Journal of Petrology Advance Access originally published online on August 31, 2005
Journal of Petrology 2006 47(2):231-254; doi:10.1093/petrology/egi073
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Dissolution of Quartz, Albite, and Orthoclase in H2O-Saturated Haplogranitic Melt at 800°C and 200 MPa: Diffusive Transport Properties of Granitic Melts at Crustal Anatectic Conditions
SCHOOL OF GEOLOGY AND GEOPHYSICS, UNIVERSITY OF OKLAHOMA, NORMAN, OK 73019, USA
RECEIVED DECEMBER 26, 2003; ACCEPTED JULY 19, 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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We have conducted experiments on dissolution of quartz, albite, orthoclase, and corundum into H2O-saturated haplogranite melt at 800°C and 200 MPa over a duration of 120–1488 h with the aim of ascertaining the diffusive transport properties of granitic melts at crustal anatectic temperatures. Cylinders of anhydrous starting glass and a single mineral phase (quartz or feldspar) were juxtaposed along flat and polished surfaces inside gold or platinum capsules with
10 wt % added H2O. Concentration profiles in glass (quenched melt) perpendicular to the mineral–glass interfaces and comparison with relevant phase diagrams suggest that melts at the interface are saturated in the dissolving phases after 384 h, and with longer durations the concentration profiles are controlled only by diffusion of components in the melt. The evolution of the concentration profiles with time indicates that uncoupled diffusion in the melt takes place along the following four linearly independent directions in oxide composition space: SiO2, Na2O, and K2O axes (Si-, Na-, and K-eigenvectors, respectively), and a direction between the Al2O3, Na2O, and K2O axes (Al-eigenvector), such that the Al/Na molar ratio is equal to that of the bulk melt and the Al/(Na + K) molar ratio is equal to the equilibrium ASI (= mol. Al2O3/[Na2O + K2O]) of the melt. Experiments in which a glass cylinder was sandwiched between two mineral cylinders—quartz and albite, quartz and K-feldspar, or albite and corundum—tested the validity of the inferred directions of uncoupled diffusion and explored long-range chemical communication in the melt via chemical potential gradients. The application of available solutions to the diffusion equations for the experimental quartz and feldspar dissolution data provides diffusivities along the directions of the Si-eigenvector and Al-eigenvector of (2·0–2·8) x 10–15 m2/s and (0·6–2·4) x 10–14 m2/s, respectively. Minimum diffusivities of alkalis [(3–9) x 10–11 m2/s] are orders of magnitude greater than the tetrahedral components of the melt. The information provided here determines the rate at which crustal anatexis can occur when sufficient heat is supplied and diffusion is the only mass transport (mixing) process in the melt. The calculated diffusivities imply that a quartzo-feldspathic source rock with initial grain size of 2–3 mm undergoing hydrostatic, H2O-saturated melting at 800°C (infinite heat supply) could produce 20–30 vol. % of homogeneous melt in less than 1–10 years. Slower diffusion in H2O-undersaturated melts will increase this time frame. KEY WORDS: chemical diffusion; haplogranite; mineral dissolution experiments; crustal anatexis
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Mechanical mixing during melt segregation and transport (Wickham, 1987a
, 1987b; Brown et al., 1995) may play a role in homogenizing granitic magmas, but diffusion in the melt ultimately controls the attainment of chemical equilibrium (e.g. Lesher, 1994; Shaw, 2004). Understanding the diffusive transport properties of silicate melts helps to constrain the time frames of some igneous processes that entail the production or homogenization of silicate liquids (e.g. Watson, 1982, 1996; Baker, 1990, 1991; Sawyer, 1991; Lesher, 1994; Barbero et al., 1995; Harris et al., 2000; Acosta-Vigil et al., 2002). Knowledge of the diffusive transport properties of granitic melts can shed light on speciation in the melt that can be tested or augmented by spectroscopic studies [e.g. compare Wolf & London (1994) with Mysen et al. (1981, 1999), Gan & Hess (1992) and Toplis & Schaller (1998)]. Accurate information on liquid speciation is essential for constructing rigorous thermodynamic models. The diffusion coefficient matrix (D) is a product of the Onsager kinetic matrix (L) and a matrix of thermodynamic chemical potentials (µ); thermodynamic properties of the melts can be retrieved through a knowledge of D (e.g. Chakraborty, 1995).
This study complements that of Acosta-Vigil et al. (2002, 2005) in the investigation of diffusivities and directions of uncoupled chemical diffusion in composition space (e.g. Chakraborty, 1995) in H2O-saturated haplogranitic melts at typical crustal anatectic temperatures. To obtain this information we conducted experiments on dissolution of quartz, albite, orthoclase, and corundum into metaluminous haplogranitic melt at 800°C and 200 MPa H2O. The starting haplogranite melt had the composition of the 200 MPa H2O minimum (Tuttle & Bowen, 1958), and the 115°C interval between eutectic and experimental temperature ensured mineral dissolution and the development of oxide concentration gradients in the melt. Concentration profiles of the oxide components in the glass (quenched melt) were measured perpendicular to the mineral–glass interfaces. Published solutions to the diffusion equations were used, together with constraints provided from the evolution of concentration profiles with time, to determine part of the diffusion matrix of the system by inversion of the concentration profiles. The results confirm the distinctly different behavior of Na and K in relation to Al gradients in the melt (Acosta-Vigil et al., 2002), and can be used to estimate the rate at which melting and melt homogenization can occur during crustal anatexis in an end-member case of infinite (transitory) heat supply and diffusion in the melt as the only mixing mechanism.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Starting materials and experimental methods
The starting materials used in this study include hydrothermal quartz (McCurtain County, Oklahoma, USA), albite (Copelinha, albite I, and Urucum, albite II, both from pegmatite mines in Minas Gerais, Brazil), orthoclase (Little Three pegmatite, California, USA), corundum (source unknown), and synthetic anhydrous metaluminous haplogranite glass (Corning Lab Services, New York, USA) with the nominal composition of the haplogranite eutectic at 200 MPa H2O (Tuttle & Bowen, 1958
). Table 1 shows mean electron microprobe analyses of minerals and starting anhydrous glass and some experimental glasses.
