Solutions and Thermobarometry - PowerPoint Presentation

Slide1

Solutions and Thermobarometry

Lecture 12Slide2

Plagioclase Solution

Unlike alkali feldspar, Na-

Ca

feldspar (plagioclase) forms a complete solid (and liquid) solution.

Let’s construct the melting phase diagram from thermodynamics.

For simplicity, we assume both liquid and solid solutions are ideal. Slide3

Plagioclase Solution

Condition for equilibrium:

e.g.:

Chemical potential is

Combining these:

standard states are the pure end member solids and liquids.Slide4

Plagioclase Solution

The

l.h.s

. is simply

∆

G

m

for the pure component:rearranging

Since XAn = 1 - XAb

error in book:

Ab

on lhs should be AnSlide5

Plagioclase Solution

From:

We can solve for mole fraction of Ab in the liquid:

The

mole fraction of any component of any phase in this system can be predicted from the thermodynamic properties of the end-members

.

In the ideal case, as here, it simply depends on

∆

Gm and T.In a non-ideal case, it would depend on

Gexcess as well.Computing the equation above (and a similar one for the solid), we can compute the phase diagram.Slide6

We now have enough thermodynamics to put it to some real use: calculating the temperatures and pressures at which mineral assemblages (i.e., rocks) equilibrated within the Earth

.Slide7

Some theoretical considerations

We have seen that which phase assemblage is stable and the composition of those phases depends on

∆G

r

, which we use to calculate K

We also know

∆G

r depends on T and P.Reactions that make good geothermometers are those that depend strongly on T.

What would characterize a good geothermometer?A good geobarometer would be one where K depends strongly depending on P

A good geothermometer will have large ∆H; a good geobarometer

will have large ∆V.Slide8

Univariant Reactions

Univariant (or invariant) reactions provide possible

thermobarometers

.There are 3 phases in the Al

2

Si

2

O5 system.When two coexist, we need only specify either T or P, the other is then fixed.All three can coexist at just one T and P.First is rare, second is rarer.Slide9

Garnet Peridotite Geobarometry

Original approach of Wood and

Banno

generally assumed ideal solution

Garnet becomes the high pressure aluminous phase in the mantle, replacing spinel.

Aluminum also dissolves in the orthopyroxene (also clinopyroxene)

We can write the reaction as:

Mg

2Si2O

6+MgAl2SiO6 = Mg

3Al2Si3O12l.h.s

. is the opx solid solution - Al end member does not exist as pure phase.Significant volume change associated with this reaction (but also depends on T).

Other complexities arise from Ca, Fe, and Cr in phases.Slide10

Garnet Peridotite Geobarometry

Subsequent refinements used asymmetric solution model to match experimental data.

Recognize two distinct sites in

opx

crystal:

Smaller M1: Al substitutes here

Larger M2:

Ca substitutes hereP given by

where C3 is constant and other parameters depend on K, T, and composition.Slide11

Solvus Equilibria

Another kind of

thermobarometer

is based on exsolution of two phases from a homogenous single phase solution.

This occurs when the excess free energy exceeds the ideal solution term and inflections develop, as in the alkali feldspar system.

Because it is strongly temperature dependent and not particularly pressure dependent, this makes a good geothermometer.Slide12

Temperature in Peridotites

Temperatures calculated from compositions of co-existing orthopyroxene (enstatite) and clinopyroxene (diopside) solid solutions, which depend on T.

Ca

2+

Slide13

Exchange Reactions

There are a number of common minerals where one or

more

ions substitutes for others in a solid solution.

The Fe

2+

–Mg

2+ substitution is common in ferromagnesian minerals.Let’s consider the exchange of Mg and Fe between olivine and a melt containing Mg and Fe.This partitioning of these two ions between melt and olivine depends on temperature.We can use a electron microprobe to measure the composition of olivine and co-existing melt (preserved as glass). Slide14

Olvine-Melt Geothermometer

Reaction of interest can be written as:

MgO

ol

+

FeO

l

= MgOl + FeOol(note, this does not involve redox, so we write it in terms of oxides since these are conventionally reported in analyses. We could write it in terms of ions, however.)Assuming both solid and liquid solutions are ideal, the equilibrium constant for this reaction is:

Unfortunately ∆H for the reaction above is small, so it has weak temperature dependence.Slide15

Roeder & Emslie Geothermometer

Roeder &

Emslie

(1970) decided to consider two separate reactions:

MgO

liq

–> MgOOl and FeOliq –> FeOOl Based on empirical data, they deduced the temperature dependence as:

and

See Example 4.3 for how to do the calculation - biggest effort is simply converting wt. percent to mole fraction.Slide16

Buddington and Lindsley

Oxide Geothermometer

Recall this diagram from Chapter 3

Things get interesting in real systems containing Ti, because both magnetite and hematite are solid solutions.

Partition of Fe and Ti between the two depends on

T

and ƒ

O2

.

rutileSlide17

Magnetite & Ilmenite

Magnetite &

Ilmenite

at high T in a gabbro

Ilmenite

exsolving

from magnetite at low TSlide18

The reaction of interest is:

y

Fe

2TiO

4

+ (1-

y

)Fe3O4 + ¼O2

= yFeTiO3 + (

3/2

-y)Fe2O3

magnetite s.s. hematite

s.s. The equilibrium constant for this reaction isThe reaction can be thought of as a combination of an exchange reaction:Fe

3O4

+ FeTiO3 = Fe3TiO

4 + Fe2

O3magnetite + illmenite =

ulvospinel

+ hematite

plus the oxidation of magnetite to hematite:

4Fe

3

O

4

+ O

2

= 6Fe

2

O

3

Buddington

and

Lindsley

Oxide GeothermometerSlide19

Computing Temperature and Oxygen Fugacity

The calculation is complex because the system cannot be treated as ideal (except

titanomagnetite

above 800˚C). Equilibrium constant is:

and

Must calculate

λ’s

using asymmetric solution model (using interaction parameters), then solve for T and ƒO2

. Example 4.4 shows how.Slide20

Update

There have been a number of revisions to

the Fe-

Ti

oxide

geothermobarometer

since the work of

Buddington and Lindsley. One of the most recent is by Ghiorso and Evans (2008). This is far more sophisticated and takes account of crystal structure and the specific sites in the crystal lattices where substitution occurs.This allows more accurate estimate of T and

fO2, but is computationally far more complex.They have an online calculator at: http://melts.ofm-research.org/CORBA_CTserver/OxideGeothrm/OxideGeothrm.php

From

Ghiorso

and Evans (2008). Slide21
Slide22

Next up: MELTS modelling

Visit the MELTS

web page

http://melts.ofm-

research.org

to find out more about this software. Several possible downloads from here, including Rhyolite-Melts (for Mac, but you need an X-Windows system) and

Rhyolite_MELTS

for Excel (Windows only).We will run some examples on this site.Visit the CalTech magmasource web site: http://magmasource.caltech.edu

/alphamelts/. Read about installing alphaMELTS.

Download and install the latest version (1.5) and any necessary virtual machine program (for Windows).