Cassiterite dissolution and Sn diffusion in silicate melts of...

Chemical Geology 441 (2016) 162–176

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Chemical Geology

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Cassiterite dissolution and Sn diffusion in silicate melts of variablewater content

Yuping Yang a,b,⁎, Youxue Zhang b, Adam Simon b, Peng Ni b

a MLR Key Laboratory of Metallogeny and Mineral Assessment, Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing 100037, Chinab Department of Earth and Environmental Sciences, the University of Michigan, Ann Arbor, MI 48109-1005, USA

⁎ Corresponding author at: MLR Key LaboratoryAssessment, Institute of Mineral Resources, Chinese AcBeijing 100037, China.

E-mail address: [email protected] (Y. Yang).

http://dx.doi.org/10.1016/j.chemgeo.2016.07.0210009-2541/© 2016 Elsevier B.V. All rights reserved.

a b s t r a c t
a r t i c l e i n f o
Article history:Received 20 December 2015Received in revised form 8 June 2016Accepted 23 July 2016Available online 27 July 2016

Experiments to constrain cassiterite dissolution kinetics in rhyolitic melts with 0.1–5.9 wt% H2Owere conductedat 1023–1373 K and 0.5 GPa in a piston-cylinder apparatus. Care was taken tominimize convection in the exper-imental charge. Tin diffusivity was found to be concentration dependent. The diffusion profiles were fit well byassuming that tin diffusivity depends exponentially on tin concentration, which is roughly linearly related toSiO2 or SiO2 + Al2O3 concentration. Tin diffusivity was found to increase with temperature following the Arrhe-nius relation, with activation energy decreasing from 161 kJ/mol in dry rhyolite to 93 kJ/mol in hydrous rhyolitecontaining 5.9 wt% H2O. Tin diffusivity increases exponentially with H2O concentration, by about 3.2 orders ofmagnitude at 1123 K from 0 to 6wt% H2O, and decreases exponentially with SiO2 concentration, by about 0.7 or-ders ofmagnitudewhen SiO2 concentration increases by 10wt%. The equation to describe Sn2+diffusivity in rhy-olitic to dacitic melt (64–76 wt% SiO2) at about 0.5 GPa is:

lnDSn ¼ −18:194þ 0:17 76–CSiO2

� �− 19418−1389wð Þ=T;

where DSn is in m2/s, CSiO2andw are SiO2 and H2O concentrations in wt%, and T is in Kelvin. The solubility of cas-

siterite (or tin concentration at cassiterite saturation) in rhyolitic melts increases strongly with increasingtemperature.

© 2016 Elsevier B.V. All rights reserved.

Keywords:Cassiterite solubilityTin diffusivity

1. Introduction

Tin deposits are generally associated with highly-fractionated gran-ites and their rhyolitic volcanic equivalents, where Sn is found domi-nantly as the mineral cassiterite (SnO2) (Linnen et al., 1995; Keslerand Wilkinson, 2013). Most granite-related tin deposits are lode de-posits clustered around cupolas at the top of these intrusions. Cassiteriteis found in pegmatites, wherein cassiterite crystallized directly fromwater-rich silicate melt, and quartz veins, stockworks, and dissemina-tions where cassiterite precipitated from a magmatic-hydrothermalfluid (Lehmann, 1990; Heinrich, 1990; Linnen, 1998; Audetat et al.,2000). For both mechanisms of Sn enrichment, the transport of Snfrom the melt to the vapor phase or to cassiterite is largely controlledby the diffusion of Sn in the melt. Hence, it is critical to understand Sndiffusion in granitic melts. In addition, it is important to know the satu-ration behaviour of cassiterite in silicatemelts to evaluate the possibilityof magmatic cassiterite formation.

of Metallogeny and Mineralademy of Geological Sciences,

Sn diffusivity data in the literature are limited. Behrens and Hahn(2009) reported Sn tracer diffusion data in trachytic and phonoliticmelts. They also explored the effect of H2O and found that the additionof 1–2 wt.% H2O increases the Sn diffusivity by about one order of mag-nitude in these melts. Because tin deposits are generally related to gra-nitic melts, their results have only limited applicability to tin deposits.Linnen et al. (1995, 1996) investigated the effects of fO2

andmelt compo-sition on tin diffusivity in haplogranitic melts containing about 6 wt%H2O. However, they only conducted experiments at one temperatureand one H2O content (but at different fO2

), and their diffusion data arescattered, which might be due to possible convection during their ex-periments (Zhang et al., 2010).

Numerous studies investigated cassiterite solubility in graniticmelts. Earlier cassiterite solubility work was largely published inRussian. Stemprok (1990) reviewed experimental SnO2 solubility datain Russian and Czech literature, which are for dry systems at1573–1873 K and hydrothermal systems at 1023–1073 K with a rangeof oxygen fugacity fromNNO to air, and derived the temperature depen-dence of tin concentration at cassiterite saturation (TCCS) in felsicmelts,which is about 2.7 wt.% Sn at 1573 K and 0.26wt.% at 1023 K. Taylor andWall (1992) reported cassiterite solubility data, but Linnen et al. (1995)concluded that the data were compromised because loss of tin into the

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163Y. Yang et al. / Chemical Geology 441 (2016) 162–176

fluid phase and into the capsule were not considered. Linnen et al.(1995) examined the dependence of cassiterite solubility on oxygen fu-gacity at 1123 K and 200 MPa in a hydrous rhyolite, and found that tinconcentration at cassiterite saturation (TCCS) depends strongly on fO2

,ranging from 2.2 wt.% at FMQ-0.84 to approximately 630 ppm atFMQ+ 3.12. Linnen et al. (1996) studied the effect of melt compositionon cassiterite solubility: at reduced conditions (FMQ-0.57) TCCS de-creases from~8wt.% to 2.2wt.% as the Al/(Na+K) cation ratio (aluminasaturation index or ASI) increases from 0.64 to 1.0, and increases from2.2 to 3.2 wt.% as ASI further increases from 1.0 to 1.2; and at oxidizedconditions (FMQ + 3.0), TCCS decreases from ~5 wt.% to 0.05 wt% asASI increases from0.64 to 1.0, and then stays at 0.05wt% as ASI increasesfrom 1.0 to 1.2. Bhalla et al. (2005) investigated cassiterite solubility atdifferent temperature, fO2

and additional volatiles, and found that TCCSincreases from 0.25 to 0.95 wt.% in melts containing 1.12 wt.% F withan increasing temperature from 973 K to 1123 K at NNO buffer.

Here, we report new experimental data that examine the effectsof temperature (1023–1373 K) and melt H2O concentration(0.1–5.9 wt%), and the role of Sn speciation, on Sn diffusivity in rhy-olitic melts at 0.5 GPa. As a side product, cassiterite solubility data arealso reported.

2. Experimental and analytical methods

2.1. Starting materials

The starting rhyolitic glass samples CIT, KS, and H6a have similarcompositions on an anhydrous basis (Table 1), but contain 0.1, 0.9 and5.9 wt% dissolved H2O, respectively. CIT and KS are natural samples(Newman et al., 1986), and H6a is a synthetic hydrous rhyolitic glasswith 5.9 wt% H2O (Hui et al., 2008). The rhyolitic glass compositionsare listed in Table 1, with ASI of 1.0 for CIT and KS and 1.2 for H6a.Note that these glass pieces initially contain dissolved H2O before ourexperiments, and no liquid water was added to any experimentalcharge or capsule for our experiments. Two starting cassiterite crystalswere used: one is from Ximeng, Yunnan Province, China, and theother from Cochabamba, Bolivia. Both were purchased from onlinegem vendors. The two cassiterite crystals are essentially pure SnO2

(Table 1).

2.2. Experimental details

We performed cassiterite dissolution experiments by using a 12.7-mm piston-cylinder apparatus at 0.5 GPa and 1023–1373 K at the Uni-versity of Michigan. A relatively low pressure for piston-cylinder

Table 1Compositionsof the starting materials (oxide wt%).

CassiteriteXimeng

CassiteriteCochabamba

Rhyolite CIT RhyoliteKS

Rhyolite H6a

Anhydrousa Anhydrousa

SnO2 99.59 99.77 bdl bdl bdlSiO2 bdl bdl 76.30 76.46 74.67TiO2 bdl bdl 0.05 0.06 0.26Al2O3 bdl bdl 12.98 12.43 13.44FeOt 0.11 0.29 0.91 1.02 1.72MgO bdl bdl 0.02 0.03 0.27CaO bdl bdl 0.41 0.49 1.22Na2O bdl bdl 4.06 4.25 3.92K2O bdl bdl 5.28 5.01 4.49H2O nd nd 0.10 0.90 5.90Total 99.70 100.06 100.11 99.75 99.99A.S.I. 1.02 1.00 1.20

H2O concentration is determined by FTIR, and other oxide concentrations are determinedby electron microprobe.

a The glass composition is calculated on H2O-free basis and normalized to 100%. bdl:below detection limit; nd: not determined.

experiments was chosen because cassiterite ores are typically relatedto shallow crustal processes (Ishihara, 1977; Taylor and Wall, 1992).Data from the same lab have shown that consistent data can be obtainedat 0.5 GPa (e.g., Zhang et al., 2000; Zhang and Behrens, 2000). Table 2shows the run conditions of the experiments. The experimental proce-dures are similar to those of Chen and Zhang (2008, 2009) and are brief-ly described below.

