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Garnet-clinopyroxene geothermometer

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Abstract

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al2O3-Na2O-SiO2 is as follows:

$$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$

where P is pressure, and Q1, Q2, and K D are given by the following equations

$$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$

(mole fractions in garnet)

$$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$

[mole fractions in clinopyroxene Mg = MgSiO3, Fe = FeSiO3, Ca = CaSiO3, Al = (Al2O3-Na2O)] K D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene.

Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe2++Fe3+.

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Abbreviations

R :

gas constant

T :

absolute temperature

P :

pressure

X :

mole fraction

γ:

activity coefficient

a :

activity

μ:

chemical potential

H :

enthalpy

S :

entropy

A ij C ijk :

binary and ternary Margule's parameters

V :

molar volume

Opx :

orthopyroxene

Cpx :

clinopyroxene

Gar :

garnet

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Authors and Affiliations

  1. Department of Geology, Brooklyn College, CUNY, 11210, Brooklyn, New York, USA

    S. K. Saxena

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Saxena, S.K. Garnet-clinopyroxene geothermometer. Contr. Mineral. and Petrol. 70, 229–235 (1979). https://doi.org/10.1007/BF00375352

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