-4 The Nature of Silicate Melts Silicate melts are ionic solutions composed of anionic clusters (or polymers) sharing exchangeable cations. -4 The anionic clusters are dominated by tetrahedrally coordinated cations because of the high field strength (charge/radius Z/r) of Si, the dominate cation (SiO2 = 35 to 75 wt.%). MgZ/r = 4.35, Mg-O ionic bond strength = Z/coord no. = 2/6 = 1/3 SiZ/r = 22.22, Si-O ionic bond strength = Z/coord no. = 4/4 = 1 Futhermore, unlike the Mg-O bond the Si-O bond is significantly if not dominantly covalent in character.

Non-Bridging Oxygen Bridging Oxygen

decreasing abundance 3-D networks TO2 1-D Chains TO3 2-D Sheets T2O5 Raman Spectra Studies indicate that 4 different types of anionic clusters dominate most silicate melts. 3-D networks TO2 1-D Chains TO3 decreasing abundance 2-D Sheets T2O5 Isolated Tetrahedra TO4

O= + Oo 2 × O- M-O-M + T-O-T 2 M-O-T The average NBO/T of a silicate melt is a measure of the population distribution of anionic clusters existing in the melt, which is a function of its bulk composition. The average NBO/T ratio represents the summation of many reactions of the type: M-O-M + T-O-T 2 M-O-T O= + Oo 2 × O- free oxygen bridging oxygen non-bridging oxygens Equil. constant K = a(O-)2 / a(O=)×a(Oo) There are many such reactions in any silicate melt involving differing metals and differing anion tetrahedral clusters. The magnitude of the equilibrium constants (K) for any given reaction is a function of the relative Z/r of the Metal versus T cations. There is thus a competition between metal cations in a melt for oxygen ions with which to bond. Because of the Si-O bond strength and its abundance, Si is one of the strongest players.

Equil. constant K = a(O-)2 / a(O=)×a(Oo) M-O-M + T-O-T 2 M-O-T O= + Oo 2 × O- free oxygen bridging oxygen non-bridging oxygens The more basic a metal oxide, the greater the value of the equilibrium constant, and thus the lower the number of bridging oxygens and the more depolymerized the melt. Equil. constant K = a(O-)2 / a(O=)×a(Oo) Base Acid H, K, Na, Ca, Mg, Fe2+, Al, Fe3+, Cr, Ti, Si, P, C, S, O, Cl, F Increasing field strength Z / r

Basicity of a Melt As in the case of silicate minerals, there is not enough oxygen to coordinate all the Si4+ ions without being sharing with other metal cations. The result is a solution consisting of negatively charged tetrahedrally-coordinated clusters or polymers that are loosely held together by other metal ions in higher coordinated sites. The addition of oxides that are more acidic than Si (such as Ti, P, C) have equilibrium constants that are less than 1 and thus promote the increased polymerization of the melt by robbing Si complexes of O-. The addition of basic oxides to a melt decreases the polymerization of the melt by providing addition oxygen to coordinate Si. The activity of O= reflects the summation of all such reactions in a given melt and is taken as a measure of the basicity of a melt. The ratio of non-bridging oxygens to tetrahedral cations (NBO/T) of a melt is a measure of its average degree of polymerizations and thus another measure of the basicity of a melt, whose advantage is that it can be simply calculated from the chemical composition of the melt. NBO = 2 × O – 4 × T = ∑ n(NMi)n+ T = No. Network-forming cations T = SiO2 + KAlO2 + NaAlO2 (CaAl2O4 MgAl2O4 +TiO2 + Ca2(PO4)2)

Estimated fraction of major anion complexes in silicate melts versus the parameter: NBO/T

Equil. constant K = a(O-)2 / a(O=)×a(Oo) > 1 The common oxide components of silicate melts can be classified in terms of their acid/base character: Act as bases, giving oxygens to anionic tetrahedrally coordinated anions, promoting the conversion of bridging oxygens to non bridging oxygens and thus depolymerizing the melt. Bases: H2O, K2O, Na2O M-O-M + T-O-T 2 M-O-T O= + Oo 2 × O- free oxygen bridging oxygen non-bridging oxygens Equil. constant K = a(O-)2 / a(O=)×a(Oo) > 1

