EXPERIMENTAL STUDIES OF MAGMA MIXING

The paper is devoted to experiments on mixing of natural melts of different compositions at 1300-1850° C and 1-12 kbars. Two series of experiments were carried out: one involving gravity-driven convective mixing and one involving diffusive mixing. The results demonstrate the effectiveness of mixing of contrasting magmas in the course of relative motion. Less viscous mafic melt transforms into andesitic much more easily than viscous silicic melt. The latter tends to “dissolve” into the mafic melt. Diffusive runs revealed selective behavior of alkalies and other components due to diffusion. Uphill diffusion of alkalies may cause double-diffusive convection in intercoupled melts. Diffusive interaction of two contrasting melts is explained as a multistage chemical reaction following the principle of acid-base interaction of components in silicate melts.     

Olivine dissolution in basaltic melt

The main purpose of this work is to understand and quantify diffusive and convective olivine dissolution in basaltic melt. Crystal dissolution and growth in a magma chamber is often accompanied by the descent or ascent of the crystal in the chamber due to gravity. The motion induces convection that enhances mass transport. Such convective dissolution and growth rates have not been quantified before. MgO diffusivity in the melt (D_MgO), MgO concentration of the interface melt (C₀) and the effective thickness of the compositional boundary layer (δ) are necessary parameters to model the convective dissolution. Experiments of non-convective olivine dissolution in a basaltic melt were conducted at 1271-1480 °C and 0.47-1.42 GPa in a piston-cylinder apparatus. At specific temperature and pressure conditions, multiple experiments of different durations show that the interface melt reaches near-saturation within 2 min. Therefore, diffusion, not interface reaction, is the rate-controlling step for non-convective olivine dissolution in basaltic melt. The compositional profile length and olivine dissolution distance are proportional to the square root of experimental duration, consistent with diffusive dissolution. D_MgO and C₀ are obtained from the experimental results. D_MgO displays Arrhenian dependence on temperature, but the pressure dependence is small and not resolved. C₀ increases with increasing temperature and decreases with increasing pressure. Comparison with literature data shows that D_MgO depends strongly on the initial melt composition, while C₀ does not. δ is estimated from fluid dynamics. D_MgO/δ, which characterizes the kinetic and dynamic aspects of convective crystal dissolution, is parameterized as a function of temperature, pressure, and olivine composition. Convective olivine dissolution rate in basaltic melt can be conveniently calculated from the model results. Application to convective crystal growth and xenolith digestion is discussed.     

The effect of experiment geometry on the mechanism and rate of dissolution of quartz in basanite at 0.5 GPa and 1350 °C

Mineral dissolution is an important factor in many magmatic processes such as melting, assimilation and magma mixing. Since it is not possible to determine dissolution rates or mechanisms from natural samples, experimental measurements are very useful. However, the geometry of the crystal–melt system can have a large effect on the measured rate, depending on whether the contaminated melt formed during dissolution is gravitationally stable or unstable. This study examines the effects of the crystal–melt geometry on the dissolution rate and mechanism. The experiments were performed using basanite melt and cylinders and spheres prepared from a single crystal of natural quartz. All of the experiments were performed in the piston cylinder apparatus at 0.5 GPa and 1350 °C. Four crystal–melt geometries were used: (1) quartz cylinders on top of a column of melt; (2) quartz cylinders beneath a column of basanite melt; (3) quartz cylinders in the middle of column of melt; (4) quartz spheres on top of a column of basanite melt. These geometries allow an examination of non-convective, convective and mixed non-convective/convective dissolution. Sphere experiments were included, as this has been the most commonly used geometry in previous experimental studies. In all of the experiments quartz dissolves directly into the basanite without formation of cristobalite or tridymite. Quartz on top of a column of melt dissolves at a rate almost proportional to the square root of time and forms a silica-rich compositional boundary layer that is gravitationally stable. All of the samples show well-defined compositional gradients in the boundary layer; however, the melt at the interface varies in composition with time and plots of concentration as a function of distance normalized to time show that the diffusion rate of SiO₂ increases with time. These data suggest that the rate-controlling step during quartz dissolution is interface reaction rather than cation diffusion. Quartz on the bottom of a column of basanite dissolves much more quickly than in the quartz-on-top experiments and the dissolution rate is linear, due to the periodic gravitational instability and resultant convection of the boundary layer. Even though interface kinetics are the rate-controlling step in quartz dissolution, convection causes an increase in dissolution rate because it replenishes the boundary layer with new, silica-undersaturated melt, which dissolves the quartz more quickly than the contaminated melt. These data suggest that the interface reaction rate is controlled by the degree of undersaturation of the solvent melt in the dissolving component. Both quartz-in-middle and quartz sphere experiments dissolve at a rate intermediate between the two extremes and both show a power law rate. Both dissolve by a combination of convective and non-convective dissolution but the sphere experiments are affected by an additional factor. During the experiment the sphere can sink through the capsule causing forced convection which adds another complication to the interpretation of the dissolution rate data. The results of this study indicate that the choice of experiment geometry plays a major role in determining the observed dissolution rate. Mineral spheres, which have been widely used in the past, are not ideal for dissolution studies. Instead, dissolution rates and mechanisms are best determined in the absence of convection. These experiments have an additional advantage in that for diffusion-controlled dissolution, they allow determination of cation diffusivity. Received: 2 March 2000 / Accepted: 11 April 2000     

