Na-K interdiffusion in alkali feldspar melts

Geochimica et Cosmochimica Acta, Vol. 62, No. 17, pp. 2997–3007, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/98 $19.00 1 .00

Pergamon

PII S0016-7037(98)00226-9

Na-K interdiffusion in alkali feldspar melts CARMELA FREDA,1 and DON R. BAKER2 1

CNR Centro di Studio per gli Equilibri Sperimentali in Minerali e Rocce, Universita` degli Studi La Sapienza, P.le Aldo Moro, 5, I-00185 Roma, Italy 2 Earth and Planetary Sciences, McGill University, Montreal, Quebec H3A 2A7, Canada (Received September 16, 1997; accepted in revised form June 22, 1998)

Abstract—Na-K chemical interdiffusion between albite and orthoclase melts has been measured at 1.0 GPa between 800 and 1600°C and at 2.0 GPa, 1400°C, in anhydrous melts and in hydrous, 5.5 wt% H2O, melts at 1.0 GPa, 1200 and 1400°C. Anhydrous Na-K diffusivities at Xor 5 0.5 display Arrhenian behavior even through the inferred glass transition. After correction for diffusion occurring during heating Na-K interdiffusion can be described by D 5 2.39(11.7,20.98) 3 1025 exp(2145.8 6 6.8/RT) where D is the diffusion coefficient in m2s21, 145.8 is the activation energy in kJ mol21, R is the gas constant, and T is the temperature in kelvins. These diffusivities are four decades greater than estimated Si-Al diffusivities in the same melts due to the low alkali-oxygen bond valence, or cation field strength, and the abundance of appropriate charge-balanced locations for alkalis in alkali feldspar melts. Extrapolation of diffusion coefficients to 600 – 650°C for comparison with Na-K interdiffusion in alkali feldspar crystals demonstrates that melting increases diffusion by six orders of magnitude. The effect of pressure on Na-K diffusion at 1400°C is not measurable in this system and suggests that only minor dilation of the coordinating oxygen polyhedra which enclose alkalis in the melt is necessary for diffusion. A preliminary Arrhenius equation for alkali diffusion in silicic melts with 6 6 0.5 wt% H2O was calculated using results of this and previous studies D 5 4.97(10.85,20.73) 3 1026 exp(2115.8 6 1.8/RT). The effect of H2O only increases diffusivities by approximately a factor of four, distinctly different from the three orders of magnitude differences between Si-Al, Zr, and P diffusion in anhydrous and hydrous granitic melts. The differing behavior of alkalis and these other cations in hydrous silicic melts is associated with differences in the type and abundance of coordination polyhedra and the low bond valences and cation field strengths of alkalis. Copyright © 1998 Elsevier Science Ltd under different conditions of temperature, pressure, and H2O content. Because Na and K diffusivities appear to be virtually independent of melt composition over the range from basalt to rhyolite (Smith, 1974; Henderson et al., 1985), we think that our data on amorphous feldspar can be extended over a wide magmatic compositional range.

1. INTRODUCTION

Alkalis display the most rapid diffusion coefficients in silicate melts and, therefore, could be most affected during magmatic differentiation and contamination (e.g. Hofmann, 1980; Watson, 1982; Watson and Jurewicz, 1984; Johnston and Wyllie, 1988; Koyaguchi, 1989; Baker, 1990; Watson and Baker, 1991; van der Laan and Wyllie, 1993). Despite this potential, and despite the observation that Na and K are present in significant amounts in all igneous rocks, only a few studies have been dedicated to the measurement of alkali chemical diffusion (Smith, 1974; Watson and Jurewicz, 1984). Data are available on alkali tracer diffusion in synthetic glasses of different compositions (Jambon and Carron, 1976; Beherens, 1992) and in complex natural melts (Margaritz and Hofmann, 1978; Watson, 1981; Jambon, 1982; van der Laan et al., 1994). However, very few data are available on Na-K chemical interdiffusion which is the most common process in nature; often only K diffusivity is measured and an estimated value is given for Na (Smith, 1974; Watson and Jurevicz, 1984; Baker, 1992; Chekhmir and Epel’baum, 1991; Bai and Koster van Groos, 1994). Moreover, no comprehensive study exists on the effects of H2O and pressure on Na-K interdiffusion. The purpose of this investigation is to measure the Na-K interdiffusion coefficients between albite and orthoclase melts

2. EXPERIMENTAL TECHNIQUES 2.1. Glass Synthesis Glasses of albite and orthoclase composition were used in these experiments. The glasses were made from reagent-grade SiO2, Al2O3, K2CO3, or Na2CO3. Oxides and carbonates were ground together under ethanol, decarbonated and melted in air. The orthoclase composition was melted at 1600°C, four times for 1 h, once for 3 h, and then, after adding 5 % of initial weight of K2CO3, once more for 14 h. The glass was crushed after each fusion and finally ground to a grain size of less than 70 mm. The albite glass is that used in Baker (1995) which was melted 1 h at 1400°C, 1 h at 1500°C, and 6 h at 1500°C; between each fusion the glass was crushed. The glass was melted an additional 45 h at temperatures between 1490 and 1550°C followed by grinding to a fine powder. The glasses were crystal-free and homogeneous within the precision of electron microprobe analysis (Table 1). However, the albite glass is slightly peraluminous and the orthoclase glass slightly peralkaline. Both glasses were stored in a drying oven at 110°C. Glasses were hydrated before use in experiments XI and XII. Aliquots of anhydrous glasses were hydrated with 5.5 wt% H2O by melting at 1.5 GPa, 1250°C for 30 min in Pt capsules in a piston 2997

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C. Freda and D. R. Baker Table 1. Composition of starting materials

SiO2 A12O3 Na2O K2O Total

Albite glass

Orthoclase glass

69.14 (0.28)1 19.26 (0.23) 11.42 (0.23) — 99.82 Na0.97A10.99Si3.02O8

65.13 (0.49) 18.52 (0.25) — 17.76 (0.16) 101.41 K1.04A11.00Si3.00O8

1 sigma errors based upon replicate analyses of glasses by electron microprobe.

