasi- chemical or polymer models based on the Temkin equation to be successfully applied in multi-component systems, it should be remem- bered that the assumption of full dissociation of the «basic» oxide in the standard state is unlike- ly to be generally true as pointed out by Fraser (1977). The correct treatment of the behaviour of amphoteric oxides in melts thus requires cross- calibration of the standard states for the different end-member oxide components present. Fig. 4. Effects of different added oxides on the forsterite-enstatite-liquid equilibrium (after Kushiro, 1973). Fig. 5. Phase relations in the system diopside- forsterite-quartz. 558 Donald G. Fraser 10. Conclusions Metallurgical oxide-activity measurements and the quasi-chemical or polymer theoretical models developed to interpret the variation of oxide activity with composition in binary sili- cate melts may be used to calculate the propor- tions of silicate structural units, or structons, in melts. The Lux-Flood acid-base system may be extended to describe the behaviour of ampho- teric oxides such as Al2O3 and Fe2O3 by the in- troduction of a second acidic reaction to pro- vide an amphoteric pair for each oxide. The ox- idation state of Fe and other altervalent oxides increases with increasing basicity in response to the stabilization of the acidic reaction of the higher oxidation state. Application of these models to multi-com- ponent silicate melts requires measurement or calibration of the acid-base constants and cali- bration of the different oxide standard states noted by Fraser (1977) and may require exten- sion of the simple Temkin fused salt model to allow for the separate behaviour of metal ions of different charge recently reported in the NMR data of Lee and Stebbins (2003). This model thus provides a multi-parameter frame- work for the characterization of the behaviour of melts and melt-solid equilibria which can be fitted using similar methods to those adopted by Ghiorso et al. (2002), or Berman and Brown (1984). An advantage is that the structon model is based on a first-order extension to the regular solution model so that a closer relationship to structural data so that extrapolation may be pos- sible. In addition, the acid-base constants which describe the melt properties are relatable to fun- damental chemical parameters such as the opti- cal basicity scale based on the 1S 0→3P1 UV- transition proposed by Duffy and Ingram (1971). REFERENCES ASIMOW, P.D., M.M. HIRSCHMAN and E. STOLPE (2001): Calculation of peridotite partial melting from thermo- dynamic models of minerals and melts, IV. Adiabatic decompression and the composition and mean proper- ties of mid-ocean ridge basalts, J. Petrol., 42, 963-998. BECKETT, J.R. (2002): Role of basicity and tetrahedral spe- ciation in controlling the thermodynamic properties of silicate liquids, Part 1. The system CaO-MgO-Al2O3- SiO2, Geochim. Cosmochim. Acta, 66, 931-107. BERMAN, R.G. and T.H. BROWN (1984): A thermodynamic model for multicomponent melts, with application to the system CaO-Al2O3-SiO2, Geochim. Cosmochim. Acta, 48, 661-678. 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, S. IGNATOWICZ and J.W. TOMLINSON (1952a): The electrical conductivity of sil- icate melts: systems containing Ca, Mn, Al, Discuss. Faraday Soc., 4, 281-286. BOCKRIS, J.O’M., J.A. KITCHENER and A.E. DAVIES (1952b): Electric transport in liquid silicates, Trans. Faraday Soc., 48, 536-548. CRIPPS-CLARK, C.J., R. SRIDHAR, J.H.E. JEFFES and F.D. RICHARDSON (1974): Chain distribution and transition temperatures for phosphate glasses, in Physical chem- istry of process metallurgy, edited by J.H.E. JEFFES and R.J. TAIT (Inst. Mining. Met., London). DISTIN, P.A., S.G. WHITEWAY and C.R. MASSON (1971): Solubility of oxygen in liquid iron from 17 858 to 19 608°C. New technique for the study of slag-metal equilibrium, Canad. Metall.Quart., 10, 73-78. DUFFY, J.A. and M.D. INGRAM (1971): Establishment of an optical scale for Lewis basicity in inorganic oxyacids, molten salts and glasses, J. Am. Chem. Soc., 93, 6448- 6454. EGGLER, D.H. (1974): Effect of CO2 on the melting of peri- dotite, Carnegie Inst. Wash. Yearbook, 73, 215-224. FINCHAM, C.J.B. and F.D. RICHARDSON (1954): The behav- iour of sulphur in silicate and aluminate melts, Proc. R. Soc., 223A, 40-61. FLOOD, H. and T. FÖRLAND (1947): The acidic and basic properties of oxides, Acta Chem. Scand., 1, 952-1005. FLORY, P.J. (1936): Molecular size distribution in linear condensation polymers, J. Am. Chem. Soc., 58, 1877- 1885. FLORY, P.J. (1953): Principles of Polymer Chemistry (Cor- nell University Press). FRASER, D.G. (1975): Activities of trace elements in silicate melts, Geochim. Cosmochim. Acta, 39, 1525-1530. FRASER, D.G. (1977) Thermodynamic properties of silicate melts, in Thermodynamics in Geology, edited by D.G. FRASER (D. Reidel Pub. Co., Dordrecht), 303-325. FRASER, D.G. (2003): Acid base properties, structons and the thermodynamic properties of silicate melts, Geochim. Cosmochim. Acta, 67, A103. FUDALI, R.F. (1965): Oxygen fugacities of basaltic and an- desitic magmas, Geochim. Cosmochim. Acta, 29, 1063- 1075. GEMMELL, A., D.G. FRASER and K. REFSON (2003): Molec- ular dynamics simulations of diffusion in a silica melt, Eos, Trans. Am. Geophys. Un., 84 (46), Fall Meet. sup- pl., abstr. V11D-0528. GHIORSO, M.S. and R.O. SACK (1995): Chemical mass transfer in magmatic processes, IV. A revised and inter- nally consistent thermodynamic model for the interpo- lation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pres- sures, Contrib. Min. Petrol., 119, 197-212. 