Lithos 122 (2011) 189–200

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Source controlled 87Sr/86Sr isotope variability in granitic magmas: The inevitableconsequence of mineral-scale isotopic disequilibrium in the protolith

Federico Farina ⁎, Gary StevensCentre for Crustal Petrology, Department of Earth Sciences, University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa

⁎ Corresponding author. Tel.: +27 762421424; fax: +E-mail addresses: farina@sun.ac.za (F. Farina), gs@su

0024-4937/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.lithos.2011.01.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 August 2010Accepted 5 January 2011Available online 14 January 2011

Keywords:Granitoid rocksDisequilibrium meltingSr isotopes

The broad Sr isotopic variability exhibited by granitoid rocks is commonly interpreted to reflect the mixing ofmagmas from different sources. However, evidence from granites and migmatites indicates that melting andmagma extraction from crustal sources can occur sufficiently rapidly that trace-element and isotopicequilibration between liquid and residual phases is commonly not achieved. Additionally, evidence fromunmelted high-grade metamorphic rocks indicates that major reactant minerals in the fluid-absent meltingprocess, principally biotite and plagioclase, do not always attain equilibrium during regional metamorphism.When these two circumstances occur in combination, the melt does not inherit its radiogenic isotopicsignature from the bulk source in a simple way. In such situations, the isotopic composition of the melt will bedependent on the isotopic compositions of the reactant phases and the stoichiometry of the melting reaction.This study has used information from experimental studies of fluid absent partial melting in metapelites andmetagreywackes to investigate the consequences of Sr isotopic disequilibrium between the reactant mineralsfor magma composition. The study demonstrates that a range of isotopically distinct magmas can arise fromprogressive melting of a single source that is able to undergo melting through different reactions astemperature increases. When translated to the typically layered sources constituted by sedimentary andvolcano-sedimentary rocks, this process will produce magmas characterized by Sr isotope variability thatreflects the differences in melting reaction stoichiometry within the different layers, even with no bulk-rockisotopic variability between layers. This study demonstrates that the Sr isotope variability commonlyobserved within granitic suites, as well as at the grain and sub-grain scale within individual magmatic bodies,can be primary, reflecting differences in composition between magma batches produced from the progressivemelting of a single source.

27 21 8083129.n.ac.za (G. Stevens).

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Sr isotopic information is important in shaping our views ofgranitoid petrogenesis on a number of levels. Firstly, whole-rock Srisotopic variation has been shown to exist within such rocks on a scalethat varies from regional (km) to that of the outcrop (m) and isregarded as evidence that granitoid plutons and silicic volcaniccomplexes do not commonly form by differentiation of a singleoriginal parentmagma. Initial 87Sr/86Sr heterogeneitywithin granitoidbodies can be associatedwithwell-defined internal contacts preservedbetween different rock types (e.g. Halliday et al., 1980; Kistler et al.,1986; Tsuboi and Suzuki, 2003); can be cryptic, with detailedpetrographic surveys required for its detection (e.g. Farina et al.,2010); or, occult and existing in the apparent absence of anymineralogical or other geochemical evidence for contrasting magmabatches (e.g. Deniel et al., 1987; Helps et al., 2003; Mohr, 1991).

Secondly, Sr isotopic variation has commonly been described betweenphenocrysts and the groundmass in silicic volcanic rocks (e.g. Tepleyet al., 2000) and alsowithin individual feldspar phenocrysts (Gagnevinet al., 2005; Knesel et al., 1999; Tepley et al., 2000;Waight et al., 2000).In this case, the isotopic ratio variations recorded from core to rimwithin the crystals is interpreted to reflect progressive changes in themagma composition from which the mineral crystallized. Thus, thecommon occurrence of primary isotopic heterogeneity at whole-rock,grain and sub-grain scale, suggests that many granitoid rocks areassembled from isotopically contrasting magma batches.

The origin of the isotopic variability described above is usuallyexplained in two ways: (i) by arguing, from the perspective thatgranites image their sources, the isotopic variability is interpreted toreflect isotopic heterogeneity in the source which has not beenobliterated by magmatic processes (e.g. Deniel et al., 1987); (ii) byarguing, from the magma mixing perspective, the isotopic heteroge-neity is interpreted to result from mixing between granitic andmantle-derived basaltic magmas (e.g. Gagnevin et al., 2005). Boththese hypotheses appear to adequately explain the typical range ofSr-isotopic variation in granites. Thus it is surprising that the great

190 F. Farina, G. Stevens / Lithos 122 (2011) 189–200

majority of recent studies documenting isotopic variation at differentscales within silicic to intermediate igneous bodies, only invokemixing with mantle-derived magma to interpret the genesis of theserocks.

The two hypotheses referred to above are both underpinned by theassumption that equilibrium between melt and solid residue isattained in the source during melt generation. This results in themagmas inheriting the isotopic ratio of their bulk sources at the timeof anatexis (Harris and Ayres, 1998). This assumption is clearly invalidif heating during the pre-anatectic metamorphic event, melting andextraction of the magma are rapid enough to not allow for completeequilibration between the bulk source and the melt (i.e. disequilib-rium partial melting). In this case the melt will have an isotopiccomposition that is inherited from the minerals involved in themelting reaction and thus, as demonstrated experimentally byHammouda et al. (1996) and Knesel and Davidson (1996, 1999,2002), a single source may generate magma batches with different Srisotopic compositions. Although numerous studies have discussedvarious aspects of disequilibrium partial melting of metasedimentarysources (e.g. Harris and Ayres, 1998; Perini et al., 2009; Tommasiniand Davies, 1997), themechanisms bywhich Sr isotopic diversitymayarise in magmas produced from a single source are not wellunderstood and have not been adequately modelled. The result isthat, with the noteworthy exception of Zeng et al. (2005a, b), thisprocess is generally not considered as an explanation for the existenceof isotopic heterogeneity in granitoid rocks.

The principal objective of this paper is to investigate the extent towhich isotopic heterogeneity in granitoid systemsmay result from themixing of magmas generated from a single source. This work focuseson 87Sr/86Sr systematics, both because the Sr isotopic composition ofnatural rocks and minerals has been extensively investigated, andbecause the Sr isotopic composition of anatectic melts is dependenton the behaviour of minerals that are major reactants in the meltingprocess, such as plagioclase, biotite, muscovite and hornblende.Additionally the melting behaviour of these minerals in quartzsaturated sources is reasonably well known from experimentalstudies (e.g. Montel and Vielzeuf, 1997; Patiño Douce and Harris,1998; Pickering and Johnston, 1998; Vielzeuf and Montel, 1994).

