Diffusion of hydrous species in model basaltic melt

Accepted Manuscript Diffusion of hydrous species in model basaltic melt Li Zhang, Xuan Guo, Qinxia Wang, Jiale Ding, Huaiwei Ni PII: DOI: Reference:

S0016-7037(17)30427-1 http://dx.doi.org/10.1016/j.gca.2017.07.019 GCA 10381

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Geochimica et Cosmochimica Acta

Received Date: Revised Date: Accepted Date:

28 October 2016 6 June 2017 11 July 2017

Please cite this article as: Zhang, L., Guo, X., Wang, Q., Ding, J., Ni, H., Diffusion of hydrous species in model basaltic melt, Geochimica et Cosmochimica Acta (2017), doi: http://dx.doi.org/10.1016/j.gca.2017.07.019

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Diffusion of hydrous species in model basaltic melt

Li Zhang1,2, Xuan Guo1, Qinxia Wang1, Jiale Ding1, Huaiwei Ni1,* 1

CAS Key Laboratory of Crust-Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China 2

Bayerisches Geoinstitut, Universität Bayreuth, 95440 Bayreuth, Germany

Corresponding author: Huaiwei Ni E-mail: [email protected] Tel. 86-551-63600297

For Geochimica et Cosmochimica Acta on September 28th, 2016

1

Abstract Water diffusion in Fe-free model basaltic melt with up to 2 wt% H2O was investigated at 1658–1846 K and 1 GPa in piston-cylinder apparatus using both hydration and diffusion couple techniques.

Diffusion profiles measured by FTIR are

consistent with a model in which both molecular H2O (H2Om) and hydroxyl (OH) contribute to water diffusion.

OH diffusivity is roughly 13% of H2Om diffusivity,

showing little dependence on temperature or water concentration.

Water diffusion is

dominated by the motion of OH until total H2O (H2Ot) concentration reaches 1 wt%. The dependence of apparent H2Ot diffusivity on H2Ot concentration appears to be overestimated by a previous study on MORB melt, but H2Ot diffusivity at 1 wt% H2Ot in basaltic melt is still greater than those in rhyolitic to andesitic melts.

The

appreciable contribution of OH to water diffusion in basaltic melt can be explained by enhanced mobility of OH, probably associated with the development of free hydroxyl bonded with network-modifying cations, as well as higher OH concentration. Calculation based on the Nernst-Einstein equation demonstrates that OH may serve as an effective charge carrier in hydrous basaltic melt, which could partly account for the previously observed strong influence of water on electrical conductivity of basaltic melt.

2

1. INTRODUCTION

Water is one of the most abundant and pivotal volatile component in terrestrial and lunar magma.

Water diffusivity is a critical parameter for quantitative modeling of

water loss or gain of volcanic glass (Saal et al., 2008; Giachetti and Gonnermann, 2013), bubble growth and resorption (Proussevitch and Sahagian, 1998; McIntosh et al., 2014) and explosive volcanic eruption (Ruprecht and Bachmann, 2010; Lloyd et al., 2014).

Furthermore, water is present in silicate melts in the form of both

molecular H2O (H2Om) and hydroxyl (OH), which are different with respect to both their concentration and mobility (Zhang et al., 1991; Ni et al., 2013).

This

multi-species diffusion problem is theoretically inspiring in terms of the coupling of diffusion and speciation reaction as well as the relationship between the apparent total water (H2Ot) diffusivity and the diffusivities of the two hydrous species. Most of previous studies on water diffusion in silicate melts focused on felsic to intermediate melt compositions (e.g., Shaw, 1974; Zhang et al., 1991; Nowak and Behrens, 1997; Zhang and Behrens, 2000; Liu et al., 2004a,b; Behrens et al., 2004; Ni and Zhang, 2008; Ni et al., 2009a,b; Schmidt et al., 2013; Fanara et al., 2013; Ni et al., 2013; Persikov et al., 2014).

Zhang et al. (1991) investigated dehydration in

rhyolitic melt within a limited H2Ot range (< 2 wt%) and concluded that H2Om is the mobile species while OH diffusivity is negligible.

Zhang and Behrens (2000)

showed that if H2Om diffusivity was assumed to increase exponentially with H2Ot

3

concentration, the basic idea in Zhang et al. (1991) could be applicable for higher H2Ot concentration.

This speciation-based diffusion model found great success in

later studies for rhyolitic and dacitic melts (Liu et al., 2004a; Ni and Zhang, 2008; Ni et al., 2009b).

However, in andesitic melt, Behrens et al. (2004) found that some

H2Ot diffusion profiles were better fit by constant H2Ot diffusivity than by H2Ot-dependent diffusivity, which implies a role for OH diffusion.

Ni et al. (2013)

resolved the contribution of OH to water diffusion in andesitic melt and found OH diffusivity to be 10% – 20% of H2Om diffusivity at low H2Ot concentration.

These

results suggest that OH diffusion is probably more significant in depolymerized melts than in polymerized melts. With respect to the mafic systems, Zhang and Stolper (1991) investigated water diffusion in a mid-ocean ridge basalt (MORB) melt with low H2Ot content (<0.4 wt%) at 1573–1773 K and 1 GPa.

