Diffusion In Silicate Melts Research Articles

Rapid Ag diffusion in granitic melt: Implications for Ag mineralization and melt inclusion record

Element diffusion in silicate melts is an important process in the transport and enrichment of metals in magmatic and magmatic-hydrothermal systems, but the diffusivity of Ag, unlike other metals such as Cu, Mo, and W, is still unknown. In this study, Ag diffusion in granitic melts with up to 6.9 wt% H2O was investigated at 973–1673 K and 0.1–1 GPa in a piston cylinder apparatus and a cold seal vessel, using both a diffusion couple approach and an argentite (Ag2S) dissolution approach. Silver concentration profiles were analyzed by LA-ICP-MS on recovered samples. Silver solubility, determined by Ag concentration at melt-argentite interface, increases with increasing temperature. Silver diffusivity is found to increase with increasing temperature and water content but to decrease with pressure. At 1 GPa, Ag diffusivity in granitic melt can be described by the following expression:lnDAg,1GPa=-13.77±0.46-13341±534-700±39wTwhere D is Ag diffusivity in m2/s, w is the water content in wt%, and T is the temperature in K. The pressure effect over 0.1–1 GPa gives an activation volume of 11.3 cm3/mol for Ag diffusion. While not being on a par with the mobility of Na and Li, Ag diffusion is among the most rapid, comparable to Cu and faster than other species including H2O and Fe. This implies that Ag diffusion in melt is unlikely to be a rate-limiting step for Ag enrichment into exsolved fluid bubbles or sulfide blobs. Furthermore, melt inclusions in silicate minerals are expected to record Ag concentration in the bulk melt instead of an elevated concentration in the presence of an Ag-rich boundary layer. Our Ag diffusivity data also suggest that a few tens of hours are long enough to homogenize Ag concentration in melt in solubility or partition experiments at temperatures above 800 °C.

Deep neural network potentials for diffusional lithium isotope fractionation in silicate melts

Diffusional isotope fractionation has been widely used to explain lithium (Li) isotope variations in minerals and rocks. Isotopic mass dependence of Li diffusion can be empirically expressed as D7LiD6Li=67β, where D is the diffusivity of a Li isotope. The knowledge about temperature and compositional dependence of the β factor which is essential for understanding diffusion profiles and mechanisms remains unclear. Based on the potential energy and interatomic forces generated by deep neural networks trained with ab initio data, we performed deep potential molecular dynamics (DPMD) simulations of several Li pseudo-isotopes (with mass = 2, 7, 21, 42 g/mol) in albite, hydrous albite, and model basalt melts to evaluate the β factor. Our calculated diffusivities for 7Li in albite and model basalt melts at 1800 K compare well with experimental results. We found that β in albite melt decreases from 0.267±0.006 at 4000 K to 0.225±0.004 at 1800 K. The presence of water appears to slightly weaken the temperature dependence of β, with β decreasing from 0.250±0.012 to 0.228±0.031 in hydrous albite melt. The calculated β in model basalt melt takes much smaller values, decreasing from 0.215±0.006 at 4000 K to 0.132±0.015 at 1800 K. Our prediction of β in albite and hydrous albite melts is in good agreement with experimental data. More importantly, our results suggest that Li isotope diffusion in silicate melts is strongly dependent on melt composition. The temperature and compositional effects on β can be qualitatively explained in terms of ionic porosity and the coupled relationship between Li diffusion and the mobility of the silicate melt network. Two types of diffusion experiments are suggested to test our predicted temperature and compositional dependence of β. This study shows that DPMD is a promising tool to simulate the diffusion of elements and isotopes in silicate melts.