2. Isotopic disequilibrium during anatexis

Disequilibrium during prograde metamorphism, melting andextraction of the melt from the source occurs when the time requiredfor equilibrium to be attained is greater than that during which thesystem is open to diffusion between coexisting phases (e.g. Harris andAyres, 1998). The duration of the equilibration period (i.e. the periodduring which chemical exchange can occur) is a function of twofactors: i) the prograde metamorphic history, which determines howlong the protolith resides at a temperature above the relevantblocking temperature, but below that of anatexis. During this part ofthe protolith's history diffusion rates are relatively slow but scaleproportionally with temperature; ii) the duration of residency of meltin the source. This will be controlled by themelting rate (controlled bythe rate of heat supply and reaction kinetics) and the mechanism ofmelt extraction from the source. During this period, diffusion will berelatively fast due to the presence of melt and the higher temperature.Diffusion rates of different elements in the variousminerals of interestare spread over many orders of magnitude at any given temperature.Consequently, the degree to which equilibrium is attained varies as afunction of the chemical species considered. In the sense used here,disequilibrium melting refers to an incongruent partial melting eventwhere the melt was not in Sr isotopic equilibrium with the residuumprior to melt extraction. In detail, the rate of Sr-isotope equilibrationbetween melt and restite (i.e. the crystalline residue) depends also onmineral grain size, proportion and composition, as well as 87Srdiffusion rate in the different phases (Jenkin et al., 1995). The rate-

limiting parameter in the equilibration process is the volumediffusivity of Sr isotopes in plagioclase, both because plagioclase isthe major Sr reservoir in metasedimentary assemblages and becausediffusivity within plagioclase is slower than in micas (Giletti, 1991;Giletti and Casserly, 1994). A study of Sr diffusion in plagioclase byRutherford backscatter spectroscopy (Cherniak and Watson, 1994)indicates slower chemical Sr diffusion rates (i.e. diffusion in achemical potential gradient) than Sr self diffusion (i.e. diffusion inthe absence of a chemical gradient to homogenise isotopic variation)and hence isotopic ratios can equilibrate more rapidly than elementalconcentrations. Harris and Ayres (1998) report as an example, that Srdiffusion length scales are 40–80% of self diffusion length scales at700 °C for plagioclase of oligoclase to andesine composition.

Experimental information on Sr diffusion is difficult to translate intopredictions of natural rock behaviour during anatexis, as the rates ofheating and melting, as well as the residence time of the melt in thesource before extraction, is poorly constrained in natural rocks.However, Rb–Sr mineral isochrons in medium- to high-grade regionalmetamorphic rocks such as amphibolites, granulites and eclogites (e.g.Cliff and Meffan-Main, 2003; George and Bartlett, 1996; Glodny et al.,2008), commonly yield ages that are older than the established age ofmetamorphism, implying that the system was not completely resetduring the metamorphic event. Thus, in high-grade rocks, that did notexperience fluid-assisted re-crystallization, such as granulites oreclogites, isotopic resetting appears to be either kinetically locked, orrestricted by sluggish inter-mineral diffusion which demonstrably doesnot lead to full isotopic homogenization. Thus, despite prolongedresidence at high temperature, inter-mineral Sr tracer diffusion does notsignificantly alter the Sr isotopic signature of feldspar, amphibole orpyroxene and in many cases does not even fully reset micas (Glodnyet al., 2008). These results are consistent with the small volumes ofmajor element equilibration in high-grade metamorphic rocks andextremely sluggish rates ofmetamorphic reactions (Baxter andDePaolo,2000; Carlson, 2002). Many of themetamorphic rocks referred to abovewill have followed thermal histories unaffected by direct heat inputfrom mantle magmas. In contrast extensive melting of the crust is verylikely to require the addition of substantial mantle heat via thismechanism (e.g. Annen et al., 2006). Thus, information from studies ofmetamorphic rocks probably underestimates to a considerable degree,the Sr isotopic disequilibrium inherent to granite source rocks at thetime of anatexis. Ifmelting occurs rapidly in such sources, as is predictedby the multi-sill intra-plating model of Annen et al. (2006), and melt israpidly removed from the site of origin, then equilibration between themelt and residual phases is unlikely to be achieved.

Rapid rates of melt production and extraction, preventingchemical or isotopic equilibration after melting, are mimicked byexperimental studies that have investigated disequilibrium partialmelting (Hammouda et al., 1996; Knesel and Davidson, 1996, 1999).Several studies have investigated the possibility that natural rocksbehave in a similarway and have used zircon andmonazite dissolutionrates during anatexis to test trace element equilibration duringmelting. The concentration of LREE and Zr in granitic melts formedby anatexis of ametasedimentary protolith is mainly controlled by thesolubility of monazite and zircon, respectively. If melt extraction ratesexceed the rate at which these minerals dissolve, the melt remainsunder-saturated with respect to these elements and direct measure-ment of segregation rates in natural rocks can be obtained fromexperimental constraints of zircon and monazite dissolution rates inrelevant melts. Harris et al. (2000) and Villaros et al. (2009) used thisapproach to calculate source residence times as short as 50 years forHimalayan leucogranites and of less than 500 years for the S-typeleucogranites of the Cape Granite Suite (South Africa), respectively.These values match with those inferred from experimental worksindicating that deformation-assisted melt segregation is an efficientmechanism to move melt from the source to local sites of dilation ontimescales of 10−1–104years (Rutter and Neumann, 1995). Similarly,

Fig. 1. 87Sr/86Sr evolution of plagioclase, biotite and muscovite through time in ahypothetical source rock. The final 87Sr/86Sr ratio for the minerals has been calculatedafter a period of 200 Ma and 300 Ma since the last isotopic equilibration. The white starrepresents the Sr isotopic composition of the three phases at time t0. The initial mineralRb and Sr concentration is reported. Mineral abbreviations are according to Kretz(1983).

191F. Farina, G. Stevens / Lithos 122 (2011) 189–200

trace element disequilibrium melting has been inferred from a largenumber of geochemical studies on migmatite terranes and anatecticcomplexes (Barbero et al., 1995; Nabelek and Glascock, 1995; Sawyer,1991; Watt and Harley, 1993; Zeng et al., 2005a). Migmatites providethe simplest case for investigating equilibrium/disequilibriummeltingsince the compositions of both the protolith and the presumedanatectic melt (i.e. leucosome) can commonly be established. Manystudies, comparing the trace element as well as Sr and Nd isotopiccompositions for leucosome, melanosome and un-melted protolithsets, suggest that partial melting occurred via a disequilibriummechanism (Barbero et al., 1995; Nabelek and Glascock, 1995; Wattand Harley, 1993; Zeng et al., 2005a, b).

In other studies where the composition of the source of silicicmagmatism has been inferred, significant differences between the87Sr/86Sr of the melt and that of the likely protolith have beenproposed. For example, data from Himalayan leucogranites and theirassociated protoliths suggest that the minimum 87Sr/86Sr observedwithin the leucogranites exceeds that of the protolith by about 0.005–0.01 (Harris and Ayres, 1998). In addition, disequilibrium partialmelting during anatexis has been described for two cases of contactmelting in the Sierra Nevada batholiths where the source–meltrelationship is unambiguous (Knesel and Davidson, 1999; Tommasiniand Davies, 1997). Tommasini and Davies (1997) described partialmelting of the Rattlesnake Gulch granite by intrusion of trachyande-site magma while Knesel and Davidson (1999) described partialmelting of a granitoid rock caused by intrusion of olivine basalt. Inboth cases, the partial melts (now quenched to glasses) are in markedSr isotopic disequilibrium with their sources and record centimetre-scale 87Sr/86Sr heterogeneities. Despite the obvious differences insetting, these contact scenarios may provide a best-fit naturallaboratory for intra-plating induced anatexis of the deep crust,where, at least for some source rocks, heating must be effectivelyinstantaneous. It is noteworthy that, although this contributionfocuses on Sr isotopes, disequilibriummelting has been also describedfor Nd and Pb isotopes (e.g. Ayres and Harris, 1997; Waight andLesher, 2010). The 143Nd/144Nd composition of anatectic melts isprimarily dependent on the behaviour of accessory phases such asapatite and monazite, which contain most of the total REE fraction inthe majority of crustal rocks (Ayres and Harris, 1997). In contrast, Pbisotopic equilibration relies on the behaviour of both accessory androck-forming minerals. According to Hogan and Sinha (1991), the Pbisotopic composition of a melt is controlled by the proportion of lowradiogenic Pb derived from rock-forming phases relative to the highlyradiogenic Pb contributed from accessory minerals. The existence, inmany granites, of inherited zircons recording U/Pb ages of theirprotoliths demonstrates that whole rock Pb isotopic equilibration isprobably never truly attained.