cylinder using a 1.91 cm NaCl-Pyrex-crushable alumina assembly. Water was added by microsyringe, and capsules were welded while immersed in a water bath to eliminate volatile loss during welding. Loaded capsules were stored at 110°C for a minimum of 1 h to homogenize the H2O. H2O concentrations were determined by weight loss upon ignition to 1020°C for 8 h. The H2O content of the hydrated orthoclase glass was 5.4 wt% and that of the hydrated albite glass was 5.6 wt%. These hydrated glasses were stored in air before use in experiments. 2.2. Experimental Procedures All anhydrous and hydrous experiments were performed using the diffusion couple technique. Diffusion couples were assembled by firmly packing the orthoclase composition into the lower half of a cylindrical graphite capsule (1 mm inside diameter 3 6 mm long). The top half of the capsule was filled with the albite composition and closed with a graphite lid. In order to avoid water loss, the graphite capsules with hydrated glasses were placed into platinum capsules which were welded closed in a water bath. Experiments were performed in a piston-cylinder apparatus. Experiments at 1.0 GPa utilized a 1.91 cm NaCl-glass-crushable alumina assembly (Hudon et al., 1994). At 1600 and 1492°C the glass was fused silica whereas at lower temperatures Pyrex was used. The experiment at 2.0 GPa utilized a 1.25 cm NaClPyrex-crushable alumina assembly. For all anhydrous experiments the capsules were loaded, placed into the completed assemblies, and stored overnight at 110°C before use. The samples were pressurized and heated simultaneously until a pressure of 0.2 GPa above the run pressure and a temperature of 150 –200°C below the temperature of interest was reached; then the pressure was slowly reduced to the experimental pressure and maintained to within 0.05 GPa of the desired pressure. The samples were heated at a rate of 300°C/min until 20°C below the experimental temperature and then heated at 50°C/min; typically the temperatures exceeded the desired run temperature by 4°C for the first 30 s of each experiment. Temperatures were measured with Type C thermocouples located within 1 mm of the middle of the capsule. Temperature gradients along the capsules were less than 15°C (Hudon et al., 1994). Samples were quenched at a rate of 2000°C/min by turning off the furnace power. Most experiments were performed between 1200 and 1600°C at 1.0 GPa. These temperatures are above the melting temperature of albite at 1.0 GPa (Boettcher et al., 1982) and below the leucite liquidus for orthoclase composition at this pressure, 1500°C (Lindsley, 1966). Because the 1 atm glass transition temperature for orthoclase is 948°C (Richet and Bottinga, 1995), most experiments in this study measured diffusion between an equilibrium (albite) and a supercooled (orthoclase) melt. This is also the situation for the 2.0 GPa, 1400°C experiment. The 1 atm glass transition temperature for albite is 827°C (Richet and Bottinga, 1995). Therefore, it is probable that both orthoclase and albite compositions were glasses during the experiment at 1.0 GPa, 800°C. The quenched samples were mounted in epoxy, sectioned longitudinally, and polished for electron microprobe analysis. As shown in Fig. 1, we were able to avoid deformation in the graphite capsules, and we maintained the reservoir geometry during the diffusion experiments. Chemical analyses were made with a JEOL 8900 Superprobe with five

Fig. 1. Pictures showing a typical capsule after an experiment. (a) experiment XI A, P 5 1.0 GPa, T 5 1400°C (Tavg 5 1309), 5.5 wt% H2O added; (b) experiment IX A, P 5 1.GPa, T 5 1200°C (Tavg 5 1173). The geometry of the capsules is very well preserved for both hydrous experiments (graphite capsule welded in Pt capsule) and anhydrous experiments (only graphite capsule used).

wavelength dispersive spectrometers using 15 kV accelerating voltage, 5 nA beam current, 10 mm beam diameter, with 20 s counting time on the peaks and 10 s on the backgrounds. Standards used were natural crystalline albite for Na and orthoclase for Si, Al, and K; data were reduced using the ZAF correction technique. For all but one sample, IV A, three traverses (60 –160 analysis points each) parallel to the diffusion direction were made; spacing between analytical points varied from 20 to 60 mm. 2.3. Boltzmann-Matano Analysis Diffusion coefficients, D’s, were calculated from the analytical traverses for different compositions using Boltzmann-Matano analysis (Crank, 1975; Baker, 1993). To calculate the diffusivity at any concentration the following equation is solved: C

Dc 5 2

1 dx 2t dC

E

xdC

(1)

Cbkg

where DC is the diffusivity (in m2s21) at concentration C at position x along the traverse, dx/dC is the derivative of the position respect to concentration, t is the experiment duration (in s), Cbkg is the high or the low initial concentration depending on the x location with respect to the Matano interface (where x 5 0). To perform Boltzmann-Matano analysis, we fitted the analytical profiles with two third-order, or rarely second-order, polynomials. These polynomials can be easily integrated

Table 2. Experimental conditions and measured diffusion coefficients Run

1 2 3

1

0

2

3

Xor 5 0.25

Xor 5 0.50

Xor 5 0.75

Texp( C)

Tavg( C)

Time(s)

n

1600 1492 1400 1300 1200 800 1400 1200

1467 1381 1331 1246 1173 800 1309 1163

120 120 240 240 480 11,700 240 480

3 2 3 3 3 3 3 3

DK(m2s21) 9.03(60.20) 3 10210 4.32(60.05) 3 10210 2.02(60.17) 3 10210 1.96(61.00) 3 10210 9.10(64.70) 3 10211 2.89(60.45) 3 10212 6.24(60.14) 3 10210 3.23(60.11) 3 10210

DNa(m2s21) 1.46(60.24) 3 1029 3.92(60.23) 3 10210 1.81(60.70) 3 10210 2.30(60.22) 3 10210 7.77(60.92) 3 10211 1.29(60.21) 3 10212 6.83(60.69) 3 10210 3.52(60.61) 3 10210

DK(m2s21) 1.35(60.02) 3 1029 3.87(60.04) 3 10210 2.38(60.24) 3 10210 2.24(60.51) 3 10210 1.09(60.04) 3 10210 2.25(60.35) 3 10212 7.24(60.61) 3 10210 3.78(60.38) 3 10210

DNa(m2s21) 1.18(60.13) 3 1029 5.24(60.68) 3 10210 3.46(60.40) 3 10210 2.33(60.32) 3 10210 1.37(60.14) 3 10210 2.38(60.21) 3 10212 7.40(60.53) 3 10210 3.62(60.22) 3 10210

