Petrology and Cooling Rates of the Valhalla Complex, British Columbia, Canada
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JOURNAL OF PETROLOGY VOLUME S7 NUMBER 4 PAGES 733-765 1996
FRANK S. SPEAR*1 AND RANDALL R. PARRISH*
'DEPARTMENT OF EARTH AND ENVIRONMENTAL SCIENCES, RENSSELAER POLYTECHNIC INSTITUTE, TROY, NY 12180, USA
"GEOLOGICAL SURVEY OF CANADA, 601 BOOTH STREET, OTTAWA, ONT., KIA 0E«, CANADA
Petrology and Cooling Rates of the
Valhalla Complex, British Columbia,
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Canada
Rocks from the Valhalla metamorphic core complex, British INTRODUCTION
Columbia, Canada, have experienced granulite Jades Cooling rates of metamorphic terranes can serve as a
metamorphism at conditions of 820±30°C, 8±1 kbar. Peak useful constraint on the unroofing history because, in
metamorphism was accompanied by dehydration melting of general, the more rapidly an area is denuded, the
muscovite, but not biotite, followed by minor back reaction more rapidly it will cool. Geochronology, in which
of garnet + K-feldspar + H20- sillimanite + biotite+plagio - minerals with different closure temperatures are
close.' At conditions very near those of the peak, extensive analyzed, has been used extensively to infer cooling
shearing produced s-c (schistositS-cisaillement) fabrics, ribbon rates in metamorphic terranes (here called geochro-
quartz and grain size reduction of garnet at several locations. nologic cooling rates). Cooling rates can also be
Gamet-biotite Fe-Mg exchange thermometry yields tempera- determined from analysis of diffusional zoning in
tures that range from 580 to 1051°C Low temperatures are metamorphic minerals (here called petrologic
calculated from biotite modified dominantly by Fe-Mg cooling rates). Few systematic studies have been
exchange with garnet; high temperatures are calculated from Fe-published comparing petrologic with geochronologic
rich biotites produced from the above retrograde reaction. Geo- cooling rates. Such a comparison is critically
thermometry is useless in these rocks to estimate peak tempera-important because petrologic cooling rates rely on
ture a priori, but is very useful to help constrain the complex extrapolations of diffusivities determined in the
reaction history of biotites. Geochronology on monazite, zircon,laboratory over many orders of magnitude, and it is
allanite, titanite, hornblende, muscovite, biotite and apatite has important to evaluate the internal consistency of
been used to constrain the timing of the metamorphic peak at cooling rates determined by the two methods.
67—72 Ma and the average cooling rate to 24 ± 6°C/Ma. Dif-
The application of diffusion theory to the deter-
fusion modeling of Fe-Mg exchange between biotite inclusions
mination of petrologic cooling rates has been dis-
and host garnet yields cooling rates of either 3-80°C/Ma or
cussed extensively (e.g. Dodson, 1973, 1986; Lasaga
200-2500° C/Ma, depending on the choice of diffusion coeffi-
et al., 1977; Onorato et al., 1979, 1981; Tracy &
cients. The former value is consistent with the average cooling
Dietsch, 1982; Lasaga, 1983; Ozawa, 1983; Wilson
rate of 24° C/Ma for the complex determined from geochronol-
& Smith, 1984, 1985; Munrill & Chamberlain, 1988;
ogy, but the faster rate cannot be ruled out and may indicate
Spear, 1991; Spear & Florence, 1992; Ehlers et al.,
initial very rapid cooling by thrusting of the complex onto cooler
1994), and procedures based on the shape of zoning
basement It is suggested that cooling rates determined from
profiles have been presented. Most of this work has
geochronologic vs petrologic methods may not be directly com-
focused on zoning in garnet, and the closure tem-
parable because petrologic methods sample near-peak nuta-
perature of the garnet-biotite thermometry is one of
morphic cooling rates whereas geochronologic methods sample
the most frequently used approaches.
post-peak to ambient cooling rates.
In this paper, a slight variation on the garnet-
biotite closure temperature method is presented in
which closure temperatures of biotite inclusions
KEY WORDS geothermometry; geodavnology; gartut diffusion;
cooling raits; Valhalla compUx within garnet are modeled as a function of biotite
•Corresponding author.
Telephone (518) 276-6101 But: (518) 276-8627.
e-mail: ipcar@haroligco.rpi.edu
HTTP://www.geai^ebHi/laat»fl7ipear/v»lha]]a/va]ha]la.ritml © Oxford University Pros 1996JOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
size. The method is applied to rocks from the Val- morphosed at sillimanite + K-feldspar grade and the
halla complex, British Columbia, and compared typical matrix assemblage found in metapelites is
with cooling rates determined from geochronology. garnet + biotite + sillimanite + K-feldspar + plagio-
The Valhalla complex is an excellent area in which clase + quartz + ilmenite ± rutile. Very little chlorite
to compare petrologic with geochronologic cooling is present and retrograde muscovite has only been
rates because the geology and structure are well observed in one thin section.
characterized, thermal history is relatively simple, Textures and compositional zoning for the five
and geochronologic cooling rates have been samples of paragneiss used in this study are presented
examined in considerable detail (Carr et al., 1987; in Figs 3-8; compositions of selected minerals are
Parrish */a/., 1988). listed in Table 1. Garnets range from 1 to 6 mm
diameter, are typically rounded and embayed, and
locally show reaction zones on the rims of biotite ±
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GEOLOGICAL SETTING sillimanite (e.g. Fig. 3a, upper right corner of white
The Valhalla complex is located in the southeast box; Fig. 6, left side of large garnet). Included within
corner of British Columbia, Canada (Fig. 1, inset). It garnet are biotite, quartz, plagioclasc (rare), silli-
is one of a number of exposures of fault-bounded, manite (rare) and rutile (ilmenite ± rutile is found in
high-grade metamorphic core complexes that make the matrix).
up the Shuswap complex (Armstrong, 1982; Brown
& Read, 1983). Garnet is zoned from core torim.Xcn [part (b),
Figs 3-7] is low in the cores (O-035-0-O76) and
Figure 1 shows geologic relations of the Valhalla increases slightly (generallySPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
Columbia River
fault zone
Lower
Arrow
Lake
87-52, V6[-
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V7 Pas more paragneissji
Valkyr
extensional
shear zone%
49°15'
Valhalla Complex Hanging wall of Slocan Lake
and Valkyr extensional faults
Paleocene-Early Eocene Middle Eocene
leucogranitic rocks Coryell syenite
100-110 Ma Late Cretaceous
granodiorite gneiss plutonic rocks
Metamorphic rocks of Middle Jurassic
upper amphibolite facies, plutonic rocks
age uncertain
Metamorphic rocks of
mainly greenschist facies,
Figure 1 Late Pafeozoic-Early
Mesozoic in age
Geochronological and
petrological samples
Fig. 1. Geologic map of the Valhalla complex, British Columbia. Inset shows location of Valhalla complex in western North America.
Numbers refer to sample numbers discussed in text.
