Diffusion-induced fractionation of niobium and tantalum during continental crust formation

Earth and Planetary Science Letters ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Diffusion-induced fractionation of niobium and tantalum during continental crust formation Horst R. Marschall a,b,n, Ralf Dohmen b,c, Thomas Ludwig d a

Department of Geology & Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol BS8 1RJ, UK c Institut für Geologie, Mineralogie und Geophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany d Institut für Geowissenschaften, Universität Heidelberg, Im Neuenheimer Feld 234–236, 69120 Heidelberg, Germany b

art ic l e i nf o

a b s t r a c t

Article history: Received 19 March 2013 Received in revised form 30 May 2013 Accepted 31 May 2013 Editor: T.M. Harrison

Differentiation of the Earth into its major spheres – crust, mantle and core – has proceeded dominantly through magmatic processes involving melting and melt separation. Models that describe these differentiation processes are guided by elemental abundances in the different reservoirs. Elements are fractionated between coexisting phases during partial melting, and geochemical models are generally based on the fundamental assumption that trace-element equilibrium is established between the partial melts and the restitic minerals. The element pair niobium and tantalum is key to the distinction of different melting regimes involved in crustal differentiation, but equilibrium partition models have largely failed to reproduce the Nb/Ta patterns observed in nature, posing a long-standing geochemical conundrum. Here we demonstrate that kinetic fractionation of Nb and Ta by diffusion may have produced the low Nb/Ta observed in the continental crust. On the basis of the diffusivities of Nb and Ta in rutile (TiO2) determined experimentally in this study, we conclude that equilibrium cannot be expected for the natural range of grain sizes, temperatures and time scales involved in partial melting of crustal rocks. Instead, the observed fractionation of the geochemical twins, Nb and Ta, in the silicate Earth most likely proceeds by partial – as opposed to complete – equilibration of rutile and melt. Hence, the assumption of bulk equilibrium during partial melting for the processes of crustal differentiation may not be justified, as is demonstrated here for Nb/Ta. The concept presented here is based on kinetic fractionation melting and explains the observed low Nb/Ta ratio of the continental crust. & 2013 Elsevier B.V. All rights reserved.

Keywords: rutile TiO2 diffusion partial melting Nb–Ta

1. Introduction 1.1. The Nb–Ta geochemical conundrum Fundamental questions about the differentiation of the silicate Earth include the timing and mechanism of the formation and differentiation of the continental crust (Rudnick et al., 2000). Among the most characteristic geochemical anomalies of continental rocks are a depletion of the elements Nb, Ta and Ti relative to elements with similar melt–rock partitioning behaviour and relative to their abundances in the mantle and in primitive basalts (Hofmann, 1988). In addition, the Nb/Ta ratios of the accessible crust and mantle are lower than that of primitive chondrites, and it has been suggested that Nb is preferentially enriched in the core, leaving the silicate Earth with a sub-chondritic Nb/Ta ratio n Corresponding author at: Department of Geology & Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA. Tel.: +1 508 289 2776; fax: +1 508 457 2183. E-mail address: [email protected] (H.R. Marschall).

(Münker et al., 2003). Furthermore, differentiation of the crust– mantle system has produced a significant variation in Nb/Ta ratios, and this ratio has been identified as a key geochemical tool to identify crust formation processes (Green, 1995; Foley et al., 2002; Rapp et al., 2003). Most importantly, the continental crust has a lower Nb/Ta ratio (¼ 12 to 13) than the bulk silicate Earth (BSE; Nb/Ta ¼14 70.3; Münker et al., 2003). The geochemical behaviour of the trace elements Nb and Ta is intimately linked to that of the more abundant element titanium. The dominant mineral hosts of Ti, Nb and Ta in crustal rocks are sphene (¼ titanite) and the Ti 7Fe oxides rutile, ilmenite and Ti-magnetite. Rocks of basaltic composition are metamorphosed to eclogite at conditions prevailing in the upper mantle and in deep sections of thickened crust, where partial melting processes can take place. The Nb and Ta budget in eclogites is almost exclusively stored in the ubiquitous mineral rutile (Zack et al., 2002; Aulbach et al., 2008), and eclogites retain rutile in the restite during partial melting processes (Ryerson and Watson, 1987; Klemme et al., 2002; Gaetani et al., 2008; Xiong et al., 2011). Consequently, Nb–Ta fractionation processes have to be approached with a close focus

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Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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2

on Ti minerals and their ability to fractionate Nb from Ta during partial melting processes (Green and Pearson, 1987; Rapp et al., 2003; Schmidt et al., 2004; Klemme et al., 2005; Xiong et al., 2011; John et al., 2011). Experimental work on Nb and Ta partitioning between rutile and silicate liquid has revealed that both elements are strongly compatible in rutile and that Ta is either equally or more compatible than Nb (Green and Pearson, 1987; Schmidt et al., 2004; Klemme et al., 2005; Xiong et al., 2011). This invariably leads to the prediction that melts in equilibrium with any rock containing restitic rutile will have Nb/Ta ratios similar to or higher than its protolith. This is in stark contrast to the low Nb/Ta ratios observed in the continental crust, which represents the extracted magmas produced by partial melting. Equilibrium-melting models largely fail to explain the Ti–Nb–Ta depletion of the continental crust in combination with its low Nb/ Ta ratio (see detailed discussion in Supplementary material). Consequently, the assumption of equilibrium between minerals and liquid during melting and melt extraction has to be revisited, and effects of kinetic fractionation of trace elements need to be considered. We, therefore, determined kinetic fractionation of Nb and Ta during diffusion in rutile and investigate the consequences for Nb–Ta fractionation during partial melting. Diffusive equilibration of melt and restitic minerals is controlled by (i) melting temperature, (ii) the duration of melt–rock interaction prior to melt extraction, (iii) the grain size distribution in the restite and (iv) the diffusivities of the trace elements in the trace-element hosting minerals. Whereas the first three parameters can be derived from published models and experimental data and from observations in natural rocks, the diffusivities of Nb and Ta in rutile have to be determined experimentally. 1.2. Previously published diffusion data on Nb and Ta in rutile Self-diffusion of O and Ti and tracer diffusion of mono-, di-, triand tetravalent ions in rutile has been investigated in a number of studies (review by van Orman and Crispin, 2010). The pentavalent cations, however, have not been studied in great detail, despite their high abundance in natural rutile (Zack et al., 2004; Meinhold, 2010) and their importance for technical applications (Sheppard et al., 2007b). Sheppard et al. (2007a, 2009) have investigated Nb diffusion in pure and Nb-doped rutile at oxidising conditions (f O2 ¼ air). In both cases they found diffusivities slightly slower than those reported for Ti self-diffusion in rutile under the same conditions. However, their experiments were affected by recrystallisation of the diffusion couple and they could only use certain sections of the analysed profiles that they interpreted as diffusion controlled. The results of these studies have been rejected by other workers (van Orman and Crispin, 2010). No data on Ta diffusion (or any other pentavalent ion) in rutile have been published to date. In this paper, we present the results of a series of experiments on Nb and Ta diffusion in rutile over a wide temperature range at oxidation conditions relevant for geologic processes. 1.3. Substitution of Nb and Ta in rutile The incorporation of Nb and Ta into the mineral structure of rutile has been the centre of attention in a number of studies in the mineralogical and geochemical sciences, as well as in material science. Most geochemical studies treat rutile as stoichiometric TiO2 and search for substitution mechanisms that charge balance the incorporation of pentavalent Nb and Ta into octahedral Ti sites, where they replace tetravalent Ti. The dominant substitution mechanism for Nb and Ta in rutile in equilibrium with natural silicate melts is probably a coupled substitution involving trivalent

