Garnet is notably absent in mafic to felsic lithologies, in low-P metamorphic terranes, and in Mg-rich bulk compositions in high-P regionally metamorphosed terranes. In the absence of garnet, existing mineral barometers cannot be applied for estimating metamorphic pressure. A new garnet-free, hornblende-plagioclase barometer has been formulated based on the reaction tremolite + tschermakite + 2 albite = 2 pargasite + 8 quartz. The intra- and cross-site mixing parameters for hornblende were retrieved exclusively from experimental data in the P-T window 1–15 kbar and 650–950 °C, after screening the available data for the presence of quartz. A linear least-squares fit to the coexisting hornblende and plagioclase composition in the experiments yields the following barometric expressions:

\begin{eqnarray*}&&\mathit{P}_{1}(kbar)\ =\ [{-}9.326\ +\ 0.01462T\ (K)\ +\ R\mathit{T}ln\mathit{K}_{ideal}\ {-}\ 98.698\mathit{X}^{A}\ _{Na}\ {-}\ 33.213\mathit{X}^{A}\ _{K}\ {-}\ 20.338\mathit{X}^{M4}_{Na}\ {-}\ 39.101\mathit{X}^{M13}_{Fe^{2+}}\\&&+\ 100.392\mathit{X}^{M2}\ _{Al}\ +\ 131.03\mathit{X}^{M2}\ _{Fe^{2+}}\ +\ 82.479\mathit{X}^{M2}\ _{Fe^{3+}}\ {-}\ 118.653\mathit{X}^{T1}\ _{Al}\ {-}\ 2R\mathit{T}ln{\gamma}_{Ab}]/({-}{\Delta}\mathit{V})\end{eqnarray*}


\begin{eqnarray*}&&\mathit{P}_{2}(kbar)\ =\ [{-}1.869\ +\ 0.0076T\ (K)\ +\ R\mathit{T}ln\mathit{K}_{ideal}\ {-}\ 102.692\mathit{X}^{A}_{Na}\ {-}35.251\mathit{X}^{A}_{K}\ {-}\ 15.969\mathit{X}_{Na}^{M4}\ {-}\ 40.499\mathit{X}^{M13}\ _{Fe^{2+}}\\&&+\ 93.069\mathit{X}^{M2}\ _{Al}\ +\ 130.750\mathit{X}^{M2}\ _{Fe^{2+}}\ +\ 74.226\mathit{X}^{M2}\ _{Fe3+}\ {-}\ 104.402\mathit{X}^{T1}\ _{Al}\ {-}\ 2R\mathit{T}ln{\gamma}_{Ab}]/({-}{\Delta}\mathit{V})\end{eqnarray*}


\[\mathit{K}_{ideal}\ =\ \left[\frac{16(\mathit{X}_{Na}\mathit{^{A}})(\mathit{X}^{T1}_{Al})}{(\mathit{X}_{{\square}}\mathit{^{A}}(\mathit{X}^{T1}_{Si})(\mathit{X}_{Ab})}\right]^{2}.\]

Xij denotes the mole fraction of cation i in site j of amphibole, XAb and γAb are the mole fraction and activity coefficient of albite in plagioclase, respectively, and ΔV is the volume change for the reaction. In the expression for P2, the first two terms in the numerator on the right-hand side corresponding to ΔH° and ΔS°, respectively, were adopted from an internally consistent thermodynamic database. In the expression for P1, the first term on the right-hand side of the numerator, Δ(−9.326 kJ) = ΔH° + a9, where a9 is a mixing parameter, and the second term ΔS° = 0.01462 kJ/K, were retrieved by a linear least-squares fit to the experimental data. The formulations reproduced experimental P values within 2 kbar for 83% of the experimental runs. The cumulative precision (1σ) of pressure estimated using the formulations varied between 800 and 2000 bars for errors propagated due to uncertainties in P-T, volume, and thermometric estimate, and inaccuracies in estimated composition of phases. In natural assemblages spanning a pressure range of 2.5 to 12.5 kbar, the quartz–hornblende–plagioclase barometers yielded pressure within 2 kbar of the P-value recommended by the authors, and is consistent with the stable Al2SiO5 polymorph in associated metapelites.

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