The Garnet-Cpx-Phengite Barometer

Recommended calibration and calculation method, updated 1 March 1996

The barometer uses the equilibrium

pyrope + 2grossular = 6diopside + 3Al₂Mg_-1Si_-1

The calibration is based on the self-consistent thermodynamic dataset of Holland and Powell (1990, J Metamorphic Geol. 8, 89-124). We have fitted a linear expression to the isopleths of lnK such that the linearised isopleths deviate by less than 100 bars from those calculated from the full dataset in the applicable part of the P-T range 6 - 40 kbar, 400 - 900°C:

P(kbar) = 28.05 + 0.02044T - 0.002995T.lnK

where T is in Kelvin and the lnK term is calculated as follows:

In the phengite (right-hand) term, Si cations are per formula unit of 12(O,OH), and M1 are the dioctahedral cation sites. Ideal mixing on sites was used for data extraction in mica end members by Holland and Powell (1990) and so must also be used in the application. Cancellation of the site terms held in common between the muscovite and celadonite end members leads to the formulation above.

Activity models for garnet and clinopyroxene are a major source of uncertainty in applying the barometer. An independent test of its accuracy is provided by the experiments of Schmidt MW (1993, Am. J. Sci. 293, 1011-1060). The barometer calibration above overestimates the experimental pressures by a little over 3 kbar when the acitivity models outlined below are used. Until such time as there is better characterisation of the a-X relations in all three phases, and better thermochemical data on the Tschermak exchange in phengite, we recommend the following:

(Note that, because of the limitations of HTML, I have used y in place of the small greek letter gamma to represent an activity coefficient)

make an empirical correction of -0.000543 to the T.lnK term coefficient (on the assumption that the discrepancy with the Schmidt experiments, and with certain other natural data sets, lies mainly in the inadequacy of the activity models), so that

P(kbar) = 28.05 + 0.02044T - 0.003539T.lnK
use simple Mg-Ca mixing in garnet.
Normalise the analysis to 12 oxygens, 8 cations.
Then, X_Mg = Mg/3, X_Ca = Ca/3, X_Al = Al/2, where Mg etc. represents the number of Mg cations per formula unit.
lna(prp) = 3ln(X_Mg) + 3ln(y_Mg) + 2ln(X_Al)
lna(grs) = 3ln(X_Ca) + 3ln(y_Ca) + 2ln(X_Al)

From Newton and Haselton (1981), with units converted to J/mol:
ln(y_Mg) = [(13807 - 6.276T).X_Ca.(1-X_Mg)]/RT
ln(y_Ca) = [(13807 - 6.276T).X_Mg.(1-X_Ca)]/RT
use the reciprocal salt-solution model of Holland (1990, CMP 105, 446-453) for Cpx.
Normalise the analysis to 6 oxygens, 4 cations. Then X_{Ca, M2} = Ca cations, X_Mg,M1 = Mg cations.
For long-range-disordered or Fe³⁺-bearing pyroxene:
lna(di) = ln(X_Ca,M2.X_Mg,M1) + lny_CaMg
From Holland (1990),
ln(y_CaMg) = {X_Na,M2[W_A(X_Al,M1+X_Fe3+,M1)+(W_A-W_B)X_Fe2+,M1]}/RT
where W_A = 26000 J, W_B = 25000 J.
For ordered omphacite near the di-jd join, an additional activity coefficient y_ord,di appears, arising from the Landau ordering model. Its value can be calculated from equation (12b) of Holland (1990).
use ideal mixing on sites for phengite.
Using the activity expressions in Holland and Powell (1990)
a(Al₂Mg_-1Si_-1) = X_Al,M2.X_Al,T2/(X_Mg,M2.X_Si,T2)
For a microprobe analysis normalised to 11 oxygens (without H₂O) this can be expressed in terms of cations as
(Al+Si-4).(4-Si)/[Mg.(Si-2)]

Content last modified 17 July 1996