In conclusion, the available evidence frommigmatite terranes, un-melted high-grade metamorphic rocks and experiments, as well asindirect evidence from granitoid rocks shows convincingly that traceelement and isotopic disequilibrium occurs during anatexis andsegregation of the melt from the source. When this happens the meltdoes not inherit its radiogenic isotopic signature from the bulk sourcein a simple way and its isotopic composition is dependent on: i) theisotopic compositions of the reactant phases (for the Sr system this isthe function of their initial Rb/Sr ratio and of the time elapsed sincelast isotopic homogenization) ii) the stoichiometry of the meltingreaction; and, iii) the extent of isotopic re-equilibration between meltand residuum prior to melt segregation. The remainder of this workinvestigates the consequences of disequilibrium melting for the Srisotopic compositions of granitoid melts and magmas.

3. The model: mineral 87Sr/86Sr evolution through time

The changes that occur through time in the 87Sr/86Sr ratios of Sr-and Rb-bearing minerals are represented by means of the equation

describing the decay of parent 87Rb to the stable daughter 87Sr. Weconsider the Sr isotopic behaviour of muscovite, biotite andplagioclase, as all of these phases may be important reactants in themelting reactions by which granites arise. Although alkali feldspar is acommon Rb- and Sr-bearing phase in granites, its contribution tosource processes has not been considered in this work. The reasons forthis are that fertile sources for granitic magmas are usually fullyhydrated, and in such rocks K-feldspar is commonly not part of thepre-anatectic assemblage. Additionally, K-feldspar is not commonly amajor reactant in fluid-absent melting reactions that consume micas,being a product of the fluid-absent melting of muscovite (PatiñoDouce and Harris, 1998; Pickering and Johnston, 1998) and either aminor product or a reactant during fluid-absent melting of biotite,depending on the H2O/K2O of the melt relative to biotite (Carringtonand Watt, 1995). In the modelling presented here, muscovite, biotiteand plagioclase are proposed to have the initial Rb and Sr composi-tions shown in Fig. 1, these are similar to those of muscovite, biotiteand plagioclase in two Himalayan metapelites (Harris and Ayres,1998; Table 1). Assuming that these phases had the same 87Sr/86Srisotopic composition at time t0 (i.e. 0.708), and considering twodifferent cases, where the time elapsed since t0 is 200 Ma and 300 Marespectively, the final 87Sr/86Sr acquired by the different phases hasbeen calculated (Fig. 1). Plagioclase has low Rb/Sr (b1) and its 87Sr/86Sr does not increase significantly through time. In contrast,muscovite has higher Rb/Sr≈1 and hence acquires a higher 87Sr/86Sr than plagioclase. Rb is strongly compatible in biotite while Sr iscommonly very low (b20 ppm), thus this mineral is characterized byan extremely high Rb/Sr (generally N100) ratio, resulting in very high87Sr/86Sr through time. It is noteworthy that the effect of time is towiden the 87Sr/86Sr difference between the different phases inaccordance with their inherent Rb/Sr ratio: the gap existing betweenthe 87Sr/86Sr of plagioclase and biotite changes from≈0.98 to ≈1.47,as the time elapsed since the last homogenization event in theprotolith increases from 200 to 300 Ma (Fig. 1).

192 F. Farina, G. Stevens / Lithos 122 (2011) 189–200

The 87Sr/86Sr isotopic composition and the Sr content of biotite,muscovite and plagioclase calculated as previously described andshown in Fig. 1, are used in the following sections to determine the87Sr/86Sr of a variety of model partial melts. The isotopic compositionof the melt (87Sr/86Srm) can be calculated from the stoichiometry ofthe melting reaction, by means of the following equation: 87Sr/86Srm=(∑xjCj87Sr/86Srj)/∑xjCj (1), where xj is the weight propor-tion of mineral j (one of the reactant in the melting reaction), Cj and87Sr/86Srj are the concentration of Sr and the isotopic composition ofmineral j, respectively. This equation is identical to Eq. (9) in Zenget al. (2005a, b).

Assuming that the three phases have 87Sr/86Sr ratios which havenot been reset prior to melting, the isotopic character of the melt isdependent on the proportions of the Sr-bearing phases consumed bythe melting reaction. For example, a high biotite over plagioclase ratiogenerates a high 87Sr/86Sr melt composition, while an increase in theamount of plagioclase consumed over biotite produces a decrease inthe 87Sr/86Sr of the melt. Two end-member cases are considered:

1) Situations where the source can be considered to be composi-tionally homogenous and where Sr isotopic variability in themelts produced will be a function of changes to the stoichiometryof the melting reaction as anatexis progresses. Based onexperimental works of Montel and Vielzeuf (1997), PatiñoDouce and Harris (1998) and Pickering and Johnston (1998), wehave considered how the stoichiometry of the melting reactionvaries in the following cases: i) Fluid-absent partial melting of ametapelite primarily composed of Ms+Pl+Qtz (mineral abbre-viations after Kretz, 1983); ii) Fluid-absent partial melting of asource composed of Ms+Bt+Pl+Qtz, with a switch frommuscovite-dominated melting at relatively low temperature tobiotite melting as temperature increases. iii) Partial melting of aprotolith composed of Bt+Pl+Qtz.

2) Situations where the major element composition of the metase-dimentary source is heterogeneous, i.e. the protolith consists ofcompositionally contrasting domains (e.g. interlayered clay- andsilt-rich sediment), but with homogenous Sr isotopic composition.Based on the experimental work of Patiño Douce and Beard (1995,1996) and Stevens et al. (1997) we have considered how the Srisotopic composition of the partial melt may change in response tovariations in melting reaction stoichiometry induced by Mg/Feratio and TiO2 content changes in the source.

It is important to consider that the range of variability in 87Sr/86Srcomposition induced by variations of the melting reaction stoichiom-etry, as calculated in the following paragraphs, will bemaximum valuesbecause no partial re-equilibration by diffusion between the reactantphases is considered in the calculation. Finally, this work is based on thecrucial assumption that the melt leaves its source in discrete batches.This appears to have validity as an increasing number of recent workshave demonstrated, on the basis of field, geochronological andgeophysical evidence, that granitoid rocks are formed by the assemblyof discretemagmabatches (e.g. de Silva andGosnold, 2007; Farina et al.,2010; Glazner et al., 2004). Rock deformation experiments (e.g. Rutterand Neumann, 1995) have challenged the long standing notion of afundamental rheological threshold (critical melt fraction) below whichmelt cannot be extracted and indicate that deformation enhancedsegregation ofmelt can occur at very lowmelt fractions (5–10 vol.%, e.g.Brown, 2007; Petford et al., 2000).

