Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2

The enthalpies of solution of several synthetic garnets on the join Mg₃Al₂Si₃O₁₂-Ca₃Al₂Si₃O₁₂ (pyrope-grossular) and of several synthetic clinopyroxenes on the join CaMgSi₂O₆-CaAl₂SiO₆ (diopside-Ca-Tschermak's molecule) were measured in a melt of composition 2PbO · B₂O₃ at 970 K. The determinations were made with sufficient precision so that thermochemical characterizations of the solid solutions could be achieved.The pyrope-grossular solutions show positive enthalpies of mixing. The non-ideality in the range 0–30 mole % grossular is relatively the largest and is in good agreement with the predictions of Ganguly and Kennedy (1974) based largely on cation partitioning of natural high grade metamorphic garnets with biotite, and with the deductions of Hensenet al. (1975) based on measurement of the compositions of synthetic pyrope-rich garnets equilibrated with anorthite, Al₂SiO₅ and quartz. However, the garnets show smaller excess enthalpies at higher grossular contents. This would lead to an asymmetric solvus with a critical temperature lower than predicted by the symmetrical regular solution model of Ganguly and Kennedy (1974). The composition-dependent non-ideality can be understood by simple ionic size considerations in solid substitution and is analogous to the situations for the calcite-dolomite and enstatite-diopside solvi.The heats of solution of pyropes crystallized in the range 1000–1500°C were all the same, within the precision of measurement, and thus we have found no evidence for temperature-dependent cation disordering as a possible explanation of the high entropy of pyrope, as suggested by Charluet al. (1975). Positional disorder of dodecahedral Mg is a more probable reason.The diopside-CaTs join is also non-ideal, with the larger positive enthalpy deviations near the diopside end. The calorimetric data in the magnesian range are consistemt with the model for completely disordered tetrahedral Si and Al which results from the free energy derivations of wood (1975) based on syntheses of diopside-rich aluminous pyroxenes in the presence of anorthite and quartz. At higher Al concentrations the calorimetric data seem more consistent with the ‘local charge-balance’ model of Wood (1975).No evidence for temperature-dependent disorder was found for either the diopside or CaTs end-members.     

Spinel-garnet lherzolite transition in the system CaO-MgO-Al2O3-SiO2 revisited: an in situ X-ray study

Large discrepancies are reported for the near-solidus, pressure-temperature location of the spinel to garnet lherzolite univariant curve in the system CaO-MgO-Al₂O₃-SiO₂ (CMAS). Experimental data obtained previously from the piston-cylinder apparatus indicate interlaboratory pressure differences of up to 30% relative. To investigate this disparity—and because this reaction is pivotal for understanding upper mantle petrology—the phase boundary was located by means of an independent method. The reaction was studied via in situ X-ray diffraction techniques in a 6-8 type multianvil press. Pressure is determined by using MgO as an internal standard and is calculated from measured unit cell volume by using a newly developed high-temperature equation of state for MgO. Combinations of real-time and quenched-sample observations are used to bracket the phase transition. The transition between 1350 and 1500°C was reversed, and the reaction was further constrained from 1207 to 1545°C. Within this temperature range, the transition has an average dT/dP slope of ∼40 ± 10°C/kbar, consistent with several previous piston-cylinder studies. Extrapolation of our curve to 1575°C, an established temperature of the P-T invariant point, yields a pressure of 25.1 ± 1.2 kbar. We also obtained a real-time reversal of the quartz-coesite transition at 30.5 ± 2.3 kbar at 1357°C, which is about 2 to 4 kbar lower in pressure than previously determined in the piston-cylinder apparatus.     

Pyroxene geothermometry and geobarometry: experimental and thermodynamic evaluation of some subsolidus phase relations involving pyroxenes in the system CaO-MgO-Al2O3-SiO2

One petrogenetic grid for plagioclase-, spinel- and garnet-lherzolite analogues in the system CaO-MgO-Al₂O₃-SiO₂ is presented from 1 bar to 30 kbar and 400 to 1500°C. Another grid for olivine-gabbro, spinel-gabbro and garnet-pyroxenite analogues in the same system is presented from 1 bar to 25 kbar and 500 to 1500°C. Both grids show the distribution of the mineral assemblages and the variations in the composition of clinopyroxene with temperature and pressure. They were developed by applying simple thermodynamic mixing models of clinopyroxene to experimentally determined clino-pyroxene compositions.Calcium tschermak's pyroxene (CaAl₂SiO₆) in complex CaMgSi₂O₆-CaAl₂SiO₆-Mg₂Si₂O₆ clinopyroxenes is best represented by a local charge balance mixing model where Enthalpy and entropy changes of subsolidus reactions involving variations in the CaAl₂SiO₆ and Mg₂Si₂O₆ content of clinopyroxene are interdependent due to nonideal mixing of these two end-members. CaAl₂SiO₆ can strongly reduce the mutual solubility of clinopyroxene and orthopyroxene at moderate pressures and high temperatures. Failure to take this into account can result in temperature underestimates (up to 150°C) of spinel-lherzolites, garnet-pyroxenites, low pressure garnet-lherzolites, spinel-gabbros, and high pressure plagioclase-lherzolites and olivine-gabbros. However, at temperatures and pressures where the Al₂O₃ content of clinopyroxene is low (e.g. garnet-lherzolite nodules in kimberlite), the mutual solubility is adequantely represented by experimental results in the system CaO-MgO-SiO₂.     