Their results were roughly consistent with the model of

H2Ot diffusivity being proportional to H2Ot concentration, which was attributed to an H2Om-dominated diffusion mechanism similar to what operates in rhyolitic melt (Zhang et al., 1991).

This conclusion was echoed by Okumura and Nakashima

(2006) in their investigation of water diffusion in a basaltic glass at ambient pressure. However, Zhang and Ni (2010) found that the diffusivity data in Zhang and Stolper (1991) extrapolated to 1 wt% H2Ot are significantly off the compositional trend constrained by experimental data for felsic and intermediate melts.

Furthermore, in

view of the findings in Behrens et al. (2004) and Ni et al. (2013) regarding OH

4

diffusion in andesitic melt, the role of OH diffusion might be even more significant in the more depolymerized basaltic melt, therefore challenging the H2Om-dominated mechanism proposed by Zhang and Stolper (1991).

The only other study on water

diffusion in basaltic melt is from Persikov et al. (2010), but their “haplobasalt” composition (Albite45-Diopside37-Wollastonite18) is clearly not a satisfactory analogue of naturally occurred basalts. To collect more reliable data of water diffusivity and evaluate the importance of OH diffusion in basaltic melt, we have carried out hydration and diffusion couple experiments at 1658–1846 K and 1 GPa for basaltic melt with up to 2 wt% H2Ot. The experimental results are useful not only for more robustly constraining the dependences of water diffusivity on H2Ot concentration and melt composition, but also for clarifying the underlying physical mechanism that governs water diffusion in silicate melts.

Their implication for electrical conduction in hydrous basaltic melts

will also be discussed.

2. EXPERIMENTAL AND ANALYTICAL METHODS 2.1. Starting material For synthesis of starting glasses used in diffusion experiments, the targeting composition was taken from the average composition of basalt in the calc-alkaline series of island-arc volcanic suites (Hess, 1989).

But to avoid iron-associated

complexities, including Fe-Pt alloying, Fe valence change and reduction of glass

5

transparency, we opted for a haplobasaltic composition by replacing Fe2+ with Ca and Mg while keeping the original molar Ca/Mg ratio.

Reagent-grade oxides and

carbonates were mixed and fused twice at 1823 K in a 1-bar furnace to obtain the model anhydrous basaltic glass.

The glass composition as analyzed by electron

microprobe (Table 1) is similar to the MORB used in Zhang and Stolper (1991) but differs significantly from the haplobasalt studied in Persikov et al. (2010). A series of hydrous glasses were prepared by fusing the mixture of anhydrous glass powder and distilled water (sealed in Pt capsules) at 1623 K and 0.5 GPa for 10 h in two end-load piston cylinder apparatuses, one located at the University of Science and Technology of China (USTC) and the other at the Bayerisches Geoinstitut (BGI), Germany.

The highest permissible water content without causing crystallization

during quench was found to be about 2 wt%. All of the synthesized glasses are transparent, with the hydrous glasses being crystal- and bubble-free while the anhydrous glass containing a small amount of air bubbles.

As determined from FTIR analysis, the H2Ot concentration of the

nominally anhydrous glass is 0.03 wt%, and the hydrous glasses contain 0.1–2.0 wt% homogeneously distributed water.

2.2. Diffusion experiments Glass cylinders of 2.6 mm diameter were prepared for diffusion experiments.

In

one set of experiments, aimed at determining OH diffusivity at extremely low H2Ot

6

concentration, a piece of 4-mm long anhydrous glass cylinder with both ends polished was sealed in a Pt capsule (3 mm diameter and 0.15 mm wall thickness).

The other

set of experiments following the double diffusion couple approach developed by Ni et al. (2013) was designed for water diffusivity over a broad range of H2Ot concentration. For each diffusion couple sealed in a Pt capsule, a 2.5 mm-long hydrous glass cylinder was placed on top of an anhydrous or less hydrous glass cylinder of 1.5 mm length, with their polished surface touching each other.

Two diffusion couples with

different combination of water contents investigated in a single experimental run allow to more accurately constrain the dependence of water diffusivity on H 2Ot concentration (Ni et al., 2013). Diffusion experiments were carried out in 3/4˝ end-load piston cylinder apparatuses at the USTC and at the BGI.

The sample assembly was composed of

talc, pyrex glass, graphite heater and crushable alumina or MgO.

A type-S

thermocouple (Pt-Pt95Rh5) atop the Pt capsule served to monitor the temperature, and the temperature at the sample was estimated to be 15 K higher than the thermocouple reading.

A “piston-out” procedure was applied for pressurization, with a friction

correction of 18% on the nominal pressure.

The sample charge was first relaxed at

573 K and 1 GPa for at least 3 h, and then rapidly (in ~60 s) heated to a target temperature in the range of 1593–1831 K.

After a dwell time of 2–4 min to allow

for diffusive exchange of water, power was immediately turned off to achieve rapid quench with an onset cooling rate of ~80 K/s.

