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

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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 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 (WFeMgCpx), 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 (WFeMgCpx = -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 (Jkbar-1 mol-1). The regressed and obtained thermometer formulation is as follows: T(°C) = {2784 + 14.52 P + (2601 + 1.44 P) (2Xgrs Xprp - A) + (1183 + 6.98 P) (Xgrs2 - A) - 105(2XgrsXalm + B) + (814.6 + 3.61P) (Xgrs2 + B) - (254.6 + 8.42 P) (2XprpXalm - Xalm2 + C) - 83.6 (Xprp2 - 2XprpXalm + C) + 1388 Xsps 462 (XMgCpx - XFeCpx)}/{InKD + 1.431 +0.695 (2XgrsXprp + Xgrs2 - 2A) + 0.203 (Xgrs2 - 2XgrsXalm) + 0.922Xsps} - 273, where T = temperature, P = pressure (kbar), A = 0.5 Xgrs(Xprp X - Xalm - Xsps), B = 0.5 Xgrs (Xprp - Xalm + Xsps), C = 0.5 (Xgrs + Xsps) (Xprp - Xalm), Xprp = Mg/(Fe2+ + Mn + Mg + Ca)Grt, Xalm = Fe/(Fe2+ + Mn + Mg + Ca)Grt, Xsps = Mn/ (Fe2+ + Mn + Mg + Ca)Grt, Xgrs = Ca/ (Fe2+ + Mn + Mg + Ca)Grt, X MgCpx = Mg/ (Al + Fetotal + Mg)Cpx, XFeCpx = Fe2+/(Al+Fe total + Mg)Cpx, KD =(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 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.

Original languageEnglish
Pages (from-to)495-508
Number of pages14
JournalJournal of Metamorphic Geology
Volume27
Issue number7
DOIs
Publication statusPublished - 2009

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Garnets
clinopyroxene
garnet
Statistical methods
statistical analysis
Thermometers
Temperature
temperature
Graphite
Capsules
Enthalpy
Entropy
Thermodynamics
Calibration
enthalpy
graphite
entropy
thermodynamics
calibration
Experiments

Keywords

  • Clinopyroxene
  • Excess interaction
  • Garnet
  • Regular solution
  • Thermometer

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geology

Cite this

@article{65bf2c8660a74df397dea7d19b6b0061,
title = "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 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 (WFeMgCpx), 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 (WFeMgCpx = -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 (Jkbar-1 mol-1). The regressed and obtained thermometer formulation is as follows: T(°C) = {2784 + 14.52 P + (2601 + 1.44 P) (2Xgrs Xprp - A) + (1183 + 6.98 P) (Xgrs2 - A) - 105(2XgrsXalm + B) + (814.6 + 3.61P) (Xgrs2 + B) - (254.6 + 8.42 P) (2XprpXalm - Xalm2 + C) - 83.6 (Xprp2 - 2XprpXalm + C) + 1388 Xsps 462 (XMgCpx - XFeCpx)}/{InKD + 1.431 +0.695 (2XgrsXprp + Xgrs2 - 2A) + 0.203 (Xgrs2 - 2XgrsXalm) + 0.922Xsps} - 273, where T = temperature, P = pressure (kbar), A = 0.5 Xgrs(Xprp X - Xalm - Xsps), B = 0.5 Xgrs (Xprp - Xalm + Xsps), C = 0.5 (Xgrs + Xsps) (Xprp - Xalm), Xprp = Mg/(Fe2+ + Mn + Mg + Ca)Grt, Xalm = Fe/(Fe2+ + Mn + Mg + Ca)Grt, Xsps = Mn/ (Fe2+ + Mn + Mg + Ca)Grt, Xgrs = Ca/ (Fe2+ + Mn + Mg + Ca)Grt, X MgCpx = Mg/ (Al + Fetotal + Mg)Cpx, XFeCpx = Fe2+/(Al+Fe total + Mg)Cpx, KD =(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 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.",
keywords = "Clinopyroxene, Excess interaction, Garnet, Regular solution, Thermometer",
author = "Daisuke Nakamura",
year = "2009",
doi = "10.1111/j.1525-1314.2009.00828.x",
language = "English",
volume = "27",
pages = "495--508",
journal = "Journal of Metamorphic Geology",
issn = "0263-4929",
publisher = "Wiley-Blackwell",
number = "7",