Role of basicity and tetrahedral speciation in controlling the thermodynamic properties of silicate liquids, part 1: the system CaO-MgO-Al2O3-SiO2

Activity coefficients of oxide components in the system CaO-MgO-Al2O3-SiO2 (CMAS) were calculated with the model of Berman (Berman R. G., “A thermodynamic model for multicomponent melts with application to the system CaO-MgO-Al2O3-SiO2,” Ph.D. dissertation, University of British Columbia, 1983) and used to explore large-scale relationships among these variables and between them and the liquid composition. On the basis of Berman’s model, the natural logarithm of the activity coefficient of MgO, ln(γMgOLiq), and ln(γMgOLiq/γSiO2Liq) are nearly linear functions of ln(γCaOLiq). All three of these variables are simple functions of the optical basicity Λ with which they display minima near Λ ∼ 0.54 that are generated by liquids with low ratios of nonbridging to tetrahedral oxygens (NBO/T) (<0.3) and a mole fraction ratio, XSiO2Liq/XAl2O3Liq, in the range 4 to 20. Variations in ln(γCaOLiq) at constant Λ near the minimum are due mostly to liquids with (XCaOLiq + XMgOLiq)/XAl2O3Liq < 1. The correlations with optical basicity imply that the electron donor power is an important factor in determining the thermodynamic properties of aluminosilicate liquids.For a constant NBO/T, ln(γCaOLiq/γAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) form curves in terms of XSiO2Liq/XAl2O3Liq. The same liquids that generate minima in the Λ plots are also associated with minima in ln(γCaOLiqγAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) as a function of XSiO2Liq/XAl2O3Liq. In addition, there are maxima or sharp changes in slope for NBO/T > 0.3, which occur for XSiO2Liq/XAl2O3Liq ranging from ∼0 to ∼6 and increase with increasing NBO/T. The systematic variations in activity coefficients as a function of composition and optical basicity reflect underlying shifts in speciation as the composition of the liquid is changed. On the basis of correlations among the activity coefficients, it is likely that the use of CaO, an exchange component such as SiMg−1 and two of MgO, CaAl2O4, or MgAl2O4 would yield significant savings in the number of parameters required to model the excess free energy surface of liquids over large portions of CMAS relative to the use of oxide end members.Systematic behavior of thermodynamic properties extends to small amounts of other elements dissolved in otherwise CMAS liquids. For example, ln(XFe2+Liq/XFe3+Liq) at constant oxygen fugacity is linearly correlated with ln(γCaOLiq). Similarly, ln(CS), where CS is the sulfide capacity is linearly correlated at constant temperature with each of the optical basicity, ln(aCaOLiq) and ln(γCaOLiq), although the correlation for the latter breaks down for low values of Λ. The well-known systematic behavior of sulfide capacity as a function of optical basicity for systems inside as well as outside CMAS suggests that ln(γCaSLiq) is also a simple function of optical basicity and that the relationships observed among the activity coefficients in CMAS may hold for more complex systems.     

The MgO-Al2O3-SiO2 system: free energy of pyrope and Al2O3-enstatite

Using the model of fictive ideal components, Gibbs free energies of formation of pyrope and Al₂O₃-enstatite have been determined from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range of 1200–1600 K. The negative free energies in kJ/mol are:

     

6.

Enthalpies of formation at 970 K of compounds in the system MgO-Al₂O₃-SiO₂ from high temperature solution calorimetry     

T.V Charlu  R.C Newton  O.J Kleppa 《Geochimica et cosmochimica acta》1975,39(11):1487-1497