Clinopyroxene dissolution in basaltic melt

The history of magmatic systems may be inferred from reactions between mantle xenoliths and host basalt if the thermodynamics and kinetics of the reactions are quantified. To study diffusive and convective clinopyroxene dissolution in silicate melts, diffusive clinopyroxene dissolution experiments were conducted at 0.47–1.90 GPa and 1509–1790 K in a piston-cylinder apparatus. Clinopyroxene saturation is found to be roughly determined by MgO and CaO content. The effective binary diffusivities, D_MgO and D_CaO, and the interface melt saturation condition, , are extracted from the experiments. D_MgO and D_CaO show Arrhenian dependence on temperature. The pressure dependence is small and not resolved within 0.47–1.90 GPa. in the interface melt increases with increasing temperature, but decreases with increasing pressure. Convective clinopyroxene dissolution, where the convection is driven by the density difference between the crystal and melt, is modeled using the diffusivities and interface melt saturation condition. Previous studies showed that the convective dissolution rate depends on the thermodynamics, kinetics and fluid dynamics of the system. Comparing our results for clinopyroxene dissolution to results from a previous study on convective olivine dissolution shows that the kinetic and fluid dynamic aspects of the two minerals are quite similar. However, the thermodynamics of clinopyroxene dissolution depends more strongly on the degree of superheating and composition of the host melt than that of olivine dissolution. The models for clinopyroxene and olivine dissolution are tested against literature experiments on mineral–melt interaction. They are then applied to previously proposed reactions between Hawaii basalts and mantle minerals, mid-ocean ridge basalts and mantle minerals, and xenoliths digestion in a basalt at Kuandian, Northeast China.     

Diffusive dissolution in ternary systems: analysis with applications to quartz and quartzite dissolution in molten silicates

Exact solutions to equations governing isothermal diffusive dissolution of a crystalline slab in a ternary liquid were obtained to include the effect of coupled chemical diffusion in the liquid. These analytical results, supplemented by approximate solutions valid for slow dissolving, provide new insights into the characteristics of diffusive dissolution in ternary systems. Dissolution rate is proportional to square root of time in diffusive dissolution. The coefficient of proportionality is a function of diffusion coefficients, liquidus relation, melt composition at the crystal–melt interface, and compositions of the dissolving crystal and starting melt. In the limit of slow dissolving, the dissolution rate can be written in terms of three dimensionless parameters that are functions of the aforementioned parameters. Dissolution rate is proportional to the diffusion rate of the slow eigen component in the melt when the diffusion rate of the minor eigen component is much slower than the diffusion rate of the major eigen component.Laboratory experiments of diffusive dissolution of single crystals and polycrystalline aggregates of quartz in a haplodacitic melt (25 wt.% CaO, 15 wt.% Al₂O₃, and 60 wt.% SiO₂) were conducted at 1500°C and 1 GPa. Measured dissolution distances (X_b, in microns) are proportional to the square root of experimental run time (t, in seconds), X_b = −0.620 (±0.019) √t. Chemical concentration profiles measured from quenched melts are invariant with time when displayed against the distance (measured from the crystal–melt interface) normalized by the square root of time. The melt compositions at the crystal–melt interface, extrapolated from the measured diffusion profiles in the quenched melts, are within 0.2 wt.% of the independently measured quartz liquidus in the ternary CaO–Al₂O₃–SiO₂ at 1500°C and 1 GPa. These results suggest that crystal and melt are in chemical equilibrium at their interface shortly after the onset of dissolution. Diffusive dissolution of quartz and quartzite is characterized by slow dissolving. Using quartz liquidus as one of the boundary conditions, it has been shown that the calculated dissolution distances and concentration profiles are in good agreement with the experimentally measured ones. Coupled diffusion played an essential role in quartz and quartzite dissolution in haplodacitic to haplobasaltic melts, and is likely to play an important role in diffusion-limited kinetic processes such as crystal growth and dissolution in natural melts of basaltic–rhyolitic compositions.     