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Mineral and glass cylinders
1·7 or 2·5 mm in diameter and 2–4 mm in length were prepared by drilling the starting materials with diamond coring bits. Mineral and glass cylinder surfaces to be in contact during the experiment were polished flat to a 0·3 µm alumina grit finish. Cores were cleaned with de-ionized, ultra-filtered (DIUF) water in an ultrasonic bath. Mineral and glass cores were loaded inside platinum or gold capsules (1·8 or 2·6 mm i.d.) with enough DIUF water (10 wt %) to ensure saturation of the melt. Capsules were sealed by d.c. argon plasma arc welding while keeping the capsule frozen to prevent volatilization of added water. To ensure no leakage, capsules were placed overnight in an oven at 130°C and then reweighed.
Experiments were conducted in water-pressurized NIMONIC 105® cold-seal pressure vessels inclined 15° from the horizontal. Capsules were placed with their long axes parallel to the vessels, such that the mineral–melt interfaces remained near vertical during the experiment. Target temperature and pressure were 800°C and 200 MPa, respectively; variations in these target values during the experiments were 2°C and 1 MPa. Temperature was monitored with an internal chromel–alumel thermocouple, and pressure was monitored with a factory-calibrated Heise bourdon tube gauge; uncertainties in temperature and pressure are <10°C and <10 MPa, respectively. The samples were first pressurized cold, and then the temperature was raised to the target value at a rate of 40°C/min. Oxygen fugacity was controlled indirectly by the composition of the reaction vessels at 0·5 log units below the Ni–NiO buffer, based on the fO2 dependence of tin solubility in H2O-saturated haplogranite melts [measured by Wolf et al. (1994) and compared with Taylor & Wall (1992) and Linnen et al. (1996)]. Experiments were quenched isobarically at a rate of 75°C/min using a jet of air and water. After quench, capsules were weighed, punctured, placed in a desiccator overnight, and then reweighed to check for the loss of free water (indicating H2O saturation at run conditions and providing an estimate of water dissolved into the melt). Products were mounted in Buehler Transoptic® thermal plastic, ground to the center of the cylinders, and polished to a final grit size of 0·3 µm for microprobe analysis.
Two series of experiments were conducted (Table 2): (1) those in which a core of quartz, albite, or orthoclase was juxtaposed against a core of haplogranitic glass (single-mineral dissolution experiments); (2) experiments in which a cylinder of glass was sandwiched between cores of quartz and albite, quartz and orthoclase, or albite and corundum (‘sandwiched glass’ experiments). The single-mineral dissolution experiments were conducted to obtain concentration gradients of the different oxide components in the liquid resulting from diffusion along different directions in composition space (defined by mineral–glass vectors). The sandwiched glass experiments were conducted to test the validity of the inferred directions of uncoupled diffusion in the melt (see below), to explore the long-range chemical communication in melt via chemical potential gradients (e.g. see the results of the albite–glass–corundum sandwich experiment), and to understand the generation of granite liquids in nature throughout intermediate steps between ‘simple’ single-mineral dissolution experiments and complex natural rock melting experiments (e.g. Mehnert et al., 1973; Büsch et al., 1974; Arzi, 1978; Acosta-Vigil et al., 2004, and unpublished work in review).
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Analytical methods
Starting materials and experimental products were analyzed with a Cameca SX-50 electron microprobe at the University of Oklahoma. Matrix reduction used the PAP correction algorithm (Pouchou & Pichoir, 1985
). Mineral phases were analyzed using an accelerating voltage of 20 kV, a beam current of 10 nA, and a 3 µm spot size. Counting times for all elements except Ca, Ba, Sr and Fe were 30 s on peak, 45 s for Ca, Ba and Sr, and 60 s for Fe. Calculated 3
minimum detection limits (in wt %) were 0·06 for SiO2, 0·03 for Al2O3 and Na2O, 0·01 for CaO and K2O, 0·02 for Fe2O3, 0·05 for P2O5, 0·09 for BaO, and 0·07 for SrO. The glasses were analyzed using an accelerating voltage of 20 kV, a beam current of 2 nA, and a 20 µm defocused spot. Sodium, potassium, and aluminum were concurrently analyzed first to minimize alkali volatilization and attendant changes in elemental ratios. Counting times were 30 s on peak for all elements, yielding calculated 3 minimum detection limits of 
0·02 wt % for Na2O, K2O and Al2O3, and 0·05 wt % for SiO2. Based on counting statistics, analytical uncertainties relative to their reported concentrations in glass are in the range of 0·5–1·0 % for SiO2 and Al2O3, and 1·5–3·0 % for Na2O and K2O. Using these methods, the loss of sodium and grow-in of aluminum and silicon intensities during analysis are negligible and comparable with or less than the analytical uncertainties, so that no corrections to the data are needed (Morgan & London, 1996). H2O concentrations in glass are calculated by difference of the electron microprobe analyses totals from 100%. The accuracy of water by difference, using the current analytical methods, is equal to or better than ±10% relative (Morgan & London, 1996; Acosta-Vigil et al., 2003). The maximum uncertainty for the reported ASI values is ±0·035 (ASI = mol. Al2O3/[CaO + Na2O + K2O]), calculated by the propagation of errors. To ensure (1) that diffusion in the melt occurred only in the direction perpendicular to the mineral–melt interface, and (2) statistical accuracy at critical points in the diffusion profile, we conducted several analytical transverses throughout the experimental glasses: three transverses perpendicular to the mineral–melt interface for each experiment—one at the center of the cylinder and two more at 100–200 µm from each of the cylinder sides—plus two additional transverses parallel to the interface at distances of 30 and 100 µm from the interface. |
RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Run products and dissolution rates
The experiments involved dissolution of the starting mineral phase(s) into the melt, with no significant new mineral growth in the silicate liquid or at the mineral–melt interface. Mineral–melt interfaces for quartz and corundum remained flat during dissolution, but these became irregular at the 10–100 µm scale during feldspar dissolution (Fig. 1). Back-scattered electron imaging shows no recrystallization or alteration of quartz, orthoclase, or corundum during the experiments. Albite, however, shows minor recrystallization to a binary feldspar solid solution, mostly along fractures connected to the interface (Fig. 1, Table 3). With this exception, relict feldspars close to the interface melt show no change in composition with respect to the starting feldspars (Table 3).