The enthalpies of solution of petrologically important phases in the system MgO-Al₂O₃-SiO ₂ were measured in a melt of composition 2PbO · B₂O₃ at 970 ± 2K. The substances investigated included synthetic and natural (meteoritic) enstatite (MgSiO₃), synthetic aluminous enstatite (MgSiO_30.9Al₂O_30.1), synthetic and natural cordierite (Mg₂Al₄Si₅O₁₈), synthetic and natural sapphirine (approx. 7MgO·9Al₂O₃ · 3SiO₂), synthetic spinel (MgAl₂O₄), natural sillimanite (Al₂SiO₅), synthetic forsterite (Mg₂SiO₄), synthetic pyrope (Mg₃Al₂Si₃O₁₂), natural quartz (SiO₂), synthetic periclase (MgO) and corundum (Al₂O₃). Improvement in standardization of the calorimeter solvent made possible greater precision in this study than obtainable in former work in this laboratory on some of the same substances.The enthalpies of formation of enstatite, synthetic cordierite, forsterite and spinel are in reasonable agreement with values previously determined by solution calorimetry. The enthalpy of formation of enstatite is about 0.7 kcal less negative than the value for clinoenstatite resulting from the HF calorimetry of Torgesen and Sahama (J. Amer. Chem. Soc.70. 2156–2160, 1948), and is in accord with predictions based on analysis of published pyroxene equilibrium work. Aluminous enstatite with 10 wt.% Al₂O₃ shows an enthalpy of solution markedly lower than pure MgSiO₃: the measurements lead to an estimate of the enthalpy of formation at 970 K for MgAl₂SiO₆ (Mg-Tschermak) orthopyroxene of + 9.4 ± 1.5 kcal/mole from MgSiO₃ and Al₂O₃.Comparison of the enthalpies of formation of synthetic cordierite and anhydrous natural low-iron cordierite shows that they are energetically quite similar and that the synthetic cordierite is not likely to have large amounts of (Al, Si) tetrahedral disorder. Comparison of the enthalpies of formation of synthetic sapphirine and natural low-iron sapphirine shows, on the other hand, that the former is not a good stability model for the latter. The lower enthalpy of formation of the high-temperature synthetic sample is undoubtedly a consequence of cation disordering.The enthalpy of formation of natural sillimanite is considerably less negative than given by the tables of Robie andWaldbaum (U.S. Geol. Surv. Bull.1259 1968).The measured enthalpy of formation of synthetic pyrope is consistent with that deduced from published equilibrium diagrams in conjunction with the present measured enthalpy of formation of aluminous enstatite. Calculation of the entropy of synthetic pyrope from the present data yields surprisingly high values and suggests that synthetic pyrope is not a good stability model for natural pyrope-rich garnets. Hence, considerable doubt exists about the direct quantitative application of experimental diagrams involving pyropic garnet to discussions of the garnet stability field in the Earth's outer regions.     

7.

Energetics of multicomponent diffusion in molten CaO-Al₂O₃-SiO₂     

Yan Liang  Andrew M. Davis 《Geochimica et cosmochimica acta》2002,66(4):635-646

The energetics of multicomponent diffusion in molten CaO-Al₂O₃-SiO₂ (CAS) were examined experimentally at 1440 to 1650°C and 0.5 to 2 GPa. Two melt compositions were investigated: a haplodacitic melt (25 wt.% CaO, 15% Al₂O₃, and 60% SiO₂) and a haplobasaltic melt (35% CaO, 20% Al₂O₃, and 45% SiO₂). Diffusion matrices were measured in a mass-fixed frame of reference with simple oxides as end-member components and Al₂O₃ as a dependent variable. Chemical diffusion in molten CAS shows clear evidence of diffusive coupling among the components. The diffusive flux of SiO₂ is significantly enhanced whenever there is a large CaO gradient that is oriented in a direction opposite to the SiO₂ gradient. This coupling effect is more pronounced in the haplodacitic melt and is likely to be significant in natural magmas of rhyolitic to andesitic compositions. The relative magnitude of coupled chemical diffusion is not very sensitive to changes in temperature and pressure.To a good approximation, the measured diffusion matrices follow well-defined Arrhenius relationships with pressure and reciprocal temperature. Typically, a change in temperature of 100°C results in a relative change in the elements of diffusion matrix of 50 to 100%, whereas a change in pressure of 1 GPa introduces a relative change in elements of diffusion matrix of 4 to 6% for the haplobasalt, and less than 5% for the haplodacite. At a pressure of 1 GPa, the ratios between the major and minor eigenvalues of the diffusion matrix λ₁/λ₂ are not very sensitive to temperature variations, with an average of 5.5 ± 0.2 for the haplobasalt and 3.7 ± 0.6 for the haplodacite. The activation energies for the major and minor eigenvalues of the diffusion matrix are 215 ± 12 and 240 ± 21 kJ mol⁻¹, respectively, for the haplodacite and 192 ± 8 and 217 ± 14 kJ mol⁻¹ for the haplobasalt. These values are comparable to the activation energies for self-diffusion of calcium and silicon at the same melt compositions and pressure. At a fixed temperature of 1500°C, the ratios λ₁/λ₂ increase with the increase of pressure, with λ₁/λ₂ varying from 2.5 to 4.1 (0.5 to 1.3 GPa) for the haplodacite and 4 to 6.5 (0.5 to 2.0 GPa) for the haplobasalt. The activation volumes for the major and minor eigenvalues of the diffusion matrix are 0.31 ± 0.44 and 2.3 ± 0.8 cm³ mol⁻¹, respectively, for the haplodacite and −1.48 ± 0.18 and −0.42 ± 0.24 cm³ mol⁻¹ for the haplobasalt. These values are quite different from the activation volumes for self-diffusion of calcium and silicon at the same melt compositions and temperature. These differences in activation volumes between the two melts likely result from a difference in the structure and thermodynamic properties of the melt between the two compositions (e.g., partial molar volume).Applications of the measured diffusion matrices to quartz crystal dissolution in molten CAS reveal that the activation energy and activation volume for quartz dissolution are almost identical to the activation energy and activation volume for diffusion of the minor or slower eigencomponent of the diffusion matrix. This suggests that the diffusion rate of slow eigencomponent is the rate-limiting factor in isothermal crystal dissolution, a conclusion that is likely to be valid for crystal growth and dissolution in natural magmas when diffusion in liquid is the rate-limiting factor.     