3þ

5þ

4þ

cations, such as Al þ Nb ¼ 2Ti (Horng and Hess, 2000; Klemme et al., 2005; Xiong et al., 2011). It has also been suggested that Nb and Ta may be substituting for octahedral Ti charge 5þ balanced by the creation of octahedral Ti vacancies, i.e., 4Nb þ 4þ & ¼ 5Ti (Klemme et al., 2005; Xiong et al., 2011). However, cation vacancies are rare in the rutile structure at geologically relevant conditions, and become only relevant at f O2 much higher than 105 Pa (Sasaki et al., 1985; Nowotny et al., 2008). The cation vacancy mechanism is therefore not likely to be relevant for rutile in geologic settings. Rutile is close to stoichiometric TiO2 at oxygen partial pressure of air at atmospheric pressure (f O2 ¼ 20 kPa). However, at reducing conditions, relevant to geologic settings, a number of defects become more frequent and rutile is better represented by the formula TiO2−x (Sasaki et al., 1985; Nowotny et al., 2008). The dominant defects are interstitial Ti3þ , interstitial Ti4þ and O vacancies (Nowotny et al., 2006, 2008). The density of O vacancies is high and whereas it is largely independent of f O2 at oxidising conditions, it increases with decreasing f O2 at low oxygen fugacity (Nowotny et al., 2008). At constant temperature, the density of triand quadrivalent Ti interstitials increases by ∼2:5 orders of magnitude between oxidising (air) and reducing conditions (i.e., at the fayalite ¼magnetite + quartz buffer, FMQ) (Nowotny et al., 2008). At oxygen fugacities relevant for geological conditions (f O2 between the iron-wustite and haematite–magnetite buffers), natural rutile is hardly translucent and has a metallic lustre. This is due to the delocalisation of electrons and the narrowing of the band gap between the valence band and the conduction band, turning rutile (TiO2−x ) into a semiconductor (Nowotny et al., 2008). Pure rutile is translucent and almost colourless at f O2 ¼ air and is an electric insulator with a large band gap (Nowotny et al., 2008; Colasanti et al., 2011). At f O2 of the haematite–magnetite buffer (and below) pure rutile acquires a deep blue colour due to the 3þ 4þ presence of significant trivalent Ti and the Ti –Ti charge transfer absorption (Colasanti et al., 2011). The high density of vacancies and the delocalisation of electrons facilitates the incorporation of pentavalent cations without the need for chargecompensating trivalent cations and it enables the diffusion of the 5þ aliovalent Nb and Ta into pure rutile. Charge balance of Nb and 5þ Ta on octahedral Ti sites and interstitial sites is provided by O vacancies over a wide range of f O2 , and may be expressed by the 5þ 4þ substitution 2Nb þ O2− ¼ 2Ti þ &O (where &O is an O 5þ 3þ 4þ vacancy) or NbM þ Tii ¼ TiM þ Ti4þ (where M and i are metal i and interstitial sites, respectively). Diffusion coefficients for selfdiffusion of O and Ti in rutile (van Orman and Crispin, 2010) are significantly higher than the coefficients for Nb and Ta (this study; Fig. 3) and are therefore not limiting the diffusivities of the pentavalent ions. It has also been suggested that Nb incorporation into rutile and the fractionation of Nb/Ta in nature could be caused by a partial reduction of Nb to trivalent Nb (Horng and Hess, 2000). However, 3þ the existence of significant Nb in rutile or silicate melt has been disproved by experimental work over a wide range of f O2 (Klemme et al., 2005; Burnham et al., 2012). The relative partitioning of Nb and Ta between rutile and melt is independent of f O2 (Klemme et al., 2005), and XANES spectroscopy on glasses over a large range in T, P and f O2 demonstrated that Nb and Ta were exclusively present in the pentavalent state (Burnham et al., 2012).

2. Experimental methods In this study, two different experimental setups were employed to determine diffusivities of Nb and Ta in crystallographically oriented rutile: (1) Thin film diffusion couples were prepared by pulsed laser deposition (Dohmen et al., 2002a) and annealed in

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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gas mixing furnaces between 850 and 1150 1C and controlled f O2 (at the FMQ buffer). The TiO2 thin films were enriched with 1–3 wt% Nb and Ta (and Sm). The annealed samples, as well as the starting material, were analysed by secondary-ion mass spectrometry in the depth-profiling mode. (2) Rutile single crystals (mm-sized) placed in rutile-saturated Nb+Ta-doped silicate melt at 1250 1C for ∼6 days, again at f O2 at the FMQ buffer. Concentration profiles along the c- and a-axis of the run product rutiles were measured by electronprobe microanalysis. In all experiments diffusion of Nb and Ta was investigated simultaneously, which reduces the uncertainties in relative diffusivities of the two elements. 2.1. Sample preparation We have used the well-established protocol at Ruhr-Universität Bochum to prepare single crystals for diffusion experiments (Chakraborty, 1997; Dohmen et al., 2007). All crystals were prepared from a single green coloured, transparent, gem quality, synthetic rutile crystal, which is oriented parallel to the optical axis and hence the c-axis (tetragonal symmetry). Cross sections of ∼2:5 mm thickness were cut perpendicular to the c-axis and polished with a final polishing step using alumina suspension (OPA, Struers). From these cross sections smaller crystals were cut with a diamond wire saw to prepare crystals with the approximate dimensions of 2  2  2.5 mm3. For the majority of diffusion experiments we have coated these crystals with a 20–100 nm thin film of TiO2 , which is simultaneously doped in the oxides Nb2 O5 , Ta2 O5 , and Sm2 O3 . The thin films were deposited using the pulsed laser deposition system at the Institut für Geologie, Mineralogie und Geophysik, Ruhr-Universität Bochum (Dohmen et al., 2002a). For the target material we have used a synthetic polycrystalline pellet of TiO2 , enriched with 3 wt% Nb2 O5 , 3 wt% Ta2 O5 , and 6 wt% Sm2 O3 . The oxides were mixed in a mortar and cold-pressed into pellets, which were then sintered at 1200 1C in air for 20 h. The depositions were performed using an Excimer laser producing 193 nm laser pulses and a laser fluence of ∼5 J=cm2 . Prior to deposition, the crystals were heated in situ in the vacuum chamber at 400 1C for 10 min to remove possible volatile adsorbents. For the melt exchange experiment an Fe-free basaltic–andesitic glass doped with 1200 μg=g Nb2 O5 and 40 μg=g Ta2 O5 was synthesised with the nominal composition given in Supplementary Material. The composition was chosen such that the melt is rutile saturated at the experimental conditions according to Klemme et al. (2005). The powder mix was heated at 1450 1C for 3 h and quenched. The material was crushed, ground and re-heated at 1350 1C for 3 h, which produced a homogenous glass judged from visual inspection. 2.2. Diffusion experiments The thin film diffusion couples were annealed in gas mixing furnaces at Institut für Geologie, Mineralogie und Geophysik, Ruhr-Universität Bochum and the melt exchange experiment was performed in a similar setup at the Department of Earth Sciences, University of Bristol. With a continuous flow of CO and CO2 we have controlled the oxygen fugacity at conditions approximately equivalent to FMQ (Huebner, 1971). For the melt exchange experiment a rutile crystal was embedded into the powder within a platinum crucible and annealed at 1250 1C for 6 days. The experimental conditions are reported in Table 1. A LEO 1530 high-resolution thermally aided field emission gun scanning-electron microscope (SEM) at Bochum was used to characterise the thin films. It is equipped with electron backscatter diffraction (EBSD) detector, backscatter electron (BSE) detector, and an energy-dispersive detector system. EBSD was employed to