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Dissolution rates were calculated by mass balance using starting and final SiO2 and Al2O3 concentration profiles in the glass, together with quartz, albite, and orthoclase compositions. This method indicates a retreat of the interfaces proportional to the square root of time after
120–384 h (Fig. 2), suggesting that dissolution is interface reaction-controlled up to 120–384 h and becomes diffusion-controlled afterwards (e.g. Cooper & Kingery, 1964).
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Chemical composition of the glasses
All experimental glass columns are characterized by (1) a reaction–diffusion zone adjacent to the mineral–glass interfaces, hereafter referred as the ‘boundary layer’, in which gradients in the concentration profiles of the oxide components are present, and (2) a zone beyond the boundary layer in which the concentration profiles are flat.
Single-mineral dissolution experiments
After 384 h, the compositions of glasses within the boundary layer at 20 µm from mineral–melt interfaces lie very close to the liquidus surfaces for the respective minerals in the H2O-saturated quartz–albite–orthoclase system at the experimental conditions (5–10 normative wt % off the 800°C liquidus isotherms as taken from Tuttle & Bowen, 1958) (Fig. 3). Feldspars and interface melts are not strictly in equilibrium because the feldspars should be binary and not end-members (see Tuttle & Bowen, 1958). Albite shows signs of very local equilibration with the interface melt in the timeframe of the experiments; orthoclase does not. The location of the interface melts very close to the liquidus surfaces after 384 h of run duration, however, strongly suggests that they are saturated in the dissolving mineral phases.
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), albite (
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) dissolution experiments. Each point represents the mean value of three analyses along the interface. Numbers close to the points refer to run duration in hours. The curved lines correspond to the projections of the liquidus surfaces of quartz and feldspar in the haplogranite system at the experimental conditions (from Tuttle & Bowen, 1958The dissolution of quartz vs feldspars produced contrasting concentration profiles in the melt. Quartz dissolution involved mainly addition of silica and dilution of alumina and alkalis in the boundary layer. Beyond the boundary layer, the concentrations of silica, alumina, and alkalis are similar to those in the starting hydrated glass (Table 4, Fig. 4). The molar ratios Al/Na, Al/K, and Na/K remained nearly constant throughout the entire melt column and equal to the values in the starting hydrous glass (Fig. 4, see insets). These facts indicate that diffusion of silicon occurs only within the boundary layer and does not involve coupling with any other component in melt.
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Upon dissolution of albite, the concentrations of alumina, sodium, and potassium in the glass increase monotonically within the boundary layer toward the mineral–glass interface, whereas silica decreases (Table 4, Fig. 5). Beyond the boundary layer, the concentrations of alumina and silica and the Al/Si molar ratios are similar to those in the starting hydrated glass, whereas alkali concentrations and Na/Si and K/Si molar ratios change significantly with respect to the starting glass (Table 4). This indicates that diffusion of aluminum and silicon takes place only within the boundary layer, whereas alkalis diffuse throughout the entire (
2000–4000 µm long) melt column. This further reveals (1) that alkalis can diffuse much faster than silicon and aluminum, and (2) that aluminum and sodium decouple upon entering the melt during the dissolution of albite. By ‘decouple’ we mean that although a certain amount of sodium or potassium diffuses together with aluminum (the concentration profiles of alkalis match exactly those of alumina in all the runs), the rest diffuses further beyond the boundary layer and therefore diffuses independently of aluminum. Although the shapes of the concentration profiles for both alkalis are similar in albite dissolution runs, the direction of diffusion for sodium is opposite to that for diffusion of potassium: sodium diffuses downhill away from the interface, producing an increase in its concentration throughout the melt column with respect to the starting glass, and potassium diffuses uphill toward the interface, with an overall decrease in its concentration (Fig. 5). These changes in concentration are above analytical uncertainties.
