Dear Horst and others

I made a study a few years ago of various Grt-Opx-Pl-Qtz pressure
calibrations (Fitzsimons & Harley 1994, J.Pet. 35, 543-76) and, although
this work is now out-of date and did not look specifically at any of the
calibrations you have used, you might find our conclusions useful.

We applied four different Grt-Opx-Pl-Qtz calibrations to two suites of
rocks using the solution models recommended by the authors of each
calibration. We then compared the results, and in each case found
consistent differences in P-T results (in some cases as large as 4 kbar for
the same sample). Full details are given in the paper, but I'll try and
summarize the results below...

Given that this was done almost 10 years ago, I'd appreciate comments from
anyone who has kept up-to-date with more recent calibrations, thermodynamic
data, and mixing models...

We looked at four calibrations.

Firstly the Mg calibration calculated from thermodynamic data by Newton and
Perkins (1982; Amer. Miner. 67, 203-22), and the Fe calibration derived
from experimental data by Bohlen et al. (1983; Contrib. Miner. Petrol. 83,
52-61).

And secondly the Mg and Fe calibrations published by Essene (1989; In:
Daly, Cliff and Yardley, Evolution of Metamorphic Belts, Geol. Soc. Lond.
Spec. Publ. 43, 1-44). These two calibrations were re-calculated from
available thermodynamic and experimental data so as to be mutually
consistent, whereas the N&P and B et al. calibrations were independently
derived are not consistent.

Activity models were straightforward for Opx and Pl, since all calibrations
used the same models (ideal 2 site mixing for Opx after Wood and Banno 73,
and Al avoidance model for Pl after Newton et al. 1980), but there were
different recommendations for the Grt solution model, which turned out to
be important. N&P and B et al. both used a ternary Fe-Mg-Ca regular
solution model for garnet, but with quite different values for the
interaction parameters. Essene used the asymmetric Fe-Mg-Ca-Mn quaternary
mixing model of Ganguly and Saxena (1984) with modified Ca-Fe interaction
parameters after Anovitz and Essene (1987).

The main differences in calculated P conditions were as follows:

The Essene calibrations (Mg and Fe) always yielded higher pressures than
the N&P and B et al. calibrations.. At 800oC, the differences between the
two Fe calibrations (B et al. and Essene) was 0.9-1.5 kbar, and 0.9-3.8
kbar for the two Mg calibrations (N&P and Essene).

We then tried to demonstrate whether the P differences were due solely to
different choices of standard thermodynamic data (delta S, delta H, delta
V) in each calibration, solely due to the different choice of solution
model for garnet, or some combination of the two.

To cut a long story short (see the paper for more details) We found that at
800oC (T relevant to my samples) the different thermodynamic data used by
the two Fe calibrations (B et al. and Essene) could account for a P
difference of about 1.2 kbar, and thus was probably the main factor
controlling the observed P difference in my samples (0.9-1.5 kbar). We
also decided that the discrepancy is likely to be due to delta H. We
compared the two calibrations with the Holland & Powell (1990)
thermodynamic database and found that the latter yielded pressures between
the two, but closer to B et al. (within 0.5 kbar).

Results were quite different for the two Mg calibrations. At P-T
conditions relevant to my rocks (5-8 kbar, 800oC), N&P thermodynamic data
yield pressures higher than Essene, but within 0.5 kbar. This could not
account for the observed discrepancy in the rocks (0.9-3.8 kbar),
particularly as the difference was in the opposite sense - N&P gave lower
pressures when applied to my rocks. In this case there must be a
significant difference due to the garnet solution model.

We noted that the observed P difference in the rocks decreased with
increasing XMg in garnet, and showed that the difference was controlled by
the Fe-Mg interaction parameters used. N&P assumed that Fe-Mg mixing is
ideal, whereas the Ganguly and Saxena model used by Essene assumes
non-ideal and asymmetric mixing, with the largest degree of non-ideality
for the garnet compositions of my rocks (XMg in Grt = approx. 0.6). At
that the time that I was writing the paper the most recent garnet model was
that of Berman (1990), which supported a near-ideal mixing model for Fe-Mg
in garnet.

So in conclusion, We decided that N&P was the best calibration (which
matches with the comments of Vyacheslav Fonarev in his e-mail on the
subject), because its garnet solution model was the most consistent with
recent data, whereas Essene used a mixing model inconsistent with the
latest results (as presumably did B et al. since the discrepancy between
their calibration and that of Esseene seemed to be due largely to delta H,
and not mixing models).

In the case of the calibrations you have used, you would also need to
consider both potential differences in thermodynamic data and in mixing
models. I don't know very much about the Lal calibration, but I know that
Perkins and Chipera (1985; Contrib. Miner. Petrol. 89, 69-80) derived
internally consistent calibrations for the Fe and Mg end-members, and that
they used the Ganguly and Saxena mixing model for garnet. They noted that
their Mg calibration can yield anomalously high pressures, and suggested
that this must reflect either the Grt or Opx mixing models-I'd suggest that
again this is due to the Fe-Mg mixing in the garnet mixing model. Also
note that some of the equations at the end of their paper contained errors,
which were later corrected (Perkins & Chipera 1985, Errata, Contrib.
Mineral. Petrol. 90, p. 410).

As for the Bhattacharya et al. (1991) model, I did make an attempt to look
at this calibration, which was published as I started to write up my
results, but the more I looked at their equations, the less I understood.
After several attempts I still couldn't reproduce their equations as
printed in the paper, and I decided that they probably contained some
errors and therefore I ignored the calibration. I'd be interested to hear
if anyone could confirm whether there are mistakes in this paper, or
whether the problem was with my maths.

Hope this is of some use.

Cheers

Ian




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Ian Fitzsimons
Tectonics Special Research Centre
School of Applied Geology
Curtin University of Technology
GPO Box U1987, Perth, WA 6845
AUSTRALIA
Phone (Direct line): +61 8 9266 2455
Phone (Geology Office): +61 8 9266 7968
Fax: +61 8 9266 3153
E-mail: [log in to unmask]
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