3

Table 1 Run conditions of experiments and determined diffusion coefficients for Nb and Ta in rutile. Run

Temperature run duration

log (fO2)

(1C)

(bar)

(h)

Pre-annealing experiment RtNbTaSm10a 1093 0.17 Diffusion parallel to the c-axis RtNbTaSm15 850 262.2 RtNbTaSm17 900 42.3 RtNbTaSm18 900 138.1 RtNbTaSm19 900 313.7 RtNbTaSm13 1047 1.83 RtNbTaSm9 1093 0.62 RtNbTaSm11 1093 2.92 RtNbTaSm1 1100 3.00 RtNbTaSm14 1147 1.25 b RtNbTaM1 1250 144.5

DNb

DTa

DNb/DTa

(Pa) (10−18 m2/s) (10−18 m2/s)

−10.0 −5.0 of rutile −14.1 −13.3 −13.3 −13.3 −10.7 −10.0 −10.0 −11.0 −9.2 −7.9

−9.1 0.015 −7.3 0.060 −7.3 0.083 −7.3 0.090 −5.7 8.0 −5.0 20 −5.0 15 −6.0 30 −4.2 40 −2.9 700

Diffusion parallel to the a-axis of rutile 1250 144.5 −7.9 −2.9 RtNbTaM1b

90

o 0:009 n.d. n.d. 0.005 4.9 11.5 3.8 5 24 200

4 1:7 n.d. n.d. 18.0 1.6 1.7 3.9 6.0 1.7 3.5

30

3.0

n.d., not determined (diffusion profile too short to quantify with the given depth resolution of the SIMS analysis). Oxygen fugacity was set equivalent to the fayalite ¼ magnetite+quartz buffer (FMQ), except for RtNbTaSm1, for which Δ logðf O2 ÞFMQ ≈−1. a Pre-annealing experiment to re-crystallize the thin film, diffusion profile too short to identify with the given depth resolution of the SIMS analysis. b Melt-exchange diffusion experiment.

characterise the extent of crystallisation in the initially amorphous thin film. A cross section of the sample RtNbTaM1 was polished for analysis with the JEOL JXA-8600 electron microprobe at the Department of Earth Sciences, University of Bristol. Various profiles were measured perpendicularly from the surface towards the core of the crystallographically oriented rutile single crystal. Four elements were analysed (Ti, Si, Nb, and Ta) in the wave-length dispersive mode with an acceleration voltage of 25 kV and a beam current of 80 nA. Counting times were 400 s for the peak and 200 s for the background. The measurement conditions were optimised to obtain reasonable statistics for the Nb and Ta concentrations. Secondary ion mass spectroscopy (SIMS) analyses were performed using the Cameca ims 3f ionprobe installed at the Institut für Geowissenschaften, Universität Heidelberg. Modifications to the instrument include improved high voltage power supplies, a completely re-designed magnet control and a new electron multiplier counting system. The in-house developed control and analysis software LabSIMS is based on LabVIEW. − Depth profiling analyses were performed using a 14.5 keV 16 O primary ion beam, which was rastered over a square area of the sample surface. This area was 200  200 μm2 wide for earlier analyses and 150  150 μm2 wide for later analyses. The secondary magnification was set to an imaged field of 150 μm, and a 400 μm field aperture was employed to limit the secondary ion beam, which reduces the diameter of the area analysed to ∼35 μm. This blocks the contribution of ions derived from the edge of the rastered area during depth profiling. It discriminates for ions derived from the flat bottom of the crater, resulting in secondary ions that give a good representation of the element abundances with progressing depth of sputtering. Positive secondary ions were nominally accelerated to 4.5 keV and the energy window was set to 720 eV with an offset of 90 eV (energy filtering). The instrument was used at its lowest mass resolution (m=Δm10%≈400). Molecular interferences were suppressed sufficiently with one notable exception: 93Nb is interfered by 46Ti47Ti (46Ti47Ti/ 50 Ti≈1  10−4 ). This interference was corrected for by assuming

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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3. Results After the diffusion anneal the initially greenish and transparent crystals became very dark with a metallic lustre at the thin film surface, which indicates that free electrons were formed during the annealing. Nevertheless the crystal was stable at the experimental conditions as shown for example by the homogeneous EBSD patterns characteristic for rutile surfaces perpendicular to the c-axis. However, small crystals have formed on the surface (see Supplementary material) that may have concentrated the dopants due to their finite solubility in the rutile structure. Samarium was added as an indicator for the artefacts, which govern the depth resolution of the SIMS depth-profile measurements. All measured profiles of samples annealed at high temperatures show a much steeper slope for Sm compared to Nb and Ta (Fig. 1). This indicates that Sm diffuses much more slowly, but also that it is much less soluble in rutile and hence concentrates within the nanometersized crystals formed at the surface. The Sm profile was, therefore, used as an internal reference for the depth resolution. The comparison of the profiles of the samples from the time series at 1093 1C (Table 1) shows very little change in the Sm profile shape and length. In contrast, Nb and Ta show a systematic increase in the profile length with time. Another obvious feature of all profiles is that the diffusion profile lengths of Nb are systematically longer than those of Ta, or to be more exact, the slope of the concentration profiles of Nb is systematically lower than that of Ta (Fig. 1). The profiles of Nb and Ta were fitted with the analytical solution of the continuity equation with the respective boundary and initial conditions. The effects of the sample surface and