8.

Alkali-free tourmaline in the system MgO-Al₂O₃-B₂O₃-SiO₂-H₂O     

Günter Werding  Werner Schreyer 《Geochimica et cosmochimica acta》1984,48(6):1331-1344

An end member of the tourmaline series with a structural formula □(Mg₂Al)Al₆(BO₃)₃[Si₆O₁₈](OH)₄ has been synthesized in the system MgO-Al₂O₃-B₂O₃-SiO₂-H₂O where it represents the only phase with a tourmaline structure. Our experiments provide no evidence for the substitutions Al → Mg + H, Mg → 2H, B + H → Si, and AlAl → MgSi and we were not able to synthesize a phase “Mg-aluminobuergerite” characterized by Mg in the (3a)-site and a strong (OH)-deficiency reported by Rosenberg and Foit (1975). The alkali-free tourmaline has a vacant (3a)-site and is related to dravite by the □ + Al for Na + Mg substitution. It is stable from at least 300°C to about 800°C at low fluid pressures and 100% excess B₂O₃, and can be synthesized up to a pressure of 20 kbars. At higher temperatures the tourmaline decomposes into grandidierite or a boron-bearing phase possibly related to mullite (“B-mullite”), quartz, and unidentified solid phases, or the tourmaline melts incongruently into corundum + liquid, depending on pressure. In the absence of excess B₂O₃ tourmaline stability is lowered by about 60°C. Tourmaline may coexist with the other MgO-Al₂O₃-B₂O₃-SiO₂-H₂O phases forsterite, enstatite, chlorite, talc, quartz, grandidierite, corundum, spinel, “B-mullite,” cordierite, and sinhalite depending on the prevailing PTX-conditions.The (3a)-vacant tourmaline has the space group R3m with $\text{a =15.90}\text{A}\text{?}$, $\text{c = 7.115}\text{A}\text{?}$, and $\text{V = 1557.0}\text{A}\text{?}{}^3$. However, these values vary at room temperature with the pressure-temperature conditions of synthesis by $\text{±0.015}\text{A}\text{?}\text{in a}$, $\text{±0.010}\text{A}\text{?}\text{in c}$, and $\text{±4.0}\text{A}\text{?}{}^3\text{in V}$, probably as a result of MgAl order/disorder relations in the octahedral positions. Despite these variations intensity calculations support the assumed structural formula. Refractive indices are n_o = 1.631(2), n_E = 1.610(2), Δn = 0.021. The infrared spectrum is intermediate between those of dravite and elbaite. The common alkali and calcium deficiencies of natural tourmalines may at least partly be explained by miscibilities towards (3a)-vacant end members. The apparent absence of (3a)-vacant tourmaline in nature is probably due to the lack of fluids that carry boron but no Na or Ca.     

9.

CaO-MgO-Al₂o₃-SiO₂ liquids: chemical and isotopic effects of Mg and Si evaporation in a closed system of solar composition     

L. Grossman  A.V. Fedkin 《Geochimica et cosmochimica acta》2003,67(21):4205-4221

A method is shown for calculating vapor pressures over a CMAS droplet in a gas of any composition. It is applied to the problem of the evolution of the chemical and Mg and Si isotopic composition of a completely molten droplet having the composition of a likely refractory inclusion precursor during its evaporation into the complementary, i.e. modified solar, gas from which it originally condensed, a more realistic model than previous calculations in which the ambient gas is pure H_2(g). Because the loss rate of Mg is greater than that of Si, the vapor pressure of Mg_(g) falls and its ambient pressure rises faster than those of SiO_(g) during isothermal evaporation, causing the flux of Mg_(g) to approach zero faster and MgO to approach its equilibrium concentration sooner than SiO₂. As time passes, δ²⁵Mg and δ²⁹Si increase in the droplet and decrease in the ambient gas. The net flux of each isotope crossing the droplet/gas interface is the difference between its outgoing and incoming flux. δ²⁵Mg and δ²⁹Si of this instantaneous gas become higher, first overtaking their values in the ambient gas, causing them to increase with time, and later overtaking their values in the droplet itself, causing them to decrease with time, ultimately reaching their equilibrium values. If the system is cooling during evaporation and if mass transfer ceases at the solidus temperature, 1500 K, final MgO and SiO₂ contents of the droplet are slightly higher in modified solar gas than in pure H_2(g), and the difference increases with decreasing cooling rate and increasing ambient pressure. During cooling under some conditions, net fluxes of evaporating species become negative, causing reversal of the evaporation process into a condensation process, an increase in the MgO and/or SiO₂ content of the droplet with time, and an increase in their final concentrations with increasing ambient pressure and/or dust/gas ratio. At cooling rates <∼3 K/h, closed-system evaporation at P^tot ∼ 10⁻³ bar in a modified solar gas, or at lower pressure in systems with enhanced dust/gas ratio, can yield the same δ²⁵Mg in a residual CMAS droplet for vastly different evaporated fractions of Mg. The δ²⁵Mg of a refractory residue may thus be insufficient to determine the extent of Mg loss from its precursor. Evaporation of Mg into an Mg-bearing ambient gas causes δ²⁶Mg and δ²⁵Mg of the residual droplet to fall below values expected from Rayleigh fractionation for the amount of ²⁴Mg evaporated, with the degree of departure increasing with increasing fraction evaporated and ambient pressure of Mg. δ²⁶Mg and δ²⁵Mg do not depart proportionately from Rayleigh fractionation curves, with δ²⁵Mg being less than expected on the basis of δ²⁶Mg by up to ∼1.2‰. Such departures from Rayleigh fractionation could be used in principle to distinguish heavily from lightly evaporated residues with the same δ²⁵Mg.     

