Geothermobarometry

Methodology

Geothermobarometry relies upon understanding the temperature and pressure of the formation of minerals within rocks. There are several methods of measuring the temperature or pressure of mineral formation or re-equilibration relying for example on chemical equilibrium between minerals, or by measuring the chemical composition and/or the crystal-chemical state of order of individual minerals, or by measuring the residual stresses on solid inclusions or densities in fluid inclusions.

"Classic" (thermodynamic) thermobarometry relies upon the attainment of thermodynamic equilibrium between mineral pairs/assemblages that vary their compositions as a function of temperature and pressure. The distribution of component elements between the mineral assemblages is then analysed using a variety of analytical techniques, such as electron microprobing (EM), scanning electron microscopy (SEM), and mass spectrometry (MS). There are numerous extra factors to consider such as oxygen fugacity and water activity (roughly, the same as concentration) that must be accounted for using the appropriate methodological and analytical approach (e.g. Mössbauer spectroscopy, micro-raman spectroscopy, infrared spectroscopy, etc.). Geobarometers are typically net-transfer reactions, which are sensitive to pressure but have little change with temperature, such as garnet-plagioclase-muscovite-biotite reaction that involves a significant volume reduction upon high pressure:

${\displaystyle \underset{\mathsf{\text{Fe-Al garnet}}}{\underbrace{{\mathsf{\text{Fe}}}_{\mathsf{3}}^{}{\mathsf{\text{Al}}}_{\mathsf{2}}^{}{\mathsf{\text{Si}}}_{\mathsf{3}}^{}{\mathsf{\text{O}}}_{\mathsf{12}}^{}}}\mathsf{+}\underset{\mathsf{\text{Ca-Al garnet}}}{\underbrace{{\mathsf{\text{Ca}}}_{\mathsf{3}}^{}{\mathsf{\text{Al}}}_{\mathsf{2}}^{}{\mathsf{\text{Si}}}_{\mathsf{3}}^{}{\mathsf{\text{O}}}_{\mathsf{12}}^{}}}\mathsf{+}\underset{\mathsf{\text{muscovite}}}{\underbrace{{\mathsf{\text{KAl}}}_{\mathsf{3}}^{}{\mathsf{\text{Si}}}_{\mathsf{3}}^{}{\mathsf{\text{O}}}_{\mathsf{10}}^{}{\mathsf{(}\mathsf{\text{OH}}\mathsf{)}}_{\mathsf{2}}^{}}}\stackrel{\mathsf{-}\rightharpoonup }{\leftharpoondown \mathsf{-}}\underset{\mathsf{\text{plagioclase}}}{\underbrace{\mathsf{3}{\mathsf{\text{CaAl}}}_{\mathsf{2}}^{}{\mathsf{\text{Si}}}_{\mathsf{2}}^{}{\mathsf{\text{O}}}_{\mathsf{8}}^{}}}\mathsf{+}\underset{\mathsf{\text{biotite}}}{\underbrace{{\mathsf{\text{KFe}}}_{\mathsf{3}}^{}{\mathsf{\text{AlSi}}}_{\mathsf{3}}^{}{\mathsf{\text{O}}}_{\mathsf{10}}^{}{\mathsf{(}\mathsf{\text{OH}}\mathsf{)}}_{\mathsf{2}}^{}}}}$

Since mineral assemblages at equilibrium are dependent on pressures and temperatures, by measuring the composition of the coexisting minerals, together with using suitable activity models, the P-T conditions experienced by the rock can be determined.

After one equilibrium constant is found, a line would be plotted on the P-T diagram. As different equilibrium constants of mineral assemblages would occur as lines with different slopes in the P-T diagram, therefore, by finding the intersection of at least two lines in the P-T diagram, the P-T condition of the specimen can be obtained.

Despite the usefulness of geothermobarometry, special attention should be paid to whether the mineral assemblages represent an equilibrium, any occurrence of retrograde equilibrium in the rock, and appropriateness of calibration of the results.

Elastic thermobarometry is a method of determining the equilibrium pressure and temperature attained by the host mineral and its inclusion on the rock history from the excess pressures exhibited by mineral inclusions trapped inside host minerals. Upon exhumation and cooling, contrasting compressibilities and thermal expansivities induce differential strains (volume mismatches) between a host crystal and its inclusions. These strains can be quantified in situ using Raman spectroscopy or X-ray diffraction. Knowing equations of state and elastic properties of minerals, elastic thermobarometry inverts measured strains to calculate the pressure-temperature conditions under which the stress state was uniform in the host and inclusion. These are commonly interpreted to represent the conditions of inclusion entrapment or the last elastic equilibration of the pair.

Data on geothermometers and geobarometers is derived from both laboratory studies on synthetic (artificial) mineral assemblages and from natural systems for which other constraints are available.

For example, one of the best known and most widely applicable geothermometers is the garnet-biotite relationship where the relative proportions of iron and magnesium in garnet and biotite change with increasing temperature, so measurement of the compositions of these minerals to give the Fe-Mg distribution between them allows the temperature of crystallization to be calculated, given some assumptions.

Assumptions in thermodynamic thermobarometry

In natural systems, chemical reactions occur in open systems with unknown geological and chemical histories, and the application of geothermobarometers relies on several assumptions that must hold in order for the laboratory data and natural compositions to relate in a valid fashion:

• That the full mineralogical assemblage required for the thermobarometer is present. If not all of the minerals of the reaction are present, or did not equilibrate with each other simultaneously, then any pressures and temperatures calculated for the ideal reaction will deviate from those actually experienced by the rock.
• That chemical equilibrium was achieved to a satisfactory degree. This could be impossible to demonstrate definitively, if the minerals of the thermobarometer assemblage are not all observed in contact with each other.
• That any minerals in a two-mineral barometer or thermometer grew in equilibrium, which is assumed when the minerals are seen to be in contact.
• That the mineral assemblage has not been altered by retrograde metamorphism, which can be assessed using an optical microscope in most cases.
• That certain mineralogical assemblages are present. Without these, the accuracy of a reading may be altered from an ideal, and there may be more error inherent in the measurement.
• That minerals present in thin section are in the same solid solution state as in the model. Many minerals such as feldspars and augite have a range of solid solution variations. Each variation can effect the model and the way a rock is metamorphosed over time.

Assumptions in elastic thermobarometry

In natural systems, the elastic behaviour of minerals can be easily perturbed by high-temperature re-equilibration, plastic or brittle deformation, leading to an irreversible change beyond the elastic regime that will prevent reconstructing the "elastic history" of the pair.

• The major assumption behind elastic geobarometry is that the host and the inclusion have experienced initially the same pressure and that deformation of the host-inclusion system is elastic, hence reversible, and can therefore be inverted to obtain the entrapment pressure of the inclusion.
• The shape of the inclusion is assumed to be spherical but calculations for non-spherical shapes are available.
• For several host-inclusion pairs the elastic properties for the host and the inclusion are assumed to be isotropic. For some pairs, anisotropic solutions are available (e.g. quartz in garnet, zircon in garnet).
• Simple calculation methods assume linear elasticity.