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 Fe 3+ 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: image 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/(Fe 2+ + Mn + Mg + Ca) Grt , X alm = Fe/(Fe 2+ + Mn + Mg + Ca) Grt , X sps = Mn/(Fe 2+ + Mn + Mg + Ca) Grt , X grs = Ca/(Fe 2+ + Mn + Mg + Ca) Grt , X Mg Cpx = Mg/(Al + Fe total + Mg) Cpx , X Fe Cpx = Fe 2+ /(Al + Fe total + Mg) Cpx , K D = (Fe 2+ /Mg) Grt /(Fe 2+ /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.