The GarnetCpxPhengite Barometer
Recommended calibration and calculation method, updated 1 March 1996
The barometer uses the equilibrium
pyrope + 2grossular = 6diopside + 3Al_{2}Mg_{1}Si_{1}
The calibration is based on the selfconsistent thermodynamic dataset of Holland and Powell (1990, J Metamorphic Geol. 8, 89124). 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 PT 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 (righthand) 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, 10111060). 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 aX 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 MgCa 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}.(1X_{Mg})]/RT
ln(y_{Ca}) = [(13807  6.276T).X_{Mg}.(1X_{Ca})]/RT

use the reciprocal saltsolution model of Holland
(1990, CMP 105, 446453) for Cpx.
Normalise the analysis to 6 oxygens, 4 cations. Then X_{Ca, M2} = Ca cations, X_{Mg,M1} = Mg cations.
For longrangedisordered or Fe^{3+}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 dijd 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(Al_{2}Mg_{1}Si_{1}) = X_{Al,M2}.X_{Al,T2}/(X_{Mg,M2}.X_{ Si,T2})
For a microprobe analysis normalised to 11 oxygens (without H_{2}O) this can be expressed in terms of cations as
(Al+Si4).(4Si)/[Mg.(Si2)]
Content last modified 17 July 1996