Slocan Lafce
10 fault 10
5 5
SL SL
-5 204B- -5
km 121B-84&529-83 8 7 - 5 2 , Passmore, km
G w i l l i m Creek V 6 , V 7 , V8
shear zones
Mulvey gneiss Paleogene granitoids
Q granitoids
Late Cretaceous
Paragneiss Focenc Corvoll svenitf Jurassic granitoids and
Fig. 2. Schematic east-west cross-section at latitude 49°45'N of central Valhalla complex with geochronological and petrological sample
localities projected into the section. Locality for sample V9 is not shown because it is uncertain where it resides relative to Gwillim Creek
shear zone owing to the probable absence of Mulvey gneiss at the latitude of ~ 49°3OTSJ.
735JOURNAL OF PETROLOGY VOLUME 37 NUMBER AUGUST 1996
• 7
s
l
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4
(a;
Fig. 3. Sample V6A. (a) Photomicrograph showing large garnet with thin reaction zone in upper right corner. Foliation is composed of
sillimanite ± minor biotite. (Note the numerous small garnet crystals elongated in the foliation plane.) Width of field is 8 mm. White box
shows area of (b)-(d). (b) and (c) X-ray composition maps showing distribution of Ca and Fe/(Fe + Mg) in upper right part of garnet in
(a). Ca is higher near the rim (Jfg,, = 0-053) than the core (X^, = 0-045). Fe/(Fe + Mg) is practically unioned in the core (0-742-0-748),
and increases slightly near the rim where late biotite is present, (d) Sketch of garnet showing values of Fe/(Fe + Mg) in garnet (filled
circles: numbers range from 0-742 to 0-792) and biotite (filled squares: numbers range from 0-494 to 0-403). Numbers in boxes are
temperatures calculated from garnet—biotite Fe—Mg thermometry using either the garnet core composition [Fe/(Fe + Mg) = 0-748] plus
biotite indicated by the arrow or the garnet-I-biotite pair indicated by the two arrows. Numbers in parentheses refer to analytical spots
listed in Table 1. Plagiodase analyses 100 and 103 from Table 1 are out of the figure area.
inspection will reveal that there is a correlation garnet host. These data will be used below to infer
between biotite Fe/(Fe + Mg) and biotite size: petrologic cooling rates.
smaller crystals have lower Fe/(Fe + Mg). This Biotite Fe/(Fe + Mg) and Ti contents are a
observation is consistent with the interpretation that function of location in the sample. The lowest Fe/
the Fe—Mg zoning in garnet, as well as the dis- (Fe + Mg) values are observed in biotites that are
tribution of biotite Fe/(Fe + Mg), is the product of included in garnet, and the lowest values are associ-
diffusion in response to gradients caused by Fe—Mg ated with the smallest crystal inclusions (see Fig. 6d).
exchange between biotite inclusions and adjacent The highest Fe/(Fe + Mg) is generally observed in
736SPEAR AND PARRISH PETROLOGY AND CXDOLING OF VALHALLA COMPLEX
• * • • , * $ , -
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(b) X(Grs) (c) Fe/(Fe+Mg)
Fig. 3. Qmtamti.
matrix biotite. The TiO2 contents of biotites range One distinctive feature of several samples is a
from 1-5 to 5-5 wt%. The highest TiO 2 content is strong planar fabric, as shown in Fig. 8 (sample
found in biotites that are included within quartz or V6E). The foliation is defined by aligned biotite and
plagioclase grains (e.g. V6A analysis 92: 5-56 wt%). sillimanite, and ribbons of quartz. Sillimanitc in the
Locally, relatively high TiO 2 contents are found in foliation has been pulled apart; garnet has experi-
biotites included within garnet (e.g. V7D analysis enced grain size reduction and many crystals are
165: 517 wt%), although in general, biotites now lozenge shaped with well-defined pressure
included within garnet have TiO 2 contents that are shadows. Some garnets have been deformed into
between 3 and 5 wt%. Matrix biotites have TiO 2 sigmoid-shaped crystals. This texture is interpreted
contents that range from 1-5 to 4 wt%. In one as a high-temperature shear fabric.
sample (V9C) two grains of biotite were found P-T conditions during shearing are constrained by
included within garnet with TiO 2 contents of 007 the nature of the reactions that are observed. Pro-
wt%. duction of biotite in pressure shadows adjacent to
Minimum and maximum X/^ contents of plagio- garnet occurred by reaction (1), which consumes
clase are listed in Table 1. Plagioclase is very nearly garnet and K-feldspar. Zoning in garnet character-
homogeneous in samples V6A and V7D, and Xf^ istically shows an increase in Fe/(Fe + Mg) towards
variesJOURNAL OF PETROLOGY VOLUME 37 NUMBER • AUGUST 1996
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(b) X(Grs)
Fig. 4. Sample V6B. (a) Photomicrograph; (b) and (c) X-ray composition maps; (d) iketch ihowing Fe/(Fe + Mg) in garnet (filled
circlet) and biotite (filled squarei), and• calculated garnet—biotite temperaturei unrig indicated pain. (See Fig. 3 for diicuuion of
labels. Note that thii lample does not show the ihear fabric evident in samples V6A, V7C, V7D and V6E.)
transfer reaction (1). Most importantly, the sym- be made based on phase equilibria and geothermo-
metry of the zoning profiles around garnets, and the barometry. Geobarometers applicable to the pelitic
absence of truncated zoning profiles (Fig. 8b), gneisses include garnet + plagioclase + sillimanite
requires that at least some of the diffusion that + quartz (GASP), garnet + plagioclase + biotite +
occurred in response to reaction (1) occurred after quartz (GPBQ), and garnet + rutile + sillimanite
grain size reduction, otherwise grain reduction + ilmenite (GRAIL). Figure 9 shows the array of P—
would have truncated the zoning profiles. That is, T conditions calculated from these equilibria using
reaction (1) probably occurred during and following calibrations of Hodges & Crowley (1985: GASP),
deformation. Finally, the absence of late muscovite Hoisch (1991: GPBQ) and Bohlen et al. (1983:
gTowth indicates that hydration must have occurred GRAIL). Slopes of both garnet + plagioclase equi-
above the stability of muscovite + quartz. Therefore, libria are similar and give an array of pressures that
the strain recorded by these rocks must have span ~ 3 kbar (i.e. ±1*5 kbar) at a single tem-
occurred very near the metamorphic peak. perature. At temperatures above muscovite
breakdown, the minimum pressure inferred from
garnet + plagioclase equilibria is 7 kbar. GRAIL
equilibria intersect garnet + plagioclase equilibria
Peak metamorphic pressures providing a consistent estimate of pressure of 8 ± 1
An estimate of the peak metamorphic conditions can kbar at 800°C.
738SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
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Avg Grt core:
0.736
Fig. 4. Coniijuui.