Dissolution kinetics of plagioclase in the melt of the system diopside-albite-anorthite,and origin of dusty plagioclase in andesites

The textures and kinetics of reaction between plagioclase and melts have been investigated experimentally, and origin of dusty plagioclase in andesites has been discussed. In the experiments plagioclase of different compositions (An₉₆, An₆₁, An₅₄, An₂₃, and An₂₂) surrounded by glasses of six different compositions in the system diopside-albite-anorthite was heated at temperatures ranging from 1,200 to 1,410° C for 30 min to 88 h. Textures were closely related to temperature and chemical compositions. A crystal became smaller and rounded above the plagioclase liquidus temperature of the starting melt (glass) and remained its original euhedral shape below the liquidus. Whatever the temperature, the crystal-melt interface became rough and often more complicated (sieve-like texture composed of plagioclase-melt mixture in the scale of a few m was developed from the surface of the crystal inward; formation of mantled plagioclase) if the crystal is less calcic than the plagioclase in equilibrium with the surrounding melt, and the interface remained smooth if the crystal is more calcic than the equilibrium plagioclase. From these results the following two types of dissolution have been recognized; (1) a crystal simply dissolves in the melt which is undersaturated with respect to the phase (simple dissolution), and a crystal is partially dissolved to form mantled plagioclase by reaction between sodic plagioclase and calcic melt (partial dissolution). The amount of a crystal dissolved and reacted increased proportional to the square root of time. This suggests that these processes are controlled by diffusion, probably in the crystal.Mantled plagioclase produced in the experiments were very similar both texturally and chemically to some of the so-called resorbed plagioclase in igneous rocks. Chemical compositions and textures of plagioclase phenocrysts in island-arc andesites of magma mixing origin have been examined. Cores of clear and dusty plagioclase were clacic (about An₉₀) and sodic (about An₅₀), respectively. This result indicates that dusty plagioclases were formed by the partial melting due to reaction between sodic plagioclase already precipitated in a dacitic magma and a melt of intermediate composition in a mixed magma during the magma mixing.     

Modeling diffusive dissolution in silicate melts

Here empirical models for calculating self-diffusion coefficients and diffusion matrices are combined with MELTS, a thermodynamic model for silicate minerals and melts, to estimate diffusive dissolution rates, interface melt compositions and melt diffusivities. Simulations of olivine dissolution experiments in basalt show that the overall model is capable of accurately reproducing diffusive dissolution rates, and the resulting diffusion profiles, over a range of pressures and temperatures. However, the overall model is less successful at reproducing olivine dissolution in andesite, diopside dissolution in either basalt or andesite, or anorthite dissolution in picrite. Yet, even for these systems the predicted dissolution rates are generally within about a factor of two of the measured ones. Comparisons between simulations and experiments suggest that errors in the self-diffusion and thermodynamic models are responsible for the differences, and show that dissolution experiments could be a powerful way of testing and calibrating these and similar models. The overall model will also be a useful tool for designing future experiments, and for identifying the parameters that control diffusive dissolution (and crystallization) in silicate melts under a wide range of conditions.     

The effects of potassium addition on the rate of quartz dissolution in the CMAS and CAS systems

Quartz dissolution in melts in the KCAS and KCMAS systems results in the formation of a silica- and potassium-enriched boundary layer next to the dissolving crystals. The presence of potassium in CAS melts has no discernible effect on dissolution rate compared with that in K-free melts with otherwise similar composition despite a small decrease in the diffusivity of silica in the potassium-bearing melts. The decrease in silica diffusivity is offset by an increase in the solubility of silica in the K-bearing melts. Addition of potassium to CMAS melts results in a large decrease in the dissolution rate of quartz. Even though the solubility of silica is enhanced, the addition of potassium leads to large changes in the structure of the melt in the boundary layer (as measured by NBO/T), which results in a large decrease in the diffusivity of silica and thus slower dissolution. There is significant diffusive coupling of Al₂O₃, CaO and MgO during dissolution, which leads to local uphill diffusion of these components. K₂O is decoupled from the other components, as shown by its much thicker diffusion zone. Potassium moves through the boundary layer as a result of two homogeneous reactions: uphill diffusion in which potassium diffuses into the silica-enriched melt adjacent to the dissolving quartz crystal and downhill diffusion in the region furthest from the crystal–melt interface where SiO₂ and K₂O diffuse away from the interface together.     