DK(m2s21) 1.76(60.10) 3 1029 8.23(60.24) 3 10210 4.75(60.78) 3 10210 3.50(60.31) 3 10210 1.17(60.40) 3 10210 1.56(60.26) 3 10212 9.88(60.49) 3 10210 5.26(60.34) 3 10210

DNa(m2s21) 1.11(60.19) 3 1029 7.82(60.84) 3 10210 5.14(60.50) 3 10210 2.93(61.53) 3 10210 1.62(60.17) 3 10210 3.60(60.11) 3 10212 1.02(60.05) 3 1029 5.03(60.08) 3 10210

1400

1331

240

3

2.01(60.19) 3 10210

2.42(60.81) 3 10210

2.54(60.48) 3 10210

3.16(60.64) 3 10210

3.73(60.48) 3 10210

4.94(60.68) 3 10210

Na-K interdiffusion

1.0 GPa III A IV A VA VI B IX A XA XI A 5.5% H2O XII A, 5.5% H2O 2.0 GPa VIII A

0

Experimental temperature. Average temperature calculated following Yinnon and Cooper (1980) as discussed in text. Number of traverses used to calculate diffusion coefficients.

2999

3000

C. Freda and D. R. Baker

Fig. 2. Chemical diffusion profiles between orthoclase and albite melts (experiment XI A, P 5 1.0 GPa, T 5 1400°C (Tavg 5 1309), 5.5 wt% H2O added). (a) Na2O and K2O wt% concentrations along the capsule. (b) Cation concentrations, expressed in atoms per formula unit on the basis of eight oxygens, along the diffusion profile. One can observe that diffusion occurs only for Na and K cations. The diffusion profile length, which does not reach the end of the reservoir, is the same for both the elements.

and the Matano interface found. The integrations and derivations are performed to calculate the diffusivity at different points along the concentration profile. As previously demonstrated (e.g., Crank, 1975), Boltzmann-Matano analysis provides best results in the middle of the diffusion profile (0.5 mole fraction orthoclase in these experiments).

diffusion occurring during the time of heating and the total duration of the experiment. This Tavg is then used to recalculate a new Arrhenius relationship and the procedure for calculating Tavg repeated until Tavg reaches a constant value. The Tavg for each experiment is given in Table 2 and all diagrams use Tavg rather than Texp. To ensure that diffusion was the only transport process involved in these experiments (e.g., no convection) two experiments were performed at Texp 5 1200°C for different durations, 480 and 2400 s (Table 2 lists only the shorter run). Unfortunately diffusion of Na reached the K-rich end of the capsule in the longer experiment. Because of the nonsymmetric nature of this diffusion couple, K did not reach the end of the longer Na-rich part. The noninfinite geometry of this experiment makes strict application of Boltzmann-Matano analysis impossible. However, the estimated diffusivity in this experiment is 1 3 10210 m2s21 at XOr 5 0.5 which is consistent with the K diffusion coefficient at the same composition in the short experiment, 1.09 3 10210 m2s21 (Table 2). The consistency between the two experiments demonstrates that diffusion is the sole transport process in these experiments. Three analytical traverses were made on most samples also to investigate the possibility of convection. One traverse was along the centre line of the capsule, and the other two were half way between the centre and the edge of the capsule. In all cases the profiles were similar to each other and similar to ideal profiles (based upon error functions); diffusion coefficients calculated from each profile were similar to each other. The shapes of the profiles and the similarity of calculated diffusivities indicate that convection did not occur and that the traverses were parallel to the diffusion path.

3. RESULTS

3.1. Uncertainties and Corrections for Diffusion During Heating Diffusion coefficients were calculated at three compositions along each diffusion profile. These compositions correspond to orthoclase mole fractions of 0.25, 0.5, and 0.75 (Table 2). These diffusion coefficients are the average of three traverses (with exception of experiment IV A where only two traverses were performed) and their associated standard deviations. Based upon previous studies in this laboratory the reproducibility of each diffusion measurement calculated by BoltzmannMatano analysis is within 40% relative (Baker and Bossa´nyi, 1994). Run durations in Table 2 are the time between when the temperature was reached and when the experiment was quenched. Alkali diffusion in melts is so rapid that significant transport may have occurred during heating of experiments to run temperatures. A zero-time experiment performed at 1600°C produced a diffusion profile 1 mm in length clearly demonstrating that diffusion was occurring during heating. To correct for any diffusion which may have occurred during heating to run temperatures, we followed the iterative technique of Yinnon and Cooper (1980). This technique uses the Arrhenius relationship determined from the measured experimental temperatures, Texp, and diffusion coefficients to calculate an average temperature, Tavg, for each experiment based upon the integrated

Fig. 3. Na (open squares) and K (filled diamonds) chemical diffusion coefficients vs. mole fraction orthoclase for anhydrous experiments at P 5 1.0 GPa and different average temperatures. Every data point is the average of the diffusion coefficients measured from three (or two for experiment IV A) analytical traverses. The size of the error bars is almost always comparable with the symbol size, except that in few cases at XOr 5 0.25 or 0.75

Na-K interdiffusion

3001

5.5 wt% H2O, are increased by only approximately a factor of four above anhydrous measurements (Fig. 4). In Fig. 4 the temperature dependence of the diffusion coefficients for 0.5 mole fraction orthoclase is displayed. Alkali diffusion can be described by the Arrhenius equation: D 5 Do exp(2Ea/RT)

(2)

where Do (derived from the intercept, i.e., when T is infinite) is the preexponential factor in m2s21, Ea (derived from the slope of the line) is the activation energy in kJ mol21, R is the gas constant in Jk21 mol21, and T is the temperature in kelvins. For all anhydrous experiments at 0.5 mole fraction orthoclase the Arrhenius equation for Na-K interdiffusion when Texp values are considered is D 5 4.03(12.8,21.6) 3 1026 exp(2129.5 6 6.9/RT), whereas when Tavg’s are used Arrhenius changes slightly to Fig. 4. Arrhenius diagram of Na2 (squares) K (diamonds) interdiffusion at XOr 5 0.5 and P 5 1.0 GPa plotting measured diffusion coefficients against 10000/Tavg (when Tavg is expressed in kelvins). Filled symbols are anhydrous measurements and open symbols are hydrous ones. The Arrhenius line for the hydrous data was fitted using the diffusion coefficients in this study and those measured by Bai and Koster van Groos (1994) at P 5 450 and 560 MPa in a granitic melt 1 6.4 wt% H2O (filled stars). The diffusion coefficients measured by Chekhmir and Epelbaum (1991) at P 5 50 MPa in albite-orthoclase glass 1 1.7 wt% H2O (open stars) fall on the same line, but were not used to fit the line. Si-Al interdiffusion calculated from Eyring equation from viscosities (Dingwell, 1987; White and Montana, 1990; Baker, 1996) of albite melt (filled triangles) and orthoclase melt (filled circles) and Ca-Sr interdiffusion in albite melt (crosses) from Fujii (1981) are reported for comparison.