}

TY - JOUR

T1 - A new formulation of garnet-clinopyroxene geothermometer based on accumulation and statistical analysis of a large experimental data set

AU - Nakamura, Daisuke

PY - 2009

Y1 - 2009

N2 - 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 (WFeMgCpx), 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 (WFeMgCpx = -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 (Jkbar-1 mol-1). The regressed and obtained thermometer formulation is as follows: T(°C) = {2784 + 14.52 P + (2601 + 1.44 P) (2Xgrs Xprp - A) + (1183 + 6.98 P) (Xgrs2 - A) - 105(2XgrsXalm + B) + (814.6 + 3.61P) (Xgrs2 + B) - (254.6 + 8.42 P) (2XprpXalm - Xalm2 + C) - 83.6 (Xprp2 - 2XprpXalm + C) + 1388 Xsps 462 (XMgCpx - XFeCpx)}/{InKD + 1.431 +0.695 (2XgrsXprp + Xgrs2 - 2A) + 0.203 (Xgrs2 - 2XgrsXalm) + 0.922Xsps} - 273, where T = temperature, P = pressure (kbar), A = 0.5 Xgrs(Xprp X - Xalm - Xsps), B = 0.5 Xgrs (Xprp - Xalm + Xsps), C = 0.5 (Xgrs + Xsps) (Xprp - Xalm), Xprp = Mg/(Fe2+ + Mn + Mg + Ca)Grt, Xalm = Fe/(Fe2+ + Mn + Mg + Ca)Grt, Xsps = Mn/ (Fe2+ + Mn + Mg + Ca)Grt, Xgrs = Ca/ (Fe2+ + Mn + Mg + Ca)Grt, X MgCpx = Mg/ (Al + Fetotal + Mg)Cpx, XFeCpx = Fe2+/(Al+Fe total + Mg)Cpx, KD =(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 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.

AB - 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 (WFeMgCpx), 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 (WFeMgCpx = -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 (Jkbar-1 mol-1). The regressed and obtained thermometer formulation is as follows: T(°C) = {2784 + 14.52 P + (2601 + 1.44 P) (2Xgrs Xprp - A) + (1183 + 6.98 P) (Xgrs2 - A) - 105(2XgrsXalm + B) + (814.6 + 3.61P) (Xgrs2 + B) - (254.6 + 8.42 P) (2XprpXalm - Xalm2 + C) - 83.6 (Xprp2 - 2XprpXalm + C) + 1388 Xsps 462 (XMgCpx - XFeCpx)}/{InKD + 1.431 +0.695 (2XgrsXprp + Xgrs2 - 2A) + 0.203 (Xgrs2 - 2XgrsXalm) + 0.922Xsps} - 273, where T = temperature, P = pressure (kbar), A = 0.5 Xgrs(Xprp X - Xalm - Xsps), B = 0.5 Xgrs (Xprp - Xalm + Xsps), C = 0.5 (Xgrs + Xsps) (Xprp - Xalm), Xprp = Mg/(Fe2+ + Mn + Mg + Ca)Grt, Xalm = Fe/(Fe2+ + Mn + Mg + Ca)Grt, Xsps = Mn/ (Fe2+ + Mn + Mg + Ca)Grt, Xgrs = Ca/ (Fe2+ + Mn + Mg + Ca)Grt, X MgCpx = Mg/ (Al + Fetotal + Mg)Cpx, XFeCpx = Fe2+/(Al+Fe total + Mg)Cpx, KD =(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 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.

KW - Clinopyroxene

KW - Excess interaction

KW - Garnet

KW - Regular solution

KW - Thermometer

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