Origin of mantle (rapakivi) feldspars: experimental evidence of a dissolution- and diffusion-controlled mechanism

Experiments designed to simulate the dissolution of alkali feldspar during magma mixing produced plagioclase mantles that are texturally and compositionally similar to those in some hybrid volcanic rocks. In hydrous dacite melt (69% SiO₂) at 0.8 GPa, 850°C, orthoclase (Or₉₃) and sanidine (Or₃₀) partially dissolved and were mantled by sodic plagioclase (An_25–30). Although plagioclase nucleated epitaxially as a thin shell on the alkali feldspar surface near the time of initial resorption, plagioclase subsequently grew inward —mostly in the form of parallel blades — toaard the receding dissolution surface. Orthoclase dissolved at a rate approximately proportional to the square root of run duration, indicating diffusional control. Plagioclase grew inward within a static boundary zone of melt that formed between the original crystal-dacite interface and the dissolution surface. During orthoclase dissolution, this boundary zone rapidly and simultancously gained Na (by diffusion from dacite) and lost K (by diffusion into dacite); Ca diffused more slowly into this zone, from which non-feldspar species were mostly excluded. Plagioclase was stable where sufficient Ca had diffused in that the boundary zone melt intersected the plagioclase-saturation liquidus. Plagioclase subsequently grew toward the receding dissolution surface as the Ca compositional gradient (and hence the site of plagioclase saturation) stepped inward. Crystallization of plagioclase in the form of parallel blades allowed continued diffusive exchange of melt components between the dissolution surface and the host melt. Bladed growth also served to maintain (at blade tips) proximity of plagioclase to the dissolution surface, thereby apparently preserving (locally) a thin zone of low-variance melt. In natural systems, mantling of alkali feldspar by plagioclase will occur in a similar manner when (a) P, T, or X are changed to induce alkali feldspar dissolution, (b) sufficient Ca is available in the host melt to drive (by diffusion) boundary zone melt compositions to plagioclase saturation, and (c) temperatures are low enough to stabilize sodic plagioclase and to maintain a coherent boundary zone. These reqjirements are satisfied in volcanic systems when alkali feldspar is juxtaposed during mixing with hybrid melts of dacitic composition. Mantled feldspars in some intrusive systems (i.e., rapakivi granites) may form by a similar dissolution- and diffusion-controlled mechanism. Textural evidence of a similar origin may be obscurred in intrusive rocks, however, by products of late-stage magmatic and subsolidus processes.     

An investigation of disequilibrium growth processes of plagioclase in the system anorthite-albite-water by methods of numerical simulation

Compositional zoning of plagioclase is useful as a recorder of dynamic geological conditions if the mechanisms of crystal growth are known. Although the present lack of quantitative information on specific kinetic processes limits their accuracy, numerical simulations of phenoycryst plagioclase growth are useful both for identifying the most influential kinetic processes (for example, diffusion) that should receive priority in experimental measurements and for designing informative growth experiments. The interaction of kinetic processes at a crystal face is so complex that the overall result cannot be assessed intuitively. A primary purpose of these papers is to explore this interaction in the plagioclase system as quantitatively as data permit.The growth of a single face of a plagioclase crystal in an infinite melt was simulated in computer models for: (1) anhydrous and hydrous plagioclase melts; (2) for different undercoolings; and (3) for both interface-controlled and melt-transport controlled growth. Major uncertainties include the velocity and nonequilibrium partitioning laws in the interface-controlled model, and transport coefficients for melt components. Comparison of computed models with published growth velocity data for anhydrous melts was used to estimate a transport coefficient (with the form for diffusion), and that coefficient was extrapolated to hydrous melts on the basis of the Stokes-Einstein relationship.The results of simulations suggest that undercoolings reasonable for plutonic systems could result in deviations of crystal composition from that in equilibrium with the melt of several mole % An; geothermometers based on the assumption of equilibrium partitioning will be in error significantly. Similarly, the volatile content and composition of melt trapped during growth would deviate significantly from bulk melt properties. The velocity of crystal growth and deviation of crystal composition from equilibrium show low sensitivity to water content because larger water contents result in greater accumulation of water at the interface and a consequent depression of effective undercooling.The large magnitude of the derived transport parameter suggests that local convection as well as diffusion may occur during growth in the anhydrous system. The addition of water to the system reduces viscosity and increases the density gradients near the crystal, making local convection even more probable. Our meagre knowledge of transport by diffusion and convection in the melt is probably the most important factor limiting the accuracy of growth simulations.     