10.

A thermodynamic model for multicomponent melts,with application to the system CaO-Al₂O₃-SiO₂     

Robert G. Berman 《Geochimica et cosmochimica acta》1984,48(4):661-678

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

11.

Shear viscosities of CaO-Al₂O₃-SiO₂ and MgO-Al₂O₃-SiO₂ liquids: Implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts     

Michael J. Toplis  Donald B. Dingwell 《Geochimica et cosmochimica acta》2004,68(24):5169-5188

The shear viscosity of 66 liquids in the systems CaO-Al₂O₃-SiO₂ (CAS) and MgO-Al₂O₃-SiO₂ (MAS) have been measured in the ranges 1-10⁴ Pa s and 10⁸-10¹² Pa s. Liquids belong to series, nominally at 50, 67, and 75 mol.% SiO₂, with atomic M²⁺/(M²⁺+2Al) typically in the range 0.60 to 0.40 for each isopleth. In the system CAS at 1600°C, viscosity passes through a maximum at all silica contents. The maxima are clearly centered in the peraluminous field, but the exact composition at which viscosity is a maximum is poorly defined. Similar features are observed at 900°C. In contrast, data for the system MAS at 1600°C show that viscosity decreases with decreasing Mg/(Mg + 2Al) at all silica contents, but that a maximum in viscosity must occur in the field where Mg/2Al >1. On the other hand, the viscosity at 850°C increases with decreasing Mg/(Mg + 2Al) and shows no sign of reaching a maximum, even for the most peraluminous composition studied. The data from both systems at 1600°C have been analysed assuming that shear viscosity is proportional to average bond strength and considering the equilibrium:

Al^[4]-(Mg,Ca)_0.5⇔(Mg,Ca)_0.5-NBO+Al_XS     

12.

Experimental study of the Mg₃Al₂Si₃O₁₂-Na₂MgSi₅O₁₂ system at 7.0 and 8.5 GPa: Implication for the formation of Na-bearing garnets     

A. V. Bobrov  Yu. A. Litvin 《Doklady Earth Sciences》2008,419(2):339-343

     

13.

Some thermodynamic properties of the Berman and Brown model for CaO-Al₂O₃-SiO₂     

Lawrence M. Barron 《Geochimica et cosmochimica acta》1986,50(12):2727-2733

The and (1984) excess free energy model (B&B) is extremely convenient to use in modelling multicomponent solutions. However, spinodal calculations reveal that their calibration of this model for CaO-Al₂O₃-SiO₂ produces liquation tielines that do not appear to be in agreement with experimental work. In addition, their calibration contains some strongly negative excess entropy parameters and these permit a most unusual inverted liquation field to start at approximately >2115°C, wt% (SiO₂, Al₂O₃, CaO) = (70, 16, 14). This inverted field expands rapidly to cover most of the ternary for T> 2300°C and continues to expand at all higher temperatures. The Berman and Brown calibration for this system carries these negative excess entropies of mixing because the solution model is very strongly asymmetric as a result of the use of normal oxide mole weights in modelling the configurational entropy of mixing. A suggestion is made for a fairly natural restriction on the relative sizes of empirical models for excess versus configurational entropy.

Expressions are presented for the general consolute condition (all solution models) and for the second and third partials of the B&B G^x model.     

14.

Dissolution of jarosite [KFe₃(SO₄)₂(OH)₆] at pH 2 and 8: Insights from batch experiments and computational modelling   总被引：1，自引：0，他引：1  

Adrian M.L. Smith  Karen A. Hudson-Edwards  William E. Dubbin 《Geochimica et cosmochimica acta》2006,70(3):608-621

Jarosite [KFe₃(SO₄)₂(OH)₆] is a mineral that is common in acidic, sulphate-rich environments, such as acid sulphate soils derived from pyrite-bearing sediments, weathering zones of sulphide ore deposits and acid mine or acid rock drainage (ARD/AMD) sites. The structure of jarosite is based on linear tetrahedral-octahedral-tetrahedral (T-O-T) sheets, made up from slightly distorted FeO₆ octahedra and SO₄ tetrahedra. Batch dissolution experiments carried out on synthetic jarosite at pH 2, to mimic environments affected by ARD/AMD, and at pH 8, to simulate ARD/AMD environments recently remediated with slaked lime (Ca(OH)₂), suggest first order dissolution kinetics. Both dissolution reactions are incongruent, as revealed by non-ideal dissolution of the parent solids and, in the case of the pH 8 dissolution, because a secondary goethite precipitate forms on the surface of the dissolving jarosite grains. The pH 2 dissolution yields only aqueous K, Fe, and SO₄. Aqueous, residual solid, and computational modelling of the jarosite structure and surfaces using the GULP and MARVIN codes, respectively, show for the first time that there is selective dissolution of the A- and T-sites, which contain K and SO₄, respectively, relative to Fe, which is located deep within the T-O-T jarosite structure. These results have implications for the chemistry of ARD/AMD waters, and for understanding reaction pathways of ARD/AMD mineral dissolution.     