Optically transparent and clear volumes of cassiterite crystals weredrilled and cut into ~2.6-mm-diameter and ~0.9-mm-thick discs, anddoubly-polished. The doubly polished sample allowed us to opticallyexamine the cassiterite wafers, and to choose the best wafers (withthe fewest inclusions) for our experiments. Also, polished cassiteritesurface makes a better (smooth and no gap) contact with polished rhy-olitic glass surface. Rhyolitic glass was drilled and cut into ~2.6-mm-di-ameter and ~1.5-mm-thick discs, and polished on one side. The glassand cassiterite discs were fit tightly into a graphite capsule. Tominimizeconvection, care was taken so that the interface between the glass andcassiteritewas horizontal, and the glasswas placed above the cassiteritedisc because the interfacemelt produced by cassiterite dissolution is ex-pected to be denser than the initial melt. Then, the graphite capsulewasfit into an MgO pressure medium, which was placed inside a graphiteheater, and then into a BaCO3 pressure medium. To minimize the tem-perature gradient inside the capsule and to improve the accuracy oftemperature determination, relatively short samples were used, with atotal cassiterite + glass thickness of 2.4 mm. To optimize the consisten-cy in the actual temperature ofmultiple experiments at a given nominaltemperature–pressure condition, we used the same sample size andcapsule geometry for all experiments, and the cassiterite–melt interfacewas placed in the middle of the graphite heater. In one experiment, aplatinum capsule rather than a graphite capsule was used to examineSn diffusivity under a more oxidizing condition.

In all runs, the charge was first pressurized to the target pressure byusing a piston-out procedure, which involves pressurizing to about5–10% higher than the target pressure and then allowing the assemblyto relax back to the target pressure. To improve the pressure reliability,the assemblywas relaxed at 473 K for ~12 hwhen KS or CITwas used asthe starting glass. A lower relaxation temperature of 373 Kwas used forthe hydrous rhyolitic glass H6a (5.9 wt%water) to avoid water loss. Theassembly is then heated up to the target temperature in about 30s at aprogrammed rate. The sample is maintained at the pressure and tem-perature for a planned duration, and then quenched by turning off thepower. The thermal history is recorded by a computer. Variation at thetarget temperature is typically ±1 K. Overshooting is b6 K and lastsb4 s. During quench, the temperature drops to ½ of the experimentaltemperature in b6 s. The reported pressure is corrected pressure usingthe nominal pressure (from the area of the ram and piston and the oilpressure in the ram) multiplied by 0.94 based on the calibration of Huiet al. (2008) andNi and Zhang (2008). There is temperature gradient in-side the capsule, so the temperature at the cassiterite–melt interface iscorrected based on the thermal gradient calibrated by Hui et al.(2008). Because the diffusion distance is small as will be seen later,the temperature variation across the diffusion profile is small (b1 K ifthe interface is aligned with the hottest spot).

After each experiment, the assembly was embedded in epoxymounts, grounded to reveal the center of the diffusion couple, and sin-gly polished for electron microprobe analyses (Fig. 1). Afterwards, thesection was doubly polished for FTIR analyses.

2.3. Analytical methods

Compositional profiles were measured by using a Cameca SX100electron microprobe in the Electron Microbeam Analysis Laboratory ofthe University of Michigan. For the KS and CIT sample assemblies, apoint beam of 15 keV accelerating potential and 4 nA beam currentwas used. For the H6a assembly with 5.9 wt% H2O, the same voltageand current were used, but a raster beam of 3 μm by 3 μm was

Table 2Summary of experimental conditions and results.

ExpNo. Starting melt H2O(wt%)

T (K) t (s) SnOt C0(wt %)

logD0 (m2/s)for Sn

logDSi (m2/s) SiO2 = 70 wt% logDAl (m2/s)

CassDis9 H6a 5.9 1023 634 0.551±0.073

–12.698±0.125

CassDis6 H6a 5.9 1123 299 1.525±0.048

–12.167±0.033

CassDis12 H6a 5.9 1123 1519 1.612±0.033

–12.262±0.024

CassDis8 H6a 5.9 1223 239 5.003±0.037

–11.932±0.010

–12.203±0.037

CassDis10 KS 0.9 1173 18,026 5.371±0.053

–14.581±0.012

–14.123±0.037

CassDis3 KS 0.9 1273 18,092 9.560±0.035

–13.925±0.007

–13.503±0.016

–13.49±0.06

CassDis1 KS 0.9 1373 1856 12.831±0.044

–13.638±0.009

–13.153±0.013

–13.21±0.05

CassDis11 CIT 0.1 1273 18,000 12.492±0.043

–14.679±0.009

–14.221±0.018

–14.21±0.05

CassDis13 CIT 0.1 1373 3633 2.211±0.029

-13.627±0.013

P=0.5 GPa for all experiments. Platinum capsule is used for CassDis13, and graphite capsule is used for the other runs. D0 for Sn is defined in Eq. (4) with a common a0 = 0.1521 wt%−1

andmeans Sndiffusivity at trace Sn concentration.DSi values at SiO2=70wt.% is obtained using Eq. (5c)with a common a=0.130wt%−1. Al2O3 concentration profiles arefit by assuminga constant Al diffusivity DAl.

164 Y. Yang et al. / Chemical Geology 441 (2016) 162–176

employed. Pure SnO2 single crystal is used as the standard for Sn. Be-cause Sn is present at major element concentration level in our experi-mental charges, a counting time of 20 s at the peak (similar to that forother elements) is used.

Two approaches were conducted to estimate the secondary fluores-cence effect near the interface in microprobe analysis. First, a cassiteritecrystal wafer was physically placed together with a “blank” rhyoliticglass in a graphite capsule. Thenwithout any experiment the entire cap-sule was embedded in epoxy and polished to expose the center. Twomicroprobe traverses were then analyzed from the interface into therhyolitic glass to measure the secondary fluorescence effect profile di-rectly. Second, a Monte Carlo simulation package PENEPMA by Llovetand Salvat (2006) was employed to simulate the same profile in a rhy-olitic glass next to a cassiterite crystal. At each point away from the in-terface, 1 to 3 million electrons were simulated and typically a 1σerror of ~1% relative was achieved for the Sn Lα peak X-ray counts.After simulation at each point, Sn Lα2 peak X-ray density was dividedby that of a pure cassiterite crystal (SnO2) obtained at the same runcondition to calculate SnOt concentration. For simplification, theoretical

Fig. 1. Image of experiment Run CassDis10. The red short dashed lines show the positionwhere SnOt profiles were measured; the black long-dashed vertical and horizontal linesshow the position where H2O and CO2 profiles were measured. (For interpretation ofthe references to colour in this figure legend, the reader is referred to the web version ofthis article.)

X-ray peaks instead of convolved X-ray spectrumwas used, also no ZAFcorrection was applied. SnOt (see next paragraph for the meaning ofSnOt) profiles obtained from both methods have been plotted in Fig. 2.The apparent SnOt concentration quickly diminishes to ~0.05 wt% at~2 μm away from the interface. Because we only use data in the glassat ≥2 μmaway from cassiterite, the secondary fluorescence effect is neg-ligible in our analysis.

Tin in rhyolitic melts can be in the form of Sn2+ or Sn4+ dependingon the fO2

(Linnen et al., 1995, 1996). We will report total Sn oxide con-centrations in the melt as SnOt (similar to the notation of FeOt). For ex-periments in graphite capsules, the oxygen fugacity in our experimentalcharge is relatively low, below NNO based onmeasured CO2 concentra-tions in the melt (Holloway et al., 1992). Sn in the melt is dominantlySn2+ under such conditions (Linnen et al., 1995). The SnOt concentra-tion in the far-field glass (i.e., the initial glass) is below the detectionlimit (~0.035 wt% using 2σ of the measurement scatter) of the electronmicroprobe, and the measured SnOt concentration is often slightly neg-ative due to interference of other characteristic X-ray peaks on the back-ground of Sn Lα peak at 3.44 keV (e.g. potassium Kα at 3.31 keV andcalciumKα at 3.69 keV). To compensate for the apparent negative back-ground, we added a small constant (0.02wt%) to the concentration pro-files so that the average far-field SnOt concentration is zero. Thisaddition has no effect on diffusivity determination, and only an insignif-icant effect on the estimation of the interface SnOt concentration.

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

4 8 12 16 20

SnOt (Monte Carlo)SnOt (Measured)

SnO

t(wt%

)

x (µm)

Fig. 2. Apparent tin concentration profile due to secondary fluorescence near the interfaceby Monte Carlo simulation using PENEPMA and by microprobe measurement in a non-experimented cassiterite-rhyolite couple.


Fig. 1 shows a back-scattered electron (BSE) image of a polished ex-perimental charge of CassDis10, where three profiles were measuredperpendicular to the interface. There is a crack in this sample attributedto shrinkage during quench and stress release during decompression(Fig. 1), and some other samples in our experiments have similar crackswhich are subparallel to the crystal-melt interfaces. Effort was made tominimize the widening of the cracks during polishing by repeatedlyrefilling the cracks by epoxy. The cracks are mainly in the rhyoliticglass adjacent to the interface. In these cases, a couple of profiles weremeasured at different distances from the interface, and then these pro-files were re-connected smoothly across the cracks and combined intoone composite profile (Zhang et al., 1989). For experiment CassDis1,there is a crack at the interface, leading to uncertainty as to whetherthe interface melt was preserved or lost. Based on data from other ex-periments, the interface SnOt concentration can be roughly determined.