Nitrogen diffusion in silicate melts under reducing conditions

Abstract The behavior of nitrogen during magmatic degassing and the potential kinetic fractionation between N and other volatile species (H, C, O, noble gases) are poorly known due to the paucity of N diffusion data in silicate melts. To better constrain N mobility during magmatic processes, we investigated N diffusion in silicate melts under reducing conditions. We developed uniaxial diffusion experiments at 1 atm, 1425 °C, and under nominally anhydrous reducing conditions (fO2 ≤ IW-5.1, where IW is oxygen fugacity, fO2, reported in log units relative to the iron-wüstite buffer), in which N was chemically dissolved in silicate melts as nitride (N3–). Although several experimental designs were tested (platinum, amorphous graphite, and compacted graphite crucibles), only N diffusion experiments at IW-8 in compacted graphite crucibles for simplified basaltic andesite melts were successful. Measured N diffusivity (DN) is on the order of 5.3 ± 1.5 × 10−12 m2 s−1, two orders of magnitude lower than N chemical diffusion in soda-lime silicate melts (Frischat et al. 1978). This difference suggests that nitride diffusivity increases with an increasing degree of melt depolymerization. The dependence of N 3– diffusion on melt composition is greater than that of Ar. Furthermore, N3– diffusion in basalticandesitic melts is significantly slower than that of Ar in similarly polymerized andesitic-tholeiitic melts at magmatic temperatures (1400–1450 °C; Nowak et al. 2004). This implies that N/Ar ratios can be fractionated during reducing magmatic processes, such as during early Earth's magma ocean stages.

Effect of alkalis on water diffusion in silicate melts based on new experimental data for a shoshonitic melt

Water diffusion is an important mechanism affecting magmatic water content, vapor bubble growth, and the dynamics of volcanic eruptions. Water diffusivity in silicate melts is dependent on temperature, pressure, H2O content and speciation, and melt composition. While a general model has recently been developed for water diffusivity in calc-alkaline (subalkaline) melts as a function of silica content, the effect of alkalis on water diffusion is less clear due to the lack of experimental data for alkali-rich melts and a systematic evaluation. Here, water diffusion in shoshonitic melt with up to 1.6 wt% H2O was investigated at 1654–1926 K and 1 GPa in a piston cylinder apparatus using both hydration and diffusion couple methods. Diffusion profiles measured by FTIR microspectroscopy are in accordance with a modified speciation-based diffusion model which takes into account different mobility of hydroxyl (OH) and molecular H2O (H2Om). The diffusivity ratio DOH/DH2Om in shoshonitic melt increases with increasing temperature and falls into the range of 0.24–0.55, greater than the values for all of the melts previously investigated. The remarkable contribution of OH to water diffusion in shoshonitic melt is attributed to a substantial presence of free OH species (OH bonding with network-modifying cations but here especially with K or Na). The total H2O diffusivity in shoshonitic melt can be expressed as:DH2Ot=e-12.11-16765T1+Ce-11.14+17381-262.6CT,where D is in m2/s, T is temperature in K, and C is H2Ot content in wt% (DH2Ot reduced to DOH at C = 0). The above equation replicates the experimental data within 0.1 natural log unit. The total H2O diffusivities at 1 wt% H2Ot in three alkali-rich melts, including shoshonite, trachyte and phonolite, appear to fall onto a single Arrhenian trend line over a broad temperature range of 1100–1900 K. Compared to the general water diffusivity model for calc-alkaline melts, water diffusivities in alkali-rich silicate melts are generally higher and roughly twofold at the same P-T-H2Ot-XSi conditions, with XSi being the mole fraction of Si among all cations. Excess alkalis decrease degree of melt polymerization and promote formation of mobile K-OH and Na-OH species, thereby having a positive influence on water diffusion and vapor bubble growth in magma.

Effect of Structural Dynamical Property of Melt on Water Diffusion in Rhyolite Melt

Water diffusion in silicate melts is one of the key processes that controls the volcanic eruption style in subduction zones. Diffusion coefficients of water in rhyolite melts are discussed in the context of a water diffusion model that was initially proposed for silica glass. We aim to clarify fundamental properties of water diffusion within the silicate melt structure. The model explains the water concentration dependence of water diffusivity in rhyolite melt, considering the effect of the water concentration on activation energy for diffusion. The dependence of the activation energy upon the total water concentration seems to be related to a change in the structure dynamical property of the melt (i.e., viscosity). The empirical relation between water diffusivity and viscosity is also explained by our present model. We conclude that the water diffusion model proposed for silica glass can be applied to rhyolite melt. Water diffusion in rhyolite melt seems to be controlled by the same atomic process as in ...