15.

A model for silicate melt viscosity in the system CaMgSi₂O₆-CaAl₂Si₂O₈-NaAlSi₃O₈     

James K. Russell  Daniele Giordano 《Geochimica et cosmochimica acta》2005,69(22):5333-5349

Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi₂O₆ (Di)-CaAl₂Si₂O₈ (An)-NaAlSi₃O₈ (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (b_i=1,2.6, c_j=1,2..6) representing linear (e.g., b_i=1:3) and higher order, nonlinear (e.g., b_i=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of T_g for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have T_g values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.     

16.

Thermochemistry of glasses along joins of pyroxene stoichiometry in the system Ca₂Si₂O₆-Mg₂Si₂O₆-Al₄O₆     

Richard L. Hervig  Derry Scott  Alexandra Navrotsky 《Geochimica et cosmochimica acta》1985,49(7):1497-1501

Enthalpies of solution in 2PbO · B₂O₃ at 974 K have been measured for glasses along the joins Ca₂Si₂O₆ (Wo)-Mg₂Si₂O₆ (En) and Mg₂Si₂O₆-MgAl₂SiO₆ (MgTs). Heats of mixing are symmetric and negative for Wo-En with W_H = ?31.0 ± 3.6 kJ mol^?. Negative heats of mixing were also found for the En-MgTs glasses (W_H = ?33.4 ± 3.7 kJ mol^?).Enthalpies of vitrification of pyroxenes and pyroxenoids generally increase with decreasing alumina content and with decreasing basicity of the divalent cation.Heats of mixing along several glassy joins show systematic trends. When only non-tetrahedral cations mix (outside the aluminosilicate framework), small exothermic heats of mixing are seen. When both nontetrahedral and framework cations mix (on separate sublattices, presumably), the enthalpies of mixing are substantially more negative. Maximum enthalpy stabilization near compositions with Al/Si ≈ 1 is suggested.     

17.

The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO₄-OH-HCO₃-CO₃-CO₂-H₂O system to high ionic strengths at 25°C     

Charles E Harvie  Nancy Møller  John H Weare 《Geochimica et cosmochimica acta》1984,48(4):723-751

The mineral solubility model of Harvie and Weare (1980) is extended to the eight component system, Na-K-Mg-Ca-H-Cl-SO₄-OH-HCO₃-CO₃-CO₂-H₂O at 25°C to high concentrations. The model is based on the semi-empirical equations of Pitzer (1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.     

18.

The bearing of the system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ on fassaitic pyroxene     

Kosuke Onuma  Masahide Akasaka  Kenzo Yagi 《Lithos》1981,14(3):173-182

The system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi₂O₆-rich portion is Cpx + An + Mel and that in the CaMgSi₂O₆-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO₆ component of the system. The Al₂O₃ content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al₂O₃ with 3.9 wt.% Fe₂O₃. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO₆ content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl₂SiO₆ and CaFeAlSiO₅ components as crystallization proceeds. These results agree with those obtained in the experimental study.     

19.

Stability of sapphirine-bearing mineral assemblages in the system FeO-MgO-Al₂O₃-SiO₂ and metamorphic P-T parameters of aluminous granulites     

K. K. Podlesskii 《Petrology》2010,18(4):350-368

Consistent thermodynamic data on the properties of pure mineral end members and the mixing properties of solid solutions in the system FeO-MgO-Al₂O₃-SiO₂ were employed to simulate phase relations of sapphirine, garnet, spinel, orthopyroxene, cordierite, quartz, Al silicates, and corundum. Compositional variations of the solid solutions with temperature notably modify the topology of the P-T diagrams, which differ from the petrogenetic grids widely used in the literature. It is worth noting that the evaluation of P-T metamorphic conditions based on reaction relations in sapphirine-bearing assemblages cannot be so far considered reliable enough. The lower stability limit of the sapphirine + quartz assemblage in the system in question is possibly located at much lower P-T parameters: at least 835°C and ∼6 kbar. The sapphirine + kyanite assemblage can be stable at temperatures below 860°C and a pressure of ∼11 kbar, and the stability field of the sapphirine + olivine assemblage is narrow and constrained to temperatures no higher than ∼800°C.     

20.

