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Diffusive exchange of trace elements between alkaline melts: implications for element fractionation and timescale estimations during magma mixing

The diffusive exchange of 30 trace elements during the interaction of natural mafic and silicic alkaline melts was experimentally studied at conditions relevant to shallow magmatic systems. In detail, a set of 12 diffusion couple experiments have been performed between natural shoshonitic and rhyolitic melts from the Vulcano Island (Aeolian archipelago, Italy) at a temperature of 1200 {\deg}C, pressures from 50 to 500 MPa, and water contents ranging from nominally dry to ca. 2 wt. %. Concentration-distance profiles, measured by Laser Ablation ICP-MS, highlight different behaviours, and trace elements were divided into two groups: (1) elements with normal diffusion profiles (13 elements, mainly low field strength and transition elements), and (2) elements showing uphill diffusion (17 elements including Y, Zr, Nb, Pb and rare earth elements, except Eu). For the elements showing normal diffusion profiles, chemical diffusion coefficients were estimated using a concentration-dependent evaluation method, and values are given at four intermediate compositions (SiO2 equal to 58, 62, 66 and 70 wt. %, respectively). A general coupling of diffusion coefficients to silica diffusivity is observed, and variations in systematics are observed between mafic and silicic compositions. Results show that water plays a decisive role on diffusive rates in the studied conditions, producing an enhancement between 0.4 and 0.7 log units per 1 wt.% of added H2O. Particularly notable is the behaviour of the trivalent-only REEs (La to Nd and Gd to Lu), with strong uphill diffusion minima, diminishing from light to heavy REEs. Modelling of REE profiles by a modified effective binary diffusion model indicates that activity gradients induced by the SiO2 concentration contrast are responsible for their development, inducing a transient partitioning of REEs towards the shoshonitic melt.


Introduction
Mass transport by diffusion is involved in several magmatic processes, such as crystal nucleation and growth or dissolution (e.g. Liang, 2003), mass exchange during the mixing of magmas (e.g. Morgavi et al., 2016, Laeger et al., 2016, or through the interaction between magmas and the host rocks or xenoliths (e.g. Watson, 1982). Being a time-dependent process, diffusion is often used to estimate the timescales of geological processes. Examples are the study of diffusion profiles in zoned crystals (e.g. Demouchy et al., 2006;Chakraborty, 2008;Costa et al., 2008, Faak et al., 2014 and melt inclusions (e.g. Ferguson et al., 2016), as well as the use of rocks showing evidence of magma mixing as volcanic chronometers (e.g. Perugini et al., 2015, Rossi et al., 2017. For a successful application of petrological techniques based on the diffusion process, an accurate knowledge of the diffusive behaviour for the investigated chemical elements is mandatory. In the last decades, a large number of studies provided a great wealth of data about diffusivities for major and trace elements in a wide range of silicate melt compositions (for a detailed summary of diffusion data in silicate melts, see Zhang et al., 2010, and references therein). However, the currently available dataset still lacks diffusivity data for many elements, especially for natural melt compositions. For example, the first data of rare earth elements (REE) diffusion coefficients in basalt were just recently provided by Holycross and Watson (2016). Effects of dissolved water on diffusion in magmas are poorly constrained, and investigations on hydrous magmas are often focused on silicic compositions (Watson, 1979; the TAS diagram (Le Bas et al., 1986) of both end-members, and chondrite-normalized compositions and REE patterns are presented in Fig. 2. End-member compositions follow similar patterns, with negative anomalies in Nb-Ta and Ti, which are distinctive of subduction magmas (e.g. Pearce, 1982). In the REE diagram, both end-members show similar light REE abundances, with a small Eu anomaly in the shoshonite and a pronounced one in the rhyolite.
The Sr and Eu negative spikes in the rhyolite suggest that crystallization of plagioclase was involved in its genesis. The abundance of heavy REEs of the end-members diverge, with the rhyolite progressively being more enriched towards the heavier elements. Concentration contrasts are significant, especially for Ba, Sr, Cr, V and Eu.

Experimental setup
Natural rock samples were cleaned with distilled water and crushed to fine powder.