Concentration (µg/g)

10,000

RtNbTaSm1 SIMS; thin film T = 1100 ºC t = 3.0 h

1000

Nb

100

Ta

10

Sm 1 0

0.5

1.0

1.5

2.0

RtNbTaSm19 SIMS; thin film T = 900 ºC t = 313.7 h

10,000

Concentration (µg/g)

a small initial concentration of Nb in the rutile when fitting diffusion profiles to the SIMS data. For the concentration profiles the count rates of 93Nb, 152Sm and 181Ta were normalised to the count rate of 50Ti. The proposed rutile reference material R10 was used to determine relative ion yields (Luvizotto et al., 2009). The sputtering rate and hence the depth scale is calibrated using a white light (phase shift) interference microscope from ATOS, Darmstadt, Germany, operating in the wave mode. The sputtering rates were linearly dependent on the primary beam current (see Supplementary material). We determined a normalised sputtering rate of ð179 7 5Þ  10−5 m=s=A for rutile (for the 200  200 μm2 rastered area). Sputtering durations are converted to a depth scale using this factor. In addition, the 50Ti signal serves as a direct indicator for the sputtering rate. Sources of uncertainty in the extraction of diffusion coefficients from SIMS depth profiles are sputtering-induced roughness, atomic intermixing, and initial roughness of the sample surface, which control the effective depth resolution and lead to convolution of the true diffusion profile (Ganguly et al., 1988; Dohmen et al., 2002b; Dohmen, 2008). The contribution of the sputteringinduced roughness and atomic intermixing is calibrated with measurements on the un-annealed or pre-annealed reference samples following the procedure of Hofmann (1994) (see Dohmen et al., 2002b; Dohmen, 2008). The surface roughness of such samples is typically below 10 nm as indicated from interference light microscopy measurements. The steepness of the measured concentration gradient at the thin film/substrate interface of the reference samples is the major indicator for the depth resolution as defined by the specific analytical setup, such as beam current and measurement geometry. Our calibrations have shown that with the given measurement settings atomic intermixing can be accounted for by a mixing length of ∼5 nm and the sputteringinduced roughness by a s of only ∼6 nm, similar to earlier findings (Dohmen et al., 2002b). The resulting fit for the Ta, Nb, and Sm profiles are shown in Supplementary material.

1000

Nb 100

Ta 10

Sm 1 0

0.5

1.0

1.5

2.0

RtNbTaSm9 SIMS; thin film T = 1093 ºC t = 0.62 h

10,000

Concentration (µg/g)

4

1000

Nb 100

Ta

10

Sm 1 0

0.5

1.0

1.5

2.0

Depth (µm) Fig. 1. Concentration-depth profiles of Sm, Ta, and Nb in three different experimental run products. It can be immediately recognised from the respective slopes that DSm 5 DTa o DNb . The solid black lines are best fits of the profiles considering convolution effects of the depth profiling. For Sm a step function was assumed as in the short-anneal profiles (see Supplementary material). (a) RtNbTaSm1, (b) RtNbTaSm19 and (c) RtNbTaSm9.

sputtering-induced roughness, as well as the interatomic mixing as calibrated on the reference samples (see above), were also considered. The simple geometry of the diffusion couples (thin film + substrate) allows reducing the diffusion problem to a onedimensional system. We have used the analytical solution of Lovering (1938) for an isolated composite semi-infinite medium, where the two diffusion media (polycrystalline film and single crystal substrate) have different, but constant diffusion coefficients. The original analytical solution was for a thermal conductivity problem and we translated this into a diffusion problem following Crank (1975). The detailed equations are given in Supplementary material. The rutile crystal recovered from the melt exchange experiment after the diffusion anneal within the melt had preserved its original shape. No evidence of significant resorption was found at

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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5

Concentration (wt%)

0.25

0.20

Nb

0.15

0.10

Ta

0.05

0

0

10

20

30

40

50

60

70

80

90

Concentration (wt%)

0.08

0.06

Fig. 3. Arrhenius plot showing diffusion coefficients of Nb and Ta in rutile parallel to the c-axis from this study compared to various other elements. Note that Nb and Ta diffusivities were determined simultaneously in all experiments to reduce the uncertainties on the relative diffusivities of the two elements. Data from the literature (dotted lines) are Ti self-diffusion at f O2 ¼ FMQ (Hoshino et al., 1985; van Orman and Crispin, 2010); O self-diffusion was found to be independent of f O2 between air and nickel-nickel oxide (NNO) (Moore et al., 1998). The fast diffusion mechanism for O is shown, which is relevant for dry conditions (Moore et al., 1998). Pb diffusion at f O2 between NNO and FMQ (Cherniak, 2000); Hf and Zr were found to have the smallest and very similar diffusion coefficients, independent of f O2 (Cherniak et al., 2007).

Nb 0.04

Ta 0.02

0 0

10

20

30

40

50

60

70

80

90

Fig. 2. (a) Back-scattered electron image of the rutile–glass contact from the run product of experiment RtNbTaM1. The bright needles within the glass region are rutile crystals and hence the melt was clearly rutile saturated. No other crystalline phase was observed than rutile. The solid line indicates the location of the electron microprobe profile. (b,c) Concentration profile for Nb and Ta measured with the electron microprobe perpendicular to the melt–rutile interface (b) parallel to the crystallographic c-axis and (c) parallel to the crystallographic a-axis.

the crystal edges. Additional rutile needles had formed in the melt (Fig. 2a) since the melt was over-saturated in TiO2 with respect to rutile, and some rutile may have precipitated on the surface of the large single crystal. All concentration profiles measured show that Nb and Ta concentrations increase continuously from the core to the surface (e.g., Fig. 2b and c). These profiles were fitted with the complementary error function, the analytical solution for a semiinfinite one-dimensional geometry with a fixed surface concentration as given by Crank (1975, see Supplementary material). The fitted EPMA profiles revealed that Nb diffused faster than Ta, hence DNb 4 DTa (the symbol D is used for diffusion coefficients, whereas in this paper partition coefficients are symbolised by the letter K to avoid confusion). This result is consistent with the thinfilm experiments analysed by SIMS. Furthermore, we have found that the diffusion in rutile is anisotropic, with D parallel to the

crystallographic c-axis of rutile being larger by a factor of ∼8 than D parallel to the crystallographic a axes. The diffusion tensor is fully determined by the diffusivities along these two axes, due to the tetragonal symmetry of rutile. Our experiments span more than four orders of magnitude in the determined diffusion coefficients. The large temperature range investigated (850–1250 1C) minimises the uncertainties on activation energies and eliminates the need for extrapolation of experimental data to temperatures relevant for partial melting in nature. All our experiments demonstrate that diffusion coefficients for Nb in rutile are several times higher than those for Ta, with a best estimate of DðNbÞ=DðTaÞ ¼ 4:0 (Fig. 3). This opens the door for significant kinetic fractionation of the two elements. The temperature-dependent diffusion coefficients are (Fig. 3) logðDNb Þ ¼ −2:28ð 70:40Þ−ð1:972 7 0:051Þ  104 =T with D0 ¼ 5:3  10