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Orthoclase dissolution experiments yield observations comparable with those for albite (Fig. 6). The migration of aluminum and silicon takes place only within the boundary layer, whereas alkalis diffuse throughout the entire melt reservoir. Upon entering the melt, aluminum and potassium (from orthoclase) become decoupled. Potassium diffuses down its concentration gradient away from the interface, increasing its concentration throughout the melt, whereas sodium diffuses uphill toward the interface, decreasing its concentration in the melt beyond the boundary layer.
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We note that in all the feldspar dissolution experiments, the Al/Na molar ratio is constant at any time throughout the entire melt (Table 4, Figs 5 and 6). As the Al/Na ratio in the starting glass (
1·75) is different from that in albite (1) and orthoclase (>>1·75), and diffusion of aluminum occurs only within the boundary layer, these observations require that sodium diffuses throughout the entire melt column to erase any gradient in the Al/Na molar ratio. Despite the large fluxes of alkalis in opposite directions, the ASI throughout the entire melt column at any experimental time remains constant within analytical uncertainty, and equal to the ASI of melt at equilibrium, ASI 1·025 ± 0·035.
Sandwiched glass experiments
Metaluminous haplogranite system. The experiments in which glass was sandwiched between quartz and feldspars produced results comparable with those of the single-mineral dissolution experiments (Table 4, Fig. 7). Silica concentration in the glass increases toward quartz and decreases toward feldspars. Alumina and alkali concentrations increase toward feldspars and decrease toward quartz. The Al/Na molar ratio is constant throughout the glass. The Al/K molar ratio is constant except within the boundary layer close to feldspars, where it increases toward the interface. The ASI is constant throughout the glass except in the boundary layers close to feldspars, where it increases slightly toward the interfaces, although it remains constant within analytical uncertainty.
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Peraluminous haplogranite system. The only significant differences between the sandwich experiment in the peraluminous system (corundum–glass–albite) and those in the metaluminous system are the greater ASI values throughout the entire glass and the notable increase in ASI within the boundary layers toward corundum and, importantly, toward albite as well (Table 4, Fig. 7).
Effects of glass hydration–melting and an H2O fluid phase
The starting glass cores are anhydrous. For the correct interpretation of results, it is important to determine if hydration–melting of the glass cores is complete prior to mineral dissolution. A study of H2O diffusion (Acosta-Vigil et al., 2005) showed that cylinders of the starting dry haplogranite glass 3·5 mm in diameter and 4–6 mm long (larger than in the current study) are completely hydrated and compositionally homogeneous after 48–60 h at the current run conditions. After 69 h of reaction in orthoclase dissolution experiment Acasi 286 (Table 2), glass farther than 30–50 µm from the mineral–melt interface is homogeneous (concentration profiles are flat) and compositionally identical to the starting hydrated glass CG 1 (Tables 1 and 2, Fig. 8a). This demonstrates that dissolution of orthoclase was just beginning after about 69 h, an experimental duration longer than that required for complete hydration–melting of the glass cylinders. Therefore, mineral dissolution in the current experiments is initiated in homogeneous, hydrous liquid.
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During initial cold pressurization of capsules, the gold or platinum tubes collapse around the length of the cores, squeezing almost all of the added water to strain shadows at the ends of the capsule. After hydration–melting of the glass cores, there is about 4–5 wt % free H2O fluid inside the capsule in contact with the mineral and melt cylinders. To verify that oxide concentration profiles in glass were produced only by dissolution of the mineral phase into melt at the interface and transport of components through the liquid, and was not influenced by lateral diffusion from the sides of the melt column via an aqueous vapor film, we conducted a 384 h orthoclase dissolution experiment using a glass core previously hydrated at the experimental conditions (Acasi 292, Table 2). An additional 1 wt % water was added to the capsule to keep the melt just at H2O saturation. Concentration profiles produced in this experiment are functionally identical to those in a 384 h orthoclase dissolution experiment starting with an anhydrous glass core. Small differences in K2O and Al/K profiles (Fig. 8b) are explained by the different lengths of starting glass cores (the starting anhydrous core being slightly shorter, implying a smaller volume for K diffusion as compared with the pre-hydrated core). Otherwise the behavior in both experiments is exactly the same, with aluminum diffusing about 250 µm away from the interface, sodium diffusing toward the interface throughout the entire melt reservoir to maintain a constant Al/Na ratio, and K diffusing away from the interface to maintain a constant ASI throughout the melt column. No irregular concentration profiles corresponding to sidewall diffusion from the melt–capsule interface were found in the current experiments [compare with fig. 2 of Acosta-Vigil et al. (2002)
and relevant discussion]. These observations confirm that neither an excess H2O fluid phase in the capsule nor starting with anhydrous glass cylinders has any effect on the resultant concentration profiles in experimental glasses. |
ORIGIN OF THE CONCENTRATION PROFILES IN EXPERIMENTAL GLASSES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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There are three main processes that potentially can govern the concentration profiles of melt components during the dissolution of a mineral phase into the melt: (1) the interface reaction or process by which mineral components detach from the mineral surface to enter the melt; (2) the diffusion of components through the melt; (3) convection in the melt (e.g. Donaldson, 1985
; Zhang et al., 1989). Convection did not occur or was not significant in these experiments because: (1) the concentrations of the oxide components in the glasses vary monotonically with the distance from the mineral–melt interface (compare with Shaw, 2000); (2) with increasing time the width of the melt boundary layer increases whereas the mineral dissolution rate decreases [Table 2 and Fig. 2; compare with Watson (1982)]. There are three conditions to be fulfilled for the profiles to be solely controlled by diffusion in the melt: (1) the composition of the interface melt is at the liquidus of the dissolving mineral phase at the conditions of the experiments; (2) the retreat of the mineral–melt interface is proportional to the square root of time; (3) the concentration profiles overlap when plotted against distance normalized to the square root of time (e.g. Crank, 1975; Zhang et al., 1989; Liang, 1999). Regarding condition (1), Fig. 3 shows that after 384 h the interface melts are located very close to the liquidus surfaces of quartz and feldspars. Figure 2 shows that condition (2) is reasonably satisfied after 384 h of experimental time. Figure 9 shows that condition (3) also seems to hold after 384 h. However, we call attention to the observation that concentration profiles in albite and orthoclase dissolution experiments cannot rigorously overlap when plotted against distance normalized to time, because of the uphill diffusion of melt components throughout the entire melt column and the finite nature of the melt reservoir. Condition (3) seems to hold only for the case of semi-infinite melt reservoirs (see Acosta-Vigil et al., 2002). We conclude that concentration profiles in the current experiments are controlled both by the kinetics of the interface reaction and diffusion in melt during an initial period of 240–384 h, but solely by diffusion of components in melt afterwards. Therefore, concentration profiles in experiments with durations 
384 h can be reasonably described mathematically in terms of chemical diffusion in a multicomponent system.