A general model of water diffusivity in calc-alkaline silicate melts and glasses

The calc-alkaline magma series (basalt, andesite, dacite, and rhyolite) commonly occurring at subduction zones are typically hydrous. Water diffusivity in silicate melt is a crucial parameter controlling the transport and evolution of water throughout magma differentiation. Based on experimental data accumulated over the past three decades, we develop a unified, mechanistic and quantitative model of water diffusion and diffusivity in calc-alkaline silicate melts and glasses. This model involves the following features: (1) the coupling of water diffusion and water speciation; (2) an exponential increase of molecular H2O (H2Om) diffusivity with the mole fraction of total water (X), DH2Om=D0exp(aX), and OH diffusivity (DOH) independent of total water content; (3) the influence of temperature and melt/glass composition on water speciation, the parameter a, and the ratio DOH/D0; and (4) the influence of temperature, composition and pressure on D0. Using the mole fraction of Si among all cations (YSi) to index melt/glass composition, we find that total water (H2Ot) diffusivity at 1wt% H2Ot decreases with increasing YSi (i.e., from basaltic to rhyolitic composition) at high temperature (T>1300K) but this trend is reversed in the low temperature range (T<900K). A vast majority of diffusivity data, including those used for model development and those excluded, can be reproduced by our model within a factor of 2, only slightly greater than experimental uncertainty. This new model allows to trace the evolution of water diffusivity along the liquid line of descent, and is particularly useful when the composition of interest is intermediate between the specific compositions previously investigated.

Isotope fractionation by diffusion in silicate melts: Insights from molecular dynamics simulations

Molecular dynamics simulations were performed to determine the isotope effect on diffusion in SiO2 and MgSiO3 liquids. The influence of an element’s atomic mass on its diffusivity can be expressed in terms of the empirical relation D1D2=m2m1β. For Si, β has a value of ∼0.05 in both SiO2 and MgSiO3 liquids, and is independent of pressure. The exponent β for Mg in MgSiO3 is larger, 0.135 at 1atm, and decreases with pressure, to 0.084 at 50GPa. Varying the mass and concentration of an isotope of one element is also found to have a significant influence on the diffusivity of other elements, due to the cooperative motions of the many atoms that are involved in diffusion. Interdiffusion between basaltic and rhyolitic magmas is inferred to be capable of producing isotope fractionations of tenths of per mil in Si, and tens of per mil in Mg. Significant diffusive fractionation of Si and Mg isotopes is also possible during the growth of olivine phenocrysts, if the growth rate is on the order of cm/yr or faster.

Isotope Fractionation by Thermal Diffusion in Silicate Melts

Isotopes fractionate in thermal gradients, but there is little quantitative understanding of this effect in complex fluids. Here we present results of experiments and molecular dynamics simulations on silicate melts. We show that isotope fractionation arises from classical mechanical effects, and that a scaling relation based on Chapman-Enskog theory predicts the behavior seen in complex fluids without arbitrary fitting parameters. The scaling analysis reveals that network forming elements (Si and O) fractionate significantly less than network modifiers (e.g., Mg, Ca, Fe, Sr, Hf, and U).

Compositional dependence of alkali diffusivity in silicate melts: Mixed alkali effect and pseudo-alkali effect

Compositional dependence of alkali diffusivities in silicate melts is modeled by explicitly considering mixed alkali and “pseudo-alkali” effects. The well-known mixed alkali effect describes that the presence of light alkalis (Li, Na) retards diffusion of heavy alkalis (K, Rb, Cs) and vice versa, which can be attributed to stronger interaction between dissimilar alkalis and reduction of favorable sites for the alkali in question. Due to the same reasons, Ca, which has similar ionic radius as Li and Na but carries more charge and greater field strength, also impedes the migration of light alkalis. In this regard Ca behaves as a “pseudo-alkali,” and I refer to the influence caused by Ca on Li and Na diffusion as the “pseudo-alkali effect,” which belongs to the category of mixed cation effects in glass literature. Pseudo-alkali effect is expected to exist also between other size-matching divalent cations and alkali cations, such as Ba blocking K diffusion. Mixed alkali and pseudo-alkali effects are manifested mainly by an increase in the activation energy for diffusion. Sodium diffusivities for melt compositions ranging between albite, orthoclase, and anorthite reveal that the amplitude of the pseudo-alkali effect is much larger than that of the mixed alkali effect. Furthermore, the activation energy increases more rapidly as more Ca substitutes for Na, but the mixed alkali effect approaches saturation as K substitutes for sodium. A general model based on mixed alkali effect and pseudo-alkali effect, together with a special treatment relating Cs diffusion to melt polymerization, successfully characterizes existing experimental data on alkali diffusion in silicate melts. Enthalpies of mixing between end-member melts (e.g., Ab-Or melts and Ab-An melts) inferred from the model agree well with previous experimental investigations.

