An experimental study was carried out to investigate the equilibrium between Fe oxy-component and hydroxy-component in Ti-bearing calcic amphiboles, as described in the dehydrogenation/oxidation reaction

\[Fe^{2+}\ +\ OH^{{-}}\ =\ Fe^{3+}\ +\ O^{2{-}}\ +\ 1/2H_{2},\]

for which the equilibrium constant (K) can be expressed as

\[\mathit{K}\ =\ \mathit{f}_{H_{2}}(28.94)\frac{(\mathit{X}_{Fe^{3+}})^{2}(\mathit{X}_{{\square}})^{2}}{(\mathit{X}_{Fe^{2+}})^{2}(\mathit{X}_{OH})^{2}}\ {\cdot}\ {\Phi}\ =\ \mathit{K}_{x}\ {\cdot}\ {\Phi}.\]

where □ = H-vacancy on the O3 anion position, ϕ is the activity coefficient term, and Kx represents the thermodynamic mole fraction term (i.e., the K expressed as mole fractions rather than activities).

The variation in Kx was quantified experimentally by annealing experiments on amphiboles of two different compositions: a mantle-derived kaersutite from Greenland, and a crustal pargasite from the Tschicoma Formation from the Jemez Mountains, New Mexico, volcanic complex. The conditions of the experiments ranged from 700–1000 °C, 1–10 kbar, and fH2 from that of the HM to GM solid buffer assemblages. The results, combined with similar data for a titanian pargasite from Vulcan’s Throne, Arizona (Popp et al. 1995), define the variation in log Kx as a function of T, P, and amphibole composition as given by the equation:

\[log\mathit{K}_{x}\ =\ 4.23\ {-}\ \frac{4380}{\mathit{T(K)}}\ +\ {\{}1.37\ {\cdot}\ [(Ti\ +\ Al_{total}apfu)\ {-}\ 2.49]{\}}\ +\ \left\{\frac{88}{\mathit{T(K)}}\ {\cdot}\ [\mathit{P}\ {-}\ 1(kbar)]\right\}\]

If the T, P, and amphibole composition are known, values of log Kx calculated from the equation predict the equilibrium logfH2 of any experiment to within ~0.1 to 0.3 log units. It is assumed that a similar uncertainty in log fH2 would also to apply to the conditions of formation of natural amphiboles in the same composition range. If log fO2 at the time of equilibration can be estimated independently for natural samples (e.g., mantle-derived amphiboles), the H2O activity also can be estimated.

An alternate approach for estimating H2O activity from amphibole-bearing mantle rocks is to use a variety of H2O-buffering equilibria among end-member components in olivine, two-pyroxenes, amphibole, and other phases: e.g., 2 tr +2 fo = 5 en + 4 di + 2 H2O.

A self-consistent thermodynamic database (THERMOCALC, Holland and Powell 1990) can be used to determine the aH2O of such univariant H2O-buffering equilibria as a function of P and T.

A mantle amphibole assemblage from Dish Hill (sample DH101-E, McGuire et al. 1991) was used to calculate aH2O using the two different methods. The mean value of log aH2O determined from seven different dehydration reactions is −1.70, with a 1σ range of ±0.50. That range of water activity is in good agreement with the value of log aH2O = −1.90 ± 0.3 obtained using the dehydrogenation/oxidation equilibrium, along with an estimate of log fO2.

The use of xenolith amphiboles to infer values of aH2O in the mantle requires that the H content of the amphibole does not change significantly during ascent or eruption. Changes in H content have significantly different effects on the dehydration and dehydrogenation equilibria, such that, comparison of the aH2O estimates from the two different methods may permit quantification of H loss.

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