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:
• andSee 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.