Carbon dioxide and argon diffusion in silicate melts: Insights into the CO 2 speciation in magmas

To investigate the influence of temperature and composition on the diffusivities of dissolved carbon dioxide and argon in silicate melts, diffusion experiments were performed at magmatic pressure and temperature conditions in (a) albite melts with excess Na 2O (0–8.6 wt%) and a constant Si/Al ratio of 3, and (b) albite 70quartz 30 to jadeite melts with decreasing SiO 2 content and a constant Na/Al ratio of 1. We obtained diffusion coefficients at 500 MPa and 1323–1673 K. In the fully polymerized system Ab 70Qz 30 – Jd, the change in composition only has a weak effect on bulk CO 2 diffusivity, but Ar diffusivity increases clearly with decreasing SiO 2 content. In the system Ab + Na 2O, bulk CO 2 and Ar diffusivity increase significantly with gradual depolymerisation. The relatively small change in composition on molar basis in the depolymerized system leads to a significantly larger change in diffusivities compared to the fully polymerized Ab 70Qz 30–Jd join. Within error, activation energies for bulk CO 2 and Ar diffusion in both systems are identical with decreasing silica content (Ab + Na 2O: 159 ± 25 kJ mol −1 for bulk CO 2 and 130 ± 8 kJ mol −1 for Ar; Ab 70Qz 30–Jd: 163 ± 16 kJ mol −1 for bulk CO 2 and 148 ± 15 kJ mol −1 for Ar) even though this results in depolymerisation in one system and not the other. Although there is a variation in CO 2 speciation with changing composition as observed in quenched glasses, it has previously established that this is not a true representation of the species present in the melt, with the ratio of molecular CO 2 to carbonate decreasing during quenching. Thus, diffusion coefficients for the individual CO 2 species cannot be directly derived by measuring molecular CO 2 and CO 3 2- concentration-distance profiles in the glasses. To obtain diffusivities of individual CO 2 species, we have made two assumptions that (1) inert Ar can be used as a proxy for molecular CO 2 diffusion characteristics as shown by our previous work and (2) the diffusivity of CO 3 2− can be calculated assuming it is identical to network forming components (Si 4+ and Al 3+). This is derived from viscosity data (Eyring eqn.) and suggests that CO 3 2− diffusion would be several orders of magnitude slower than molecular CO 2 diffusion. The systematics of measured bulk CO 2 diffusivity rates and comparison with the Ar proxy all suggest that the faster molecular CO 2 species is much more dominant in melts than measurements on resulting quenched glasses would suggest. This study has confirmed an observation of surprisingly consistent bulk CO 2 diffusivity across a range of natural compositions were Ar diffusivity significantly increases. This is consistent with an actual increase in molecular CO 2 mobility (similar to Ar) that is combined with an increase in the proportion of the slower carbonate in the melt. These results demonstrate that the CO 2 diffusion and speciation model provides an insight into the transport processes in the melt and is promising and an alternative tool to in situ speciation measurements at magmatic conditions, which at the moment are technically extremely difficult. We present the first high pressure high temperature in situ MIR spectra of a CO 2 bearing albitic glass/melt suggesting that molecular CO 2 is a stable species at high temperature, which is qualitatively consistent with the modelled CO 2 speciation data.

