Full text of DOI:10.1007/s004100100256

Contrib Mineral Petrol 72001) 141: 494±504
DOI 10.1007/s004100100256
R. Abart á R. Sperb
Metasomatic coronas around hornblendite xenoliths in granulite
facies marble, Ivrea zone, N Italy. II: Oxygen isotope patterns
Received: 11 September 2000 / Accepted: 5 February 2001 / Published online: 17 May 2001
Ó Springer-Verlag 2001
Abstract Up to 20-cm-wide metasomatic reaction bands
Introduction
formed coronas around hornblendite xenoliths in a
marble matrix during high grade metamorphism in the
The stable isotopes of oxygen have been used as tracers
Ivrea zone. The coronas are comprised of an innermost
for ¯uid±rock interaction and material transport in
monomineralic clinopyroxene layer, a garnet±clinopy-
metamorphic environments for three decades now 7for a
roxene layer and an outermost scapolite±clinopyroxene
review see Nabelek 1991). In this context, stable isotope
layer. The oxygen isotope composition of the original
fronts at lithologic contacts are of particular interest
hornblendite core is 7& relative to V-SMOW and the
7e.g., Bickle and Baker 1990; Abart and Pozzorini 2000).
oxygen isotope composition of the marble matrix is
The evolution of the geometry of an initially sharp front
19.7&. The oxygen isotope transition across the corona
re¯ects the extent of advective and di€usive/dispersive
is represented by a di€usion front with a step disconti-
tracer transport and the relative rates of transport and
nuity at the inner margin of the corona. The systematics
isotopic exchange between the transport medium and
of the inter-mineral fractionations indicates preservation
the solids of the rock 7e.g., Bickle and McKenzie 1987;
of the oxygen isotope compositions from high temper-
Abart and Sperb 1997). Quantitative information about
atures and maintenance of grain-scale oxygen isotope
the processes that lead to the formation of a stable iso-
equilibrium duringcorona formation. The oxygen iso-
tope front can be derived through the ®tting of a
tope pattern is interpreted in terms of a moving
mathematical expression that adequately describes the
boundary di€usion problem. The growing reaction band
processes involved to the observed stable isotope pat-
and the reactant hornblendite and marble represent a
tern. This approach is referred to as ``inverse modeling''
total of ®ve media with di€erent transport properties
of stable isotope fronts. To make the approach tractable
and movingseparation surfaces. Bulk oxygen di€usion
the processes must be idealized by simplifyingassump-
was at least three orders of magnitude faster then ex-
tions. In particular, inverse modelingmust be based on
pected from volume di€usion, suggesting that transport
simple initial and boundary conditions. Amongothers, a
was enhanced by relatively fast di€usion alongrgain
time invariant system geometry is one of the central
boundaries. Oxygen di€usivities in the individual layers
assumptions commonly made 7e.g., Bickle and Baker
correlate with the oxygen volume di€usivities in
1990; Bickle 1992; Cartwright 1994; Eppel and Abart
the major constituent minerals of the respective
1997). In this communication we investigate an example,
layers, suggesting mineralogical control on bulk oxygen
where this assumption is invalid. We discuss oxygen
di€usion.
isotope transport associated with the growth of up to
20-cm-wide multilayer metasomatic coronas that formed
around hornblendite xenoliths in a marble matrix at
granulite facies conditions in the Ivrea zone 7Abart et al.
R. Abart 7&)
Institut fur Mineralogie und Petrologie,
Karl-Franzens-Universitat Graz, Graz, Austria
2001). In this example, a gradient of 12& in d18O from
the isotopically light hornblendite to the isotopically
comparatively heavy marble is accommodated mainly
within the metasomatic reaction band at the interface
between the two incompatible rock types. An analysis of
the observed isotope pattern is complicated by the fact
that the oxygen isotope pattern developed simulta-
neously with the growth of the reaction band. We adopt
E-mail: rainer.abart@kfunigraz.ac.at
Tel.: +43-316-3805541
Fax: +43-316-3809865
R. Sperb
Seminar fur angewandte Mathematik,
ETH-Zurich, Zurich, Switzerland
Editorial responsibility: J. Hoefs

495
xenoliths are primarily derived from massive pyroxenites and
hornblendites, both of which crop out nearby. The xenolith ma-
terial was probably tectonically eroded from the country rocks
duringdeformation. The intrusive features of the marbles crosscut
structures that are associated with peak metamorphism 7Wilhelm
1998). This puts a maximum age constraint of about 270 Ma to
the incorporation of the xenoliths into the marble. Another type
of xenoliths is represented by oligoclasite fragments. These frag-
ments were probably derived from oligoclasite dikes that occur
sporadically in ma®c and ultrama®c granulite facies rocks of the
Ivrea zone. Stahle et al. 71990) obtained U±Pb zircon ages of
225‹13 Ma from similar dikes in the Finero complex some 10 km
east of Val Fiorina. The fact that oligoclasite fragments are also
present as xenoliths suggests that mobilization of the marbles and
incorporation of country rock fragments probably occurred syn-
chronous to or after formation of the oligoclasite dikes. This
event pertains to an episode of increased circulation of hydro-
thermal ¯uids in the Late Triassic and Early Jurassic 7Vavra et al.
1999), which caused widespread metasomatic phenomena in the
Ivrea zone 7Stahle et al. 1990). This puts a lower limit on the age
of xenolith formation. The hornblendite xenoliths were incom-
patible with the marble matrix at high grade conditions and
up to 20-cm-wide coronas developed at the hornblendite/marble
interfaces.