In the above calculations, unzoned garnet core occurred. The amount of HjO present in micropores
compositions were used with matrix plagioclase. It is rocks at these conditions is probably much less
should be noted that most samples contain only a than 0-5 vol. % and could not produce this much
restricted range of plagioclase compositions, which is partial melt.
why the equilibria cluster fairly tightly. Only one The absence of muscovite and the presence of the
sample (V6B) contains inclusions of plagioclase that assemblage sillimanite + K-feldspar + quartz requires
can be used to provide a constraint on the pressure temperatures in excess of muscovite + quartz
evolution. A plagioclase inclusion in garnet in breakdown by the reaction
sample V6B has a composition of An^ (see Table 1;
Fig. 4), which, when used in conjunction with the muscovite + plagioclase + quartz
garnet core composition, gives a pressure that is ~ 2 = sillimanite + K-feldspar + liquid (r>700°C). (2)
kbar higher than the pressure obtained from the
garnet rim and matrix plagioclase (see dashed line in Furthermore, a pegmatite at location V8 contains
Fig. 9). The implication of this result is that the the assemblage corundum + K-feldspar + plagio-
prograde P-Tpa.th may have involved earlier higher clase + biotite (+ minor retrograde muscovite),
pressures, or nearly isobaric heating. It should be which constrains the P-T conditions to lie above the
noted that kyanite has not been reported anywhere reaction
from the Valhalla complex, providing an upper limit muscovite
on the pressure. = corundum + K-feldspar + H2O (r>800°C). (3)
Peak metamorphic temperatures: Prograde development of garnet + K-feldspar most
dehydration melting probably occurred by the vapor-absent melting
Peak temperatures of the Valhalla complex are best reaction
constrained by dehydration and vapor-absent biotite + sillimanite + plagioclase + quartz
melting reactions (Fig. 9). Abundant migmatite = garnet + K-feldspar + liquid (7">750°C). (4)
testifies to an episode of partial melting in these rocks
and the volume of leucosome in some samples (5- Finally, the absence of orthopyroxene requires that
20%) suggests that dehydration melting has the vapor-absent melting reaction
739JOURNAL OF PETROLOGY VOLUME S7 NUMBER 4 AUGUST 1996
• B t "
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Grt i
(a)
(b) X(Grs)
Fig. 5. Sample V7C. (a) Photomicrograph; (b) and (c) X-ray composition maps; (d) sketch showing Fe/(Fe + Mg) in garnet (filled
circles) and biotite (filled squares), and calculated gamet-biotite temperatures using indicated pairs. (See Fig. 3 for discussion oflabels.)
740SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
Grt core +
956
Grt core +
1002
,784I12>
* .641
393
|123)
Grt core +
929
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Avg Grt core: 0.645
Grt core +
678
V7C
Fig. 5. Continued.
biotite + quartz pair is unjustified. To illustrate this point, diagrams
= orthopyroxene + K-feldspar + liquid( T< 84O°G) depicting the array of Fe/(Fe + Mg) in garnet and
(5) biotite and temperatures calculated by Fe-Mg
exchange thermometry between garnet and biotite
has not been crossed (see Appendix for details of the are shown for each of the samples in Figs 3—7. [In
calculation of this reaction for variable XFc in this discussion, the garnet—biotite Fe—Mg exchange
biotite). Together, these reactions constrain the peak thermometer calibration of Hodges & Spear (1982)
P-Tconditions to be 820±30°C, 8± 1 kbar. has been used to obtain temperature. This cali-
A constraint on the timing of the partial melting bration corrects for effects of Ca on Fe and Mg
relative to fabric development can be gained from activities in garnet, and yields similar results to cali-
examination of the orientation of sillimanite inclu- brations based on Berman's (1990) garnet model.
sions in garnet. The topmost part of the large garnet Application of the model of Patifio Douce et al.
in Fig. 3 (V6A) contains numerous sillimanite inclu- (1993), which also corrects for the effects of Ti and
sions that are oriented in an arc that parallels the Al6 in biotite, yields results that are 20-40°G lower
outline of the top of the crystal, and some of these than those reported here, but does not change any of
inclusions are oriented 90° to the dominant fabric in the stated conclusions of this work.] The total range
the matrix. Of particular note is that all of these of garnet-biotite temperatures is 580-1051°C and
inclusions are contained in the part of the garnet rim the range of garnet core + matrix biotite tempera-
that has slightly higher grossular (Fig. 3b). The tures is 730—1051 °C. This wide array of computed
interpretation is that the high-grossular garnet rim temperatures is a function of the reaction history of
was produced by reaction (4), and that the garnet the sample and the fact that both biotite and garnet
produced by this reaction overgrew a preexisting sil- preserve aspects of their prograde and retrograde
limanite fabric that was at high angle to the present chemical changes: garnet through chemical zoning
matrix fabric. and biotite in the variability of compositions in dif-
ferent textural settings.
Geothermometry: a guide to the reaction The textural and chemical heterogeneity of bio-
history tites can be used to help understand the reaction
Geothermometry using Fe-Mg exchange between history of each sample, if the peak temperature is
garnet and biotite cannot be used to infer peak tem- known, which in this case it is. Based on their tex-
peratures because the a priori assumption of equi- tural positions, the earliest formed biotites are those
librium between any particular biotite and garnet that are included within garnet. Most of these bio-
741JOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
\
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; * *
(a) V7D
Fig. 6. Sample V7D. (a) Photomicrograph; (b)-(d) X-ray composition maps. Numbers in (c) show Fe/(Fe + Mg) for garnet rim and
core. White box in (c) shows location of map in (d). (d) Fe/(Fe + Mg) in biotite inclusions (gray) within garnet (black). [Note the
correlation between biotite composition and size: small biotite inclusions have lower Fe/(Fe + Mg).] Garnet is zoned from 0723 to
0-806 towards large biotite inclusion. Width of field: 12 mm for (a); 2-8 mm for (d).
tites have reequilibrated during cooling by Fe-Mg between the highest and lowest values in the sample.
exchange with garnet (discussed in detail below), but When used in conjunction with the garnet core
there are a few grains that are found included within compositions, these biotites yield temperatures of
plagioclase or quartz grains that are themselves ~870°C (see Fig. 3d, analysis 92). Assuming that
included within garnet. These biotites have the these biotites have not changed composition since
highest TiC>2 contents of any grains in the suite (e.g. they were included during prograde metamorphism,
sample V6A, analysis 92, Table 1: TiO 2 = 5-56 the only explanation for the calculated temperature
wt%) and values of Xyc that are intermediate of ~870°C is that the garnet core composition must
7*2SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
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(b) X(Grs)
£-0.330
0.336
Grt core:
0.723> 0^325 °- 3 5 2 .
0.313
0.34a
Grt: 0.317,
0.806 0.277^
0.347
(d) Fe/(Fe+Mg) 0.339 ., J 0.316
Fig. 6. Continued.
have shifted towards lower Fe/(Fe + Mg) since the (assuming P is constant) as are the changes in com-
biotites were included. Reactions (1) and (4) both positions of all other minerals, so that the value of
result in a shift in biotite and garnet towards lower the equilibrium constant is continuously adjusted to
Fe/(Fe + Mg) with progress to the right. Moreover, values appropriate for the 7* and P. At the end of the
the amount of progress on reaction (1) can be quan- simulation, the biotite composition is constrained to
tified using differential thermodynamics (the Gibbs match that of the inclusion, and the calculated com-
Method; e.g. Spear & Peacock, 1989) in the fol- positions of all other minerals reflect equilibrium
lowing manner. Garnet, biotite and plagioclase with that of biotite. The change in temperature
compositions assumed to be representative of the necessary to achieve this model equilibrium is only
metamorphic peak (820°C) are used to define a 10°C, indicating that the inclusion of biotite within
reference value for the equilibrium constant for garnet occurred very near the metamorphic peak.
reaction (1). The Fe/(Fe + Mg) of biotite is then used [It might be wondered why the change in tem-
as an independent monitor variable and incremented perature required to achieve equilibrium with
until the value matches that of the included biotite. included biotites is not 50°C, reflecting the difference
At each step, the change in temperature is calculated between the peak temperature (820°C) and the
743JOURNAL OF PETROLOGY VOLUME S7 NUMBER 4 AUGUST 1996
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(b) X(Grs) i
Fig. 7. Sample V9C. (a) Photomicrograph; (b) and (c) X-ray compoiition raapi; (d) iketch showing Fe/(Fe + Mg) in garnet (rilled
circles) and biotite (filled squares), and calculated garaet-biotite temperatures using indicated pairs. (See Fig. 3 for discussion oflabels.)
744SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
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Kg. 7. Continual.
calculated garnet core + biotite inclusion tem- biotites far from garnet in this sample should
perature (870°C). The answer is that the difference therefore reflect peak metamorphic compositions.
in calculated garnet + biotite temperatures depends Finally, temperatures computed from matrix
only on the Fe-Mg exchange reaction whereas biotite and garnet core compositions in samples
reaction (1) is a continuous net transfer reaction that V6A, V6B, V7C and V7D record temperatures from
displays a relatively large shift in Fe/(Fe + Mg) with 900 to 1050°C. These anomalously high tempera-
temperature.] tures may be explained by noting that progress of
Matrix biotites display variable Fe/(Fe + Mg) and reaction (1) in the retrograde hydration sense (i.e.
TiC>2 contents. Biotites touching garnet typically from right to left) results in biotite and garnet with
have the lowest TiO 2 and Fe/(Fe + Mg) of matrix progressively higher Fe/(Fe + Mg). Garnet is con-
biotites. When used with garnet rim compositions, sumed, and garnet rim has higher Fe/(Fe + Mg) than
these biotites yield apparent temperatures of 587- garnet core, producing a composition gradient that
650°C. These are interpreted as closure temperatures is modified by diffusion. In addition, matrix biotite
in response to Fe-Mg exchange between biotite and produced or equilibrated with reaction (1) during
adjacent garnet during cooling. Slightly higher TiO2 cooling will have a higher Fe/(Fe + Mg) than biotite
contents and Fe/(Fe + Mg) are observed in matrix at the metamorphic peak and will yield anomalously
biotites not touching garnet (e.g. 3—4 wt %; Table high temperatures when used for thermometry with
__X). Temperatures computed with these biotites and garnet core (Robinson et al., 1982; Robinson, 1991).
garnet rims that are not directly in contact with Spear & Florence (1992) have found that this
biotite are 688-750°C. It is probable that Fe-Mg mechanism could readily produce apparent gar-
exchange occurred between these garnet rims not net + biotite temperatures that were 100°C in excess
directly in contact with biotite, and matrix biotite. of the metamorphic peak.
However, based on observations of minimal zoning It is informative to compute the amount of
in garnet adjacent to biotite inclusions (discussed reaction progress along reaction (1) required to shift
below), it is inferred that this exchange was minor. garnet Fe/(Fe + Mg) from the core values to the
Therefore, these temperatures (688-750°C) are observed rim values, which can be achieved using
interpreted as the temperatures at which retrograde differential thermodynamic modeling (the Gibbs
net transfer reaction (1) ceased. Interestingly, Method; Spear & Peacock, 1989). As before, the
sample V9C does not contain sillimanite so reaction inferred compositions at the metamorphic peak
(1) could not have operated in this sample. Matrix were used to define reference values for all equi-
745JOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
k -
i.
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(a) V6E
(b) Fe/(Fe+Mg: Grt (c)Fe/(Fe+Mg):Bt
Fig. 8. Sample V6E. (a) Photomicrograph showing well-developed shear fabric (white lines) in garnet + tillimanite + biotite +
K-feldspar +quartz+ plagiodase assemblage. Shear fabric is produced by alignment of sillimanite and biotite crystals and shape of
garnet crystals. (Note the ligmoidal shape of garnet crystal outlined by foliation bands.) White box shows location of X-ray maps in
(b) and (c). (b and c) X-ray composition maps enhanced to show Fe/(Fe + Mg) zoning in gamet (b) and biotite (c). (Note absence of
zoning in garnet except where in contact with biotite and increase in Fe/Mg in biotite approaching garnet.) Width of field: 14 mm for
(a); 2-4 mm for (b).
librium constants in the peak mctamorphic assem- (Fe + Mg) owing to the retrograde progress of
blage. The value of Fe/(Fe + Mg) in garnet was reaction (1). When these model biotite compositions
then incremented sequentially (at constant P) until are used for thermometry in conjunction with
the value matched that of the garnet rim. The garnet core compositions, the calculated tempera-
change in temperature required to achieve a match tures are 100-200°C higher than the peak tem-
with the garnet rim was 50-100°C, with the net perature. Inasmuch as retrograde progress of
transfer reaction shutting down at ~700°C, con- reaction (1) consumes HjO, the total reaction pro-
sistent with the matrix biotite + garnet rim tem- gress is probably limited by H2O availability. The
peratures of 70O-750°C. At the end of the maximum amount of water required to drive
simulation, matrix biotite has a higher Fe/ reaction (1) the observed amount is ~2 vol. %,
746SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
Table 1: Selected analyses of garnets, biotttes andplagioclasefrom the Valhalla complex
Selected garnet analyses
Sample no.: V6A V6A V6B V6B V7C V7C V7D V7D V9C V9C
Comments: Core Rim Core Rim Core Rim Core Rim Core Rim
Analysts noj 1 9 2 67 1 12 185 8 131 101
Wt%oxkhs
SiO 2 38-22 38-50 38-00 37-79 38-91 36-81 38-51 3802 38-23 38-20
AbO, 21-94 22-15 21-89 21-65 22-28 21-08 22-17 21-79 21-67 21-75
MgO 6-16 5-02 6-38 3-12 8 86 6-01 7-25 436 5-78 4-32
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FoO 32-64 3404 31-92 34-28 28-67 32-44 29-55 33-33 31-49 32-22
MnO 0-61 0-64 0-57 1-58 0-46 0-90 0-65 1-22 2-29 3-32
CBO 1-63 1-91 1-63 223 2-34 2-74 2-52 2-72 1-28 1-42
Total 101-11 102-26 100-39 100-63 101-52 98-96 100-55 101-44 100-71 101 -24
Cttlontper 12 oxygens
SI 2-980 2-986 2-978 3-005 2-968 2-961 2983 2-984 2-998 3-004
Al 2-017 2-025 2022 2030 2-004 1-999 2024 2-016 2-003 2-016
Mg 0-716 0-580 0-745 0-370 1-007 0-600 0-837 0-510 0-675 0-506
Fo 2+ 2-128 2-208 2092 2-280 1-829 2-182 1-914 2-188 2-065 2-119
Mn 0-034 0-042 0-038 0-105 0030 0-061 0-036 0081 0-152 0-221
Ca 0-136 0-159 0-137 0-190 0-191 0-236 0-209 0-229 0-106 0-120
Fa/(Fe+Mg) 0-748 0-792 0-737 0-860 0-645 0-784 0-696 0-811 0-754 0-807
Pyrope 0-238 0-194 0-247 0-126 0-329 0-195 0-279 0-170 0-225 0-171
Almandine 0-706 0-739 0-695 0-774 0-598 0-709 0-639 0-727 0-689 0-714
Spessaitlna 0-011 0-014 0-013 0036 0010 0-020 0012 0-027 0-051 0076
Granular 0-045 0-053 0-045 0-065 0-062 0-O77 0070 0-076 0-035 0-040
(continued on nextpaga)
which may have exsolved from melts produced by decompression with heating to the peak conditions.