Diffusion in silicate melts: II. Multicomponent diffusion in CaOAl₂O₃SiO₂ at 1500°C and 1 GPa     

Yan Liang  Frank M. Richter  E.Bruce Watson 《Geochimica et cosmochimica acta》1996,60(24):5021-5035

Chemical diffusion profiles in molten CaO---Al₂O₃---SiO₂ have been measured over a large range of compositions at 1500°C and l GPa. The diffusion profiles have been inverted for effective binary diffusion coefficients (EBDCs) and for the chemical diffusion matrix. The EBDCs are shown to depend strongly on both composition and direction of diffusion in composition space. The dependence of EBDCs on direction in composition space, which for the system studied here can be as large as a factor of seven, severely limits the applicability of EBDCs to interdiffusion in any direction other than the one used to derive the EBDCs.

The chemical diffusion matrix for molten CaO---Al₂O₃---SiO₂ was determined using diffusion profiles from two or three mutually orthogonal diffusion couples in the ternary composition space. All features of the diffusion profiles shown in this work can be reproduced by representing the chemical fluxes in the three-component system as a linear combination of concentration gradients via a 2 × 2 diffusion matrix. Chemical diffusion in molten CaO---Al₂O₃---SiO₂ shows clear evidence of strong diffusive coupling among the components. This can be seen in the uphill diffusion profiles of components that were initially uniform, in the fact that the apparent rate of diffusion of some components is a strong function of direction in composition space, and most quantitatively in the magnitude of off-diagonal elements of the diffusion matrix relative to the magnitude of the diagonal elements. SiO₂ for example, is found to be strongly coupled with CaO in relatively silicic melts, whereas Al₂O₃ is strongly coupled with CaO in less silicic melts. Furthermore, the coupling of CaO with either Al₂O₃ or Si02 reverses sign between more and less polymerized compositions. Interdiffusion profiles in natural melts have numerous features that suggest similar coupling between Al₂O₃ and CaO and between SiO₂ and CaO.     

TK	1200	1300	1400	1500	1600
Pyrope	4869.92	4747.05	4614.26	4462.63	4311.00
Al2O3-enstatite	1257.25	1244.28	1191.93	1158.67	1125.64

Enthalpies of formation at 970 K of compounds in the system MgO-Al2O3-SiO2 from high temperature solution calorimetry

The enthalpies of solution of petrologically important phases in the system MgO-Al₂O₃-SiO ₂ were measured in a melt of composition 2PbO · B₂O₃ at 970 ± 2K. The substances investigated included synthetic and natural (meteoritic) enstatite (MgSiO₃), synthetic aluminous enstatite (MgSiO_30.9Al₂O_30.1), synthetic and natural cordierite (Mg₂Al₄Si₅O₁₈), synthetic and natural sapphirine (approx. 7MgO·9Al₂O₃ · 3SiO₂), synthetic spinel (MgAl₂O₄), natural sillimanite (Al₂SiO₅), synthetic forsterite (Mg₂SiO₄), synthetic pyrope (Mg₃Al₂Si₃O₁₂), natural quartz (SiO₂), synthetic periclase (MgO) and corundum (Al₂O₃). Improvement in standardization of the calorimeter solvent made possible greater precision in this study than obtainable in former work in this laboratory on some of the same substances.The enthalpies of formation of enstatite, synthetic cordierite, forsterite and spinel are in reasonable agreement with values previously determined by solution calorimetry. The enthalpy of formation of enstatite is about 0.7 kcal less negative than the value for clinoenstatite resulting from the HF calorimetry of Torgesen and Sahama (J. Amer. Chem. Soc.70. 2156–2160, 1948), and is in accord with predictions based on analysis of published pyroxene equilibrium work. Aluminous enstatite with 10 wt.% Al₂O₃ shows an enthalpy of solution markedly lower than pure MgSiO₃: the measurements lead to an estimate of the enthalpy of formation at 970 K for MgAl₂SiO₆ (Mg-Tschermak) orthopyroxene of + 9.4 ± 1.5 kcal/mole from MgSiO₃ and Al₂O₃.Comparison of the enthalpies of formation of synthetic cordierite and anhydrous natural low-iron cordierite shows that they are energetically quite similar and that the synthetic cordierite is not likely to have large amounts of (Al, Si) tetrahedral disorder. Comparison of the enthalpies of formation of synthetic sapphirine and natural low-iron sapphirine shows, on the other hand, that the former is not a good stability model for the latter. The lower enthalpy of formation of the high-temperature synthetic sample is undoubtedly a consequence of cation disordering.The enthalpy of formation of natural sillimanite is considerably less negative than given by the tables of Robie andWaldbaum (U.S. Geol. Surv. Bull.1259 1968).The measured enthalpy of formation of synthetic pyrope is consistent with that deduced from published equilibrium diagrams in conjunction with the present measured enthalpy of formation of aluminous enstatite. Calculation of the entropy of synthetic pyrope from the present data yields surprisingly high values and suggests that synthetic pyrope is not a good stability model for natural pyrope-rich garnets. Hence, considerable doubt exists about the direct quantitative application of experimental diagrams involving pyropic garnet to discussions of the garnet stability field in the Earth's outer regions.     

