There are ways to get around the closure temperature problem.  These have
been published and use inverse methods to calculate closure temperatures
for minerals.  They calculate the temperatures by taking into
consideration equilibrium constraints, modal constraints, and the
measured isotopic compositions of all phases in the rocks.  The general
strategy is to solve sets of equations, starting with the lowest closing
exchange-couple and then to work up temperature, solving for each phase
and the temperature that it closes to exchange with the minerals that are
open to exchange.  The assumptions are identical to those made in mineral
pair thermometry.  The principal constraints are in choosing samples to
minimize uncertainties, and to test the closed system assumptions
(something that can be done).  Another aspect to these inverse methods is
that they are independent of the mechanisms by which minerals close to
isotopic exchange (e.g., diffusion, recrystallization, new grain growth).

Several people have outlined this approach.  The final line in an A.T.
Anderson paper in the late 1960's states that this approach can in
principal be done, but he won't do it in his paper because the appropriate
calibrations for isotopic exchange had not been made.  I wrote a paper in
EPSL (1993) that outlines some of the methods and provides worked
examples, equations, sampling strategies, and consideration of
propagation of uncertainties.  There are many other papers that are
related, including some by Perry, Gregory, Sharp, and Louckes.
Note that I consider these inverse approaches to be independent and
complementary to the forward modelling approaches such as those advocated
by Giletti, Eiler, Jenkin.  There is considerably more that can be done
with this.

Also not that empirical calibrations cannot be used for these
calculations because they fold-in the systematic exchange effects that
occur during metamorphism and cooling of high-temperature rocks.

I don't think it is a crime to ask for recent papers.  It never crossed my
mind to interpret Ilya's posting as an indication that he had ignored
early papers.  For thermometry and exchange studies, I like the Deines
paper, those of Anderson in the 1960's and others written much earlier.

If this seems a bit punchy it is because I just returned from
the hospital with my two-day-old and my usual sense of restraint has not
kicked in.

James


-----------------------------------

James Farquhar, UH 5102
Dept of Chemistry, Mail Code 0356
9500 Gilman Drive, UCSD
La Jolla Ca, 92093

858 5346053
858 5347042 (Fax)
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