Fe-Mg Exchange Between Olivine and Liquid, as a Test of Equilibrium: Promises and Pitfalls

Fe-Mg Exchange Between Olivine and Liquid, as a Test of Equilibrium: Promises and PitfallsKeith PutirkaCalifornia State University, Fresno

Roeder and Emslie (1970) conducted experiments (n= 44) atT = 1150 – 1300 oCfO2 = 10-0.68 – 10-12

Mg(olivine) + Fe2+(Liquid) = Mg(Liquid) + Fe2+(Olivine)

Roeder and Emslie (1970) conducted experiments (n= 44) atT = 1150 – 1300 oCfO2 = 10-0.68 – 10-12


KD(Fe-Mg)ol-liq = 0.30

and appears to be (mostly) independent of T, Xi, P

But Matzen et al. (2011) show that the canonical value of 0.30 may be too low, even at 1 atm (instead, KD = 0.34)

So KD = 0.30 or KD = 0.34?

Why are these experimental values so different?Sources of error when determining KD

1. Experimental Error - is it random? (an oft implicit assumption)

2. Oxygen buffer log[fO2] (trivial)3. fO2 Fe3+/Fe2+ ratios in the liquid (not trivial)


-0.4 0.1 0.6

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

KD(Fe-Mg)ol-liq Jayasuria et al. (2004)

KD(F

e-M

g)ol

-liq

K&C

1991

Experimental Data (LEPR) Yielding ol + liqwith reported fO2

n = 1110

We can’t ignore model error with regard to Fe3+/Fe2+

Using Jayasuria et al. (2004), KD is systematically higher than using Kress & Carmichael (1991)

The ensuing T error is 30-70oC

Jayasuria et al. (2004) Eqn. 12 works well for calibration data, but over-predicts Fe2O3/FeO for test data

0.01 0.1 1 100.01

0.1

1

10

Calibration Data

Test Data

1-to-1 line

Molar Fe2O3/FeO Jayasuria et al. (2004; Eq. 12)

Mo

lar

Fe

2O

3/F

eO

Me

asu

red

Experiments: Fe2O3/FeO measuredCalib. Data: n = 218Test data: n = 127

Compare Calibration & Test data for Jayasuria et al. Eqn. 12

Global Data SetSlope = 0.79

Intercept = 0.10R2 = 0.73

SEE = ± 0.36N = 345

Kress & Carmichael (1991; Eqn. 7) performs slightly better for test data

0.01 0.1 1 100.01

0.1

1

10

Calibration Data

Test Data

1-to-1 line

Molar Fe2O3/FeO Kress & Carmichael (1991, Eq. 7)

Mol

ar F

e2O

3/F

eO M

easu

red


…..and for Kress & Carmichael (1991) Eqn. 7



SEE = ± 0.33N = 345

Kress & Carmichael (1988) performs even better still

0.01 0.1 1 10 1000.01

0.1

1

10

100

Calibration Data

Test Data

1-to-1 line

Molar FeO1.464/FeO Kress & Carmichael (1988)

Mol

ar F

eO1.

464/

FeO

Mea

sure

d


….. and Kress & Carmichael (1988) is better still



SEE = ± 1.0N = 345

A global regression cleans up some of the scatter

0.01 0.1 1 100.01

0.1

1

10

Calibration Data

Calibration Data

1-to-1 line

Molar Fe2O3/FeO - New Calibration

Mol

ar F

e2O

3/F

eO M

easu

red

Experiments: Fe2O3/FeO measuredCalib. Data: n = 345

A new model based on a global regression



SEE = ± 0.24N = 345

So fO2 Fe3+/Fe2+ represents an important source of error in KD

What about experimental error?

Can (at least some of it) be random?

First, we need a model to predict KD…

0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

0.7

KD Predicted (GSA abstract)

KD M

easu

red

(usi

ng K

&C

1988

)

R2 = 0.24SEE = ± 0.04

n = 1190

Model in GSA Abstract: KD(Fe-Mg)ol-liq = 0.41 - 0.004[CaO wt. %] – 0.008[TA] - 0.006[TiO2 wt. %]

To get KD, we assume experimental error is random

KD variations mostly reflect experimental error

A New Model: KD(Fe-Mg)ol-liq = 0.44 - 0.0069[Al2O3 wt. %] - 0.0069[TiO2 wt. %]

0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

0.7

KD Predicted (Al + Ti model)

KD M

easu

red

(usi

ng n

ew F

e3+/

Fe2+

m

odel

)

R2 = 0.30SEE = ± 0.04

n = 1510

Could some error be random? Run Duration

0.1 1 10 100 1000 10000

-0.3

-0.2

-0.1

5.55111512312578E-17

0.1

0.2

0.3

Duration of Experiment (hours)

Erro

r on

KD

Could some error be random? Temperature

800 1000 1200 1400 1600 1800 2000

-0.3

-0.2

-0.1

5.55111512312578E-17

0.1

0.2

0.3

Temperature (oC)

Erro

r on

KD

Could some error be random? Composition (Mg)

0.001 0.01 0.1 1 10 100

-0.3

-0.2

-0.1

5.55111512312578E-17

0.1

0.2

0.3

Error on MgO Measurement in Olivine

Erro

r on

KD49.5% >0

50.5% <0

Why, then, do Matzen et al. (2011) obtain a higher KD = 0.34?

