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

Abstract

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:Tð CÞ ¼f2784 þ 14:52 P þ ð2601 þ 1:44 PÞð2X grs X prp À AÞ þ ð1183 þ 6:98 PÞðX grs 2 À AÞÀ 105ð2X grs X alm þ BÞ þ ð814:6 þ 3:61PÞðX grs 2 þ BÞ À ð254:6 þ 8:42 PÞð2X prp X alm À X alm 2 þ CÞ À 83:6ðX prp 2 À 2X prp X alm þ CÞ þ 1388 X sps À 462ðX Mg Cpx À X Fe Cpx Þg=flnK D þ 1:431 þ 0:695ð2X grs X prp þ X grs 2 À 2AÞ þ 0:203ðX grs 2 À 2X grs X alm Þ þ 0:922X sps g À 273;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.

Effect of clinopyroxene composition on Fe–Mg distribution coefficient between garnet and clinopyroxene

“…4). In addition, such non-ideal mixing property was not observed from compilation of high-pressure and high-temperature experimental data at least for low-Xjd clinopyroxene (Nakamura, 2009). The negative correlation between lnK D and Xjd may appear only for high-Xjd (>0.50) omphacite (Hirajima, 1996), although the data compiled here do not show such correlation even for high-Xjd omphacite (Fig.…”

“…1) in order to avoid chemical modification during the decompression. Replacement of omphacite by symplectites may cause the modification of the original chemical compositions at UHP conditions (e.g., Nakamura andHirajima, 2000). Quantitative analyses of garnet and omphacite were performed with wavelength-dispersive X-ray spectrometry (JEOL JXA-8230) at Okayama University.…”

“…Since the proposal of the prototype geothermometer by Råheim and Green (1974), many researchers have recalibrated the garnet-clinopyroxene geothermometer, by mainly introducing non-ideal terms for variations in garnet composition (e.g., Ellis and Green, 1979, Powell, 1985, Pattison and Newton, 1989, Ai, 1994, Ganguly et al, 1996, Krogh-Ravna, 2000, Nakamura, 2009). However, the effect of changes in clinopyroxene composition on distribution coefficient between garnet and clinopyroxene (K D ) has not been paid much attention in these calibrations except for a few works (e.g., Berman et al, 1995).…”

Evidence for partial melting of eclogite from the Moldanubian Zone of the Bohemian Massif, Czech Republic

“…4), was probably also created at this decompression stage by the overgrowth of relic garnet within the melt. The P-T conditions of the decompressional stage were also estimated by applying the above mentioned geothermobarometer (Nakamura, 2009;Beyer et al, 2015) to the compositions of the Grt III rim and Cpx III ( Table 1). The obtained P-T conditions are around 950°C, 1.7 GPa, when assuming that total Fe is Fe…”

“…The omphacite inclusions (Cpx I) in Grt II are richer in jadeite content than the other matrix grains (Cpx II and III). Therefore, P-T conditions at the peak-P stage were estimated by applying a garnet-clinopyroxene geothermometer (Nakamura, 2009) and a garnet-clinopyroxene geobarometer (Beyer et al, 2015) to the core compositions of Grt II and Cpx I (Table 1). Total Fe was also treated as Fe 2+ in this calculation.…”