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Geochimica et Cosmochimica Acta 113 (2013) 94–112
www.elsevier.com/locate/gca
The signature of devolatisation: Extraneous 40Ar systematics
in high-pressure metamorphic rocks
Andrew J. Smye a,⇑, Clare J. Warren b, Mike J. Bickle c
b
a
Jackson School of Geosciences, University of Texas, Austin, TX 78712, USA
Department of Environment, Earth and Ecosystems, The Open University, Milton Keynes MK7 6AA, UK
c
Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK
Received 21 September 2012; accepted in revised form 11 March 2013; Available online 29 March 2013
Abstract
The validity of using the 40Ar/39Ar system for thermochronology relies on the assumption that the source mineral is surrounded by a grain boundary reservoir defined by an effective 40Ar concentration of zero. However, the presence of extraneous 40Ar (Are ) in metamorphic rocks shows that this assumption is invalid for a significant number of cases. Are is common in
micas that have equilibrated under (ultra-)high pressure (ðU ÞHP ) conditions: metasediments from six Phanerozoic ðU ÞHP
terranes yield apparent 40Ar/39Ar phengite ages K 50% in excess of the age of peak ðU ÞHP conditions, whereas cogenetic
mafic eclogites yield ages up to 700% older despite lower K2O concentrations. A model is developed that calculates Are
age fractions as a function of variable mica–fluid K D , bulk K2O and porosity under closed system conditions. Measured
Are concentrations in mafic eclogites are reproduced only when porosities are K 104 volume fraction, showing that mafic
protoliths operate as closed systems to advective solute transport during subduction. Porosities in eclogite-facies metapelites
are K 102 , reflecting loss of significant volumes of lattice-bound H2O relative to mafic rocks during subduction. Retention of
locally-generated 40Ar in mafic eclogites shows that the oceanic crust is an efficient vehicle for volatile transport to the mantle.
Ó 2013 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
The decay of 40K to 40Ar in mica has been routinely used
for decades to constrain the rates of cooling and, therefore,
exhumation of orogenic crust. Traditionally, the retention
of radiogenic argon in a host mica grain is thought to be
controlled by thermally-activated diffusion (Harrison and
McDougall, 1980a,b). Using this concept, measured
40
Ar/39Ar ratios correspond to the time since the mineral
cooled below the temperature range over which 40Ar is lost
from the grain by intracrystalline diffusion (Dodson, 1973).
The concept of closure temperature (T c ) is only valid given
the following assumptions: (1) the distribution of 40Ar in a
mica grain is controlled by Fick’s law of diffusion in which
⇑ Corresponding author.
E-mail address: [email protected] (A.J. Smye).
0016-7037/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.gca.2013.03.018
the diffusion of 40Ar produced by the decay of lattice-bound
40
K is dependent on temperature and grain geometry; (2)
the mica equilibrates with no argon present in the lattice
(i.e. no inheritance), or contains argon of atmospheric composition (atmospheric 40Ar/36Ar = 295.5); (3) at temperatures above the closure temperature interval, the mica
grain operates as an open system in that argon is efficiently
removed from the grain and partitioned into a grain boundary reservoir with an effective zero concentration. Furthermore, the analytical solution to the diffusion–production
equation requires that a target mica grain cools at a rate
which is directly proportional to the inverse of the temperature. This is a reasonable assumption for slowly-cooled
terranes, but a significant source of error for rocks that
experience rapid cooling (Warren et al., 2012).
The closure temperature concept has been successfully
applied to noble gas thermochronological studies across a
wide spectrum of metamorphic terranes. However, in
high-dP/dT tectonic regimes such as subduction zones, the
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40
Ar/39Ar system in mica commonly yields anomalously old
ages, often in excess of the age of peak metamorphism estimated by U–Th–Pb, Sm–Nd, Lu–Hf and Rb–Sr geochronology—all systems in which the diffusion rates of the
daughter nuclide are slower than that of argon (Ruffet
et al., 1995; Scaillet, 1996; Sherlock and Kelley, 2002; Di
Vincenzo et al., 2006; Warren et al., 2010, 2011). Such ages
show that (ultra-)high pressure (ðU ÞHP ) mica grains have a
propensity to include extraneous 40Ar (Are ). Following the
terminology developed by Damon (1968) and Dalrymple
and Lanphere (1969), this extraneous 40Ar refers to the
additional 40Ar responsible for measured 40Ar/36Ar ratios
in excess of atmospheric values (>295.5). Excess 40Ar is
the component of 40Ar, apart from atmospheric 40Ar, that
is incorporated into rocks and minerals by processes other
than in-situ radioactive decay of 40K. Inherited 40Ar refers
to any 40Ar that is produced within mineral grains by the
decay of 40K before the event being dated. Both excess
and inherited 40Ar are forms of extraneous 40Ar. It is
important to note that once 40Ar becomes orphaned from
parent 40K, it becomes excess 40Ar. For example, if 40Ar
transport distances are less than typical hand-sample
length-scales, the sample can be described as containing
inherited 40Ar despite the constituent minerals containing
excess 40Ar. Inherited 40Ar is prevalent in granulite-facies
metamorphic rocks (Foland, 1979) and mantle xenoliths
(Kelley and Wartho, 2000), whereas excess 40Ar is common
in fluid inclusions (Cumbest et al., 1994) and rocks adjacent
to focused zones of high-strain (Vance et al., 1998b) and
granite intrusions (Kelley et al., 1986). Extraneous 40Ar is
less common in greenschist and amphibolite grade metamorphic rocks and micas (Brewer, 1969).
The presence of Are shows that at least one of the governing assumptions to the closure temperature concept is invalid. Given that Are concentrations often vary between, and
within, individual ðUÞHP mica grains (e.g. Scaillet, 1996;
Warren et al., 2010), uncertainty over the diffusion parameters Ea and D0 are unlikely to provide an explanation.
Rather, the spuriously-old 40Ar/39Ar mica ages must be
caused by either incomplete resetting of the 40K–40Ar system
(inherited 40Ar), or the accumulation of radiogenic 40Ar (excess 40Ar) in a grain-boundary reservoir to concentrations
high enough to facilitate partitioning of argon back into
the target mica grain. Incorporation of locally-derived excess 40Ar in the source mineral is controlled by mineral–fluid
K D , porosity, and the external transmissive timescale of argon out of the local system (Baxter, 2003). Diffusive removal
of inherited 40Ar is controlled by the interplay between time
(t), effective diffusion radius (r) and temperature (the Fourier number: Dt=r2 ), such that it is possible for a 1 millimeter
diameter mica grain to retain 95% inherited 40Ar for
0.5 Ma at 550 °C and 3 GPa (e.g. Warren et al., 2012). Furthermore, the strongly incompatible nature of argon (mineral–fluid K D between 103 and 105 ; Kelley, 2002), means
that the concentration of Are in a mica grain is critically
dependent on the capacity of the grain-boundary reservoir
to retain and accumulate argon, controlled by the availability and connectivity of the fluid phase.
Aqueous fluids promote chemical and physical evolution
of the Earth’s lithosphere by accelerating reaction kinetics
95
during advective solute transport (Bickle and McKenzie,
1987) and exerting a dominant control on rock-mechanical
properties (Paterson and Kekulawala, 1979; Chopra and
Paterson, 1984; Mackwell et al., 1985; Kohlstedt, 2006).
In particular, fluids released by dehydration reactions instigate mantle melting and the production of arc magmas
(Peacock, 1993; Schmidt and Poli, 1998) in addition to
intermediate-depth earthquakes (Peacock, 1990). Despite
their importance, values of permeability and porosity in
metamorphic rocks are poorly constrained. Measured
grain-scale porosities in exhumed metamorphic rocks are
between 103 and 106 volume fraction (Norton and
Knapp, 1977). However, despite common usage, such measurements reflect time-integrated values, of which the relevance to metamorphic conditions is uncertain. The
importance of understanding porosity is amplified by the
fact that permeability of crustal media increases as the cubic or higher power of porosity (Norton and Knapp,
1977), meaning that sub-percent-level porosities generated
by metamorphic reactions have the potential to cause order-of-magnitude increases in permeability (Connolly,
2010). Estimates of lithospheric permeabilities based on
near-surface (2–3 km) measurements and calculated metamorphic fluid-fluxes span 16 orders of magnitude (1023 –
107 m2; Ingebritsen and Manning, 2010).
In this paper, we determine whether the concentrations
of Are measured in ðU ÞHP phengites can be explained by
accumulation of 40Ar produced by bulk-rock K2O in a
closed system, as a function of porosity and mica–fluid
K D . This calculation places maximum limits on the porosity
volume fraction present at the time of mica growth or equilibration under ðU ÞHP conditions and provides a limiting
case against which we consider whether removal of internally-derived 40Ar by fluid-loss during devolatisation is necessary in mafic eclogites and eclogite-facies metasediments.
We show that porosities in mafic eclogites are consistent
with hydration or limited fluid-loss during subduction,
whereas Are concentrations in phengite from ðU ÞHP
metasediments reflect loss of 40Ar related to devolatisation.
Finally, we consider the combined effects of matrix phases,
porosity, permeability and argon diffusivity on controlling
the accumulation of Are in ðU ÞHP rocks and the case in
which valid “Dodsonian” (Dodson, 1973) cooling ages are
predicted to occur.
