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Major and trace elements models of granitic melts as a function of PT conditions: reconciling experimental/thermodynamic data and trace elements geochemistry. Jean-François Moyen1,* 1- Department of geology, university of Stellenbosch. Private Bag X-01, Matieland 7602, South Africa. * Corresponding author. [email protected] Abstract Geochemical models of crustal melting generating granitic melt is hampered by the following limitations: (1) major and trace elements are largely disconnected; (2) the variations due to the changes in P-T conditions are difficult to take into account; (3) the role of accessory minerals, with high partition coefficients for some elements, is seldom modeled. Here, we propose an improved model addressing these three issues; it is based on thermodynamical modeling of partially molten rock (pseudosections) and extraction of melt major elements and modal proportions from the pseudosection. The modal proportion are then used to calculate the melt trace elements contents, taking into account the solubility of accessory minerals. The predicted compositions are compared with experimental melts and natural granites; there is a reasonable fit for major elements with experiments, but the lack of data for trace elements hinders further comparison. For real granites, a large part of natural rocks have compositions that do not match the pure melts, suggesting that a granite can not be simply equated to a silicate melt but also contains other components.

1.

Introduction

Trace elements modeling is a valuable tool in igneous petrology[1-3], that is widely used to discuss the source and evolution of magmatic rocks. Granitic rocks are generally modeled primarily in term of partial melting of a source rock, as fractional crystallization is often regarded to play only a minor role in high-viscosity magmas. Classical melting models are used to test hypothesis on the sources and melting processes, by calculating the trace elements content of a melt generated from a source of known trace elements characteristics, and equilibrated with a solid residuum of known modal composition; the resulting model is then compared to the studied rocks. While powerful and generally giving good results, this approach has several shortcomings: 1. The models are “unaware” of the P-T conditions of melting. Indeed, in most or all such models, the modal composition of the restite is either assumed, or constrained by mass balance, by “substracting” the melt composition from the source rock; the restite composition is then recalculated in terms of mineral proportions. This approach, however, needs to make assumptions on the mineral chemistry of the restitic phases –yet, mineral compositions do show a large diversity, as a function of the system’s bulk composition, and of the P-T conditions. In addition, geochemical models more or less implicitely use a fixed composition restite over a large range of melt fractions; yet, variations of melt fractions within a given system do correspond to variations of the P-T

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conditions, which in turn must imply changes in the mineral chemistry and/or assemblage of the restite. 2. Major and trace elements systematics are decoupled. Since the major elements composition of the restite is a function of P, T and melt fraction, it is not easy to model using a reasonably simple set of equations. In contrast, the trace elements behaviour is largely independent of the details of the mineral chemistry; therefore, trace elements are far easier to model, and most geochemical studies are restricted to them. These two first points effectively result in the study of granite geochemistry to be split in two largely disconnected approaches, with no common ground: geochemist discuss the trace element evolution of the melts, with no reference to P-T conditions and few insights on major elements composition, while experimental petrologists describe the major elements composition of the melts as a function of P-T conditions. 3. Accessory minerals are poorly, if at all, taken into account. When trace elements become abundant, typically in crustal melts, they tend to form mineral phases of their own, such as zircon, monazite or allanite. This strongly complicates trace elements modeling, since elements such as Zr do not behave as trace elements relative to these phases, and the classical approach based on partition coefficients (Kd) can not be used to model the trace element behaviour in this case. Furthermore, even a small amount of these minerals will dramatically affect the trace elements balance of the melt: 0.1 wt% of zircon, for instance, would contain the equivalent of 500 ppm of Zr in the melt, more than the typical Zr content in a granite! Classically, accessory minerals are treated in a more or less empirical way in geochemical models, by arbitrarily adding minute amounts of these phases in the residuum and using approximate Kd. This is, however, not a completely satisfactory approach –especially bearing in mind that the solubility of accessory phases in granitic melts is a function of T and melt major elements chemistry [4-6], providing a strong link between P-T conditions and trace elements, on one hand, and major and trace elements, on the other hand; this link is seldom taken into account in trace elements models. The aim of this work is to try and address the above-mentionned shortcomings, and to propose a model able to predict the major and trace elements composition of a granitic melt, formed from a source of given (major and trace) composition, as a function of the P-T conditions. Here, we’re working with S-type melts (partial melts of metasediments, at P < 10 kbar) as a “proof of concept”, because they represent the compositions for which the most comprehensive dataset is available. Nevertheless, we strongly contend that, in principle, this approach is of more general application and can be used, with appropriate modifications, to magmatic rocks in general –provided their composition is mostly related to melting processes, and not to further evolution (mixing, fractionation).

2.

Construction of the model

The approach proposed here is able to calculate trace elements contents in a melt, given the modal proportions of the system, the major elements composition of the

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melt and the trace elements content in the source. It can, therefore, be applied to a variety of case; for instance, it could be applied to “raw” experimental data, using the modal proportions and the glass analysis of a charge at the end of a run. It can also be applied to interpolated experimental data over the P-T space, as was done in [7]. In this paper, however, I choose a slightly different route; the modal and major elements data are modeled from the thermodynamical properties of melt and minerals. While slightly less directly constrained than simple experimental data, this approach has shown to give results consistent with observations [8-10] , which is expected since the thermodynamical database of Holland and Powell [8] used here is calibrated with experimental data. It also has the great advantage to be completely independent from the published experiments, allowing to investigate a large range both of starting compositions and of P-T conditions. 2.1.

Modal proportions and melt major elements

The repartition of major elements in metamorphic (and partially molten) rocks is controlled by the thermodynamical properties of the mineral (and melt) phases. For a given bulk composition, it is possible to build a “pseudosection” showing the stable mineral (s.l.) phases in the P-T space, together with their composition. This model needs (1) numerical routines making these calculations, generally by minimization of Gibbs free energy; (2) a database of mineral and melts thermodynamical properties. 2.1.1. Construction of pseudosections In this study, the program used is “PERPLE_X” [11, 12]. PERPLE_X uses grided minimization on a regularly spaced grid, and allows the extraction of modal compositions and mineral chemistry on a P-T grid. Several mineral databases can be used, depending on the system to be modeled; a large number of mineral models are indeed supplied with PERPLE_X. Here, I’m focusing on the melting of metasedimentary lithologies, and therefore decided to use the database of [8]. The melt model is from Holland et al. [9], expanded by White et al. [10]. It is technically applicable only to leucocratic melts, but this is a reasonable approximation over most of the realistic P-T conditions for crustal melting [13]. This stage of the model is the most critical; indeed, the choice of the mineral and melt models will completely define both the melt major elements composition, and the mineral modal proportions, which have the bigger impact on the melt trace elements contents. Calculations have been made in the Na2O-K2O-CaO-Al2O3-FeO-MgO-SiO2H2O system, for which good thermodynamic models exist; this means that MnO, P2O5 and TiO2 are not modeled. This is not critical for MnO (which substitutes nearly perfectely for Fe). It is a minor problem for P2O5, since phosphates are high-Kd phases for trace elements, but this is largely dealt with the further incorporation of monazite and xenotime solubility in the model. It is potentially a major issue for TiO2, because Ti is known to impact biotite stability [14]; therefore, both the melt proportions and the melt major elements contents might be flawed. In addition, ilmenite have relatively high partition coefficients for a number of trace elements, and needs to be at least partially taken into account. Therefore, I adopted the procedure outlined in the following paragraph to estimate the ilmenite amount in the residuum.

