Calculation of Peridotite Partial Melting from Thermodynamic Models of Minerals and Melts. I. Review of Methods and Comparison with Experiments

Thermodynamic calculation of partial melting of peridotite using the MELTS algorithm has the potential to aid understanding of a wide range of problems related to mantle melting. We review the methodology of MELTS calculations with special emphasis on the features that are relevant for evaluating the suitability of this thermodynamic model for simulations of mantle melting. Comparison of MELTS calculations with well–characterized peridotite partial melting experiments allows detailed evaluation of the strengths and weaknesses of the algorithm for application to peridotite melting problems. Calculated liquid compositions for partial melting of fertile and depleted peridotite show good agreement with experimental trends for all oxides; for some oxides the agreement between the calculated and experimental concentrations is almost perfect, whereas for others, the trends with melt fraction are comparable, but there is a systematic offset in absolute concentration. Of particular interest is the prediction by MELTS that at 1 GPa, near–solidus partial melts of fertile peridotite have markedly higher SiO_2 than higher melt fraction liquids, but that at similar melt fractions, calculated partial melts of depleted peridotites are not SiO_2 enriched. Similarly, MELTS calculations suggest that near–solidus partial melts of fertile peridotite, but not those of depleted peridotite, have less TiO_2 than would be anticipated from higher temperature experiments. Because both experiments and calculations suggest that these unusual near–solidus melt compositions occur for fertile peridotite but not for depleted peridotite, it is highly unlikely that these effects are the consequence of experimental or model artifacts. Despite these successes of the results of calculations of peridotite melting using MELTS, there are a number of shortcomings to application of this thermodynamic model to calculations of mantle melting. In particular, calculated compositions of liquids produced by partial melting of peridotite have more MgO and less SiO_2 than equivalent experimentally derived liquids. This mismatch, which is caused by overprediction of the stability of orthopyroxene relative to olivine, causes a number of other problems, including calculated temperatures of melting that are too high. Secondarily, the calculated distribution of Na between pyroxenes and liquid does not match experimentally observed values, which leads to exaggerated calculated Na concentrations for near–solidus partial melts of peridotite. Calculations of small increments of batch melting followed by melt removal predict that fractional melting is less productive than batch melting near the solidus, where the composition of the liquid is changing rapidly, but that once the composition of the liquid ceases to change rapidly, fractional and batch melting produce liquid at similar rates per increment of temperature increase until the exhaustion of clinopyroxene. This predicted effect is corroborated by sequential incremental batch melting experiments (Hirose & Kawamura, 1994, Geophysical Research Letters, 21, 2139–2142). For melting of peridotite in response to fluxing with water, the calculated effect is that melt fraction increases linearly with the amount of water added until exhaustion of clinopyroxene (cpx), at which point the proportion of melt created per increment of water added decreases. Between the solidus and exhaustion of cpx, the amount of melt generated per increment of water added increases with temperature. These trends are similar to those documented experimentally by Hirose & Kawamoto (1995, Earth and Planetary Science Letters, 133, 463–473)

Towards an understanding of thallium isotope fractionation during adsorption to manganese oxides

We have conducted the first study of Tl isotope fractionation during sorption of aqueous Tl(I) onto the manganese oxide hexagonal birnessite. The experiments had different initial Tl concentrations, amounts of birnessite, experimental durations, and temperatures, but all of them exhibit heavy Tl isotope compositions for the sorbed Tl compared with the solution, which is consistent with the direction of isotope fractionation observed between seawater and natural ferromanganese sediments. However, the magnitude of fractionation in all experiments (? ? 1.0002–1.0015, where ?=205Tl/203Tlsolid/205Tl/203Tlliq is smaller than observed between seawater and natural sediments (? ? 1.0019–1.0021; Rehkämper et al., 2002, Earth. Planet. Sci. Lett. 197, 65–81). The experimental results display a strong correlation between the concentration of Tl in the resulting Tl-sorbed birnessite and the magnitude of fractionation. This correlation is best explained by sorption of Tl to two sites on birnessite, one with large isotope fractionation and one with little or no isotope fractionation. Previous work (Peacock and Moon, 2012, Geochim. Cosmochim. Acta 84, 297–313) indicates that Tl in natural ferromanganese sediments is oxidized to Tl(III) and adsorbed over Mn vacancy sites in the phyllomanganate sheets of birnessite, and we hypothesize that this site is strongly fractionated from Tl in solution due to the change in oxidation state from aqueous Tl(I). In most experiments, which have orders of magnitude more Tl associated with the solid than in nature, these vacancy sites are probably fully saturated, so various amounts of additional Tl are likely sorbed to either edge sites on the birnessite or triclinic birnessite formed through oxidative ripening of the hexagonal starting material, with unknown oxidation state and little or no isotopic fractionation. Thus each experiment displays isotopic fractionation governed by the proportions of Tl in the fractionated and slightly fractionated sites, and those proportions are controlled by how much total Tl is sorbed per unit of birnessite. In the experiments with the lowest initial Tl concentrations in solution (?0.15–0.4 ?g/g) and the lowest concentrations of Tl in the resulting Tl-sorbed birnessite (?17 ?g Tl/mg birnessite), we observed the largest isotopic fractionations, and fractionation is inversely proportional to the initial aqueous Tl concentration. Again, this correlation can be explained by the simultaneous occupation of two different sorption sites; vacancy sites that carry isotopically fractionated Tl and a second site carrying slightly fractionated Tl. The fractionation factors observed in nature exceed those in the experiments likely because the Tl concentrations in seawater and in ferromanganese sediments are three to four orders of magnitude lower than in our experiments, and therefore the second slightly fractionated sorption site is not significantly utilized. Temperature (6–40 °C) and experimental duration (3 min–72 h) appear to have little or no effects on isotope behaviour in this system