2. OPEN VERSUS CLOSED SYSTEMS
In an open system, the diffusive flux of radiogenic argon
produced by the decay of 40K within the mica grain is
dependent on the temperature-sensitive diffusion coefficient,
distance, and the chemical potential gradient of argon between the mineral and its surroundings (Fig. 1a. Once in
the grain-boundary reservoir, radiogenic argon is transported out of the mica–fluid system by advection and/or
diffusion along grain boundary pathways at rates greater
than the rate at which argon diffuses inside the host mica
(Baxter, 2003). During devolatisation, elevated fluid pressures are expected to develop a connected porosity network
through which advective solute transport will control the
removal of 40Ar from the local system (e.g. Rubie, 1986;
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a
b
40
Ar
40
Ar
40
Ar
40
Ar
40
Ar
Open system
Closed system
Fig. 1. Open and closed system scenarios for argon transport at T> T c . (a) Open system—the flux of argon through the grain boundary
medium exceeds the diffusive flux of argon out of the source mineral. Radiogenic argon diffuses out of the target mica, across the grain
boundary, and is effectively transported by a combination of advection and diffusion to an external sink. Either the volume or the transport
velocity of the interconnected grain boundary reservoir ensures that it has an effectively infinite capacity for argon storage. (b) Closed system—
the flux of argon from the source mineral exceeds the grain boundary flux of argon to an external sink. The grain boundary argon
concentration increases as a function of time and K2O content of the protolith, eventually reaching levels such that argon will partition back
into the mica in detectable quantities.
John et al., 2012). Following prograde fluid-loss, grain
boundary transport of 40Ar will be governed by bulk diffusion which is expected to be effective over length-scales
K 1 m in rock matrices that have experienced a 10-million-year-long regional metamorphic cycle (Rubie, 1986;
Baxter et al., 2002). The end-member open system is defined
by a grain boundary reservoir that has a zero 40Ar concentration, thus preventing any 40Ar from partitioning back
into the host mica grain (Kelley, 2002). In reality no system
is entirely open and all fluid–mineral systems contain trace
quantities of Are (e.g. Kelley et al., 1986; Cumbest et al.,
1994; Stuart et al., 1995). The ultimate macroscale sink
for argon in any geological system is the atmosphere. However, argon is highly incompatible and will strongly partition into grain boundary fluids in metamorphic rocks, or
into melts in magmatic systems (Kelley, 2002). More specifically, Etheridge et al. (1983) used Rayleigh-Darcy modeling to show that under lithospheric conditions where the
metamorphic fluid pressure is greater than or equal to the
minimum principal compressive stress, convective fluid flow
will be established through a network of connected veins,
providing a mesoscale sink for crustal volatiles. Given that
metamorphic porosities are expected to be extremely small
(107 –103 vol. fraction; Ganor et al., 1989; Skelton et al.,
2000), the role of deformation in forming interconnected
vein systems is likely an important factor in the transport
of volatiles such as argon (Vance et al., 1998a). Fluid inclusions also have the potential to act as a sink for smaller
quantities of argon (Cumbest et al., 1994), relative to vein
and melt systems. The general assumption of open system
argon transport in a wide spectrum of crustal environments
is supported by the fact that both the K–Ar and 40Ar/39Ar
methods commonly yield geologically meaningful age data
that are free from analytically-detectable Are (e.g. Wijbrans
and McDougall, 1987, 1988).
At temperatures in excess of mineral closure temperatures, the accumulation of radiogenic 40Ar in a metamorphic system is controlled by the degree to which
radiogenic 40Ar is removed to an external sink. This transmissivity depends on the active mechanism of grain boundary solute transport and can be advective and/or diffusive.
Baxter (2003) defined the transmissive timescale (sT ) as
the characteristic time for 40Ar to escape through the local
intergranular medium to a sink for argon, located at a distance L from the source mineral. For diffusive transport,
2
sT ¼ DL , where D is the total effective diffusivity of argon,
whereas for advective transport, sT ¼ VL , where V is the total effective velocity (Baxter, 2003). In order for a metamorphic system to retain locally-derived 40Ar, sT must be
comparable or greater than the timescale of 40Ar
production.
On cooling through the closure temperature interval,
attainment of argon thermodynamic equilibrium becomes
limited by the rate of intracrystalline diffusion of argon
through the source mineral, not solely by sT . Baxter
(2003) showed that in systems where the ratio of the timescale of local diffusional exchange between source mineral
and grain boundary, and sT (the diffusional exchange
parameter, De, of Baxter, 2003) exceeds 15, the source mineral diffusively exchanges fast enough to maintain local
equilibrium. In the case when De < 15, to be expected at
sub-closure temperatures, the source mineral cannot exchange argon fast enough to maintain local equilibrium,
leading to retention of radiogenic 40Ar.
Rates of intergranular diffusion along dry grain boundaries are up to 16 orders of magnitude slower than for
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aqueous fluid-bearing grain boundaries (1024 versus
108 m2 s1 Rubie, 1986; Scaillet, 1996), but still 103 orders
of magnitude faster than typical rates of volume diffusion
through a crystalline lattice Manning (1974). Accordingly,
fluid-poor systems will have longer values of sT compared
to fluid-rich systems. In a fully-closed system a strong correlation should exist between Are and bulk K2O as 40Ar is
locally produced in the rock and not transported over
length scales greater than grain dimensions. Foland (1979)
and Sherlock and Kelley (2002) observed such a correlation
between Are concentration and bulk K2O in fluid-poor
rocks of the Arden pluton in the Appalachian mountains
and the Tavsanli Zone, NW Turkey respectively. A wealth
of evidence from in-situ UV laser and bulk step-heating
studies demonstrate that ðU ÞHP metamorphic rocks provide the most extreme examples of Are accumulation under
fluid-poor, low sT conditions (e.g. Li et al., 1994; Ruffet
et al., 1995; Scaillet, 1996; Sherlock and Kelley, 2002; Di
Vincenzo et al., 2006; Warren et al., 2011).
(35.1 Ma, Rubatto and Hermann, 2001). Similarly, Giorgis
et al. (2000) record phengite ages from the Sulu eclogite terrane, China, between 80% and 400% older than the accepted age of peak ðU ÞHP metamorphism (217 Ma, Ames
et al., 1993). It is also apparent from Fig. 2a that rock composition exerts a strong control on the concentration of Are
(Scaillet et al., 1992; Baxter et al., 2002). In general,
40
Ar/39Ar mica ages from mafic eclogites are older than
those from white mica in cogenetic metapelites. For example, Di Vincenzo et al. (2006) showed that phengite from
mafic eclogites of the UHP Dora Maira terrane of the Western Alps yielded ages >52 Ma older than phengite from
associated orthogneisses and >34 Ma older than phengite
derived from eclogite-facies marbles. Provided that Are is
locally produced, these data show that despite higher concentrations of K2O, metapelites lose a larger fraction of
radiogenic 40Ar during devolatisation than mafic
lithologies.
Elevated 40Ar/39Ar white mica ages can be explained by
incorporation of Are , or by the removal of K2O. The latter
is typically associated with margarite formation in response
to chemical weathering and is relatively uncommon (De
Jong et al., 2001). It is important to note that the effect of
excess 40Ar on apparent age will be maximized in lowK2O micas where the atomic ratio of excess 40Ar to supported, radiogenic, 40Ar exceeds that expected in micas with
higher weight % K2O. To illustrate this, Fig. 2b shows contours of constant muscovite weight % K2O plotted as a
function of excess age and number of atoms of excess
40
Ar. Single grain phengite 40Ar/39Ar data from a representative mafic eclogite, collected from the Eastern Alps
(CWT13 Warren et al., 2011), plot along a linear array,
subparallel to 10 wt.% K2O, showing that intergrain age
Fig. 2a shows 40Ar/39Ar phengite ages from a global
compilation of ðUÞHP terranes; the ages are normalised
to the respective timing of ðU ÞHP metamorphism, constrained by independent geochronology (U–Th–Pb; Sm–
Nd; Lu–Hf; Rb–Sr). All data plotted correspond to phengite that grew during the peak of ðU ÞHP metamorphism. The
majority of these ages lie within 100% excess of the peak
ðU ÞHP age. However, phengite from the Dora Maira complex, Western Alps, records ages >700% older (Scaillet,
1996) than the peak of Alpine ðU ÞHP metamorphism
Sezia Zone
Age of peak (U)HP event
Lithologies
Mafic
Marble
Orthogneiss
Pelite
Eastern Alps
Turkey
Oman
Dabie Sulu
Dora Maira
b
30
.%
25
Excess Age (Ma)
3. EXCESS ARGON IN ðUÞHP METAMORPHIC
TERRANES
a
97
8
wt
O
K2
9
10
11
12
20
15
10
5
0
1
10
100
Excess 40Ar age equivalent (%)
1000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Atoms of excess 40Ar (x1015 g-1)
Fig. 2. Excess argon in ðU ÞHP rocks. (a) Global compilation of phengite single-grain 40Ar/39Ar ages from ðUÞHP terranes expressed as
percentage excess relative to independently-derived ages of peak ðU ÞHP metamorphism. Symbol notation: circles = mafic eclogite;
squares = metapelite; diamonds = marble; triangles = orthogneiss. Data sources: Dora Maira – Scaillet (1996), Rubatto and Hermann (2001),
Di Vincenzo et al. (2006), Sulu – Ames et al. (1993), Giorgis et al. (2000); Oman – Warren et al. (2003), Warren et al. (2010); Turkey – Sherlock
et al. (1999), Sherlock and Kelley (2002); Eastern Alps – Smye et al. (2011), Warren et al. (2011); Sesia Zone – Ruffet et al. (1995), Rubatto
et al. (1999). (b) Contours of constant mica K2O plotted as a function of excess age in Ma, and the number of atoms of incorporated Are
(atoms g1). Representative single grain phengite 40Ar/39Ar data from an East Alpine mafic eclogite (orange circles; CWT13 Warren et al.,
2011) are plotted over the contours. Atomic quantities calculated using a diffusive cooling age of 28.05 Ma (Warren et al., 2011), an average
phengite K2O value of 10.34 (n = 15; 1.88% 2r, Warren et al., 2011) and a muscovite density of 2.81 g cc1 (Deer et al., 1997). Error bars are
1r.