−3

ð1Þ

m2 =s and Q ¼ 377:5 7 9:8 kJ=mol, and

logðDTa Þ ¼ −2:20ð 7 1:42Þ−ð2:05 7 0:19Þ  104 =T

ð2Þ

with D0 ¼ 6:3  10−3 m2 =s and Q ¼ 392 7 36 kJ=mol. The diffusion coefficients determined for Nb and Ta in rutile are higher than those of Pb, Zr and Hf as determined in earlier studies, and the two pentavalent ions show a higher activation energy (Fig. 3). Diffusion of the pentavalent ions is slower than self-diffusion of Ti and O in rutile (Fig. 3). The possible effects of kinetic fractionation in natural partial melting and melt extraction scenarios depend on grain sizes, temperatures and the time scales involved.

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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4. Equilibrium melting Conventionally, partial melting of silicate rocks is envisioned to proceed through complete equilibration of each and every portion of melt with the restitic minerals, after which melt and restitic minerals are separated. Geochemical models that describe this process employ either a batch melting scenario or a fractional melting scenario (e.g., Shaw, 1970; Hofmann, 1988). In a batch melting scenario, the total generated melt equilibrates with the restitic minerals before it is extracted from the rock volume. In a fractional melting scenario, subsequent portions of melt are generated, equilibrated with the restitic minerals and extracted from the rock volume. The melt is then pooled and homogenised externally. Rayleigh melting is the extreme case of fractional melting, in which an infinite number of infinitely small melt portions are extracted, with each melt portion in equilibrium with the restitic minerals at the time of their extraction. The time constraint for equilibrium batch melting is that the generated melt remains in contact with the restitic minerals long enough to reach chemical equilibrium prior to its extraction. In a fractional melting scenario, this time span has to elapse for each individual melt fraction, which renders Rayleigh melting an impossible scenario and an entirely theoretical exercise. The concentration of trace elements in the melt and restite in these models is calculated from the total fraction of melt, and the bulk partition coefficients between melt and restitic minerals. The bulk partition coefficient is the sum of the mineral–melt partition coefficients of all minerals multiplied by their modal abundances in the restitic rock. Mineral-melt partition coefficients are, therefore, of central importance to all partial melting models. However, it is crucial to recognise that all these models are based on the assumption of complete equilibrium between each extracted melt batch and the restitic minerals. The elements Nb and Ta in highpressure crustal rocks, such as eclogite and granulite, are almost exclusively governed by rutile. Hence, bulk rock-melt partitioning of Nb and Ta during crustal partial melting is determined by partitioning and equilibration of rutile and melt. Equilibration of minerals with a melt (or fluid) may proceed through two different mechanisms, i.e., diffusion or dissolution– reprecipitation. The latter process has been used to explain observations in natural rocks and has been reproduced in experiments, mostly in fluid–mineral interaction processes, but also in mineral–melt systems (Nakamura and Shimakita, 1998; Putnis, 2002, 2009; Harlov et al., 2007; Lucassen et al., 2012). The dissolution–reprecipitation process is driven by the difference in free energy between the dissolving and the precipitating phases. This difference is large for reactions that involve changes in the mineral polymorph, or in the major or minor element composition of the minerals. Yet, it diminishes for reactions that involve only small changes in their trace-element contents, such as high and low-Nb rutile. Dissolution–reprecipitation processes generally produce very homogenous minerals without any growth zones or zones of diffusive enrichment or depletion, except for the sharp interface between the original and the reprecipitated domains in crystals where the process was not completed. Natural rutile, in contrast, commonly shows significant growth zoning and diffusion zoning in Nb and Ta (Schmidt et al., 2009; Lucassen et al., 2010; Kooijman et al., 2012), arguing against the widespread occurrence of dissolution–reprecipitation of rutile. Also, the rutile single crystal in our rutile–melt experiments did not undergo any dissolution–reprecipitation in the presence of the melt. Instead, it clearly shows elemental zonation produced by diffusion (Fig. 2). Equilibration of Nb and Ta between rutile and melt is, therefore, unlikely to proceed through a dissolution– reprecipitation process. However if it did, the Nb–Ta fractionation mechanism would be independent of the solid-state diffusion of

Nb and Ta in rutile, and instead would be governed by their diffusion in the melt relative to the reaction progress of the dissolution–reprecipitation process. In such a case, an equilibrium batch melting model may realistically describe the process, if all rutile in the protolith was dissolved and reprecipitated in the process. Future detailed investigation of natural rutile may reveal under what conditions dissolution–reprecipitation processes occur in rutile. Yet, for the reasons listed above, we consider this mechanism unlikely and do not further discuss it in this paper. Experimental work on Nb and Ta partitioning between rutile and silicate liquid has revealed that both elements are strongly compatible in rutile (Green and Pearson, 1987; Foley et al., 2000; Schmidt et al., 2004; Klemme et al., 2005; Klimm et al., 2008; Xiong et al., 2011). At high temperatures ( 4 1000 1C), Ta is even more compatible than Nb, whereas lower-T experiments revealed identical rutile–melt partition coefficients for Nb and Ta (Schmidt et al., 2004; Xiong et al., 2011). For high-T melting scenarios this invariably leads to the prediction of high Nb/Ta ratios in melts in equilibrium with any rock containing restitic rutile, and low Nb/Ta ratios in the restitic rock. This is in stark contrast to the low Nb/Ta ratios observed in the continental crust; the differentiated continental crust represents the extracted melt and should therefore comprise a Nb/Ta ratio higher than the bulk silicate Earth (BSE), if it was generated through equilibrium melting. In the same way, sphene, ilmenite and other Fe–Ti oxides all show a preference of Ta over Nb in experiments (Green and Pearson, 1987; Tiepolo et al., 2002; Prowatke and Klemme, 2005; Klemme et al., 2006; Xiong et al., 2011) and are therefore not suitable to explain the low Nb/Ta ratio of the continental crust. At low temperatures (900–1000 1C) no fractionation of the Nb/Ta ratio between restite and melt is expected from the rutile/melt partitioning experiments (Schmidt et al., 2004; Xiong et al., 2011), and no differences in Nb/Ta should arise from crustal melting at these temperatures.