Subsequently, these powders were melted in air at 1600°C for 4 h (Nabertherm® HT 04.17) at atmospheric pressure inside a Pt crucible and quenched to produce a glass (for details, please refer to Vetere et al., 2015a). The glass was then crushed, and the process was repeated, to ensure a homogenous glass. Finally, the produced glass was crushed again before the preparation of the experimental capsules.
Hydrous glasses were produced at high pressure and temperature using Au80Pd20 alloy tubes with a diameter of 5 mm and a length of 40 mm. The capsules were filled with rock powder and, when necessary, distilled water, in several steps (the procedure is described in detail in Vetere et al., 2014). Glasses of both end-members were produced as nominally dry (ND, i.e. no added water) and adding water up to nominal H2O concentrations of 1 wt.% and 2 wt.%.
After loading, capsules were welded shut, and then glasses were synthetized at 300 MPa and 1200 °C in an Internally Heated Pressure Vessel (IHPV; Berndt et al., 2002) for 24h. The samples were quenched isobarically after switching off the furnace. Such a procedure gives an initial cooling rate of ca. 200 °C/min. For quality control of the glass synthesis procedure, bulk analyses were carried out in chips from the two ends of the produced glass cylinders, in order to ensure homogeneity. Karl Fischer titration (KFT) was used to measure the water content, and iron oxidation state (Fe 2+ /Fe 3+ ratio) was characterized by a colorimetric wet-chemical analysis (Schuessler et al., 2008). After the synthesis, the glass samples were cut to obtain cylinders with a length of ca. 5-6 mm. Finally, each cylinder was finely polished on one side.
Diffusion experiments were performed using the diffusion couple method. In detail, couples of rhyolite and shoshonite glass cylinders with the same nominal water content were juxtaposed by their polished side and placed in an Au80-Pd20 capsule. The capsules were hermetically closed by welding. Then, capsules were compressed in a cold seal pressure vessel (CSPV) to check for tightness and to observe the adaptation of the capsule to sample shape.
The experiments were run in a vertically operating IHPV at a temperature of 1200°C and pressures of 50, 100 and 300 MPa (plus one additional experiment at 500 MPa). The denser shoshonitic glass was placed at the bottom to avoid gravitational instability. The IHPV was pressurized with argon and the experiments were run at the intrinsic oxygen fugacity of the vessel which was estimated by Berndt et al. (2002) to be close to the MnO-Mn3O4 buffer (NNO+3.7) at water saturated conditions. Since the water content of the melts was below the saturation limit, oxygen fugacities were lower in our experiments. In our rhyolitic and shoshonitic glasses produced in the IHPV, Fe 2+ /Fe ratios were, respectively, in the order of 0.7 and 0.85 in dry glasses; and 0.6 and 0.7 in hydrous (2 wt.% H 2 O) glasses . This would indicate an fO2 of roughly -7.5, slightly above the NNO buffer for the dry melts (Kress and Carmichael, 1991). Experimental time ranged between 1 h and 4 h (plus one additional zero-time experiment at 2 wt. H2O and 300 MPa). Heating ramps of 30, 50 and 20 °C/min from ambient temperature to 100, 1150 and 1200 °C, respectively, were used. After each run, a rapid quench device (Berndt et al., 2002) was activated, allowing the capsule to fall into the cold part of the vessel and cool quickly. A total of 12 experiments (including the zerotime experiment) were run successfully and utilized for the present study (Table 3).

Analytical procedures
A double polished section was prepared for each experiment, with thickness of ca. 200 μm.
Concentrations of H2O, major elements and trace elements were obtained by Fourier Transform infrared spectroscopy (FTIR), electron microprobe (EPMA) and laser ablation-inductively coupled plasma-mass spectroscopy (LA-ICP-MS), respectively. In each case, chemical concentrations were determined along a linear profile centred at the interface between the two end-members and extending to 1-1.5 mm to each side (resulting in a total profile length of ca.

2-3 mm).
Water concentration by FTIR was obtained using a Bruker IFS88 spectrometer coupled to an IR-Scope II microscope at the Institut für Mineralogie, Leibniz Universität Hannover, Germany (for details please refer to González-García et al., 2017).