7

With computer-recorded thermal

history, the diffusion that occurred during heating and cooling was accounted for by calculating an effective experimental duration, as described in Zhang and Behrens (2000), with an estimated activation energy of 220 kJ/mol for water diffusion. After the diffusion experiment, the recovered sample was mounted into epoxy resin and doubly polished to 150–250 m thickness for FTIR analyses.

The samples

(especially those from the hydration experiments) often contain some cracks perpendicular to the cylindrical axis (Figs. S1 and S2), causing some complexity in the measurement of diffusion profiles and water diffusivity.

2.3. FTIR analyses Initial water contents of the starting glasses were determined by a PerkinElmer Frontier FTIR spectrometer at the USTC.

The MIR setup (MIR source + KBr

beamsplitter + MIRTGS) was adopted for a majority of samples.

For the O-H

stretching band at 3550 cm–1, its peak height was used to calculate water content according to the Lambert-Beer law, with a molar absorptivity of 63 L·mol–1·cm–1 (Dixon et al., 1995).

For glasses with >1.4 wt% H2Ot, this strong MIR band easily

got oversaturated, therefore the two combination bands at 4520 cm–1 and at 5200 cm–1 were measured using the NIR setup (NIR source + CaF2 beamsplitter + NIRTGS) to obtain OH concentration and H2Om concentration, respectively.

Calibration of the

NIR bands was also from Dixon et al. (1995), but the procedure of baseline correction was simplified by applying two linear tangential baselines.

8

This simplification may

lead to <10% uncertainty in the calculation of H2Ot concentration, but will not cause a major effect on the determination of water diffusivity, which is mostly constrained by the length of diffusion profile. Diffusion profiles preserved in the quenched samples were measured along the centerline by a Spotlight 200 microscope system (involving an MCT detector) attached to the PerkinElmer Frontier FTIR spectrometer. consists of 70 to 120 points.

Each profile typically

At each point, an FTIR spectrum was collected using a

rectangular aperture of 10 m width and 200 m length, with 64 scans through 6000–2000 cm–1.

The obtained infrared spectra were processed similarly as done in

obtaining the initial water contents of glasses.

Our diffusion profiles were at least

800 m long, implying a minimal convolution effect in FTIR microspectroscopy.

3. EXPERIMENTAL RESULTS We conducted seven diffusion couple experiments and four hydration experiments at 1608–1846 K (Table 2).

The two samples from Run# HBS-BGI-DC3 at 1608 K

and one from Run# HBS-BGI-DC4 (DC4b) at 1658 K were severely crystallized, forbidding diffusion profile acquisition.

The lower bound of allowable experimental

temperature was therefore limited at 1658 K.

For most other samples, the water

contents at the flat regions of diffusion profiles remain the same as the initial water contents (Figs. S3 and S4), confirming that our data can be treated as a diffusion problem in infinite (for diffusion couple) or semi-infinite (for hydration) medium.

9

In

one sample from Run# HBS-USTC-DC7 (DC7a) at 1846 K, the highest temperature explored, the anhydrous half was undesirably overhydrated to >0.14 wt% H2Ot. After dismissing the problematic samples, in total 14 diffusion profiles were successfully obtained, 10 from the diffusion couple experiments and 4 from the hydration experiments (Figs. S1-S4).

Mole fraction of total water (X) is related to

H2Ot concentration (C in wt%) by X = C/18.015/[C/18.015+(100-C)/35.03], in which 35.03 g/mol is the molar mass of anhydrous basalt on a single oxygen basis. At the two ends of the profiles from diffusion couple experiments (i.e., outside the flat regions in Fig. S3), we observed modest degree of dehydration of the hydrous half and hydration of the anhydrous half over a short distance, as already documented in previous studies (e.g., Zhang and Behrens, 2000).

Alteration in H2Ot concentration

also occurred near the sidewalls of Pt capsules.

Nevertheless, the initial water

contents were exactly retained at the flat regions of diffusion profiles measured along the centerline.

Therefore, we conclude that the observed changes in water content at

the rims of samples did not affect the diffusive exchange between the two halves. Diffusion profiles at the two ends of samples from the 4 hydration experiments were found to be always symmetric with respect to center of sample.

The H2Ot

concentration at the melt-capsule interface was elevated consistently to ~600 ppm over the investigated temperature range.

In view of the high intrinsic water fugacity

in the sample assembly caused by the decomposition of talc, we suggest that the gained water originated from the ingassing of hydrogen through the Pt capsule in the

10

form of H2, in addition to any trapped moisture in the capsule.

The incoming H2 was

expected to be quickly oxidized to H2O at the melt-capsule interface, presumably by trapped O2 inside the capsule and trace of ferric iron in the melt.

4. DISCUSSION AND APPLICATION 4.1. Diffusivity model and diffusion mechanism We first tried to fit the measured diffusion profiles with error function, which corresponds to a model of water diffusivity independent of H2Ot concentration. While acceptable fitting quality is obtained for the hydration profiles (Fig. S4), those profiles from diffusion couple experiments involving high H2Ot concentration cannot be well fitted, as shown in Fig. 1a.

Furthermore, for several experiments at similar

temperature, the diffusivity extracted from error function fits shows a positive correlation with average H2Ot concentration.