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variations are explained by variable Are concentrations
alone and that the effect of intergrain variation in 40K concentration is small. Importantly, these calculations show
that single phengite grain ages reflect local fluid–mica isotopic disequilibrium and that the scale of argon isotopic equilibrium under ðU ÞHP conditions is smaller than the
intergranular distance (103 –106 m).
Stable isotope data from ðU ÞHP rocks are also consistent with short length scales of fluid–rock interaction indicated by the ubiquity of Are . Several studies document
observations that ðU ÞHP rocks often retain recognizable
vestiges of pre-subduction fluid–rock interaction. For
example, elevated d18 O and dD values from eclogitic parageneses of the Sulu UHP terrain, China, were acquired
in an ancient hydrothermal system prior to subduction
and were not reset beyond millimeter to centimeter
length-scales during coesite-grade metamorphism (Rumble
and Yui, 1998). Similarly, pre-subduction oxygen isotope
heterogeneities in eclogites of the Western Alps imply
time-integrated fluid fluxes across lithological contacts as
low as 1.6 cm3 cm2 (Philippot and Rumble, 2000). Furthermore, Getty and Selverstone (1994) showed that millimeter-scale d18O heterogeneities associated with tuffaceous
banding in an eclogite from the Eastern Alps were preserved throughout HP metamorphism and subsequent Barrovian overprinting.
4. FLUID–MICA ARGON EXCHANGE MODEL
At subduction zones hydrated lithosphere returns to the
mantle, heating up during descent and releasing mineralbound fluid by devolatisation reactions (Peacock, 1990).
The fraction of protolith-derived argon that is retained by
mica on equilibration under ðU ÞHP conditions reflects the
extent to which the rock has behaved as an open or closed
system to volatile loss during subduction. In the following
section we present a model for calculating the concentrations of Are in phengite as a function of variable K D , porosity, and mica modal-abundance for the case where no argon
is lost between the timing of protolith formation and mica
growth/equilibration. When applied to natural phengite
40
Ar/39Ar datasets from the Eastern Alps and Oman, this
allows the metamorphic porosity to be estimated and provides a limiting case to assess the extent of fluid-loss during
subduction. Model results help constrain the mechanisms
by which argon and other volatiles are transported into
the mantle, in addition to better informing sampling strategy for 40Ar/39Ar geochronology in ðU ÞHP terranes.
4.1. Solubility of Argon
The relative solubilities of argon between cogenetic
ðU ÞHP phases control the distribution of Are . The solubility
of argon in hydrous fluids strongly depends on both temperature and salinity (Weiss, 1970; Crovetto et al., 1982;
Smith and Kennedy, 1983), varying between 10 and
100 ppm bar1 across the likely range of metamorphic temperatures and fluid salinities (Kelley, 2002). The solubility
of argon in minerals is less well-constrained, largely due
to a lack of experimental data and the propensity for argon
to adsorb onto mineral defects (e.g. Broadhurst et al.,
1992). Existing data show that argon solubilities in silicate
minerals are J 3 orders of magnitude smaller than fluid
values: clinopyroxene – 0.09 ppb bar1 (Brooker et al.,
1998); olivine – 1 ppb bar1 (Brooker et al., 1998); plagioclase – 1.8 ppb bar1 (Kelley, 2002) and K-feldspar –
0.7 ppb bar1 (Wartho et al., 1999). Measurements of argon solubility in quartz vary over at least 3 orders of magnitude, between 3.75 ppb bar1 (Roselieb et al., 1997) and
2000 ppb bar1 (Watson and Cherniak, 2003). If the solubility data of Watson and Cherniak (2003) are applicable
to natural systems, quartz has the potential to be the dominant sink of crustal argon (Baxter, 2003). Whereas fluid
inclusions in vein quartz are abundant and likely have the
potential to act as a sink for significant quantities of argon
(Cumbest et al., 1994), further work is required to understand the role of fluid inclusions in rock-forming quartz
as a sink for volatiles.
There is a dearth of experimental data constraining the
solubility of argon in hydrous minerals used for 40Ar/39Ar
geochronology. Although Onstott et al. (1991) undertook
preliminary experiments to show that argon solubility in
biotite is between 3.6 and 36 ppm bar1, the accuracy of
the results was compromised by inclusion of atmospheric
argon. Nevertheless, the observation that muscovite is commonly observed with lower Are concentrations than cogenetic biotite (e.g. Brewer, 1969; Roddick et al., 1980)
confirms a relative solubility order for the micas. Measurements on phlogopite indicate that argon solubilities in micas are 1 order of magnitude greater than K-feldspar
(1.8 ppb bar1: Roselieb et al., 1999). To date, there are
no argon solubility data available for phengite. Accordingly, these relative solubility data suggest that K D between
muscovite and fluid lies between 105 and 103 under metamorphic conditions.
4.2. The model
We calculate apparent mica ages in a model in which the
exchange of 40Ar between mica and a fluid-filled porosity in
a closed system is simulated according to mass balance.
This is equally applicable to mica fractions containing
either inherited or excess 40Ar. Controlled by a particular
value for the partition coefficient, inherited 40Ar will diffuse
out of the grain until a balance is attained between the
grain-boundary network and the grain itself. Similarly, in
the case of excess 40Ar, argon will diffuse into the grain until
the same balance is reached. Critical parameters are porosity (/), volume fraction of mica (mm ), mica–fluid partition
coefficient (K D ) and relative densities (q/ ; qwr and qm ). Model mica is treated as muscovite, incorporating the range in
K D discussed above. No argon is lost or gained in the rock
volume under consideration between the time of protolith
formation and the time of mica growth/equilibration. The
parental link between 40K and 40Ar is preserved on the volume scale, but not necessarily on the grain scale.
Model assumptions are illustrated in Fig. 3. Following
the approach of Nabelek (1987) and Banner and Hanson
(1990), the distribution of 40Ar in both the mica and fluid
are calculated before and after equilibration. Argon
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exchange between mica and fluid is simulated as being
instantaneous, which is acceptable for the model simulation; in reality argon exchange will occur over a finite time
period (sss , Baxter, 2003), controlled by the transmissive
timescale and total local sink capacity. Model mica contains 10.9 wt.% K2O and has a density (qm ) of 2.81 g cc1,
analogous to typical ðU ÞHP phengite (Deer et al., 1997).
The pore-fluid has a density of (q/ ) 1 g cc1, in the range
appropriate for high P–T conditions (Norris and Henley,
1976). The following section outlines the necessary equations to simulate closed system 40Ar exchange.
Prior to fluid–mica interaction, the concentration of
40
Ar in the fluid–rock system (C i ) is defined by mass balance where the total argon is the sum of that in the fluid
phase (C /;i ) and the solid phase (C wr;i ):
C i ¼ FC /;i þ ð1 F ÞC wr;i
ð1Þ
F, the mass fraction of fluid present in the whole-rock, is
related to the porosity volume fraction by:
F¼
/q/
/q/ þ ð1 /Þqwr
ð2Þ
99
The concentrations of 40Ar in the solid (C wr ) and fluid
(C / ) after equilibration are calculated using a bulk argon
distribution coefficient (D ¼ K D mm , where mm is the mass
fraction of mica present):
Ci ¼ F
C wr
þ ð1 F ÞC wr
D
ð3Þ
The equilibrated 40Ar concentration in mica is calculated by dividing C wr by the mass fraction of mica. This
yields a concentration which, together with the initial system 40K concentrations, is converted to atomic values and
used to calculate the age of the mica fraction. It is important to recognize that the calculated ages are the maximum
expected for a closed system given protolith and metamorphic ages.
Previous models of the accumulation of Are in mineral–
fluid systems employ a reactive-transport approach, assessing the degree to which partitioning of 40Ar into the rock
matrix retards advective–diffusive removal of Are out of
the rock volume (Baxter et al., 2002; Baxter, 2003). The
particular strength of this approach is that it allows predictions of the spatial and temporal distribution of Are in a
Fig. 3. Schematic figure illustrating the differences between inherited and excess 40Ar. Between time t1 (protolith formation) and time t2
(metamorphic recrystallisation and isotopic equilibration), 40Ar builds up in K-bearing minerals in the protolith. At time t2 , K-bearing
minerals recrystallise. In an open system (ai), all the protolith-derived 40Ar is removed from the local rock volume. In a closed system,
protolith-derived 40Ar is retained in the local rock volume where it partitions between fluid and matrix phases according to relative argon
solubilities. In this case, new K-bearing minerals incorporate excess Ar into their structures (bi). A mineral that escapes recrystallization
during metamorphism (ci), will contain inherited 40Ar, which is removed according to the efficiency of volume diffusion. As rocks start to cool
through the mineral closure temperatures, ”new” Ar (light gray text) starts to be retained. Either a ”true” cooling age is yielded (aii) or ages
are contaminated with excess (bii) and inherited (cii) 40Ar. Panel d links the events, t1 , t2 and t3 with the temperature (T) evolution of a rock
undergoing subduction-related metamorphism.
