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Practical Aspects of Mineral Thermobarometry

Thermobarometer Calibration

The aim of this section will be to cover briefly such topics such as

You can read about these subjects in Spear 1993, chapter 8, pp. 241-244, and chapter 15, pp. 511-537.

Here's some provisional content, from lecture course handouts:

Condition for heterogeneous equilibrium

[Spear, p. 511]. A balanced chemical reaction such as Grs + 2 Ky + Qtz = 3 An could also be written in the form 3 An - Grs - 2 Ky - Qtz = 0, reminding us that the mass of each system component is conserved, and that reaction coefficients can be positive ("products") or negative ("reactants"). At equilibrium, a similar relationship holds among the chemical potentials of phase components (n are the reaction coefficients and there are m phase components):

i.e. there is no free energy difference between "reactants" and "products".

Expand the expression for heterogeneous equilibrium

[Spear, p. 512]. Adding up, for all the phase components, the expressions µi = µ°i + RTln(ai), gives us

deltaGR = 0 = deltaG0 + RTlnK

where K is the equilibrium constant or activity product, which depends on measured phase compositions. G0 is the standard state free energy change - something we can calculate if we have thermochemical data. Expanding deltaG0 to see what thermochemical data are needed, we get:

The subscripts and limits reflect the fact that thermochemical data are generally tabulated at 298K and 1 bar.

Linear approximation for solid-solid reactions

[Spear, p. 523]. deltaCP  = 0. The deltaCP terms adjust deltaH and deltaS for different P and T. The heat capacities of solid phases vary sympathetically, so deltaCP is small, and can often be ignored, particularly over small ranges of temperature.

deltaV constant. The volume integral brings the enthalpies from their reference pressure P0 (1 bar) up to the pressure of interest (usually several thousand bars). deltaV is not a function of P or T if all solids are roughly equally compressible, so the volume integral becomes deltaV(P - P0). Also, P0 is negligible compared to P.

This gives us the greatly simplified expression

which, for a given value of lnK, is the equation of a straight line on a P-T diagram. The curve for lnK = 0 (i.e. K = 1) is the curve for pure phases, such as might be determined in the experimental laboratory. Other values of lnK displace the curve across the P-T diagram.

Dependence of lnK on T and P

[Spear, pp. 515-6]

where deltaS and deltaV are calculated at the P and T of interest. Also remember the Clausius-Clapeyron equation:

; or, more strictly,

Therefore, a good geobarometer needs a large deltaV, in order to have a large sensitivity to P and for curves of constant K to have a low slope on the P-T diagram.

Geothermometry and geobarometry using multivariant equilibria

At equilibrium

DGP,T = DH1,T - T.DST + (P-1).DV + RT.lnK = 0

K is the equilibrium constant, the product of the activities of end members in the phases of variable composition.

The Grt-Pl-Ky-Qtz geobarometer

Ca3Al2Si3O12 + 2Al2SiO5 + SiO2 = 3CaAl2Si2O8

grossular(Grt) + kyanite + quartz = anorthite(Pl)

Substituting thermochemical data, dividing through by the gas constant R, and expanding K gives the calibration:

7635 - 19.66T + 0.7963(P-1) + 3Tln(XCa,Pl /XCa,Grt) = 0

DV is large, because of the density difference between open feldspar and close-packed garnet and kyanite structures. The P-T slope is relatively low, making this equilibrium useful as a barometer. Uncertainty on calculated P is about ± 1.3 kbar.

The Grt-Bt Fe-Mg exchange thermometer

Fe3Al2Si3O12 + KMg3AlSi3O10(OH)2 = Mg3Al2Si3O12 + KFe3AlSi3O10(OH)2

Almandine (Grt) + Phlogopite (Bt) = Pyrope(Grt) + Annite (Bt)

DG for cation exchange is small, and the calibration here is fitted to exchange equilibrium experiments

6266 - 2.35T + 0.029(P-1) + 3TlnKD = 0

KD is most simply expressed as (Mg/Fe)Grt /(Mg/Fe)Bt

DV is very small, and cation exchange equilibria are generally insensitive to pressure. The usually-quoted uncertainty on calculated T is ± 50°.


An amphibolite-facies metapelitic schist from the Eastern Alps contains garnet of composition (% end members) Alm80Sps3Prp13.5Grs3.5 , biotite with Mg/Fe = 0.91, and plagioclase An15 , together in apparent equilibrium with kyanite and quartz. From these data we calculate the two P-T curves. Their intersection (with a surrounding box of uncertainty) gives us an estimate of the conditions of equilibration.

Self-consistent data-sets

[ Material to incorporate from Petrology course lecture slides ]


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This page last modified 12 October 2004