Sulfur in Magmas

Research Article| April 01, 2010 Sulfur in Magmas Nicole Métrich; Nicole Métrich 1Laboratoire Pierre Süe/SIS2M, CNRS-CEA, CE-Saclay, France Search for other works by this author on: GSW Google Scholar Charles W. Mandeville Charles W. Mandeville 2American Museum of Natural History Central Park West at 79th Street, New York, NY 10024, USA E-mail: nicole.metrich@cea.fr; cmandy@amnh.org Search for other works by this author on: GSW Google Scholar Author and Article Information Nicole Métrich 1Laboratoire Pierre Süe/SIS2M, CNRS-CEA, CE-Saclay, France Charles W. Mandeville 2American Museum of Natural History Central Park West at 79th Street, New York, NY 10024, USA E-mail: nicole.metrich@cea.fr; cmandy@amnh.org Publisher: Mineralogical Society of America First Online: 09 Mar 2017 Online ISSN: 1811-5217 Print ISSN: 1811-5209 © 2010 by the Mineralogical Society of America Elements (2010) 6 (2): 81–86. https://doi.org/10.2113/gselements.6.2.81 Article history First Online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Nicole Métrich, Charles W. Mandeville; Sulfur in Magmas. Elements 2010;; 6 (2): 81–86. doi: https://doi.org/10.2113/gselements.6.2.81 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyElements Search Advanced Search Abstract Sulfur is a ubiquitous element whose variable valence states (S2−, S0, S4+, S6+) allow it to participate in a wide variety of geochemical and biogeochemical processes. Depending on its redox state and controlling species, sulfur dissolved in magma may be fractionated into a water-rich phase and sulfur-bearing minerals. Retrieving information on the original sulfur abundance and isotopic signature of a magma is challenging and requires deciphering the different processes that may have operated during its evolution en route to the surface. Advances made in thermodynamic modeling, experimentation on sulfur solubility and diffusion in silicate melts, and microanalytical techniques for probing sulfur's speciation and isotopic signature at the micrometer scale are providing an outstanding picture of sulfur evolution in magmas. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Isotope fractionation in silicate melts by thermal diffusion

The phenomenon of thermal diffusion (mass diffusion driven by a temperature gradient, known as the Ludwig-Soret effect) has been investigated for over 150 years, but an understanding of its underlying physical basis remains elusive. A significant hurdle in studying thermal diffusion has been the difficulty of characterizing it. Extensive experiments over the past century have established that the Soret coefficient, S(T) (a single parameter that describes the steady-state result of thermal diffusion), is highly sensitive to many factors. This sensitivity makes it very difficult to obtain a robust characterization of thermal diffusion, even for a single material. Here we show that for thermal diffusion experiments that span a wide range in composition and temperature, the difference in S(T) between isotopes of diffusing elements that are network modifiers (iron, calcium and magnesium) is independent of the composition and temperature. On the basis of this finding, we propose an additive decomposition for the functional form of S(T) and argue that a theoretical approach based on local thermodynamic equilibrium holds promise for describing thermal diffusion in silicate melts and other complex solutions. Our results lead to a simple and robust framework for characterizing isotope fractionation by thermal diffusion in natural and synthetic systems.

Diffusion Data in Silicate Melts

Atomic scale diffusion in silicate melts plays a critical role in a variety of magmatic processes, as long recognized by geologists (Bowen 1921). Geochemists have investigated diffusion in silicate melts (including stable liquids and supercooled liquids and glasses) using a variety of methods as micro-analytical tools becoming available (e.g., Medford 1973; Jambon and Carron 1976; Magaritz and Hofmann 1978a,b; Hofmann 1980; Shimizu and Kushiro 1984; Zhang et al. 1991a; Koepke and Behrens 2001; Saal et al. 2008). The investigations were aimed at understanding the mechanisms of diffusion, the effect of temperature, pressure, H2O content, f O2, and more generally melt composition on the diffusivities, and to measure the diffusivity values for geological applications. A large database is now available. This chapter reviews diffusion data relevant to magmatic systems. The large body of literature on diffusion in simple-system melts, of interests to glass and ceramic scientists, is not included in this review, nor are the calculated diffusivities from ab initio and molecular dynamics methods. This review covers literature diffusion data (except multicomponent diffusion matrix data, and those of H, C, O and noble gases) in multicomponent silicate melts (the term melts as used in this chapter also includes glasses), including melts with mineral compositions and including glasses. This chapter complements the other chapters on diffusion in silicate melts, which cover H, C and O diffusion (Zhang and Ni 2010, this volume), noble gas diffusion (Behrens 2010, this volume), theories and models of self and tracer diffusion (Lesher 2010, this volume), and multicomponent diffusion (Liang 2010, this volume). We have compiled experimental data on self, tracer and effective binary diffusion in Online Supplementary Table 1 (found at http://www.minsocam.org/MSA/RIM ), with about 3600 entries of individual diffusivity …

