A thermodynamic model for F-Cl-OH partitioning between silicate melts and apatite including non-ideal mixing with application to constraining melt volatile budgets

The abundance and composition of volatiles in subvolcanic melts play a key role in controlling eruptive styles of volcanoes, but they are difficult to determine directly due to volatile loss during magma transport to the surface and eruption. Most constraints on volatile abundances are obtained by studying melt inclusions in minerals, but not all samples contain suitable inclusions, and they can be modified by a range of post-entrapment and re-equilibration processes. Apatite incorporates several volatile elements such as F, Cl, H, C and S into its structure, and thus has been proposed as an alternative tool for tracking the melt volatile contents. However, application of the apatite approach replies on the partitioning of volatiles between apatite and silicate melts, which has been found to show non-Nernstian behaviour but yet to be quantified. Here we propose a thermodynamic model that considers the non-ideal mixing in apatite solution, and includes the interaction parameters (W-G) and Gibbs free energy properties calculated by regressing experimental data from the literature. We find that W-G for the Cl-F binary join is larger than those for the Cl-OH, and F-OH joins, indicating a stronger non-ideality. We propose two equations for calculating the exchange coefficients (K-D) between apatite (Ap) and silicate melts as: ln (K-DOH-F(Ap-melt)) = -1/RT x {94, 600(+/- 5600) - 40(+/- 0.1) x T - 1000 x [7(+/- 4) x (X-F(Ap) - X-OH(Ap)) - 11(+/- 7) x X-Cl(Ap)]} and ln (K-DOH-Cl(Ap-melt)) = - 1/RT x {72, 900(+/- 2900) - 34(+/- 0.3) x T - 1000 x [5(+/- 2) x (X-Cl(Ap) - X-OH(Ap)) - 10(+/- 8) x X-F(Ap)]} where temperature (T) is in kelvins, apatite compositions are expressed in mole fractions (X-i(Ap)), and R is the universal gas constant. With the two equations above, we established a calculation procedure for estimating the water concentrations in the melt, and have developed it into an online calculator (https://apthermo.wovodat.org/). Application of this method to volcanic apatite from the literature (e.g. from Pinatubo, Campi Flegrei, Santiaguito and Augustine) gives melt water concentrations that are equivalent or higher than those measured from melt inclusions. Our new calibrations of the exchange coefficients allow us to obtain more robust estimates of melt volatile budgets, which provide more insights into the effects of volatiles on a variety of volcanic and plutonic phenomena. (C) 2019 The Authors. Published by Elsevier Ltd.