5. Kinetic fractionation melting Equilibrium-melting models largely fail to explain the Ti–Nb–Ta depletion of the continental crust in combination with its low Nb/ Ta ratio (see detailed discussion in Supplement). Consequently, the assumption of equilibrium between minerals and liquid during melting and melt extraction has to be revisited. The vast majority of geochemical models are based on the assumption of complete equilibrium between restitic rocks and extracted melts. Yet, a small number of studies have modelled the diffusive equilibration of trace elements in partially molten rocks with implications for the grain sizes and time scales required to justify the assumption of equilibrium (Richter, 1986; Qin, 1992). These studies also concluded that some elemental and isotopic anomalies observed in crust- and mantle-derived magmatic rocks were possibly produced by the effects of diffusion and incomplete equilibration in the source region of the melts (Qin, 1992; Burnard, 2004; van Orman et al., 2006). Here we pursue the scheme of these earlier models and investigate the consequences of partial melting on Nb and Ta diffusion in restitic rutile. The details of the batch partial melting model are discussed below, whereas details on diffusion modelling and input parameters are presented in Supplementary material. The possible effects of kinetic fractionation in natural partial melting and melt extraction scenarios depend on grain sizes, temperatures and the time scales involved. Grain sizes of rutile in eclogite are typically in the range of 30–300 μm (Mauler et al., 2001; Zack et al., 2002), but reach up to several millimetres in some cases (Xiao et al., 2006). In lower-crustal granulites, rutile may occur as small grains (∼100 μm), but often forms grains in the

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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range of 0.5–5 mm (Vry and Baker, 2006; Luvizotto and Zack, 2009). High-temperature metamorphism leading to anatexis and the generation of felsic melts occurs on time scales of millions of years. Yet, partial melting and separation of melt from restitic rocks must be subdivided into several physical processes that operate much more rapidly, namely melting, melt segregation and melt extraction (Harris et al., 2000). Melting typically proceeds by dehydration of hydrous minerals or by the influx of hydrous fluid above the wet solidus of the rock. The rate-limiting factor for dehydration melting is the heat flux, which has to provide the latent heat of fusion. Models predict that a lower limit of hundreds to thousands of years are required for generating significant portions of partial melt once the solidus is reached (Rutter and Mecklenburgh, 2006). This time limit is violated, however, if overstepping of the melting temperature occurs, in which case melting proceeds much more rapidly once it is initiated, and significant melt fractions may be generated within years to decades (Harris et al., 2000). In subducting slabs, melting of the relatively hot surface of the slab may be triggered by the influx of hydrous fluids derived from metamorphic dehydration of rocks located deeper inside the slab. Flux melting probably proceeds on a timescale of weeks or months (Harris et al., 2000). Once formed, the melt starts to segregate into pods and veinlets, which will mechanically separate it from the restitic minerals and will largely prohibit further equilibration of partial melt and restite. It has been argued, based on trace-element disequilibria in granites, that separation of silica-rich melts from restites may be completed within less than one century in some cases and in less than ten thousand years in a more conservative estimate (Harris et al., 2000). Models of the rheology of partially molten rocks also suggest that efficient melt extraction assisted by deformation proceeds on timescales of 101 –104 years (Rutter and Mecklenburgh, 2006; Rushmer and Knesel, 2011). A significant portion of the continental crust was formed in the Archaean, and models suggest a two-stage process, where primitive

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basaltic crust is extracted from the mantle, similar to the formation of modern oceanic crust. In a second stage, this primitive crust was partially melted at high pressures to form Na-rich intermediate to felsic liquids that generated intrusions of the trondhjemite–tonalite–granodiorite (TTG) series dominating the Archaean crustal record (Clemens et al., 2006; Xiong et al., 2009). This second stage was suggested to occur either by subduction of the basaltic crust along island arcs (Drummond and Defant, 1990; Foley et al., 2002), or on the base of thick oceanic plateaux (Kröner, 1985; Willbold et al., 2009). Early Archean TTG gneisses dating back as far as 3.8 Ga show a large spread in Nb/Ta ratios, reaching from subchondritic to strongly superchondritic values (Rapp et al., 2003; Xiong et al., 2011; Hoffmann et al., 2011). Hence, the mechanism that fractionated the two elements had already affected the oldest accessible crust. Studies on Archaean TTG rocks combined with experimental work demonstrated that TTG melts were most likely generated by melting of hydrous, amphibole-bearing basaltic rocks at 45–75 km depth and temperatures between 750 and 950 1C (Clemens et al., 2006; Xiong et al., 2009; John et al., 2011). A common feature of these experiments is that they produced rutile-bearing restitic assemblages along with felsic, Na-rich magmas that resemble the major and trace-element compositions of the Archaean TTG. Equilibrium melting would require sufficient time for diffusion of elements in and out of the refractory minerals, which depends on the kinetic parameters discussed above. The physical model displayed in Fig. 4 demonstrates the mechanism of trace-element fractionation during partial melting, starting with a rutile-bearing protolith with equilibrated Nb and Ta (Fig. 4a). Approximately 99% of the rock's Nb and Ta budget are controlled by the rutile. The protolith has no trace-element anomalies for the sake of simplicity. Rutile remains a stable phase to high degrees of partial melting of eclogite; however, its modal abundance decreases with progressive melting, saturating the growing melt fraction in rutile (Ryerson and Watson, 1987; Klemme et al., 2002; Gaetani et al., 2008; Xiong et al., 2011). The dissolved portion of the rutile

Fig. 4. Schematic drawing showing the mechanisms and geochemical effects of partial melting with incomplete diffusive equilibration of Nb and Ta between melt and rutile. Sections (a)–(e) depict a time series through partial melting and melt extraction with time scales approximated by the arrows.

