thermo barometry

7/29/2019 Thermo Barometry

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Thermobarometry


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Solid solutions

Rx ky+chl=st+q+H2O can be broken in two41Al2SiO5+4Fe5Al2Si3O10(OH)8=10Fe2Al9Si4O23(OH)

+13SiO2+11H2O &

41Al2SiO5+4Mg5Al2Si3O10(OH)8=10Mg2Al9Si4O23(OH)+13SiO2+11H2O

If 2nd Rx is subtracted from 1st

10Mg St+4Fe Chl= 10Fe St+4Mg Chl

Fe-Mg exchange Rx


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Since G= for i components sum nii and at equilibrium

10MgSt + 4FeCh = 10FeSt + 4MgCh or

10(FeStMgSt) 4(MgChFeCh) = 0 and the chemical

potential of each can be written in activity term

e.g. FeSt = *FeSt + RT ln aFeSt (*FeSt is the chem potenial of

pure FeSt at given P-T)

10(*FeSt - *MgSt )- 4(*MgCh - *FeCh ) = -10RT ln aFeSt

aMgSt

+ 4RT ln aFeCh

aMgCh

Since * = G the LHS is simply the free energy change of the

Rx


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Gexch = -RT ln a10

FeSt a4

MgCh

a10MgSt a4

FeCh

This free energy is known as Fe-Mg exchange potential;

Activity needs to be related to mole fraction

Assuming ideal mixing of component i on n equivalentsites in a mineral activity is ai = Xi

n Since St has two moles

of Fe and Ch has 5 moles of Fe aFeSt= X2

FeSt and aFeCh=

X5FeCh and thus above eq. becomes

Gexch = -RT ln X20

FeSt X20

MgCh

X20MgSt X20

FeCh

-Gexch = 20RT ln XFeSt XMgCh

XMgSt XFeCh (ratio of mole fraction is

known as distribution coefficient)


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lnKD = -Hoexch /mRT +S

oexch /mR (P-10

5)Voexch/mRT

For most Fe-Mg exchangesVoexch~ 0so this eq reducesto that of a straight line (y=mx+b) (y=lnKD ; m (slope)=Hoexch /mR; x=1/T and b=intercept on the y axis)

It can be used as a thermometer if 1) either thermodynamic

data is available for end members 2) or the Rx can becalibrated through exp studies or with other thermometers


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When solid solution results in impure phases the

activity of each phase is reduced

Use the same form as for gases (RT ln P orln f)

Instead of fugacity, we use activityIdeal solution: ai = Xi n = # of sites in the phase on

which solution takes place

Non-ideal: ai = gi Xiwhere gi is the activity coefficient


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Example: orthopyroxenes (Fe, Mg)SiO3

Real vs. Ideal SolutionModels

Activity-composition relationships for the enstatite-ferrosilite mixture in orthopyroxene

at 600oC and 800oC. Circles are data from Saxena and Ghose (1971); curves are model

for sites as simple mixtures (from Saxena, 1973)


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Consider the reaction:

2CaMgSi2O6(cpx) + Fe2SiO4(ol)

2CaFeSi2O6(cpx) + Mg2SiO4(ol)

We can calculate:

rG = 2fGCaFeSi2O6 + fGMg2SiO4

- 2fG

CaMgSi2O6+

fG

Fe2SiO4

ol

SiOFe

cpx

OCaMgSi

ol

SiOMg

cpx

OCaFeSio

raa

aaRTKRTG

42

2

62

42

2

62lnln


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This equation tells us that ln K is a function of

pressure and temperature. Thus, if we had a rockwith clinopyroxene and olivine which we can assume

were in equilibrium, we could calculate ln K from a

microprobe analysis and an activity model. Given an

independent estimate of P, we could calculate T, orvice versa.

If the above equation was relatively independent of

pressure, we could use it as a geothermometer even

if we did not have an independent estimate ofpressure. Similarly, if the reaction is relatively T-

independent, we might have a geobarometer.