D 5 2.39(11.7,20.98) 3 1025 exp(2145.8 6 6.8/RT). Arrhenius parameters describing Na-K diffusion at other compositions along diffusion profiles, Xor 5 0.25 or 0.75, are within error of these determined at Xor 5 0.5. The hydrous melt Na-K diffusion results of this study have been combined with K chemical diffusion measurements in a granitic melt 1 6.4 wt% H2O determined at 450 and 560 MPa (Bai and Koster van Groos, 1994) to calculate a preliminary Arrhenius equations for K diffusion in silicic melts with 6 6 0.5 wt% H2O. If Texp’s are used the Arrhenius equation is D 5 2.49(11.9,21.1) 3 1026 exp(2111.0 6 6.4/RT), and using Tavg’s it is

3.2. Effects of Temperature, Composition, Pressure, and H2O One of the diffusion profiles of experiment XI A is shown as an example (Fig. 2a,b ). As with all experiments listed in Table 2 the diffusion couple is infinite, i.e., the concentrations of the diffusing species do not reach the ends of the reservoir. This condition is necessary for rigorous application of BoltzmannMatano analysis. It can also be observed that the profile length is the same for Na and K and that the only diffusion which occurred in these experiments appears to be the exchange of these two cations (Fig. 2b). The diffusion coefficients in the anhydrous experiments vary from about 1029 m2s21 at 1600°C (Tavg 5 1467°C) to about 10212 m2s21 at 800°C (Table 2, Figs. 3, 4). At the same temperature the D values are quite similar for every composition (Fig. 3) with a maximum difference of a factor of two at 800°C. Due to the small differences in diffusivity at different compositions attempts to fit the profiles with a constant diffusivity were unsuccessful. The effect of pressure is even less than the effect of composition. The experiment at 2.0 GPa, 1400°C (Tavg 5 1331°C) yielded diffusivities within error of those measured at 1.0 GPa, 1400°C (Table 2). These results demonstrate that pressure does not have a measurable effect on K and Na interdiffusion in this system at Texp 5 1400°C (Tavg 5 1331°C). The effect of H2O on Na-K interdiffusion is minor. The diffusion coefficients measured under hydrous conditions,

D 5 4.97(10.85,20.73) 3 1026 exp(2115.8 6 1.8/RT). Although the compositions used in this study and in that of Bai and Koster van Groos (1994) are different, the effects of composition on alkali diffusion in silicic melts are expected to be minor (Smith, 1974; Henderson et al., 1985). The validity of combining K diffusion measurements in granitic melt with those in alkali feldspar melts is supported by the close correspondence between the calculated Arrhenius line for K diffusion in hydrous melts and Na-K interdiffusion measurements in alkali feldspar melts 11.7 wt% H2O (Chekhmir and Epel’baum, 1991) which were not used in the calculation of the line (Fig. 4). 4. DISCUSSION

4.1. Diffusion of Alkalis Compared to Other Elements The Na-K interdiffusion coefficients measured in this study are orders of magnitude above those of network former interdiffusion in alkali feldspar melts. In Fig. 4 the Si-Al interdiffusion coefficients in alkali feldspar melts have been estimated from measured high-pressure viscosities in albite and orthoclase melts at temperatures between 1400 and 1600°C and pressures between 0.75 and 2.5 GPa (Dingwell, 1987; White and Montana, 1990; Baker, 1996) through use of the Eyring equation (see Baker, 1990). Additionally the orthoclase melt viscosity measurements at 2.5 GPa (White and Montana, 1990)

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C. Freda and D. R. Baker

can be used to estimate an activation energy for Si-Al diffusion of approximately 450 kJ mol21. These estimated Si-Al interdiffusion coefficients are four orders of magnitude below those of Na-K (Fig. 4) and the activation energy for Si-Al interdiffusion almost four times that measured for Na-K. The interdiffusion coefficients of the alkaline-earths Ca and Sr measured in albite melt by Fujii (1981) at 1400°C and pressures of 0.25 and 2.0 GPa are approximately one decade below Na-K interdiffusion coefficients (Fig. 4). These differences between diffusion of alkalis, alkaline-earths, and network formers are not anomalous and have been observed repeatedly in diffusion studies on natural compositions (cf. review by Watson and Baker, 1991). The progressive increase in diffusion coefficients from Si-Al through Ca-Sr to Na-K in alkali feldspar melts is correlated with decreasing field strength, Z/r2 (Z is cation charge, r is cation radius or the cation-oxygen bond length), which we prefer to express using the valence of the cation-oxygen bond. Similar correlations between tracer diffusion and cation properties have been observed previously (e.g., Hofmann, 1980; Henderson et al., 1985). Comparison of Na-K interdiffusion in feldspar melts with Si-Al interdiffusion and Zr and P chemical diffusion in rhyolitic melts demonstrates that bond valence, or field strength, alone does not simply control diffusivity. It is the bond valence, or field strength, combined with the ability of the melt to accommodate cations in suitable charge-balanced coordination polyhedra which are instrumental in controlling rates of diffusion in highly polymerized melts such as alkali feldspar compositions. Studies of the structures of feldspar glasses demonstrate that Na and K are coordinated by oxygens associated with rings of 6 (Si,Al)-O tetrahedra which dominate the structure of the glass and most probably of isocompositional melts (see reviews by Mysen, 1988; Brown et al., 1995; McMillan and Wolf, 1995; Stebbins, 1995). The Na-O bond length for eight-coordinated Na in albite melt is 0.235 nm; in orthoclase and albite-orthoclase glasses K is nine- to ten-fold coordinated and K-O bond lengths are between 0.3 and 0.306 nm (Brown et al., 1995). The bond valences for these two cations are 0.17 and 0.09 v.u., respectively (Brown et al., 1995). Silicon and aluminum in feldspar melts and glasses are four-coordinated and have bond lengths which vary from 0.163 to 0.168 nm, and bond valences of 0.98 v.u. and 0.74 v.u., respectively (Brown et al., 1995). Phosphorus is four-coordinated with a bond length of 0.154 nm and a bond valence of 1.20 v.u., and zirconium is six-coordinated with a bond length of 0.210 nm and a bond valence of 0.66 v.u. (Brown et al., 1995). The abundance of large structures into which alkalis reside in feldspar melts combined with their low bond valences, or field strengths, are responsible for the high diffusion coefficients of these cations; at 1200°C (Tavg 5 1163) the measured interdiffusion coefficient is approximately 1 3 10210 m2s21. Cations with higher bond valences display much slower diffusion. At similar conditions of temperature and pressure the interdiffusion of Si and Al is approximately 2 3 10214 m2s21 (Baker, 1990; calculated from White and Montana, 1990); interdiffusion of these cations in granitic melts is characterized by a preexponential factor of 6.7 3 102 m2s21 and an activation energy of 236 kJ mol21 (Baker, 1990). Oxides of these cations have solubilities in the range of tens of weight percent which reflect the ability of the melt to accomodate these cations