O= + Oo 2 × O- Acids: Ti-O-Ti + T-O-T 2 Ti-O-T The common oxide components of silicate melts can be classified in terms of their acid/base character: Acids: TiO2, P2O5, CO2 Act as acids competing with Si for oxygen to achieve tetrahedral coordination. They promote the increased polymerization of the melt by taking non-bridging oxygens from Si anion clusters to form their own anion clusters, or substitute for Si in its anion clusters. Ti-O-Ti + T-O-T 2 Ti-O-T O= + Oo 2 × O- free oxygen bridging oxygen non-bridging oxygens Equil. constant K = a(O-)2 / (a(O=)×a(Oo)) < 1

Amphoteric behaviour reflects solid solution in tetrahedral sites Act as an acid in tetrahedral coordination charge-balanced by K or Na as the components KAlO2 + NaAlO2. Al2O3 in excess of alkalis acts as a base. Amphoteric: Al2O3, Fe2O3, Cr2O3 SiO2 constitutes between ~35 and 75% of most terrestrial igneous melts. Some of the Al3+ and Fe3+ occupy tetrahedral sites, substituting for Si, if other elements in higher coordinated sites (such as Na+ and K+, and even Ca2+) are available for local charge balance as the components: KAlO2, NaAlO2, CaAl2O4 Note the viscosity peak at Na/Al ratio of 1, corresponding to maximum Al substitution of Al for Si in tetrahedral sites – maximum polymerization.

Extrapolations of phase equilibria in simple systems Qualitative Applications of acid-base model Extrapolations of phase equilibria in simple systems to more complex natural systems. Korzinski’s Rule # 1: a rise in the basicity of a melt enlarges the liquidus volume of minerals rich in basic oxides at the expense of minerals rich in acidic oxides, and vice versa. Korzinski’s Rule # 2: a rise in the basicity of a melt shifts the compositions of eutectics, peritectics, and cotectics towards the acid components.

Extrapolations of phase equilibria in simple systems Qualitative Applications of acid-base model Extrapolations of phase equilibria in simple systems to more complex natural systems. Korzinski’s Rule # 1: a rise in the basicity of a melt enlarges the liquidus volume of minerals rich in basic oxides at the expense of minerals rich in acidic oxides, and vice versa. Effect of P2O5 addition +

Prediction of Liquid Immiscibility Qualitative Applications of acid-base model Prediction of Liquid Immiscibility The degree of polymerization in Si-rich melts is high and thus the availability of O= ions to coordinate other metal cations is low. As temperature decreases, it becomes increasingly favourable for acidic components to form their own immiscible liquids rater than substitute for Si. In binary systems, the width of the liquid immiscibility gap is proportional to the field strength (Z/r) or acidity of the oxide Acidic Basic Mg Ca Ba Na K Z/r 2.5 1.9 1.3 0.9 0.6

Prediction of Trace element partitioning between coexisting immiscible Liquid Immiscibility Acid trace elements partition preferentially into the basic immiscible melt because of the higher activity of non-bridging oxygens with which to achieve their preferred coordination number

The viscosity of silicate melts is sensitive to composition Acidic melts are more viscous than basic melts, with viscosity being inversely proportional to: 1/~ NBO / T. rhyolites Log Viscosity (poise) andesites basalts Adding a relatively basic component (eg Na2O) to a silicate melt will decrease the melts viscosity. Adding a relatively acidic component (eg. P2O5)to a silicate melt will increase the melts viscosity.

A 2 Lattice Model for Silicate Melts Quantitative Applications of acid-base model Activity-composition models for the thermodynamic calculation of phase equilibria A 2 Lattice Model for Silicate Melts Assumption: Silicate melts are made of two types of chemical components. Network Formers (NF) consisting of Si and other high field strength elements capable of substituting for Si in tetrahedral anion clusters, or forming their own tetrahedral anion clusters. Network Modifiers (NM) which compete with the tetrahedrally coordinated anion clusters for oxygen - those involved in charge balancing elements in tetrahedral coordination Mixing of cations is restricted to either the NF or NM sites, but there is no interchange of cations between the two.