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MULTICOMPONENT DIFFUSION MODELING |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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General approach
A background on multicomponent chemical diffusion can be found elsewhere (e.g. Trial & Spera, 1994
; Chakraborty, 1995). The current modeling aims to elucidate all or part of the diffusion matrix, D. The matrix D contains information about the directions in composition space along which diffusion is uncoupled (eigenvectors of D, 
i), and the diffusivities along these directions (eigenvalues of D, 
i) at the given P–T–X conditions (e.g. Chakraborty, 1995). Our approach to gain information about the eigenvectors is different from previous ones. Previous studies have used results from diffusion couple experiments (or isothermal interdiffusion experiments; Trial & Spera, 1994) for determining the entire diffusion matrix in silicate liquids (e.g. Kress & Ghiorso, 1993; Chakraborty et al., 1995a; Liang et al., 1996; Mungall et al., 1998). Rather than diffusion couples, we began with dissolution experiments utilizing phases that contain only a single oxide component: corundum (Acosta-Vigil et al., 2002), quartz (this work), and H2O (Acosta-Vigil et al., 2005). This approach produces relatively simple concentration profiles in the melt because diffusion occurs mainly along the single uncoupled direction that is responsible for the diffusive transport of the oxide component (SiO2, Al2O3, H2O) added to the interface melt. Therefore, information about individual directions of uncoupled diffusion in the system can be obtained directly from the study of experimental concentration profiles. Diffusion data along additional directions of uncoupled diffusion in compositional space are then derived by dissolution of more complex mineral phases (e.g. feldspars: this work), each of which adds only one new component (e.g. K or Na) to the previously defined system. In this manner, diffusion data for all of the principal components in the granitic system can be derived from a succession of glass hydration–melting and single-mineral dissolution experiments. These results can be tested and verified afterward via additional complex mineral dissolution experiments (e.g. Acosta-Vigil et al., 2002) or with sandwiched glass experiments (this work). In a system with N components, D is an N – 1 by N – 1 matrix, and the number of linearly independent eigenvectors is N – 1, each of them with an associated eigenvalue. The eigenvectors represent a new set of chemical components whose fluxes are independent of each other (e.g. Chakraborty, 1995). Each eigenvector is related to any other set of chemical components (e.g. oxide components) by N – 1 coefficients, which specify the proportions of the old components (oxides) in that particular eigenvector. P is an N – 1 by N – 1 matrix made of the eigenvector coefficients arranged in columns. For instance, Pij is a coefficient of P that refers to the proportion of the old component i in the eigenvector j. As eigenvectors represent directions of uncoupled diffusion, these coefficients refer to the relative amounts of old components migrating at the same time and speed (see also Mungall et al., 1998). We rely on this observation to gain information on the eigenvectors (matrix P) from the analysis of the oxide concentration profiles. Finally, to elucidate the eigenvalues of D we inverted the concentration profiles in melt produced by diffusion along three directions in composition space: quartz–, albite–, and orthoclase–water-saturated metaluminous haplogranite (Fig. 10). The procedure has been used previously (e.g. Trial & Spera, 1994; Mungall et al., 1998; Acosta-Vigil et al., 2002) and the reader is referred to these publications for a detailed explanation. During inversion of concentration profiles we used the information gained on the eigenvectors as additional constraints.
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Eigenvectors of D: constraints from compositional profiles
Quartz dissolution experiments show that neither aluminum nor alkalis are coupled with the diffusion of silica, because incorporation of silica into the melt produces proportionate dilution of the other components (compare with Sato, 1975
; Watson, 1982; Chekhmir & Epel'baum, 1991; Shaw, 2000; Acosta-Vigil et al., 2002). The collinearity of starting hydrous melt, quartz, and melt compositions from the boundary layers of all the quartz dissolution experiments demonstrates this conclusion (Fig. 11). In contrast, moderate coupling of CaO with SiO2 in the system CaO–Al2O3–SiO2 at 1500°C and 1 GPa produces compositions of bulk and boundary layer melts that are not collinear with quartz (Liang, 1999, fig. 5). Therefore, the coefficients of P associated with Si (the direction in composition space along which silica migrates to erase its concentration gradients), referenced to a six-oxygen oxide component stoichiometry, are PAlSi 0, PNaSi 0, PKSi 0, and PSiSi = 1 (Table 5).