Water and CO2 concentrations in the experimental silicate glasseswere determined by using the Autoimage microscope of a Perkin-Elmer GX Fourier Transform Infrared Spectrometer (FTIR) at theUniver-sity of Michigan, with LN2-cooled MCT detector and KBr beamsplitter.The molecular water and OH concentrations were determined by thepeak height of the absorption bands at 5230 and 4515 cm−1 by usingthe molar absorptivities from Newman et al. (1986). Baselines were fitby smooth curves drawn with a French curve. Zhang (1999) discussedthe pros and cons of different fitting methods for these IR peaks andsimple French curve fitting is still often used. Total water contentswere obtained by summation of the concentrations of both species.

3. Results

A summary of experimental conditions and analytical results areprovided in Table 2. To constrain the temperature dependence of Sn dif-fusivity, a large range of experimental temperature is necessary. On theother hand, the experimental temperature must be higher than theliquidus of the melt, which limited the temperature choice. BecauseH2O in crustal granitic melts can be variable, three H2O contents werechosen to examine the dependence of Sn diffusivity on H2O. Selectedcompositional profiles are shown in Figs. 3, 4 and 5. All compositionalprofiles (in figures and digital data) can be found in SupplementaryMaterials.

3.1. SnOt diffusion profiles

Fig. 3 shows SnOt concentration profiles in eight out of nine experi-ments. The remaining experiment was conducted in a Pt capsule andthe data will be shown in Fig. 10 and discussed later. The quality ofSnOt concentration profiles is high. SnOt concentration decreases grad-ually to essentially zero with distance away from the interface.

Viscosity in granitic melt is high at our run conditions thus convec-tion in the experimental charge is unlikely. Nonetheless, we conductedtime-series experiments in hydrous melt H6a at 1123 K (CassDis6 andCassDis12 in Table 2) for 299 s and 1519 s. The SnOt as well as otheroxide concentration profiles of the two experiments nearly overlapwhen the distance is normalized (divided) by t1/2 (Fig. 4). The interfaceSnOt concentration and Sn diffusivity in the two experiments are simi-lar, confirming that cassiterite-dissolution process is diffusion con-trolled, meaning no convection had occurred and interface reactionrate is high enough for the interface to be considered in equilibrium(Zhang et al., 1989; Yu et al., 2016). In addition, themultiple concentra-tion profiles in the same experimental charge overlap, also supportingthe absence of convection.

3.2. Concentration profiles of other components

Diffusion in the melt during cassiterite dissolution is largely the ex-change of tin oxide with other oxide components. When the interfaceSnOt concentration is below 2 wt% (experiments at 1023–1123 K), the

concentration variation in the other components is only slightly aboveanalytical uncertainty, and the other concentration profiles cannot bewell resolved. In five experiments, the interface SnOt concentration isabove 5 wt%, and the concentration gradients of other componentscan be well resolved.

Fig. 5 presents electron microprobe data for major oxides in theglasses (i.e., quenched melts) as a function of distance from thecassiterite-melt interface at 1273 K for about 5 h (CassDis3), in whichthe interface SnOt concentration is 9.6 wt%. As illustrated in Fig. 5, theconcentrations of SiO2 and Al2O3 in the melt decrease towards thecassiterite-melt interface, as expected. Concentrations of TiO2 andMgO are relatively low, and their profiles are scattered. FeO and CaOdis-play uphill-diffusion profiles towards the interface, whereas Na2O andK2O show weak uphill diffusion away from the interface. Because CaOand FeO concentrations in the cassiterite crystals are much lower thanthose in the initial melt, when cassiterite dissolved in the melt, FeOand CaO “should” decrease towards the cassiterite-melt interfaceowing to dilution by cassiterite dissolution. However, at the interfacemelt, their concentrations are high, and there is a minimum in themid-dle of the profile, indicating that these components diffuse uphill to-wards the less polymerized melt at the interface. Conversely, there is amaximum in themiddle of the Na2O and K2O concentration profiles, in-dicating uphill diffusion towards the more polymerized melt. Both ofthese phenomena have been observed in other systems (e.g., Watson,1982; Zhang et al., 1989; Chen and Zhang, 2008, 2009). Quantifying up-hill diffusion profiles requires either an approximatemethod such as themodified effective binary diffusion model (Zhang, 1993), or the fulltreatment of multicomponent diffusion by using the diffusivity matrix.In natural systems, however, cassiterite dissolution and growth are ex-pected to occur at small degrees of under/supersaturation, i.e., when Snconcentration is still at trace element or at most minor element level.Hence, Sn concentration variation in the melt would not cause notice-able concentration gradients in the major oxides, and the multicompo-nent diffusion effects are expected to be negligible. Here, we will onlyfocus on quantifying Sn diffusion and the cassiterite dissolutionprocesses.

3.3. Interface melt and far-field melt compositions

The interface melt compositions, listed in Table 3, were obtained byextrapolatingmeasured concentration profiles usingfitting (Section 5.3).The SnOt concentration in the interface melt increases with temperaturefor the same starting glass (CassDis13 does not follow the trend becausea Pt capsule rather than graphite capsulewas used), as expected. The far-fieldmelt compositions are averages of themany pointsmeasured at thefar-field, and are listed in the Supplementary file. Because the diffusiondistance is short compared to the length of the starting glass, the far-field composition is the initial composition, and its variation indicatesday-to-day errors in electronmicroprobe calibration and small heteroge-neity in the starting glass.

The SiO2 concentration of the melt at the interface is negatively cor-related with the SnOt concentration at the interface (Fig. 6), and can beroughly estimated from the dilution by cassiterite dissolution, i.e., as theinitial SiO2 concentration multiplied by (1–SnOt/100). The interfacemelt compositions for Al2O3 show the same character as SiO2. ForNa2O and K2O, due to uphill diffusion towards the farfield, their inter-face concentrations are lower than those estimated from the dilution ef-fect. For FeO and CaO, due to uphill diffusion towards the interface, theirinterface concentrations are even higher than the far-field concentra-tion. For TiO2 and MgO, their concentrations are low and diffusion pro-files cannot be well resolved.

3.4. H2O concentrations

To examine whether there was significant water loss in the meltduring the experiments, water concentration profiles in the hydrous

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

CassDis 9_1023 K_634 s_H6a

fitting curve Iprofile1profile2profile3profile4fitting curve II

SnO

t(w

t%)

-0.4

0

0.4

0.8

1.2

1.6

2

0 50 100 150 200 250

CassDis 12_1123K_1519 s_H6a


SnO

t(w

t%)

0

0.4

0.8

1.2

1.6

0 20 40 60 80 100



-1

0

1

2

3

4

5

6

0 10 20 30 40 50 60

CassDis 10_1173 K_18026 s_KS


SnO

t(wt%

)

-1

0

1

2

3

4

5

6

0 20 40 60 80 100 120 140


fitting curve Iprofile1profile2profile3profile4profile5fitting curve II

-2

0

2

4

6

8

10

12

0 20 40 60 80 100 120

CassDis 3_1273 K_18092 s_KS

fitting curve Iprofile1profile2profile3fitting curve II

0

4

8

12

16

0 10 20 30 40 50 60 70

CassDis 1_1373 K_1856 s_KS

fitting curve Iprofile1profile2profile3profile4profile5fitting curve II

SnO

t(w

t%)

0

4

8

12

16

0 10 20 30 40 50 60 70

CassDis 11_1273 K_18000 s_CIT


x (µm) x (µm)

Fig. 3. SnOt concentration profiles in H6a, KS and CIT. Fitting curve I (red dashed curve) assumes DSnOt is constant, and fitting curve II (blue solid curve) assumes DSnOt decreasesexponentially with SiO2 concentration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


samples conducted at relatively high temperatures and for relativelylong durations were measured using FTIR. If water loss is negligible inthese experiments, it should also be negligible in other experiments.Fig. 7 shows examples of infrared spectra of KS and H6a.

For every samplewithH2Omeasurements after the experiment, twoH2O profiles were measured. One profile was measured perpendicular

to the cassiterite-melt interface and right in the middle of the samplecharge, referred to as the perpendicular profile, and the other wasmea-sured parallel to and near the interface, referred to as parallel profile(Fig. 1). Themeasured H2O profiles (Fig. 8) are aimed at evaluating pos-sible H2O loss within the short SnOt concentration profiles near the cen-ter of the experimental charge. From Fig. 8, for the experimental charge

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8

CassDis6_1123 K_299 s_H6aCassDis12_1123 K_1519 s_H6a

SnO

t(wt%

)

x/t1/2 ( 1/2)

µm

µm

Fig. 4. SnOt concentration profiles of time-series experiments at 1123 K in H6a. Thehorizontal axis is distance divided by the square root of time.