Diffusive fractionation of volatiles and their isotopes during bubble growth in magmas

Bubbles grow in decompressing magmas by simple expansion and by diffusive supply of volatiles to the bubble/melt interface. The latter phenomenon is of significant geochemical interest because diffusion can fractionate elements and isotopes (or isotopologues) of dissolved components. This raises the possibility that the character of volatile components in bubbles may not reflect that of volatiles dissolved in the host melt over the lifetime of a bubble—even in the absence of equilibrium vapor/melt isotopic fractionation. Recent experiments have confirmed the existence of an isotope mass effect on diffusion of the volatile element Cl in silicate melt [Fortin et al. (Isotopic fractionation of chlorine during chemical diffusion in a dacitic melt and its implications for isotope behavior during bubble growth (abstract), 2016 Fall AGU Meeting, 2016)], so there is a clear need to understand the efficacy of diffusive fractionation during bubble growth. In this study, numerical models of diffusion and mass redistribution during bubble growth were implemented for both “passive” volatiles—those whose concentrations are generally well below saturation levels—and “active” volatiles such as CO₂ and H₂O, whose elevated concentrations and limited solubilities are the cause of bubble nucleation and growth. Both diffusive and convective bubble-growth scenarios were explored. The magnitude of the isotope mass effect on passive volatiles partitioned into bubbles growing at a constant rate R in a static system depends upon R/D _L, K _d and D _H/D _L (K _d = bubble/melt partition coefficient; D _H/D _L = diffusivity ratio of the heavy and light isotopes). During convective bubble growth, the presence of a discrete (physical) melt boundary layer against the growing bubble (of width x _BL) simplifies outcomes because it leads to the quick onset of steady-state fractionation during growth, the magnitude of which depends mainly upon R?x _BL/D _L and D _H/D _L (bubble/melt fractionation is maximized at R?x _BL/D _L ≈0.1). Constant R is unrealistic for most real systems, so other scenarios were explored by including the solubility and EOS of an “active” volatile (e.g., CO₂) in the numerical simulations. For plausible decompression paths, R increases exponentially with time—leading, potentially, to larger isotopic fractionation of species partitioned into the growing bubble. For volatile species whose isotope mass effects on diffusion have been measured (Cl, Li), predicted isotope fractionation in the exsolved vapor can be as large as ?4‰ for Cl and ?25‰ for Li.     

Crystallization processes in an artificial magma: variations in crystal shape,growth rate and composition with melt cooling history

A large (4.8 m³, 1.3x10⁷ g) artificial mafic melt with a bulk composition similar to that of a basalt (but with a high CaO content of 17 wt%) was generated during a demonstration of in situ vitrification and was allowed to cool naturally. During the melting process, convection was vigorous, resulting in a chemically and thermally homogeneous melt body. Once heating was complete, the cooling rate was rapid with the temperature dropping from 1500°C to 500°C in 6 days within the interior of the 3 m diameter, 1.5 m thick body. A 20 h period of constant temperature (1140°C) observed during colling was the result of latent heat released by widespread crystallization. The final crystalline assemblage consists of diopsidic to hedenbergitic pyroxene and anorthitic feldspar, with a subordinate amount of potassic feldspar, plus a small amount of evolved glass. The compositions and proportions of phases agree well with those predicted by the MELTS thermodynamic model. Thermal and textural evidence suggest that convection within the melt ceased coincident with formation of the first crystals. Textural investigation of core samples reveals large (up to 1 cm in length) acicular diopsidic pyroxenes in a matrix of smaller feldspar and zoned pyroxene crystals (500 m in length). Crystal shape and pyroxene composition vary as a function of position within the solidified body, as a function of cooling rate. Both crystal size and degree of crystallinity are highest in the central, most slowly-cooled parts of the rock. Crystal shape is characterized by tabular, equilibrium-growth forms in the slowly-cooled areas, grading to highly skeletal, dendritic forms at the rapidly-cooled edges of the body. The pyroxene crystals are dominantly homogeneous diopside, but crystals are characterized by thin Fe-rich hedenbergitic rims. These rims were deposited when Mg in the melt was depleted by diopside growth, and melt temperature had cooled sufficiently to allow Fe-rich pyroxene growth. Crystal growth rates can be calculated based on thermal behavior of the melt, reinforced by thermodynamic modelling, and are determined to be between 10^-7 and 10^-8 cm/s in the central part of the melt. These estimates agree well with growth rates in natural systems with similar cooling rates. Pyroxene crystals that formed at a higher cooling rates are characterized by higher Al and lower Mg contents relative to tabular equilibrium crystalline forms, presumably as a result of disequilibrium melt compositions at the crystal-melt interface.New Mexico Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA     

Mechanisms and rates of quartz dissolution in melts in the CMAS (CaO–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>) system