Fig. 5. Arrhenius diagram for Na-K interdiffusion compared with extrapolated tracer diffusion coefficients of Na and K in albite and orthoclase glasses from Jambon and Carron (1976). The calculated Arrhenian fit to anhydrous experimental data from this study is also shown.

inside charge-balancing polyhedra of oxygen anions. The high field-strength elements Zr and P are the slowest diffusing cations in anhydrous rhyolitic melts with diffusivities of approximately 3 3 10216 m2s21 and 1 3 10216 m2s21, respectively, at 1200°C and pressures similar to those of this study (Harrison and Watson, 1983, 1984). Zirconium and phosphorus display high activation energies for diffusion, 409 and 601 kJ mol21, and high preexponential factors, 0.098 and 2.2 3 105 m2s21, respectively (Harrison and Watson, 1983, 1984). The low diffusivity of P and Zr, particularly Zr whose charge is the same as Si but has a lower bond valence, is attributed to the difficulty of creating charge-balanced polyhedra for these cations in anhydrous rhyolitic melts due to low proportion of nonbridging oxygens in silica-rich melts. The inability of silicarich melts to create abundant charge-balanced oxygen polyhedra for Zr and P is demonstrated by the low solubilities of zircon, 2800 ppm Zr (Harrison and Watson, 1983), and apatite, 800 ppm P (Harrison and Watson, 1984), at 1200°C in rhyolitic melts. These correlations lead us to the conclusion that any future model for the prediction of cation diffusion in silicate melts must include both the bond valence of the cation-oxygen bond and some measure of the melt’s ability to create chargebalancing polyhedra. 4.2. Tracer vs. Chemical Diffusion In Fig. 5 the experimental data of Na-K interdiffusion coefficients are compared with the 1-atm tracer diffusion data of Na and K in albite and orthoclase glasses (Jambon and Carron, 1976) extrapolated up to 1600°C. The Na tracer diffusion in both amorphous albite and orthoclase at every temperature is higher than the Na-K interdiffusion coefficient. The K tracer diffusion coefficients are lower than the Na-K interdiffusion coefficient at the highest temperatures and become comparable

Na-K interdiffusion

below 1000°C. These observations can be explained by the ion interaction effect in a binary system (Manning, 1968): D Na2K 5

d1na Or D* Na D* K X Ab D* Na 1 X Or D* K d1nX Or

(3)

where DNa-K is the interdiffusion coefficient, D*Na or D*K is the tracer diffusion coefficient, XAb or Or is the mole fraction of albite or orthoclase, and aOr is the molar activity of orthoclase in an albite-orthoclase melt or glass. When the system behaves ideally the thermodynamic factor, the second term on the right hand side of the equation, equals 1. Activity-composition measurements on mixtures of albite and orthoclase melts at 1 atm and 1200 –1600°C indicate that over the compositional range of 0.2 # Xor # 1 the components mix virtually ideally (Rammensee and Fraser, 1982). Assuming ideality at 1.0 GPa and using the tracer diffusivities measured in glasses, the Na-K interdiffusion coefficient has been calculated (Fig. 5). At all temperatures the agreement between experimental and calculated Na-K diffusivities is always within a factor of three. Although calculated, 88.9 kJ mol21, and measured, 145.8 kJ mol21, activation energies are obviously distinct from one another, such a close correspondence between experimental and calculated diffusion coefficients supports the validity of extrapolating tracer diffusivities measured in alkali feldspar glasses into the melt region. At 1000°C and below comparison of experimental and calculated Na-K interdiffusion reveals apparently anomalous behavior. At these lower temperatures the experimental values are near to, and below, the values of K tracer diffusion in orthoclase and albite glasses which is inconsistent with Eqn. 3 and the assumption of ideal mixing of Or and Ab components in the melt or glass. The reduction in the measured Na-K interdiffusion coefficient is attributed to the probable nonideality in the melt or glass at these lower temperatures and is a manifestation of the mixed alkali effect (e.g., Chakraborty, 1995). Comparison of our study with the multicomponent diffusion experiments of Chakraborty et al. (1995 a,b) in SiO2-Al2O3K2O melts demonstrates the complexity which may occur when diffusion in silicate melts involves more than just alkali exchange. Chakraborty et al. (1995 a,b) studied diffusion between melts of approximately equal K2O/Al2O3 weight ratios, but differing SiO2 concentrations. They found diffusive coupling between Al2O3 and K2O which led to uphill diffusion of the former and values of the DK2O-K2O elements in diffusion matrices which were about four orders of magnitude less than the DNa-K coefficients of this study. No coupling between alkalis and other ions was found in this study, but we have observed diffusive coupling in preliminary diffusion experiments between albite and anorthite. 4.3. Na-K Diffusion in Melts, Glasses, and Crystals The Na-K interdiffusion measured in the anhydrous system occurs in equilibrium melts at the highest temperatures, between an equilibrium melt and a supercooled melt at temperatures between 1500 and 1200°C, and possibly between two glasses at 800°C. Despite the different physical and thermodynamic states of the system, Na-K interdiffusion appears Arrhenian at all temperatures, unlike tracer diffusion in some systems

