The barometer tremolite + tschermakite + 2 albite = 2 pargasite + 8 quartz: Constraints from experimental data at unit silica activity, with application to garnet-free natural assemblages

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: P1(kbar) = [-9.326 + 0.01462T (K) + RTlnK ideal - 98.698X A Na -33.213X A K -20.338X M4 Na -39.101X M13 Fe ²⁺+ 100.392X M2 Al + 131.03X M2 Fe³⁺ + 82.479X M2 Fe³⁺ -118.653X T1 Al -2RTlnγ Ab ]/(-ΔV) and P2(kbar) = [-1.869 + 0.0076T (K) + RTlnK ideal -102.692X A Na- 35.251X A K -15.969X M4 Na - 40.499X M13 Fe²⁺ + 93.069XM 2 Al + 130.750X M2 Fe²⁺ + 74.226XM 2 Fe³⁺ -104.402X T1 Al -2RTlnγ Ab ]/(-ΔV) Where denotes the mole fraction of cation i in site j of amphibole, X Ab and γ Ab 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 P 2 , 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 P 1 , the first term on the right-hand side of the numerator, ΔĤ (.9.326 kJ) = ΔH° + a 9 , where a 9 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 Al 2 SiO 5 polymorph in associated metapelites.