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2.1.2. Corrections for Ti- and Ti-bearing minerals Since Ti-bearing phases can play a significant role, but are only poorly accounted for in the thermodynamical mineral model, it was necessary to device a correction for estimating the Ti contents. This was done by a simple mass balance, considering three possible “sinks” for TiO2 in the studied system: the melt (but only a limited amount of titanium can be dissolved in the melt, as evidenced by the low TiO2 values of experimental glasses [14]); the biotite (whose TiO2 content can vary from 1 to 4 %, and was here taken as 2 %, which seems to be a reasonable value in experimental biotites derived from common metasedimentary sources [14-19]); and Ti-oxydes (equated to ilmenite for simplicity, although other titaniferous minerals can occur). Experiments (listed previously) have shown ilmenite to be stable up to ca. 1050 °C. Above that temperature (which, in metasediments, is well above the biotite-out), the TiO2 resides completely in the melt. Below that temperature, the TiO2 contents in the melt was considered to be controlled by a solubility equation, which was taken as TiO2 = (77 − SiO2 ) × 0.05 (eq. 1) This equation corresponds to the best fit line of natural leucogranites and experimental melts together in SiO2 vs. TiO2 binary diagrams. When ilmenite is stable, the following procedure was therefore followed: (1) the amount of TiO2 present in the biotite is calculated; (2) The “pseudo-Ti saturation” of the melt is computed from equation (1); (3) If the remaining TiO2 (after Biotite was formed) excesses this value, the excess titanium is used to build ilmenite; if not, the melt is undersaturated in titanium and no ilmenite is formed (this situation is never or rarely seen with normal lithologies).

2.2.

Trace elements contents of the melt

The trace elements part of the model largely draws on the inspirational work of Montel [20] , whose procedure is largely followed. The melt’s trace element contents depends, in theory, on the melt fraction, the modal proportions of the restitic minerals, and the mineral-melt partition coefficients [1, 21] , and equation such as Shaw’s [21] can be used: Cl 1 (eq. 2) = C 0 F + D.(1 − F )

where Cl is the composition in the liquid, C0 in the source; D the bulk repartition coefficient and F the melt fraction [22]. D is D = ∑KDi Xi (eq. 3) i

(with Xi: proportion of mineral i in the residue; Kdi: partition coefficient of an element between melt and mineral i). This equation is convenient to use, because it relies solely on the knowledge of the mineral proportions in the solid restite, and is independent of any other considerations (stoechiometry of the melting reaction, initial mineral proportions, etc.). However, it implies complete equilibrium between the melt and the restite, and is applicable only

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in that case. Since this is already the assumption made for pseudosection calculation, anyway, this equation was used. It must be pointed out that, despite the fact that solid-melt equilibrium is probably an approximation for natural systems, it gives reasonably good results, probably owing to the following reasons: (1) during crustal melting, slow heating and restricted heat availability result in long residence time before extraction, making equilibrium or near-equilibrium feasible; (2) other equations in existence for modeling trace elements during melting do not hugely depart from the values predicted by Shaw’s equation, except for small melt fractions[1, 2]. Here however, the typical melt fractions are 2050 %, and at these values the choice of the melting equation is largely irrelevant. However, things are slightly more complicated for crustal melts, because of the potential presence of accessory phases such as zircon (ZrSiO4), monazite ([LREE,Th]PO4) or xenotime ([HREE,Y]PO4 ) in the restite. These minerals do have “trace” elements in their formula, and, as outlined in the introduction, cannot be modeled using the Kd-based approach. Common practice is to treat them empirically –by using “pseudo-partition coefficients” and adding, by trial and error, “appropriate” amounts of them in the residuum to arrive to realistic melt compositions. There is, however, a more correct approach, based on the solubility of accessory phases in granitic melts. Experimental studies [4-6] show that only a limited amount of accessory minerals can be dissolved in granitic melts (depending on the temperature and the chemistry of the melt). Therefore, it is possible to calculate a melt composition (without accessories); check it against the saturation value for the relevant minerals; and ascribe the excess trace element to the accessory phase. 2.3.

Accessory minerals solubility equations

Mineralogical studies in granites show that two main associations of accessory minerals are represented [23] : zircon, apatite, monazite and xenotime in S-type granites, and zircon, apatite, sphene and allanite in I-types. In this study, focusing on S-type melts, we consider zircon, monazite and xenotime; apatite is left apart, because of the relatively low amounts of P2O5 in crustal rocks, and the high solubility of apatite in aluminous melts [5] . Furthermore, apatite has partition coefficients for REE which are orders of magnitude below the monazite’s and xenotime’s coefficients [20] , and therefore is likely to have a comparatively minor role. The following minerals models have been used, following [20] : - For zircon, the model used is from [6] , with a modification: both Zr and Hf are used to build zircon. Zr and Hf are assumed not to be fractionated during zircon formation, i.e. (Zr/Hf)zircon = (Zr/Hf)melt = (Zr/Hf)total. - Monazite is modeled after [4] , with Th being also used to build monazite; a term W/R of -572 K [20]is used to model the Th fractionation into monazite. - No model is published for xenotime; as suggested by [20] , we used the same model as for monazite, forming xenotime from HREE (Tb, Dy, Er, Yb, Lu) and Y, without any frctionnation between these elements. Xenotime is actually seldom if at all needed in the model, because HREE contents, being generally one to two orders of magnitude lower than LREE contents, are commonly to low to allow xenotime formation. The use of this rather poorly constrained model is therefore not problematic.

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2.4.

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Calculation procedure

Again following [20] , the following procedure is used for each node of the P-T grid (Figure 1): (1) An initial estimation of trace elements contents (without accessories) is calculated from the pseudosection-predicted modal proportions, and a set of partition coefficients. I used the internally consistent set of [20] , which has been developed precisely for this application, and has the advantage to give consistent values for all elements and all minerals, whereas most published Kd sets (see review in [22]) are generally only partial, addressing either a restricted set of elements or a limited number of minerals. (2) For each accessory mineral, a saturation value is calculated from the equations described above. If the melt content exceeds the saturation value, the excess concentration is ascribed to the appropriate accessory phase (zircon for Zr and Hf, monazite for LREE and Th, xenotime for HREE and Y). (3) The accessory minerals are now included in the modal composition, and this corrected composition is used to recalculate a melt trace element composition; the procedure is followed again from step 1 onwards until the models converges to a stable value (typically 5-30 iterations). This recursive procedure is needed, because accessory phases have high partition coefficients for trace elements other than the one used to build them, and therefore do affect the melt contents in other elements. (4) When the model has reached a stable value, the final accessory proportions and trace elements contents are extracted. Trace elements not constituting an accessory phase in themselves (LILE, HFSE, transition metals) are calculated from the modal proportions as in step 1. For trace elements constituting an accessory mineral, the final composition is either the saturation value calculated in step 2, or the value evaluated in step 1 –whichever is lowest. Practically, the model is developed using Microsoft Excel; the recursive stage is treated using the “iteration” function1. The resulting file is a large (ca. 50 Mo for a 50x50 grid!) file; iterative calculations when changing a sensitive parameter (e.g. LREE or HREE content of the source) takes several minutes on a modern computer. Data is outputted in a dedicated sheet, that can be then used for graphical representation; in this case, it was exported to R/GCDkit[24].

3.

Comparison between numerical model and experimental melt

A check of the validity of the model can be obtained by calculating the melts theoretically produced from a source with the same composition as those used in experimental studies. Here, 7 source materials were used (Table 1). Unfortunately, no 1

Tools>options>calculation ; checkbox « iteration ».