Major element oxide concentration profiles (SiO2, TiO2, Al2O3, FeO, MgO, MnO, CaO, Na2O, K2O) were obtained with a Cameca SX-100 electron microprobe at the Institut für Mineralogie, Leibniz Universität Hannover. Operating conditions were an accelerating voltage of 15 kV, a beam current of 4 nA and a defocused beam diameter of 10 μm, to minimize alkali loss in the glass analysis. Spacing of analyses in the central region of the profiles was kept as small as possible (typically 12-13 μm) and was widened to 30 μm at the end. Precision and accuracy were determined by measuring VG-568 (rhyolite) and VG-2 (basalt) reference glasses (Jarosewich et al., 1980;Helz et al., 2014). Obtained analytical errors vary from 1% for SiO2 to 10% for minor oxides. In addition, to check for reproducibility, and for possible convection effects a second profile was acquired parallel to the first one but with a shift of ca. 1 mm towards the rim (for major element data in these experiments, the reader is referred to González-García et al., 2017).
Concentration profiles of 30 trace elements (Cs, Rb, Ba Sr, Co, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ta, V, Cr, Pb, Th, U, Zr, Hf, Sn and Nb) in the diffusion couple glasses were obtained at the Department of Physics and Geology, University of Perugia.
The instrumentation consisted in a Teledyne Photon Machine G2 laser ablation device equipped with the two-volume HelEx 2 cell coupled to a Thermo Fischer Scientific iCAP Q quadrupole mass spectrometer (Petrelli et al., 2016a). A circular 20 μm spot size and 20 µm spot spacing was used in most of the analyses with the exception of experiment P300-H2-4, where 25 microns were used for both spot size and spacing. To avoid interference and keep a suitable resolution, every second spot was offset 20 microns to one side, configuring a zig-zag pattern (Fig 3). Ablation times were 25 seconds per spot, preceded by a 25 second background measurement and followed by 25 seconds of washout. Data reduction was completed with Iolite v3.32 software (Paton et al., 2011). NIST SRM 610 glass (Pearce et al., 1997) was analysed as reference material for the external calibration, and the basaltic glass BCR2G (Wilson, 1997) was used as quality control. The SiO2 profiles obtained by electron microprobe were used as internal standard. Analytical precision is about 12% for concentrations close to 0.1 ppm and better than 5% above 20 ppm; accuracy is always better than 10% (Petrelli et al., 2016b).

Results
Quenched experimental products are crystal-free glasses and show variable amounts of bubbles. Samples from 300 and 500 MPa experiments are bubble-free while in experiments at 50 and 100 MPa small amounts of bubbles were observed near the contact of the diffusion halves . Given the small size of the bubbles and their hypothesized composition (N2 and minor amounts of water in the hydrous runs), they are considered to have a negligible effect in the diffusive process. Although some water flux between melts can be present during experimental heating, H2O profiles produced by FTIR analyses show uniform water content across the couples , indicating that no net flux of H2O was present during experiment due to water activity contrasts between the end-members.
Concentration-distance profiles of six major elements (SiO2, TiO2, FeO, MgO, CaO, and K2O) are characterized by the expected asymmetric sigmoidal shapes, extending deeper into the mafic melts due to different diffusivities in melts of different polymerization degree. A particular case is that of Al2O3, with evident signs of uphill diffusion in the rhyolitic side of the couple (but lack of maximum in the shoshonite), an effect that can be explained and predicted by coupled diffusion (e.g. Liang et al., 1996)  Elements with a normal behaviour (group I) are Rb, Cs, Sr, Ba, Co, V, Cr, Eu, Th, U, Sn, Ta and Hf. These elements are characterized by sigmoidal shape profiles with variable degrees of asymmetry, caused by variation in base composition along the profile (Fig. 4). In binary variation diagrams, elements with normal diffusive behaviour show linear to slightly non-linear trends (S-shape), in which the deviation from linearity correlates with the difference in diffusion rates between the two involved elements. Sr has a virtually identical behaviour to that of Ba, and hence they show a very good linear relation while V, Cr or Eu, characterized by higher diffusivity contrasts, produce more prominent deviations from the linear trend when compared to Ba.