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rock volume to be made. Reactive-transport modeling of
Are removal during devolatisation is complicated by the
time-variant nature of porosity (DePaolo and Getty,
1996) and the need for detailed K–Ar isotopic profiles to
constrain the length scale of argon transport through the
rock matrix (Baxter et al., 2002). In comparison, the mass
balance model used here evaluates the time-integrated effects of fluid-loss on Are concentrations. By assuming that
no internally-derived 40Ar is lost from the rock volume
since the timing of formation, calculated porosities reflect
the time-integrated fluid fraction required to explain the
concentrations of Are measured in ðU ÞHP phengites. The
porosities are then treated as maximum values against
which thermodynamic predictions of fluid-loss can be
compared.
conditions where all Are resides in the mica and fluid,
respectively.
Typically, eclogite-facies metapelites contain 20–
60 vol.% phengite, compared to <10 vol.% in mafic eclogites. Fig. 4b shows that in order for phengite in ðU ÞHP pelites to have younger apparent 40Ar/39Ar ages than mafic
eclogites the effective porosity must be at least an order of
magnitude larger in pelites than in mafic rocks. Given that
the model maximizes phengite Are concentrations by
assuming no loss of Are from the fluid–rock system along
with minimum porosities, it acts as a limiting case against
which the effects of devolatisation in ðU ÞHP rocks can be
evaluated. Violation of the model assumptions by either larger effective porosities, Are removal by fluid loss, or partitioning into local mineral sinks, reduces the magnitude of
the calculated excess age fraction.
4.3. Model results
Excess Age Fraction
Model results are shown as contours of constant fluid–
mineral partition coefficients (Fig. 4a) and mica volume
fraction (Fig. 4b) on a plot of excess age fraction against
porosity. Excess age fractions are defined as the fraction
of Are retained by the mica at T > T c . The maximum excess
age fraction is the age of the protolith less the age of metamorphism; excess age fractions greater than 1 are caused by
the addition of excess 40Ar. For example, an excess age
fraction of 0.5 for a mica grain which cools through T c at
30 Ma after residing at T > T c for 10 Ma corresponds to
a measured age of 35 Ma. Porosities correspond to the
maximum volume fraction of fluid necessary to explain a
specific mass fraction of Are in muscovite at the time the
rock cools through the closure temperature. At T < T c , argon exchange will be governed by reaction-rate-controlled
dissolution–precipitation mechanisms (DePaolo and Getty,
1996), which operate at faster rates than volume diffusion of
argon in mica (Baxter, 2003). Fig. 4 shows that for any given value of K D or mm , the concentration of Are within the
mica fraction increases as a function of decreasing /. Contours of constant K D (Fig. 4)a and muscovite fraction
asymptotically approach end-member closed (excess age
fraction = 1) and open (excess age fraction = 0) system
5. APPLICATION OF THE MODEL TO NATURAL
40
AR/39AR DATASETS
In order to assess whether the Are in ðU ÞHP rocks might
be generated in-situ prior to the peak of ðU ÞHP metamorphism, we model argon systematics in phengites using data
from two recently published 40Ar/39Ar single-grain phengite datasets: the Tauern Window HP nappes of the Eastern
Alps (Warren et al., 2011) and the As Sifah HP terrane in
Oman (Warren et al., 2010). Due to poorly-constrained values of K D for matrix phases, we only consider argon exchange between the mica and fluid fractions, treating the
remainder of the rock mass as inert.
5.1. The Tauern Window
The Tauern Window in south-central Austria exposes
the metamorphosed remnants of the European continental
margin and Tethyan oceanic basin that were subducted and
underplated during the collision between Europe and
Adria. The Eclogite Zone is a Triassic–Jurassic volcanosedimentary succession (Kurz et al., 1998) which was subducted to 20–26 kbar and 550 C between 30–37 Ma
(Glodny et al., 2005; Smye et al., 2011). Following
1.0
1.0
a
b
0.8
0.8
10-3
0.6
10
0.4
0.6
100%
-4
0.4
0.2
0.2
0.0
10-6
10%
10-5
10-5
10-4
10-3
10-2
Porosity (vol. frac.)
10-1
0.0
10-6
1%
0.1%
10-5
10-4
10-3
10-2
10-1
Porosity (vol. frac.)
Fig. 4. Mica–fluid argon exchange model. (a) Excess age fraction plotted as a function of fluid volume fraction (porosity; /) for values of
K Dm/ between 103 –105 . Calculations employ a value of mm of 0.3 and assume the grain-boundary fluid has a zero 40Ar initial concentration;
(b) Excess age fraction–/ curves for a range of mica volume fractions ranging from 0.001 to 1. Calculations use a K D of 104 .
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eclogite-facies metamorphism, the Eclogite Zone was overprinted by a regional Barrovian event (ca. 7 kbar, 520–
570 C; Zimmermann et al., 1994) between 27 and 31 Ma
(Inger and Cliff, 1997; Glodny et al., 2005; Gleiner et al.,
2007). On the basis of numerical diffusion calculations
(Wheeler, 1996; Warren et al., 2011, 2012), phengite
(0.5 mm diameter) growing under HP conditions prior to
Barrovian metamorphism, and subsequently cooling at
30 C Ma1, is expected to yield an age of 28.05 Ma.
Sample CWT13 is a foliated eclogite collected from the
central portion of the Eclogite Zone, containing: garnet + omphacite + quartz + glaucophane + muscovite + epidote + calcite + ankerite + rutile + paragonite.
Paragonite is subordinate and smaller (<400 lm diameter)
than muscovite; collectively the mica volume fraction is
<0.05. Muscovite is celadonite-rich and contains 6.9–
7.2 c.p.f.u. Si per 22 O; this, together with their textural
alignment with omphacite and garnet grains, indicates that
they grew during the HP event. Single-grain fusion
40
Ar/39Ar laserprobe ages from 10 white-mica grains fall
between 36 and 59 Ma. Apparent 40Ar/39Ar phengite ages
cluster between 36 and 43 Ma whereas paragonite analyses
yield ages in the range of 48–59 Ma (Warren et al., 2011).
The protolith age of sample CWT13 is loosely constrained
to 110 Ma (Bousquet et al., 2002).
Sample CWT12 is an Eclogite Zone metapelite comprised of garnet, quartz, phengite, chlorite, albite, rutile
and kyanite. Phengite is abundant (0.5 volume fraction)
and has a high Tschermak content (6.73 c.p.f.u. Si),
Table 1
Model parameters used for the East Alpine and Oman
phengite datasets.
Eastern Alps
tpr
tc
tm
mm
40
Ar/39Ar phengite
age
Excess age fraction
40
Ar/39Ar
Oman
CWT13
110
28.05
33
0.05
48–59
CWT12
300
28.05
33
0.5
37–44
CWO408
298
75
80
0.05
83–125
CWO410
298
75
80
0.4
77–89
0.24–
0.37
0.03–
0.05
0.04–
0.22
0.008–
0.06
101
indicative of growth under HP conditions. A total of 17
phengite grains (>820 lm diameter) yielded single-grain
apparent 40Ar/39Ar ages between 37 and 44 Ma (Warren
et al., 2011). A bulk-protolith age of 300 Ma is consistent
with the Eclogite Zone metapelites being derived from subducted Variscan crust (Kurz et al., 1998).
Table 1 details the model parameters used to simulate
closed system argon exchange in samples CWT13 and
CWT12, the results of which are shown in Fig. 5a. Using
a value of K D ¼ 104 , porosity volume fractions of 3–
6 105 and 4–6 103 are required to account for the observed excess age fractions in samples CWT13 and 12
respectively.
5.2. The As Sifah eclogite terrane, Oman
Mafic eclogites, intercalated with pelitic and calcareous
metasediments, are exposed toward the northeastern edge
of a window through the Semail ophiolite in Saih Hatat,
northeastern Oman. The eclogites and host metasediments
experienced peak conditions of 16–22 kbar and 520–
550 C (El-Shazly, 2001; Warren and Waters, 2006) during
subduction of the Permian shelf sequence. The protolith age
of the succession is best constrained by a 298 Ma zircon extracted from a tuffaceous horizon (Gray et al., 2004). U–Pb
zircon ages of 79.06 0.32 Ma (2r, ID-TIMS; Warren
et al., 2003) and 82.06 0.83 Ma (1r, SHRIMP; Gray
et al., 2004) are interpreted as representing the timing of
eclogite-facies metamorphism. Rb–Sr phengite–whole-rock
isochrons (El-Shazly et al., 2001) and U–Pb rutile ages
(Warren et al., 2005) of 78 2 Ma and 79.6 1.1 Ma
respectively, suggest that the HP terrane cooled quickly
during exhumation; zircon fission-track ages span 66–
70 Ma (Saddiqi et al., 2006). Numerical diffusion modeling
(Wheeler, 1996; Warren et al., 2012) yields ages between
72.5 and 78.4 Ma (Warren et al., 2010) assuming that mica
grew concomitant with peak T (550 C) at 79–82 Ma and
cooled at rates between 10 and 50 C Ma1 in an open
system.