CassDis3 using KS (0.9wt% initial H2O) as the starting glass at 1273K for3 h, the perpendicular profile shows that there is no water loss within600 μm of the interface, but further away from the interface, there isminor water loss. The parallel profile shows also that there is no waterloss in the middle area of the sample, but there is some water lossnear the graphite capsule. For the run CassDis1 in KS, since the durationis only about 30 mins, both the perpendicular and parallel profiles indi-cate no significant water loss. For the run CassDis8 using H6a (5.9 wt%initial H2O) as the starting glass, there is minor water loss near thegraphite capsule, but no detectable water loss in themiddle of the sam-ple where tin diffusion wasmeasured. These results are consistent withcalculated H2O diffusion distance using Ni and Zhang (2008).

Based on the measured water concentrations of the experimentalcharge, we conclude that there is no significant water loss within theSnOt concentration profiles near the center of the experimental charge,meaning that tin diffusion occurred at constant water concentrations.

4. Disscussion and applications

4.1. Fitting procedures of SnOt concentration profiles and results

Tin diffusion in our experiments was modeled as one-dimensionaldiffusion into a semi-infinite melt reservoir (Crank, 1975, p. 298–308;Zhang et al., 1989; Zhang, 2008). The interface melt composition doesnot changewith time in our time-series experiments, indicating that in-terface reaction rate is rapid compared to diffusion. For this diffusionproblem, adopting the effective binary diffusion treatment, the one-dimensional diffusion in the melt in the interface-fixed referenceframe can be written as (Zhang et al., 1989):

∂C∂t

¼ ∂∂x

D∂C∂x

� �−V

∂C∂x

ð1Þ

where V ¼ A=ffiffit

p, and hence L ¼ 2A

ffiffit

p

with initial condition: C|t=0 = C∞ at x N 0,boundary condition 1: C|x=∞ = C∞ at t N 0,

and boundary condition 2: D∂C∂x jx=0 = V (C|x=0−Cc) at t N 0,

where t is time, x is the distance in themelt from the cassiterite-melt in-terface, D is the effective binary diffusivity, C is the concentration(e.g., wt.%) of a given component (density variation along the diffusionprofile in themelt is ignored), C∞ is the concentration in the initial melt,Cc is the concentration in the crystal, V is themelt growth rate (differingfrom the mineral dissolution rate by a constant factor of the density ra-tio ≈ 6.99/2.33 = 3) and L is the melt growth distance.

The analytical solution in the case of a constant D and rapid interfacereaction rate is as follows (Zhang et al., 1989)

C x; tð Þ ¼ C∞ þ C0−C∞ð Þerfc x=ffiffiffiffiffiffiffiffi4Dt

p−α

� �=erfc −αð Þ; ð2Þ

where C0= C|x=0 (assumed to achieve a near-saturation concentrationrapidly), and the parameter α (¼ A=

ffiffiffiffiD

p) satisfies:

ffiffiffiπ

pαeα

2erfc −αð Þ ¼ C0−C∞ð Þ= Cc−C0ð Þ; ð3Þ

where Cc is the concentration of the component in the crystal. For Sn incassiterite, Cc = 100 wt% if concentration in the melt is expressed asSnO2, but 89.38 wt% if expressed as SnOt, as done here, or 78.76 wt% ifexpressed as elemental Sn.

After measuring concentration profiles, the SnOt profile was fit byusing Eq. (2) to obtain the dissolved SnOt concentration (C0) at theinterface (tin concentration at cassiterite saturation) and the effec-tive binary diffusivity (D) of SnOt. To fit a profile, we first estimatedthe approximate C0 from the plotted profile, and used Eq. (3) tosolve for α. This value was then used in Eq. (2) to fit the profile,obtaining C0, C∞, and D. A new α value was then calculated fromthe new C0 and C∞ values were calculated iteratively. After abouttwo or three iterations, the fitting parameters became stable, andwe obtained the values of SnOt concentration (C0) at the interfaceand the SnOt diffusivity (D). The fitting results are shown as dashedcurves in Fig. 3.

From Fig. 3, when the interface SnOt concentration (C0) is low(≤2.5 wt%), the fit using Eq. (2) is excellent. However, when the SnOt

concentration is high (≥10 wt%), the fit using the samemethod assum-ing D is constant does not match data well. Near the interface, the slopeof the data is not so steep as the dashed fit curve, indicating the actualeffective binary diffusivity is greater than the constant D. Further awayfrom the interface in the melt, the slope of the data is steeper than thedashed fit curve, indicating the actual effective binary diffusivity issmaller than the constant D. This is understandable because SiO2 andAl2O3 concentrations decrease significantly from the far-field melt tothe interface melt, and it has been demonstrated that divalent cationdiffusivities increase from more silicic melt to less silicic melt (Zhanget al., 2010).

Treating concentration dependent diffusion is not trivial. Onemethod is the Boltzmann analysis for the case of crystal dissolution(e.g., Zhang et al., 1989). This method requires high-quality profilesin both concentration and distance. Even though our SnOt concentra-tion data quality is high, the profiles are short, meaning that a smallerror in the distance can cause significant error. In addition, using theBoltzmann analysis can only provide diffusivities but cannot showhow well the concentration profiles are fit. An alternative methodis to prescribe a function on how D depends on C, and fit the concen-tration profiles (e.g., Zhang and Behrens, 2000; Behrens and Zhang,2001). Different functions can be tried. Limited data in the literatureindicate that diffusivity D is often an exponential function of someconcentration (i.e., lnD is linear to concentration) (Zhang, 2010).For example, lnDSiO2

in basalt-andesite-rhyolite decreases linearlywith SiO2 concentration (Watson, 1982; Lesher and Walker, 1986),lnDMg decreases linearly with SiO2 + Al2O3 (Zhang et al., 2010),and lnDAr in rhyolite melts increases linearly with H2O content(Behrens and Zhang, 2001). In this work, we test the assumptionthat lnDSnOt decreases linearly with SiO2 + Al2O3 concentration.For our data, this assumption is equivalent to the assumption thatlnDSnOt is linear to SiO2 or Al2O3 concentration (or sums of mole frac-tions of Si and Al) because SiO2 and Al2O3 are roughly proportional toeach other. Furthermore, because SiO2 + Al2O3 decreases linearly asSnOt increases, the assumption is also equivalent to the assumptionthat lnDSnOt increases linearly with SnOt concentration. The assump-tion means the SnOt diffusivity increases from highly polymerized

68

70

72

74

76

78

80

0 20 40 60 80 100 120

SiO2

profile1profile2profile3

-0.2

-0.1

0

0.1

0.2

0.3

0 20 40 60 80 100 120

TiO2


11

11.5

12

12.5

13

0 20 40 60 80 100 120

Al2O

3


0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 20 40 60 80 100 120

FeO


-0.1

-0.05

0

0.05

0.1

0.15

0 20 40 60 80 100 120

MgO


0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 20 40 60 80 100 120

CaO


3

3.5

4

4.5

5

0 20 40 60 80 100 120

Na2O


4

4.5

5

5.5

0 20 40 60 80 100 120

K2O


x (µm) x (µm)

Fig. 5. Representative electron microprobe analyses of other major elements as a function of distance away from cassiterite-melt interface in experiment CassDis3 (1273 K, 0.5GPa,18,092 s). The vertical axes are oxide wt%.


melt to less polymerized melt. Hence, the following diffusivity rela-tion is used in solving Eq. (1),

DSnOt ¼ D0 exp a0CSnOtð Þ ð4Þ

where D0 is the diffusivity at zero tin concentration (far-field melt),and the parameter a0 is a constant characterizing the dependenceof tin diffusivity on the concentration of SnOt (CSnOt). Note that D0

is the Sn diffusivity in high-silica granitic melts when Sn concentra-tion is less than a few thousand ppm. That is, D0 is Sn diffusivity for

Table 3Interface melt compositions (wt%).

Exp. No. Startingmelt

SnOt SiO2 TiO2 Al2O3 FeO MgO CaO Na2O K2O

CassDis9 H6a 0.551 69.6 0.25 12.6 1.6 0.28 1.28 3.3 4.2CassDis6 H6a 1.525 69.4 0.25 12.5 1.9 0.28 1.35 3.0 4.1CassDis12 H6a 1.612 69.7 0.25 12.5 1.9 0.28 1.40 3.3 4.0CassDis8 H6a 5.003 66.5 0.25 12.2 2.0 0.28 1.57 3.4 3.8CassDis10 KS 5.371 70.8 0.06 11.1 1.3 0.03 1.30 3.7 4.2CassDis3 KS 9.560 68.5 0.06 11.2 1.3 0.03 1.00 3.3 4.0CassDis1 KS 12.831 64.0 0.06 10.8 1.4 0.03 1.10 3.3 3.8CassDis11 CIT 12.492 65.0 0.05 10.3 1.3 0.02 1.20 3.5 3.5CassDis13 CIT 2.199 75.0 0.05 12.5 0.9 0.02 0.52 4.0 4.7

Platinum capsule is used for CassDis13, and graphite capsule is used for the other runs.