The second group of elements (group II) displays different extent of uphill diffusion, i.e., diffusion against the concentration gradient of the diffusing element (Fig. 5). Uphill diffusion has often been observed for major element diffusion in multicomponent silicate melts (e.g. Guo and Zhang, 2016), and few studies have described the same effect for trace elements (Zhang et al., 1989;van der Laan et al., 1990;Richter, 1993;Lesher, 1994). The elements included in this group are Y, Zr, Nb, Pb and, most notably, all trivalent-only REEs (La to Sm and Gd to Lu; Fig 5). The exception among REEs is Eu, which shows a normal diffusion profile. Uphill diffusion is evident in the profiles by concentration minima and maxima near the original interface between the two halves of the couples. We have observed a prominent effect in La, Ce, Pr, Nd and Sm (the light REEs), for which a very deep concentration minimum is identified, reaching concentrations well below that of the end members. This minimum is usually accompanied by a wide and less prominent maximum in the shoshonitic side. It is worth noting that group II elements are always elements with low starting concentration gradients (Table 1), with more prominent minima in the REEs with more similar initial starting concentrations in both melts (e.g. for Nd). Binary variation elements of group II elements always result in highly asymmetric trends, with compositions extending much higher and lower than the starting endmembers compositions. The deep minimum correlates to Ba concentration of ca. 69 wt.% SiO2 and the weak maximum near 54 wt% SiO2 is present. No appreciable differences in distribution are observed when considering experiments at different pressure, time and water contents.
Since the heating times are significant in relation to the experiment times, an approximate value of effective ramp-up times (teff) was estimated in the 300 MPa, 2 wt.% H2O experiment set by comparing the concentration-distance profiles of the zero-time experiment to that of 1 hour and 4 hour experiments (Zhang and Behrens, 2000). Results indicate effective heating times to be in the order of 80 to 120 seconds, short enough to not significantly affect the experimental results.
A common test to prove possible undesirable effects (e.g. convection) in experiments with different duration, is to plot the concentration versus distance normalized by the square root of time. Applying this methodology to the REE profiles, datasets from experiments P300-H2-4 (4 h) and P300-H2-1 (1 h) collapse to the same curve (Fig. 6). This is evidence that the process producing this kind of profiles is controlled only by diffusion.

Determination of diffusion coefficients for group I elements
Chemical diffusion coefficients were determined for all 13 group I trace elements displaying normal diffusion profiles. Given the evident asymmetry of the profiles, a simple, constant diffusivity model cannot be applied. Hence, diffusivities were obtained along the profiles using a concentration-dependent diffusivity approach (Sauer and Freise, 1962), which is a modification of the original Boltzmann-Matano method (Boltzmann, 1894;Matano, 1933).
These methods have been used when diffusivities vary as a function of the concentration of the diffusing element itself (e.g. Nowak and Behrens, 1997), and also when diffusivities depend on the concentrations of other elements (Baker, 1989). The procedure involves: (1) smoothing the analytical profiles by a single polynomial function (for examples, refer to Electronic Annex 2), (2) normalization of the compositional range and (3) applying the solution for one dimension, molar volume independent diffusion as follows: where x is the distance along the profile (in meters); t is the experimental time (in seconds);  Table 2. Table 3  Cs show that this constraint does not apply to very large cations, consistent with the model of Mungall (2002). Table 3, the most determining factor for the diffusion rates is the presence of water. Fig. 8 shows how diffusion coefficients are related to water content in the system. The relation between the water content and log D can be fit by a linear equation, in the form log D = a*w + b, in which a is the slope and w is the water concentration in weight percent. We also find that in the 50-500 MPa range, pressure does not have a significant impact on the diffusion coefficients and, as consequence, we can be confident in the reliability of this linear equation to the pressure range mentioned above. Table 4 summarizes the calculated equation parameters and their relative errors.

As reported in
Moreover, the effect of water is not uniform for all measured elements. This is evident in Fig. 9 where the slope in log D vs H2O plot, (a parameter, fig. 10 and

Viscosity-diffusion systematics
Given the indications of a systematic variation of diffusivities, especially in the more silicic compositions, an attempt was made to relate the measured diffusion coefficients with the correlation schemes proposed by Fanara et al. (2017) based on viscosity-diffusivity relations.