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Feldspar dissolution experiments show that the migration of alkalis through melt does not require concomitant migration of silicon or aluminum; hence, neither silicon nor aluminum is coupled with the diffusion of alkalis. Although Na and K diffuse in the same direction during the dissolution of corundum and andalusite (Acosta-Vigil et al., 2002
), these components diffuse in opposite directions in the current feldspar dissolution experiments at the same P–T–X conditions, suggesting that Na and K can diffuse independently of each other. The coefficients for K are PAlK 0, PNaK 0, PKK 1 and PSiK 0, and those for Na are PAlNa 0, PNaNa 1, PKNa 0 and PSiNa 0 (Table 5).
Feldspar dissolution experiments also show that the migration of aluminum through melt requires concomitant migration of alkalis and, therefore, sodium and potassium are coupled with the diffusion of aluminum. The constant Al/Na molar ratio throughout the entire melt column at any experimental time implies that sodium is coupled with aluminum during diffusion along Al, and that the relative molar amounts of Al and Na diffusing together are equal to the molar Al/Na ratio in the bulk melt (boundary layer + rest of melt cylinder). The constant ASI throughout the entire melt reservoir, equal to the ASI of melt at equilibrium, implies that potassium is also coupled with aluminum, and that the amount and direction of potassium diffusing with aluminum (and sodium) is such that the molar ratio Al/(Na + K) of this diffusing component is equal to the ASI of melt at equilibrium (see Fig. 12a). Following the previous observations we derive the following coefficients for Al (always referenced to the six-oxygen oxide component stoichiometry): PAlAl 1, PNaAl 0·184, PKAl 0·142 and PSiAl 0 (Table 5).
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The orientations of the eigenvectors are invariant properties of the system at fixed P–T–X conditions and, therefore, are independent of the compositional direction along which diffusion takes place (e.g. Chakraborty, 1995
). Together with Acosta-Vigil et al. (2002), the directions of uncoupled diffusion described above have been derived from diffusion concentration profiles along four different directions that intersect at the starting glass composition, three of them at high angle (Fig. 10). In addition, melt concentration profiles in the metaluminous quartz–feldspar sandwiched glass experiments are comparable with those in the single-mineral experiments. This supports the validity of the inferred directions of uncoupled diffusion. The addition of corundum in the albite–corundum sandwiched glass experiment makes the system peraluminous, and consequently Al has a slightly different stoichiometry with respect to the metaluminous system (Fig. 12b; see also Acosta-Vigil et al., 2002).
Eigenvalues of D: inversion of concentration profiles
The single-mineral dissolution experiments have been modeled using the solutions to the diffusion equations provided by Smith et al. (1955) [as described by Acosta-Vigil et al. (2002)] and Liang (1999). These solutions are appropriate for diffusive mineral dissolution into a semi-infinite melt reservoir, with the mineral–melt interface retreating at a constant velocity (Smith et al., 1955) or proportionally through the dissolution parameter 
to the square root of both time and the diffusivity of the slowest component in melt (Liang, 1999). These solutions are convenient to model the quartz dissolution experiments, but not entirely appropriate to model the feldspar experiments because melt in the latter constitutes a finite reservoir. Their application to the feldspar experiments, however, can provide a good estimate of the diffusivity along the Al-eigenvector (see Acosta-Vigil et al., 2002). These solutions assume that diffusion takes place only in one direction in space, that D is constant for the range in compositions of the melt, and that the changes in melt density with composition are negligible. We chose a six-oxygen stoichiometry for the oxide components, and H12O6 as the solvent. The six-oxygen basis permits comparison with previous sources of similar data (e.g. Mungall et al., 1998), but is otherwise an arbitrary choice. The following modeling strategy was observed: (1) we inverted simultaneously all the concentration profiles in glass obtained by dissolution of a single mineral at different run times; (2) the eigenvector directions were fixed according to the observations regarding the evolution of concentration profiles with time (Table 5); (3) Si was calculated by applying the solutions to the quartz dissolutions runs with durations of 384 h; (4) Al was calculated by inverting the concentration profiles from the albite and orthoclase dissolution experiments with durations of 384 h.