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trace element data exist for experimental melts from metasediments, and therefore this comparison is limited to major elements. Melt fractions (F) predicted by the model match very satisfactorily the experimental F values (Figure 2), regardless of the source composition. This outlines the strong control exerted by the amount of water present in the system, and the water solubility in the melts, on the melt fraction, and is very adequately predicted by the melt model [9, 10] Major elements systematic of the modeled melts mimics reasonably well the experimental data. All liquids (experimental and modeled) are strongly leucocratic and peraluminous (Figure 3a),. The K/Na ratios are more variable, reflecting the source’s ratios. For a given source however, there is reasonable agreement between models and experimental liquids (Figure 3b). Individual element compositions (at 10 kbar) were investigated for two contrasted sources: a pelitic source (Carino gneisses[15] ) and a grauwacky source (CEV[25]). Elements variations as a function of T show common features for both lithologies. The model is able to adequately predict the absolute amounts of some elements (H2O, SiO2, CaO, Na2O, K2O) ; even more significantly, it is able to reproduce their evolution with increasing temperature. FeO, MgO and TiO2 are in good, but not excellent, agreement. For Ti, this outlines the unsatisfactory nature of our saturation estimates, and the need for thermodynamical mineral and melts models in systems including Ti. The imperfect fit for iron and magnesium is not unexpected, since the model is specifically built for leucocratic melts –which the experimental glasses aren’t, featuring 3-7 wt% FeO+MgO. Actually, the result is better than could be expected (or feared). Finally, surprisingly enough, the model predicts rather poorly the Al2O3 contents in the melts, especially in the grauwacky system. This probably has to do with the problem with the biotite model, outlined below. It is also worth noting that the model worsens with increasing temperature; again, this is not surprising, since the White et al. [10] model is explicitly designed to deal with leucocratic, relatively low temperature, melts. The match for the phase boundaries is more difficult to check; indeed, experimental studies commonly focus on a relatively small temperature window, in which no or few phase boundaries are encountered. Whenever a comparison is possible, the phase boundaries modeled match only poorly the experimental limits, with differences of commonly > 100 °C. The numerical model (based on the database of [8] ) under-estimates biotite stability, which it predicts to disappear between 760 and 840 °C at 10 kbar, whereas the observed boundary is at 820-975 °C (and even more for some orthogneissic assemblage made of biotite-plagioclase-quartz, [26]). Garnet stability is overestimated, with the garnet-out line being predicted at 1100-1150 °C, and observed at 975-1100 °C (at 10 kbar). Yet, 975 °C is already a quite extreme value for geological conditions, and it is likely that little or no granitic melts are really generated above this temperature. Therefore, all natural granites must coexist with garnet, and this is predicted by the model regardless of the actual position of the garnet-out boundary. Plagioclase is predicted to be stable up to 1000-1050 °C, but its

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disappeance is rarely observed in experimental charges, generally not investigating this sort of temperatures. In amphibolites [7], plagioclase is stable up to 1100 °C in fluid absent system; the predicted value might therefore not be too far of the mark. The sillimanite stability is correctely modeled, when it’s present, probably owing to the better knowledge of the thermodynamical properties of aluminosilicates [27] . Consequently, the observed discrepancies do probably not greatly impact the melt model (except for Al2O3); this is in agreement with the above observations on major elements melt composition. This suggests that the less well constrained component in the database [8-10] is not the melt model, but rather the model for some of the solid phases, biotite especially. This may comes from the fact that the melt compositions in pelitic systems do not show large variations, and are close to eutectic compositions (at least for temperatures not too extreme); melt compositions are therefore well constrained. Melt fractions are also constrained by the amount of water in the system; this implies that the bulk composition of the restite is approximately correct, but the model « chooses » an incorrect mineral assemblage to accommodate it in the restite,.

4.

Controls on the melt chemistry 4.1.

Influence of the major elements composition of the source

As stated above, the difference in major elements compositions between liquids from different sources resides mostly in their K-Na-Ca systematics, which reflects the source’s composition. In terms of trace elements, for which no experimental data exist, some scatter does appear, as a function of the source. Fig. 5 shows the modeled composition, using different sources, and comparing solely melts formed between 800 and 900 °C and 7 and 10 kbar, i.e. melts formed by biotite fluid-absent melting in lower-crust conditions, the most likely setting for S-types formation. The source composition affects the REE pattern in two ways : (1) the HREE (Yb, Y, and therefore La/Yb) content of the melts is controlled mostly by the amount of garnet in the residuum. Garnet being a product of the biotite incongruent melting reaction, it is more abundant in melts from a « pelitic » source, i.e. one with high Al2O3 contents ; (2) the presence, or absence, of an Eu anomaly is controlled by the plagioclase amount in the residuum ; it turns out to be controlled by the initial plagioclase :K-feldspar content of the source, or its Ca+Na/K ratio. It is worth noting that, at these temperatures, monazite is normally not stable ; therefore, it plays no role in REE systematic. Based on REE distribution, two groups of models appear : the liquids derived from « pelitic » sources ( the Carino gneiss from Vielzeuf and Holloway [15] and the muscovite schist MS from Patiño-Douce and Harris [18]) display poorly fractionated REE patters with a pronounced Eu anomaly ; the « greywacke » sources (CEV from

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Montel and Vielzeuf [25], MBS from Patiño-Douce and Harris [18] and HQ-36 from Patiño-Douce and Johnston [16]), in contrast, produce a strongly fractionated REE pattern with no Eu anomaly. The source HP from Pickering and Johnston [19] is somehow intermediate, with a poorly fractionated REE pattern but no Eu anomaly, corresponding to its intermediate composition, both Al rich but with low Na+Ca/K ratio. Other trace elements show very little source-induced variations ; the differences observed between different (modelled) melts mostly relate to increasing melt fractions. 4.2.

Influence of the trace elements concentration of the source

The trace elements contents of the source does control the melt’s concentrations, as could be expected. However, for the accessory mineral controlled elements, this effect is somehow compensated by the role of accessory phases, that buffer the melt’s compositions. At temperatures where monazite and zircon are stable, the melts compositions are effectively just a product of the accessory solubility, and are independent of the source. At higher temperatures however, the source effect becomes important and the melt composition becomes controlled by source contents. The implication of this observation should, however, not be overestimated. Indeed, the variations due to increasing F (and T) values for a given source are of the same order of magnitude than the source-induced variations. In addition, it is worth stressing than, in particular for REE, a variation of a factor 2 to 5 is not very significative, most rocks suites showing more inter-sample diversity than that! The typical “interpretable” variations are of one order of magnitude or more, as emphasized by the use of logarithmic scales for the construction of REE diagrams. 4.3.

Controls on the melt trace elements contents: major minerals

As pointed in the above discussion, the main control on the melt’s chemistry is the nature of the solid residuum equilibrating with it. In general, for one single element, one phase with high partition coefficient plays a major role, whereas the other minerals are subordinate (Figure 7). This is, for instance, the case for Rb, whose repartition is controlled mostly by biotite, with a sudden increase in Rb contents on the biotite-out line (Figure 7a). Likewise, Sr is controlled by the progressive breakdown of plagioclase (Figure 7b); the relatively progressive nature of plagioclase destruction (the albitic end-member being progressively incoroporated in the melt, while the remaining plagioclase becomes increasingly calcic [28, 29] ) results in a smooth augmentation of Sr contents with temperature. Yb shows a slightly more complicated pattern (Figure 7h). It is controlled by garnet abundance, and the garnet-out line corresponds to a steep increase in Yb contents (1100°c at 10 kbar). However, an other less important “step” is observed at a lower temperature (900°C at 10 kbar), corresponding to the moment where the garnet abundance starts decreasing –i.e., the moment where the melting reaction changes, and the peritectic products of the early, relatively low temperature reactions are in

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turn incorporated in the melt. This transition is also observed for La (Figure 7f) and, to a lesser degree, Zr (Figure 7d); for these elements, a slight decrease of the contents is observed, corresponding to the incorporation in the melt of La- and Zr- poor pahses (garnet and orthopyroxene), effectively diluting these elements in the melt. 4.4.