(2) during crystallization. The absence of early kyanite limits the amount of
Sample V9C is the only sample that records a decompression toJOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
Table 1: continued
Selected biotite analyses'
Sample no.: V6A V6A V6B V6B V7C V7C we V7D V7D V9C V9C
Analysis no.: 92 94 79 71 84 99 92 165 182 36 67
Comments: IncQtz Matrix Matrix Matrix IncGrt Matrix Matrix IncGrt Matrix IncGrt Matrix
HIT1 HiTi LowTl LowTi HITI LowTl HIT1 LowTl
Wl % oxides
SiO2 35-61 35-84 35-32 34-15 36-97 36-70 36-57 37-33 35-68 3609 35-89
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AI2O3 1803 18-27 18-90 19-33 18-37 1807 18-98 18-12 18-64 1802 17-95
TIO2 5-56 3-36 4-01 1-62 3-95 3-73 2-38 5-17 4-06 1-85 3-36
MgO 10-02 11-56 9-16 9-28 16-25 11-67 12-75 1403 10-13 11-71 10-61
FeO 17-43 17-56 18-69 19-63 12-10 15-95 14-91 11-67 18-58 18-39 17-48
MnO 0-00 002 0-06 006 003 008 0-05 0-07 0-11 0-14 0-19
CaO 0-00 002 000 0-02 000 0-10 0-00 0-00 0-O4 006 0-04
Na 2 0 0-29 0-32 0-20 0-78 0-53 0-11 0-20 0-27 0-15 0-26 0-O9
KjO 9-15 8-79 9-10 8-73 8-82 9 48 9-49 9-46 9-32 9-11 9-73
Total 96-00 95-74 95-43 93-50 9602 94-89 95-33 96-11 98-71 96-63 95-34
Cttions per 22 oxygens (tnhydrous)
Si 2-657 2-682 2-671 2-656 2685 2-688 2-716 2-707 2-661 2-720 2-710
Al* 1-343 1-318 1-329 1-344 1-315 1-312 1-284 1-293 1-339 1-280 1-290
Af 0-248 0-294 0-356 0-428 0-258 0-292 0-378 0-256 0-300 0-321 0-308
Ti 0-313 0-189 0-228 0089 0-216 0-211 0-133 0-282 0228 0-105 0-191
Mg 1-118 1-289 1032 1076 1-651 1-309 1-411 1-616 1-126 1-315 1-194
Fe1* 1-091 1099 1-182 1-277 0-735 1-004 0-926 0-708 1-159 1-159 1-104
Mn 0-000 0001 0-O03 0004 0002 0-005 0-O03 0004 0-O07 0009 0012
XOctahedral 2-770 2-872 2-801 2-874 2-862 2-821 2-851 2-766 2-820 2-909 2-809
Ca 0000 0002 0000 0002 0000 0-008 0000 0000 0003 0005 0003
Na 0042 0047 0030 0-117 0074 0016 0-029 0038 0-021 0038 0013
K 0-874 0-839 0-878 0-866 0-817 0-911 0-899 0-875 0-887 0-876 0-937
ZAslte 0-916 0-888 0-908 0-985 0-891 0-935 0-928 0-913 0-911 0-919 0-953
Fe/(Fe+Mg) 0-494 0-460 0-534 0-543 0-308 0-434 0-336 0-318 0-507 0-468 0-480
Compositions of selected plaglodase
Sample no.: V6A V6A V6B V6B V6B V7C V7C V7C V7D V7D V9C V9C
Analysisna: 103 100 83 86 87 127 103 123 1 5 137 141
Core/rim: core rim (1) core rim rim (2) rim (3)
Matrix Matrix Matrix
Min/lnt/Max Min Max Min Int Max Min Int Max Min Max Int Max
X*n 0-35 0-38 0-22 0-33 0-44 0-41 0-50 0-55 0-39 0-41 0-28 0-33
#
F and Cl values from frve samples range from 0-08 to 0-2 w t % . ( 1 ) Inclusion within garnet (2) Touching gamet in a reaction zone on the
rim. (3) Included within biotite in a reaction zone on the gamet rim. Analytical procedures are identical to those described by Kohn etal.
( 1 9 9 3 ) . Universal Transverse Mercator zone 11 coordinates; V 6 , 5 4 6 9 1 1 ; V7, 541 869; V 9 , 4 7 2 925.
748SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
14
I I I
Valhalla Complex
Peak P-T conditions
12
10
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500 600 700 800 900
T°C
Fig. 9. P-T diagram for the Valhalla complex. Gray area ihowi peak P-7" condition! as inferred from phue equilibria and geobarometry.
Arrowi ihow inferred P-T path. GRAIL equilibria after Bohlen it al. (1983). Gamet-plagioclaie barometry after Hodga & Crowley
(11985) and Hoisch (1991). Dashed line is equilibrium curve for a plagiodase inclusion within garnet Dehydration melting reactions
from Huang & Wyllie (1973, 1974) and Vielzeuf & Clemens (1992). Isopleths of JTpe(biodte) for the reaction phlogopite + quartz = enstatite
+ K-feldspar + liquid were calculated as described in the Appendix. Numbers in parentheses refer to reactions discussed in text.
rates) has been discussed by a large number of 1994). Most typically, an attempt is made to match
workers (e.g. Dodson, 1973, 1986; Lasaga tt al., the zoning profile in a mineral such as garnet by
1977; Lasaga, 1983; Wilson & Smith, 1984, 1985; varying the cooling rate. It is assumed that the
Spear, 1991; Spear & Florence, 1992; Ehlers et al., driving force for diffusion is the change in garnet rim
1994). The method is based on the assumption that composition in response to changing temperature
the observed zoning i3 diffusion controlled where the and constrained by the distribution coefficient for
diffusion is driven by compositional changes at the Fe-Mg exchange between garnet and biotite. Biotite
rim of the mineral. These compositional changes are is typically assumed to diffuse rapidly compared with
assumed to be known functions of temperature, and garnet; this assumption is supported by the generally
hence time, for a specified cooling rate. In most small or nonexistent zoning profiles in biotites from
studies a 'forward modeling' approach is adopted many rocks. With these assumptions, it is possible to
whereby zoning profiles are computed, usually by compute an apparent temperature or closure tem-
numerical methods, for a specified set of initial and perature .based on the composition of biotite
boundary conditions. (assumed to be homogeneous) and garnet, as a
One application that has received considerable function of position in the garnet. Spear (1991),
attention is the modeling of garnet zoning profiles Florence & Spear (1991) and Spear & Florence
where garnet is in contact with biotite (e.g. (1992) have explored implications of various dif-
Thompson & England, 1984; Spear et al., 1990; fusion models on the interpretation of thermobaro-
Spear, 1991; Spear & Florence, 1992; Ehlers et al., metric results and P-T paths. Alternatively, it is
749JOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
possible to examine closure temperature at the (a) Snufl BJotile Inchoion (b) Large Btottst Inclusion
garnet core as a function of garnet radius and Final
Garnet
cooling rate (e.g. Spear, 1991; Ehlers etal., 1994).