The model results are presented in Table 6. Comparison between theoretical (Smith et al., 1955) and experimental profiles for quartz, albite, and orthoclase dissolution experiments are shown in Fig. 13. Results for Al are similar to those obtained by Acosta-Vigil et al. (2002) using corundum dissolution experiments in the H2O-saturated peraluminous haplogranite system at the same P–T conditions. Although diffusivities for the alkalis were not obtained directly by the method described above, application of the equation x2 = Dt (e.g. Chakraborty, 1995) to data from Acosta-Vigil et al. (2002, 2005; this work) provides minimum chemical diffusivities of (3–9) x 10–11 m2/s for sodium and potassium.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Comparison with previous diffusion studies
Several studies of major element diffusion in granitic liquids (Watson, 1982
; Baker, 1990, 1991; van der Laan & Wyllie, 1993) have provided effective binary diffusion coefficients (EBDC; Cooper, 1968) that are applicable to problems involving diffusion along the same directions of the diffusion couples in these experiments. They are not directly comparable with our diffusion coefficients, which are thought to represent diffusivities along chemical directions of uncoupled diffusion. Chakraborty et al. (1995b) found that in peralkaline and peraluminous portions of the system K2O–Al2O3–SiO2 at 1100–1600°C and 1 atm, diffusion of aluminum is coupled with a certain amount of potassium in the same direction, whereas diffusion of potassium does not involve migration of aluminum. These eigenvectors are in agreement with those obtained in the current study. Mungall et al. (1998) conducted diffusion couple experiments along several directions in composition space of the metaluminous H2O-saturated haplogranite system at 1300–1600°C and 1 GPa, and also derived values for Al and Al comparable with our results (see also Acosta-Vigil et al., 2002). Freda & Baker (1998) investigated the diffusion of Na and K between albite and orthoclase melts at 1200–1500°C, 1 GPa, and dry conditions. They observed that in the alkali feldspar system, alkalis interdiffuse independently of the other components. This is in accord with our observations in the H2O-saturated haplogranite system, though we have also found that simultaneous migration of both alkalis can occur in either the same or opposite directions (Acosta-Vigil et al., 2002). The diffusive transport properties of haplogranite melts do not vary from metaluminous to peraluminous systems (compare with Acosta-Vigil et al., 2002). These similarities in the diffusion properties of a system at different pressure and temperature, or among systems with slightly different composition, are consistent with previous observations in the ternary K2O–Al2O3–SiO2 and CaO–Al2O3–SiO2 systems, which showed only a small dependence of the eigenvector directions on pressure and temperature (Chakraborty et al., 1995a, 1995b; Liang et al., 1996, and references therein) or composition (peralkaline to peraluminous, Chakraborty et al., 1995a, 1995b). However, the stoichiometry of eigenvectors can be appreciably different in systems of very different composition. For instance, several workers (Sato, 1975; Watson, 1982; Donaldson, 1985; Chekhmir & Epel'baum, 1991; Shaw, 2000) have found that potassium and sodium diffuse toward SiO2-rich environments (e.g. as a result of dissolution of quartz) in basaltic systems, which we did not observe in our experiments. Such differences from the current study probably reflect significant changes in the coordination environments of elements and, hence, structure of the melt.
Interaction between H2O and haplogranite components
Experimental data presented in this paper and by Acosta-Vigil et al. (2002, 2003, 2005) indicate that H2O in haplogranitic melts interacts preferentially with sodium and aluminum rather than with silicon and potassium. The concentration of H2O in melt seems to increase toward the mineral–melt interfaces in the corundum and several albite dissolution experiments, whereas it remains approximately constant in quartz and orthoclase dissolution experiments (Fig. 14a and b). This is in accordance with the observation by Holtz et al. (1992a, 1995), Behrens (1995), and Romano et al. (1996) that H2O solubility increases with the Na/K ratio of the melt, and with a growing body of experimental evidence pointing to an association of excess aluminum and H2O or its dissociated components in granitic melts. For instance, various experimental studies have revealed that the capacity of granitic melts to dissolve H2O increases with their excess alumina concentration (Dingwell et al., 1984, 1997; Holtz et al., 1992b; Linnen et al., 1996; Behrens & Jantos, 2001; Acosta-Vigil et al., 2002). Mungall et al. (1998) deduced a slight coupling of hydrogen to aluminum during diffusion in H2O-saturated haplogranite melt. Acosta-Vigil et al. (2003) have shown that H2O plays an essential role in dissolving excess alumina in granitic melts (see also Clemens & Wall, 1981; Patiño Douce, 1992; Dingwell et al., 1997). Hence, excess aluminum and sodium seem to decrease the activity of H2O in granitic melt, suggesting that H2O or its dissociated components interact preferentially with these elements compared with silica and potassium. These observations can be relevant to the mechanisms of H2O dissolution in granitic melts (e.g. Schmidt et al., 2000; Zeng et al., 2000).
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Diffusion of group IA cations
In accordance with previous studies on diffusion in silicate (basaltic to granitic) melts at higher temperatures and variable pressures (1200–1600°C, 0·001–10 kbar: Watson, 1982
; Baker, 1990; Mungall et al., 1998), we find that chemical diffusion of alkalis is much faster (at least 3–4 orders of magnitude) than diffusion of the tetrahedral components of melt. There is a difference, however, in the behaviour of group IA cations during tracer vs chemical diffusion. Tracer diffusivities for group IA cations generally decrease with increasing atomic number, and hence with increasing ionic radius and mass; this occurs at a variety of dry glass and melt compositions, temperatures, and pressures (Jambon & Carron, 1973, 1976; Jambon, 1982; Lowry et al., 1982; Henderson et al., 1985). Our diffusion studies in wet haplogranite liquids at 800°C (Acosta-Vigil et al., 2002, 2005; this work) show, however, that chemical diffusivities for sodium and potassium are comparable with, and at least of the same magnitude as those for hydrogen (10–11–10–10 m2/s). In agreement with this, Mungall et al. (1998) have found that calculated eigenvalues for Na, K, and H at 1600°C are degenerate within the precision of their experimental data. This indicates that at least for the particular case of group IA cations and wet haplogranite melts, chemical diffusivity does not depend primarily on ionic volume or mass. These differences are probably due to the different nature of (and possibly different diffusion mechanisms involved in) tracer vs chemical diffusion (e.g. see Hofmann, 1980; Dunn, 1986). Finally, we note that compared with potassium, sodium has a special role in charge-balancing aluminum (Acosta-Vigil et al., 2002; this work). This is shown by the constant Al/Na molar ratio during the existence of Al gradients in melt. This does not seem to be due to differences in diffusivities; it is more likely to be produced by differences in the coordination environments, perhaps related to the energetics of their bonds (Acosta-Vigil et al., 2005).