In their work, a convergence towards Eyring diffusivity was observed for melts with low viscosities, with a progressively higher decoupling from Eyring diffusivity at higher melt viscosities. This trend was first suggested by Dingwell (1990) and is not uncommon in the literature (e.g. Behrens and Stelling, 2011). Observed power laws of cations of different ionic charge differ, thus resulting in a different degree of decoupling. This results in a low interelemental diffusivity variation at low viscosities and a more differential behaviour at higher viscosities.
The Eyring equation is defined as follows: where kB is the Boltzmann constant, λ is the interatomic jump distance and η is the viscosity of the melt. This equation provides a way to relate diffusion of network former elements to melt viscosity (e.g. Zhang, 2010). For the calculation of the Eyring diffusivities, a jump distance of 0.4 nm is assumed in this work, a value similar to atomic spacing in silicates.
A comparison between diffusivities measured in this work and melt viscosities is shown in Figure 10, where elements are separated by ionic charge. Melt viscosities were calculated using the model described by Giordano et al. (2008) and are listed in Table 3. Experimental diffusivities are always higher than calculated Eyring diffusivity, and as previously outlined, diffusivities in melts with lower viscosities (most mafic and water-rich) tend to approach more to Eyring diffusivity that that of higher viscosity (most felsic and water-poor). However, we note that no single trend can be observed for all melts, and instead a different behaviour is observed for melts with different water content. This is especially evident in the divalent  previously noted, probably consists in a mixture of Sn 2+ and Sn 4+ ), a group not considered by Fanara et al. (2017). A high interelemental dispersion is observed in this group, with decoupling between particular elements (i.e., no single trend can be observed for all of them).
On the other hand, a single trend appears to be valid for both dry and hydrous melts. Results show that tetravalent cations diverge from Eyring diffusivity at lower viscosities, following the behaviour of monovalent, divalent and trivalent cations. In this plot, Sn stands out from U, Th and Hf, which can be interpreted as further evidence of a significant presence of Sn 2+ in the melt.

Treatment of uphill diffusion
A method to model trace element uphill diffusion is the modified effective binary diffusion approach proposed by Zhang (1993) in which activity gradients, instead of concentration gradients, are used to describe the diffusive flux (Zhang, 1993;Richter, 1993;Lesher, 1994). In this model, the basic approach is described by where Ji is the diffusive flux of component i, Di is referred as the intrinsic diffusivity, ai is the activity and i the activity coefficient. In this approach, diffusing components would tend to achieve a constant activity (i.e., chemical potential), allowing them to diffuse against their own concentration gradient if the activity coefficient varies with composition. An alternative way to visualize this effect would be to use melt-melt partition coefficients: uphill diffusion could thus be viewed as an element trying to achieve transient partition equilibrium between two structurally different melts. The concept of transient equilibrium during interdiffusion of complex silicate melts was originally introduced by Watson (1982). In addition, it has been observed that in experiments with two immiscible melts, alkalis are enriched in the more polymerized melts (Watson and Jurewicz, 1984), and many others (most notably, HFSE) are enriched in less polymerized melts (Zhang, 1993;Watson, 1976). To achieve this transient equilibrium (Watson, 1982), some components may need to move against their own concentration gradients. The equilibrium concentration Ce to which elements would tend to accommodate is defined as (Zhang, 1993): where C-i and C+i are the initial concentrations of element i in the two end-members; Db is the diffusivity that can be assimilated to SiO2 or SiO2 + Al2O3 (network forming species) effective binary diffusivity in the system; and Cf is half the difference between the equilibrium concentrations in both sides of the couple. This parameter is related to the two-liquid partition coefficient K as follows (Zhang, 1993): The concentration-distance profiles resulting from diffusion of a component in this context can be modelled by As given by equations (4), (5) and (6), in order to quantitatively model the uphill diffusion phenomena observed here by the modified EBD approach, a precise knowledge of three variables is mandatory: (1) diffusivity of SiO2 or SiO2+Al2O3 (network formers), (2) intrinsic EBD coefficients (i.e., self-diffusivities) of trace elements, and (3) the value of Cf, which defines the equilibrium concentration and is related to the melt-melt partition coefficient Ksho/rhy. Although we have insufficient data of two of these variables (Cf and Di), it is possible to use the modified EBD model to obtain information on the causes and evolution of uphill diffusion in the shoshonite-rhyolite system. We have implemented the modified EBD approach described above (Zhang, 1993) in a script in Python programming language, using a forward finite differences model (Press et al., 1986). Very scarce data is available on the self-diffusion of trace elements in literature. In the present modelling, we have used the value Nd self-diffusion in basalt-rhyolite diffusion couple experiments provided by Lesher (1994) as reference, which is in the range of 2.5 to 3.3 times the diffusivity of SiO2. Finally, the value of Cf was adjusted in the finite difference model to obtain a good visual fit of the profiles.