4. Disequilibrium melting of homogeneous sources withincreasing temperature

4.1. Fluid-absent melting of a muscovite-bearing metapelitic source

Patiño Douce and Harris (1998) conducted partial melting experi-ments on metapelitic rocks from the High Himalayan Crystalline

Sequence; these rocks are considered likely sources of the MioceneHimalayan leucogranites. The experiments used a starting materialconsisting of quartz, plagioclase andmuscovite (93 vol.% of the rock) andcontaining minor amounts of garnet (≈5 vol.%) and biotite (≈2 vol.%).Fluid-absent experiments were conducted between 700 and 900 °C and0.6 to 1.0 GPa and produced melts that are identical in major elementcomposition to Himalayan leucogranites. The relevant solidus extendsfrom approximately 730 °C at 0.6 GPa to 790 °C at 1 GPa and has apositive dP/dT slope of 5 MPa/°C (Fig. 2a). The hypothetical 87Sr/86Sr ofthemelt produced in this study has been determined using the 87Sr/86Srisotopic composition and Sr content of the 200 Ma aged muscovite andplagioclase illustrated in Fig. 1, in combinationwith the stoichiometry ofthe melting reaction at different P–T conditions, as extrapolated fromTable 2 in Patiño Douce and Harris (1998). The 87Sr/86Sr of the melt ispositively correlated with the muscovite to plagioclase ratio involved inthe melting reaction. In Fig. 2b, melt 87Sr/86Sr is plotted against meltfraction: the 87Sr/86Sr of the melt increases up to a maximum at meltfraction of 16 wt.% and 23 wt.% (i.e. 800 °C and 850 °C) for the 0.6 and1.0 GPa experiments, respectively, then decreases with further plagio-clase consumption asmelting proceeds. In the 0.6 GPa experimentsmelt87Sr/86Sr increases slightly again from 850 °C (i.e. melt fraction 28 wt.%)due to a small amount of biotite entering the melt. Similar results werepresented by Zeng et al. (2005a, b) based onmodelling of disequilibriumpartial melting of a metapelitic source to explain the Sr and Nd isotopiccomposition of leucosomes from the Goat Ranch migmatite complex(California).

Thisworkdemonstrates that in a sourcewithinwhichmuscovite andplagioclase were last in Sr isotopic equilibrium 200 Ma prior to theanatectic event, muscovite dehydration melting is theoretically able togenerate temperature-related variations in the 87Sr/86Sr of the melts ofaround 0.002 (Fig. 2b), asmelting progresses fromprimarily consumingmuscovite and quartz, to consuming quartz and plagioclase.

4.2. The progression from muscovite to biotite fluid-absent melting

Experimental studies have shown that muscovite- and biotitefluid-absent melting reactions intersect at high pressure where biotitecomponents become miscible within high-pressure phengitic micas(Le Breton and Thompson, 1988; Patiño Douce and Harris, 1998;Vielzeuf and Holloway, 1988). The P–T location of this intersection is amatter of debate, with Vielzeuf and Holloway (1988) proposing apressure of 1.6 GPa at 875 °C, and Patiño Douce and Harris (1998)suggesting a pressure perhaps as low as 1 GPa (Fig. 2a). The preciselocation of this point mainly depends on the Mg-number of the biotiteand the Ti and F contents of both biotite and muscovite. However, it iswell established that at intermediate crustal depths, i.e. at pressure≤1 GPa, muscovite-fluid-absent melting will begin at lower tempera-ture than that of biotite. The experiments performed by Patiño Douceand Harris (1998) and Vielzeuf and Holloway (1988) inferred biotiteto be a product of muscovite incongruent melting under fluid absentconditions at pressure between 1 and 0.6 GPa. In contrast, Pickeringand Johnston (1998) suggested that the higher temperature portionsof the muscovite melting interval could overlap with the conditionsrequired for biotite melting (i.e. biotite and muscovite meltconcurrently) for pressures close to that of intersection betweenmuscovite and biotite fluid-absent melting reactions.

In this section we consider the progressive melting of muscovite-and biotite-bearingmetapelitic sources at 1.0 GPa, as investigated in theexperiments of Pickering and Johnston (1998). In this set of experimentsfluid-absent melting occurs initially by concurrent muscovite andbiotite breakdown and then at higher temperatures, progresses tobiotite melting. At the lowest temperature investigated (i.e. 812 °C),approximately 1–2 wt.% melt was produced via the complete break-down of muscovite (initial modal abundance of 6.7 wt.%). Theabundance of biotite, quartz and plagioclase were reduced from theirvalues in the starting material, with a corresponding increase in the

Fig. 2. a) Comparison of muscovite and biotite dehydration-melting solidi. Grey lines PH98(1) and PH98(2) are the solidi for muscovite–biotite schist and muscovite schist,respectively (Patiño Douce and Harris, 1998). The grey dashed line is the dehydration melting solidus for end-member muscovite+albite+quartz, determined by Petö (1976). Theblack lines are solidi for dehydration melting of biotite (with mg-numbers in parentheses)+plagioclase+quartz in protolith without muscovite (Patiño Douce and Beard, 1995,1996; Vielzeuf and Montel, 1994). The black dashed line is the solidus for phlogopite+quartz (Vielzeuf and Clemens, 1992). b) 87Sr/86Sr ratios of the melt as a function of degree ofmelting. The proportion of reacting phases used to calculate the87Sr/86Sr of the melt is extrapolated from Table 2 of Patiño Douce and Harris (1998).

193F. Farina, G. Stevens / Lithos 122 (2011) 189–200

alkali feldspar and aluminium silicate proportion. The biotite meltingreaction spans a temperature interval of about 160 °C (812–975 °C),over which melt fraction increased steadily to about 30 wt.%. Thehypothetical 87Sr/86Sr composition of the melts produced from theseexperiments has been calculated using the 87Sr/86Sr isotopic composi-tion and Sr content of the 200 Ma aged muscovite, biotite andplagioclase illustrated in Fig. 1, in combination with the amounts ofreactant phases consumed by themelting reaction as extrapolated fromPickering and Johnston (1998). The 87Sr/86Sr in the melt increases by0.0005 (from 0.717613 to 0.718146) as the melting reaction progressesfrommuscovite- to biotite-dominated dehydrationmelting. The paucityof consistent experimental data on thepartialmelting behaviour of two-mica metasedimentary sources does not allow this process to bemodelled in more detail. However, we suggest that in general, theprogression from muscovite to biotite dominated fluid-absent meltingwill produce an increase in the 87Sr/86Sr of the resultingmelt, due to thehighly radiogenic character of biotite with respect to muscovite (Rb/Sr≈1, low 87Sr/86Sr) and plagioclase.

4.3. Biotite fluid-absent melting

The experiments of Montel and Vielzeuf (1997) and Vielzeuf andMontel (1994) are useful in constraining the biotite fluid-absentmelting behaviour of metagreywackes. These experiments wereperformed at 0.5, 0.7, 0.8 and 1 GPa over the temperature interval800 °C to 955 °C on a natural metagreywacke composed of quartz(40 wt.%), plagioclase (32 wt.%), biotite (25 wt.%) with minor mon-azite, apatite, zircon, tourmaline and pyrite. Fig. 3a shows the P–Tconditions of the experiments and the ratio of biotite to plagioclaseconsumed in the melting reaction (data extracted from Table 9 inMontel and Vielzeuf, 1997). These data are considered particularlyreliable, as the authors applied a variety of approaches to constrainand cross-check the phase proportion calculations. The ratio of biotiteto plagioclase consumed by the melting reaction varies between 1.6and 6.5 over the P–T range considered and does not show anycorrelation with pressure. The ratio increases as the melting reactionprogresses with temperature increase, then declines towards the

point of biotite disappearance. A decrease in the biotite to plagioclaseratio consumed by the melting reaction, and hence a decrease in87Sr/86Sr as a function of increasing temperature, was predicted by theexperiments of Knesel and Davidson (1999) and observed by theseauthors for the natural Tungsten Hills glasses. The maximum biotite/plagioclase ratio is reached at 851, 913 and 874 °C for experimentsperformed at 0.5, 0.8 and 1.0 GPa, respectively (melt fractionsestimated by mass balance are 27, 34, and 29 vol.%, respectively).The variability exhibited by the stoichiometry of the melting reactionat different temperatures results in large changes in the 87Sr/86Sr ofthe resultant melt (Fig. 3b, c). The total 87Sr/86Sr variability exhibitedby the melt produced over the temperature range varies by about0.003 for a 200 Ma protolith and 0.05 for a 300 Ma protolith.