The typical low phase number, high variance metasomatic
assemblages of the reaction band are not suitable for pressure±
temperature derivation from a phase petrologic analysis of the
mineral paragenesis. Nor is there any appropriate mineral pair
for cation exchange thermometry. The occurrence of mizzonitic
scapolite in the outermost layer of the reaction band puts a
lower limit of 550 °C on the temperature of metasomatism, as
this is the lower thermal stability limit for mizzonite 7Orville
1974). Temperatures of 780 °C obtained from pargasite-bearing
coronas around pyroxenite xenoliths from Val Fiorina 7Wilhelm
1998) may be regarded as an upper temperature limit for corona
formation. This is in agreement with over-concordant U±Pb ages
of newly grown monazites from which Vavra and Schaltegger
71999) infer that the closure temperature of monazite, at 780 °C,
was not exceeded duringany post-peak metamorphic thermal
pulse.
the formalism available for movingboundary di€usion
problems to investigate the interplay of corona growth
and oxygen transport. Modeling results allow derivation
of relative transport properties of the individual mineral
layers of the metasomatic reaction band. Discussion of
the model results, in the light of experimentally deter-
mined di€usivities, sheds light on the mechanisms of
di€usion.
Geological background
The Ivrea zone is an approximately northeast±southwest striking
unit primarily comprised of upper amphibolite facies to granulite
facies metasediments and metabasites. A sketch of the regional
geology is shown in Fig. 1. Metamorphic grade increases form
upper amphibolite facies in the southeast to granulite facies in the
northwest 7Zingg 1983; Henk et al. 1997). The high grade meta-
morphism of the Ivrea zone has been dated at 270 Ma by Gebauer
71993) and by Vavra et al. 71999). Unroo®ngof the Ivrea zone
started in the Permian 7Brodie et al. 1989) and lasted at least into
the late Triassic and early Jurassic 7Bertotti et al. 1993). At that
time the Ivrea zone was still or again at temperatures of at least
500 °C 7Stahle et al. 1990).
In Val Fiorina, some 12 km southeast of Domodossola 7see
Fig. 1), a lithologically diverse granulite facies metamorphic se-
quence of the basal Ivrea zone is exposed in the river bed. The
sequence comprises metasediments 7metapelites and marbles),
metavolcanics 7amphibolites), as well as ma®c and ultrama®c ig-
neous rocks 7gabbros, hornblendites, pyroxenites and lenses of
peridotite). Rivalenti et al. 71997) derived peak metamorphic
temperatures of 700±900 °C and pressures of 7±10 kbar from a
variety of geothermometers and geobarometers applied to samples
from Val Fiorina. The marbles of Val Fiorina are highly de-
formed and ``intrude'' the more competent country rocks along
apophyses and dike-like structures 7Schmid 1967). The marbles
contain abundant centimeter- to decimeter-sized xenoliths. The
Fig. 1 Schematic sketch of the
regional geology of the Ivrea
zone giving an indication of the
samplinglocality in Val Fiorina:
CMBL Cossato±Mergozzo±
Brissago line; PL Pogallo line;
IL Insubric line

496
A summary of the mineral compositions is given in
Table 1. Clinopyroxene is the only phase that is pre-
sent in all mineral layers. It generally contains more
than 75 mol% of the diopside±hedenbergite solid so-
lution series, up to 25 mol% of the Tschermak's
molecule and up to 10 mol% of the acmite component.
Garnet occurs in the original hornblendite and in the
garnet±clinopyroxene layer of the reaction band. Gar-
nets from the original hornblendite contain almandine
735±45%), pyrope 725±35%), grossular 718±22%) and
andradite 75±10%) and essentially no spessartine
component. The garnets from the garnet±clinopyrox-
ene layer are comprised of grossular 765±75%),
almandine 715±20%) and andradite 710±15%). The
pyrope content is generally less than 5% in these
garnets. The hornblende of the original hornblendite is
a magnesio-pargasite. Scapolite has mizzonitic com-
position and the anion site is primarily occupied by
carbonate. For a detailed presentation of the mineral
chemistry see Abart et al. 72001).
Petrography of the metasomatic coronas
The coronas that formed at the interfaces between
hornblendite xenoliths and the marble matrix may be
described as multilayer reaction bands. A schematic
illustration of the reaction band geometry is given in
Fig. 2. The succession of mineral layers comprises:
· unaltered hornblendite with pargasitic hornblende,
pyrope±almandine garnet, and clinopyroxene,
· a monomineralic clinopyroxene layer,
· a grandite±garnet clinopyroxene layer,
· a scapolite±clinopyroxene layer,
· impure calcite marble matrix.
The thickness of the individual layers may vary con-
siderably from one xenolith to another. Generally, the
garnet±clinopyroxene layer is the most prominent; the
monomineralic±clinopyroxene layer and the scapolite±
clinopyroxene layer are usually comparatively thin. The
textural features of the individual layers were described
in detail by Abart et al. 72001). We adopt the terminol-
ogy of Joesten 71977). ``Mineral layer'' or simply ``layer''
refers to a body of rock with a speci®c mineral assem-
blage. ``Reaction band'' refers to the set of layers that
separates the incompatible reactant assemblages.