Results show a good agreement between the model and the experiments (Fig. 11) and confirm the partitioning of REEs, Y, Zr, Nb and Pb towards less polymerized melts. In other words, activities are significantly higher in silicic melts than in mafic melts, resulting in a partition flux towards the shoshonitic side of the couples. Table 5 summarizes the values used to model the uphill diffusion profiles. The model produces an inflection in the interface position of all elements, which is a consequence of assuming one value of DSiO2 for each end-member, and thus producing a discontinuous first derivative dC/dx. Uphill diffusion arises as a consequence of the interplay between initial concentration difference and the variation of activity coefficients. The shape of the diffusion profile is the result of the interplay between the end-member starting concentrations and the transient partitioning of the element between shoshonitic and rhyolitic melts, as already observed by Watson (1982) and van der Laan et al., (1994); the asymmetry is the consequence of the major element diffusivity contrast in the melts (here represented by SiO2 diffusivity) and the intrinsic diffusivity of the trace element.
Therefore, the higher diffusivities present in the most mafic melt produce the wider and lower maximum observed in the shoshonitic side of the profiles. In the LREE, the small concentration contrast and the high value of the partition coefficient result in very prominent uphill diffusion.
On the contrary, the higher compositional contrast in the HREE between both halves and the lower value of KSho/Rhy result in progressively milder uphill diffusion (Fig. S2 in the Electronic Annex 2). The model suggests that the value of Ksho/rhy is around 3 for LREE, and diminishes to roughly 1.6 for the heaviest REES (Tm, Yb and Lu). Similarly, best fits were obtained using intrinsic diffusivity factors (Di) varying from 3.5 (La, Ce and Pr) to 2 (Tm, Yb and Lu). Y, Zr and Nb can be modelled with parameters similar to that of the HREE elements. Finally, Pb shows a more longitudinally extended profile than other group II elements, and in consequence, it can be only modelled assuming a much higher intrinsic diffusivity factor of ∼10. The same parameters are valid for both nominally dry and hydrous experiments through our experimental pressure range. The modelled partition data are similar in magnitude with previously published experimental partitioning data in immiscible rhyolitic and basaltic liquids, where partition coefficients of REE were found to be in the range between 3.7 and 4.3 (Watson, 1976;Ryerson and Hess, 1978), and also to that in natural immiscible melts observed in lunar melt inclusions (Shearer et al., 2001).
The modified EBD model is also capable to reproduce the behaviour of group I elements for which intrinsic diffusivities and melt-melt partitioning data are known ( fig. 11 and Table   5). Eu can be fit reasonably well by assuming parameters similar to that of Sm and Gd, and this is also the case for Sr, which can be modelled assuming an intrinsic diffusivity of 10xDSiO2 and Ksho/rhy of 2.5 (Lehser, 1994). These results indicate that the primary cause behind the normal behaviour of europium is very likely a change in initial conditions (that is, initial concentration gradient and direction of diffusive flux) with respect to the trivalent REEs, and that the presence of a fraction of Eu 2+ is not necessarily related. This is expected from previous studies in multicomponent systems, in which uphill diffusion in a component can disappear by changing the direction of diffusion in the compositional space, and hence indicating that this feature does not only depend on activity gradients (e.g. Chakraborty et al., 1995).

Implications
Results presented here support an elemental fractionation process between the fastest (the LFS elements) and slowest diffusivities (V, Hf, Nb). Given that the diffusivity contrast is lower in the mafic end-member, the fractionation trends would be more prominent towards the more evolved component. A suitable fractionation indicator could thus be the Ba/V ratio. Ba diffusion is around one order of magnitude faster than V in hydrous Rh70 melt, but only 0.3 orders of magnitude in hydrous Lt58. As a result, the Ba/V ratio vs. distance plot (Fig. 12) displays a maximum in the rhyolitic side while keeping the ratio approximately constant in the shoshonite. The maximum fractionation is Ba/V = 25, markedly higher than the ratios measured in the end-members at great distances from the interface.