0.35

0.4

0.45

0.5

0.55

0.6

40004500500055006000

CassDis1_1373K_1856s_KS

Abs

orba

nce

Abs

orba

nce

0.4

0.6

0.8

1

1.2

1.4

1.6

40004500500055006000


Wavenumbers (cm-1)

H2Om

H2Om

OH

OH

Fig. 7.Representative infrared spectra in the experimental charge. CassDis 1 for KS sample,and CassDis8 for H6a.


most geological applications because Sn concentration is typicallyb0.01 wt% in natural high-silica granitic melts. Hence, D0 will be re-ferred to as Sn diffusivity or SnOt diffusivity. Preliminary fittingshows that this diffusivity relation fits the concentration profiles al-most perfectly, and the parameter a0 does not vary much outsidefitting error from one experiment to another. To further constrainthe model for practical applications, a0 is treated to be roughly inde-pendent of temperature and H2O content (no data are available to re-solve the dependence of a on H2O because the highest SnOt isb6.0 wt% for experiments with 5.9 wt% H2O). That is, we fixed a0 asa single constant independent of temperature and H2O content,and allowed D0 in Eq. (4) to vary from one experiment to another,to obtain a grand fit of all the SnOt concentration profiles. This resultsin the value of a0 being 0.1521 ± 0.0027 when SnOt concentration inEq. (4) is in wt%. Fig. 3 shows that the fits (solid curves) are excellent,demonstrating that Eq. (4) approximately describes the dependenceof DSn on CSnOt, in which the value of a0 is roughly constant. Becausethese fits are much better than the fits obtained by assuming con-stant diffusivity (dashed curves), especially when the interfaceSnOt concentration is high, the C0 values obtained from the fits byusing Eq. (4) were used as the SnOt concentration at cassiteritesaturation.

The meaning of the parameter a0 in Eq. (4) needs some clarification.The increase of SnOt diffusivity from the far-field melt to the interfacemelt is likely related to a decrease in the concentration of SiO2 orSiO2 + Al2O3 rather than an increase in the concentration of SnOt

along the diffusion profile because the degree of polymerization of thesilicate melt is related to SiO2 or SiO2 + Al2O3. Hence, at the more fun-damental level, Eq. (4) may be written in terms of the concentrationsof SiO2 or SiO2 + Al2O3 as follows:

DSnOt ¼ D01 exp a1 76–CSiO2

� � ð4aÞ

62

64

66

68

70

72

74

76

78

0 2 4 6 8 10 12 14

S iO

2(w

t%)

SnOt (wt%)

Fig. 6. The relationship of SiO2 concentration and SnOt concentration at the interface inexperiment CassDis1 (1373 K, 0.5GPa, 1856 s).

DSnOt ¼ D02 exp a2 89–CSiO2þAl2O3

� � ð4bÞ

where CSiO2and CSiO2 + Al2O3

are in wt% (one could also use mole frac-tions) on an anhydrous basis. Fig. 9 plots the dependence of the calculat-ed DSnOt along concentration profiles of measured SiO2 concentration.Based on the plots, a1 ≈ 0.17 wt%−1. Similarly, it can be found thata2 ≈ 0.15 wt%−1.

4.2. Tin species in the experimental charge

Tin has two common oxidation states: +2 and+4. Oxygen fugacityin our piston-cylinder experiments is not buffered. A graphite capsulewas used in all experiments except for one, and the oxygen fugacity isexpected to be below NNO (e.g., Holloway et al., 1992). The interfaceSnOt concentration in CassDis6 and CassDis12 (both are at 1123 K and0.5 GPa with 5.9 wt% H2O and Al/(Na + K) = 1.2) is 1.568 wt%, equiv-alent to 17,500 ppm SnO2, or logSnO2 = 4.24. Using Fig. 3 in Linnenet al. (1996) for logSnO2 as a function of logfO2

at 1123 K and 0.2 GPawith ~6.0 wt% H2O, the corresponding logfO2

is about FMQ, which likelyapplies to all experiments using H6a as the starting glass in graphitecapsule (CassDis6, CassDis8, CassDis9, and CassDis12). Linnen et al.(1995) also showed that the solubility of tin in Sn4+ state at 1123 K isonly about 600 ppm SnO2, which is achieved under oxidizing conditions(FMQ+ 2.3). That is, the oxidation state of tin dissolved in the melt forexperiments CassDis6 and CassDis12 is mostly (96.6%) in Sn2+ state,and only 3.4% of the dissolved tin is in Sn4+ state. Because the graphitecapsule does not provide a perfect fO2

buffer, it is not possible to arguethat all experimentswere at logfO2

of FMQ. Nonetheless, the experimen-tal conditions are fairly reducing, andmost dissolved tin is in the formofSn2+. Hence, the concentrations of tin are denoted by SnOt and the Sndiffusivities we report are Sn2+ diffusivities.

One experiment (CassDis13) was conducted in a Pt capsule. Fig. 10shows SnOt concentration profiles in this experiment. Both CassDis11

x (µm) x (µm)

0

0.5

1

1.5

0 500 1000 1500 2000 2500

CassDis1_parallel profile

0

0.5

1

1.5

0 400 800 1200 1600

CassDis1_perpendicular profile

0

0.5

1

1.5

0 200 400 600 800 1000 1200

CassDis3_perpencidular profile

0

0.5

1

1.5

0 400 800 1200 1600 2000 2400


0

2

4

6

8

10

0 100 200 300 400 500 600 700 800


H2O

t (w

t%)

H2O

t (w

t%)

H2O

t (w

t%)

0

2

4

6

8

10

0 500 1000 1500 2000 2500


Fig. 8.Water concentration profiles of experimental charges at 1223 K, 1273 K, 1373 K. Perpendicular line means a traverse measured near the axis of the glass cylinder perpendicular tothe cassiterite-glass interface. Parallel line means a traverse in the glass parallel to and near the interface.

Fig. 9. Calculated Sn diffusivity along diffusion profiles using fitting results versusmeasured SiO2 concentration.

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

CassDis13_1373K_3633s_CIT_Pt capsule

SnOtprofile1profile2profile3profile5profile4profile6profile7

SnO

t (wt%

)

x (µm)

Fig. 10. SnOt concentration profile of CassDis 13 using Pt capsule. Fitting curve (red curve)is fitted assuming DSnOt is constant. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)



and CassDis13 contained the same dry rhyolitic melt (CIT containingabout 0.1 wt% H2O). The run temperature for CassDis11 was 1273 Kand that for CassDis13 was 1373 K. If the oxygen fugacity were thesame, the SnOt concentration at cassiterite saturation (TCCS) of themelt should be higher for CassDis13 than for CassDis11 because TCCS in-creases with temperature. Using the temperature dependence of TCCSfor the KS sample in a graphite capsule, the expected interface SnOt con-centration for CassDis13 would be 18.7 wt%, but it is only 2.2 wt% inCassDis13, which is about 12% of the estimated solubility undergraphite-capsule conditions. The low interface SnOt concentration inCassDis13 is attributed to themore oxidizing condition in the Pt capsulethan in the graphite capsule. On the other hand, even this 12% is stillhigh compared to only 3.4% of all Sn being Sn4+ in graphite capsule.That is, even in the Pt capsule, the concentration of Sn2+ in the melt isstill most likely much higher than that of Sn4+. This inference is consis-tent with the fact that Sn diffusivity in CassDis13 is not lower than thatpredicted from other Sn diffusivity data obtained from experiments ingraphite capsules.

4.3. Dependence of D0 on temperature and H2O content

The fitting results of SnOt diffusivity (D0) obtained from differentruns and its associated error are given in Table 2, and also shown inFig. 11 as solid circles, diamonds and triangles, as a function of temper-ature and H2O contents. The data demonstrate a strong increase of D0

with H2O concentration in themelt. TheD0 data for KS samples contain-ing about 0.9 wt% H2O (3 points) follow the Arrhenius relation well andare fit as:

lnD0 ¼ −18:445−17625

T; ð5Þ

where D0 is in m2/s and T is in K. Eq. (5) reproduces the lnD0 values towithin about 0.22 natural logarithm units.

TheD0 data for H6a containing about 5.9wt%H2O (4 points) also fol-low the Arrhenius relation well and can be fit by:

lnD0 ¼ −18:302−11119

T; ð6Þ

Eq. (6) reproduces the lnD values to within 0.19 natural logarithmunits.

-34

-32

-30

-28

-26

-24

0.6 0.7 0.8 0.9 1 1.1

H6aKSCITCassDis13 in Pt capsuleLinnen1996Behrens2009Dry trachyteBehrens2009Wet trachyteBehrens2009Dry phonoliteBehrens2009Wet phonolite

lnD

o (D

o in

m2 /s

)

1000/T (T in K)

Fig. 11. Cassiterite diffusivity as a function of temperature and comparison with previousstudies. Data from this work are shown as solid symbols. One experiment was conductedin platinum capsule (blue solid square on CIT) and the rest were in graphite capsule. Thedata from Linnen et al. (1996) are for wet rhyolite containing 5–7 wt% H2O. The wettrachyte and wet phonolite of Behrens and Hahn (2009) contain respectively 1.13 wt%and 1.68 wt% H2O. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

All the D0 data in the graphite-capsule experiments (i.e., underreducing conditions) can be fit as follows:

lnD0 ¼ −18:194− 19418−1389wð Þ=T; ð7Þ

wherew is H2O concentration in wt%. Eq. (7) reproduces experimen-tal lnD0 to within 0.464. The activation energy for SnOt diffusion is161 kJ/mol in dry rhyolite, decreasing to 93 kJ/mol at 5.9 wt% H2O.The effect of water content on Sn diffusivity is very strong. UsingEq. (7), Sn diffusivity at 1123 K (a typical granitic magma tempera-ture) increases by 3.2 orders of magnitude when water content in-creases from 0 to 6 wt%. At 973 K, the effect of H2O on Sndiffusivity is even stronger. Both the strong increase of SnOt diffusiv-ity with increasing H2O and the significant decrease of the activationenergy are consistent with results of previous studies on trace ele-ment diffusion in granitic melts (Watson, 1979; Mungall et al.,1999; Zhang et al., 2010). The strong effect of H2O on diffusivity ingranitic melts has often been explained by the effect of H2O to depo-lymerize highly polymerized granitic melts (Watson, 1979; Stolper,1982; Mungall, 2002; Zhang et al., 2010).