The dissolution rate of minerals in silicate melts is generally assumed to be a function of the rate of mass transport of the released cations in the solvent. While this appears to be the case in moderately to highly viscous solvents, there is some evidence that the rate-controlling step may be different in very fluid, highly silica undersaturated melts such as basanites. In this study, convection-free experiments using solvent melts with silica activity from 0.185–0.56 and viscosity from 0.03–4.6 Pa s show that the dissolution rate is strongly dependent on the degree of superheating, silica activity and the viscosity of the solvent. Dissolution rates increase with increasing melt temperature and decreasing silica activity and viscosity. Quartz dissolution in melts with viscosity <0.59–1.9 Pa s and silica activity <0.47 is controlled by the rate of interface reaction as shown by the absence of steady state composition and silica saturation in the interface melts. Only in the most viscous melt with the highest silica activity is quartz dissolution controlled by the rate of diffusion in the melt and only after a long initiation time. The results of this study indicate that although a diffusion-based model may be applicable to dissolution in viscous magmas, a different approach that combines the interplay between the degree of undersaturation of the melt and its viscosity is required in very fluid melts.This revised version was published online September 2004 with a correction to Figure 8.     

Competing effects of crystal chemistry and silicate melt composition on trace element behavior in magmatic systems: insights from crystal/silicate melt partitioning of the REE,HFSE, Sn,In, Ga,Ba, Pt and Rh

We present new partition coefficients for the REE, HFSE, Sn, In, Ga, Ba, Pt and Rh between clinopyroxene, olivine and basaltic melt as a function of crystal chemistry and melt composition at temperatures of 1190–1300 °C and 1-bar pressure. Two components, namely \(\mathrm {Al_2O_3}\) and \(\mathrm {Na_2O}\), were chosen to be investigated since they are known to affect the structure of silicate melts and especially clinopyroxene crystal chemistry. The amount of \(^{[4]}\mathrm{Al}\) in clinopyroxene will result in an increase of \(D_i^\mathrm{{cpx/melt}}\) even after applying a correction factor to account for the effect of melt polymerization. Moreover, the positive correlation between \(^{[4]}\mathrm{Al}\) and \(D_i^\mathrm{{cpx/melt}}\) is not restricted to the REE, but also applies for Sn, Ga, In, and Ba. The addition of up to 2.6 wt% \(\mathrm {Na_2O}\) to the silicate melt universally increases the \(D_i^\mathrm{{cpx/melt}}\) without any concomitant change in crystal chemistry or a significant effect in melt polymerization. This compositional effect is likely due to the ability of Na to break REE–Al complexes in the melt. Our results emphasize the importance of considering all variables that affect the behavior of trace elements in magmatic systems before applying the lattice strain model and derive meaningful results for the changes in the parameters of the crystallographic sites.     

Chemical mass transfer in magmatic processes

Lasaga's (1982) Master Equation for crystal growth is solved for multicomponent systems in situations which allow for coupled diffusion of melt species. The structure of the solution is explored in some detail for the case of a constant diffusion coefficient matrix. Incorporating these results, the growth of plagioclase is modeled in undercooled tholeiitic melts by approximating interface growth rates with (1) a reduced growth rate function and with (2) calculated solid-liquid solution properties obtained from the silicate liquid solution model of Ghiorso et al. (1983; appendix of Ghiorso 1985). For this purpose algorithms are provided for estimating the liquidus temperature or the chemical affinity of a multicomponent solid solution precipitating from a complex melt of specified bulk composition. Compositional trends in initial solids produced by successive degrees of undercooling are opposite to those predicted in the binary system NaAlSi₃O₈-CaAl₂Si₂O₈. Calculations suggest that the solid phase and interface melt compositions rapidly approach a steady state for a given degree of undercooling. Consequently, the overall isothermal growth rate of plagioclase forming from tholeiitic melts appears to be entirely diffusion controlled. In magmatic systems the multicomponent growth equations allow for the formation of oscillatory zoned crystals as a consequence of the couplingr between interface reaction kinetics and melt diffusion. The magnitude of this effect is largely dependent upon the asymmetry of the diffusion coefficient matrix. Methods are described to facilitate the calibration of diffusion matrices from experimental data on multicomponent penetration curves.Experimental results (Lesher and Walker 1986) on steady state Soret concentration profiles resulting from thermal diffusion in MORB and andesitic liquids are analyzed using the theory of multicomponent linear irreversible thermodynamics. Under conditions where the entropy production is minimized, a linear relationship is derived between liquid chemical potentials and temperature. This relationship is utilized to evaluate the validity of the solution model of Ghiorso et al. (1983) in melts up to 300° C above their liquidus. The results indicate that configurational entropies are accurately modeled for MORB and andesite bulk compositions. The modeling fails in two four-component systems tested. Equations are derived which allow the calibration of multicomponent regular solution parameters from steady state Soret arrays. An algorithm is demonstrated which permits the calculation of steady state Soret concentration profiles, given an overall bulk melt composition and temperature gradient. This algorithm uses the liquid solution properties of Ghiorso et al. (1983) and constants obtained from the experimental measurements of Lesher and Walker (1986).     

