Thermobarometry

Lecture 12

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.

Some theoretical considerations

• We have seen that which phase assemblage is stable and the composition of those phases depends on ∆Gr, which we use to calculate K o We also know ∆Gr depends on T and P.

• Reactions that make good geothermometers are those that depend strongly on T.

•

o What would characterize a good geothermometer?

• Similarly, a good geobarometer would be one strongly depending on P

• A good geothermometer will have large ∆H; a good geobarometer will have large ∆V.

Univariant Reactions• Univariant (or

invariant) reactions provide possible thermobarometers.

• There are 3 phases in the Al2Si2O5 system.o When two coexist, we need

only specify either T or P, the other is then fixed.

o All three can coexist at just one T and P.

o First is rare, second is rarer.

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:• Mg2Si2O6+MgAl2SiO6 = Mg3Al2Si3O12

• l.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.

Garnet Peridotite Geobarometry

• Subsequent refinements used asymmetric solution model to match experimental data.

• Recognize two distinct sites in opx crystal:o Smaller M1: Al substitutes hereo Larger M2: Ca substitutes here

• P given by

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

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.

Temperature in Peridotites

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

Ca2+

Exchange Reactions• There are a number of

common minerals where one or more ions substitutes for others in a solid solution.o The Fe2+–Mg2+ substitution is common

in ferromagnesian minerals.

• Let’s consider the exchange of Mg and Fe between olivine and a melt containing Mg and Fe.o This partitioning of these two ions

between melt and olivine depends on temperature.

o We can use a electron microprobe to measure the composition of olivine and co-existing melt (preserved as glass).

Olvine-Melt Geothermometer

• Reaction of interest can be written as:MgOol + FeOl = MgOl + FeOol

o (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.

Roeder & Emslie Geothermometer

• Roeder & Emslie (1970) decided to consider two separate reactions:

• MgOliq –> 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.

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 ƒO2.

• The reaction of interest is:yFe2TiO4 + (1-y)Fe3O4 + ¼O2 = yFeTiO3 + (3/2 -y)Fe2O3

magnetite s.s. hematite s.s.• The equilibrium constant for this reaction is

• The reaction can be thought of as a combination of an exchange reaction:

Fe3O4 + FeTiO3 = Fe3TiO4 + Fe2O3

magnetite + illmenite = ulvospinel + hematite• plus the oxidation of magnetite to hematite:

4Fe3O4 + O2 = 6Fe2O3

Buddington and Lindsley

Oxide Geothermometer

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.