These two findings suggest that water

diffusivity in silicate melt must vary with H2Ot concentration.

Persikov et al. (2010)

assumed H2Ot diffusivity to be an exponential function of H2Ot concentration. However, this simple model also produces considerable misfit (Fig. 1a). Zhang et al. (1991) developed a mechanistic water diffusivity model for rhyolitic melt.

There are three assumptions in their model: (1) molecular H2O (H2Om) is the

dominating diffusing species; (2) the contribution of OH to water diffusion is negligible; (3) local equilibrium is always maintained for the H2O speciation reaction, H2Om + O = 2OH (here O denotes an anhydrous oxygen atom).

11

Zhang and Behrens

(2000) further showed H2Om diffusivity to be an exponential function of H2Ot concentration rather than being constant.

However, for andesitic melt, Ni et al.

(2013) found significant misfit at low H2Ot content by using this speciation-based model, and pointed out this misfit was due to neglect of OH diffusion.

They

provided a solution by developing a modified speciation-based H2O diffusion model, which assumes (a) H2Om diffusivity is an exponential function of H2Ot concentration; and (b) OH diffusivity is a non-zero constant. We found that our diffusion couple profiles could also be fit well by this model.

Moreover, the dependence of H2Om

diffusivity on H2Ot concentration appears to be weak and almost negligible. Therefore, we set both H2Om diffusivity and OH diffusivity to be constant at given temperature and pressure.

Diffusion couple profile can be fitted excellently with this

modified speciation-based model (Fig. 1a).

Furthermore, the dependence of H2Ot

diffusivity on H2Ot concentration yielded by this model agrees well with the result from Boltzmann-Matano analysis (Fig. 1b), which makes no a priori assumption on the diffusivity-concentration relationship. For the modified-speciation based diffusion model, its mathematical formulation is as follows (Zhang, 1999; Wang et al., 2009),   



¶X ¶t

 ¶ æ ¶X ö DH O ç ¶x è 2 t ¶x ÷ø

K

¶ XH O ¶ æ 2 m ç DH 2Om ¶x è ¶x

DOH

2 X OH 2453    exp 1.547    X H 2 Om  X O T  

12

¶ X OH ö ÷  2¶x ø





 dX DH2Ot  DH2Om 1  OH 2dX 



dX OH     DOH 2dX 

dX OH 1 2X   2dX 4 X ( X  1)(1  4 / K )  1



The definitions of symbols are summarized in Table 3.





Essentially, equation (1) is

the governing diffusion equation, equation (2) gives the temperature-dependent equilibrium constant of the speciation reaction H2Om + O = 2OH, and equations (3) and (4) relate H2Ot diffusivity to the diffusivities of the two hydrous species. Because the equilibrium water speciation in basaltic melt is currently still unknown, the expression of K in equation (2) is borrowed from the result for andesitic melt (Ni et al., 2009a).

All the profiles from diffusion couple experiments are fitted well

using this model (Fig. S3), and the obtained diffusivities of the hydrous species alongside the DOH/DH2Om ratio are reported in Table 4. It should be noted that for the hydration profiles, because H2Ot concentration is extremely low (X < 0.0012), the differential term in equation (4) essentially equals unity and the extracted DH2Ot diffusivity approximates OH diffusivity, which is also reported in Table 4.

Both DH2Om and DOH data line up nicely in the Arrhenius plot

with similar slope (Fig. 2), except that Run# HBS-BGI-DC5 at 1828 K gives anomalously lower diffusivity than most data.

The reason for this outlier run is not

clear, but may be associated with the longer time (~2 min) taken for heating to the

13

target temperature (and therefore leading to the large correction on experimental duration, see Table 2).

Nevertheless, the OH diffusivities obtained from the two sets

of experiments, hydration and diffusion couple, generally show excellent agreement. After dismissing the outliers from Run# HBS-BGI-DC5, least squares fitting yields the following expressions for the diffusivities of hydrous species in basaltic melt,

and

lnDOH = (–6.731 ± 0.796) + (–26095 ± 1387)/T,

(5)

lnDH2Om = (–4.539 ± 1.047) + (–26304 ± 1819)/T,

(6)

where DOH and DH2Om are both in m2/s.

The fitting results yield an activation energy

of ~220 kJ/mol for both OH diffusion and H2Om diffusion.

The DOH/DH2Om ratio is

nearly constant (~0.13) within the investigated temperature range. One would expect that the diffusion of OH (a charged species) should involve a higher activation energy than for H2Om (a neutral species).

However, different

transport processes are increasingly coupled with increasing temperature and pressure, and will eventually converge to a uniform rate and mechanism (Ni et al., 2015). In vibrant hydrous basaltic melt at high temperature, the interaction between H2Om and local melt structure could be stronger than conventionally thought.

The energy

barrier for the transport of H2Om to overcome may not be significantly lower than that for OH.

Furthermore, due to the limited temperature range in our experiments, the

precision of inferred activation energies may not allow to resolve a small difference between H2Om and OH.