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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releases Nb and Ta into the melt, which has at this point no significant Nb–Ta anomaly and a Nb/Ta ratio identical to the initial and remaining rutile (Fig. 4b). The partial dissolution of the rutile grains strongly enriches the melt in Nb and Ta, generating a transient disequilibrium between the newly formed melt and the restitic rutile (see Supplementary material for a quantitative discussion of the parameters). The high partition coefficients of Nb and Ta demand that these elements diffuse from the melt into the restitic rutile to re-establish traceelement equilibrium. A negative Nb–Ta anomaly develops in the melt and the faster diffusivity of Nb in rutile leads to a more rapid uptake of Nb into the rutile compared to Ta (Fig. 4c). This leads to a transient stage where the melt shows a Nb/Ta ratio lower than that of the protolith and the restite. After typically hundreds to thousands of years the melt is separated from the restitic minerals, starts to pool in pods and veinlets inhibiting further equilibration, and is finally extracted from the rock volume (Fig. 4d). Intra-grain Nb–Ta zonation in the rutile will diffuse away for rocks that stay at high temperatures, but the bulk restite and bulk extracted melt will preserve the high and low Nb/Ta ratios, respectively (Fig. 4e). Single rutile grains will preserve the Nb/Ta ratio produced during partial melting, because both elements are highly incompatible in the rock-forming minerals, and their Nb/Ta ratio within one rock sample will depend on grain size. The prediction of our kinetic fractionation model is that the faster diffusion of Nb in rutile leads to a preferential enrichment of Nb in the restitic grains, initially along their edges (Fig. 5a). This creates a high-Nb/Ta zone that migrates from the rim to the core of the grain with time while decreasing in amplitude as Ta diffusion also becomes significant (Fig. 5a). At the same time, the finite volume of melt is preferentially depleted in Nb and develops a low Nb/Ta ratio. This lowers the Nb/Ta ratio at the rutile–melt interface and imprints a low Nb/Ta ratio onto the rim zone of the rutile (Fig. 5a). The high-Nb/Ta zone migrates towards the centre of the grain, while the low-Nb/Ta zone widens, but both zones decrease in amplitude as Ta also diffuses into the rutile. After extensive equilibration times (∼1 Ma at 850 1C for a grain with 500 μm radius), the entire grain is equilibrated and shows a constant Nb/ Ta ratio from core to rim, which is identical to the Nb/Ta ratio of the surrounding melt and to the initial ratio (Fig. 5a). Note, however, that the concentrations of Nb and Ta in the equilibrated rutile are higher than in the initial rutile, whereas they are significantly lowered in the melt. The Nb/Ta ratio of the bulk rutile as a function of time is calculated by integrating over the timedependent core–rim profiles. Note that the volume of the grain increases with the cube of the radius and that anomalous zones in the core–rim profile that are closer to the edge of the grain, therefore, have a stronger leverage on the ratio of the bulk grain. The Nb/Ta ratio of the bulk rutile and of the coexisting melt as a function of equilibration time are most relevant for the geochemical evolution of the melt–restite system and for the differentiation of the continental crust (Fig. 5b). Diffusive fractionation is a transient process, and its magnitude will depend on grain size, temperature and equilibration time. A decrease of Nb/Ta from 14 to 12, as observed in the continental crust relative to the BSE, would require that melt and restitic rocks equilibrated for an average of no longer than ∼104 years during differentiation of the continental crust (Fig. 5b). The wide range in Nb/Ta ratios found in TTG gneisses and eclogite xenoliths and the weak or lacking correlation of Nb/Ta with any other geochemical tracer (Rudnick et al., 2000; Rapp et al., 2003; Aulbach et al., 2011) are predicted for the kinetically controlled process, but are difficult to reconcile with equilibrium melting models. The time scales and temperatures involved in melt segregation in crustal rocks are in many cases sufficient for Nb – but not for Ta – to reach equilibrium between the restitic rutile grains and the

Fig. 5. Modelled Nb/Ta ratios of rutile and melt in partial melting scenario. (a) Core-to-rim internal zonation of rutile grain at different melt–restite equilibration times. (b) Rutile and melt evolution as a function of time. The curves show the evolution of the Nb/Ta ratio integrated over the entire rutile grain(s) in the restite and that of the bulk melt as a function of time for two different relative diffusivities of Nb and Ta typically observed in our experiments. BSE, bulk silicate Earth; CC, continental crust.

partial melts. Nb/Ta ratios are predicted to be out of equilibrium over more than six orders of magnitude in time and to produce melts with Nb/Ta ratios significantly lower than the protolith (Fig. 5). The maximum amount of decrease in the melt's Nb/Ta ratio is mainly controlled by the rutile–melt partition coefficients and therefore dominantly a function of temperature. At low temperatures, the ratio in the restitic rutile is only slightly elevated compared to the protolith, due to mass balance and the large partition coefficients. The temperature–time plot in Fig. 6 displays three fundamentally different melting regimes, depending on the (non-)equilibrium of two elements between restitic minerals and melt: (1) The green field in the upper right corner is the field of equilibrium partitioning of Nb and Ta between melt and rutile. This is the classical melting model that all previous studies build on (two different shapes for a Nb–Ta trough as it would appear in a multi-element plot are given for low and high temperature, respectively). However, very high melting temperatures or exceedingly long equilibration times would be needed to reach this field. (2) The lower left corner (blue shading) is a scenario with very short equilibration times at low temperatures. These conditions do not allow for any diffusive equilibration of Nb

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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Fig. 6. Temperature–time plot displaying different melting regimes for Nb and Ta and restitic rutile. The principle regimes are non-equilibrium fusion (blue field, bottom left), kinetic fractionation melting (reddish fields, from top left to bottom right) and equilibrium melting (green field, top right), respectively. Shades of red fields depict kinetic fractionation regimes for 10, 100 and 1000 μm grain diameter, respectively. Boxes for various natural melting regimes depict estimates for the time scales of melting and segregation of individual melt batches, rather than total durations of partial melting events. Also displayed are schematic multi-element plots (“spidergrams”) that depict the incompatible-element patterns of melts produced in the different fields. Nb–Ta troughs are predicted to vary in depth and slope depending on the degree of rutile–melt equilibration. Grey boxes mark temperature ranges important for the dominant melting mechanisms in natural rocks (PWS, pelite wet solidus; BWS, basal wet solidus; Ms-DM, muscovite dehydration melting).

and Ta between rutile and melt, and the melt would simply extract the trace elements that are released by fusion of rutile. The melt would in this case be enriched in Nb and Ta with respect to the equilibrium scenario, and its Nb/Ta ratio would mimic that of the initial rutile. The melt in this non-equilibrium fusion scenario has a shallow and unfractionated Nb–Ta trough (Fig. 6). (3) The red fields in the centre of the diagram depict the parameter space (T; t, grain size) in which Nb–Ta fractionation is predicted to be controlled by the differential diffusion of the two elements in the restitic rutile (kinetic fractionation melting). This process would result in a melt composition with a significant Nb–Ta trough and a low Nb/Ta ratio. Most scenarios for melting in crustal environments, including the conditions estimated for the generation of TTG magmas, lie in the kinetic fractionation melting field and cannot be expected to produce melts that are in trace-element equilibrium with their restites. Our model predicts that rutile and the restitic rock will retain concentrations of Nb and Ti close to equilibrium in almost all crustal melting scenarios (except for cases with very rapid melt segregation), whereas Ta will be depleted with respect to the equilibrium scenario. In contrast, the melt will contain an excess of Ta, because of the insufficient time available for Ta to diffuse back into the restitic rutile. Hence, the diffusive fractionation of Nb and Ta combined with their high compatibility in rutile is predicted to generate partial melts from rutile-bearing rocks with negative Ti, Nb and Ta anomalies in combination with Nb/Ta ratios significantly lower than the protolith. The restite, in contrast, will be Ti, Nb and Ta rich with slightly elevated Nb/Ta ratios, which may contribute to the source of ocean island basalts and continental intraplate volcanoes. Kinetic fractionation melting, therefore, provides a satisfactory model for the observed Nb/Ta ratios of the

