GEOTHERMOBAROMETRY
An excellent way to tell pressure and temperature conditions that metamorphic rocks achieved is
from mineral assemblages, as we have discussed thus far. The second way is using chemical
compositions of minerals that are solutions of various minerals. The equilibrium relationships
among solid solutions minerals serve as geothermometers and/or geobarometers.
Geothermometry
Consider the assemblage garnet + biotite. Both of these minerals contain Fe and Mg, that can be
exchange between them as temperature and/or pressure change. We can write the exchange reaction
as:
phlogopite + almandine = annite + pyrope.
or
.
We can write an equilibrium constant, KD, for this reaction, that relates the ratios of Mg/Fe in both
minerals at a given temperature and pressure:
Some equilibrium constants are primarily a function of temperature. This is the case for Fe-Mg
exchange between garnet and biotite:
where R is the thermodynamic gas constant, ∆H is enthalpy of the reaction and ∆S is the entropy of
the reaction. The graphical representation of the equilibrium constant as a function of temperature is
shown in Figures 27-5 and 27-7. Note from Figure 27-7 that the garnet-biotite equilibrium constant
is also a slight function of pressure.
The full equation for the equilibrium constant that also incorporates the pressure effect is:
What makes Fe-Mg exchange between biotite and garnet an excellent thermometer is that it does
not involve a large change in molar volumes of the minerals, because Mg2+ and Fe2+ have almost
the same ionic radius. Therefore, pressure dependence of the thermometer is minimal.
Geobarometry
Some element exchanges involve minerals that have very different molar volumes (densities).
Therefore, the transfer of elements from one mineral to the other involves a large ∆V. An exchange
that involves a large ∆V is highly dependent on temperature.
For example, consider the following exchange reaction that involves the exchange of Ca between
plagioclase and garnet:
3 CaAl2Si2O8 (An in plag) = Ca3Al2Si3O12 (Gross in grt) + 2 Al2SiO5 (Sil) + SiO2 (Qtz)
The equilibrium constant for this reaction (called the GASP barometer) can be written as:
The
and
are cubed because in the first, Ca can exchange on three sites and in the
second, three feldspars are involved. The relation between the equilibrium constant and pressure for
the GASP barometer is given by:
.
Graphical solution to this equation is shown in Figure 27-9. Note that at high pressure there is fairly
strong dependence of the exchange reaction on temperature. Therefore, to get an accurate
determination of pressure, an independent determination of temperature has to be made, for
example from the garnet-biotite Fe-Mg geothermometer.
A note about geobarometers and geothermometers: Their accuracy depends on experimental data
from various labs and how the data is interpreted. Thus, there are usually several equations for
individual geothermometers and geobarometers. Many geothermometers and geobarometers are
listed in Table 27-4.
Applications
Equilibrium exchange recording peak temperatures
In many terranes, geothermometers and geobarometers record very well the P-T conditions that
existed at the peak temperatures that the rocks attained. The figure below shows such an example
from a terrane in granulites from Tanzania (after Coolen, 1980).
Derivation of P-T-t paths from zoned crystals
More interesting are rocks in which all minerals do not preserve equilibrium of peak metamorphic
conditions. Some minerals cannot exchange elements after they grow because the diffusion of the
elements through their crustal structure is negligible even at high temperatures. Therefore, they
preserve the equilibrium element exchange with other minerals at the time of their growth. Garnet
is such a mineral. Very often, garnets become chemically zoned as they grow in a changing P-T
field. Figure 27-12 shows a case where plagioclase grains were caught-up in a growing garnet
crystal in the Archean Wopmay orogen, Canada. Application of the GASP barometer gives
evidence that the garnet grew while the rocks were decompressing (Figs. 27-12; 27-13). The garnetbiotite Fe-Mg thermometer indicates the temperature range at which the decompression occurred.
With today techniques, we can date the different zones in garnet. Therefore, we can get absolute
dates for the P-T conditions of individual growth zones.