14

4.2. H2Ot diffusivity compared with previous studies H2Ot diffusivity in basaltic melt can now be calculated by combining equations (5)–(6) with equations (2)–(4), with an example shown in Fig. 3 for 1846 K and 1 GPa.

Clearly, in the low H2Ot concentration range (<0.1 wt%) in basaltic melt,

water diffusion is overwhelmingly dominated by OH, OH diffusivity and H2Ot diffusivity are essentially identical, which corroborates our practice of using error function to fit the hydration profiles.

The contribution of OH continues to exceed

that of H2Om until H2Ot concentration increases to 1 wt%.

The conventional wisdom

of H2Om domination becomes valid only at even higher H2Ot concentration. For the convenience of application to magmatic processes, we provide the following equation for approximate calculation of H2Ot diffusivity (DH2Ot is in m2/s) as a function of temperature (T in K) and water content (C in wt%): 

DH2Ot  e

6.731

26095 T

 1.36 0.126 1  Ce 

C+

2274 182.7 C  290.6 C T

   



This empirical expression is applicable for temperature in the range of 1658–1846 K and water content up to 2 wt%, and is able to reproduce the calculation results using equations (2)–(6) within 1% relative. Compared with existing experimental data, at least for T > 1300 K, H2Ot diffusivity at 1 wt% H2Ot in silicate melts follows the sequence rhyolite < dacite < andesite < basalt (Fig. 4).

Furthermore, there appears to be a consistent trend for

activation energy, increasing from 110 kJ/mol for rhyolite, to 144 kJ/mol for dacite, to 168 kJ/mol for andesite, and to 189 kJ/mol for basalt. 15

Zhang and Ni (2010)

developed a general expression of H2Ot diffusivity at 1 wt% H2Ot for rhyolitic to andesitic melts, but they found that the data for MORB melt in Zhang and Stolper (1991) could not be described by that equation.

By contrast, our data significantly

fall below those in Zhang and Stolper (1991) but are in good agreement with the model prediction of Zhang and Ni (2010), as shown in Fig. 4a.

We suspect that

Zhang and Stolper (1991) probably overestimated H2Ot diffusivity at 1 wt% H2Ot in basaltic melt, which was extrapolated from their experimental data at 0.2 wt% H2Ot assuming a proportional relationship.

Indeed, when the two data sets are compared

at 0.2 wt% H2Ot, their agreement appears to be significantly improved (Fig. 4b). The good agreement between our results and previous studies also corroborates the validity of using an Fe-free analogue for basaltic melt.

4.3. Perspective from melt structure The contribution of OH to water diffusion was not found by earlier studies on rhyolitic and dacitic melts (e.g., Zhang and Behrens, 2000), but was only resolved recently for more depolymerized melts, including andesitic melt in Ni et al. (2013) and basaltic melt in the present study.

There are at least three considerations from

the perspective of melt structure that may help to explain this difference. Firstly, andesitic and basaltic melts, with a lower degree of polymerization, have lower viscosity than rhyolitic and dacitic melts (Hess and Dingwell, 1996; Richet et al., 1996; Giordano and Dingwell, 2003a; Whittington et al., 2009a; Ni et al., 2015).

16

Diffusivities of atomic species, especially those with low mobility, are strongly coupled with viscosity.

For example, the Eyring equation declares that Si diffusivity

is inversely proportional to melt viscosity (Glasstone et al., 1941; Zhang et al., 2010), and experimental data show that Si diffusivity in basaltic melt is higher than that in rhyolitic melt by nearly 4 orders of magnitude (Baker, 1992; Lesher et al., 1996). OH diffusivity is also expected to increase significantly from rhyolitic to basaltic melt. Furthermore, the equilibrium constant of the water speciation reaction appears to increase from rhyolitic to andesitic melt (Zhang and Ni, 2010).

This trend may

continue to hold toward basaltic melt although it awaits experimental confirmation. This means that for the same temperature, pressure and H2Ot concentration, there is more OH present in the more depolymerized melts.

The differential term in equation

(4), which corresponds to the weight for the relative contribution of OH to water diffusion, also increases with increasing K. Last but perhaps more importantly, NMR spectroscopic studies have demonstrated that in depolymerized melts, OH bonds not only with network-forming cations such as Si and Al but also with network-modifier cations such as Ca and Mg (Xue and Kanzaki, 2004, 2008; Xue, 2009). The latter kind of OH, often referred to as free hydroxyl or OH– (Xue and Kanzaki, 2004), also becomes more abundant with increasing temperature (Moretti et al., 2014).

Due to its weaker bonding with cation,

free hydroxyl is expected to have higher mobility than Si-OH or Al-OH.

17

All the three microscopic mechanisms above can rationalize why OH plays a more perceptible role in water diffusion in the more depolymerized melts.

In essence, OH

in depolymerized melts is more mobile and more abundant than that in polymerized melts.

4.4. OH contribution to electrical conduction Silicate melts are ionic conductors, and electrical conductivity of silicate melts is useful for interpreting magnetotelluric data and probing the status of molten regions (such as water content of magma) in Earth’s interior (e.g., Gaillard, 2004; Ni et al., 2011).

