A new formulation of garnet–clinopyroxene geothermometer based on accumulation and statistical analysis of a large experimental data set

Published experimental data including garnet and clinopyroxene as run products were used to develop a new formulation of the garnet–clinopyroxene geothermometer based on 333 garnet–clinopyroxene pairs. Only experiments with graphite capsules were selected because of difficulty in estimating the Fe³⁺ content of clinopyroxene. For the calibration, a published subregular‐solution model was adopted to express the non‐ideality of garnet. The magnitude of the Fe–Mg excess interaction parameter for clinopyroxene (W_FeMg^Cpx), and differences in enthalpy and entropy of the Fe–Mg exchange reaction were regressed from the accumulated experimental data set. As a result, a markedly negative value was obtained for the Fe–Mg excess interaction parameter of clinopyroxene (W_FeMg^Cpx = ? 3843 J mol^?1). The pressure correction is simply treated as linear, and the difference in volume of the Fe–Mg exchange reaction was calculated from a published thermodynamic data set and fixed to be ?120.72 (J kbar^?1 mol^?1). The regressed and obtained thermometer formulation is as follows: where T = temperature, P = pressure (kbar), A = 0.5 X_grs (X_prp ? X_alm ? X_sps), B = 0.5 X_grs (X_prp ? X_alm + X_sps), C = 0.5 (X_grs + X_sps) (X_prp ? X_alm), X_prp = Mg/(Fe²⁺ + Mn + Mg + Ca)^Grt, X_alm = Fe/(Fe²⁺ + Mn + Mg + Ca)^Grt, X_sps = Mn/(Fe²⁺ + Mn + Mg + Ca)^Grt, X_grs = Ca/(Fe²⁺ + Mn + Mg + Ca)^Grt, X_Mg^Cpx = Mg/(Al + Fe^total + Mg)^Cpx, X_Fe^Cpx = Fe²⁺/(Al + Fe^total + Mg)^Cpx, K_D = (Fe²⁺/Mg)^Grt/(Fe²⁺/Mg)^Cpx, Grt = garnet, Cpx = clinopyroxene. A test of this new formulation to the accumulated data gave results that are concordant with the experimental temperatures over the whole range of the experimental temperatures (800–1820 °C), with a standard deviation (1 sigma) of 74 °C. Previous formulations of the thermometer are inconsistent with the accumulated data set; they underestimate temperatures by about 100 °C at >1300 °C and overestimate by 100–200 °C at <1300 °C. In addition, they tend to overestimate temperatures for high‐Ca garnet (X_grs ≈ 0.30–0.50). This new formulation has been tested against previous formulations of the thermometer by application to natural eclogites. This gave temperatures some 20–100 °C lower than previous formulations.