Fig. 11 also compares published Sn diffusivity data in a hydrous rhy-olitic melt (Linnen et al., 1996), and those in trachyte and phonolitemelts (Behrens and Hahn, 2009), with our data. There are numerousSn diffusion data in Linnen et al. (1995, 1996) at 1123 K and 5–7 wt%H2O, and the data demonstrate that Sn diffusivity is roughly constantat logfO2

≤ FMQ+ 0.6, and then decreases by about one order of magni-tude as logfO2

increases to ≥ FMQ+ 2.0. The data indicate that Sn4+ dif-fusivity is about an order of magnitude lower than Sn2+ diffusivity. InFig. 11, we only included their data at reduced conditions(logfO2

≤ FMQ+0.6) and formeltswith Al/(Na+K)=1.00 to 1.13, sim-ilar to those in our runs. It can be seen that Sn diffusivity data reported inLinnen et al. (1996) are similar to those in our study, but are morescattered. The scatter is attributed to their experimental design, inwhich a single cassiterite crystal was placed in the center of the glassfragments, resulting in sinking of the crystal (forced convection) duringthe experiment as well as a slanted cassiterite-melt interface prone toconvection (Zhang et al., 1989, 2010). (Note that convection does not af-fect their Sn solubility data.) The diffusivity results of Behrens and Hahn(2009) are different from ours because their trachyte and phonolite aredifferent in compositions fromour rhyolite. Tin diffusivity in dry phono-lite and dry trachyte is higher than that in dry rhyolite (CIT) and almostthe same as that in rhyolite containing 0.9 wt% H2O (KS).

Fig. 12 compares Sn2+ effective binary diffusivity with diffusivity ofother components in dry rhyolitic melts that contain about 74–77 wt%SiO2. It can be seen that Sn2+ diffusivity is similar to Cs+, Nd3+ andGa3+ diffusivities, and smaller than diffusivity of other alkalies, Ca2+,Sr2+, Ba2+, and CO2, and larger than that of Ce3+, Zr4+ and P5+. It issomewhat surprising that Sn2+ diffusivity is smaller than that of theother divalent ions, but Sn2+ diffusivity in this study (and in nature dur-ing cassiterite dissolution and growth) is largely coupled with Si diffu-sion in the opposite direction, which might account for the small valueof Sn2+ diffusivity.

4.4. Diffusivity of SiO2 and Al2O3

As discussed earlier, FeOT, CaO, Na2O and K2O diffusion profiles oftenare not monotonic and cannot be treated using the effective binary ap-proach. The concentrations of TiO2, MgO andMnO are low and the pro-files are scattered. The concentration profiles of SiO2 and Al2O3 aretypically monotonic and effective binary diffusivities can be obtained.Because SiO2 and Al2O3 concentration gradients are largely due to thedilution of SnOt, when ΔSnOt (SnOt in the interface melt minus that inthe farfield melt) is less than a few wt%, SiO2 and Al2O3 concentrationprofiles are not well resolved. Since ourmain goalwas to study Sn diffu-sion, no extra effort wasmade to improve the SiO2 (and Al2O3) concen-tration profile quality.

10-15

10-14

10-13

10-12

10-11

50 55 60 65 70 75 80

DSi

(m2 /

s)

SiO2 (wt%)

12

3

4

56

7

8

9

10

Fig. 13. SiO2 diffusivity as a function of SiO2 concentration. Data from this study are shownin solid lines 1–5: 1. SiO2 diffusivity in “dry” melts (CIT) at 1273 K (CassDis11). 2. SiO2

diffusivity in melts containing 0.9 wt% H2O (KS) at 1173 K (CassDis10). 3. SiO2

diffusivity in melts containing 0.9 wt% H2O (KS) at 1273 K (CassDis3). 4. SiO2 diffusivityin melts containing 0.9 wt% H2O (KS) at 1373 K (CassDis1). 5. SiO2 diffusivity in meltscontaining 5.9 wt% H2O (KS) at 1223 K (CassDis8). Literature data are as follows: 6. SiO2

diffusivity in “dry” melts at 1573 K (Watson, 1982; Lesher and Walker, 1986). 7. SiO2

diffusivity in “dry” melts at ~1750 K (Lesher and Walker, 1986). 8. SiO2 diffusivity inmelts containing 0.77 wt% H2O at ~1573 K (Koyaguchi, 1989). 9. SiO2 diffusivity in meltscontaining 0.77 wt% H2O at ~1773 K (Koyaguchi, 1989). 10. SiO2 diffusivity in meltscontaining 4.77 wt% H2O at ~1573 K (Koyaguchi, 1989). The black lines 1, 6, and 7 (seethe online version for colour) are for “dry” melts at 1273, 1573 and 1750 K. The redlines 2, 3, 4, 8, and 9 are for melts containing 0.8–0.9 wt% H2O at 1173, 1273, 1373, 1573and 1773 K. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

-4

-3

-2

-1

0

1

2

3

4

0.7 0.8 0.9 1 1.1

H6aKSCITCassDis13 in Pt capsuleLinnen1996Bhalla2005

1000/T (T in K)

lnC

o (C

o in

wt%

)

Fig. 14. SnOt concentration (in wt%) at cassiterite saturation as a function of temperaturefor different samples in this work, and from literature studies. Data from this work areshown as solid symbols. One experiment was conducted in platinum capsule (blue solidsquare on CIT) and the rest were in graphite capsule. The data from Linnen et al. (1996)and Bhalla et al. (2005) are those with the similar fO2

and A.S.I with this work. (Forinterpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)

Fig. 12. Comparison of Sn2+ diffusivity (large solid red squares) in dry high-silica rhyolitemelt with diffusivity of univalent (black symbols), divalent (red symbols), trivalent (bluesymbols), tetravalent and pentavelent (navy blue symbols), and neutral molecular CO2.Adapted from Fig. 73 of Zhang et al. (2010). For data sources, see Zhang et al. (2010).(For interpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)


For SiO2, when ΔSnOt is larger than 9wt% (3 experiments), the con-centration variation of SiO2 across the profile is large such that the SiO2

concentration profile is well resolved. Examination of the SiO2 profilesindicates that SiO2 diffusivity decreases with increasing SiO2 + Al2O3

concentration, similar to the dependence of SnOt diffusivity onSiO2 + Al2O3 (Eq. (4b)). Two more experiments have ΔSnOt of about5 wt%, in which the dependence of SiO2 diffusivity on the concentrationof SiO2 is not well constrained but nonetheless estimated. Using a simi-lar relation as Eq. (4) to fit the SiO2 concentration profile results in goodfits of the measured data. The results DSiO2

as a function of SiO2 concen-tration are shown in Fig. 13 along with some literature data. Most datain the figure indicate that logDSiO2

decreases with increasing SiO2, orDSiO2

depends on SiO2 concentration as follows:

DSiO2¼ D0 exp −aCSiO2

� �: ð8aÞ

where a is a fitting parameter, D0 is hypothetical DSiO2at zero SiO2 con-

centration, CSiO2is in wt%. Although Eq. (8a) casts DSiO2

as a function ofthe SiO2 concentration, it is possible that more fundamentally DSiO2

de-pends on SiO2+Al2O3 concentration (that is, the degree of polymeriza-tion) although we cannot resolve the difference based on the limitedavailable data. Examination of Fig. 13 shows that the slopes of thelines are almost the same, meaning that the value of a is roughly con-stant for different experiments. We therefore fit all five concentrationprofiles (CassDis1, CassDis3, CassDis8, CassDis10, and CassDis11) by as-suming a common a. In order not to extrapolateDSiO2

to the hypotheticalzero SiO2 concentration, we express the fit results as follows:

DSiO2¼ D70 exp –a CSiO2

–70� �

: ð8bÞ

whereD70 isDSiO2at 70wt% SiO2, which iswithin the data coverage. The

parameter a is constrained to be 0.130 ± 0.010 wt%−1, and D70 valuesdepend on temperature and water concentration and are given inTable 2. Hence, DSnOt

increases more rapidly than DSiO2as SiO2 concen-

tration decreases. At the interface melt (where diffusivity is bestconstrained), Si diffusivity is about 0.4 to 1.0 times Sn diffusivity.

For Al2O3, the total Al2O3 concentration variation from the farfield tothe interface melt is small and the concentration profile is scattered.Hence, the dependence of Al2O3 diffusivity on SiO2 concentration isnot constrained. For 5 experiments, the total Al2O3 concentration

variation is large enough (0.7 wt% to 2.1 wt%), and the profiles werefit to obtain constant DAl2O3

, reported in Table 2. Aluminum diffuses atabout the same rate as Si in our experiments.