Because OH is a charged species, it may serve as a potential charge carrier in

hydrous basaltic and andesitic melts.

The contribution of an ionic species i to

electrical conduction can be evaluated from diffusivity through the Nernst-Einstein equation 

i =

1 Di ci ( zi F )2  Hi RT



where i is the contribution of the ionic species to electrical conductivity (in S/m), Di, ci and zi are the diffusivity (in m2/s), the concentration (in mol/m3), and the valence of the species, and Hi is the Haven ratio depending on the diffusion mechanism. For comparison, we use Na, the ion with typically the highest diffusivity, as a reference.

At low H2Ot concentration, Na diffusivity is similar in basaltic and

andesitic melts (Lowry et al., 1982), and is higher than OH diffusivity in andesitic melt by more than an order of magnitude (Fig. 5). But for basaltic melt, Na diffuses 18

faster than OH diffusivity by only a factor of 2–4.

In hydrous melt, the mobility of

ions will be enhanced in correspondence to reduced viscosity.

Watson (1981)

showed that Na diffusivity in rhyolitic melt is nearly doubled upon the addition of 3.5 wt% water. The influence of water on Na diffusivity in basaltic melt is probably similar or even weaker.

OH diffusivity may also increase with increasing H2Ot

concentration although this effect cannot be easily resolved.

Overall, it is reasonable

to expect that the DOH/DNa ratio is roughly independent of H2Ot concentration.

If

one assumes that OH and Na diffuse by a similar mechanism so that their Haven ratio is cancelled out, the contribution of OH to electrical conduction relative to Na can be expressed as follows:

 OH DOH cOH    Na DNa cNa





The concentration of OH at different H2Ot can be calculated from the equilibrium constant K.

As shown in Fig. 6, OH contribution is generally no more than several

percent of Na contribution in andesitic melt unless for very high H2Ot concentration. But in basaltic melt, OH contribution can become even greater than Na contribution, which makes OH an effective charge carrier in hydrous basaltic melt. It has been noticed that water enhances electrical conductivity of basaltic and andesitic melts more significantly than the effect for rhyolitic and dacitic melts (Ni et al., 2011; Guo et al., 2016; Guo et al., 2017). An explanation given in Guo et al. (2016) suggested that in the depolymerized melts network-modifying cations other than Na (e.g., Mg and Ca) play a major role in electrical conduction, and that adding 19

water mobilizes these cations more effectively than it does for Na, the predominant charge carrier in rhyolitic melt.

Our analysis above provides a second mechanism.

That is, at least for basaltic melt, adding water not only enhances the mobility of cations, OH itself (an anion) also contributes to carrying electrical charge.

4.5. Application to bubble growth in magma In addition to melt viscosity and water solubility, water diffusivity is another critical parameter in determining the rate of bubble growth, an important process in explosive volcanic eruption (Proussevitch and Sahagian, 1998; Liu and Zhang, 2000; Lensky et al., 2004; Houghton and Gonnermann, 2008).

Based on the bubble

growth model developed by Proussevitch and Sahagian (1998), slightly modified by Liu and Zhang (2000), we compare bubble growth in basaltic melt and rhyolitic melt with 2 wt% H2O and 1573 K and 50 MPa, corresponding to a P-T condition in a volcanic conduit (Fig. 7).

The parabolic shape of the growth curves indicates that

bubble growth is controlled by water diffusion instead of by viscous flow.

Higher

water diffusivity in basaltic melt leads to appreciably faster bubble growth than in rhyolitic melt.

This may facilitate separation of the bubbles from basaltic magma

and have a major impact on the eruption dynamics.

5. CONCLUSIONS Water diffusion in silicate melts is conventionally thought to be dominated by

20

neutral H2O molecules rather than the charged OH species.

However, the present

study shows that OH is mobile enough for contributing significantly to water diffusion in basaltic melt, especially at low H2Ot concentration.

In view of the

results from NMR investigations, the high mobility of OH is probably due to the notion that a significant fraction of OH is free hydroxyl bonded with network-modifying cations instead of with Si or Al.

The strong influence of water

on electrical conductivity of basaltic melt can be accounted for, at least partly, by OH serving as an effective charge carrier in addition to cations.

Acknowledgements We thank Youxue Zhang for instructive suggestions and Yan Liang for insightful and constructive comments.

This work was supported by the National Natural

Science Foundation of China (41473058), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB18000000), and the Fundamental Research Funds for the Central Universities of China.

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27

Table 1 Chemical composition of basaltic glasses (in wt%) used in H2O diffusion studies HBS-dry

MORB

Haplobasalt

(this study)

(Zhang and Stolper, 1991)

(Persikov et al., 2010)

SiO2

51.97

50.60

62.20

TiO2

1.06

1.88

Al2O3

16.32

13.90

FeOt

0.03

12.50

MgO

11.21

6.56

6.79

CaO

15.34

11.40

14.15

Na2O

2.79

2.64

6.34

K2O

0.89

0.17

MnO

0.23

P2O5

0.21

Total H2O (IR) NBO/T

10.50

99.61

100.09

99.98

0.03

0.4

<0.1

0.798

0.826

0.677

Major element composition of HBS-dry was analyzed by a Shimadzu 1600 electron microprobe with a defoucus beam of 15 kV, 10 nA, and 5 m across.