Chemical gradient at diffusive interfaces in magma chambers

The results of high pressure experiments on diffusion and Soret separation in natural silicate melts show that the diffusive behaviour between natural silicic and mafic magmas can be approximately modelled as if the system were a binary mixture of SiO₂ and other components such as MgO+FeO+CaO. Steady state compositional profiles across a diffusive interface between silicic and mafic magma layers are calculated on the basis of phenomenological relationships for the fluxes of chemical species and heat in the binary mixtures, using the experimental data of diffusion and Soret coefficients in natural silicate melts. The compositional profiles show a curvature with a minimum SiO₂ value within the interface due to the Soret effect and temperature dependence of diffusion coefficient. The compositional gradient at the lower half of the diffusive interface is similar to that resulting from the Soret separation of a mafic melt regardless of the composition of the silicic magmas. These results suggest that picritic magma can be formed in the interfacial region between the mafic and silicic magma layers. The compositional gradient explains chemical variation of mafic to picritic inclusions in a mixed andesite of the Abu Volcano Group, Japan.     

Cu diffusivity in granitic melts with application to the formation of porphyry Cu deposits

We report new experimental data of Cu diffusivity in granite porphyry melts with 0.01 and 3.9 wt% H₂O at 0.15–1.0 GPa and 973–1523 K. A diffusion couple method was used for the nominally anhydrous granitic melt, whereas a Cu diffusion-in method using Pt₉₅Cu₅ as the source of Cu was applied to the hydrous granitic melt. The diffusion couple experiments also generate Cu diffusion-out profiles due to Cu loss to Pt capsule walls. Cu diffusivities were extracted from error function fits of the Cu concentration profiles measured by LA-ICP-MS. At 1 GPa, we obtain \({D_{{\text{Cu, dry, 1 GPa}}}}=\exp \left[ {( - {\text{13.89}} \pm {\text{0.42}}) - \frac{{{\text{12878}} \pm {\text{540}}}}{T}} \right],\) and \({D_{{\text{Cu, 3}}{\text{.9 wt\% }}{{\text{H}}_{\text{2}}}{\text{O}},{\text{ 1 GPa}}}}=\exp \left[ {( - 16.31 \pm 1.30) - \frac{{{\text{8148}} \pm {\text{1670}}}}{T}} \right],\) where D is Cu diffusivity in m²/s and T is temperature in K. The above expressions are in good agreement with a recent study on Cu diffusion in rhyolitic melt using the approach of Cu₂S dissolution. The observed pressure effect over 0.15–1.0 GPa can be described by an activation volume of 5.9 cm³/mol for Cu diffusion. Comparison of Cu diffusivity to alkali diffusivity and its variation with melt composition implies fourfold-coordinated Cu⁺ in silicate melts. Our experimental results indicate that in the formation of porphyry Cu deposits, the diffusive transport of magmatic Cu to sulfide liquids or fluid bubbles is highly efficient. The obtained Cu diffusivity data can also be used to assess whether equilibrium Cu partitioning can be reached within certain experimental durations.     

Monazite solubility and dissolution kinetics: implications for the thorium and light rare earth chemistry of felsic magmas

A series of monazite dissolution experiments was conducted in a hydrous (1–6 wt.%) granitic melt at 8 kbar over the temperature range 1,000–1,400° C. A polished cube of monazite was immersed in a natural obsidian melt and allowed to partially dissolve. Electron microprobe traverses perpendicular to the crystal-melt interface revealed concentration gradients in the LREEs and P. Diffusivities of the LREEs and P were calculated from these profiles, yielding the following Arrhenius relations for the LREEs: D=0.23 exp(–60.1 kcal mol^–1/RT) at 6% water D=2.30×10⁷ exp(–122.1 kcal mol^–1/RT) at 1% water These results demonstrate the importance of dissolved water on REE diffusion. Phosphorus diffusivities are nearly identical to those of the rare-earths, suggesting that P diffusion charge-compensates REE diffusion. The concentration of LREEs required for monazite saturation in these melts is given by the level of dissolved LREEs at the crystal-melt interface. These values also show a dependence on dissolved water, with LREE_sat=60 ppm at 6% H₂O when extrapolated down to 700° C, and LREE_sat=30 ppm at 1% H₂O. Calculated dissolution rates based on the above parameters indicate that minute (<30 m diameter) monazite crystals will be readily digested by an enclosing anatectic magma under reasonable geologic conditions (i.e., T=700–800° C and >2% H₂O), whereas larger (> 50 m) crystals will likely be residual over the duration of an anatectic event. The low solubility of monazite in this melt suggests that the LREE depletion observed in some felsic differentiation suites may be the result of monazite crystallization. Limited experimental and geochemical/petrologic evidence indicates that compositional changes in the melt accompanying differentiation decrease the solubility of monazite drastically. Kinetic and chemical constraints may also lead to localized monazite saturation and inclusion in major phases or even other accessories. Variations in the REE composition of monazite from different parageneses probably reflects the REE pattern of the parent melt, and may be due to gradational differences in the stability of individual or subgroup REE-complexes as a function of melt composition. Particularly important in this regard seems to be the lime+alkali/alumina balance of the melt and its volatile content.     

