Models for estimating the pressure and temperature of igneous rocks from co-existing clinopyroxene and liquid compositions are calibrated from existing data and from new data obtained from experiments performed on several mafic bulk compositions (from 8-30 kbar and 1100-1475 degrees C). The resulting geothermobarometers involve thermodynamic expressions that relate temperature and pressure to equilibrium constants. Specifically, the jadeite (Jd; NaAlSi2O6)-diopside/hedenbergite (DiHd; Ca(Mg, Fe) Si2O6) exchange equilibrium between clinopyroxene and liquid is temperature sensitive. When compositional corrections are made to the calibrated equilibrium constant the resulting geothermometer is(i) 10(4)/T = 6.73 - 0.26*ln[Jd(pr*)Ca(liq*)Fm(liq)/DiHd(px*)Na(liq*)Al(liq)]- 0.86*ln[Mg-liq/Mg-liq + Fe-liq] + 0.52*ln[Ca-liq]an expression which estimates temperature to +/- 27 K. Compared to (i), the equilibrium constant for jadeite formation is more sensitive to pressure resulting in a thermobarometer(ii) P = - 54.3 + 299* T/10(4) + 36.4*T/10(4)ln[Jd(px)/[Si-liq](NaAlliq)-Na-2*-Al-liq*]+ 367*[(NaAlliq)-Al-liq*]which estimates pressure to +/- 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Na-liq represent the cation fraction of the given oxide (NaO0.5) in the liquid and Fm = MgO + FeO. The mole fractions of Jd and diopside + hedenbergite (DiHd) components are calculated from a normative scheme which assigns the lesser of Na or octahedral Al to form Jd; any excess Al-VI forms Calcium Tschermak's component (CaTs; CaAlAlSiO6); Ca remaining after forming CaTs and CaTiAl2O6 is taken as DiHd. Experimental data not included in the regressions were used to test models (i) and (ii). Error on predictions of T using model (i) is +/- 40 K. A pressure-dependent form of (i) reduces this error to +/- 30 K. Using model (ii) to predict pressures, the error on mean values of 10 isobaric data sets (0-25 kbar, 118 data) is +/- 0.3 kbar. Calculating thermodynamic properties from regression coefficients in (ii) gives V-f(Jd) of 23.4 +/- 1.3 cm(3)/mol, close to the value anticipated from bar molar volume data (23.5 cm(3)/mol). Applied to clinopyroxene phenocrysts from Mauna Kea, Hawaii lavas, the expressions estimate equilibration depths as great as 40 km. This result indicates that transport was sufficiently rapid that at least some phenocrysts had insufficient time to re-equilibrate at lower pressures.
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