Water content was measured by FTIR

spectroscopy using the calibration for the 3550 cm–1 band by Dixon et al. (1995). NBO/T is the number of non-bridging oxygen atoms per tetrahedrally coordinated cation.

For MORB, Fe3+

accounts for 13.6% of total iron (Bezos and Humler, 2005) and is counted as network-forming cation.

28

Table 2 Experimental conditions of water diffusion experiments at 1 GPa Run #a

Tdwell (K)

Tcorrected (K)

tdwell (s)

teffective b (s)

Initial H2Ot c (wt%)

Final H2Ot d (wt%)

1693

1708±20

132

150

0.33/0.74

0.33/0.74

0.31/0.71

0.31/0.71

0.31/1.77

0.32/1.78

0.28/1.13

0.28/1.11

0.21/1.92

n.a.

Crystallization

0.21/1.04

n.a.

Crystallization

0.16/1.90

0.16/1.92

Partial crystal.

0.16/1.04

n.a.

Crystallization

0.39/1.53

0.39/1.51

0.36/0.95

0.36/0.95

0.03/1.98

0.04/1.98

0.03/1.02

0.03/1.02

0.03/1.98

0.14/2.02

0.03/0.95

0.04/0.95

Comment

Diffusion couple HBS-USTC-DC1

a b

HBS-USTC-DC2

a

1697

1712±20

161

174

b HBS-BGI-DC3

a

1593

1608±20

189

209

b HBS-BGI-DC4

a

1643

1658±20

172

187

b HBS-BGI-DC5

a

1813

1828±20

117

148

b HBS-USTC-DC6

a

1748

1763±20

144

163

b HBS-USTC-DC7

a

1831

1846±20

113

122

b

Elevated H2Ot

Hydration HBS-USTC-Hy1

1818

1833±20

149

159

0.03

0.03/0.06

HBS-USTC-Hy2

1747

1762±20

202

212

0.03

0.03/0.06

HBS-USTC-Hy3

1686

1701±20

157

168

0.03

0.03/0.06

HBS-USTC-Hy4

1666

1681±20

232

237

0.03

0.03/0.06

a

Each diffusion couple experiment contains two diffusion couples with different water contents.

b

Effective experimental duration at the corrected temperature (see text for details).

c

FTIR-determined water contents of the starting glasses.

d

FTIR-determined water contents in the post-experiment samples.

profile.

For diffusion couple runs, the numbers represent water contents at the two flat regions of the diffusion

For hydration runs, the numbers are the water content at the flat region (sample interior) and that at the sample-capsule interface, respectively. 29

Table 3 Definition of symbols Notation C X x t D P T K



c F H z R

Definition

Unit/Value

Weight percentage Mole fraction Distance Time Diffusivity Pressure Temperature Equilibrium constant Electrical conductivity Ion concentration Faraday’s constant Haven ratio Valence Gas constant

wt% m s m2/s Pa K S/m mol/m3 96485 C/mol

8.3145 J/(mol·K)

30

Table 4 OH and H2Om diffusivities extracted from fitting using the modified speciation model Run # Diffusion couple HBS-USTC-DC1 HBS-USTC-DC2 HBS-BGI-DC4 HBS-BGI-DC5 HBS-USTC-DC6 HBS-USTC-DC7

logDOH

logDH2Om

R2

1846

0.12 0.10 0.11 0.17 0.12 0.10 0.10 0.12 0.14 0.14

–9.64±0.01 –9.58±0.01 –9.53±0.01 –9.50±0.01 –9.73±0.01 –9.41±0.01 –9.39±0.01 –9.31±0.01 –9.33±0.01 –9.07±0.01

–8.73±0.01 –8.58±0.01 –8.57±0.01 –8.73±0.01 –8.81±0.01 –8.39±0.01 –8.40±0.01 –8.39±0.01 –8.48±0.01 –8.21±0.01

0.9997 0.9998 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9998 0.9995

1818 1747 1686 1666

– – – –

–9.12±0.02 –9.36±0.03 –9.59±0.05 –9.64±0.04

– – – –

0.9981 0.9957 0.9869 0.9944

T (K) a b a b a a b a b b

Hydration HBS-USTC-Hy1 HBS-USTC-Hy2 HBS-USTC-Hy3 HBS-USTC-Hy4

1708 1712 1658 1828 1763

Best DOH/DH2Om

Errors are given at 2 level.

31

Figure Captions

Fig. 1. Diffusion profile for sample HBS-USTC-DC6a measured by FTIR and fitted by different models.

(a) Profile and fits; and (b) Inferred H2Ot diffusivity as a

function of the mole fraction of H2Ot.

Erfc: error function (constant diffusivity);

exponential: DH2Ot = D0eaX; speciation-based model: DH2Om = D0eaX and DOH = 0. Best fit was obtained using the modified speciation-based diffusivity model: DH2Om = constant and DOH = constant, and the inferred H2Ot-dependent DH2Ot is in good agreement with the result from Boltzmann-Matano analysis.

