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Ian Carmichael spent 45 years thinking about and working on the activities of components in silicate melts and their use to estimate physicochemical conditions at eruption and in the source regions of igneous rocks. These interests, principally in major components such as Si[O.sub.2], led us to think about possible ways of determining the complementary activity coefficients of trace components in silicate melts. While investigating the conditions of accretion and differentiation of the Earth, a number of authors have determined the partitioning of trace elements such as Co, Ni, Mo and W between liquid Fe metal and liquid silicate. These data have the potential to provide activity information for a large number of trace components in silicate melts. In order to turn the partitioning measurements into activities, however, we need to know the activity coefficient of FeO, [γ.sub.FeO] in the silicate. We obtained [γ.sub.FeO] as a function of melt composition by fitting a simple model to 83 experimental data for which the authors had measured the FeO content of the silicate melt in equilibrium with metal (Fe-bearing alloy) at known [f.sub.O2]. The compositional dependence of [γ.sub.FeO] is weak, but, when calculated in the system Diopside-Anorthite-Forsterite, it decreases towards the Forsterite apex. A similar approach for Ni, for which twice as many data are available, leads to similar composition dependence of activity coefficient and confirms the suggestion that [γ.sub.NiO]/[γ.sub.FeO] is almost constant over a wide range of silicate melt composition. The activity coefficients for FeO were used in conjunction with measured Mo and W partitioning between Fe-rich metal and silicate melt to estimate activity coefficients for trace Mo[O.sub.2] and W[O.sub.3] dissolved in silicate melt. When combined with data on Mo- and W-saturated silicate melts a strong dependence of activity coefficient is observed. Calculated in the system Diopside-Anorthite-Forsterite, both Mo[O.sub.2] and W[O.sub.3] exhibit similar behaviour to FeO and NiO in that activity coefficients decrease as Forsterite content increases. The effect is much larger for Mo and W, however, [γ.sub.MoO2] and [γ.sub.WO3] varying by factors of 20 and nearly 100, respectively, in this system. In order to illustrate the potential applications of the metal-silicate partitioning approach to determine the activity coefficients of volatile elements, we used it to determine activity coefficients of PbO, Cu[O.sub.0.5] and In[O.sub.1.5] in a silica-saturated melt at 1,650°C. We find values of 0.22, 3.5 and 0.02, respectively, indicating a strong dependence on cation charge. The value for Cu[O.sub.0.5] is in excellent agreement with experimental data of Holzheid and Lodders (Geochim Cosmochim Acta 65:1933-1951, 2001), which shows that the method is viable. When combined with thermodynamic data on the gas species, we find that Pb is the most volatile of the 3 elements under 'normal' terrestrial conditions of oxygen fugacity but that In should become the most volatile under strongly reducing conditions such as those of the solar nebula. The oxygen fugacity dependence of volatility has implications for the high relative abundance of In in silicate Earth. We conclude that metal-silicate partitioning experiments are a viable means for determining activities of trace components in silicate melts and are particularly useful if the metal of the element is unstable or volatile at igneous temperatures. Keywords Activities * Trace elements * Silicate melts * Volatilities, Introduction Ian Carmichael broke new ground in igneous petrology with his use of the compositions of groundmass phases to estimate the activities of major oxide components in magmatic liquids. The [...]