Metaluminous to slightly peraluminous granitic magmas, similarto I-type granites, may be produced by fluid-absent partial melting ofbiotite and hornblende (Skjerlie and Johnston, 1992, 1996). Although,the effect of amphibole melting has not been modelled here, someconsideration of its role in shaping the 87Sr/86Sr of such magmas ispertinent. Hornblende fluid-absent melting typically occurs at highertemperatures (N900 °C) than those required for biotite fluid-absentmelting. Additionally, hornblende is characterized by a low Rb/Sr,resulting in a minor increase in 87Sr/86Sr within hornblende throughtime. Therefore, in the type of disequilibrium melting modelled here,the effect of hornblende fluid-absent melting in a rock alreadyundergoing anatexis by biotite breakdownwould be to lower the 87Sr/86Sr of the melt significantly as temperature of melting increases,resulting in an increase in the proportion of hornblende relative tobiotite consumed by the melting reaction.

5. Disequilibrium melting of a chemically heterogeneous source

Based on the results of several sets of experiments on fluid-absentpartial melting of metasedimentary rocks at crustal pressures(Stevens et al., 1997; Vielzeuf and Holloway, 1988; Vielzeuf andMontel, 1994) it seems reasonable to assume that for the melting offertile metapelites and metapsammites, the volume of magmaproduced during anatexis does not exceed 1/3 the volume of the

Fig. 3. a) P–T diagram showing the conditions at which Vielzeuf and Montel (1994) performed their experiments (white stars) and the ratios in which biotite and plagioclase wereconsumed by the melting reaction at different P–T conditions. The dark grey line indicates the upper limit of biotite stability according to Vielzeuf and Montel (1994). b) and c) 87Sr/86Sr melt composition calculated using the stoichiometries of the melting reaction at different temperatures as extrapolated from the experiments of Montel and Vielzeuf (1997).Time since the last isotopic homogenization is 300 Ma for (b) and 200 Ma for (c).

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source (i.e. approximately 30 vol.% melt is produced at 900 °C).Consequently, a mid-sized pluton of 1000 km3 would be generated bypartial melting of a sphere of source rock with a radius of 6.2 km. Suchlarge volumes of metasedimentary rock are very likely to becompositionally variable, typically as a consequence of layeringbetween more clay-rich and more sand-rich fractions. These domainswill be characterized by different mineral proportions and probablydifferentmineral assemblages. This will result inmelt being generatedvia reactions that are subtly to significantly different betweendifferent domains. Consequently, as suggested by Clemens et al.(2009), compositional heterogeneities in granitic plutons and silicicvolcanic complexes may be produced by partial melting of compo-sitionally different domains within a single metasedimentary sourceregion. In the following section we model the Sr isotopic signature ofmelts produced by partial melting of sectors of the source character-ized by different major element compositions. This modellingassumes that the different domains in the source share the sameisotopic signature at the onset of melting. This assumption is useful indemonstrating that melts with contrasting 87Sr/86Sr composition canbe produced from an isotopically homogeneous source as a result ofmajor element controls on melting reaction stoichiometry. The morelikely case of a source characterized by domains with different major,trace element and isotopic composition has not been modelled herebecause of the enormous range of possibilities. However, this has beentaken into account in the discussion.

5.1. Effect of biotite composition on reaction stoichiometry and biotitestability

We havemodelled the 87Sr/86Sr composition of themelts formed bypartialmelting of a compositionally zonedmetagreywacke consisting ofbiotite, plagioclase and quartz. Two sets of experiments are considered.Patiño Douce and Beard (1995, 1996) performed experiments onsynthetic biotite gneisses consisting of quartz (34 wt.%), plagioclase

(27 wt.%), biotite (37 wt.%) and minor ilmenite (2 wt.%) that differedonly in the compositions of the biotite. Three different biotites wereused (Mg#=55, 3.9 wt.% TiO2; Mg#=22, 4.6 wt.% TiO2; and,Mg#=0.5, 1 wt.% TiO2). Stevens et al. (1997) investigated biotitefluid-absent melting for four synthetic metagreywacke bulk composi-tions in the temperature interval between 750 and 1000 °C and atpressures of 0.5 and 1 GPa. The bulk chemical variations considered alsoresult from differences in the biotite compositions used: three TiO2-freesynthetic biotites and one natural (TiO2=2.29 wt.%), with Mg#s of 49,62, 81, 58 respectively, were used in these experiments.

We determined the hypothetical 87Sr/86Sr of the melts using the87Sr/86Sr isotopic composition and Sr content of the 200 Ma agedbiotite and plagioclase illustrated in Fig. 1. The amounts of biotite andplagioclase consumed by the melting reaction at different P–Tconditions for the different bulk compositions have been extrapolatedfrom the modal abundances determined in the experiments. In Fig. 4,the 87Sr/86Sr of the melts, calculated from the experiments of PatiñoDouce and Beard (1995, 1996), have been plotted against the Mg#of the source. It is noteworthy that, if experiments performed at sameP–T conditions are compared, the 87Sr/86Sr of the melt and the Mg# ofthe source are positively correlated. This agrees with the observationof Patiño Douce and Beard (1995, 1996) that the amount ofplagioclase consumed in the melting reaction increases (thus thebiotite to plagioclase ratio consumed decreases) with decreasing Mg#in biotite. Moreover, the variability of the 87Sr/86Sr of the meltcalculated at different pressure and temperature conditions increasesas the bulk source Mg# increases. Therefore, sources with higher Mg#are able to generate melts characterized by more variable 87Sr/86Srcomposition as temperature increases. The experiments of Stevenset al. (1997) show that the solidus temperature increases by 25 to50 °C with increasing Mg# of the source over the bulk compositionalrange investigated (Mg# 49 to 81). The data suggest that TiO2 doesnot influence the beginning of melting but dramatically raises theupper temperature limit for the coexistence of biotite and melt (by

Fig. 4. 87Sr/86Sr melt compositions calculated at different P–T conditions for sources having contrasting Mg# composition. The amount of biotite and plagioclase consumed by themelting reaction has been extrapolated from the table reporting experimental modal abundances in Patiño Douce and Beard (1995; Table 4) and Patiño Douce and Beard (1996;Table 4). Circles and squares represent experiments performed at 0.7 and 1.0 GPa, respectively. Lines tie 87Sr/86Sr melt compositions from experiments performed at the samepressure and temperature conditions with sources having contrasting Mg#: light and dark grey lines are for the 0.7 and 1.0 GPa experiments, respectively. In diagram a) experimentsfrom both Patiño Douce and Beard (1995) and Patiño Douce and Beard (1996) are compared. The comparison is limited to experiments performed at 900–925 °C, these temperaturesare the ones that overlap between the two works. In fact, the experiments of Patiño Douce and Beard (1995) are performed at higher temperature than those of Patiño Douce andBeard (1996) due to their higher solidus temperature (Fig. 2a). In diagram b) the 87Sr/86Sr melt compositions from the two bulk source Mg# composition of Patiño Douce and Beard(1996) are compared.