Fig. 2. Diffusivities of H2Om and OH in basaltic melt at 1 GPa extracted from least squares fitting of experimental diffusion profiles (Table 4).

Open diamonds are OH

diffusivity (≈ H2Ot diffusivity) from error function fitting of hydration profiles.

For

diffusion couple profiles fitted by the modified speciation-based model, H2Om diffusivity and OH diffusivity are shown in solid circles and solid diamonds, respectively.

Straight lines are Arrhenius fits corresponding to equations (5) and (6).

Error bars are shown at 2 level while the vertical error bars are within the size of symbols.

Fig. 3. Absolute (solid curves) and relative contribution (dashed curves) of OH and H2Om to H2Ot diffusivity in basaltic melt at 1846 K and 1 GPa.

Fig. 4. (a) Total water diffusivity at 1 wt% H2Ot and 1 GPa in silicate melts, compared with calculations using the model (dashed lines; their eqn. 26) in Zhang and Ni (2010). 32

(b) Total water diffusivity at 0.2 wt% H2Ot and 1 GPa in silicate melts.

Data sources:

N(13): Ni et al., (2013); N&Z(08): Ni and Zhang (2008); B(04): Behrens et al. (2004); Z&S(91): Zhang and Stolper (1991).

Fig. 5. Comparison of the diffusivities of hydrous species with Na diffusivity in nominally anhydrous basaltic and andesitic melts. melt are from Ni et al. (2013).

Water diffusivities in andesitic

Na diffusivity from Lowry et al. (1982) is similar in

the two melts.

Fig. 6. Contribution of OH to electrical conductivity relative to the contribution of Na in two hydrous silicate melts, based on the Nernst-Einstein equation using the diffusivity data from Lowry et al. (1982), Ni et al. (2013) and the present study.

Fig. 7. Bubble growth in basaltic melt and rhyolitic melt with 2 wt% H2O at 1573 K and 50 MPa using the model of Liu and Zhang (2000). this study and Ni and Zhang (2008).

Water diffusivity is based on

Water solubility and melt viscosity are based

on Zhang et al. (2007) and Hui and Zhang (2007), respectively. radius is set to be 1 m.

33

The initial bubble

Figure1

0.04

(a) HBS-USTC-DC6a 1763 K, 163 s

1.5

0.02

1 FTIR erfc exponential speciation modified speciation

0.01

0 -1500

0.5

0 -1000

-500

0

500

1000

1500

x (μm) CH2Ot (wt%) 2000

0

0.5

1

1.5

2

(b) HBS-USTC-DC6a 1763 K, 163 s

DH2Ot (μm2/s)

1500

1000

erfc exponential speciation modified speciation Boltzmann-Matano method

500

0

0

0.01

0.02

XH2Ot

0.03

0.04

CH2Ot (wt%)

XH2Ot

0.03

2

Figure2

T (°C) -8

1600

1550

1500

1450

1400

1350

logD (D in m2/s)

-8.5

DH2Om -9

DOH

-9.5

-10 0.54

0.56

0.58

1000/T (T in K)

0.6

0.62

Figure3

1

2500 OH

D (μm2/s)

2000

0.8

D H2Ot

1500

D H2O

0.6

X X m/d d · m

0.4

1000

DOH·dXOH/2dX

500 0

0.2

H 2O m

0

0.5

1

H2Ot (wt%)

1.5

2

0

Contribution of hydrous species

1846 K, 1 GPa

Figure4

T (°C) -8

1700

1600

1500

1400

1300

1200

logDH2Ot (D in m2/s)

(a) MO

-9 Bas alt A nd

RB Z&S (91

(thi s st udy

esit e

-10

B(0 4

)

1 wt% H2Ot ~ 1 GPa )

)

Dac ite B (

04) Rhyo lite N &Z(0 8)

-11 0.5

0.55

0.6

0.65

0.7

1000/T (T in K) T (°C) -8

1700

1600

1500

1400

1300

1200

logDH2Ot (D in m2/s)

(b) -9

Bas alt

(thi s st udy

MOR B Z& S (91)

)

-10 A nd

esite

N (1

3)

Daci te B( 04) Rhyol ite N& Z(08)

-11

-12 0.5

0.2 wt% H2Ot ~ 1 GPa

0.55

0.6

1000/T (T in K)

0.65

0.7

Figure5

DH2Om

T (°C) -8.5

1700

1600

1500

1400

1300

logD (D in m2/s)

-9

DNa

DOH -9.5 Basalt

-10

DOH -10.5

-11 0.5

Andesite

0.55

0.6

1000/T (T in K)

0.65

Figure6

10

6w Basalt (

1

σOH/σNa

2w Basalt (

Andesite

0.1

) t% H 2O t ) t% H 2O t

O) (6 wt% H2 t

(2 wt% Andesite

0.01 1200

1300

1400

T (°C)

H2Ot)

1500

1600

Figure7

bubble radius (μm)

300

1573 K 50 MPa 2 wt% H2O

200

basalt

100

rhyolite

0

0

500

1000

t (s)

1500

2000