559 Acid-base properties and structons: towards a structural model for predicting the thermodynamic properties of silicate melts GHIORSO, M.S., M.M. HIRSCHMANN, P.W. REINERS and V.C. KRESS (2002): The pMELTS: a revision of MELTS for improved calculation of phase relations and major ele- ment partitioning related to partial melting of the man- tle to 3 GPa, Geochem. Geophys. Sys., 1030 GÖTZ, J. and C.R. MASSON (1970): Trimethylsilyl derivatives for the study of silicate structures, Part I. A direct method of trimethylsilylation, J. Chem. Soc. A, 2683-2686. GUGGENHEIM, E.A. (1952): Mixtures (Clarendon Press, Ox- ford). HILDEBRAND, J.H. and R.L. SCOTT (1950): The Solubility of Non-Electrolytes (Publ. Reinhold). HOLZHEID, A. and T.L. GROVE (2002): Sulfide saturation limits in silicate melts and their im pli ca tions to core formation scenarios for terrestrial planets, Am. Miner- al., 87, 227-237. HUGGINS, M.L. (1954): The structure of amorphous materi- als, J. Phys. Chem., 58, 1141-1146. KUSHIRO, I. (1973): Liquidus boundaries between olivine, pyroxene, CaSiO3, and silica polymorphs at 1 atm, Carnegie Inst.-Wash. Yearbook, 72, 497-502. LEE, S.K. and J.F. STEBBINS (2003): The distribution of sodium ions in aluminosilicate glasses: a high-field Na-23 MAS and 3Q MAS NMR study, Geochim. Cos- mochim. Acta, 1699. LENTZ, C.W. (1964): Silicate minerals as sources of trimethylsilyl silicates and silicate structure analysis of sodium silicate solutions, Inorg. Chem., 3 (4), 574-579, doi: 10.1021/ic50014a029. LUX, H. (1939): «Acids» and «bases» in a fused salt bath: Determination of oxygen-ion concentration, Z. Elektro- chemie, 45, 303-309. MASSON, C.R. (1965): An approach to the problem of ionic distribution in liquid silicates, Proc. R. Soc., 287A, 201-221. MASSON, C.R. (1972): Thermodynamics and constitution of silicate slags, J. Iron Steel Inst., 210, 89-92. MORETTI, R. and G. OTTONELLO (2003): Polymerization and disproportionation of iron and sulfur in silicate melts: insights from an optical basicity-based approa- ch, J. Non-Cryst. Solids, 323, 111-119. MORRIS, R.V. and L.A. HASKIN (1974): EPR measurement of the effect of glass composition on the oxidation states of europium, Geochim. Cosmochim. Acta, 38, 1435-1445. MYSEN, B.O. (1997): Aluminosilicate melts: structure, composition and temperature, Contrib. Mineral. Petrol., 127, 104-118. MYSEN, B.O., D.H. EGGLER, M.G. SEITZ and J.R. HOL- LOWAY (1976): Carbon dioxide in silicate melts and crystals, Part 1. Solubility measurements, Am. J. Sci., 276, 455-479. NAVROTSKY, A. (1995): Energetics of silicate melts, Rev. Mineral., 32, 121-144. O’NEILL, H. ST.C. and J.A. MAVROGENES (2002): The sul- fide capacity and the sulfur content at sulfide saturation of silicate selts at 1400°C and 1 bar, J. Petrol., 43, 1049-1087. OTTONELLO, G. (2001): Thermodynamic constraints arising from 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). PAUL, A. and R.W. DOUGLAS (1965a). Ferrous-ferric equi- librium in binary alkali silicate glasses, Phys. Chem. Glasses, 6, 207-211. PAUL, A. and R.W. DOUGLAS (1965b) Ferrous-ferric equilib- rium in binary alkali silicate glasses, Phys. Chem. Glasses, 6, 212-215. RICHARDSON, F.D. (1956): Activities in ternary silicate melts, Trans. Farady Soc., 52, 1312-1324. RICHARDSON, F.D. and L.E. WEBB (1956): Oxygen in molten lead and the thermodynamics of lead oxide-silica melts, Trans. Inst. Min. Metall., 64, C529-C555. STEBBINS, J.F. (1987): Identification of multiple structural species in silicate glasses by Si-29 NMR, Nature, 330, 465-467. STEBBINS, J.F., P.F. MCMILLAN and D.B. DINGWELL (Editors) (1995): Structure, dynamics and properties of silicate liquids, Mineral. Soc. Am., Rev. Mineral., 32, pp. 616. TEMKIN, M. (1945): Mixtures of fused salts as ionic solu- tions, Acta Phys. Chim. U.R.S.S., 20, 411-420. TOOP, G.W. and C.S. SAMIS (1962a): Activities of ions in silicate melts, Trans. Met.-Soc. A.I.M.E., 224, 878-887. TOOP, G.W. and C.S. SAMIS (1962b): Some new ionic con- cepts of silicate slags, Canad. Met. Quart., 1, 129-152. WAFF, H.S. and D.F. WEILL (1975): Electrical conductivity of magmatic liquid effects of temperatures, oxygen fu- gacity and composition, Earth Planet. Sci. Lett., 28, 254-260. XUE, X. and M. KANZAKI (2003): The dissolution mecha- nism of water in alkaline earth silicate melts: One view from 1H MAS NMR, Geochim. Cosmochim. Acta, 67, A543.