Controls on the melt trace elements content: accessory minerals

As predicted, the accessory phases play a very significant role for the elements that they accommodate: monazite for the LREE and zircon for Zr and Hf. This is evidenced in Figure 7c-d and e-f, comparing the calculations with and without taking into account the accessory phases. Without accessories, the distribution of these elements is simply controlled by a dilution surface, with the contents decreasing as 1/F, and yielding a more or less hyperbolic curve as a function of T. With accessories, however, this surface is truncated at a certain “height”, corresponding to the saturation value. At higher temperatures (= lower concentrations), the dilution suface is observed. At lower temperature however, decreasing solubility of monazite or zircon in the melt results in decreasing contents of LREE and Zr (and increasing amounts of the relevant accessory phase in the residuum). The surface below the disappearance of the accessories is a saturation surface [4, 20]. This produces a “ridge” in the P-Tconcentration surfaces, below which the melt is saturated in resp. Zr or LREE, while above it is undersaturated. This, however, is not true if one of the major phases partitions strongly the element. Figure 7g-h compares the melt composition for Yb, with and without accessories. Despite the fact that Yb is strongly partitioned into both zircon (KdZrc/Yb = 516) and monazite (KdMnz/Yb = 440), the difference between the two calculations is marginal (about 10-15 %). Here, the high Kd’s for the accessory minerals is overcome by the effect of the volumetrically important phases (garnet, in that case): despite a Kd which is one order of magnitude lower in garnet (KdGrt/Yb = 38), garnet is 100-1000 times more abundant than the accessories, resulting in an effect orders of magnitudes more important. Therefore, the control exerted on Zr and LREE by resp. zircon and monazite is significant solely because no major mineral has significant Kd’s for these elements. 4.5.

Compositional variations in the P-T space

An interesting feature of this model is that the trace element geochemistry of the melts does show very consistent variations over the P-T space, suggesting that to some degree the melt chemistry could be used as an indicator of the P-T conditions of genesis. This is fairly obvious with REE (fig. 8); indeed, the light REE (La-Nd) contents is largely controlled by the presence or absence of monazite, and hence by the temperature, whereas the heavy REE (Gd-Lu) content depends on the presence or absence of garnet and is largely a pressure indicator. Therefore, the REE patterns of the melts (fig. 8) broadly fall in 4 groups. At low temperature and low pressure, monazite is stable but not garnet, resulting in poorly

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fractionated REE pattersn depleted in LREE but not in HREE. At higher pressure, garnet is present and the REE pattern show overall low values, both for LREE and HREE. At higher temperatures, above monazite-out, the low pressure melts show a LREE and HREE rich pattern, while the high pressure melts (which probably correspond to the most common granite production situation) give fractionated, LREE enriched and HREE depleted patterns, that are not unlike the Archaean TTG’s patterns [7, 30], for the same reason: garnet is a major phase in the residuum.

5.

Comparison with natural S-type granites

S-type granites are generally regarded as being, at least in part, partial melts of sediments; it is therefore necessary to compare the modeled melts with real S-types. I compiled > 350 analysis, from the Archaean to the Miocene. The most abundant samples in the database are granites from the French Hercynian Belt (195 samples [31-35] ); the panafrican Cape Granite suite of South Africa (45 samples [36] ); the Proterozoic Harney Peak leucogranite in Dakota (36 samples [37] ); and the Miocene himalayan leucogranites (33 samples, [38-40] ). The granitoids are both from the “biotite-cordierite” and the “muscovite-biotite” (occasionally muscovite-tourmaline) type [41]. There is little match between the modeled melt and the natural examples of S-types granites (Figure 9a-d), neither for major nor trace elements. For major elements, this misfit had already been noted [20, 25, 42], the experimental melts being always leucocratic when compared to their natural counterparts. Here, we show, in addition, that the pure melts are also rather different from the granites in terms of trace elements systematic. This difference is very significant, and cannot only be ascribed to imperfections of the model. For instance, for LREE, the model predicts that the liquids should be enriched relative to the source (except in the low temperature domain of monazite stability), corresponding to an incompatible behavior of these elements. The positive correlation (or absence thereof) between SiO2 and LREE also confirms this conclusion. However, real granites define a rather well constrained array in SiO2 vs. LREE diagrams, with a distinct negative correlation and an overall depletion relative to likely sources, demonstrating an (apparent) compatible behavior. This is a major, first order difference that is difficult to ascribe solely to model imprecision and calls for a more fundamental explanation. For the Himalayan leucogranites, that are very REE depleted, it has been proposed [40] that the REE depletion is an effect of disequilibrium melting, without global equilibration between the liquids and the residual solids. This would allow to trap the REE (and Zr) in monazite and zircon crystals, that never equilibrate with the melt. While this is certainly a plausible explanation for low volume, low temperature granites such as the Miocene Himalayan leucogranites, it seems difficult to use as a general explanation. Indeed, it fails to account for the observed LREE-SiO2 correlation. It is also difficult to imagine that large volumes of granitic melts (like the large batholiths and granitic domes of cordierite-bearing material from the Hercynian belt[43]) could have been formed completely out of equilibrium, especially when they

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show a continuity with diatexites and metatexites were solids and liquids are intimately intermingled. Therefore, we conclude that the “misfit” described here corresponds to a fundamental difference between granites and melts from metasediments; in other words, granites are not (purely) melts; or, if they are, they are melts with a composition evolved away from their source. Granites can depart from pure melts either by addition or removal of other material. Added material can include mafic melts [20, 25], elements of restite [44], or peritectic crystals (garnet) formed by the biotite dehydration-melting reaction [42, 45]. As an illustration, we show on Figure 9c-d the effect of “reincorporating” into the melt all the peritectic garnet, whose composition has also been extracted from the pseudosection (for major elements) and calculated as a crystal in equilibrium with the melt (for traces). It can be seen that, for some granites, garnet entrainment can indeed provide an adequate explanation for their departure from melt compositions. Removal of material from a granitic magma (fractional or equilibrium crystallization) seems unlikely in cold, felsic magmas, on the ground of their high viscosity, and of the lack of cumulates of balancing composition. On the other hand, layering and intraplutonic variations are a common feature of granitic plutons, suggesting that at least some degree of in-situ differenciation can happen. To investigate the effects of this, we calculated a model (using the procedure described in this paper), starting with a bulk composition corresponding, both for major and trace elements, to a melt generated at 900°C (± 50) and 8.5 kbar (±0.5), as predicted in our modeling. The predicted compositions, in particular for the accessory-mineral related elements (Zr, LREE) do show the typical pattern of S-type granites, with the tight negative correlations (Figure 9e-f); the granites follow a trend of progressive magma cooling. This suggests that in-situ differenciation can play a role in S-type granites genesis. Interestingly, the muscovite-bearing granites do correspond to lower temperatures, in good agreement with petrological studies of such rocks [18, 38-41]. Detailed considerations on S-type granites genesis are beyond the scope of this paper, and would anyway require a case by case study. For the purpose of this paper, suffice to say that this shows that our approach is indeed potent enough to be used as a tool for the construction of detailed models of granite geochemistry: it supplies a melt composition, which can be used as a firm base for further interpretations. From our quick calculations, some of the differences between real granites and anatectic melts can be explained by (1) addition of a Fe-Mg and HREE rich component (garnet?); (2) removal (during cooling and in-situ fractionation?) of accessory minerals, resulting in Zr and LREE depletion.

6.

