The barometer tremolite plus 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, horn-blende-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 degrees 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: P-I(kbar) = [-9.326 + 0.01462T(K) + RTlnK(ideal) - 98.698X(Na)(A) - 33.213(K)(A) - 20.338X(Na)(M4) - 39.101X(Fe2+)(M13) + 100.392X(At)(M2) + 131.03XFe(2+)(M2) + 82.479X(Fe2+)(M2) -118.653X(Al)(Tl) - 2RTln gamma(Ab)]/(-Delta V) and P-2(kbar) = [-1.869 + 0.0076T (K) + RTlnK(ideal) - 102.692X(Na)(A) - 35.251X(K)(A) - 15.969X(Na)(M4) - 40.499X(Fe2+)(M13) + 93.069X(Al)(M2) + 130.750X(Fe2+)(M2) + 74.226X(Fe3+)(M2) - 104.402X(Al)(Tl) - 2RTln gamma(Ab)]/(-Delta V) where K-ideal = 16(X-Na(A))(X-Al(Tl)) / (X-rectangle(A))(X-Si(Tl))(X-Ab) 2 X-l(j) idenotes the mole fraction of cation i in site j of amphibole, X-Ab and gamma(Ab) are the mole fraction and activity coefficient of albite in plagioclase, respectively, and Delta V 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 Delta H degrees and Delta S degrees. 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, Delta H (-9.326 kJ) = Delta H degrees + a(9) where a(9) is a mixing parameter, and the second term Delta S degrees = 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 (1 sigma) 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.