Analytical methods
The oxygen isotope compositions of mineral separates presented in
this communication represent
a samplingpro®le across the
hornblendite±marble transition from a single hand specimen
7sample 92-Fio). The hand specimen was cut into 1-cm-thick slabs
and small samples of 1±5 gwere taken from this slab. The sample
slab and the locations of individual subsamples are shown in Fig. 3.
Sample 92-Fio was taken from a decimeter-scale hornblendite xe-
nolith. As is frequently the case with such large xenoliths, the re-
action band is in part intensely deformed. In the deformed domains
the sample is a€ected by retrograde overprint. Subsamples for
mineral separation were only taken from domains that contain
pristine high-grade assemblages that were not a€ected by retro-
gression. The subsamples were crushed and sieved. Mineral con-
centrates were obtained from the fraction 63 lm<´<125 lm by
magnetic separation. Clean separates for analysis of garnet, clino-
pyroxene, and hornblende were hand-picked from the concentrates.
Oxygen isotope analyses of the mineral separates were done on a
laser ¯uorination line of the design described by Sharp 71990).
Samples of 1±2 mgwere reacted in a BrF atmosphere under a
5
slightly defocused 25-W CO2 laser beam. The liberated oxygen was
separated from excess reagent and reaction by-products cryogeni-
cally and by means of a 20-cm KBr column kept at 120 °C. Molecular
O2 was collected on a molecular sieve at liquid nitrogen temperatures
and ®nally expanded into the variable volumes of a Finnigan Del-
Fig. 2 Schematic sketch of the reaction band, volumetric propor-
tions of reactant marble and hornblendite have been estimated
from mass balance considerations 7see Abart et al. 2001)
Table 1 Chemical composi-
Hornblendite core
tions of the rock-forming
Hornblende
Na0.7Ca1.9Mg2.6Fe3+0.2Al0.7Ti0.2[Al2.1Si5.9O22]7OH)2
Ca0.8Fe2+1.2Mg0.9Al2.0Si3O12
Na0.05Ca0.937Mg0.7Fe2+0.12Fe3+0.11Al0.1)Si1.8Al0.2O6
minerals of hornblendite
xenoliths and their coronas
Garnet
Clinopyroxene
Monomineralic clinopyroxene layer
Clinopyroxene
Na0.05Ca0.937Mg0.7Fe2+0.12Fe3+0.11Al0.1)Si1.8Al0.2O6
Garnet clinopyroxene layer
Garnet
Ca2.4Fe2+0.5Mg0.1Al1.8Fe3+0.2Si3O12
Na0.06Ca0.977Mg0.48Fe2+0.29Fe3+0.14Al0.05)Si1.83Al0.17O6
Clinopyroxene
Scapolite±clinopyroxene layer
Scapolite
Na0.94K0.03Ca3.11Al5.08Si6.92O247Cl0.047CO3)0.96
Na0.06Ca0.957Mg0.51Fe2+0.27Fe3+0.11Al0.24)Si1.85Al0.15O6
)
Clinopyroxene

497
Fig. 3 Sketch of a slab from sample 92-Fio with positions of the
subsamples selected for mineral separation
Fig. 4 a Oxygen isotope compositions of mineral separates from
the reaction band of sample 92-Fio and of hornblendite and marble
bulk rock reference samples; b oxygen isotope data interpreted in
terms of normalized isotope compositions 7see text for de®nition)
taplus IR mass spectrometer. UWG-2 garnet 7Valley et al. 1995) was
used as an internal standard. Reproducibility of replicate measure-
ments was better than 0.15& 71r). Oxygen isotope compositions
are given in the conventional d-notation relative to V-SMOW.
Bulk rock hornblendite was analyzed on a conventional ¯uo-
rination line by reaction in a ClF3 atmosphere in externally heated
Ni vessels.
Carbonate samples were taken from sample slabs by means of a
dentist drill. Rock powders were reacted with 100% H3PO4 at 70 °C
on a Finnigan Kiel II device. Reproducibility of replicate mea-
surements was better than 0.1& 71r).
n=11). The bulk rock d18O values may be regarded as
reference compositions of the two reactant rock types.