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(e.g., Chakraborty, 1995). It is tempting to link the Arrhenian behavior of Na-K diffusion to the strong viscous behavior of albite liquid and glass (Richet and Bottinga, 1995). However, as discussed below, the small effect of H2O on Na-K interdiffusion and its large effect on viscosity and Si-Al diffusion indicate that the relationship between Na-K diffusion and viscosity is complex and beyond the scope of the present paper. Comparison of Na-K interdiffusion in alkali feldspar melts extrapolated down to 650 and 600°C and Na-K interdiffusion in crystalline alkali feldspar (Brady and Yund, 1983) demonstrates that diffusion in melts (or glasses) is six orders of magnitude greater than in the crystalline phase. This difference must reflect changes occurring during the melting of alkali feldspar crystals. The melting of crystalline alkali feldspar changes the number of (Si,Al)O4 tetrahedra in the rings which contain alkalis from 4 to 6 (Taylor and Brown, 1979). Differences in Na and K coordination between crystals and melts are small. The coordination of Na in high albite is 6 –7 (Deer et al., 1966) and in albite melt is 8 (Brown et al., 1995); the coordination of K in high sanidine is 9 (Deer et al., 1966) and varies between ;9 and 10 in orthoclase-albite melts (Brown et al., 1995). The million-fold increase in Na-K diffusion due to amorphization is attributed to the loss of long-range order and the increase in the number of coordinating oxygens around alkalis in feldspar melts. The effect of the loss of long-range order on diffusion has been predicted theoretically by Tsekov and Ruckenstein (1994) and also observed in studies comparing tracer diffusion in albite melt and crystals (Baker, 1995). 4.4. The Effects of Pressure The pressure effect on alkali diffusion was investigated by performing one additional experiment at 2 GPa, Texp5 1400°C (Tavg 5 1331). We chose 1400°C in order to compare our results with those from the literature (Smith, 1974; Fujii, 1981; Kushiro, 1983; Baker, 1990). As shown in Fig. 6 there is no measurable pressure effect on the Na and K interdiffusion coefficients. Whereas Si, Al, Ge, and Ga (network-forming cations) interdiffusion coefficients are sensitive to pressure, displaying a positive correlation. Even Ca and Sr (networkmodifying cations) interdiffusion coefficients in albite melts are pressure dependent, but in this case the correlation between pressure and diffusivity is negative. The pressure dependence of the diffusion coefficient can typically be expressed by the following equation: D 5 Dpo exp(2PVa/RT)

(4)

similar to the Arrhenius equation for temperature dependence. In this equation Dpo is the diffusivity at zero pressure, P is the pressure, Va is the activation volume, R is the gas constant and T the temperature in kelvins. Our results demonstrate that at 1400°C the activation volume for interdiffusion of Na and K is zero. The activation volume for the interdiffusion of networkformer cations Si and Al is negative with a value of approximately 213.2 cm3mol21 (Baker, 1990). The activation volume for Ca-Sr interdiffusion in albite melt is positive with a value of 9.5 cm3mol21 (Fujii, 1981). The negative activation volume for network-former cations is interpreted to reflect changes in the local structure of the melt (Shimizu and Kushiro, 1984; Baker, 1990) related to a transi-

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Fig. 6. Diffusion coefficients vs. pressure for network-modifying and network-former cations. Pressure does not have a measurable effect on Na and K interdiffusion coefficients. However pressure obviously has a negative effect on Ca-Sr interdiffusion coefficients and a positive effect on network-former cations interdiffusion coefficients.

tory collapse in the melt structure occurring during diffusion. This collapse could occur by temporarily increasing the coordination of Si and Al network-former cations from 4 to 5 or 6 in silicate melts (Angell et al., 1982; Kubicki and Lasaga, 1988; Baker, 1990; Xue et al., 1991). Diffusion of network-former cations occurs during the formation and destruction of these activated complexes. The positive activation volume found for Ca-Sr interdiffusion (Fujii, 1981) is interpreted to be related to dilation of the local melt structure near these cations associated with the formation of activated complexes. For Na-K interdiffusion the activation volume is zero which implies that no measurable dilation is necessary for the formation of activated complexes and diffusion. This behavior is related to the different local structure around alkalis and alkaline earths in aluminosilicate melts. Taylor and Brown (1979) found that anorthitic glass, and, therefore, presumably melt, is dominated by four-membered tetrahedral rings as in the crystalline structure of feldspars; these four-membered rings provide the charge-balanced locations for Ca cations. For glasses, and also presumably melts, of albitic and orthoclasic composisition, instead, larger six-membered tetrahedral rings with alkalis in the centre, similar to the stuffed tridymite, are dominant (Taylor and Brown, 1979; see also reviews by Brown et al., 1995; McMillan and Wolf, 1995; Stebbins, 1995). The structure of crystalline tridymite can be used to estimate the diameter of the six-membered tetrahedra ring to be 0.5 nm (Deer et al., 1966), and the structure of anorthite provides an estimate for the four-membered ring diameter, 0.42 nm (Ribbe, 1983). The different size of these rings of tetrahedra are proposed to be responsible for the different activation volumes of alkali and alkaline earths. The smaller, four-membered, rings must dilate significantly for alkaline earth diffusion and produce a measurable activation volume, but the amount of dilation of the larger, six-membered, rings necessary for alkali diffusion is much less; in this study it is unmeasurable.

Fig. 7. Diffusion coefficients vs. H2O for network-modifying and network-former cations in alkali feldspar and rhyolitic melts. Na-K interdiffusion coefficients are from this study (diamonds) with the exception of the star which is from Chekhmir and Epelbaum (1991). Ca-Sr interdiffusion coefficients (crosses) are from Fujii (1981). Si-Al interdiffusion measurements (dots) are from Baker (1991). Zr chemical diffusion coefficients (open triangles) are from Harrison and Watson (1983), and P chemical diffusion coefficients (filled triangles) are from Harrison and Watson (1984). Unfortunately, the temperature and pressure conditions at which Fujii (1981) made his comparison of hydrous and anhydrous Ca-Sr interdiffusion are not provided in his abstract.