Oxygen and Hydrogen Diffusion in Minerals

This chapter provides a summary and review of experimentally determined oxygen and hydrogen volume diffusion in minerals. A very extensive and detailed review of stable isotope exchange processes including oxygen and hydrogen volume diffusion can be found in Cole and Chakraborty (2001) and a detailed review of hydrogen diffusion in minerals, especially nominally anhydrous minerals, can be found in Ingrin and Blanchard (2006). In addition, a detailed review of oxygen and hydrogen diffusion in silicate melts is provided by Zhang and Ni (2010), and oxygen and hydrogen diffusion rates can also be found in the chapters, in this volume, on specific minerals and mineral groups (e.g., Van Orman and Crispin 2010; Cherniak 2010). Interested readers are encouraged to refer to these reviews for additional information on oxygen and hydrogen diffusion in geological materials. In this chapter only volume diffusion through the crystal lattice will be considered. The majority of the experiments employed isotope tracers (e.g., 18O, 2H). The isotope diffusion of hydrogen in the nominally anhydrous minerals is regarded as an impurity tracer diffusion mechanism, and the effective diffusion coefficients obtained from the hydrogen uptake or extraction experiments correspond to chemical interdiffusion of different species. The relationship between the measured effective diffusivity and the hydrogen diffusivity is governed by the specific reaction involved (e.g., see Kohlstedt and Mackwell 1998). Elsewhere in this volume, a detailed outline and discussion of the experimental methods employed in diffusion studies is presented by Watson and Dohmen (2010). Therefore, only a brief overview of methods commonly employed for oxygen and hydrogen diffusion studies is presented below. ### Bulk exchange experiments #### Hydrothermal bulk exchange. Carefully sized powders of either natural or synthetic crystals of the mineral of interest are loaded into a sealed tube with a known amount of 18O and/or 2H- enriched water. …

Volatile diffusion in silicate melts and its effects on melt inclusions

A compendium of diffusion measurements and their Arrhenius equations for water, carbon dioxide, sulfur, flu- orine, and chlorine in silicate melts similar in composition to natural igneous rocks is presented. Water diffusion in silicic melts is well studied and understood, however little data exists for melts of intermediate to basic com- positions. The data demonstrate that both the water concentration and the anhydrous melt composition affect the diffusion coefficient of water. Carbon dioxide diffusion appears only weakly dependent, at most, on the volatile- free melt composition and no effect of carbon dioxide concentration has been observed, although few experi- ments have been performed. Based upon one study, the addition of water to rhyolitic melts increases carbon dioxide diffusion by orders of magnitude to values similar to that of 6 wt% water. Sulfur diffusion in intermedi- ate to silicic melts depends upon the anhydrous melt composition and the water concentration. In water-bearing silicic melts sulfur diffuses 2 to 3 orders of magnitude slower than water. Chlorine diffusion is affected by both water concentration and anhydrous melt composition; its values are typically between those of water and sulfur. Information on fluorine diffusion is rare, but the volatile-free melt composition exerts a strong control on its dif- fusion. At the present time the diffusion of water, carbon dioxide, sulfur and chlorine can be estimated in silicic melts at magmatic temperatures. The diffusion of water and carbon dioxide in basic to intermediate melts is on- ly known at a limited set of temperatures and compositions. The diffusion data for rhyolitic melts at 800°C to- gether with a standard model for the enrichment of incompatible elements in front of growing crystals demon- strate that rapid crystal growth, greater than 10 −10 ms −1 , can significantly increase the volatile concentrations at the crystal-melt interface and that any of that melt trapped by the formation of melt inclusions may not be rep- resentative of the bulk melt. However, basaltic melt inclusions trapped at 1300°C are more likely to contain bulk melt concentrations of water and carbon dioxide.