The features of the oxygen isotope transition between
the relatively 18O enriched marble and the relatively 18O
depleted hornblendite across the reaction band are as
follows: A relatively smooth trend of successive out-
wards 18O enrichment is observed within the reaction
band and in the outermost 3 cm of the hornblendite
xenolith. A step discontinuity of 2.5& occurs at the in-
terface between the hornblendite and the monomineralic
clinopyroxene layer of the reaction band. The oxygen
isotope trend is continuous across all the other layer
Results
The stable isotope data are summarized in Table 2. The boundaries within the reaction band and at the interface
variation in oxygen isotope compositions of the rock- to the marble. The oxygen isotope enrichment in the
formingminerals across the reaction band of sample
outermost hornblendite is equally pronounced in garnet,
Fio-92 is illustrated in Fig. 4a. The d18O values of bulk clinopyroxene, and hornblende, and the inter-mineral
rock samples from unaltered hornblendite and marble fractionations are constant. In the hornblendite, the
are indicated by the gray and white circles at the far left hornblende is slightly enriched with respect to garnet
and right of the diagram. The hornblendite sample was and clinopyroxene by 0.13‹0.12&. Garnet and clino-
taken from a massive hornblendite that crops out in Val pyroxene are identical in d18O within the analytical
Fiorina and is petrographically similar to the hornb- uncertainty. In the garnet±clinopyroxene layer clinopy-
lendite of sample 92-Fio. The d18O 7SMOW) value of the roxene is enriched with respect to garnet by 0.45‹
original hornblendite is 7.0& 71r=0.32&, n=4). The 0.21&. The d18O values of carbonate microsamples
bulk rock marble sample was taken from a domain of taken in the garnet±clinopyroxene and in the scapolite±
the Val Fiorina marble that contains little inclusions. Its clinopyroxene layers, as well as in the marble matrix
oxygen isotope composition is 19.78& 71r=0.28&, adjacent to the reaction band, scatter between 17.8 and

498
Table 2 Oxygen isotope
Sample
Rock type
Position
cpx
7.44
7.59
8.00
gar
7.46
7.38
7.95
9.46
9.41
hbl
cc
compositions in d18O versus
V-SMOW of the rock forming
minerals in a pro®le across
the reaction band of sample
92-Fio. Positions are given in
centimeters relative to the pre-
sumed original hornblendite/
marble interface
92-Fio-Ia
92-Fio-Ia
92-Fio-Ib
92-Fio-Ic
92-Fio-Ic
92-Fio-IIa
92-Fio-IIa
92-Fio-IIb
92-Fio-IIb
92-Fio-IIc
92-Fio-IIc
92-Fio-IId
92-Fio-IId
92-Fio-IIe
92-Fio-IIe
92-Fio-IIf
Hornblendite
Hornblendite
Hornblendite
Hornblendite
Hornblendite
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
cpx layer
±16.8
±16.8
±15.8
±13.2
±13.2
±11.8
±11.8
±9.8
±9.8
±8.3
±8.3
±12.2
±12.2
±11.6
±11.6
±11.3
7.51
8.21
9.52
11.77
11.68
13.91
14.09
14.38
14.00
10.89
10.97
11.86
11.94
11.98
92-Fio-IIgcpx layer
±10.6
12.71
92-Fio-IIh
92-Fio-IIIa
92-Fio-IIIb
92-Fio-IIIb
92-Fio-IIIc
92-Fio-IIIc
92-Fio-IV
cpx layer
±9.9
±6.8
±5.8
±5.8
±4.3
±4.3
±0.25
13.04
gar±cpx layer
gar±cpx layer
gar±cpx layer
gar±cpx layer
gar±cpx layer
scp±cpx layer
14.95
14.90
15.07
14.95
15.07
15.60
15.40
15.50
15.30
15.63
15.71
17.83
18.17
18.23
18.17
18.30
18.15
18.48
18.36
92-Fio-Va
92-Fio-Va
92-Fio-Va
92-Fio-Va
Marble
Marble
Marble
Marble
0
0.5
2
4
18.5&. These compositions are depleted with respect to coordinate frame compositions that are in equilibrium
the marble reference value by 1.3±1.8&. In two samples with each other coincide and the transition between the
where coexistingcalcite and clinopyroxene were
reference marble and hornblendite compositions is
analyzed, the calcite±clinopyroxene oxygen isotope normalized to a range of 0 £ Rk £ 1.
fractionation is 2.2±2.6&.
Figure 4b gives an interpretation of the isotope data
in terms of normalized isotope composition. In the
present context we de®ne normalized isotopic composi-
tion of phase k, Rk as:
Discussion
The overall oxygen isotope pattern may be viewed as a
result of oxygen isotope exchange between the relatively
18O-enriched marble matrix and the relatively 18O-de-
pleted hornblendite xenolith. Any signi®cant advective
transport component would have resulted in an asym-
metric alteration pattern. The spherical geometry of the
coronas suggests that material transport associated with
metasomatism was mainly by di€usion. We will ®rst
investigate whether the observed oxygen isotope pattern
represents an original signature that is genetically related
to corona formation. We will then derive relations
amongthe oxygen di€usivities in the individual layers of
obs
k
hornblendite
À d
k
d
R
ˆ
;
k
marble
hornblendite
d
À d
k
k
where dmk arble is the isotopic composition of phase k that
is in oxygen isotope equilibrium with the reference
marble, and dkhornblendite is the isotopic composition of
phase k in equilibrium with the reference hornblendite,
and dokbs is the observed isotopic composition of phase k.
Rk is equivalent to the reaction progress variable as
introduced by Myers and Prestwood 71951). In this
Table 3 Coecients for oxygen volume di€usion at 750 °C and closure temperature 7Tc) estimates for oxygen di€usion in garnet,
clinopyroxene and hornblende; Tc estimates derived followingthe method of Dodson 71973) assuminga grain size of 1 mm
Mineral
Grain
geometry
D0
Ea
7kCal/mol)
Tc
7°C)
D at 750 °C
7cm2/s)
Reference
7cm2/s)
Ca-poor Garnet
Grossular
Clinopyroxene
Clinopyroxene
Hornblende
Sphere
Sphere
Cylinder
Cylinder
Cylinder
72
24.4
84
54
41
6´10±5
6.1´10±12
9´10±3
816
434
855
669
518
2.5´10±20
3.7´10±17
1´10±20
Brady 71995)
Freer and Dennis 71982)
Elphic and Graham 71994)
Farver 71989)
1.5´10±6
1´10±7
4.4´10±18
1.7´10±16
Farver and Giletti 71985)

499
the reaction band and the growth rate of the metaso- opyroxene is enriched in 18O by 0.5±1.0& with respect to
matic structure from the geometry of the oxygen isotope the grossular-rich garnet within the garnet±clinopyroxene
pattern. Finally we will discuss possible di€usion layer. This is in agreement with the model of Kohn and
mechanisms.