Although the modeling is straightforward, there is
a major problem with application of any method
that uses zoning on the rim of garnet in concert with
matrix biotite as a basis to infer pctrologic cooling Initial
Final
rates. Specifically, it is difficult at best, and impos-
Buttle
sible at worst, to be sure of the reactions that govern
the rim (boundary) composition of the garnet. Blot it*
Inasmuch as the above methods require that only
Fe—Mg exchange is operative between garnet and
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biotite, any other reactions, and especially net
transfer reactions, will render the results completely
incorrect. Robinson et al. (1982), Robinson (1991),
Spear & Florence (1992) and Florence & Spear (c)
(1993) have discussed the implications for geother-
Bkxitetize-
mometry of systems in which net transfer reactions
Fig. 10. Schematic illustration of garnet-biotitc diffusion profiles
are operative during cooling. as a function of biotite inclusion size, (si) Small biotite inclusion;
To circumvent this limitation, the method used (b) large biotite inclusion; (c) plot of T«p vi biotite size.
Dotted lines show initial (peak metamorphic) compositions;
here utilizes only biotite inclusions within garnet. continuous lines show final compositions. Gray shaded regions are
For an inclusion, there is little possibility that net constrained by mass balance to be equal areas. (Note that
transfer reactions can occur without reaction pro- T'.ppmrcm is calculated from homogeneous biotite and unmodified
ducts being optically visible. Moreover, biotite sur- garnet core.)
rounded by garnet has a great likelihood of
maintaining Fe—Mg exchange equilibrium during (Fe + Mg) in biotite is a function of the size of the
cooling. biotite inclusion: smaller crystals change composition
Chemical zoning in garnet surrounding biotite more than larger ones. In Fig. 10, the mass balance
inclusionsSPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
taking an 'eyeball' average of the diameter in grains Model calculations
that display no obvious cleavage and low birefrin- Comparison of the biotite inclusion apparent tem-
gence. This simple measure of biotite size is justified perature data with model calculations has been done
on theoretical grounds if diffusion out of the biotite using a finite difference model for diffusion in a
obeys a cylindrical geometry because for a cylin- variety of geometries (Fig. 11). A cylindrical biotite
drically symmetrical flux, the biotite mass is a geometry was chosen because it most closely corre-
function only of the area of its circular cross-section: sponds to what is believed to be the anisotropy of
nr2. Of course, the greatest difficulty lies in the esti- diffusion in biotite. A spherical geometry was also
mation of the size of a three-dimensional crystal in a tried, and it was found that the final results were not
two-dimensional thin section. Care was taken to use especially sensitive to the geometry assumed so long
only those grains that showed near-vertical contacts as the model geometry was consistent with the mea-
with host garnet. Moreover, large grains near garnet surement of biotite size.
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rims were not used because of the possibility that
these might have been in communication with the In the model, diffusion is permitted in both garnet
matrix during cooling. Because of these difficulties, host and biotite inclusion. The finite difference grid
the Iff error on the measurement of biotite diameter is set up such that the spacing of the grid is smallest
is assumed to be on the order of a factor of two [log at the gamet-biotitc interface, and coarsens with
(error) = ±0-3] and the error of the apparent tem- distance from the interface. The minimum grid
perature is estimated to be ± 30°C (Kohn & Spear, spacing is calculated as an exponential function of
1991). temperature by using the largest diffusion coefficient
D
A plot of apparent temperature vs log of biotite maximum*
diameter is shown in Fig. 11. Even with these con- maximum
siderable errors, a broad correlation can be seen to
with a lower cutoff to ensure at least four grid points
exist between biotite size and apparent temperature.
in the smallest grain. The remainder of the grid is
A regression line through the data for samples V6
calculated as a logarithmic function of grid point (i)
and V7 (filled circles) gives Tc = 486 + 93-7 log (d)
with the empirical relationship
with 7^ = 0-5 and a regression line for sample V9C
yields Tc = 538 + 58-5 log ( 800 large saving in time because of the greatly reduced
i number of grid points that are required to describe
the profiles.
&£^--'"Z. - An explicit finite difference scheme is used to solve
CIO . "^ .-- cu. the diffusion equation
..--' (1M5) •
dC cod
Oi 1.0 13 ID I.S 10
Log(dlameter) (urn)
where r is the radius (for cylindrical and spherical
geometries) and co is a constant that depends on the
Fig. 11. Plot of apparent temperature, calculated from gamet geometry (co = 0 for linear geometry, co = 1 for
core + biotite induiion thermometry, vs biotite siie (log diameter
of long axii) for lampla from the Valhalla complex. Filled circles cylindrical geometry and co = 2 for spherical geo-
are from sample locations V6 and V7 ~ 7 km west of the Slocan metry) with curvatures calculated from
Lake normal fault. Triangles are from location V9 ~ 1 4 km west
of the fault. Continuous lines are model results calculated as &C _ C,-+i Ax,- - C,(Ax, + C.-i
discussed in text using diffusion coefficients of Chakraborty &
Ganguly (1992: C&G, 1992); dashed lines are model results calcu- 5x? ~ 0.5 Ax, Ax,+1 (Ax, + Ax,+1)
lated using diffusion coefficients of Cygan & Lasaga (1985: C&L,
1985). [see equation (A-7) of Spear & Florence (1992)]. To
751JOURNAL OF PETROLOGY VOLUME 37 NUMBER • AUGUST 1996
ensure uniform numerical precision, time steps are solution increases with the number of phases and
computed as more than three phases would require a non-linear
equation solver.
V ^minimum/ **•
= 0-2*
D Diffusion coefficients
where Ajfmjnimun, is the minimum grid spacing (at the A number of values for diffusion of Fc and Mg in
rim) and R is a stability factor (.ft < 0-5 for stability garnet have been published (Lasaga et al., 1977;
of the explicit finite difference algorithm). Typically, Cygan & Lasaga, 1985; Loomis et al., 1985; Chak-
problems are run with R = 0-1—0-3. raborty & Ganguly, 1989, 1990, 1992). Of these, an
The boundary condition at the contact of the upper and lower limit of Fe-Mg binary diffusion is
garnet and biotite is defined by partitioning equi- provided by the values proposed by Cygan & Lasaga
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librium and mass balance. Partitioning equilibrium (1985) and Chakraborty & Ganguly (1990, 1992),
requires that the equation respectively, with the values at 600-700°C differing
by 2-3 orders of magnitude. Because of this large
(Mg/Fe) garnet difference, model calculations have been run with
(6)
both sets of diffusion coefficients. Cygan & Lasaga
(1985) measured only tracer diffusion for Mg in
is satisfied. A"D is a function of temperature and garnet, so it was assumed that D^ig = D^c (alter-
pressure, and the calibration of Ferry & Spear
natively, that Mg diffusion is rate limiting). Chak-
(1978) of the equilibrium has been used:
raborty & Ganguly (1990, 1992) published values
_ [-12454-0 + 4-662 r ( K ) - 0 0 5 7 P ( b ^ ) ] for tracer diffusivities of both Fe and Mg, and so the
binary Fe-Mg interdiffusion coefficient was calcu-
~ (3)(8-3144)7~(K)
lated from (Lasaga, 1979)
Mass balance (or flux balance) requires that the flux
across the garnet-biotite interface is equal:
Jgimct Jbio
For both sets of data D M 8 and Dpc arefirstcom-
or puted from the Arrhenius relationship
A^activation •+• Vactivation ( ' (ban) U
« I — -^biotite I ~rT~ I *i = D*Oi exp
" / garnet V*/biotite RT(K)
In the finite difference approximation, this becomes using the values in Table 2. Biotite diffusivities are
unknown, but assumed to be faster than those of
p. / ^ r i m L Ax.