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about 100 °C). As a consequence, rocks with insufficient TiO2 tosaturate the biotite in Ti, produce large pulses of melt (up to 35 wt.%)over narrow temperature ranges near the fluid-absent solidus while,with sufficient TiO2 to ensure Ti saturation in biotite, melt productionoccurs more gradually between 830 and 900 °C.

We consider the simple case of a metagreywacke consisting ofbiotite, plagioclase and quartz and with two compositional domains;one characterized by high Mg# and low TiO2 and the other by lowMg# and high TiO2. As temperature increases, the domain with lowMg# will melt first to produce a melt characterized by 87Sr/86Srcomposition lower than that produced by melting, at highertemperature, of the high Mg# sector of the protolith. In addition, atthe same peak of temperature, the low TiO2 domain will produce alarger volume of melt. Therefore, if we assume that the two domainsgenerate two distinct melt batches that segregate sequentially fromthe source and accumulate at the emplacement depth, the result willbe a magma chamber formed by an early less voluminous low 87Sr/86Sr batch then recharged by a more voluminous, higher 87Sr/86Srmagma.

6. The role of apatite dissolution

Apatite is an important Sr-bearing mineral, which commonlyoccurs as an accessory phase in metamorphic rocks of diverse bulkcomposition and grade. Apatite contains very little Rb and conse-quently has very low Rb/Sr values. Thus, 87Sr/86Sr of apatite isunaffected by 87Rb decay, and records the 87Sr/86Sr of the bulk systemat the time apatite formed (Tsuboi, 2005). Due to its small diffusion

coefficient at sub-solidus temperatures (≈1⁎10−14cm2s−1) apatiteis not likely to be reset during high temperature metamorphism andpartial melting (Cherniak and Ryerson, 1993).

Consequently, apatite dissolution will typically reduce the 87Sr/86Sr and increase the Sr content of anatectic melt, with the degree ofshift in both parameters being dependent on the amount of apatitedissolved and its Sr content. The relevance of this process for the 87Sr/86Sr variation in granites has been evaluated assuming that all the P inthe anatectic melt is derived from apatite dissolution. This assumptionallows a hypothetical maximum effect of apatite dissolution on melt87Sr/86Sr to be calculated. In fact, significant amounts of P can bereleased into the melt by monazite dissolution (Wolf and London,1995) and, to a minor extent, by zircon dissolution and feldsparmelting (e.g. London, 1992). The solubility of apatite in silicate liquidsdepends on the alumina saturation index of the melt, with apatitehaving a higher solubility in peraluminousmelts. The concentration ofSr in apatite varies widely from less than 50 ppm to about 800 ppmfor rocks ranging from highly fractionated granitoids to basalts(Belousova et al., 2002). For the purpose of evaluating the possiblerole of apatite in producing Sr isotopic shifts, we consider thedissolution of apatite with an average Sr content of 400 ppm and 87Sr/86Sr ratio equal to the assumed initial value (0.708). We assume ahypothetical maximum estimate of apatite dissolution in the melt of1 wt.%. As melt fractions are generally less that 30%, this translatesinto a maximum required modal abundance of apatite in the source inthe region of 0.33 wt.%. The dissolution of this amount of apatite,generating P2O5 content in the magma of 0.4 wt.% (apatite P2O5≈40 wt.%), produces a decrease in the calculated 87Sr/86Sr of the melt

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produced in the 1 GPa, 860 °C experiment of Montel and Vielzeuf(1997), of 3⁎10−4. Although this variation is one order of magnitudegreater than the common analytical error, it is at least one order ofmagnitude smaller than the variability generated by themain reactantphases. Therefore, we conclude that apatite has only a secondaryeffect on the 87Sr/86Sr of the melt. However, it is likely to play a moreimportant role in determining the Nd, Pb and Hf isotopic compositionof the melt.

7. Discussion

7.1. 87Sr/86Sr heterogeneity in granitic rocks

The ranges of melt 87Sr/86Sr composition produced by the differentprocesses described above are compared in Fig. 5. The model is basedon the assumption that all Sr bearing minerals in the source sharedthe same initial 87Sr/86Sr composition 200 Myr prior to the anatecticevent and thus, that the difference between the 87Sr/86Sr of micas andplagioclase at the onset of melting depends only on their character-istic initial 87Rb/86Sr ratios. All the processes taken into account areable to generate magmas with 87Sr/86Sr variability that is at least oneorder of magnitude greater than the best possible analytical error oncalculated whole rock Sr isotope ratios (i.e. ≈±0.00002). However,some processes result in magmas with an extremely large range of

Fig. 5. Comparison between melt 87Sr/86Sr compositional ranges modelled bydisequilibrium partial melting of a single source and natural data. Δ87Sr/86Sr is thedifference between maxima and minima 87Sr/86Sr values for natural data and modelledcases. Whole-rock 87Sr/86Sr variations (white bars), including the isotopic compositionof mafic microgranular enclaves dispersed into the granitoid mass, and 87Sr/86Sr zoningpreserved within feldspar crystals (light grey) are from Deniel et al. (1987), Inger andHarris (1993) and Scaillet et al. (1990) (A); Waight et al. (2000) (B); Tepley et al.(2000) (C); Knesel et al. (1999) (D); Gagnevin et al. (2004, 2005) (E); Halliday et al.(1980) (F) and Mohr (1991) (G). The modelled 87Sr/86Sr composition of melts (darkgrey) derives from: (1) muscovite dehydration melting at different P–T conditions,calculations based on the experiments of Patiño Douce and Harris (1998); (2) progres-sion from muscovite to biotite fluid-absent melting, calculations based on theexperiments of Pickering and Johnston (1998); (3) biotite dehydration melting atdifferent P–T conditions, calculations based on the experiments of Montel and Vielzeuf(1997); (4) biotite dehydration melting of a compositionally heterogeneous sourceformed by three domains having Mg# variable from 0.4 to 55. The calculation is basedon the experiments of Patiño Douce and Beard (1995, 1996). The short bar indicates theisotopic variability obtained by considering only the experiments of Patiño Douce andBeard (1996) for a source whose Mg# vary between 0.4 and 23.

87Sr/86Sr (Δ87Sr/86Sr up to 0.05), while others produce variations thatare two orders of magnitude smaller (Δ87Sr/86Sr≈0.0005). Thebroadest ranges of 87Sr/86Sr are produced by variations in the amountof biotite and plagioclase consumed in the melting reaction. Biotitethat is characterized by low Sr content and a high Rb/Sr ratio releasesminor amounts of Sr to the melt as it breaks down, but this Sr isstrongly enriched in the 87Sr isotope. Plagioclase, on the other hand,has a high Sr content and a low Rb/Sr ratio and releases relatively largeamounts of less radiogenic Sr as it melts. Thus, small variations in theproportion of these minerals undergoing melting strongly influencethe isotopic composition of the melt. These data predict a greaterdegree of Sr isotopic variability within granitoids generated by biotitemelting than those formed primarily by muscovite melting. Finally, itis interesting to consider the case of a source consisting of immaturesediments containing lithic and mineral fragments with differentages, whose isotopic composition has not been homogenised by aprevious metamorphic event. In this case the same phases could becharacterized by different 87Sr/86Sr at the onset of melting, dependingon their peculiar initial 87Rb/86Sr ratio and age. Therefore, the range of87Sr/86Sr magma compositions theoretically generated from thissource would be significantly greater than that predicted by thesimplified modelling in this study.