Valley 71998), which predicts a D18Ogrossular±clinopyroxene of
±0.45‹0.1& for 750 °C.
Preservation of the oxygen isotope compositions
from high temperatures is further indicated by the ob-
served calcite±diopside oxygen isotope fractionations.
Within the reaction band D18Ocalcite±clinopyroxene varies
Preservation of oxygen isotope signatures from
high temperatures
It was shown by Eiler et al. 71993, 1995) and by Jenkin from 2.2±2.6&. Based on the calibration of Chiba et al.
et al. 71994) that inter-mineral stable isotope fractiona- 71989), this translates to temperatures of 680±760 °C,
tions may be signi®cantly modi®ed by di€usive isotope which is in agreement with granulite facies conditions
exchange during cooling of high-grade metamorphic duringcorona formation. From the above consider-
rocks. The closure temperature for inter-mineral di€u- ations we conclude that the oxygen isotope compositions
sive isotope exchange depends on a number of factors observed most likely represent the signatures originally
including grain size and cooling rate. Using a grain size generated during the formation of the reaction band.
of 1 mm and a coolingrate of 5 °C per million years as a Thus, the geometry of the oxygen isotope pattern puts
lower limit, minimum values for the closure temperature constraints on oxygen transport during corona growth.
are obtained for oxygen di€usion in clinopyroxene,
garnet, and hornblende, following the method of Dod-
son 71973). Oxygen di€usivities at 750 °C as well as Oxygen di€usion
closingtemperatures, Tc, for oxygen di€usion in the
minerals of the reaction band are given in Table 3. For In an analysis of the oxygen isotope pattern associated
diopside Tc=648 °C if calculation is based on the fastest with the reaction band, it must be accounted for the fact
oxygen di€usivity ever determined experimentally 7Far- that oxygen di€usion and growth of the reaction band
ver 1989), and Tc=855 °C if based on data from Elphic occurred simultaneously. This situation may be inter-
and Graham 71994). For Ca-poor garnet a closure preted in terms of a movingboundary di€usion prob-
temperature of 816 °C is calculated based on the oxygen lem. The essential feature of such problems is the
di€usivities given by Brady 71995). The closure temper- existence of a movingsurface that separates adjacent
ature for grossular calculated from data of Freer and media. The di€usingspecies may be liberated or ab-
Dennis 71982) is 434 °C. The closure temperature for sorbed at the separation surfaces and the media on dif-
hornblende is 499 °C if calculated from the oxygen dif- ferent sides of a separation surface may have di€erent
fusivities of Farver and Giletti 71985). Diopside and Ca- transport properties. The reactant rocks and the three
poor garnet have minimum closure temperatures at or in mineral layers within the reaction band represent a total
excess of the temperature at which metasomatism took of ®ve media with di€erent transport properties. The
place. Their d18O values most probably represent the metasomatic replacement fronts represent the separation
original compositions that they obtained during growth. surfaces that move with respect to each other during
Although the closure temperatures for hornblende and corona growth. The growth rate of the metasomatic
grossular-rich garnet are signi®cantly lower than structure was controlled by di€usion of the major
temperatures during corona growth, their oxygen iso- components CaO, Al2O3, SiO2, and MgO 7Abart et al.
tope compositions received duringcorona formation
2001). Oxygen di€usion had to adjust to layer growth
were probably preserved. This is because of the lack of a and the associated displacement of separation surfaces.
reservoir of exchangeable oxygen for both phases. This scenario is referred to as a movingboundary
Hornblende and grossular-rich garnet are the only di€usion problem of type B by Crank 71975).
phases with low closingtemperatures in the hornblendite
and garnet±clinopyroxene assemblages, respectively.
In the following, the observed pattern is modeled as
di€usion in an in®nite system, which is composed of ®ve
Preservation of the oxygen isotope compositions from layers with distinct transport properties. Accordingto
high-grade conditions is also corroborated by the fact that the steady-state di€usion concept for reaction band
the compositional dependence of the garnet±clinopyrox- formation, growth is assumed to only occur at the layer
ene fractionations are in agreement with the calibrations interfaces 7Abart et al. 2001). Once generated, the indi-
of Kohn and Valley 71998). Within the hornblendite, the vidual layers maintain their transport properties such as
oxygen isotope compositions of the relatively Ca-poor porosity and the geometry of the grain-boundary net-
almandine±pyrope garnet and clinopyroxene are identical work. This is why the e€ective di€usivities are treated
within the analytical uncertainty, and hornblende is as constants. We will refer to the marble matrix, the
slightly enriched with respect to garnet and clinopyrox- scapolite±clinopyroxene layer, the garnet±clinopyroxene
ene. In the temperature range of interest, the prediction layer, the clinopyroxene layer, and to the hornblendite
from the calibrations of Kohn and Valley 71998) as layers 1 through 5, respectively. Layers 1 7marble
are D18OCa-poor:garnet±clinopyroxene
D18Ohornblende±clinopyroxene=0.2‹ 0.3&. In contrast, clin- have a ®nite thickness each. The interfaces are referred
= 0.2‹ 0.4& and matrix) and 5 7hornblendite) are semi-in®nite, layers 2±4

500
to as interface 1 through 4 from the outer to the inner where Pj and Qj are constants. Mass conservation at
boundary of the reaction band. From steady-state dif- interface j between media i and i+1 requires that:
fusion modelingit is known that the individual meta-
@Xji‡1
@t
@Xji
@t
@Ri
@xi
@Ri‡1
@xi‡1
somatic replacement reactions do not conserve volume.