Discussion

12

Model of granitic melts…

6.1.

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Summary and capacities of the model

This work shows that it is possible to succesfuly couple modeling of major and trace elements contents in anatectic melts, therefore providing a stronger base for the interpretation of geochemical signature of granitoids. The procedure proposed here is relatively flexible; it can be applied to a large range of data, as long as both the melt’s major elements content and modal proportions are available. It can be used simply as a tool to estimate more accurately trace elements in experimental glasses; or applied to compositions empirically interpolated from experiments [7, 20]. It can be used in conjunction with any sort of thermodynamical model; here, we applied it to models for crustal melts [8-10]; it could as easily be used with any other melt model, e.g. the “pMELTS” model for mantle melts [46, 47]. Finally, any improvement in the melts and modal models, either by refining the thermodynamical data, or by empirically correcting the model, will in automatically improve the results of this coupled model. 6.1.1. Problems and limitations of the model The approach proposed here suffers from two main limitations and obstacles: - It is dependent on the quality of the modal-major elements component of the model. As shown above, the model used here is reasonnably able to predict melt composition for metasediments melt. But the extrapolation to other systems would require the development of new models (or modification of existing ones), which aren’t currently available. - It seems to fail to account for the geochemistry of existing granitic suites, predicting incorrect (also not completely unrealistic) compositions. This certainly strongly underlines the fact that granites are not primary melts, and that their composition can be affected by other factors, such as entrainment/incorporation of solids, or fractional crystallization from the true melts. The first problem can be relatively easily alleviated; in theory, there is indeed no obstacle to the development of a better thermodynamic model or, failing this, the use of empirical models of mineral proportions and melt chemistry, directly based on extrapolation and interpolation of experimental data. The second issue is more problematic. Indeed, by construction, our model is only able to predict the compositions of primary melts, in equilibrium with their source. Should one of these assumptions fail, which seems to be a common situation, the model becomes less relevant to explain granites compositions. Yet, granites geochemistry is related, if only partially, to the primary melt's composition, and therefore this approach still allows to put some constrains on what is possible or not. Furthermore, it is certainly possible to expand the model and take into account further processes controlling granite’s geochemistry. 6.1.2.

Modelling other granitoids

Expanding the model to other magmatic liquids is possible, following the same logic, provided some elements are known: - A model for melt major elements and restite modal proportions as a function of P and T. This can be either a thermodynamically based model, as shown here; or a more

13

Model of granitic melts…

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empirical one. For instance, our recent model for amphibolite melting [7] derived its major elements and modal data from direct interpolation of available experimental data. - Partition coefficients for all the involved phases; despite the need for refinement of the existing value, a reasonably large dataset is available (e.g. [22]; see also the GERM projct at http://earthref.org). - A model of solubility for the accessory phases playing a role. Depending on the system considered, this could also include allanite and sphene [23]; this could prove an obstacle in the near future, since we’re not aware of published models on the solubility of these minerals. 6.2.

Controls on trace elements contents in melts

Despite its shortcomings, this model can be used to discuss some general features of granitoids geochemistry. Trace elements contents are controlled by either major or accessory minerals, themselves a function of the P-T conditions of melt formation. 6.2.1.

Major vs. accessory minerals control

Three types of trace elements can be defined from this study (see also [20]): 1. Elements such as Rb or Sr have a repartition which is controlled solely by major elements. For this group, the contents are a function of the mineral appearance/disappearance; they are directly linked to the melting reactions in the system. This also means that such elements can be used to trace the melting history of the source rock and, to some degree, to discuss the P-T conditions of melt formation. 2. Elements such as LREE or Zr are completely controlled by accessory minerals (resp. monazite and zircon). Their concentration is controlled by accessory solubility at low temperatures, and they behave as pure incompatible elements, with a concentration controlled by dilution only, at higher temperatures. 3. Finally, and in a less expected way, elements such as Y or HREE, which in theory are controlled both by major and accessory minerals, turn out to have a distribution largely a function of the major minerals, the accessory playing only a limited role. This comes from the fact that the high Kd of accessory minerals for these elements are unable to overcome the negligible amounts of this minerals in the system… Therefore, models that do not take into account accessory elements are still a reasonable approximation for this group of elements. Collectively, it appears that, apart for the accessory-building elements (LREE, Zr), the role of accessory minerals is small or second order compared to this of major minerals. To some degree, this is an “a posteriori” justification of the empirical approach used in trace elements modeling, as described in introduction.

6.2.2. Trace elements as a signature of the P-T conditions of melting?

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Model of granitic melts…

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This model predicts that melts generated in different P-T conditions should have significantly different trace elements contents; actually, to some degree, trace elements (REE) can be used to discuss the P-T conditions of melt formation. This approach has been used [7] to put some constrains on the origin of the Archaean TTG suite. Here I suggest that it could, with some caution, be used as an empirical geobarometer for the conditions of generation of granitic melts. 6.3.

Granites are not (simply) melts

Finally, a by-product of this study is the demonstration that granites (at least S-types) can not be pure anatectic melts. While this was already suggested by the leucocratic nature of the experimental liquids (compared to real granites) [25, 42], trace elements (REE in particular) do confirm this conclusion. Here, I showed that e.g. LREE and Zr should display an (apparent) incompatible behavior in anatectic melts (even taking into account the role of accessory minerals), whereas they clearly have an apparent compatible behavior in granites. This demonstrates that S-type granites can not be interpreted as simple melts, and that other processes must have played a significant role in their petrogenesis.

7.

Conclusions

In this paper, we propose a procedure for calculation of the major and trace elements of granitic melts, as a function of pressure and temperature. This allows to have integrated models of melt composition, bridging the gap between the experimental, major elements orientated studies, and the trace elements geochemistry. This approach is largely automated, in the sense that the only parameter on which the user has to make a decision is the major and trace elements composition of the source –all the melt properties are derived from it. The predicted melt, for whatever data is available for experimental melts, seems to be in good agreement with observed compositions. The variation of their composition over the P-T space also opens interesting perspectives on the interpretation of granites geochemical signature. The differences between granites and the anatectic melts (both modeled and experimental) show that granites can not be regarded as simple, direct melts. While this does to some degree restrict the interest of our modeling, it does not render it useless. In contrary, the complexity of granite’s chemistry underlines the need for good constrains on the melt composition, which is critical to provide a reliable starting point for further modeling.

8.

Acknowledgments

JFM’s post doctoral stay at Stellenbosch university is funded through NRF grant GUN 2053698, as well as a bursary from the Department of Geology, Stellenbosch University. JM Montel’s unpublished “habilitation thesis” was a great source of inspiration for this work. Discussions with G. Stevens and A. Villaros were also a

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great stimulation. Finally, all diagrams in this paper were drafted using “GCDkit”, a geochemical library by V. Janousek2 for the statistical package “R”3. The ability of GCDkit to deal gracefully with databases of up to 5000 analysis bears testimony to the quality of this piece of software, and rendered the construction of the diagrams feasible in a reasonable time –if at all.

9.