Large-scale effects of chemical diffusion
Since the work of Bowen (1921), it has been largely considered that chemical diffusion is not an effective process for modifying the composition of silicate liquids on a large scale in the time frame of magmatic processes [see reviews by Hofmann (1980) and Watson (1994)]. This may not be entirely true, however, regarding diffusion of sodium and potassium. Rather than the calculated diffusivities, the important observation here is that diffusion of alkalis can be extremely rapid when associated with the diffusion of aluminum; that is, when aluminum concentration gradients are present in the melt, sodium migrates instantaneously (compared with the time frame of the experiments) to maintain a constant Al/Na molar ratio throughout the entire melt reservoir, whereas K diffuses concomitantly and at the same rate in the direction needed to maintain or achieve the ASI of equilibrium (Acosta-Vigil et al., 2002; this work). The increase in ASI toward albite in the peraluminous sandwiched glass experiment means that there is a long-range chemical communication in the melt through chemical potential gradients that tend to be erased by the high diffusivity of the alkali elements. Acosta-Vigil et al. (2004, and unpublished data) have found that during the H2O-saturated partial melting of leucogranite cylinders 3·5 mm in diameter and 7 mm in length, at 200 MPa and 690–800°C, granitic melt distributed throughout the entire cylinder possesses constant Al/Na and ASI molar ratios at any experimental time, from 11 to 2925 h, even though variations in Al/Si may persist.
Geological applications
Diffusion is a major process controlling the chemical composition of silicate liquids during anatexis, magma mixing, assimilation, or crystallization. The wet haplogranite system under investigation here makes up 95–99 wt % of natural, restite-free granitic magmas. The experimental results presented in this work, therefore, have applications for predicting the composition of granitic liquids during these geological processes. Given an appropriate solution to the diffusion equations for a particular geological situation (e.g. Crank, 1975), application of diffusivities along directions of uncoupled diffusion will provide melt composition at a given time and distance with respect to a reference frame. These results also are relevant to interpreting the chemistry of glass inclusions trapped during crustal anatexis (Cesare et al., 1997, 2003). An important reason for the present study was to gain information about the rates at which crustal granitic melts can be produced, how homogeneous they are, and how much time it takes for them to achieve homogenization. As an example, a similar experimental program involving the dissolution of corundum into metaluminous granitic melt led to an estimate for the time required to reach the equilibrium composition of melt for a specific scenario of corundum grains dispersed in a quartzofeldspathic rock (Acosta-Vigil et al., 2002). Diffusion is not the only process that may control the production of melt; the rate of heat supply is also very important and, in many cases, is the rate-limiting factor (e.g. Rubie & Brearley, 1990). Shear during deformation or viscous flow of magma may also promote the homogenization of melts, but diffusion will operate none the less. The application of this work, therefore, could be considered as a component of a more complex problem, or could be modeled as a specific scenario. That scenario could be one in which a large mass of mafic liquid intrudes crustal quartzofeldspathic rocks that are vapor (H2O) saturated along their grain boundaries. The temperature rises to 800°C in the quartzofeldspathic rocks along the margins of the mafic body, and the supply of heat is essentially infinite, albeit transient over the period of cooling. The conditions of this scenario have been recognized in anatectic settings on a small scale (e.g. Holness et al., 2005), and they may also operate at the regional scale (e.g. Loomis, 1972). Under such conditions, our study indicates that crustal melting would be diffusion-controlled once mineral phases lose contact and each mineral dissolves at a rate governed by the diffusion of components in the melt. The diffusivity of the slowest-diffusing component in melt and the proportion of melting will determine the minimum duration of the melting event. The application of the equation x2 = Dt and the diffusivity determined for silica in this study indicates that 20–30 vol. % partial melting of a quartzofeldspathic rock with initial grain size of 2–3 mm (resulting in a mean distance of separation between restite grains of 250–500 µm) and homogenization of melt will take place in less than 1–10 years. This represents the maximum rate of crustal melting when diffusion is the only mechanism for mixing in the melt.
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SUMMARY AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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The key observation of this work is the complex relationship among Al, Na, and K during diffusion of these components through haplogranitic melt along chemical potential gradients induced by crystal dissolution. When gradients in Al exist, Na diffuses instantaneously to achieve a constant molar Al/Na ratio everywhere in the melt, and K diffuses so as to achieve or maintain the ASI value of the melt at equilibrium. Diffusion of Si produces only dilution of the other components, and no interactions with them. The maximum rate at which quartz, plagioclase, and K-feldspar can melt at 800°C and under conditions of hydrostatic stress and H2O saturation is determined by the diffusivities of their components in the melt. When used in conjunction with appropriate solutions to the diffusion equations, these diffusivities constitute an important part of a solution to the duration of crustal melting events.
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ACKNOWLEDGEMENTS |
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Support for this research was provided by National Science Foundation grants EAR-990165, INT-9603199, EAR-9618867, EAR-9625517, EAR-9404658, and a postdoctoral grant to A.A.V. from the Universidad de Granada, Spain. The Electron Microprobe Laboratory at the University of Oklahoma was created with US DOE grant DE-FG22-87FE1146 and upgraded with NSF grant EAR-9404658 and support from the University of Oklahoma Office of Research Administration. We thank Don Baker, Alberto Patiño Douce, Dennis Geist and an anonymous referee for thorough reviews that improved greatly the consistency and clarity of the manuscript.
* Corresponding author. Present address: Departamento de Mineralogía y Petrología, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18002 Granada, Spain. Telephone: +34 958 243358. Fax: +34 958 243368. E-mail: aacosta{at}ugr.es
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSORIGIN OF THE CONCENTRATION...MULTICOMPONENT DIFFUSION...DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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