Sample CWO408 is a mafic eclogite comprised of
garnet + omphacite + phengite + crossitic glaucophane +
epidote + quartz + rutile. Phengites are characterised by
high-Si core regions (>7.2 Si c.p.f.u. per 22 O) and
Fig. 5. Mica–fluid argon exchange model applied to single grain 40Ar/39Ar phengite datasets from the Tauern Window (a) and Oman (b) HP
terranes. Calculations use a K D of 104 . Model parameters are presented in Table 1. Shaded rectangles represent the range in apparent
40
Ar/39Ar ages measured.
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marginally lower rim concentrations (6.9 Si c.p.f.u.); texturally, phengite belongs to the HP assemblage. Whole-rock
XRF analysis yields a K2O content of 2.06 wt.% (Warren,
unpublished data). Single-grain fusion 40Ar/39Ar analysis of
15 phengite grains (420–840 lm size fraction), yielded ages
between 83 and 125 Ma (Warren et al., 2010) .
Sample CWO410 is an eclogite-facies phengite schist collected from a horizon enclosed within a mafic eclogite boudin. Bulk-rock K2O content is 4.11 wt.% (Warren,
unpublished data). The sample is comprised of major phengite and quartz with subordinate rutile, epidote, calcite, garnet and hematite. Celadonite–muscovite exchange is only
weakly present in phengite (typical core: 7 Si c.p.f.u.; typical rim: 6.9 Si c.p.f.u.). Greenschist-facies alteration is restricted to regions surrounding quartz-filled veins,
commonly measuring between 1 mm and 20 cm. Singlegrain fusion analysis of 19 phengite grains (840–1000 lm
size fraction) yielded apparent 40Ar/39Ar ages between
76.8 and 89.2 Ma (Warren et al., 2010).
Model results for CWO408 and CWO410 are shown in
Fig. 5b; further parameters are detailed in Table 1. Assuming that no argon is lost from the rock since the time of protolith formation, phengite in sample CWO408 equilibrated
with a grain-boundary reservoir 6 105 –4 104 volume fraction. Fluid fractions up to two orders of magnitude
larger, 3 103 –2 102 , are calculated for the pelitic
sample, CWO410.
6. DISCUSSION
Extraneous argon can originate from both the radiogenic argon produced in-situ within a ðU ÞHP mica grain
at temperatures above the closure temperature and also
from diffusive equilibration, or crystallization, of a mica
grain in a grain boundary fluid that contains 40Ar. Incorporation of in-situ derived Are would lead to mica ages between the time of equilibration under ðU ÞHP conditions
and cooling through the closure temperature range. Phengite 40Ar/39Ar ages greater than the residence time of the
ðU ÞHP terrane (<30 Ma; Kylander-Clark et al., 2012) can
only be explained by retention of inherited argon. By definition, inheritance does not account for apparent 40Ar/39Ar
ages older than the age of the protolith, which must be explained by inclusion of excess 40Ar. The model developed
above shows that extraneous argon concentrations in
ðU ÞHP phengites can be explained by partitioning of inherited or locally-generated 40Ar in a closed system with porosity K 104 volume fraction for mafic eclogites and K 102
for metapelites. These porosities are upper-bound estimates
of the time-integrated fluid volume fraction present at temperatures above phengite T c . It is important to note that in
natural systems, rock porosity is transient and fluctuates
during metamorphism (Connolly, 2010). Accordingly, the
accuracy of the porosity estimates is contingent on establishment of mica–fluid equilibrium for argon, dependent
on the mica fraction being diffusively open for argon exchange. Should thermodynamic equilibrium not be attained, for example, due to short residence times at
T > T c , the porosity estimates represent upper-bounds as
the mica fraction is under-filled with respect to Are .
Furthermore, if 40Ar is removed from the system by grain
boundary transport mechanisms or partitioning into other
mineral phases, apparent K–Ar (40Ar/39Ar) ages will be reduced, increasing the porosity estimates. Therefore, it is
important to consider the factors that will control the loss
of 40Ar during prograde metamorphism: (1) storage and release of argon from local matrix phases; (2) the diffusive
mobility of argon; (3) the availability of a fluid phase; (4)
the connectivity of the fluid phase.
6.1. Storage and release of argon from local matrix phases
Storage of locally-derived 40Ar in matrix minerals will
lower the amount of Are available for partitioning between
the fluid-filled porosity and mica fractions, leading to lower
apparent 40Ar/39Ar mica ages. However, the propensity for
argon to partition strongly in the fluid phase (KD between
103 and 105 ) means that fluids will dominate the argon storage capacity of the rock if they are present in sufficient mass
fractions. The total argon capacity of the local mineral sink
reservoir is controlled by mineral–fluid K D and mineral
modes, in addition to the mass fraction of fluid-filled porosity present (the Total Local Sink Capacity of Baxter, 2003).
Given that argon solubilities in rock-forming phases are
poorly-constrained (see Kelley, 2002 for a review) and that
metamorphic porosities are vanishingly small (106 –103 ;
Norton and Knapp, 1977; Skelton, 2011), it is important
to evaluate the potential for local matrix phases to act as
significant sinks for Are .
Fig. 6a shows contours of constant mineral sink mode
(1, 10 and 70 volume %) calculated for the cases in which
the sink phase strongly (K D ¼ 102 ) and weakly
(K D ¼ 105 ) partitions argon. Values of K D reflect the range
in experimentally-determined argon solubility for silicate
minerals. As expected, when argon solubility in the local
mineral sink phase is lower than in the mica fraction, the
fluid-filled porosity dominates the total local sink capacity
and the mica excess age fractions are lowered by < 20%
at extremely small values of porosity (< 106 ), even when
the entire remainder of the rock volume (0.7 volume fraction) is open to sequester argon. However, when argon partitions strongly (K D ¼ 102 ) into local mineral phases, as
suggested by the solubility data of argon in quartz derived
by Roselieb et al. (1997), the effect on decreasing mica Are
concentrations is dramatic (dashed lines Fig. 6a). Mineral
modes as small as 1% lower mica excess age fractions by
80% at realistic metamorphic porosities (104 ), showing
that the total local sink capacity will be dominated by the
mineral phase. The presence of such a matrix phase would
play a critical role in preventing the accumulation of Are in
coexisting K-bearing phases, permitting successful
thermochronology.
In addition to acting as sinks for argon, local K-bearing
mineral phases may also break down at temperatures greater than T c , liberating excess radiogenic argon into the grain
boundary reservoir, which may subsequently partition between the fluid-filled porosity and mica fraction. For example, in mafic protoliths, chlorite and actinolite both contain
trace amounts of K2O (1 weight %) and are predicted to
become unstable at temperatures greater than 500 C at
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A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
103
Fig. 6. The role of matrix phases. (a) Effect of local mineral sink phases on excess age fraction–/ curves. Relations calculated for a system
with mm ¼ 0:3; K Dm/ ¼ 104 and assume that the grain boundary has a zero 40Ar initial concentration. The solid line is the case where mica is
the only argon-bearing phase. Dashed lines are calculated for the case when 0.01, 0.1 and 0.7 volume fraction of a sink phase with a K D of 102
coexist with the mica fraction. Dash-dot lines use a K D of 105 for the sink phase; (b) Effect of local mineral source phases. System parameters
are as used in (c) solid line represents the case in which no source phases are present. Dotted line (scenario 1) is the case for a source phase of
0.01 volume fraction, containing 1 wt.% K2O and a tsc : tres ratio of 1:1. Dashed line (scenario 2) is the case for a source phase of 0.1 volume
fraction, 11 wt.% K2O and a tsc : tres ratio of 5:1. Dash-dot line (scenario 3) is the case for a source phase of 0.7 volume fraction, 11 wt.% K2O
and a tsc : tres ratio of 10:1.
21 kbar (Fig. 8a). Prior to the initiation of garnet growth,
plagioclase is likely to be an important carrier of inherited
Ar in both mafic and pelitic rocks during the early stages of
subduction. In alkali-rich protoliths, primary K-feldspar
and low-P metamorphic muscovite also have the potential
to act as ‘vehicles’ for argon transport. The importance of
this effect is evaluated by calculating the increase in excess
age fraction observed after introducing quantities of excess
40
Ar produced by (1) a small modal fraction (1 volume %)
of a mineral containing trace quantities of K (1 weight %)
that is stable for a period of time (denoted tsc ), equivalent
to the duration of time the mica fraction resides above T c
(tres ; tsc : tres ¼ 1 : 1); (2) a large volume fraction (10 volume
%) of a high-K mineral (11 weight %), stable for an intermediate duration prior to breakdown (tsc : tres ¼ 5 : 1); (3) a
large volume fraction (10 volume %) of a high-K mineral
(11 weight %), stable for a long duration prior to breakdown tsc : tres ¼ 10 : 1. Calculations use a mica volume fraction of 0.3 and a K D of 104 ; results are shown in Fig. 6b as
curves of excess age fraction plotted against porosity for
each scenario. As expected, scenario 1 shows that the effect
of small modal proportions of minerals containing trace
amounts of K2O is small, increasing mica excess age fractions by < 1%. Scenarios 2 and 3 illustrate the importance
of the age of the source phase, chosen here to reflect metastable biotite, expected to break down in place of muscovite
at T > 550 C and P > 20 mbar in mafic rocks (Fig. 8a). For
the extreme case when the duration of radiogenic in-growth
for the source fraction exceeds that of the muscovite fraction by a factor of ten (scenario 3), excess age fractions
are elevated by 30%. These calculations highlight that
mica ages in excess of the protolith age require the addition
of excess 40Ar, plausibly sourced from metastable biotite
and other high-K minerals that escaped recyrstallisation
during prograde metamorphism due to sluggish kinetics.