References

1 C.J. Allègre and J.F. Minster, Quantitative Models of Trace-Element Behavior in Magmatic Processes, Earth and Planetary Science Letters 38(1), 1-25, 1978. 2 H.R. Rollinson, Using Geochemical Data: Evaluation, Presentation, Interpretation, 352 pp., Longman scientific & technical, Singapore, 1993. 3 H. Martin, Petrogenesis of Archaean trondhjemites, tonalites and granodiorites from eastern Finland; major and trace element geochemistry, Journal of Petrology 28(5), 921-953, 1987. 4 J.M. Montel, A Model for Monazite/Melt Equilibrium and Application to the Generation of Granitic Magmas, Chemical Geology 110(1-3), 127-146, 1993. 5 M. Pichavant, J.M. Montel and L.R. Richard, Apatite Solubility in Peraluminous Liquids - Experimental-Data and an Extension of the HarrisonWatson Model, Geochimica Et Cosmochimica Acta 56(10), 3855-3861, 1992. 6 E.B. Watson and T.M. Harrison, Zircon saturation revisited: temperature and composition effects in a variety of crustal magmas types., Earth and Planetary Science Letters 64, 295-304, 1983. 7 J.-F. Moyen and G. Stevens, Experimental constraints on TTG petrogenesis: implications for Archaean geodynamics, in: Archean Geodynamics and Environments, K. Benn, K.C. Condie and J.-C. Mareschal, eds., AGU monographs 164, pp. Chapter 10, AGU, 2006. 8 T.J.B. Holland and R. Powell, An internally consistent thermodynamic dataset for phases of petrological interest, Journal of Metamorphic Geology 16, 309-343, 1998. 9 T.J.B. Holland and R. Powell, Calculation of phase relations involving haplogranitic melts using an internally-consistent thermodynamic data set, Journal of Petrology 42, 673-683, 2001. 10 R.W. White, R. Powell and T.J.B. Holland, Calculation of partial melting equilibria in the system CaO-Na2O-K2O-FeO-MgO-Al2O3-SiO2H2O (CNKFMASH), Journal of Metamorphic Geology 19, 139-153, 2001. 11 J.A.D. Conolly, Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation, Earth and Planetary Science Letters in press, 2005. 12 J.A.D. Conolly and K. Petrini, An automated strategy for calculation of phase diagram sections and retrieval of rock properties as a function of physical conditions, Journal of Metamorphic Geology 20, 697-708, 2002. 2 3

http://www.gla.ac.uk/gcdkit http://www.r-project.org/

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13 A.B. Thompson, Fertility of crustal rocks during anatexis, Transactions of the Royal Society of Edinburgh-Earth Sciences 87, 1-10, 1996. 14 G. Stevens, J.D. Clemens and G.T.R. Droop, Melt production during granulite-facies anatexis: experimental data from "primitive" metasedimentary protoliths, Contribution to Mineralogy and Petrology 128, 352-370, 1997. 15 D. Vielzeuf and J.R. Holloway, Experimental-Determination of the Fluid-Absent Melting Relations in the Pelitic System - Consequences for Crustal Differentiation, Contributions to Mineralogy and Petrology 98(3), 257276, 1988. 16 A.E. Patiño-Douce and A.D. Johnston, Phase-Equilibria and Melt Productivity in the Pelitic System - Implications for the Origin of Peraluminous Granitoids and Aluminous Granulites, Contributions to Mineralogy and Petrology 107(2), 202-218, 1991. 17 A.E. Patiño-Douce and J.S. Beard, Effects of P, f(O2) and Mg/Fe ratio on dehydration melting of model metagreywackes, Journal of Petrology 37(5), 999-1024, 1996. 18 A.E. Patiño-Douce and N. Harris, Experimental constraints on Himalayan anatexis, Journal of Petrology 39(4), 689-710, 1998. 19 J. Pickering and A.D. Johnston, Fluid-absent melting behavior of a two-mica metapelite: experimental contraints on the origin of the Black Hills granite, Journal of Petrology 39(10), 1787-1804, 1998. 20 J.M. Montel, Géochimie de la fusion de la croûte continentale, Mémoire d'habilitation à diriger des recherches, Université Blaise-Pascal, 1996. 21 D.M. Shaw, Trace Element Fractionation During Anatexis, Geochimica Et Cosmochimica Acta 34(2), 237-243, 1970. 22 H. Rollinson, Using geochemical data, 352 pp., Longman, London, 1993. 23 M. Cuney and M. Friedrich, Physicochemical and Crystal-Chemical Controls on Accessory Mineral Paragenesis in Granitoids - Implications for Uranium Metallogenesis, Bulletin De Mineralogie 110(2-3), 235-247, 1987. 24 V. Janousek, G. Farrow and V. Erban, Interpretation of Whole-rock Geochemical Data in Igneous Geochemistry: Introducing Geochemical Data Toolkit (GCDkit), Journal of Petrology, in press, 2006. 25 J.M. Montel and D. Vielzeuf, Partial melting of metagreywackes, part II. Compositions of minerals and melts, Contribution to Mineralogy and Petrology 128, 176-196, 1997. 26 K. Skjerlie and A.D. Johnston, Fluid-absent melting behavior of an Frich tonalitic gneiss at mid-crustal pressures: implications for the generation of anaorogenic granites, Journal of Petrology 34(4), 785-815, 1993. 27 P.M. Bell, Aluminium silicate system: experimental determination of the triple point, Science 139, 1055-1057, 1963. 28 V. Gardien, A.B. Thompson, D. Grujic and P. Ulmer, Experimental melting of biotite + plagioclase + quartz + or - muscovite assemblages and implications for crustal melting., Journal of Geophysical Research, B, Solid Earth and Planets 100(8), 15,581-15,591, 1995. 29 J.C. Clemens and D. Vielzeuf, Constraints on melting and magma production in the crust., Earth and Planetary Science Letters 86, 287-306, 1987.

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30 H. Martin, The Archean grey gneisses and the genesis of the continental crust., in: Archean crustal evolution, K.C. Condie, ed., Developments in Precambrian Geology 11, pp. 205-259, Elsevier, Amsterdam, 1994. 31 H. Downes and J.L. Duthou, Isotopic and Trace-Element Arguments for the Lower-Crustal Origin of Hercynian Granitoids and Pre-Hercynian Orthogneisses, Massif Central (France), Chemical Geology 68(3-4), 291-308, 1988. 32 H. Downes, C. Dupuy and A.F. Leyreloup, Crustal Evolution of the Hercynian Belt of Western-Europe - Evidence from Lower-Crustal Granulitic Xenoliths (French Massif-Central), Chemical Geology 83(3-4), 209-231, 1990. 33 T. Euzen, Pétrogenèse des granites de collision post- épaississement. Le cas des granites crustaux et mantelliques du Complexe de PontivyRostrenen (Massif Armoricain, France), 350 pp., Rennes, 1993. 34 Y. Georget, Nature et origine des granites peralumineux à cordiérite et des roches associées. Exemple des granitoïdes du Massif Armoricain (France) : Pétrologie et géochimie, 250 pp., Rennes, 1986. 35 B.J. Williamson, H. Downes and M.F. Thirlwall, The Relationship between Crustal Magmatic Underplating and Granite Genesis - an Example from the Velay Granite Complex, Massif-Central, France, Transactions of the Royal Society of Edinburgh-Earth Sciences 83, 235-245, 1992. 36 R. Scheepers, Geology, geochemistry and petrogenesis of late Precambrian S, I and A type granitoids in the Saldania mobile belt, Southwestern Cape Province, Journal of African Earth Sciences 21, 35-58, 1995. 37 P.I. Nabelek, C. Russ-Nabelek and J.R. Denison, Generation and crystallization conditions of the Proterozoic Harney Peak leucogranite, Black Hills, South Dakota, U.S.A.: petrologic and geochemical constraints, Contribution to Mineralogy and Petrology 110, 173-191, 1992. 38 B. Scaillet, C. France-Lanord and P. Le Fort, Badrinath-Gangotri plutons (Garhwal, India): petrological and geochemical evidence for fractionation processes in a high Himalayan leucogranite, Journal of Volcanology and Geothermal Research 44, 163-188, 1990. 39 S. Inger and N.B.W. Harris, Geochemical constraints on leucogranite magmatism in the Langtang valley, Nepal Himalayas, Journal of Petrology 34(2), 345-368, 1993. 40 M. Ayres and N.B.W. Harris, REE fractionation and Nd-isotopes desequilibrium melting during crustal anatexis: constraints from Himalayan leucogranites, Chemical Geology 139, 249-269, 1997. 41 B. Barbarin, A review of the relationships between granitoid types, their origins and their geodynamic environments, Lithos 46(3), 605-626, 1999. 42 G. Stevens, A. Villaros, J.-F. Moyen and R. Scheepers, Garnet entrainment in S-type granitic magmas: the petrogenesis of the S-type Cape Granite Suite, South Africa., Geology submitted, 2006. 43 P. Ledru, G. Courrioux, C. Dallain, J.M. Lardeaux, J.M. Montel, O. Vanderhaeghe and G. Vitel, The Velay dome (French Massif Central): melt generation and granite emplacement during orogenic evolution, Tectonophysics 342(3-4), 207-237, 2001.