Equation (6) can also be written in terms of C^m:
Table 2: Values of Do (at 1 bar) and
[0 "" £rim)/Crim] ct
(6a) "-"^ « ^ diffusion modeling
where C^m is now defined as Fe/(Fe + Mg) in the CyganftLasaga Chakraborty & Ganguly (1992)
respective phase. Simultaneous solution of equations (1985)
(6a) and (7) results in a quadratic that can be solved Mg Mg Fe
for Crim (Crim-i ' s known) in one phase and then
back substituted to obtain Cnm in the other. This Do 9-8x1(r* 1-1 X1CT3 6-4x10^
method can readily be extended to solve for any 284500 275408
AfacthaUc „ 238060
number of phases in simultaneous partitioning equi- «, 0-47 053 0-56
librium and flux balance, although the order of the
752SPEAR AND PARRISH PETROLOGY AND COOLING OF VALHALLA COMPLEX
can be seen, the slope of the model curves is broadly small. Values of biotite/gamet diffusivity of 1, 10,
consistent with the positive correlation seen in the 100 and 1000 result in model closure temperatures of
data. Indeed, the curve regressed from the data has 713, 707, 702 and 700°C, respectively (biotite dia-
very nearly the same slope as the model curves, in meter 100 (im, cooling rate 100°C/Ma). The reason
support of the assumed mechanism of biotite-garnet for the small sensitivity is that by the point that
reequilibration. Before discussing the implications of -DbiotJte/^g.mrt-10. ^ diffusion process is rate
these results, the sensitivity of the model to select limited by diffusion in garnet, so further increases in
input parameters will be addressed. biotite diffusion coefficient effect little change in the
result.
Effect of starting temperature on model results
The initial temperature (7";^^,]) used in the model Effect ofmechanism ofbiotite reequilibration
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calculations affects the calculated closure tem-
perature most strongly for models involving rapid A critical assumption of the method is that the only
cooling, and for large inclusions. The peak meta- mechanism of Fe-Mg reequilibration in biotite and
morphic temperature for the Valhalla samples is garnet is Fe-Mg exchange. As mentioned above, this
believed to be ~820°C (Fig. 9) and the models assumption is generally not valid for garnet rim-
shown in Fig. 11 are calculated using this tem- matrix biotite pairs because of the distinct possibility
perature as the starting value. For comparison, of net transfer reactions affecting the composition of
models run with T^^ of 920°C and 720°G arc matrix biotite and consuming garnet. Restricting the
compared with those of Fig. 11 in Fig. 12. The analysis to only biotite inclusions within garnet
curves are coincident for small biotites and diverge minimizes the possibility of net transfer reaction but
with increasing biotite size to become asymptotic to does not eliminate it.
the initial temperature. A possible mechanism that could affect the results
shown here is the reequilibration of biotite by a
reaction that produces ilmenite:
Effect ofchoice ofbiotite diffusion coefficient
The value of Fe-Mg interdiffusion in biotite is not
Mg-Fe—Ti biotite = Mg biotite + ilmenite.
known, but is suspected to be faster than that in
garnet. The model calculations in Fig. 11 were per- It is not clear how this reaction should be balanced,
formed with Z)0(biotite) -2D0(garnct): that is, but petrographic evidence of small inclusions of
biotite diffuses twice as fast as garnet. If a faster oxides in biotite is common. Precipitation of ilmenite
biotite diffusivity is assumed, then the model closure renders the product biotite poorer in Fe and results
temperature decreases, because less Fe is con- in a lower apparent garnet-biotite temperature.
centrated at the biotite core. However, the effect is Similar observations have been reported by
Hickmott et al. (1984) and Spear it al. (1990).
dameter (IOTI) To estimate the magnitude of the effect of ilmenite
15.8 100 158 1000
1000 precipitation on the calculated temperatures, biotite
compositions have been reconstructed using an
Effect of Tugrf THtJdCQ . assumed peak metamorphic Ti content. The highest
on model apparent temperature Ti contents in the sample suite are 0-28-0-31 cations
^ 920
p per 22 anhydrous oxygens and come from select
inclusions within garnet, quartz or plagioclase. Con-
3
e versely, Ti contents of most biotite inclusions within
| garnet range from 015 to 0-25 cations. If it is
a assumed that Ti and Fe exchange from biotite in
£ eoo - stoichiometric proportions to make ilmenite, then
a
the difference between the measured Ti content and
the inferred peak metamorphic Ti content provides a
~ i i i i i i i i i ii 1 1 1 1 1 measure of the amount of Fe that has been removed.
1.0 1.5 2.0 2-5 3.0 Incorporation of this Fe into the biotite provides a
Log(cflameter) (pm)
new estimate of the Fe/(Fe + Mg) and hence the
Fig. 12. Plot of apparent temperature vi biotite lize showing effect closure temperature.
of choice of assumed starting conditions on diffusion model results. Closure temperatures calculated using biotites
Model cooling rate is 100°C/Ma. Diffusion coefficients of Chakra-
borty & Ganguly (1992). At large biotite sizes, apparent tempera- adjusted for assumed Ti contents are higher than
tures become asymptotic to Ti those calculated using measured Fe/Mg. The shifts in
753JOURNAL OF PETROLOGY VOLUME 37 NUMBER 4 AUGUST 1996
apparent temperature range from 0 to 60cC with a GEOGHRONOLOGIG COOLING
meanof21±14°C. RATES
A measure of whether this correction improves the Previous geochronological studies in the Valhalla
accuracy of the method is whether the correction complex have been concerned mainly with dating
results in a substantial improvement in the scatter of rock units both within (Parrish, 1984, 1995; Parrish
the data about a line. The value of r2 for the uncor- et al., 1988), and above (Parrish, 1992) the complex,
rected data is 0-49 compared with a value of 045 for and with determining the chronology of fault motion
the Ti-corrected data, suggesting that the correction and subsequent lower-temperature cooling (Carr et
procedure results in little improvement to the scatter al., 1987; Parrish et al., 1988). These studies
of the data. document cooling ages which record argon closure in
the temperature range of ~530°C to ~300 c C. The
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Discussion of model results higher-temperature metamorphic and cooling
To facilitate evaluation of cooling rates based on the chronology, inferred by U-Pb dating of zircon,
diffusion modeling, the model results can be plotted monazite, allanite and titanite, is the subject of this
for a single biotite size as a function of cooling rate, section. Results will be presented in two U-Pb con-
as shown in Fig. 13. The data were projected onto cordia diagrams and a T~tfiguresummarizing all of
this figure using the linear regression for each set the chronological data for the complex.