However, the absence of phengite 40Ar/39Ar ages in excess
of protolith ages from ðU ÞHP rocks (Fig. 2b) suggests that
this phenomenon is unlikely in ðUÞHP systems and that Are
is locally-derived.
6.2. The diffusive mobility of argon during subduction
Diffusive transport of argon can proceed via solid-state
volume diffusion within mica grains, along dry or wetted
grain boundaries, and within a fluid-filled porosity. Intracrystalline volume diffusion of argon operates between
1015 and 1022 cm2 s1 (Rubie, 1986; Scaillet, 1998) significantly slower than 104 –1013 cm2 s1 (Walther and
Wood, 1984; Rubie, 1986; Scaillet, 1998) typical of diffusion
through a fluid phase. Therefore, it is important to address
whether the length scales of diffusion characteristic of a
subducting rock will hinder the effective removal of protolith-derived argon from the grain boundary network and
also the removal of lattice-bound 40Ar from phengite grains
residing at ðU ÞHP conditions.
Using the experimental parameters of Harrison et al.
(2009), Fig. 7a shows that argon within muscovite following
typical subduction P–T trajectories (Peacock, 1993) will diffuse over sub-micrometer length-scales (< 107 m; Fig. 7a),
significantly less than typical dimensions of metamorphic
mica. Fig. 7b shows the effect of convergence velocity on
cumulative diffusion length-scales; P–T path parameters
are otherwise the same as path 2 in Fig. 7a. These plots show
that, independent of convergence velocity, diffusive removal
of argon from mica equilibrating during prograde metamorphism along typical subduction-related temperature gradients will be inefficient. On reaching peak ðU ÞHP
conditions mica that has equilibrated continuously during
subduction will retain a memory of its protolith, or prograde
history. This suggests that release of protolith-derived argon
from mica, and other K-bearing phases, is controlled by
non-diffusive processes driven by gradients in chemical potential, such as dissolution–precipitation mechanisms (Wijbrans and McDougall, 1986; Putnis, 2009).
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a
b
LD=10-7m
30
c
100
1
10-9
20
10-10
2
15
10-11
3
10
10
-12
10-13
10-14
10-15
10-16
5
10-4
10-8
10
-10
10-12
10 cm.yr-1
10-14
1 cm.yr-1
-16
10
500°C
10-4
400°C
Grain-scale
10-6
300°C
10-8
10
10-18
10
600°C
10-2
Grain-scale
10-6
Diffusion length (m)
Pressure (kbar)
Cumulative diffusion length (m)
10-8
25
1000°C
900°C
800°C
700°C
100
10-2
200°C
-10
-20
10-12
100°C
10-22
10-14
10-24
0
0
100
200
300
400
500
Temperature (°C)
600
0
100
200
300
400
500
Temperature (°C)
600
700
0
5
10
15
20
25
30
Residence time (Ma)
Fig. 7. Argon diffusion calculations. (a) Calculated steady-state P–T paths followed by the top of a subducting slab using the analytical
solutions of Molnar and England (1990) and Peacock (1993). The following parameters were used for each path: convergence velocity
(V) = 8 cm yr1, subduction angle (hsub ) = 15 , basal heat flow (qm ) = 0.05 W m2, crustal density (qc ) = 3000 kg m3, thermal conductivity
(K) and diffusivity (j) of 2.5 W m1 C1 and 1 106 m2 s1, respectively. Temperature gradients are controlled by the amount of shear
heating along the slab–wedge interface (Molnar and England, 1990; Peacock, 1993). Path 1 is calculated using a shear stress (s)pof
ffiffiffiffiffi30 MPa,
path 2 s = 45 MPa and path 3 s = 60 MPa. P–T paths are contoured for the cumulative diffusion distance (LD ¼ 2 Dt, where
D = D0 :eðEa þV 0 ðPP 0 Þ=R:T Þ ) of argon in muscovite, using the experimental diffusion parameters of Harrison et al. (2009):
2 1
3
1
(P 0 = 1 GPa). (b) Effect of convergence rate on cumulative diffusion length
Ea = 263 29 kJ mol1 ; D0 = 2:3þ70
2:2 cm s ; V 0 = 14 cm mol
during subduction. Shaded rectangle highlights typical phengite grain dimensions. (c) Effect of ðU ÞHP residence time on diffusion length for
the T range: 100–1000 C. Shaded rectangle highlights dimensions of typical phengite grains.
At temperatures greater than 400 C length scales of
argon diffusion become spatially significant. Fig. 7c is a plot
of diffusion length as a function of residence time at peak T,
between 0 and 30 Ma (a plausible range for ðU ÞHP terranes;
Kylander-Clark et al., 2012; Agard et al., 2009) for a range
of geologically realistic temperatures. Millimeter-scale argon diffusion is shown to occur only at temperatures
J 500 C, independent of ðU ÞHP residence time. These results are consistent with Warren et al. (2012) who calculated
that 0.1 and 1 mm diameter muscovite grains residing at
25 kbar and 550 C for 10 Ma will retain <5% and 65%
radiogenic argon, respectively. They also showed that a
0.5 mm muscovite grain residing at the same P–T conditions for 0.5 and 20 Ma, respectively, will retain 95%
and 25% radiogenic argon. Provided that the macroscopic
grain radius represents the effective diffusion length scale,
this modeling shows that excess age fractions will be considerable in grains J 1 mm in diameter from ðU ÞHP terranes
characterized by residence times <10 Ma, even with an
effective open system grain boundary network. However,
previous work suggests that diffusion of argon in muscovite
is non-Fickian and most accurately simulated by the presence of multiple diffusion domains of differing length scales
but identical activation energies (Lovera et al., 1991; Harrison et al., 2009). Structural deformation is also expected to
enhance bulk grain argon diffusivity as a result of concomitant reductions in grain size and effective diffusion length
scale (see Baxter, 2010 for a review). Both multi-domain
diffusion and deformation of muscovite will lead to enhanced loss of 40Ar and younger cooling ages, increasing
the concentrations of Are required to explain measured
40
Ar/39Ar ages.
In the absence of a free-fluid phase, inter-crystalline diffusion ( 103 times faster than intra-crystalline diffusion;
Manning, 1974) will control the rate of inter-granular argon
exchange. The presence of an inter-granular fluid-phase will
increase the efficiency of argon transport by a combination
of advective solute transport, operating between 103 and
101 m a1, and aqueous diffusion, up to 16 orders of magnitude faster than solid-state diffusion (Rubie, 1986). Therefore, effective removal of inherited or locally-generated Are
from a mica-bearing rock will critically depend on the availability of fluids.
6.3. The availability of a grain-boundary fluid phase
Subducting sediments and oceanic crust contain free
H2O residing in pores and lattice-bound H2O in hydrous
phases. Pore fluids, occupying K 50 vol.% in subducting
sediment and K 7 vol.% (Becker and Sakai, 1989) in the
upper oceanic crust, are expelled by porosity collapse at
depths K 20 km and T K 150–300 C, depending on the
thermal structure of the subduction zone. Despite the large
fluid fluxes caused by porosity collapse in subducting sediments (0.1–1.2 103 m3 m2 a1 Hyndman and Peacock,
2003), the lack of pervasive mineralogical change, with
the exception of the smectite ) illite transition, means that
release of inherited 40Ar by dissolution is likely to be
negligible.
Release of lattice-bound H2O from hydrous phases is
controlled by dehydration reactions. In order to illustrate
the different dehydration histories for subducting mafic
and pelitic lithologies, P–T pseudosections (THERMOCALC
version 3.33; Holland and Powell, 1998) were calculated
Author's personal copy
og
lg
ta
law
law o gl ta act chl mu ru
15
o
chl
act
c
gl
hl
e
act chl ep
bi ab sph
5
400
hb
bi
ep
ab
sp
td
gc
g ky
car jd
600 400
p pa
e
g ctd
coe
qtz
-30%
-25%
-35%
ca
rc
td
-20
+60%
ep
jd
g
g
ctd
ky
g ctd ep
g ky
ar
0%
5%
+4
+3
+1
5%
g ky chl
15
5%
pa
%
+2
ep
r
ca
+1
l
ch
600
d
g ky jd
0%
ctd
chl c
550
500
450
0
+3
20
ep
-40%
+5%
+2
Pressure (kbar)
25
-45%
h
g ky car
g ep car jd
-5%
%
0
-1
ph
ru s
550
MnNCKFMASHO
(+mu+SiO2)
%
-65
%
-15
hb ep bi pl sph
500
450
c
hb e
hb a
bi a ct chl
b sp
h ep
sph
%
-65
ct
%
l ep bi ab
30
p bi
gl act chl ep bi sph
gl act ch
+a
u
u
ur
pm
u ru
le
pm
ch
ep m
ct
chl
t
a
c
l
la
g
g
ru
o
bi i ru
ru
p
bi
b
le
p
ep
ch b e
gl act chl
o
b
h
h
hb
ep bi ru
pm
10
g gl
act chl
ep mu ru
e
hl
h
lc
ru
ru
p
us
og
mu
0%
o
law
%
l
t ch
-5%
l ac
%
og
law
ru
5% %
+3 30 25%0%
+ + +2
20
ru
mu
mu
+10
Pressure (kbar)
2
SiO
105
o g ta law mu ru
nt
se
ab
%
25
b
coe
qtz
-55%
NCKFMASHTO
(+SiO2)
-10
a
-15
30
-50%
A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
0%
g ctd chl ep
ctd chl ep
g ky chl ma
p
p
ae
hl m
gc
5
400
g chl ma
m
a
i
ab
m
hl
gc
t
is
ab
gm
450
500
+5%
bi
ch
ky
td
gc
g
ae
lm
10
550
Temperature (°C)
ky
sill
600 400
450
500
550
600
Temperature (°C)
Fig. 8. P–T pseudosections calculated for mafic and pelitic compositions between 400–650 C and 5–30 kbar. Panel (a) shows stable phase
equilibria for an oxidised MORB bulk composition: 2.66 Na2O; 12.43 CaO; 0.23 K2O; 12.93 MgO; 9.26 Al2O3; 53.4 SiO2; 1.07 TiO2, 1.5 O,
(Rebay et al., 2010). The system is H2O saturated. Panel (b) is contoured for amounts of mineral-bound H2O released/consumed relative to
4 kbar and 400 C. Contours are labelled at 5% intervals and calculated for assemblages stable on the low-T side of the amphibole solvus.