4.5. Dependence of solubility C0 on temperature and H2O content

Because the interface SnOt concentration does not depend on the ex-perimental duration (comparison of CassDis6 and CassDis12), the fittedresults of the SnOt interface concentration is interpreted to be the cassit-erite solubility, ormore strictly, the SnOt concentration at cassiterite sat-uration (TCCS), as defined earlier. Fig. 14 shows the variation of thesolubilitywith temperature for different samples in this study, and com-pares these data with the data of Linnen et al. (1996) and Bhalla et al.(2005).


In Fig. 14, for both experimental runs containing 0.9 and 5.9 wt%H2O, cassiterite solubility increases with increasing T, and lnC0 showsa good linear relationship on 1/T.

Experimental C0 data on sample KS (0.9 wt% H2O) can be fit as:

lnC0 ¼ 7:73−7060T

; R2 ¼ 0:981; ð9Þ

where T is temperature in K and C0 is SnOt concentration in wt% at cas-siterite saturation. The above equation reproduces all the experimentallnC0 within 0.07. The data for sample H6a (5.9 wt% H2O) are fit as:

lnC0 ¼ 12:74−13720

T; R2 ¼ 0:990; ð10Þ

The above equation reproduces all the experimentally determinedlnC0 data within 0.10 units. Due to the strong dependence of Sn concen-tration at cassiterite dissolution on fO2

, which was not controlled in ourexperiments, no grand fitting of all data is attempted.

The value of TCCS depends strongly on temperature; with decreas-ing temperature, there is a huge drop of cassiterite solubility. Accordingto our results, for H6a melts with 5.9 wt% water, from 1273 K to 873 K,cassiterite solubility decreases from 7.14 wt% to 0.05 wt%; for KS meltswith 0.9 wt% water content, with the same temperature decrease, cas-siterite solubility decrease from 9.56 wt% to 0.70 wt%.

Linnen et al. (1996) reported that TCCS ranges from 3.7 wt.% atFMQ–0.57 to approximately 0.05 wt.% at FMQ +3.12 in a syntheticgranitic melt with A.S·I. ≈ 1.2 and 5–6 wt.% H2O at 1123 K and2 kbar. Our results indicate that cassiterite solubility in H6a (A.S.I.≈ 1.2) at 1123 K is about 1.69 wt%, corresponding to a logfO2

ofabout FMQ for the experiments that used H6a as starting materials.

Our cassiterite solubility data taken at face value suggest that at tem-peratures below 1320 K, the value of TCCS decreases as H2O concentra-tion in the melt increases. However, because (i) fO2

may increase withH2O content in the melt, and (ii) fO2

has a large effect on cassiterite sol-ubility, we are not confident to resolve the effect of H2O on cassiteritesolubility.

4.6. The mechanism of Sn reduction

Tin in cassiterite is in the form of Sn4+. In themelt, as argued earlier,Sn is mostly in the form of Sn2+, rather than Sn4+. Furthermore, theconcentration of SnOt can be up to 12 wt.%. Previous authors have dem-onstrated that in the binary Sn-O2 system, Sn4+ or Sn0 is more commonin the solid phases (e.g. Paparoni et al., 2010a, 2010b), but in the melt,Sn2+ is prevalent (Linnen et al., 1995, 1996). That is, upon cassiteritedissolution, much of SnO2 is reduced to SnO. The dissolution reactionmay be viewed as proceeding in two steps, one is dissolution and thesecond is reduction.

1: Dissolution : SnO2 cassiteriteð Þ ¼ SnO2 meltð Þ: ð11Þ

The equilibrium constant is denoted as K0 = [SnO2,melt], wherebrackets mean activity. That is, at equilibrium, the activity of SnO2 inthe melt is fixed. When the major oxide composition does not changemuch, it means that the concentration of SnO2 in the interface melt isfixed, which is the cassiterite solubility in highly oxidized melts. Basedon Linnen et al. (1995, 1996), K0 is of the order of about 500 ppm SnO2

in a hydrous granitic melt with Al/(Na + K) = 1.02 at 1123 K. Thevalue of K0 is expected to increase strongly with increasing temperature.

2: Reduction of SnO2 meltð Þ to SnO meltð Þ : SnO2 meltð Þ ¼ SnO meltð Þ þ § O2:

ð12Þ

The equilibrium constant is denoted as K1 ¼ ½SnOmelt� f O2

1=2=½SnO2;melt�.

The total solubility of Sn in mol/kg can be expressed as: K0 þ K0 K1=

f O2

1=2, as shown by Linnen et al. (1995, 1996). Because SnO2 concentra-tion in themelt is low, one could alsowrite the net reaction by combiningreactions (11) and (12):

SnO2 cassiteriteð Þ ¼ SnO meltð Þ þ § O2: ð13Þ

More difficult to constrain is the reducing agent to reduceSnO2(melt) or SnO2(cassiterite) to SnO(melt) during our cassiterite dis-solution experiments. One plausible reducing agent is FeO in the meltaccording the following reaction:

SnO2 meltð Þ þ 2FeO meltð Þ ¼ SnO meltð Þ þ Fe2O3 meltð Þ: ð14Þ

This reaction is likely always in operation. Because FeOt in our rhyo-litic melt is low, only about 1 wt%, and twomoles of FeO (143.69 g) canreduce only onemole of SnOt (134.69 g) from SnO2 to SnO, and becauseSn2+ diffusivity is expected to be not too different from Fe2+ diffusivity,reduction of SnO2 by FeOwould only be able to produce about the samewt% of SnO (or maybe a few times as much SnO) as FeO. In the experi-ment that was performed in the platinum capsule (CassDis13), the in-terface SnOt concentration (2.2 wt%) may be roughly accounted for byreaction (14).

For experiments performed in graphite capsules, C in the capsule isalso a reducing agent andmust play a major role because the SnOt con-centration in the interfacemelt when graphite is used as the capsule canreach N10 wt% at high temperatures, and is much higher than SnOt inthe interface melt when platinum is used as the capsule. The net reac-tion can be written as follows:

2SnO2 meltð Þ þ C graphiteð Þ ¼ 2SnO meltð Þ þ CO2 meltð Þ: ð15Þ

The question is how C in the graphite capsule affects the interfacemelt. The graphite capsule can reduce Fe2O3 to FeO in the melt nextto the capsule, and the resulting FeO can diffuse to the interfaceand reduce SnO2. The distance from the graphite capsule wall tothe center of the interface from different directions is about 1 mm.Because diffusion distance of SnOt is b0.1 mm, FeO diffusion distanceis expected to be ≤0.1 mm, meaning that diffusion of FeO from thegraphite-melt interface is not expected to be rapid enough to reachthe melt at the cassiterite-melt interface. Diffusivity of CO2 (Zhanget al., 2007) is about two orders of magnitude higher than that ofSnOt (Fig. 12), almost enough to reach the interface center(Fig. 15). However, CO2 is not a reducing agent. One possibility isthat a significant amount of CO (though lower concentration thanCO2) is also produced as the graphite capsule reacts with the melt.Because CO is a smaller neutral molecule compared to CO2, CO diffu-sivity is likely high enough to reach the interface center rapidly to re-duce SnO2. It is also possible there H2 is produced in the melt next tothe graphite capsule by the reaction C(graphite) + H2O(melt) =H2(melt) + CO(melt), and H2 diffusion can reach the cassiterite-melt interface. These explanations are possible, even reasonable,but there is no direct evidence to support them because CO and H2

have not been measured. Another possibility is that there may bean unknown rapid path of diffusion, e.g., along the melt-cassiteriteinterface and melt-graphite interface. Because the interface Sn con-centration is reproducible and correlates well with temperature foreach sample (Fig. 14), random mistakes such as contamination ofgraphite powder at the interface cannot explain the reduction.

4.7. Applications to natural systems

The majority of the world's Sn is sourced from ore deposits directlyrelated to high-silica granitic (often S-type but also reduced I-type)

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000 1200


0

10

20

30

40

50

60

0 500 1000 1500 2000 2500


CO

2(ppm

)C

O2(p

pm)

x (µm)

Fig. 15. Measured CO2 concentration profiles of experimental charge CassDis3.Perpendicular profile means a traverse measured near the axis of the glassperpendicular to the cassiterite-glass interface. Parallel profile means a traverse in theglass parallel to and near the interface.


magmatic systems (Lehmann, 1990; Chappell andWhite, 2001), whereSn is present as cassiterite in pegmatites, skarns and veins (Newberryand Swanson, 1986; Lehmann, 1990; Linnen et al., 1995, 1996). Thesehigh-silica granites often have been pre-enriched in Sn (e.g., 72 ppmSn, Table 4 in Lehmann, 1990; which is 550 times that in the primitivemantle, McDonough and Sun, 1995), with similar or even more enrich-ments of other elements such asRb (e.g., 979 ppmRb, 1600 times that inthe primitive mantle; same references), F, Cl, B, Be, Li, Cs and Mo(Lehmann, 1990). The pre-enrichment is thought to be due to low-degrees of partial melting of continental crust during incipient rifting(Lehmann, 1990) and high degree of crystal fractionation under re-duced conditions (Meinert, 1993).