For example, at the inner boundary of the reaction
band, only 0.7 volumetric units of clinopyroxene layer
are produced duringthe consumption of 1 volumetric
unit of hornblendite 7Abart et al. 2001). As a conse-
quence, inert markers that existed in two adjacent layers
would move with respect to each other duringcorona
growth. This phenomenon is accounted for by de®nition
of separate coordinate systems, referred to as xi, for each
of the ®ve layers i. Each reference frame is ®xed to the
solid material of the correspondinglayer. The reference
frames move with respect to one another duringlayer
growth. The position of a separation surface j at time t
with respect to the reference frame xi is referred to as
Xjiꢀt†. At t=0 only two layers, the hornblendite and the
marble, exist and all separation surfaces coincide at
Xjiꢀ0† ˆ 0. In di€usion controlled layer growth the po-
Di
À Di‡1
‡ Ri
À Ri‡1
ˆ 0
ꢀ5†
From the initial and boundary conditions it follows
that 2a1+b1=1, and b5=0. Substitution of Eq. 73) into
Eqs. 74) and 75) yields:
ꢄ
ꢀ
ꢁ
ꢅ
q
q
h
i
ai erfc aij ‡ bi ˆ Pj ai‡1 erfc
aij‡1 ‡ bi‡1 ‡ Qj
ꢀ6†
and
r
r
q
ꢂ
h
i
ꢃ
i‡1
Di
i
j
Di‡1
j
À 2
eÀa ‡ 2
eÀa ‡ bji ai erfc aji ‡ bi
p
p
ꢄ
ꢀ
ꢁ
ꢅ
ꢀ7†
q
q
À
bij‡1 ai‡1 erfc
aij‡1 ‡ bi‡1 ˆ 0
bji
with aij ˆ 4D . For each of the four interfaces two equa-
tions of thei type 76) and 77) may be written. Together
with the condition that 2a1+b1=0 this yields a system
of nine equations with 22 unknowns. The unknowns are
the constants a1,a2,a3,a4,a5,b1,b2,b3,b4, the tracer di€u-
sivities in the individual media D1,D2,D3,D4, and D5,
and the constants that describe the movement of the
interfaces b11; b21; b22; b23; b33; b34; b44; b54. Quantitative rela-
tions amongthe bij parameters may be obtained from the
volume change at metasomatic replacement fronts as
derived from steady-state di€usion modeling7Abart
et al. 2001) and from layer thickness 7see Appendix). The
equations may be solved if the oxygen isotope compo-
sitions at layer boundaries are known, and one of the bji
parameters is arbitrarily speci®ed. The parameterization
of the model is discussed in the Appendix.
sition of a separation surface j at time t is given by
q
Xjiꢀt† ˆ bijt: The initial conditions may be expressed in
terms of normalized isotope compositions:
R1ꢀx1; 0† ˆ 1; for x1 < 0; at t ˆ 0
ꢀ1†
R5ꢀx5; 0† ˆ 0; for x5 > 0; at t ˆ 0
Initial conditions may only be speci®ed for R17x1,0) and
R57x5,0), because the media 2 through 4 do not exist at
t=0. The boundary conditions may be stated as:
R1ꢀx1; t† ˆ 1; for x1 ! À1; at t > 0
ꢀ2†
R5ꢀx5; t† ˆ 0; for x5 ! ‡1; at t > 0
The solution for di€usion in an in®nite medium is 7e.g.,
Crank 1975):
A feasible set of growth rates and di€usivities ob-
tained from inverse modelingof the oxyegn isotope
transition across the reaction band is given in Table 4.
The pattern obtained from this choice of model pa-
rameters is shown in Fig. 5. The geometry of the model
front is time invariant. Both the concentrations at a
ꢀ
ꢁ
xi
p
Dit
Riꢀxi; t† ˆ ai erfc
‡ bi;
ꢀ3†
2
where Di is the di€usion coecient of the tracer in
medium i, and ai and bi are constants that have to be
determined. At the interface j between two adjacent
media, i and i+1, the concentrations are related
through:
given position and the positions of the interfaces are
p
proportional to t. If the products bijt and Dit are kept
constant identical patterns are produced. Geologically
reasonable time scales for corona formation are on the
order of 103±108 years, an upper limit on the order of
2.0´108 years is given by the supposed age of the coro-
nas. Bulk oxygen di€usivities obtained for geologically
reasonable time scales are shown in Table 5. The e€ec-
ꢂ
ꢃ
ꢂ
ꢃ
Ri Xji; t ˆ PjRi‡1 Xji‡1; t ‡ Qj;
ꢀ4†
Table 4 Model di€usivities for the individual media and tive oxygen di€usivities obtained are several orders of
displacement parameters, b, for the interfaces, the position of an
interface j with respect to the reference frame xi at time t is given by
magnitude larger than experimentally determined coef-
®cients for oxygen volume di€usion. Even for the
limitingcase, where the time of corona formation
is assumed as 2.7´108 years, the e€ective oxygen di€u-
sivity within the clinopyroxene layer is estimated at
8.5´10±15 cm2/s. This is three to four orders of magni-
tude faster than experimentally determined oxygen vol-
ume di€usion in clinopyroxene 7compare Table 3).