The range of hypothetical 87Sr/86Sr magma compositions obtainedin this study has been compared with whole-rock 87Sr/86Sr and 87Sr/86Sr zoning preserved within feldspar crystals (Fig. 5), from studies ofplutonic and volcanic granitoid rocks of different ages and geologicalsettings (Deniel et al., 1987; Gagnevin et al., 2005; Halliday et al.,1980; Inger and Harris, 1993; Knesel et al., 1999; Mohr, 1991; Scailletet al., 1990; Tepley et al., 2000;Waight et al., 2000). The broadest 87Sr/86Sr variations (≈0.02–0.03) characterize Himalayan leucogranites(Fig. 5A). These rocks are interpreted to form by muscovitedehydration melting and to represent magmas that were nearlypure melt (Patiño Douce and Harris, 1998). The other rocks in Fig. 5show a significant but more limited range of variation (b0.01) andinclude rhyolites (Knesel et al., 1999), trachyandesites (Tepley et al.,2000), zoned plutons with composition varying between diorite–granodiorite to granite (Halliday et al., 1980; Mohr, 1991) andmonzogranites hostingmicrogranular enclaves (Gagnevin et al., 2005;Waight et al., 2000). In addition, large 87Sr/86Sr variations arepreserved at the mineral-scale (Fig. 5B, C, D, E) in rocks showingfield and textural evidence interpreted to suggest a contribution ofmantle-derived magmas (Gagnevin et al., 2005; Knesel et al., 1999;Waight et al., 2000) or crustal contamination (Tepley et al., 2000) intheir genesis.

The predicted 87Sr/86Sr ranges in the magmas produced by themodelling presented in this work are typically similar to, or greaterthan, that commonly recorded in granitoid rocks. The reasons whygranitoid systems show a more restricted Sr isotopic range than thatmodelled here are likely to be three-fold. Firstly, partial isotopicequilibration in the source during heating will reduce the 87Sr/86Srgap between the different phases at the onset of melting, thus limitingthe ability of the source to producemagmas with contrasting 87Sr/86Srsignatures. Secondly, some granite magmas may be produced bymelting of relatively young volcaniclastic sequences. In this case, thetime between the crystallization of the minerals in the source andanatexis may be considerably shorter than that used in this modelling(i.e. 200 Myr). Thirdly, magmatic processes such as melt residency inthe source as melt volume grows, as well as magma mixing duringascent and at emplacement level, will homogenise the isotopicdiversity inherent to the different batches of melt as they form.

7.2. The Rb and Sr compositions of the modelled melts

In the modelling presented above the proportion of mica relativeto plagioclase consumed by the melting reaction not only controls the87Sr/86Sr signature of the magma, but also its Rb and Sr compositions,

Fig. 6. a) Sr versus Rb diagram showing the composition of modelledmelts and selectedgranitoid rocks. Granitoid rocks and modelled melts plotted are those of Fig. 5.Abbreviations for the experiments used are: PD&H '98 — Patiño Douce and Harris(1998); M&V '97 — Montel and Vielzeuf (1997); P&J '98 — Pickering and Johnston(1998); PD&B '95 — Patiño Douce and Beard (1995); PD&B '96 (Mg#0.4) and PD&B '96(Mg#23) — Patiño Douce and Beard (1996) experiments with a source having biotiteMg#=0.4 and 23, respectively. b) 87Sr/86Sr versus Rb/Sr diagram. Granitoid rocks arethose of Fig. 5. The two lines (Bt and Ms fluid-absent) are produced by the model usingexperimental data for muscovite and biotite fluid-absent melting.

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with an increase in mica proportion generating enrichment in Rb anddepletion in Sr. In Fig. 6a the Rb and Sr compositions of granitic rocksare compared with those of the modelled magma compositions. Thecomposition of modelled melts matches well with that of granitoidrocks but two main differences can be observed: i) many Himalayanleucogranites have higher Rb and lower Sr than the modelled melts;and ii) some samples of the Doon and the Criffell plutons (Hallidayet al., 1980) have Sr content up to twice that of the modelled melts.Although theoretically the reason for such differences can be thespecific Rb and Sr compositions of micas and plagioclase assumed inthe model (Fig. 1), other explanations are likely. Foremost amongst

these is that these rocks arose via melting reactions with stoichiom-etry significantly different to that used in the modelling. For example,the high Rb/Sr exhibited by most of the Himalayan leucogranites islikely to be the result of a higher mica to plagioclase ratio in themelting reaction, while the high Sr content of some of the samplesfrom the Doon and the Criffell plutons may be the result of fluid-absent melting of hornblende and plagioclase dominated rocks, or theeffect of plagioclase accumulation at the emplacement level. Inaddition, in many cases high MgO, CaO and Sr contents in graniticrocks are associated with field (the occurrence of mafic microgranularenclaves) and textural (e.g. disequilibrium features in feldspars)evidence interpreted to reflect the involvement of mantle-derivedmagmas in the genesis of these rocks.

The modelling presented here is intended to investigate topotential role of disequilibrium melting in producing Sr-isotopiccompositional variation in magmas. For this reason, the Rb, Sr and87Sr/86Sr compositions of muscovite, biotite and plagioclase have beenkept constant (Fig. 1). A consequence of this is that the modelinherently produces positive linear correlations between Rb/Sr and87Sr/86Sr for muscovite and biotite fluid-absent melting (Fig. 6b). Theslope of these lines in the Rb/Sr vs 87Sr/86Sr space depends on theinitial Rb/Sr of the micas and plagioclase, as well as on the timeelapsed since t0 (i.e. at t0 the different phases shared the same 87Sr/86Sr). Although a rough positive correlation exists between 87Sr/86Srand Rb/Sr in many granitic rocks, this correlation is not linear(Fig. 6b). The reasons for this are that the assumptions that arerequired to make the modelling simple and coherent, do not applysource rock volumes appropriate to the generation of granitoid rocks.Metasedimentary andmetavolcanic sources are layered and consist ofdomains characterized by minerals that had different Rb, Sr and 87Sr/86Sr composition at the onset of metamorphism. Secondarily, otherprocesses such asmixingwithmantle-derivedmagmas (e.g. Gagnevinet al., 2005; Waight et al., 2000) and crustal contamination (e.g.Charlier et al., 2007) may contribute to change the Rb, Sr and isotopiccomposition of granitic rocks while fractional crystallization of biotiteor plagioclase can modify the Rb/Sr ratio of the system withoutchanging the 87Sr/86Sr signature of the magma. Finally, the role of K-feldspar in the protolithmay also be relevant.When alkali feldspar is areactant in the melting reaction it contributes to the Rb, Sr and 87Sr/86Sr composition of the melt while when it occurs as peritecticproduct of anatexis it incorporates part of the Rb and Sr budget freedby the melting reaction. In the case of muscovite- and biotite-bearingsources it is possible for K-feldspar to switch, as the temperatureincreases, from being produced during muscovite fluid-absentmelting to be consumed during biotite dehydration melting.