H 2O diffusion models in rhyolitic melt with new high pressure data

Water diffusion in silicate melts is important for understanding bubble growth in magma, magma degassing and eruption dynamics of volcanos. Previous studies have made significant progress on water diffusion in silicate melts, especially rhyolitic melt. However, the pressure dependence of H 2O diffusion is not constrained satisfactorily. We investigated H 2O diffusion in rhyolitic melt at 0.95–1.9 GPa and 407–1629 °C, and 0.2–5.2 wt.% total water (H 2O t) content with the diffusion-couple method in a piston-cylinder apparatus. Compared to previous data at 0.1–500 MPa, H 2O diffusivity is smaller at higher pressures, indicating a negative pressure effect. This pressure effect is more pronounced at low temperatures. Assuming H 2O diffusion in rhyolitic melt is controlled by the mobility of molecular H 2O (H 2O m), the diffusivity of H 2O m ( D H 2O m ) at H 2O t ≤ 7.7 wt.%, 403–1629 °C, and ≤ 1.9 GPa is given by D H 2 O m = D 0 e x p ( a X ) , with D 0 = e x p ( 13.375 + 1.8875 P − 12939 + 3625.6 P T ) , and a = − 37.256 + 75884 T , where D 0 is in µm 2/s, X is mole fraction of H 2O t on a single oxygen basis, T is temperature in K, and P is pressure in GPa. H 2O t diffusivities ( D H 2O t , in µm 2/s) can be calculated from H 2O m diffusivity, or directly from the following expression: l n ( D H 2 O t / X ) = 13.47 − 49.996 X + 7.0827 X + 1.8875 P − 9532.3 − 91933 X + 13403 X + 3625.6 P T . At low H 2O t content (up to 2 wt.% if an error of a factor of 2 is allowed), H 2O t diffusivity is approximately proportional to H 2O t content: D H 2 O t = C C 0 e x p ( 9.5279 + 1.8875 P − 9698.5 + 3625.6 P T ) , where C is H 2O t content in wt.% and C 0 is 1 wt.%. The new expressions for H 2O diffusion not only reproduce our own data, but also match data in literature from different laboratories and using different methods, indicating good inter-laboratory and multi-method consistency. The new expressions cover a wide range of geological conditions, and can be applied to H 2O diffusion in rhyolitic melts in various volcanic and magmatic processes.

Molecular H2O as carrier for oxygen diffusion in hydrous silicate melts

Dissolved water is known to dramatically enhance oxygen diffusion in silicate melts, glasses and minerals. A quantitative theory has been developed to explain this phenomenon by transport via molecular H2O diffusion [Y. Zhang, E.M. Stolper, G.J. Wasserburg, Diffusion of a multi-species component and its role in the diffusion of water and oxygen in silicates, Earth Planet. Sci. Lett., 103 (1991) 228–240.]. Here we report experimental confirmation of the theory for rhyolitic melts by measuring both H2O and 18O diffusion profiles in a single experiment. In sorption experiments at 100 MPa and temperatures from 1041 to 1136 K isotopically enriched water diffused into doubly polished rhyolitic glass wafers. H2O profiles were analyzed by infrared spectroscopy and 18O profiles by SIMS. 18O diffusivities were found to be 1–2 orders of magnitude slower than bulk water diffusivities but 3–4 orders of magnitude faster than Eyring diffusivities calculated from viscosity. The data show that oxygen “self” diffusion under hydrothermal conditions is due to molecular H2O diffusion, not due to the self diffusion of oxygen itself. With this confirmation, experimental data on H2O diffusion in silicate melts can be used to infer 18O diffusion under hydrothermal conditions, and hydrothermal oxygen diffusion data in silicate minerals can be used to infer H2O diffusivity, as long as the concentration or solubility of H2O in the given phase is known.

シリケイトメルト中の水の拡散

Water diffusion in silicate melts is a controlling factor of magma ascent process in volcanic eruption, because it dominates the rates of bubble nucleation and growth in magmas and the decrease of water contents by water diffusion causes drastic changes in the physical properties of silicate melts (viscosity and density). This paper reviews experimental studies for water diffusion in rhyolitic to basaltic melts and glasses. In rhyolitic and dacitic melts (polymerized silicate melts), water mainly dissolves as hydroxyl group (OH) and molecular water (H2O), but only H2O is considered as the mobile species. The H2O diffusivities in rhyolite and dacite increase with water contents and temperature. The mechanism of water diffusion in andesite to basalt (depolymerized silicate melts) is still unclear, but some studies presented the data of total water (OH + H2O) diffusivities in andesite and basalt by assuming the diffusion of one component water. Those data show that the diffusivity of total water increases with melt depolymerization (from rhyolite to basalt) at high temperatures (e.g., > 1400 °C at 0.7 wt% water), but the magnitude relation inverts at the lower temperatures due to the difference of temperature dependences of total water diffusivity in rhyolite to basalt. Recently, a few studies explored the compositional dependence of total water diffusivity and expressed the total water diffusivity as a function of the SiO2 content or the NBO/T value. To test and develop those models, additional experimental data are needed in the future studies, and the developed-comprehensive model for water diffusion in silicate melts and glasses will make a significant contribution to understanding of volcanic eruptions.