Enhancement of bulk oxygen di€usion with respect to
oxygen volume di€usion in the corresponding solids
1
ꢂ
Medium i
ꢃ
2
bijt
Interface j
Di
bji
bij‡1
1
2
3
4
5
1
2
3
4
2,200
500
370
40
0
0
0.25
14
156
1
72
70
690

501
Fig. 5 a Stable isotope pattern
at time t=1 predicted for dif-
fusion in a composite system
comprised of ®ve media with
movingseparation surfaces;
di€usion coecients of the dif-
fusingspecies for the individual
media and the b parameters
that describe the displacement
of the separation surfaces are
given in Table 4; b volume
equivalents of reactant rocks
and newly formed mineral lay-
ers. Note that the individual
coordinate systems move with
the correspondingmedia x1, x2,
x3, x4, x5; the example is shown
for a bulk volume factor of 1,
i.e., the media x1 and x5 do not
move with respect to each other
Table 5 Oxygen di€usivities in cm2/s obtained for the individual
media for geologically reasonable time scales
grain interiors 7see Joesten 1991 and references therein).
The contribution of grain boundary di€usion to bulk
di€usion depends, amongother factors, on the volume
fraction of the polygranular medium that is occupied by
Medium
Di
t=1 s t=103 years t=105 years t=107 years the grain-boundary network 7Hart 1957).
Â
Ã
7.0´10±8
1.6´10±8
1.1´10±8
1.3´10±9
2.2´10±8
7.0´10±10
1.6´10±10
1.1´10±10
1.3´10±11
2.2´10±10
7.0´10±12
1.6´10±12
1.1´10±12
1.3´10±13
2.2´10±12
Dbulk ˆ s ꢀ1 À a†Dvol ‡ aDgb
1
2
3
4
5
2,200
500
370
40
where Dbulk is the bulk di€usion coecient of the poly-
granular medium, Dvol is the volume di€usion coecient
of the solids, Dgb is the di€usion coecient of the grain-
boundary medium, s is the tortuosity of the grain-
boundary network, and a is the volume fraction of the
medium that is occupied by the grain-boundary medi-
690
may be caused by the polygranular nature of the media. um. The volume fraction occupied by grain boundaries
Di€usion in a polygranular medium occurs by a com- may be calculated from: a=7pn)/72d), where n is the
bination of penetration alongthe grain boundaries and
lateral spreadinginto the solids by volume di€usion.
grain boundary width and d is the grain diameter. The
physical grain-boundary width is on the order of 1 nm in
From experimental data it is inferred that di€usion in metamorphic rocks. Together with a grain size of 1 mm
the grain boundary medium is about ®ve orders of this yields, aꢁ10±6 for the reaction band under consid-
magnitude faster than volume di€usion through the eration. To accommodate the inferred oxygen transport

502
within geologically reasonable time scales, this would The fact that in the outermost hornblendite the fronts
require very fast grain boundary di€usion so that Dgb/ recorded by garnet, clinopyroxene, and hornblende are
Dvol were of the order of 1010. This is in con¯ict with identical and coincide within the analytical uncertainty
experimentally determined values of 105 for Dgb/Dvol indicates that oxygen isotope equilibrium was main-
7Joesten 1991). From the condition that bulk oxygen tained on a grain scale during isotopic alteration. This
di€usion was three orders of magnitude faster than indicates that di€usive oxygen isotope exchange between
volume di€usion and usinga tortuosity of 0.1 and
the solids and the transport medium occurred at rates
Dgb=105Dvol an unrealistically large a parameter of the that are comparable with the rates of bulk oxygen
order of 10±1 is obtained. Chemical grain boundary transport on a macroscopic scale. Such a scenario may be
widths that are larger than the structural grain boundary referred to as type A kinetics grain boundary di€usion
width by one to two orders of magnitude have been after Harrison 71961). In this case, the oxygen isotope
reported from synthetic materials 7e.g., Chowdhury et composition contours advance through the medium as
al. 1995). Geologically reasonable volume fractions of nearly planar fronts, even on the scale of individual
the grain boundary network of the order of 10±4±10±2 grains. Small scale e€ects such as intra grain oxygen
require Dgb/Dvol ratios in the range of 106±108. This is isotope zoning7e.g., Eiler et al. 1995) cannot be excluded.
still larger than experimentally determined Dgb/Dvol ra- If present, such e€ects could only have a€ected minor
tios. This may be caused by the enhancement of grain portions of the individual grains, as bulk mineral sepa-
boundary di€usion on a macroscopic scale by coupling rates show reasonable equilibrium fractionations.
of oxygen transport to major element di€usion associ-
ated with reaction band formation.