4.5. The Effect of H2O The effect of H2O on diffusion coefficients measured in this and other selected studies near 1200°C is displayed in Fig. 7. As is clearly shown, H2O has a very small effect on alkali (this study) and alkaline earth (Fujii, 1981) interdiffusion in alkali feldspar melts compared to the effect of H2O on P, Zr, (Harrison and Watson, 1983, 1984) and Si chemical diffusion (Baker, 1991) in granitic melts. Such a result is not unexpected in as much as Watson’s (1981) study of the effects of H2O on Na tracer diffusion in obsidian demonstrated that H2O only increased diffusion by a small value. The Na-K interdiffusion coefficients increase by only a factor of four with the addition of 5.5 wt% of H2O. Ca-Sr interdiffusion coefficients increase by a factor of six with the addition of 4 wt% of H2O. However P, Zr, and Si diffusion coefficients increase by about three orders of magnitude with addition of 6 wt% of H2O. The strong H2O effect which decreases the activation energies by a factor of two for Si and Zr and by a factor of six for P is attributed to the interaction between H2O and bridging oxygens to form hydroxyls and nonbridging oxygens (see review by Watson, 1994) and results in the creation of additional charge-balanced polyhedra in silica-rich melts for these high field strength cations (see previous discussion). We observed that with addition of H2O the activation energy decreased by 20% and the preexponential factor for Na-K interdiffusion increased by only a factor of ten (Fig. 4). The small changes in Arrhenius parameters are attributed to the minor effect of H2O on the local structure, i.e., coordination polyhedra, related to Na and K in alkali feldspar melts. The observed Arrhenian behavior encourages the extrapolation of Na-K interdiffusion measurements to

Na-K interdiffusion

Fig. 8. Alkali chemical diffusion from this study compared with previous data for different melt compositions. The Watson (1982) Na-K interdiffusion coefficient was estimated for a feldspar-basalt diffusion couple. van der Laan and Wyllie (1993) measured Na (open triangle) and K (filled triangle) chemical diffusion between a basaltic and a granitic melt with 5 wt% added H2O. Watson and Jurewicz (1984) used an anhydrous basalt-partially molten granite couple to determine K chemical diffusion. Smith (1974) provided the most complete investigation of Na-K interdiffusion in anhydrous basaltic, andesitic, and rhyolitic melt compositions at 1 bar.

lower temperatures equivalent to those of pegmatite genesis, near 600°C. The small effect of H2O addition of Ca-Sr interdiffusion (Fujii, 1981) also is interpreted to reflect little difference in the local structure around alkaline earth cations between anhydrous and hydrous alkali feldspar melts. 4.6. Application to Contamination Calculations In order to evaluate the applicability of the results from this study to the description of alkali diffusion in the natural geological setting, we compared them with previous data obtained under different experimental conditions on different compositions of natural rocks (Fig. 8). The most exhaustive study available on alkali chemical diffusion was performed by Smith (1974) who investigated the alkali diffusion in basaltic, andesitic, and rhyolitic melts at 1 atm in a temperature range from 1100 to 1550°C. Unfortunately, this study does not give any information about the effects of H2O and pressure on alkali diffusion. The Na-K interdiffusion coefficient was estimated for a feldspar-basalt diffusion couple (Watson, 1982) at 1300°C, 0.6 GPa, and the K chemical diffusion was measured in an anhydrous basalt-granite couple at 1250°C, 1.0 GPa (Watson and Jurewicz, 1984). The only available data about the effect of H2O on alkali diffusion in natural rocks are from van der Laan and Wyllie (1993) who measured Na and K chemical diffusion between a basaltic and granitic melt with 5 wt% added H2O at 920°C, 1.0 GPa and from Bai and Koster van Groos (1994) who measured only K chemical diffusion at low temperatures, 750 –900°C, and pressures, 100 –560 MPa, in a granitic melt 1 6.4 wt% H2O. Because the results of Bai and Koster van Groos (1994) were used to constrain the Arrhenius line for hydrous alkali diffusion (Fig. 4), they are not shown as

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individual points in Fig. 8. Comparison of previous independent measurements of alkali chemical diffusion with the Arrhenius lines calculated in this study demonstrates excellent agreement. The only significant discrepancy is with the measurement of Watson and Jurewicz (1984). The low diffusion coefficient of Watson and Jurewicz (1984) is related to their experimental technique in which they studied the diffusion of K from a partially molten granite into a superliquidus basalt under anhydrous conditions. Under these conditions alkali diffusion is expected to be slower because diffusion of K into the basalt requires counter diffusion of Ca, Mg, and Fe which will be significantly slower than alkali interdiffusion (as argued by Watson and Jurewicz, 1984). This diffusive coupling between K and other ions in the melt is a multicomponent example of diffusive coupling which has been extensively studied in simple systems (e.g., Kress and Ghiorso, 1993; Chakraborty et al., 1995a,b; Liang et al., 1997). Theoretically, diffusive coupling can lead to uphill diffusion of any element (e.g., Kress and Ghiorso, 1993; Chakraborty et al., 1995a,b; Liang et al., 1997), but uphill diffusion of alkalis in natural compositions has only been observed during anhydrous diffusion between dissolving quartz and basaltic melts (Sato, 1974; Watson 1982). The coupling of alkali diffusion with other ions in natural melts appears to be substantially weakened when H2O is added. The hydrous basaltic-granitic melt interdiffusion experiments of van der Laan and Wyllie (1993) demonstrated that addition of 5 wt% H2O increases alkali diffusion coefficients to values consistent with those measured in this study, whereas diffusion coefficients of Ca, Mg, and Fe were much lower. Based upon the good agreement of all the studies we are confident that the Na-K interdiffusion coefficients measured in this study can be used as maximum values for petrologic investigations of alkali diffusion in a wide range of natural melt compositions. We estimate that these values are accurate within approximately one-half an order of magnitude for most compositions ranging from basaltic to rhyolitic melts (cf. Fig. 8). However, it should be noted that in some natural circumstances, such as the dissolution of quartz discussed above, diffusive coupling may lead to uphill diffusion which cannot be predicted from the results of this study. The observed Arrhenian behavior of Na-K interdiffusion suggests that measurements can be extrapolated to lower temperatures equivalent to those of pegmatite genesis, near 600°C. Moreover, due to the insignificant effects of H2O and pressure observed in this study on alkali diffusion, we also theorize that these diffusion coefficients are applicable for the calculation of alkali diffusive transport and contamination of melts of a wide range of temperatures, pressures, and H2O concentrations which may be found in crustal and upper mantle melts. 5. CONCLUSIONS