Although trace element uphill diffusion is a striking feature in the experiments presented throughout this work, its potential to produce relevant observable features in natural environments remains unknown. According to literature studies on simple melts composed by only few components, uphill diffusion in major elements is a temporary feature that disappears once strong concentration gradients relax (e.g. Liang, 2010), and similar conclusions can be extracted for trace elements (Lesher, 1994). As a consequence, its visibility would be limited to systems in which the diffusive flux has been frozen in an early stage, as it is the case for preeruptive magma mixing processes. A definitive sign of the development of uphill diffusion in natural systems would be the observation of strongly nonlinear trends in binary diagrams.
Uphill diffusion would, in addition, produce strong concentration variations on short length scales. Magma mixing experiments performed in dynamic conditions support this idea. In fact, Perugini et al. (2008) and Perugini et al. (2013) have shown highly nonlinear concentrationdistance profiles that could be attributed to the occurrence of transient partition leading to uphill diffusion.
This idea is contrasting to the general assumption that magma mixing tends to the chemical homogenization of the system. While it is true for major element composition and some of the trace elements, here we show that uphill diffusion has the opposite effect. Compositional gradients for elements diffusing uphill would tend to increase in the early phases of the mixing process, even when their end-member concentrations do not differ strongly. This finding puts some doubts on the use of REEs as a proxy to obtain timescales in magma mixing systems, when strong SiO2 gradients are present.
One of the main results presented here is that water is a very important conditioning factor for trace element diffusion, and its effect is not the same for all diffusing cations. Since magmas in nature are rarely dry, especially in subduction environments where water content can reach 6 to 8 wt.% (Wallace, 2005;Plank et al., 2013), this is a fundamental aspect. The concept of diffusion distance can be used to quantify the effect of the addition of water in mixing times.
The distance (x) to which a certain cation diffuses in a given time (t) is given by the expression As it is straightforward from this simple equation (assuming constant diffusivity), the diffusion distance is proportional to the square root of time. On the other hand, the time to reach a certain diffusion distance will be proportional to the diffusion coefficient. As a consequence, the time to achieve the same degree of diffusive homogenization with melts of different water content depends on the enhancement factor a produced by water. We have seen that for LFS elements, going from 0.3 to 1.9 wt.% increases the diffusivity by 1.2 to 1.4 orders of magnitude, which in turn would decrease the time required to achieve the same degree of homogenization by the same amount. For transition elements, this value would be approximately one order of magnitude. Therefore, it can be concluded that using dry diffusion coefficients to model the mixing of magmas with a certain amount of water could lead to overestimations in timescales by factor up to 25.
It should be noted that these considerations can be applied only to the restricted water concentration range covered in this study (up to 2 wt.% H2O), where we find that the influence of water in log D can be described by a linear relation. However, several previous studies with larger water concentration ranges have found that reaching 3-4 wt.% H2O, the linear relation is lost and a plateau is achieved above ~4 wt.% H2O (e.g., Harrison and Watson, 1983).

Conclusions
The diffusive exchange of 30 trace elements between shoshonitic and rhyolitic melts of In summary, our results show that, in a natural system with strong compositional gradients, the diffusive exchange is complex and it is dominated by the large SiO2 compositional gradients. This is in agreement with the observations reported in González-García et al. (2017), where strong diffusive coupling between major elements was observed. As a consequence, it should be noted that diffusion coefficients obtained in melts with constant bulk compositions are not appropriate to model complex mixing systems.            11. Results of the application of the modified EBD model (Zhang, 1993) to uphill diffusion of some REE, Y, Zr, Nb and Pb. Experimental data are from experiment P300-H2-1, and the red line is the predicted concentration modelled from the parameters in Table 5 (Zhang, 1993). Group I elements Sr and Eu are also included (bottom rows). Di is the intrinsic diffusivity of the element; DSiO2 is the effective binary diffusion coefficient of SiO2; Cf is half the difference between equilibrium concentrations at the end-members; and KSho/Rhy is the resulting melt-melt partition coefficient.