It is interestingto note that the relative magnitudes of
the di€usion coecients obtained for the individual
layers are consistent with the relative rates of experi-
Conclusions
The oxygen isotope signature of a several centimeter-
mentally determined oxygen di€usion in diopside, gros-
wide multilayer metasomatic reaction band that formed
sular, plagioclase 7taken as a proxy for scapolite),
hornblende, and calcite 7compare Table 3). E€ective
under granulite facies conditions between hornblendite
xenoliths and a marble matrix was controlled by di€u-
sive oxygen exchange between the relatively 18O-en-
oxygen di€usion was slowest in the monomineralic clin-
riched marble matrix and the relatively 18O-depleted
opyroxene layer and fastest in the marble matrix. This is
compatible with relatively slow oxygen volume di€usion
hornblendite. The systematics of the inter-mineral
in clinopyroxene and relatively fast oxygen volume dif-
fractionations indicates preservation of oxygen isotope
fusion in calcite. The correlation between bulk oxygen
signatures from high temperatures and maintenance for
di€usivities and mineral modes suggests that volume
grain scale oxygen isotope equilibrium during reaction
di€usion within grain interiors and grain boundary dif-
band formation. Bulk oxygen di€usion probably
fusion alongthe surface of a given phase are positively
occurred by a combination of grain-boundary di€usion
correlated. It appears that for phases with relatively fast
and volume di€usion. The chemical width of the grain
volume di€usion grain-boundary di€usion is also rela-
boundaries must have been signi®cantly larger than the
tively fast and vice versa. The coecient for oxygen
structural grain boundary width to allow a signi®cant
volume di€usion in calcite at 750 °C and hydrothermal
contribution of grain boundary di€usion to bulk oxygen
transport. Oxygen di€usion may have been signi®cantly
enhanced by couplingof oxyegn transport to major
element di€usion associated with reaction band for-
conditions is estimated at 1.0´10±13 cm2/s from an acti-
vation energy of Ea=41.4 kcal/mol and a pre-exponen-
tial factor of D0=7´10±5 cm2/s 7Farver 1994).
The oxygen isotope di€usion pro®le extends into
mation. Correlation between bulk oxygen di€usivities
the outermost 3 cm of the mineralogically unaltered
estimated from volume di€usion coecients of the main
hornblendite, where evidence for recrystallization or
constituent phases of the individual mineral layers, and
surface reaction is lacking. In this domain, volume dif-
bulk oxygen di€usivities derived from front geometry,
fusion is regarded as the controlling process for isotope
suggests that the transport properties of a polygranular
exchange between the transport medium and the solid
medium are intimately linked to the transport properties
phases. At the temperatures of interest, oxygen di€usion
of the constituent solids.
in hornblende is two to four orders of magnitude
7dependingon the calibration used) faster than oxygen
Acknowledgements This manuscript greatly bene®ted from the
di€usion in clinopyroxene and four orders of magnitude
faster than oxygen di€usion in garnet 7see Table 3). If
oxygen di€usion were fast along grain boundaries com-
pared with volume di€usion in the grain interiors,
hornblende should have recorded signi®cantly larger
perceptive reviews by Gregor Markl and an anonymous referee.
Financial support by the Austrian Science Foundation FWF grant
P-12903-GEO is gratefully acknowledged.
shifts than garnet and clinopyroxene at a given position, Model parameterization
and the fronts recorded by garnet and clinopyroxene
should lagbehind the front recorded by hornblende 7e.g., The b parameters are related through the volume
Barnett and Bowmanm 1995; Abart and Sperb 1997). changes at the metasomatic replacement fronts and

503
through the thickness of the individual mineral layers of and
the reaction band. If one of the b parameters is arbi-
trarily speci®ed, all the others are determined. The
b iiÀ1
r
^
Di‡1
p
x
i‡1 À xi‡1
4Di
^
2
4
3
2
4
3
5
s
Fi‰DiŠ ˆ 2
e
s
:
ꢀA5†
i‡1
bii‡1
4Di‡1
b parameters for a speci®c example may be derived from
the layer thickness, di, and the volume changes fj that
occur at the metasomatic replacement front, where layer
i is formed. The thickness at time t of layer i, which is
produced at the interface j and consumed at the interface
j±1, is given by:
b
i‡1
5
erfc
À erfc
4Di‡1
CombiningEqs. 7A4) and 7A5) ®nally yields the
relation:
^
ÀFi‰DiŠ ‡ Fi‡1‰Di‡1Š ‡ ci ˆ 0:
ꢀA6†
q q
bijt À bijÀ1t ˆ diꢀt†
The only unknowns in Eq. 7A6) are Di and Di+1, the
bulk oxygen di€usivities in two adjacent media. If one of
the di€usivities is arbitrarily speci®ed, the other is con-
strained through Eq. 7A6). Relations of type A6 may be
written for each layer boundary so that all Di's are
constrained as soon as one is arbitrarily speci®ed. This
leaves one degree of freedom, namely the relation be-
tween the b parameters and one di€usion coecient. For
a given choice of b parameters, a lower limit for the
range of possible Di values is given by the condition that
all di€usivities must be ³0.
The rates of displacement of the interface j with respect
to the coordinate systems i and i+1 are related by:
q
q
bij‡1fj ˆ bij
The layer thickness is directly observable and the volume
changes at the individual interfaces are obtained from
steady-state di€usion modeling7Abart et al. 2001).
The shape of the di€usion fronts within the individual
mineral layers is, in part, poorly de®ned because of the
limited spatial resolution of the analytical data. One
may, however, interpolate to obtain oxygen isotope
compositions at the interfaces. This provides a means to
derive quantitative relations amongthe bulk oxyegn
di€usivities in the individual layers. Let the concentra-
tions at the interfaces where layer i is produced and
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^
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where
q
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ci ˆ biixi À bii‡1xi‡1
:
^
^
Now the functions Fi[Di] and Fi‰DiŠ may be de®ned as:
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