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44 B.W. Chappell and A.J.R. White, I- and S-type granites in the Lachlan Fold Belt, Transactions of the Royal Society of Edinburgh-Earth Sciences 83, 1-26, 1992. 45 G. Stevens, Making granites: understanding the melting of Earth's crust, pp. 16, University of Stellenbosch, Stellenbosch, 2005. 46 M.S. Ghiorso, M.M. Hirschmann, P.W. Reiners and V.C. Kress, The pMELTS: A revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa, Geochemistry Geophysics Geosystems 3, art. no.-1030, 2002, 2002. 47 M.S. Ghiorso and R.O. Sack, Chemical Mass-Transfer in Magmatic Processes. 4. A Revised and Internally Consistent Thermodynamic Model for the Interpolation and Extrapolation of Liquid-Solid Equilibria in Magmatic Systems at Elevated-Temperatures and Pressures, Contribution to Mineralogy and Petrology 119(2-3), 197-212, 1995. 48 W.V. Boynton, Geochemistry of the rare-earth elements: meteorite studies., in: Rare Earth Element Geochemistry, P. Henderson, ed., pp. 63-114, Elsevier, Amsterdam, 1984. 49 S.S. Sun and W.F. McDonough, Chemical and isotopic systematics of oceanic basalts: implications for mantle composition and processes., in: Magmatism in ocean basin, A.D. Saunders and M.J. Norry, eds., Spec.Pub., pp. 313-345, 1989. 50 S.R. Taylor and S.M. McLennan, The continental crust: its composition and evolution., 312 pp., Blackwell, Oxford, 1985.

10.

Figures

Figure 1: Diagrammatic representation of the principle of calculations. Comments in section 2.1 Figure 2: Comparison of melt productivities at 10 kbar (melt fraction, F) as a function of temperature (T, °C) between modeled and experimental systems (using the same bulk compositions). The different sources used are listed table 1. In each panel, the grey “band” corresponds to the modeled melt factions, the dots to the experimental values. Figure 3: Comparison of the major elements chemistries at 10 kbar between modeled and experimental melts, for different sources. The modelled melts are represented by the field of compositions predicted (grey for pelites and hatched for greywackes), whereas individual analyses are given for experimental melts. Molecular values plotted on both diagrams. On (a): A/CNK = molecular Al/Ca+Na+K. On (b): the italicized values below the source reference code correspond to its Na/K ratio. Figure 4: Comparison of melt major elements chemistry at 10 kbar, as a function of temperature (T, °C) for modeled and experimental liquids, for two sources: the pelitic Carino gneiss [15] and the grauwacky CEV [25]. Elements expressed as weight % oxides, with composition normalized to 100 % anhydrous. In each

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panel, the grey band represents the modeled liquids, and the dots individual experimental analyses. Figure 5: Trace elements composition of the modeled melts (normalizations after [48, 49]). Note the difference between the pelitic and grauwacky sources (see section 4.1). Figure 6: Effect of the source’s composition on the melt chemistry. The major elements composition for the source is the CEV greywacke [25]. The trace elements composition varies from 0.5 to 2 times the Post-Archaean Average Shale (PAAS) [50]. Concentrations expressed in ppm, temperature (T) in °C. Figure 7: 3D perspective representations of the “surfaces” of the melt’s concentration in trace elements in the P-T space; melts are modeled with the CEV major elements composition [25] and a PAAS [50] value for traces. Note that in panels c, e and g, the values plotted are for a calculation without accessory minerals; compare with d, f and h respectively. Appearance and disappearance of either major (biotite, feldspars, garnet) or accessory (zircon, monazite) minerals controls largely the shape of the surfaces. In some case, anomalous points are numerical artifacts, corresponding to points where the Gibbs energy minimization algorithm of PERPLE_X [11] failed to converge, producing erratic results. Figure 8: REE patterns modeled from melts from a CEV source and a 1-PAAS concentration (as in figure 7). The 4 REE diagrams correspond to the 4 quadrants of the P-T space delimited by the thick lines on the P-T diagram, i.e. by the monazite-out (mnz) and garnet-in (grt) curves. Biotite out (bio) also shown for reference. The dashed lines in the PT diagrams depict melt fractions F. Figure 9: Comparison between modeled compositions (5-12 kbar) and S-type granites, in element-element (major elements in wt% and traces in ppm) or ternary (molecular, as fig. 3) diagrams. The source composition (PAAS) is also shown when applicable. Panels a and b: modeled compositions (whose field is delimited by solid lines) correspond to the CEV, one-PAAS model used above (Figs. 7-8); for each field, the temperature is indicated on the diagram. Panels c and d: same caption; the stippled field correspond to magmas made of the anatectic melt in which all of the peritectic garnet has been reincorporated. Tie lines with arrows show the resulting “vector”. In the diagrams used here, the temperature has a far less important effect, hence the larger “brackets” of temperature values for each field. Panels e and f: the model used here is the “cooling” model, starting with the major and trace composition of the liquids formed at 850-950 °C and 8-9 kbar from the CEV-1 PAAS model; the resulting compositions are shaded with dotted conturs, and temperatures are also indicated. In all these diagrams, pressure is not a very sensitive parameter, since only P>5 kbar are considered (garnet is therefore always present), and different pressures are therefore not differenciated. Table 1: Summary of the source composition of experimental studies used in this work. References are: HQ36, Patiño-Douce and Johnston [16]; Carino

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gneisses, Vielzeuf and Holloway [15]; NB, Stevens [14]; MBS, Patiño-Douce and Harris [18]; CEV, Montel and Vielzeuf [25]; MS, Patiño-Douce and Harris [18] and HP60, Pickering and Johnston [19].