We have determined the partition coefficients of a large number of trace elements between CaTi[O.sub.3] perovskite and anhydrous silicate melts at atmospheric pressure and 3 GPa. Determination of the concentration limits of Henry's law behaviour in the CaO-[Al.sub.2][O.sub.3]-Si[O.sub.2]-Ti[O.sub.2] system reveals that the incorporation of rare earth elements (REE) and tetravalent large ion lithophile elements (LIL[E.sup.4+] such as U and Th) at the Ca-site of CaTi[O.sub.3] perovskite occurs with charge compensation through Ca-vacancy formation rather than by coupled substitution of AI for Ti. When melt composition is varied, we find that partition coefficients for REE and Th are strong functions of the CaO content of the melt. The observed trends are in excellent agreement with those predicted from the Ca-vacancy model. Given that they adopt the same crystal structure and have similar trace element partitioning behaviour, CaTi[O.sub.3] perovskite and the deep mantle phase CaSi[O.sub.3] perovskite can be considered analogous to one another. When the analogy is pursued in detail, we find that partitioning into both phases follows the composition-dependence predicted by the Ca-vacancy model. Thus, substitution of REE, [U.sup.4+] and Th into CaSi[O.sub.3] in the lower mantle also occurs with Ca-vacancy formation to balance charge. Furthermore when 2+, 3+ and 4+ partition coefficients for both phases are plotted as functions of CaO melt content, the trends for CaSi[O.sub.3] and CaTi[O.sub.3] appear to be continuous. This surprising result means that partitioning into Ca-perovskite is independent of pressure and temperature and also of whether or not the host is CaSi[O.sub.3] or CaTi[O.sub.3]. One implication is that CaSi[O.sub.3] crystallising from a peridotitic magma ocean may have partition coefficients for Th and U up to about 400. Crystallisation and sequestration of as little as 0.25 volume% of this phase in the lower mantle early in earth history would make a significant contribution to current mantle heat production.

We have developed a predictive model for the partitioning of magnesium and a range of trivalent trace elements (rare earth elements, Y, In and Sc) between garnet and anhydrous silicate melt as a function of pressure, temperature and bulk composition. The model for the magnesium partition coefficient, [D.sub.Mg], is based on a thermodynamic description of the pyrope ([Mg.sub.3][Al.sub.2-] [Si.sub.3][O.sub.12]) melting reaction between garnet and melt. Simple activity-composition relations, which take explicit account of garnet non-ideality, link [D.sub.Mg] to the free energy of fusion ([DELTA][G.sub.[Florin]]) of pure pyrope without the need to invoke non-ideality in the liquid phase. The resulting predictive equation, based on the compositions of a large set (n = 160) of published garnet-melt pairs, produces values of [D.sub.Mg] that are within 20% of measured values at temperatures between 1,450 and 1,930 [degrees] C, and pressures between 2.5 and 7.5 GPa. The model for trivalent (3+) trace elements is based on the lattice strain approach to partitioning, which describes mineral-melt partition coefficients in terms of three parameters: the effective radius, [r.sub.0](3+), of the site on which partitioning takes place (in this case, the garnet X-site); the apparent site Young's modulus [E.sub.X](3+); and the partition coefficient [D.sub.0](3+) for a fictive trivalent element [J.sup.3+], with radius [r.sub.0](3+), that does not strain the crystal lattice when entering the garnet X-site. Analogous to the model for [D.sub.Mg], simple activity-composition relations link [D.sub.0](3+) to [DELTA][G.sub.[Florin]] of a hypothetical garnet component incorporating a hypothetical rare earth element [J.sup.3+] through a YAG-type charge-balancing mechanism ([J.sup.3+][Mg.sub.2][Al.sub.3][Si.sub.2][O.sub.12]). Through analysis of existing garnet-melt rare earth element partitioning data (n = 18 garnet-melt pairs), an expression is derived relating [D.sub.0](3+) to pressure, temperature and [D.sub.Mg]. Predicted [D.sub.REE/Y/Sc] values agree to within 5-50% of experimental measurements for all elements except La and Ce, which are liable to large experimental errors, spanning pressures between 2.5 and 5.0 GPa and temperatures between 1,430 and 1,640 [degrees] C. In conjunction with our new parameterisation for [D.sub.Mg], and previously published equations linking [r.sub.0](3+) and [E.sub.X](3+) to garnet major element composition, this model gives a description of trivalent REE, Y, In and Sc partitioning between garnets and anhydrous melts over a range of pressures, temperatures and compositions relevant to melting of garnet-bearing sources in the Earth's upper mantle.

A sliding redox sensor of (Ni,Mn)O + Ni metal is used to measure the oxygen fugacity, f(sub O2), of the graphite C-O equilibrium. The measurements are made for pressures ranging between 15-30 kbar and temperatures between 1100-1400 degrees centigrade. The fugacity measurements are used in estimating the fugacity of CO2 with an error of plus or minus 0.1 log units. Experimental details of fugacity measurements and an analysis of the results are given.