7.3. Disequilibrium melting in different tectonic settings

Fluid-absent melting occurs over a range of temperaturesbeginning with muscovite breakdown under upper amphibolites-facies conditions and extending through the granulite facies withbiotite and hornblende breakdown in metasedimentary and metaba-saltic protoliths, respectively (Fig.2). The geotherm in stable conti-nental crust is estimated to produce temperatures of about 500 °C atthe level of a 35 kmmoho (gradient of about 15 °C/km, e.g. Thompsonand Connolly, 1995) and, thus crustal anatexis requires anomalouslyhigh temperatures within the continental crust. The rate of meltingduring anatectic events is generally controlled by the rate of heatsupply and therefore depends on the rate at which temperatureincreases with time. Metamorphism in different tectonics environ-ments is characterized by strongly different prograde heating rates. Apositive thermal perturbation able to reach fluid-absent meltingtemperatures may be generated by crustal thickening duringcontinental collision followed by erosional exhumation and/orextensional thinning and/or lithospheric delamination and orogeniccollapse (Thompson and Connolly, 1995). For convergent orogens the

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heating rates are estimated to be in the order of 10–50 °C/Ma(Thompson and Connolly, 1995), which can be enhanced if the crust isrich in radiogenic elements (i.e. in the presence of a highly radioactivecrustal layer) and in the case of shear heating on major crustal shearzones (Nabelek and Liu, 2004). Alternatively, the heat required forcrustal anatexis may be provided by the underplating and/orintraplating of mantle-derived magma (Annen et al., 2006) incontinental arcs or by an enhanced mantle heat flux throughdetachment of the lower (mantle) lithosphere to be replaced byhotter asthenosphere. Advective heating by intruded basaltic magmascauses heating rates between about 100 °C/Ma and up to more than1000 °C/Ma depending on basalt emplacement rate, emplacementdepth and composition (Annen et al., 2006). These data suggest thatdisequilibrium melting of the type proposed in this study is mostlikely to prevail in cases where the thermal perturbation drivingmetamorphism is produced by the intrusion of mantle-derivedmagmas (e.g. subduction-related intermediate to silicic magmatism).Evidence such as thewidespread occurrence of enclaves of moremaficcomposition (commonly of intermediate silica content) dispersedinto the granitoid mass and the occurrence of disequilibrium texturalfeatures in feldspars, are interpreted to indicate periodic recharge ofthe anatectic system with mantle-derived magmas (Gagnevin et al.,2005; Knesel et al., 1999; Waight et al., 2000) and if this is correct,may indicate rocks derived from sources that have heated quicklythrough proximity with basaltic magmas. 87Sr/86Sr diversity in suchrocks is almost universally interpreted to reflect this mixing process.However, this would appear to ignore the fact that the crustallyderived melts produced in this scenario are of those most likely tohave arisen by disequilibrium melting of the type discussed here andtherefore to be isotopically variable, even if a homogenous sourceexisted.

The broadest 87Sr/86Sr variation in Fig. 5 characterizes leucogra-nites formed in a collisional setting (i.e. Himalayan leucogranites). Inthis instance, disequilibrium partial melting has been concluded to beunlikely and there are no indications of mixing with a mantle-derivedcomponent. Harris and Ayres (1998) have investigated the possibilityof Sr-isotope disequilibrium in the genesis of the extreme 87Sr/86Srvariability of Himalayan leucogranites. These authors, on the basis ofsemi-quantitative information on the rate at which the Himalayangranite protoliths have been heated obtained by studying garnetdiffusion profiles from pelitic metasediments (i.e. 15–25 °C/Ma),concluded that, while disequilibrium can be detected for 143Nd/144Nd between melts and their sources (Ayres and Harris, 1997), therate of prograde metamorphism is too slow to preserve Sr-isotopicdisequilibrium in the source. Therefore, these leucogranites form byincremental assembly of relatively small pods of anatecticmelt mainlyproduced by muscovite fluid-absent melting (Patiño Douce andHarris, 1998) within an isotopically heterogeneous source. Thisimplies that the different batches of magma assembled to formleucogranites are generated from isotopically distinct volumes withinthe protolith and do not efficiently mix during ascent oremplacement.

We suggest that 87Sr/86Sr diversity is likely to be an inherentcharacteristic of crustally derived magma, its existence simply reflectsthe fact that the source volumes involved in granitoid magmaproduction are not isotopically homogenous. In this study we havemodelled the extreme case of source rocks isotopically heterogeneousat the mineral-scale (i.e. disequilibrium partial melting). However,isotopic heterogeneity can also be preserved at a larger scale in thecase of a layered source where inter-layer complete equilibration atthe mineral-scale has been reached during heating in the pre-anatectic metamorphic event but where isotopic variations are stillpreserved between the different layers. Operation of the mineral scaledisequilibrium melting requires fast heating, while that at the layerscale is probably unavoidable in all reasonable scenarios of crustalmelting.

8. Conclusions

The large range of hypothetical melt 87Sr/86Sr compositionspredicted by the modelling conducted in this study providesimportant new insights on the origin of 87Sr/86Sr heterogeneities ingranitic plutons and silicic volcanic complexes. The metamorphicrecord predicts that Sr isotopic disequilibrium may be unavoidableduring partial melting. Thus, it would appear reasonable to suggestthat investigations into Sr isotopic variability within magmasgenerated by crustal melting should always consider the isotopicvariability that could arise from the crustal source rather thanpresuming that this automatically constitutes evidence of mixingwith mantle-derived mafic to intermediate magmas or assimilation ofthe host rock. We argue that the common occurrence of maficenclaves within granitoids does not necessary imply that the origin of87Sr/86Sr heterogeneities is related to chemical interaction betweenmantle- and crustal-derived magmas. In fact, strong whole rock Srisotopic variations have been detected also for granitic rocks that donot show any petrographic evidence of interaction with mantle-derived magmas (e.g. Deniel et al., 1987).

In summary, the results of this study indicate that if sufficient timehas elapsed since initial isotopic equilibration for constituent phasesin the protolith to evolve distinct ratios, and if isotopic equilibrium isnot attained in the source region prior to and during melt generationand magma extraction, then melts characterized by variable Srisotopic signatures will inevitably be formed. This may occur from asingle, major element homogenous source via changes to thestoichiometry of the melting reaction as melting progresses, or itmay occur via changes to melting reaction stoichiometry induced bydifferent major element bulk compositional domains within anisotopically identical source. In general, as the mica to plagioclaseratio consumed by the melting reaction increases the 87Sr/86Sr of themelt will increase. Thus, any factor that changes this ratio will inducea shift in the isotopic composition of the melt generated.

The model developed here appears to present a valid case forconsidering isotopic variability exhibited by typical granitoid suitesand individual plutons at different scales as a primary and sourceinherited characteristic. This conclusion is in agreement with thework by Clemens et al. (2009) who used a variety of lines of evidenceto conclude that much of the geochemical variation in suites of silicicigneous rocks is inherited from the magma source region. Thispossibility is not commonly considered in interpretations of Srisotopic heterogeneity in such systems. This may be due to the factthat detailed information about the source areas for granitoid rocks istypically unavailable. However, all that we know about sedimentaryand volcano-sedimentary successions and their isotopic behaviourduring high heat flux metamorphism suggests that melting of severalcubic kilometres of major element and isotopically equilibratedmaterial would be an extremely unlikely occurrence. Despite this,this assumption is made in many studies of granitoid rocks.

Acknowledgements

The authors thank John Clemens for providing a helpful informalreview of the manuscript and gratefully acknowledge support fromthe NRF through SARChI funding to GS. The authors thank T. Waightand an anonymous reviewer for their helpful and constructivereviews which greatly improved this work.

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