They have lower TiO2

lower Al2O3 lower Total Alkalis

0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

1 atm Epxpts.Matzen et al. (2011)Roeder & Emslie (1970)

MgO

Tota

l Alk

alis 0 1 2 3 4 5 6 7

0

5

10

15

20

25

30

1 atm Expts.Matzen et al. (2011)Roeder & Emslie (1970)

TiO2Al

2O3

Conclusions:

- fO2 Fe3+/Fe2+ models imprecise (± 0.3-0.4) & a source of systematic error

- Experimental error may be random

- We can predict KD from liquid composition alone

- KD(Fe-Mg)ol-liq = 0.33 ± 0.09 (Using new Fe3+/Fe2+)- Error = ±0.04 if KD=f(Xi)

- Best to propagate error on KD to get error on T

5.0 5.5 6.0 6.5 7.0 7.5 8.0-5

-3

-1

1

3

5

7

9

11

13

15

f(x) = − 4.39343992905112 x + 36.2502239969321R² = 0.514642429363058

104/T(K)

lnKe

qKeq is for Mg2SiO4 + 2 FeO = Fe2SiO4 + 2MgO

Ideal activities

DHex = -365 kJ/mole

Jayasuria et al. (2004) predict higher Fe2O3/FeO compared to Kress & Carmichael (1991)

1 100.001

0.01

0.1

1

Molar Fe2O3/FeO Jayasuria et al. (2004; Eqn. 12)

Mol

ar F

e2O

3/Fe

O K

&C

1991

; Eqn

. 7)

Experimental Data (LEPR) Yielding ol + liqwith reported fO2

n = 1110

The contrast in KDs reflects systematic offset in predictions of Fe3+/Fe2+

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

Calibration Data

Calibration Data

Molar Fe2O3/FeO New Calibration

Mo

lar

Fe

2O

3/F

eO

Me

asu

red

Linear scale illustrates unresolved error

Experiments: Fe2O3/FeO measuredCalib. Data: n = 345

A new model based on a global regression



SEE = ± 0.24N = 345

Toplis (2005) model uses olivine composition as input

KD(Fe-Mg)ol-liq model of Toplis (2005)

R2 = 0.29SEE = ±

0.04n = 1563

0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

0.7

KD(Fe-Mg)ol-liq Predicted (Toplis)

KD(F

e-M

g)ol

-liq

Mea

sure

d (N

ew N

BO/T

m

odel

)

The contrasts between the two models are not compositionally restricted

0 5 10 15 20 25 300

5

10

15

20

MgO

Jaya

suria

KD

- K

&C1

991

KD

Experimental Data (LEPR) n = 1110

% Difference in KD Calculated using Jayasuria v. Kress * Carmichael

% Difference in KD Calculated using Jayasuria v. Kress * Carmichael

30 35 40 45 50 55 60 65 70 75 800

5

10

15

20

SiO2

Jaya

suria

KD

- K

&C1

991

KD


The contrasts between the two models are not compositionally restricted

R2 = 0.9Slope = 0.67Int. = -0.03SEE = ± 0.4

0.01 0.1 1 10 1000.01

0.1

1

10

100

Molar FeO1.5/FeO Roeder & Emslie (1970)

Mo

lar

Fe

O1

.5/F

eO

Me

asu

red

Roeder & Emslie calibrated at T-independent model to predict FeO1.5/FeO

Test data (from 1995 - 2008)n = 115T = 1100 – 1300 oC

Roeder & Emslie calibrated a model at 1200 ± 5 oC – and it works well (but was not generalized)

The models we use to calculate fO2 from T (and P) can shift KD(Fe-Mg)ol-liq by up to 2.6% at 1700 oC

0.295 0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Mysen & Eugster (1983)

Schwab & Kustner (1981)

Hewitt (1978)

KD(Fe-Mg)ol-liq

log

fO

2 (

ba

rs)

Models Describing QFMT = 800-1700oCKress & Carmichael (1988)

The ensuing T error is negligible: 5 to 8 oC at 1700 oC


Using Jayasuria et al. (2004), KD is systematically higher than using Kress & Carmichael (1991)

-0.4 0.1 0.6

-0.1

-8.32667268468867E-17

0.0999999999999999

0.2

0.3

0.4

0.5

0.6

KD(Fe-Mg)ol-liq Jayasuria et al. (2004)

KD(F

e-M

g)ol

-liq

K&C

1991 Experimental Data (LEPR)

Yielding ol + liqn = 1629

But we can’t ignore model error with regard to Fe3+/Fe2+

The ensuing T error is 30-70oC

Could some error be random? Composition (Fe)

0.001 0.01 0.1 1 10 100

-0.3

-0.2

-0.1

5.55111512312578E-17

0.1

0.2

0.3

Error on FeO Measurement in Olivine

Erro

r on

KD

The contrasts between the Jayasuria and Kress and Carmichael models are not restricted with respect to composition

% Difference in KD Calculated using Jayasuria v. Kress and Car.

0 2 4 6 8 10 12 14 160

5

10

15

20

Na2O + K2O

Jaya

suria

KD

- K

&C1

991

KD


The contrasts between the Jayasuria and Kress and Carmichael models are not restricted with respect to Temperature

% Difference in KD Calculated using Jayasuria v. Kress and Car.

900 1000 1100 1200 1300 1400 1500 1600 17000

5

10

15

20

T(C)

Jaya

suria

KD

- K&

C199

1 KD


Documents

Fe-Mg Exchange Between Olivine and Liquid, as a Test of Equilibrium: Promises and Pitfalls