Non-equilibrium water/rock interactions—I. Model for interface-controlled reactions

The results of established crystal growth theory and silicate dissolution experiments are combined in developing a new model for mineral/water reactions controlled by surface processes. The overall reaction rate at steady-state is determined by coupling equations for the velocities of mass transport and interface detachment processes. Non-steady state processes can be successfully treated when interface reactions control the rate. For most sparingly soluble minerals, diffusion through the solution can be neglected as a rate-determining factor.Many surface processes are driven by the total interface under saturation, but only processes facilitating detachment contribute to dissolution. Other, non-detachment related, surface reactions result in lower dissolution rates. Slow rates of many mineral/solution reactions are attributed to the surface processes which consume the energy that would otherwise drive detachment.An analysis of the time dependence of interface reaction velocities indicates that linear rate laws apply when uniform detachment or layer-source generation mechanisms such as screw dislocations control the dissolution rate. At low interfacial undersaturations, first-order, logarithmic rate laws prevail. A parabolic time dependence occurs if surface detachment parameters vary as a function of (time)^{$\text{1}\text{2}$}.     

Dissolution of Quartz, Albite, and Orthoclase in H2O-Saturated Haplogranitic Melt at 800{degrees}C and 200 MPa: Diffusive Transport Properties of Granitic Melts at Crustal Anatectic Conditions

We have conducted experiments on dissolution of quartz, albite,orthoclase, and corundum into H₂O-saturated haplogranite meltat 800°C and 200 MPa over a duration of 120–1488 hwith the aim of ascertaining the diffusive transport propertiesof granitic melts at crustal anatectic temperatures. Cylindersof anhydrous starting glass and a single mineral phase (quartzor feldspar) were juxtaposed along flat and polished surfacesinside gold or platinum capsules with 10 wt % added H₂O. Concentrationprofiles in glass (quenched melt) perpendicular to the mineral–glassinterfaces and comparison with relevant phase diagrams suggestthat melts at the interface are saturated in the dissolvingphases after 384 h, and with longer durations the concentrationprofiles are controlled only by diffusion of components in themelt. The evolution of the concentration profiles with timeindicates that uncoupled diffusion in the melt takes place alongthe following four linearly independent directions in oxidecomposition space: SiO₂, Na₂O, and K₂O axes (Si-, Na-, and K-eigenvectors,respectively), and a direction between the Al₂O₃, Na₂O, andK₂O axes (Al-eigenvector), such that the Al/Na molar ratio isequal to that of the bulk melt and the Al/(Na + K) molar ratiois equal to the equilibrium ASI (= mol. Al₂O₃/[Na₂O + K₂O])of the melt. Experiments in which a glass cylinder was sandwichedbetween two mineral cylinders—quartz and albite, quartzand K-feldspar, or albite and corundum—tested the validityof the inferred directions of uncoupled diffusion and exploredlong-range chemical communication in the melt via chemical potentialgradients. The application of available solutions to the diffusionequations for the experimental quartz and feldspar dissolutiondata provides diffusivities along the directions of the Si-eigenvectorand Al-eigenvector of (2·0–2·8) x 10^–15m²/s and (0·6–2·4) x 10^–14 m²/s, respectively.Minimum diffusivities of alkalis [(3–9) x 10^–11m²/s] are orders of magnitude greater than the tetrahedral componentsof the melt. The information provided here determines the rateat which crustal anatexis can occur when sufficient heat issupplied and diffusion is the only mass transport (mixing) processin the melt. The calculated diffusivities imply that a quartzo-feldspathicsource rock with initial grain size of 2–3 mm undergoinghydrostatic, H₂O-saturated melting at 800°C (infinite heatsupply) could produce 20–30 vol. % of homogeneous meltin less than 1–10 years. Slower diffusion in H₂O-undersaturatedmelts will increase this time frame. KEY WORDS: chemical diffusion; haplogranite; mineral dissolution experiments; crustal anatexis