KRTVPTG oso

r ln)1()bar1,(


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Thus, a good geothermometer is one in which the

absolute value ofrH is relatively high, and rV is

near zero.

Conversely, a good geobarometer is one in whichrH is nearly zero and the absolute value ofrV is

relatively high.

P

T

P

T

K = 10 5 2

K = 2

K = 5

K = 10

Potential geothermometer Potential geobarometer


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OTHER CRITERIA

1) Reasonably accurate standard-state thermodynamicdata are either known or can be estimated from simple-

system experiments. 2) The relationships between activities of the relevant

components in complex phases and the compositions

of the phases should be well-defined. In practice,

reactions involving major constituents are generally

more useful than those involving trace components (as

concentration increases, gi 0).


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GARB

KMg3AlSi3O10(OH)2+Fe3Al2Si3O12 =

KFe3AlSi3O10(OH)2+Mg3Al2Si3O12KDFeMg

BtGr= XFeBt/XMgBtXFeGr/XMgGr

Relationship of distribution coefficient with T-P can be given by-

lnKD= - (Ho

exch /3R)1/T+So

exch /3R[(P-105)Voexch/3RT] (3 is

for the three sites involved in the exchange)

Term in the square bracket can be dropped

Remaining expression can be plotted as a linear function of 1/T


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When solid solution results in impure phases the

activity of each phase is reduced

Use the same form as for gases (RT ln P orln f)

Instead of fugacity, we use activityIdeal solution: ai = Xi n = # of sites in the phase on

which solution takes place

Non-ideal: ai = gi Xiwhere gi is the activity coefficient


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Example: orthopyroxenes (Fe, Mg)SiO3

Real vs. Ideal SolutionModels

Activity-composition relationships for the enstatite-ferrosilite mixture in orthopyroxene

at 600oC and 800oC. Circles are data from Saxena and Ghose (1971); curves are model

for sites as simple mixtures (from Saxena, 1973)


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Thus, the equilibrium constant can be written:

When dealing with element partitioning, it is common

to define a quantity called the distribution coefficient:

3

Bt

Mg

Grt

Fe

Bt

Fe

Grt

Mg

XX

XXK

3

1

KFeMg

FeMg

XX

XX

K Bt

Grt

BtMg

GrtFe

Bt

Fe

Grt

Mg

D


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Plots showing the disposition of garnet-biotite tie lines at different

temperatures on two different diagrams.


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Plot of ln KD vs. 1/T for experimentally equilibrated garnet-biotite

pairs. P = 2.07 kbar. From Ferry and Spear (1978).


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P-T diagram in which lines of constant KD for the garnet-biotite

thermometer have been plotted.


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OTHER EXCHANGE

GEOTHERMOMETERS

Fe-Mg exchange between garnet and cordierite. Fe-Mg exchange between garnet and clinopyroxene.

Fe-Mg exchange between garnet and orthopyroxene.

Fe-Mg exchange between garnet and hornblende.

Fe-Mg exchange between garnet and chlorite. Fe-Mg exchange between garnet and olivine.

Fe-Mg exchange between biotite and tourmaline.

Fe-Mg exchange between garnet and phengite.

Fe-Mn exchange between garnet and ilmenite.

Stable isotope exchange.


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SOLVUS GEOTHERMOMETERS

As name implies, these are based on a solvusbetween two immiscible phases. Examples include:

1) Two-pyroxene geothermometry - distribution of Ca

and Mg between cpx and opx.

2) Calcite-dolomite geothermometry - distribution ofCa and Mg between calcite and dolomite.

3) Two-feldspar geothermometry - distribution of K

and Na between alkali feldspar and plagioclase.

4) Muscovite-paragonite - distribution of K and Nabetween muscovite and paragonite.