Panel (c) shows a P–T pseudosection constructed for a peraluminous pelite (TH-680; Smye et al., 2011), using the fully-expanded
MnNCKFMASHO chemical system. Bulk composition in molar %: 0.09 MnO; 0.24 Na2O; 1.29 CaO; 3.33 K2O; 5.55 FeO; 3.64 MgO; 13.76
Al2O3; 70.31 SiO2; 0.185 O. Both quartz and H2O are set to excess. Panel (d) shows contours of constant H2O flux relative to 4 kbar and
400 C. Contours are labelled at 5% intervals.
between 400 and 600 C and 5–30 kbar for an oxidised
MORB (Fig. 8a and b; NCKFMASHTO) and a peraluminous pelite (Fig. 8c and d; MnNCKFMASHO) composition. The pseudosections are contoured for modal
proportions of mineral-bound H2O liberated (þDH2 O ) or
consumed (DH2 O ), expressed as a percentage relative to
the amount of free H2O present in respective greenschist-facies assemblages stable at 4 kbar and 400 C. Fig. 8a and b
are curves corresponding to the flux in lattice-bound H2O
produced by each of the P–T paths calculated in Fig. 7a,
for MORB and pelitic compositions respectively. Phase
relations considered here are restricted to temperatures
>400 C due to uncertainty over initial water contents of
the respective protoliths.
In a rock of MORB composition, dehydration occurs
dominantly by discontinuous, univariant reactions. Specifically, the stability of lawsonite exerts a strong control on
the amount of free H2O present during subduction. The
decomposition of lawsonite (red band, Fig. 8b) produces
50% change in relative free H2O content. A rock following P–T path 1 (Fig. 7a) will encounter SiO2 undersaturated conditions at pressures >20 kbar. P–T path 2 has
a sub-parallel trajectory to the lawsonite-out band in P–
T space (Fig. 9a); lawsonite decreases in modal abundance
during the low-temperature portion (<450 C) of the path,
whereas after the path crosses the sphene ) rutile transition, lawsonite modes increase, requiring the addition of
H2O. Oceanic crust following the high-s P–T path (path
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106
A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
3; Fig. 7a) will dehydrate continuously between 400 and
600 C, liberating 30% H2O relative to greenschist saturation values though the decomposition of actinolite and
chlorite. Importantly, path 3 does not facilitate lawsonite
growth.
During subduction, pelitic rocks lose up to 65%
(Figs. 8a, b and 9b) of the mineral-bound H2O stable at
greenschist facies conditions, 25% more than the maximum
DH2 O yielded by oceanic crust. Devolatisation in the pelitic
system is characterised by divariant, continuous reactions
that release H2O throughout the P–T space between 400
and 600 C and 5–30 kbar. Path 1 is dominated by the modal abundance of the hydrous phase carpholite, which, like
lawsonite, requires hydration during subduction. Paths 2
and 3 liberate similar quantities of H2O (DH2 O ¼ 56 and
52% respectively) through the successive breakdown of
chlorite, epidote and chloritoid. Phengite is stable throughout the P–T space considered.
a
40
Path 3
[sph↔ru]
20
Δ H2O (%)
[act]
MORB
0
law-out
-20
6.4. The connectivity of the grain-boundary fluid phase
[act,chl]
Path 2
law-in
-40
-60
Path 1
400
450
500
550
600
Temperature (˚C)
b
60
Pelite
[chl,ep]
40
Δ H2O (%)
[ctd]
Path 2
50
30
[chl,ctd,ep]
20
Path 3
10
Path 1
0
-10
[ctd]
-20
400
450
500
550
The order-of-magnitude larger porosity estimates calculated from mica in pelitic protoliths (Figs. 4b and 5) relative
to those calculated from mafic eclogites correlates with the
greater extent of devolatisation that is predicted to occur
during subduction to ðU ÞHP conditions. The continuous
supply of lattice-bound H2O to the grain-boundary network in pelitic rocks will cause elevated hydrostatic pressures, driving crack propagation and advective fluid
transport of protolith-derived argon. In contrast, oceanic
crust has the potential to undergo hydration during subduction due to lawsonite growth and its ability to incorporate
an entire H2O molecule, effectively buffering H2O activity
in the mafic system. Under such conditions, mafic eclogites
may remain dry until the blueschist ) eclogite transition
where glaucophane, garnet, and talc are stabilized at the expense of actinolite and chlorite. The buffering of free H2O
by lawsonite has the potential to limit available grain
boundary fluid to a layer only nanometers in thickness, thus
preventing effective dilution and removal of internallycycled argon from the system. Under dry conditions, as predicted to occur in mafic rocks, local matrix phases could
potentially dominate the total local sink capacity for argon
(Fig. 6a), whereas the elevated fluid fluxes expected in
metasediments suggest that pore fluids will be the dominant
repository for Are .
600
Temperature (˚C)
Fig. 9. Calculated flux in mineral-bound H2O for a MORB (panel
a) and pelite (panel b) undergoing subduction-related devolatization between 400 C and 600 C. Bulk compositions are the
identical to those used to calculate pseudosections shown in
Fig.8. Curves correspond to the amount of mineral-bound H2O
liberated (þDH2 O ), or consumed (DH2 O ), expressed as a percentage
relative to the modal proportion of free H2O present in respective
greenschist-facies assemblages stable at 4 kbar and 400 C. Fluxes
are plotted as a function of T for the subduction P–T paths 1
(brown), 2 (green) and 3 (blue), described in Fig. 7. Square brackets
represent the position of discontinuous reactions; the labelled phase
corresponds to the phase that is consumed. Dashed line in panel a
denotes silica-undersaturated conditions.
Mafic rocks release smaller quantities of structurallybound H2O than metapelitic rocks during subduction.
However, removal of locally-generated 40Ar in a subducting
rock will not only depend on the volume of available fluid,
but critically, the connectivity of the fluid phase. Permeability is dependent on rock rheology and exists as both fracture networks, observable over micro- to meter
lengthscales, and texturally-controlled inter-granular pathways in metamorphic rocks (Ingebritsen and Manning,
2010). In order to maintain porosities similar to those calculated above (103 –105 ) over the duration of mica equilibration/growth under ðU ÞHP conditions, a fraction of the
metamorphic fluid liberated during prograde metamorphism must remain in the rock. Thermal-petrologic models
predict that integrated fluid fluxes from subducting mafic
oceanic crust and associated sediments are between
104 and 106 m3 m2 a1 at depths between 20 and
80 km (Hyndman and Peacock, 2003). Using this range of
values, which account for the differences in thermal structure observed in subduction zones, a 5 km-thick slab undergoing dehydration will produce enough fluid to fill or form
the calculated porosities over timescales of 500 to 5,000,000
years, respectively. Adopting Manning and Ingebritsen
(1999)’s formulation for the conditions under which fluid
pressures become hydrostatic, slab permeabilities K 1020
and K 1022 m2 are required to retain metamorphic fluids
released at these production rates. These values are comparable to estimates of background crustal permeability:
1020 m2 (Connolly, 2010).
The hydraulic connectivity of a rock undergoing metamorphism is controlled by a combination of pervasive flow
through interconnected pore spaces and channelized flow
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A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
through fractures. An interconnected porosity network is
controlled by the dihedral angle (h) between fluid–mineral–mineral junctions (Graham et al., 1997). A fundamental change in fluid mobility occurs at h = 60 (Smith, 1948).
At values of h <60 , the surface energy of a wetted grainedge region is smaller than a dry grain-edge region and
the system favors open grain-edge channels, independent
of the value of /. For h >60 , dry grain-edge surface energies are smaller than the wetted grain-edge configuration
and grain-edge channels pinch-off along their length, forming a closed grain-boundary reservoir. The quartz–fluid h
will dominate texturally-defined permeability in metapelites. Holness (1993) and Holness and Graham (1995)
showed that porosity in quartz-rich rocks will be connected
within two permeability windows to C–O–H fluids at
P <11 kbar: one at temperatures <400 C and the other
at temperatures >1100 C. The topology of P–T–h contours constructed by Holness (1993) suggests a further permeability window at pressures above 11 kbar.
Connectivity in the mafic system is best represented by
the forsterite–fluid h. Watson et al. (1991) and Mibe et al.
(1999) showed that h decreases with increasing pressure
and temperature between 0.5–5 GPa and 400–1300 C;
the critical h of 60 C is attained at 2 GPa at 1000 C.
