Mantle geothermometry: experimental evaluation and recalibration of Fe–Mg geothermometers for garnet-clinopyroxene and garnet-orthopyroxene in peridotite, pyroxenite and eclogite systems
Authors: Sudholz Z. J. , Green D. H. , Yaxley G. M. , Jaques A. L. 
Published: July 2022

The reliability of eight Fe–Mg exchange geothermobarometers for garnet-bearing peridotites, pyroxenites and eclogites has been examined using a database comprised of more than 300 published peridotite, pyroxenite and eclogite experiments conducted from 10 to 70 kbar and 850 to > 1650$$^\circ{\rm C}$$

∘

C

. We have tested Fe–Mg exchange geothermometers suitable for a range of mantle lithologies, including websterite, harzburgite, wehrlite and eclogite. All geothermometers maintained an average difference in experimental and calculated temperature (T) $$\left( {\Delta {\text{T}} = {\text{T}}_{{\exp - { }}} {\text{T}}_{{{\text{calc}}}} } \right)$$

Δ
T
=

T

exp
-

T
calc

of less than $$\pm$$
±
50 °C with a standard deviation of $$\Delta {\text{T}}$$

Δ
T

between $$\pm$$
±
50 to 150 °C. Most geothermometers performed well across a narrow range in ln $${\text{Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{A}} - {\text{B}}}}$$

Kd

Fe
-
Mg

A
-
B

(where $${\text{Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{A}} - {\text{B}}}} =$$

Kd

Fe
-
Mg

A
-
B

=

$$\frac{{\left( {{\text{Fe}}_{{\text{A}}} \times {\text{Mg}}_{{\text{B}}} } \right)}}{{({\text{Fe}}_{{\text{B}}} \times {\text{Mg}}_{{\text{A}}} )}}$$

Fe
A

×

Mg
B

(

Fe
B

×

Mg
A

)

), however, systematic overestimation and underestimation of T were observed outside of the optimal range of $${\text{lnKd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{A}} - {\text{B}}}}$$

lnKd

Fe
-
Mg

A
-
B

. Increases in experimental pressure (P) adversely affected several geothermometers, particularly those calibrated empirically using natural samples. All previously published calibrations of the garnet-clinopyroxene geothermometer were unable to reliably reproduce the experimental T for both peridotite and eclogite experimental compositions, which hinders their confident application to natural datasets. To improve the state of mantle geothermobarometry we have used our experimental database to recalibrate the (1) garnet-clinopyroxene Fe–Mg exchange geothermometer, and (2) garnet-orthopyroxene Fe–Mg exchange geothermometer. Each geothermometer has been recalibrated across an extended P, T, and compositional range. The inclusion of eclogitic experiments in the calibration for the garnet-clinopyroxene geothermometer permits application to both eclogitic and peridotitic/pyroxenitic assemblages equilibrated under a wide range of PT conditions in the upper mantle. Using multiple linear regression to solve for lnKd, we found the following expressions best reproduced the experimental T (℃) of our dataset: $${\text{T}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{cpx}}}} { (}^{ \circ } {\text{C)}} = { }\frac{3356.34}{{\left( {\left( { - 0.008 \times {\text{P }}\left( {{\text{kbar}}} \right)} \right) + \left( {0.259 \times {\text{X}}_{{{\text{Ca}}}}^{{{\text{grt}}}} } \right) + \left( {0.914 \times {\text{X}}_{{{\text{Mg}}}}^{{{\text{grt}}}} } \right) + \left( { - 0.159 \times {\text{Jd}}^{{{\text{cpx}}}} } \right) + \left( {{\text{ln}}\left( {{\text{ Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{cpx}}}} } \right) + 1.265} \right)} \right)}} - 273{ }$$

T

Fe
-
Mg

grt
-
cpx

(

∘

C)
=

3356.34

-
0.008
×

P

kbar

+

0.259
×

X

Ca

grt

+

0.914
×

X

Mg

grt

+

-
0.159
×

Jd

cpx

+

ln

Kd

Fe
-
Mg

grt
-
cpx

+
1.265

-
273

$${\text{T}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{opx}}}} { (}^{ \circ } {\text{C)}} = { }\frac{1851.85}{{\left( {\left( { - 0.007 \times {\text{P }}\left( {{\text{kbar}}} \right)} \right) + \left( { - 1.83 \times {\text{X}}_{{{\text{Ca}}}}^{{{\text{grt}}}} } \right) + \left( {{\text{ln}}\left( {{\text{ Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{cpx}}}} } \right) + 1.08} \right)} \right)}} - 273$$

T

Fe
-
Mg

grt
-
opx

(

∘

C)
=

1851.85

-
0.007
×

P

kbar

+

-
1.83
×

X

Ca

grt

+

ln

Kd

Fe
-
Mg

grt
-
cpx

+
1.08

-
273

. where, $${\text{X}}_{{{\text{Ca}}}}^{{{\text{grt}}}} =$$

X

Ca

grt

=

$$\frac{{{\text{Ca}}}}{{\left( {{\text{Ca}} + {\text{Fe}} + {\text{Mg}}} \right)}}$$

Ca

Ca
+
Fe
+
Mg

, $${\text{Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{opx}}}} =$$

Kd

Fe
-
Mg

grt
-
opx

=

$$\frac{{\left( {{\text{Fe}}_{{{\text{grt}}}} \times {\text{Mg}}_{{{\text{opx}}}} } \right)}}{{({\text{Fe}}_{{{\text{opx}}}} \times {\text{Mg}}_{{{\text{grt}}}} )}} , {\text{X}}_{{{\text{Mg}}}}^{{{\text{grt}}}} =$$

Fe
grt

×

Mg
opx

(

Fe
opx

×

Mg
grt

)

,

X

Mg

grt

=

$$\frac{{{\text{Mg}}}}{{\left( {{\text{Ca}} + {\text{Fe}} + {\text{Mg}}} \right)}}$$

Mg

Ca
+
Fe
+
Mg

, $${\text{Jd}}^{{{\text{cpx}}}} = {\text{Na}} - {\text{Cr}} - 2 \times {\text{Ti}}$$

Jd

cpx

=
Na
-
Cr
-
2
×
Ti

, $${\text{Kd}}_{{{\text{Fe}} - {\text{Mg}}}}^{{{\text{grt}} - {\text{cpx}}}} =$$

Kd

Fe
-
Mg

grt
-
cpx

=

$$\frac{{\left( {{\text{Fe}}_{{{\text{grt}}}} \times {\text{Mg}}_{{{\text{cpx}}}} } \right)}}{{({\text{Fe}}_{{{\text{cpx}}}} \times {\text{Mg}}_{{{\text{grt}}}} )}},$$

Fe
grt

×

Mg
cpx

(

Fe
cpx

×

Mg
grt

)

,

with all elements calculated on the basis of 12 oxygen anions in garnet and 6 oxygen anions in clino- and orthopyroxene. Fe2+  = total Fe. Our updated calibrations resolve several issues with earlier calibrations, including a poor performance at elevated P and compositional limitations. An improvement in precision and accuracy has been demonstrated through application to the experimental calibration dataset, a second independent set of published experimental data, and to natural peridotites, pyroxenites and eclogites from on and off craton settings. Iterative PT estimates on natural datasets calculated using our updated calibrations compare well with estimates from widely used calibrations such as the Taylor (1998) two-pyroxene solvus geothermometer. We anticipate that this contribution will provide an important reference for the reliability of mantle geothermometers and that our updated calibrations will be used in future studies on peridotite, pyroxenite and eclogite inclusions in diamond and mantle-derived xenoliths.