Cassiterite solubility in silicate melts is strongly dependent on fO2,

and oxidation state has been invoked as amaster variable for the forma-tion of Sn deposits (Linnen et al., 1995). The data presented in the cur-rent study complement existing data, which demonstrate thatcassiterite solubility in reduced silicate melts (fO2

b NNO) increases sig-nificantly relative to oxidized melts (fO2

N NNO). Starting from a tin-enriched granitic magma (containing, e.g., 30 ppm Sn), assuming crys-tallization under reducing conditions, meaning that tin is essentiallycompletely incompatible (Meinert, 1993), the concentration of Sn ingranitic melt would increase by factors of 2, 4, 10 and 20 after 50, 75,90 and 95% melt crystallization. This could lead to magmatic cassiteriteformation if the magma then becomes oxidized.

However, in the case of magmatic-hydrothermal Sn deposits,i.e., skarns and veins, oxidation state cannot be the only variable thatcontrols the formation of cassiterite ores. For these deposit types,where cassiterite precipitates from a magmatic-hydrothermal aqueousfluid that transports Sn as stannous chloride (Eugster and Wilson,1985; Duc-Tin et al., 2007), the ultimate enrichment of Sn is controlledby themass transfer of Sn from the silicatemelt to an exsolved ore fluid.This inherently is related to the timing of volatile saturation, and the

salinity of the ore fluid, considering that the concentration of Sn inhigh-temperature aqueous fluid increases strongly with the concentra-tion of Cl (Duc-Tin et al., 2007). If we assume that volatile saturation inthe sourcemagmas for Sn-skarn and vein deposits is caused by fraction-al crystallization, tin as well as other incompatible elements would besimultaneously enriched. The timing of volatile saturation is dictatedby the initial water concentration of the melt. That is, Sn enrichmentof the ore fluid is favored in magmas where the silicate melt is initially“dry”; i.e., the ratio of the water content at saturation to the initialwater content is high. This allows for the concentration of Sn in themelt to increase significantly prior to volatile saturation.

Once the magma becomes fluid-saturated and hydrothermal fluid“bubbles” form, the composition of the fluid is dictated by both thepartitioning (Duc-Tin et al., 2007) and mass transfer of elements intobrine or vapor “bubbles”. Audetat et al. (2008) observed that the chem-istry of the earliest brine is positively correlated with the kind of ores toform: the earliestfluids in barren granites aremetal poor, and those thatform specific ores are enriched in the specific elements. Wagner et al.(2009) observed three stages of fluid inclusions hosted in quartz andother minerals: The stage-I fluid inclusions are highly saline(34–62 wt% NaCl equivalent) and stage-I is barren; the stage-II fluid isless saline (17–21 wt% NaCl equivalent) and ore-forming, and thestage-III fluid are even less saline (0.5–13wt%NaCl equivalent). BecauseDuc-Tin et al. (2007) showed that Sn solubility in a fluid increasesstrongly with Cl concentration in the fluid, that stage-I fluid is highly sa-line but barren may be viewed as a surprise. Wagner et al. (2009) ex-plained that tin ore formation during stage-II is due to mixing of hotmeteoric water.

Based on our results, an alternative explanation is that mass transferof Sn from themelt to the fluid played a critical role. Fluid bubble ascentmeans thatmass transfer is convective (Kerr, 1995; Zhang andXu, 2003,2008), and the mass transfer rate increases with diffusivity (Zhang,2013). The partitioning of Sn and other elements between the growingand ascending fluid bubble and themelt is hence partially controlled bydiffusivity. Because bubble growth rate is controlled by H2O diffusion, ifthe diffusivity of a given element is similar to or greater than H2O diffu-sivity, the partitioning of the element between the bubble and melt isroughly equilibrium partitioning, otherwise the element concentrationin the bubble would be below equilibrium concentration (Zhang,2015). Because Sn diffusivity is smaller by orders of magnitude com-pared to those of H2O and Na, and significantly smaller than those ofCO2, K, F, and Cl (Fig. 16) in wet granitic melt, if the stage-I fluid bubblesgrew and ascended rapidly due to high-degree of fluid oversaturation,then Na in the fluid bubble is expected to be roughly equilibriumpartitioning, but concentrations of CO2, K, F and Cl in the fluid bubbleare expected to be lower than the equilibrium partitioning concentra-tion, and Sn concentration is even lower than the equilibriumpartitioning concentration. The resulting lower concentration of Sn instage-I fluid may explain why stage I is barren as observed by Wagneret al. (2009). Then, as the degree of fluid oversaturation decreases, bub-ble growth and ascent rates slow down, the slowly diffusing elementsincluding Sn can diffuse from the melt into the bubbles, leading to theore-forming stage-II fluid. Once Sn in the melt is depleted in stage-II,the stage-III fluid would not contain much tin anymore, as observedby Wagner et al. (2009). Full numerical simulation similar to that inZhang (2015) may help explain the zonation of Sn\\W ores, but it willrequire modeling of fluid transport, evaluation of initial degree of over-saturation, assessment of the relevant partition coefficients and diffusiv-ities, assumption of nucleation rates, andmagma cooling time scale, etc.Such task is beyond the scope of this work.

In addition, our diffusion data are critical in quantifying Sn masstransfer from melt to the fluid and distinguishing the relative impor-tance of convection to diffusion. In essence, the mass transfer mode ofSn from the melt to the ore fluid is a function of the ratio of the advec-tion rate of the exsolved ore fluid relative to the rate of Sn diffusionthrough the melt. If this dimensionless ratio, referred to as the Peclet

Fig. 16. Comparison of diffusivities of different components in a high-silica rhyolitecontaining about 6.0 wt%. Total H2O (H2Ot) diffusivity is from Ni and Zhang (2008); CO2

diffusivity is from Zhang et al. (2007); Sn diffusivity is from this work. For Na, K, F andCl, no diffusivity data are available for wet rhyolite with 6 wt% H2O. For Na, wet rhyolitedata with 3.5 wt% H2O (Watson, 1981) are shown, which are even higher than bulk H2Odiffusivity. For K, dry rhyolite data (Jambon, 1982) are shown as the lower limit of theirdiffusivities, which are still high compared to Sn diffusivity. Na and K diffusivities shownmay be viewed as lower limits in high-silica rhyolite containing 6.0 wt% H2O. For F andCl, extrapolated diffusion data in wet Na-phonolite (Balcone-Boissard et al., 2009) areshown because Cl diffusion coefficients in dry rhyolite are similar to that in dry Na-phonolite.


number, is low (bb1, which is possible due to high viscosity of graniticmelt), then one can treat the ore fluid as essentially static and thepartitioning of Sn from the melt to the fluid is controlled by diffusion.If the Peclet number is high (N N 1), then tin transport from the meltto the fluid is largely controlled by convection. Our tin diffusivity datawould hence allow evaluation of Sn transport from high-silica graniticmelt to hydrothermal fluid in futuremodeling. For example, asH2O con-centration increases from 1.0 wt% to 6.0 wt% in a granitic melt, Sn con-centration would increase by at least a factor of 6, enhancing thelikelihood of tin deposit formation. On the other hand, in thiswater con-centration range, Sn diffusivity would increase by a similar factor as themelt viscosity would decrease (Hui and Zhang, 2007). Hence, the Pecletnumber does not change significantly, meaning that the relative role ofdiffusion and convection does not change significantly. Once the fluidphase is able to form capillary channels (cf. Huber et al., 2012), the Sn-rich ore fluid will percolate through the magma into the cupola andoverlying country rock. At this stage in the evolution of Sn deposits,other processes (e.g., mixing meteoric water with the ore fluid) controlprecipitation of cassiterite (Wagner et al., 2009).

5. Conclusions

Diffusive cassiterite dissolution experiments in rhyolitic melts con-taining 0.1–5.9 wt% H2O were conducted at 1023–1373 K and 0.5 GPain a piston-cylinder apparatus. At relatively high temperatures whenthe interface tin concentration is high, meaning that there is significantvariation inmajor element chemistry across the diffusion profile, the Sndiffusion profiles exhibit concentration-dependent diffusivity. We de-veloped a method to resolve the dependence of Sn diffusivity on SiO2

or SiO2 + Al2O3 concentration as an exponential function. Diffusivityof Sn (as Sn2+) has been obtained as a function of temperature, H2Ocontent and SiO2 (or SiO2 + Al2O3) concentration in the melt, andH2O plays amajor role in increasing Sn diffusivity. The activation energyof Sn diffusion decreases with increasing H2O concentration. Tin con-centration at cassiterite saturation (TCCS) increases strongly with tem-perature and decreases weakly with the increasing water content inmelts. Our Sn diffusion data together with literature data on diffusionof other elements are able to explain some of the observations on Snmineralization.

Acknowledgements

We greatly appreciate the constructive and insightful comments byE.B. Watson and Cliff Shaw. Y. Yang thanks Zhengjiu Xu for trainingand help on the piston-cylinder experiment and FTIR measurement,Gordon Moore for training and help on electron microprobe, and YiYu, Chenghuan Guo, Hejiu Hui, Jingwen Mao and Yanbo Chen for com-ments and discussion. This work is partially supported by Universityof Michigan fund, US NSF grants EAR-1019440 and EAR-1524473 toYZ, and EAR-1264560 and EAR-1250239 to ACS, National Nonprofit In-stitute Research Grants of China (No. K1206) and National Natural Sci-ence Foundation of China (No.41430314 and No.41102043). TheCameca SX100 electron microprobe at the University of Michigan waspurchased with NSF grant EAR-9911352.

Appendix A. Supplementary data and figures

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.chemgeo.2016.07.021.

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