Whereas pervasive flow through an interconnected
porosity network reflects thermodynamic equilibrium, fractures are nonequilibirum phenomena, capable of connecting pores that would otherwise be isolated. Rocks
fracture in response to externally-applied or internally-generated (i.e. devolatization) stresses exceeding the tensile
strength limit (Etheridge, 1983). The low tensile strength
of rocks, K 5 MPa, means that hydrofracturing provides
a self-regulating mechanism to control pore fluid pressures
(Morris and Henley, 1976). This is supported by recognition of petrographic evidence for multiple cracking and
sealing events in the history of a single vein (Ramsay,
1980). Fracturing also occurs in response to deviatoric
stresses under conditions of P fluid < P rock (Yardley, 1983),
forming boudinage veins and shear fractures, commonly
larger than tensile fractures e.g. Philippot and Selverstone
(1991). Both tensile and shear fractures are common in
ðU ÞHP terranes and often contain ðU ÞHP phases, highlighting the importance of channelized fluid flow as an effective
mechanism for solute transfer during subduction (e.g.
Franz et al., 2001; Widmer and Thompson, 2001; Zhang
et al., 2008; John et al., 2012). Given that garnet (Ji and
Martignole, 1994) and clinopyroxene (Kolle´ and Blacic,
1983) are two of the strongest minerals in the crustal lithosphere, eclogites have higher ultimate tensile and shear
strengths (Hacker, 1996; Jin et al., 2001) compared to cogenetic pelites in which quartz controls effective rock strength
(Hoek and Brown, 1997). Coupled with the larger volumes
of fluid released from metasediments, this shows that eclogites are less susceptible to fracture formation during subduction. Furthermore, metapelites typically comprise 10–
70 volume % of sheet silicates, compared to K 2% in eclogites, promoting the formation of planar foliation fabrics
that act as fluid percolation pathways.
Collectively, these data suggest that metapelites are expected to be more permeable to fluids released during pro-
107
grade metamorphism than cogenetic mafic rocks.
Accordingly, pelites will lose protolith-derived argon by
advective solute transport and have true porosities < 104
volume fraction at the time of mica equilibration.
6.5. A conceptual model for the accumulation of Are in
metamorphic rocks
Fig. 10 shows the competing effects of available fluid,
permeability and argon diffusion efficiency on rocks of
pelitic and mafic compositions during increasing temperature (and implied pressure). Note that the dependence of
hydraulic connectivity on dihedral angle assumes that fracture permeability is negligible. The model is equally applicable to the scenario where deformation drives hydraulic
connectivity. During the early stages of burial pores are
connected in both mafic and pelitic lithologies (stage Oi
Fig. 10a–c) and pore fluids are expelled by compaction.
As temperatures are < T c , volume diffusion is ineffective
(LD < 1010 m; Fig. 7) and argon exchange occurs by
grain-boundary dissolution–precipitation, concomitant
with the growth and consumption of new and relict metamorphic phases respectively. As H2O is released into a connected porosity network, inherited 40Ar is effectively flushed
out of the system to an external sink, ultimately residing in
the atmosphere. Pelites retain a connected porosity and lose
large amounts of H2O over the temperature interval at
which diffusion in white mica becomes efficient over
grain-scale dimensions (stage Oii Fig. 10a and c; see also
Fig. 7), thereby facilitating open system 40Ar transport to
an external sink before the rock becomes impermeable,
either when h < 60 or the dehydration fluid flux decreases.
Conversely, mafic rocks hydrate or liberate small amounts
of H2O during prograde metamorphism, becoming closed
to advective solute transport at values of T < T c (stages
Oi and Ci Fig. 10b and c). Accordingly, the volume fraction
of free fluid in mafic rocks will be significantly less than
cogenetic pelites at values of T > T c (stage Cii Fig. 10b
and c). On exhumation and associated cooling through
T c , diffusion will become inefficient and, in the absence of
a high-T fluid phase (Camacho et al., 2005), the 40Ar concentration acquired by the mica under ðUÞHP conditions
is effectively ‘locked’ into the grain.
6.6. Implications for the transport of volatiles to the mantle
Recent work has shown that the isotopic composition of
heavy noble gases and halogens in the mantle wedge and
the convecting mantle is remarkably similar to that of seawater (Holland and Ballentine, 2006; Sumino et al., 2010).
This challenges the popular concept of a noble gas ‘subduction barrier’ (Staudacher and Alle`gre, 1988) in which volatiles, with the exception of S and CO2, are returned to the
surface as pore-fluids are expelled from oceanic crust at
depths <20 km (Hyndman and Peacock, 2003; Jarrard,
2003). The retention of locally-derived 40Ar to mantle
depths in mafic eclogites provides further compelling evidence that the oceanic crust behaves as a closed system to
volatiles during subduction. Marine pore fluids could plausibly become encapsulated during the early stages of burial
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A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
)
Cii
Oii
Tc
Oi
b: mafic
θ>60°
Ci
Oi
Tc
Temperature
c
Oi
Temperature
Oii
40
40
Ar
Cii
θ( )
θ>60°
H2O released (
a: pelite
θ( )
H2O released (
)
108
Cii
Ci
40
40
Ar
Ar
40
Ar
40
40
Ar
Ar
Ar
40
Ar
40
Ar
40
Ar
40
Ar
40
Ar
40
Ar
40
Ar
40
Ar
Release of 40Ar by dissolution Release of 40Ar by diffusion Release of 40Ar by dissolution Diffusive equilibration of 40Ar
into an open system
into a closed system
into an open system
in a closed system
Fig. 10. Conceptual model for the accumulation of Are under ðUÞHP conditions. Panels a and b show the relationships between the amount
of H2O released during prograde metamorphism (black solid line), argon diffusivity (the boundary between efficient and inefficient diffusion,
T c is marked schematically as a region bounded by grey dashed lines) and dihedral angle (h, black dashed line) with increasing T during
subduction for pelitic and mafic protoliths respectively. The topology of the schematic h and H2O curves are discussed in the text. The shaded
region represents values of h > 60 , the value at which the system becomes impermeable to grain boundary flow at low porosities. Panel c
shows the four possible configurations of argon transport that a mica-bearing rock will experience during subduction to ðU ÞHP conditions;
these four stages are marked on panels a and b. Solid arrows represent dissolution exchange whereas dashed arrows represent diffusional
exchange. (Oi) Early-stage flushing of protolith-derived argon controlled by mineral dissolution and advective solute transport in a connected
grain-boundary pore network. (Oii) “Dodson” open system: as T exceeds the range of T c for argon in mica, diffusion becomes efficient at the
grain, leading to removal of lattice-bound 40Ar into a connected (open, infinite) grain boundary reservoir. (Ci) Release of 40Ar by dissolution
reactions into a closed system at T < T c . (Cii) Closed system: whilst the T conditions still allow efficient diffusion, the rock is no-longer
permeable and each individual mica grain equilibrates with its local immobile fluid argon concentration.
(h > 60 and T < T c ; Fig. 10). During subduction and concomitant heating, pore fluids will participate in dissolution–
precipitation reactions leading to mineral hydration or formation of fluid inclusions. The fact that phengites crystallizing at ðU ÞHP conditions incorporate protolith-derived 40Ar
shows that the grain boundary reservoir behaves as a closed
‘sink’ for incompatible elements, such as noble gases,
throughout subduction. Release of volatiles into the mantle
reservoir could plausibly be facilitated by increased dehydration fluid fluxes driven by lawsonite breakdown, or
when h <60 (80–150 km depth; Mibe et al., 1999).
7. CONCLUSIONS
Extraneous argon is ubiquitous in phengite that has
equilibrated under ðU ÞHP conditions. Apparent phengite
40
Ar/39Ar ages K 700% older than the age of ðU ÞHP metamorphism can be explained by incorporation of locally-generated 40Ar. Measured Are concentrations in mafic eclogites
are reproduced only when porosities are K 104 volume
fraction, showing that mafic protoliths operate as closed
systems to advective solute transport during subduction.
Porosities in eclogite-facies metapelites are K 102 , reflecting loss of significant volumes of lattice-bound H2O relative
to mafic rocks during subduction. The concentration of Are
in ðU ÞHP phengite strongly reflects the devolatisation history of the protolith. Phase equilibria calculations show
that pelitic lithologies dewater continuously throughout
subduction to ðU ÞHP conditions, flushing accumulated
40
Ar from the system. Mafic lithologies either require
hydration, or produce less H2O during subduction, therefore retaining protolith-derived radiogenic argon under
closed system conditions. Such small porosities are maintained by permeabilities K 1020 m2 during subduction.
Retention of protolith-derived 40Ar to ðU ÞHP conditions
implies that the oceanic crust is an efficient vehicle for the
transport of volatiles to the mantle.
ACKNOWLEDGMENTS
A.J.S. acknowledges support of a Jackson Postdoctoral Fellowship. C.J.W. acknowledges funding from the Natural Environment
Research Council (NE/E0114038/1 and NE/H016279/1). We are
grateful to David Shuster for his editorial handling of the manuscript. Formal reviews by Jan Wijbrans, Ethan Baxter and an
anonymous reviewer served to greatly improve the clarity of the
manuscript. This work has benefitted from fruitful discussion with
Simon Kelley, Chris Hawkesworth and Marian Holness.
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A.J. Smye et al. / Geochimica et Cosmochimica Acta 113 (2013) 94–112
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