Results obtained during the investigation of Na and K chemical diffusion between albite and orthoclase melts at 1.0 GPa between Texp 5 800 and 1600°C and at 2.0 GPa, 1400°C, in anhydrous melts and in hydrous, 5.5 wt% H2O, melts at 1.0 GPa, 1200 and 1400°C demonstrate that under the experimental conditions of this study the only diffusive transport which occurred was the exchange of Na and K cations. The alkali interdiffusion coefficients are four orders of magnitude higher

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than the estimated diffusion coefficients of network-former cations in melts of the same composition. Pressure was not observed to have a measurable effect on Na-K interdiffusion in the investigated system at Texp 5 1400°C. Alkali diffusion in both anhydrous and hydrous melts can be described by Arrhenius equations. The effect of H2O on Na-K interdiffusion is minor; under hydrous conditions the interdiffusion coefficients increase by only a factor of four and the activation energy does not change significantly relative to anhydrous diffusion. We conclude that the Na-K interdiffusion coefficients measured in this study can be used to describe the maximum rates of alkali diffusion in a wide range of melt compositions under different conditions in the crust and upper mantle. Acknowledgments—Many thanks to Steve Kecani for making graphite capsules and to Fred Bernier for performing the experiment at 2.0 GPa. C. F. also thanks Claude Dalpe´ for helping with the microprobe and Raffaello Trigila for making her stronger. We thank the three anonymous reviewers for their constructive comments. This research was supported by NSERC operating Grant OGP89662 and by C.S. per gli Equilibri Sperimentali in Minerali e Rocce del C.N.R REFERENCES Angell C. A., Cheeseman P. A., and Tamaddon S. (1982) Pressure Enhancement of ion Mobilities in Liquid Silicates from Computer Simulation Studies to 800 Kilobars. Science 218, 885– 887. Bai T. B. and Koster van Groos A. F. (1994) Pressure Effect on potassium diffusion in hydrated granitic melt. Science in China 37, 879 – 886. Baker D. R. (1990) Chemical interdiffusion of dacite and rhyolite: Anhydrous measurements at 1 atm and 10 kbar, application of transition state theory, and diffusion in zoned magma chambers. Contrib. Mineral. Petrol. 104, 407– 423. Baker D. R. (1991) Interdiffusion of hydrous dacite and rhyolitic melts and the efficacy of rhyolite contamination of dacitic enclaves. Contrib. Mineral. Petrol. 106, 462– 473. Baker D. R. (1992) Estimation of diffusion coefficients during interdiffusion of geologic melts: Application of transition state theory. Chem. Geol. 98, 11–21. Baker D. R. (1993) Measurement of Diffusion at High Temperatures and Pressures in Silicate Systems. In Short Course Handbook on Experiments at High Pressure and Applications to the Earths Mantle (ed. R. W. Luth), Vol. 21, pp. 305–355. Mineral. Assoc. Canada. Baker D. R. (1995) Diffusion of silicon and gallium (as an analogue for aluminum) network-forming cations and their relationship to viscosity in albite melt. Geochim. Cosmochim. Acta 59, 3561–3571. Baker D. R. (1996) Granitic melt viscosities: Empirical and configuration entropy models for their calculation. Amer. Mineral. 81, 126 –134. Baker D. R. and Bossa´nyi H. (1994) The combined effect of F and H2O on interdiffusion between peralkaline dacitic and rhyolitic melts. Contrib. Mineral. Petrol. 117, 203–214. Behrens H. (1992) Na and Ca tracer diffusion in plagioclase glasses and supercooled melts. Chem. Geol. 96, 267–275. Boettcher A. L., Burnham C. W., Windom K. E., and Bohlen S. R. (1982) Liquids, glasses, and the melting of silicate to high pressures. Amer. Mineral. 69, 823– 834. Brady J. B. and Yund R. A. (1983) Interdiffusion of potassium and sodium in alkali feldspars: Homogenization experiments. Amer. Mineral. 68, 106 –111. Brown G. E., Jr., Farges F., and Calas G. (1995) X-ray scattering and X-ray spectroscopy studies of silicate melts. In Structure, Dynamics and Properties of Silicate Melts. (ed. J. F. Stebbins et al.); Rev. Mineral. 32, 317– 410. MSA. Chakraborty S. (1995) Diffusion in silicate melts. In Structure, Dynamics and Properties of Silicate Melts (ed. J. F. Stebbins et al.); Rev. Mineral 32, 411–503. MSA Chakraborty S., Dingwell D. B., and Rubie D. C. (1995a) Multicomponent diffusion in ternary silicate melts in the system K2O-Al2O3-

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van der Laan S., Zhang Y., Kennedy A. K., and Wyllie P. J. (1994) Comparison of element and isotope diffusion of K and Ca in multicomponent silicate melts. Earth Planet. Sci. Lett. 123, 155–166. Watson E. B. (1981) Diffusion in magmas at depth in the Earth: The effects of pressure and dissolved H2O. Earth Planet. Sci. Lett. 52, 291–301. Watson E. B. (1982) Basalt contamination by continental crust: Some experiments and models. Contrib. Mineral. Petrol. 80, 73– 87. Watson E. B. (1994) Diffusion in volatile-bearing magmas. In Volatiles in Magmas (ed. M. R. Carroll and J. R. Holloway); Rev. Mineral 30, 371– 411. MSA. Watson E. B. and Baker D. R. (1991) Chemical Diffusion in Magmas: An Overview of Experimental Results and Geochemical Applications. In Physical Chemistry of Magmas (ed. L. L. Perchuk and I. Kushiro); Adv. Phys. Geochem. 9, 120 –151. Springer-Verlag. Watson E. B. and Jurewicz S. R. (1984) Behavior of alkalies during diffusive interaction of granitic xenoliths with basaltic magma. J. Geol. 92, 121–131. White B. S. and Montana A. (1990) The effect of H2O and CO2 on the viscosity of sanidine liquid at high pressures. J. Geophys. Res. 95, 15683–15693. Xue X., Stebbins J. F., Kanzaki M., McMillan P. F., and Poe B. (1991) Pressure-induced silicon coordination and tetrahedral structural changes in alkali oxide-silica melts up to 12 GPa: NMR, Raman, and infrared spectroscopy. Amer. Mineral. 76, 8 –26. Yinnon H. and Cooper A. R. Jr. (1980) Oxygen diffusion in multicomponent glass forming silicates. Phys. Chem. Glasses 21, 204 –211.