21

Model parameters

Intermediate calculations

Output

Other traces (LILE, HFSE, metals) Zircon saturation

Trace elements composition

Corrected Zr, Hf Monazite saturation

Corrected LREE, Th Xenotime saturation

Traces

Bulk repartition coefficients (D)

Corrected HREE, Y

Iterative loop

Source bulk compositon Major

Amount of zircon Modal proportions

Amount of monazite Amount of xenotime

Partition coefficients (KD)

Mineral thermodynamical models

Solid residuum modal proportions for non-accessory minerals (Feldspar, quartz, biotite, cordierite, garnet, pyroxenes)

Pseudosection

Melt major elements composition

0.0

0.2

0.4

F 0.6

0.8

1.0 700

700 800

800 900 1100

NB T

900

1100

T F

F

0.8

0.8

0.8

1.0

T T T

HQ-36 MBS MS

700

700 800

800 900

900 T 1.0

1.0

1100

0.6

0.6

0.6

900

0.4

0.4

0.4

800

0.2

0.2

0.2 700

0.0

0.0

0.0

F

0.0

0.0

0.0

0.2

0.2

0.2

0.4

0.4

0.4

F

F

F

0.6

0.6

0.6

0.8

0.8

0.8

1.0

1.0

Carino 1.0

CEV

1100

1100

HP-60

700

700

800

800

900 1100

900 1100

T

Ca + Na + K

(a)

1 .5 K= N =1 A/C A/CNK

Fe + Mg

(b)

Al

Model

Greywackes Intermediate

HQ36 (0.22)

K

Pelites

Experiments

MS CEVP

NB (0.44)

HP-60 HQ MBS Carino

MBS (0.68)

HP60 (0.99)

NB

Vielzeuf (1.10) Montel (2.08)

MS (1.96)

Na

Ca

900

1000

1100

1300

1300

900

T

1100

1300

16.0 15.0 14.0 700

800

900

1000

1100

1000

1100

1000

1100

T 1.5

1.0 0.5 700

800

T

900

1000

1100

700

800

T

900

1000

1100

700

800

7

T

900

T

12

H2O

6

6 2

2

3

3

2

4

4

4

3

4

8

10

8 5

6

K2O

5 4

Na2O

7

10 8

H2O

5

K2 O

4 3 2

Na2O

6

5

6

12

7

6

1100

2.5

MgO

FeOt

2 1 700

14

T

1100

1000

2.0

5 900

900

T

4

1.5 1.0

CaO

0.0 700

800

9

1100

13.0 700

T

0.5

0.5 0.0 900

Al2O3

0.8 800

2.0

2.5 2.0

2 1 0 700

0.6

TiO2

0.4 0.2 700

1.0

1300

1.0

1.5

MgO

1100

0.5

900

T

7 6 5 4 3

1.0

75 74 71 69 700

0.0

1300

14

1100

T

CaO

900

1.5

700

T

3

1300

70

15 1100

14

0.4

66

900

72

SiO2

18 17

Al2O3

16

0.6

73

19

1.0

TiO2

0.8

74 72 70 68

SiO2

700

FeOt

CEV (Grauwacke, Montel and Vielzeuf 1997)

20

76

Carino gneisses (Pelites, Vielzeuf and Holloway 1988)

700

900

1100

T

1300

700

900

1100

T

1300

700

900

1100

T

1300

700

800

900

T

1000

1100

700

800

900

T

1000

1100

700

800

900

T

1000 100 1

10

Sample/ REE chondrite

(a)

La

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Normalized by REE chondrite (Boynton 1984)

100 10 1

Sample/ Primitive Mantle

1000

(b)

Rb

Ba

Th

U

Nb

K

La

Ce

Pb

Pr

Sr

Nd

Zr

Sm

Eu

Ti

Dy

Y

Yb

Lu

Normalized by Primitive Mantle (Sun & McDonough 1989)

"Greywackes"

"Pelites"

CEV (Montel and Vielzeuf, 1997)

HQ-36 (Patiño-Douce and Johnston, 1991)

MS (Patiño-Douce and Harris, 1998)

MBS (Patiño-Douce and Harris, 1998)

HP-60 (Pickering and Johnston, 1998)

NB (Stevens, 1995) Carino (Vielzeuf and Holloway, 1988)

1500

1

50

500

1000

Ba

Yb

2

3

100

La

4

5

150

6

CEV (Grauwacke, Montel and Vielzeuf 1997)

800

900

1000

700

800

700

900

1000

700

800

1000

T

Nb Ta

15

80 100 120

La Yb

900

500 900

10

20

5

40

60

60 50

1000

300 800

T

40

900

100 700

T

30

1000

Zr

1000

20

900

700

350

Sr 150 50 800

800

T

250

500

Rb 300 100 700

Nb

1000

T

700

T

900

10

700

700

800

900

T

1000

700

800

900

1000

T

Source composition 2 times P.A.A.S. (Taylor & McLennan, 1985) P.A.A.S. 0.5 P.A.A.S.

700

800

T

(a)

(b) 200

350 300

Sr

Rb

150

250

100

200 50 10

10

1200 1100

8

1200 1100

8

1000

6 4

1000

6 P

P

900

T

900 4

800 2

800 2

700

(c)

T

700

(d)

1200

1200 1000

800

800

Zr

Zr (no

1000

access

600 400 200 0

ories)

10

600 400 200 0 10

1200 1100

8

1200 1100

8

1000

6 4

1000

6 P

P

900

T

900 4

800 2

800 2

700

(e)

T

700

(f)

150

150

La (no

100

100

La

ories)

access

50

50

0

0 10

10

1200 1100

8

1200 1100

8

1000

6 4

1000

6 P

P

900

T

900 4

800 2

800 2

700

(g)

T

700

(h)

6

6 5 4 3 2 1 0

s)

ie ssor

acce

Yb

o Yb (n

5 4 3 2 1 0 10

1200 8

1100

10

1200 8

1100

1000

6 4

T

1000

6

P

P

900

900 4

800 2

700

800 2

700

T

1000

1000

CEV (Grauwacke, Montel and Vielzeuf, 1997)

10 1

1

10

Sample/ REE chondrite 100

Garnet

Sample/ REE chondrite 100

Garnet & monazite

12

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

0.2

0.3

0.4 0.5 0.6 0.7

0.8

0.9

700

800

900

1000 T

1000

1000

2

Mnz-out

4

6

P

8

Gr

t-i

n

Bio-ou

t

10

0.1

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

1200

(nothing) Sample/ REE chondrite 10 100 1

1

10

Sample/ REE chondrite 100

Monazite

1100

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

500

100

850-900 °C

(a)

800-850 °C

(b) 900-950 °C

900-950 °C

80

400

850-900 °C

950-1000 °C

1000-1050 °C

300

60

950-1000 °C

1000-1050 °C

800-850 °C

PAAS

200

40

Zr

La

750-800 °C

PAAS 700-750 °C

700-750 °C

0

0

20

100

750-800 °C

66

68

70

72

74

76

78

80

66

68

70

72

74

76

78

80

SiO2

SiO2 10

Ca + Na + K

(d) 8

(c)

Al

4

Yb

6

Fe + Mg

PAAS 850-1000 °C 1000-1050 °C

0

2

800-850 °C

0

2

4

6

8

10

300

(e)

(f)

850-900 °C

250

100

FeO + MgO

800-850 °C

80

850-900 °C

200

PAAS

Zr

700-800 °C

150

La

60

800-850 °C

40

750-800 °C

100

PAAS

20

700-750 °C

50

650-700 °C 650-700 °C

600-650 °C

600-650 °C

0 66

68

70

72

SiO2

Biotite-Cordierite granites Muscovite-Biotite granites

74

76

78

80

66

68

70

72

SiO2

74

76

78

80

SiO2

Al2O3

FeO+MgO

Na/k

Ca+Na/K

wt. %

wt. %

wt. %

molecular

molecular

Montel and Vielzeuf (1997) Patino-Douce and Harris (1998)

69.99 75.28

12.96 14.29

7.19 3.06

2.08 1.96

2.76 2.34

Pickering and Johnston (1998)

77.14

11.2

4.69

0.99

1.29

Stevens (1995) Patino-Douce and Harris (1998) Vielzeuf and Holloway (1988) Patino-Douce and Johnston (1991)

66.33 67.03 64.35 57.36

14.34 16.26 18.13 23.24

11.50 7.38 8.70 11.31

0.44 0.68 1.10 0.22

0.70 0.99 1.68 0.33

Reference Greywacke

CEVP MS

Greywacke (int.) HP-60

Pelites

NB MBS Carino Gneiss HQ-36