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continental crust being lower than the BSE in combination with its elemental negative anomalies. This has not been achieved by equilibrium melting models. The mechanism behind the faster diffusion of Nb compared to Ta in rutile is unknown. Our experiments demonstrate that diffusion coefficients for Nb are 1.6–18 times higher than those for Ta, whereas the activation energies are very similar (Fig. 3). Diffusion is generally influenced by the mass of the diffusing ions, and Nb and Ta show large differences in their average atomic masses by a factor of approximately two (92.91 u vs. 180.95 u, respectively). However, this mass difference cannot explain the very large difference in diffusivity we found in this study, as theoretical predictions provide a limit of DNb =DTa ¼ ðmTa =mNb Þβ , where β is an empirical factor that is largest at 0.5 for ideal gases (e.g., Richter et al., 1999). Hence, the mass difference can account for a difference in the diffusion coefficients of no more than a factor of 1.4. Trace-element diffusion and mineral–melt partitioning are related to each other, as both depend on the incorporation of the trace element into crystallographic sites in the mineral structure. Partition coefficients for the two elements in most minerals, including rutile, are very similar or indistinguishable. The two elements have the same ionic charge (i.e., 5+) and the same ionic radius (64 pm; Shannon, 1976), or at least very similar radii (Tiepolo et al., 2000). This similarity in charge and radius explains the close geochemical similarity of the two elements, following Goldschmidt's rules. However, as pointed out by Goldschmidt, ionic radius and charge are not the only factors that determine substitution in minerals, but the electronegativity also influences the bond strength and, hence, the potential for substitution. Nb and Ta show differences in electronegativity (1.6 vs. 1.5, respectively; Pauling, 1960) and in their first ionisation potentials (652 kJ/mol vs. 761 kJ/mol, respectively; Kerr, 2000). This will cause differences in their bond strengths in the rutile structure, which may explain differences in their diffusivities in that mineral. This is obviously speculative, but we are unable to provide a more satisfying or quantitative explanation for the observed difference in the diffusivities of the two elements. Instead, we encourage future crystal chemical and diffusion studies to focus on this phenomenon.

6. Conclusions and model predictions This study demonstrates that Nb and Ta are significantly fractionated kinetically by diffusion in rutile, and that Nb/Ta systematics of partial melts and restites will likely be influenced by kinetic factors. Two different experimental setups were employed to determine diffusivities of Nb and Ta in rutile: (1) Thin film diffusion couples were annealed in gas mixing furnaces and the resulting diffusion profiles were analysed by SIMS in depth profiling mode. (2) Rutile single crystals were placed in rutile-saturated Nb–Ta-doped basaltic melt and lateral diffusion profiles were analysed by EPMA. Both sets of experiments demonstrate consistently and unequivocally that diffusion coefficients in rutile of Nb are 1.6–18 times higher than those of Ta for the entire temperature range. The significantly higher mobility of Nb compared to Ta in rutile may have consequences for their liquid-rock fractionation during partial melting events. Traceelement equilibrium cannot be expected for the natural range of grain sizes of rutile and the temperatures and time scales involved in partial melting of crustal rocks, as demonstrated here in a batchmelting model. Instead our results suggest that the low Nb/Ta ratios of crustal rocks and the high and variable Nb/Ta ratios observed in Archaean eclogites are caused by partial (as opposed to complete) equilibration of rutile and melt. The diffusive fractionation of Nb and Ta combined with their high compatibility in rutile predicts that partial melts generated in a rutile-bearing crust will have negative Ti anomalies in combination with Nb/Ta ratios significantly lower than

Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i

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the protolith. The restite, in contrast, will be Ti rich with slightly elevated Nb/Ta ratios. These signatures are in agreement with the overall signature of the continental crust, in contrast to the predictions derived from equilibrium melting models. Rutile–melt disequilibrium will probably govern the Nb–Ta systematics of melts and rutile-bearing restites for partial melting scenarios in the lower crust and in subducting slabs. The assumption of bulk trace-element equilibrium partial melting will have to be abandoned for the processes of crustal differentiation, at least for the element pair Nb–Ta, if the results from this study will be confirmed by studies on natural rocks. The model presented in this paper makes several predictions that may be used to test it against existing equilibrium melting models. Rutile-bearing granulites and eclogites that underwent partial melting are predicted to preserve a Nb/Ta ratio slightly higher than the rocks' protoliths. In cases where the partially melted rocks occur as orogenic eclogites or granulites with an extensive post-melting high-T history, Nb and Ta in individual rutile grains will be unzoned due to the internal diffusive equilibration. However, restricted diffusion of Nb and Ta in the silicate matrix of the rock, i.e., between different rutile grains, may help to preserve differences in Nb/Ta ratios related to the size of different rutile grains. Our model predicts that small grains would likely represent Nb/Ta ratios equilibrated with the melt, whereas large rutile grains would show elevated Nb/Ta ratios. Furthermore, inclusions in rock-forming minerals that were spatially isolated from the melt are expected to preserve the initial Nb and Ta concentrations and the Nb/Ta ratio of the protolith rutile. The concentrations of both elements in this inclusion rutile would be slightly lower than those in the diffusively enriched rutile of the rock matrix that was in contact with the melt. It is noteworthy in this context that the rutile budget of rocks is generally dominated by grains in the rock matrix as opposed to inclusions (Watson et al., 1989). Rutile-bearing partially melted xenoliths that are rapidly quenched after the partial melting event are predicted to preserve a strong intragrain zonation in Ta and Nb/Ta. Rutile grown from melt in high-T experiments (see respective field in Fig. 6) is predicted to preserve growth zoning in Ta with concentrations decreasing from core to rim, due to progressive Ta depletion in the melt. The faster diffusion of Nb is predicted to equilibrate this element in the same experiments. Finally, partially melted biotite-rich granulites that produce rutile during the melting reaction (Luvizotto and Zack, 2009) are predicted to show a stronger grain-to-grain variation in Ta and Nb/Ta than in Nb, again related to the grain size of the peritectic rutile.

Acknowledgements We are grateful to Nobu Shimizu, Andrew Putnis and Stephan Klemme for discussion and comments, and to Bruce Watson for a very insightful review that inspired a significant refinement of this paper. We thank Stuart Kearns for assistance with the electron microprobe, and Mark Harrison for editorial handling. Financial support from NSF (EAR Grant #1220533) to H.R.M. is acknowledged.

Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.epsl.2013.05.055.

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Please cite this article as: Marschall, H.R., et al., Diffusion-induced fractionation of niobium and tantalum during continental crust formation. Earth and Planetary Science Letters (2013), http://dx.doi.org/10.1016/j.epsl.2013.05.055i