calculated at a biotite diameter of 100 /an. For
samples V6A, V7C and V7D the apparent tem- Analytical methods for geochronology
perature (at 100 fim) is 673±4°G, and for sample U-Pb age determinations presented below follow
V9G it is 655 ± 6°C. The center of each box was procedures outlined by Krogh (1982), Parrish
plotted on each set of model curves with an assumed (1987), Parrish & Krogh (1987), Roddick et al.
error in apparent temperature of ± 30°C, which cor- (1987) and Parrish et al. (1992); these include air
responds to an error in the cooling rate of log (dT/ abrasion on zircon, 5small233 capsule 35
mineral dis-
dt) ~ ± 0-5. The cooling rate inferred from the solution, a mixed 2° Pb- U- U tracer, multi-
model results depends on the diffusion coefficients collector mass spectrometry and numerical error
used. The diffusivity of Cygan & Lasaga (1985) propagation. Analyses presented here were con-
requires a cooling rate of between 200 and over ducted over a number of years, and reflect variable
2500°C/Ma whereas the coefficients of Chakraborty amounts of Pb and U blanks, with ranges of 30-4 pg
& Ganguly (1992) imply a cooling rate of 3-80°C/ and 5-0 pg, respectively. Results are presented in
Ma. Table 3. Constants used for age calculations are
those recommended by Steiger & Jager (1977).
dT/dt ("C/Ma) Age of thermal peak during
10 100
metamorphism
© eoo Tc versus cooling rate V6A* In the southern part of the Valhalla complex (Fig.
biotite diameter = 100 urn V7Ct
V7D "^"^
1), a pelitic paragneiss near the village of Passmore
contains an array of monazite LT—Pb compositions
which have been described by Parrish (1990) and
Heaman & Parrish (1991). The positions of this and
..-V9C
other samples are projected into a cross-section of the
d Valhalla complex, as indicated in Fig. 2. These
monazite grains were mainly detrital in origin, with
initial crystallization ages of ~ 14 Ga corresponding
1.0 15 20 25 to the upper intercept of a discordant array on a
Log(dT/dt) CC/Ma) concordia diagram. Most isotope dilution analyses
Fig. 13. Plot of apparent temperature vi log (cooling rate) in °C/ are 79-95% discordant, this Pb loss being attributed
Ma for a model biotite diameter of 100 fun. Results using diffusion to diffusional loss during a thermal-metamorphic
coefficients of Chakraborty & Ganguly (1992: C*G, 1992) and event 75 ±5 Ma ago, the lower intercept and uncer-
Cygan & Laiaga (1985: C&L, 1985) are shown for comparison. tainty of the array of points. The degree to which
Boxes show apparent temperatures for two sample suites from
Fig. 11, in which average apparent temperature at a biotite these grains are composed of older cores and younger
diameter of 100 fim was calculated from regression of the data overgrowths is uncertain, indicating that the 79—
and plotted on the curve of C&G (1992). Error in apparent 7" is 95% discordancy in the grains is a maximum
assumed to be ±30*C, which translates to in error in inferred
cooling rate of log (dT/d/) ~ ±0-5.
estimate for the degree of individual Pb loss in single
754Table 3: U-Pb analytical data
J06pbd 2»pb. 20«pbf 207pbf 207pbf 207
Ph8
Fraction* Wt* U Pb° Pho- Corr.
235 2»pb (Ma) (Ma)
(mfl) (p.p.ra) (p.p.m.) ^Pb to) ^Pb u coef. «Pb (
^
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Mutvay Gneiss. 727-848 (UTMzone 77.4535O0E.5575400N)
zircon
1.+149 0-424 808-1 12-80 2576 126 0-18 0-0150010-20 0-0997010-22 0048201008 96-010-4 96-510-2 0-93 109-113-6
2.+149 0-658 812-3 12-78 3087 163 0-18 0-0149410-20 00992310-21 0048171007 95-610-4 96-110-2 0-94 107-413-4
3,-149 0-102 844-2 13-40 1403 59 0-18 0-0150210-20 0-0998910-24 0-0482210-12 96-110-4 96-710-4 0-87 110-115-6
4,-149 0-169 885-1 13-94 1847 76 0-20 0-0147110-20 0-0974910-23 00480610-10 94-210-4 94-510-4 0-91 102-014-6
5,-105 0-271 797-8 12-51 1735 116 0-19 0-0147210-20 0-0981210-23 0-0483510-11 94-210-4 95-010-2 0-89 116-215-0
tflintte
A-3,+149 1-134 199-5 35-93 30 13200 19-1 0-0103212-8 006632160 0-0466015-1 68-213-7 65-217-6 0-54 281250
A-4,+149 0-233 629-6 35-29 45 3574 5-3 0-0101410-19 0-0647212-3 0-0462912-2 65-010-2 63-712-9 0-81 131107
ttouvte
T-3,+149 2-818 101-6 0-903 49 5165 0-13 0-00873910-26 0-0575812-2 004779120 56-110-3 56-812-4 0-64 89197
T-4,+149 1001 91-87 0-858 34 3493 0-15 0-00907410-36 006355140 0-0507913-8 58-210-4 62-614-9 0-79 2321175
Midvey Gnaist, 529-83 (UTMzone 7 7,466200E, 5574480N)
aHanita
A-1,+149 1-494 480-7 42-76 42 21400 801 0-0732312-8 0-0113310-60 0-0468712-6 72-610-9 71-813-9 0-41 421130
n
A-2,+149 0-162 411-8 32-89 41 1996 7-22 0-0705512-9 0-0110910-19 0-0461512-8 71-110-3 69-213-9 0-67 51135
o
tftsnfto o
T-1,-149 1007 403-8 4-538 87 3589 0-32 0-00956510-18 0-0628311-1 004764110 61-410-2 61-911-4 0-61 81149
T-2.-149 2-511 442-7 4-824 88 9387 0-32 0-00928010-15 0-0609910-98 0-0476610-91 59-510-2 60-111-1 0-56 82143
KinniM Gneiss. 58-84 (UTM zone 7 7.450700E. 5463900N)
zircon
A.+149,6 0051 933-7 15-14 7369 7 006 0-0169610-12 0-116910-13 00500110-08 108-310-2 112-210-3 0-90 195-512-6
B,+149,5 0037 899-8 15-66 5307 7 006 0-0181710-11 0-125510-13 0-0501210-08 116-110-3 120-110-3 0-90 200-512-7
C+149,6 0-017 780-9 13-36 2385 6 005 0-0180610-10 0-120810-14 0-0485110-08 116-410-2 116-810-3 0-83 124-413-7
n
O
D.+149.6 0-015 1291 17-59 2816 6 004 00146210-11 00974710-14 00483610-09 93-810-2 94-410-2 0-78 116-714-0
E.-105 0050 730-8 12-98 1046 41 007 0-0184810-54 0-125610-57 00493010-14 118-011-3 120-211-3 0-97 162-316-4
F.-105 0034 542-3 8-281 2370 8 005 001611 10-14 0-107610-16 0048411009 103-010-3 103-710-3 0-82 119-214-4
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