Uphill diffusion and a new nonlinear diffusion equation in ternary non-electrolyte system

Diffusion in silicate melts often shows uphill diffusion, the diffusion of a component up its own concentration gradient. This paper presents a new nonlinear diffusion equation which can describe uphill diffusion in a ternary system and provide a criterion in what conditions uphill diffusion will take place. Cross coefficients D ij ( i≠ j) in a multi-component diffusion equation describe the strength in coupling between diffusional flows, which may cause uphill diffusion. Irreversible thermodynamics shows that cross coefficients are dependent on concentration, although their functional form is unknown. To estimate it, this paper combines an irreversible thermodynamic approach by Miller [Miller, D.G., 1959. Ternary isothermal diffusion and the validity of the Onsager reciprocity relations. J. Phys. Chem., 63, pp. 570–578] and an eigenvector analysis by Gupta [Gupta, P.K., Cooper, Jr., A.R., 1971. The [ D] matrix for multi-component diffusion. Physica, 54. pp. 39–59]. The functional forms satisfying the two conditions above are: D 1 2= φ 1( D 1 1− D 2 2) and D 2 1= φ 2( D 22− D 1 1), where φ 1 and φ 2 are concentrations in mole fraction of components 1 and 2, respectively, and D 1 1 and D 2 2 are proper diffusion coefficients. These cross coefficients give a nonlinear diffusion equation which satisfactorily describes uphill diffusion. Perturbed solutions together with numerical solutions of the nonlinear diffusion equations are presented and discussed in detail to clarify the nature of uphill diffusion.

The mechanisms of water diffusion in polymerized silicate melts

Diffusion of water was experimentally investigated for melts of albitic (Ab) and quartz-orthoclasic (Qz29Or71, in wt %) compositions with water contents in the range of 0 to 8.5 wt % at temperatures of 1100 to 1200 °C and at pressures of 1.0 and 5.0 kbar. Apparent chemical diffusion coefficients of water (D water) were determined from concentration-distance profiles measured by FTIR microspectroscopy. Under the same P-T condition and water content the diffusivity of water in albitic, quartz-orthoclasic and haplogranitic (Qz28Ab38 Or34, Nowak and Behrens, this issue) melts is identical within experimental error. Comparison to data published in literature indicates that anhydrous composition only has little influence on the mobility of water in polymerized melts but that the degree of polymerization has a large effect. For instance, Dwater is almost identical for haplogranitic and rhyolitic melts with 0.5–3.5 wt % water at 850 °C but it is two orders of magnitude higher in basaltic than in haplogranitic melts with 0.2–0.5 wt % water at 1300 °C. Based on the new water diffusivity data, recently published in situ near-infrared spectroscopic data (Nowak 1995; Nowak and Behrens 1995), and viscosity data (Schulze et al. 1996) for hydrous haplogranitic melts current models for water diffusion in silicate melts are critically reviewed. The NIR spectroscopy has indicated isolated OH groups, pairs of OH groups and H2O molecules as hydrous species in polymerized silicate melts. A significant contribution of isolated OH groups to the transport of water is excluded for water contents above 10 ppm by comparison of viscosity and water diffusion data and by inspection of concentration profiles from trace water diffusion. Spectroscopic measurements have indicated that the interconversion of H2O molecules and OH pairs is relatively fast in silicate glasses and melts even at low temperature and it is inferred that this reaction is an active step for migration of water. However, direct jumps of H2O molecules from one cavity within the silicate network to another one can not be excluded. Thus, we favour a model in which water migrates by the interconversion reaction and, possibly, small sequences of direct jumps of H2O molecules. In this model, immobilization of water results from dissociation of the OH pairs. Assuming that the frequency of the interconversion reaction is faster than that of diffusive jumps, OH pairs and water molecules can be treated as a single diffusing species having an effective diffusion coefficient The shape of curves of Dwater versus water content implies that increases with water content. The change from linear to exponential dependence of Dwater between 2 and 3 wt % water is attributed to the influence of the dissociation reaction at low water content and to the modification of the melt structure by incorporation of OH groups.