American Mineralogist, Volume 6l ,
pages 7I0714, 1976
PlagioclasegarnetAl2SiOrquartz:. s potential geobarometergeothermometer
Epwenr D. GHENI
Department of Geolo.gy,
Uniuersity of Calgary
Calgary, Alberta T2N I N4 Canada
Abstract
For the reaction 3CaAlrSirO.
:
CarAlrSisO', + 2AlrSiOu + SiO2,
the logarithm of the
apparent distribution coefficient (Kp) is log Ko
3X"%X'Jf!',o,,

3XEl"^5',".;b?9
Log Ko varies
from
0.5
to
1.4
for kyanitebearing
assemblages
and from
2.1
3.4
for sillimanite
and/or andalusitebearing
assemblages.
Using equilibrium constant equations derived
from
experimental
data on pure phases
and an ideal solution model for garnet and plagioclase
solid
solutions,
individual PI curves can be calculated
for different values of log KD. If P or T can
be independently estimated, these curves can be used as either geothermometers or geoba
rometers. The degree of nonideality of grbssular solid solution in garnet can be estimated
from calculations using
the activity coefficients
of anorthite in plagioclase
and the kyanite
sillimanite PZ equilibrium curve as a limiting case for kyanite and sillimanitebearing
assemblages.
The equilibrium can be described
by
Introduction
Plagioclase, garnet, qtJarIz, and an AlrSiOu poly
morph are a common assemblage
in regionally meta
morphosed pelitic rocks. Several workers, e.g.,Miya
shiro (1953), Sturt (1962), have suggested
that garnet
compositions can be used as
indicators of metamor
phic grade. Other workers have noted a relationship
between the CaO content of garnet, the anorthite
content of plagioclase,
and metamorphic grade (Ke
pezhinskas,
1973). Unless an appropriate mineral as
semblage of low variance is chosen, however, the
effects of bulk composition far overshadow
the P7
significance
of garnet and plagioclase
compositional
variability. In this note I will attempt to demonstrate
that the reaction
3CaAlzSi2O8
Ca3Al2
Si.O',
anorthite
grossular
+
zAt,SiO, +
SiO,
(la)
quartz
provides data on the mineral assemblage
plagioclase
garnetAlrSiOuquartz which is potentially useful
in
estimating pressures and temperatures of meta
morphism (Ghent, 1975).
Reaction (la) with kyanite as the AlrSiOu poly
morph has been studied experimentally at elevated
pressure and temperatures by Hays (1967) and by
Hariya and Kennedy (1968).
o
: +
+ 8.3e6e

where Z is the temperature
in degrees
Kelvin and P is
pressure in bars. The equation can be modified for
the presence of sillimanite or andalusite as the
AlrSiO5 polymorph by subtraction of equations of
the form of (lb) for kyanitesillimanite and kyanite
andalusite equilibria. Using the aluminum silicate
diagram of Holdaway (1971) we obtain in place of
equation
(lb):
0.3448(P
t)
o:u!]'4+7.r7rr
0.2842(P
r)
(2)
T
(1b)
where sillimanite
is the AlzSiO' polymorph and
2817.2,,
4351
_
0.26789"
_l)
(3)
t
t.,
T
where andalusite
is the ALSiO5 polymorph.
Since the minerals are not pure phases we add
terms for activity of anorthite solid solution in
plagioclase
and activity of grossular solid solution
garnet:
_1)1)
,_L3_11qq__r)
o:z:+8.3969
TT
* loe
"i"i,'"'.ii,
"'
"". "
3 log
"t',Til"J'""",j"
7t0
(l c)