Predicting the composition of minerals in equilibrium with melt Olivine MgOliq + 0.5×SiO2liq = 0.5×(Mg2SiO4) ΔG = 0.0 = ∑Gproducts = ∑Greactants GMgO + 0.5×GSiO2 =0.5×GFo GoMgOliq + R×T×ln(aMgOliq ) + 0.5×GoSiO2liq + R×T×ln(aSiO2liq)0.5 = 0.5×GoFo + R×T×ln(aFo)0.5 ΔGoT = - R×T×ln ((aFo)0.5 / (aMgOliq)×(aSiO2liq)0.5)) ΔHo - T×ΔSo = - R×T×ln ((aFo)0.5 / (aMgOliq)×(aSiO2liq)0.5)) For reactions not involving a volatile phase, Ho and So are ~ constants for small changes in temperature and pressure, thus to a first approximation: a/T + b = - R×ln ((aFo)0.5 / (aMgOliq)×(aSiO2liq)0.5))

a/T + b = - R×ln ((aFo)0.5 / (aMgOliq)×(aSiO2liq)0.5)) = - R×LnK This is the equation of a straight line. Once we have activity-composition models for olivine and silicate melt, the constants a and b can be determined by experiment. The activity of forsterite (aFo) in olivine is generally taken as: aFo = (XM1Mg)×(XM2Mg) = (XMg)2 Ideal Mixing: If we assume silicate melts are ideal mixtures, then the activities of its components are simply equal to their mole fraction: aMgOliq = XMgO aSiO2liq = XSiO2 a = slope b

Ideal Mixing: 2 Lattice Model: aMgOliq = Mg / ∑NM aSiO2liq = Si / ∑NF aMgOliq = XMgO aSiO2liq = XSiO2 2 Lattice Model: aMgOliq = Mg / ∑NM aSiO2liq = Si / ∑NF

Prediction of trace element partitioning Ideal mixing Quantitative Applications Prediction of trace element partitioning Ideally trace elements are those elements whose concentration is so low that they obey Henry’s law. Cisolid / Ciliq = K constant Ideal mixing In practice, many trace element partition coefficients vary with the composition of the silicate melt. Using a two lattice activity model one can greatly reduce this dependence Mixing of network modifiers

Increasing basicity (increasing O=) favours Fe3+ over Fe2+ Oxidation State of Magmas Korzinski observed long ago that: Fe3+ / Fe2+ increases with the basicity of a silicate melt. increasing basicity FeO Fe2+ + O= Base: K1 = ([O=] × [Fe2+])/ [FeO] Fe2O3 + O= 2 × [FeO2]-1 Acid: K2 = [FeO2-]2 / [Fe2O3] × [O=] 4[FeO2]- 4Fe2+ + 6O= + O2 Increasing basicity (increasing O=) favours Fe3+ over Fe2+ K3 = ([Fe2+]4 × [O=] × fO2 )/ [FeO2-]4

There are now formulations that enable the calculation of viscosity, density, and ratio of Fe2O3/FeO of silicate melts as the sums of partial molar quantities of their oxide components calculated taking into account whether the components are network modifiers or network formers at any given temperature, pressure, and fO2.

The Nature of Silicate Magmas Melt versus Magma glass olivine olivine glass gas gas Pillow Margin Baffin Is. Most magmas and lavas are actually 2 phase mixtures of silicate liquid and crystals. Some are three and four phase mixtures with the presence of immiscible sulfide droplets and vapour bubbles. The situation gets even more complicated when crystals of different aspect ratios raise the number of mechanical components to 5 or more.

Viscosities and Densities of Magmas are affected by the phenocrysts that they carry. For ideal crystal spheres: Einstein-Roscoe equation: Viscosity of solid - fluid mixtures: mix = (1 - 3.5 × X) - 2.5 × o X = volume fraction crystals For high aspect ratio crystals, such as plagioclase, the effect is much more significant.

Basalt Cube - % melted 60% 70% 75% Natural silicate melts, however, are complex systems with many components and thus melt over a range of temperatures. Because of the high aspect ratios of plagioclase, basalt becomes rigid in the range of 30 to 40% solidification. Note how a cube of solid basalt retains its shape to 70% melting, even as the partial melt drains out of the bottom. Basalt Cube - % melted 60% 70% 75% Philpotts & Carroll, 1996

The compositions of liquids in silicate magmas follow compositional paths constrained by the liquidus volumes of the phenocrysts they carry. For example, in the binary system Forst. – Qtz. system, the composition of the liquids follow the liquidus curves.