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NET TRANSFER REACTIONS

Many geobarometers are based on net-transfer

reactions, i.e., reactions that cause the production and

consumption of phases. Such reactions often result in

large volume changes, so the equilibrium constant is

pressure-sensitive. An example (garnet-plagioclase-olivine):

3Fe2SiO4 + 3CaAl2Si2O8

Ca3Al2Si3O12 + 2 Fe3Al2Si3O12


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THE GASP GEOBAROMETER

GASP = Garnet-AluminoSilicate-Plagioclase-quartz

This is a net transfer geobarometer based on the reaction:3CaAl2Si2O8 Ca3Al2Si3O12 + 2AlSi2O5 + SiO2

Solid solution of grossular with other garnet components,

mainly, almandine and pyrope, lowers the pressure at

which the right-hand side assemblage is stable. Solid solution of anorthite with albite in plagioclase tends

to stabilize the left-hand side to higher pressures.

Because grossular often quite dilute, the pressure-

lowering effect prevails. Garnet + plagioclase + Al2SiO5 + quartz is a common

assemblage in the crust.


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From Goldsmith (1990) we get:

P(kbars) = -2.10 + 0.0232T(C)

and the error is expected to be on the order of 1 kbar. The analogous expression for the GASP reaction with

sillimanite is:

P(kbars) = -0.6 + 0.0236T(C)

Once you have P(T), then, rG(T) = -P(T)rV,

where P(T) is the breakdown pressure of anorthite at

a given temperature for the end-member reaction, andrV = -66.2 cm

3 mol-1 at 298 K and 1 bar (the molar

volume change for the end-member reaction).


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KOZIOL & NEWTON (1988)

CALIBRATION

P(kbar) = -1.093 + 0.0228T(C)

This calibration can be written in the alternative form:

0 = -48,357 + 150.66 T(K) + (P-1)(-6.608) + RT ln K Thus, for this calibration we get:

rH(298 K,1 bar) = -48,357 J mol-1

rS(298 K,1 bar) = -150.66 J K-1 mol-1

rV(298 K,1 bar) = -6.608 J bar-1 mol-1 and it is assumed that rV is constant and rCp = 0.


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PARTIAL MOLAR VOLUMES OF


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PARTIAL MOLAR VOLUMES OF

GROSSULAR

In garnets where grossular is a minor component, the partial

molal volume of grossular is considerably different from the molal

volume.

The partial molar volume of grossular in solid solution with pyrope

can be expressed as:

where

and A = 125.25; B = -11.205; C = -0.512; D = -0.418; E = 0.94; F= 0.083. For the grossular-almandine join we get: A = 125.24; B =

-8.293; C = -1.482; D = -0.480; E = 0.914; F = 0.066.

2exp1

22 ZF

ZXDCXAVpyr

pyrgross

F

EXZ

pyr


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Geothermobarometry


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The results of applying the garnet-biotite geothermometer of Hodges and Spear (1982) and the GASP geobarometer of Koziol (1988, in

Spear 1993) to the core, interior, and rim composition data of St-Onge (1987). The three intersection points yield P-T estimates whichdefine a P-T-t path for the growing minerals showing near-isothermal decompression. After Spear (1993).

Geothermobarometry

P-T-t Paths


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SOME OTHER NET-

TRANSFER EQUILIBRIA GRIPS = Garnet-Rutile-Ilmenite-

Plagioclase-quartz.

Ca3Al2Si3O12 + 2Fe3Al2Si3O12 + 6TiO2 3CaAl2Si2O8 + 6FeTiO3 + 3SiO2

GRAIL = Garnet-Rutile-Aluminosilicate-ILmenite-quartz.

Fe3Al2Si3O12 + 3TiO2 3FeTiO3 +

Al2SiO5 + 2SiO2


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P-T diagram showing results from garnet-biotite thermometry (steep


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P-T diagram showing results from garnet-biotite thermometry (steep

lines) and GASP barometry (gentle lines). All curves are calculated

from a single set of mineral analyses from Mt. Moosilauke, NH, USA.

P-T diagram showing the results of thermobarometry calculations on


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P T diagram showing the results of thermobarometry calculations on

sample SC-160 from Coolen (1980) using a consistent set of

thermobarometers.

thermo barometry

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