Energetics of multicomponent diffusion in molten CaO-Al2O3-SiO2

The energetics of multicomponent diffusion in molten CaO-Al₂O₃-SiO₂ (CAS) were examined experimentally at 1440 to 1650°C and 0.5 to 2 GPa. Two melt compositions were investigated: a haplodacitic melt (25 wt.% CaO, 15% Al₂O₃, and 60% SiO₂) and a haplobasaltic melt (35% CaO, 20% Al₂O₃, and 45% SiO₂). Diffusion matrices were measured in a mass-fixed frame of reference with simple oxides as end-member components and Al₂O₃ as a dependent variable. Chemical diffusion in molten CAS shows clear evidence of diffusive coupling among the components. The diffusive flux of SiO₂ is significantly enhanced whenever there is a large CaO gradient that is oriented in a direction opposite to the SiO₂ gradient. This coupling effect is more pronounced in the haplodacitic melt and is likely to be significant in natural magmas of rhyolitic to andesitic compositions. The relative magnitude of coupled chemical diffusion is not very sensitive to changes in temperature and pressure.To a good approximation, the measured diffusion matrices follow well-defined Arrhenius relationships with pressure and reciprocal temperature. Typically, a change in temperature of 100°C results in a relative change in the elements of diffusion matrix of 50 to 100%, whereas a change in pressure of 1 GPa introduces a relative change in elements of diffusion matrix of 4 to 6% for the haplobasalt, and less than 5% for the haplodacite. At a pressure of 1 GPa, the ratios between the major and minor eigenvalues of the diffusion matrix λ₁/λ₂ are not very sensitive to temperature variations, with an average of 5.5 ± 0.2 for the haplobasalt and 3.7 ± 0.6 for the haplodacite. The activation energies for the major and minor eigenvalues of the diffusion matrix are 215 ± 12 and 240 ± 21 kJ mol⁻¹, respectively, for the haplodacite and 192 ± 8 and 217 ± 14 kJ mol⁻¹ for the haplobasalt. These values are comparable to the activation energies for self-diffusion of calcium and silicon at the same melt compositions and pressure. At a fixed temperature of 1500°C, the ratios λ₁/λ₂ increase with the increase of pressure, with λ₁/λ₂ varying from 2.5 to 4.1 (0.5 to 1.3 GPa) for the haplodacite and 4 to 6.5 (0.5 to 2.0 GPa) for the haplobasalt. The activation volumes for the major and minor eigenvalues of the diffusion matrix are 0.31 ± 0.44 and 2.3 ± 0.8 cm³ mol⁻¹, respectively, for the haplodacite and −1.48 ± 0.18 and −0.42 ± 0.24 cm³ mol⁻¹ for the haplobasalt. These values are quite different from the activation volumes for self-diffusion of calcium and silicon at the same melt compositions and temperature. These differences in activation volumes between the two melts likely result from a difference in the structure and thermodynamic properties of the melt between the two compositions (e.g., partial molar volume).Applications of the measured diffusion matrices to quartz crystal dissolution in molten CAS reveal that the activation energy and activation volume for quartz dissolution are almost identical to the activation energy and activation volume for diffusion of the minor or slower eigencomponent of the diffusion matrix. This suggests that the diffusion rate of slow eigencomponent is the rate-limiting factor in isothermal crystal dissolution, a conclusion that is likely to be valid for crystal growth and dissolution in natural magmas when diffusion in liquid is the rate-limiting factor.     

Alkali-free tourmaline in the system MgO-Al2O3-B2O3-SiO2-H2O

An end member of the tourmaline series with a structural formula □(Mg₂Al)Al₆(BO₃)₃[Si₆O₁₈](OH)₄ has been synthesized in the system MgO-Al₂O₃-B₂O₃-SiO₂-H₂O where it represents the only phase with a tourmaline structure. Our experiments provide no evidence for the substitutions Al → Mg + H, Mg → 2H, B + H → Si, and AlAl → MgSi and we were not able to synthesize a phase “Mg-aluminobuergerite” characterized by Mg in the (3a)-site and a strong (OH)-deficiency reported by Rosenberg and Foit (1975). The alkali-free tourmaline has a vacant (3a)-site and is related to dravite by the □ + Al for Na + Mg substitution. It is stable from at least 300°C to about 800°C at low fluid pressures and 100% excess B₂O₃, and can be synthesized up to a pressure of 20 kbars. At higher temperatures the tourmaline decomposes into grandidierite or a boron-bearing phase possibly related to mullite (“B-mullite”), quartz, and unidentified solid phases, or the tourmaline melts incongruently into corundum + liquid, depending on pressure. In the absence of excess B₂O₃ tourmaline stability is lowered by about 60°C. Tourmaline may coexist with the other MgO-Al₂O₃-B₂O₃-SiO₂-H₂O phases forsterite, enstatite, chlorite, talc, quartz, grandidierite, corundum, spinel, “B-mullite,” cordierite, and sinhalite depending on the prevailing PTX-conditions.The (3a)-vacant tourmaline has the space group R3m with $\text{a =15.90}\text{A}\text{?}$, $\text{c = 7.115}\text{A}\text{?}$, and $\text{V = 1557.0}\text{A}\text{?}{}^3$. However, these values vary at room temperature with the pressure-temperature conditions of synthesis by $\text{±0.015}\text{A}\text{?}\text{in a}$, $\text{±0.010}\text{A}\text{?}\text{in c}$, and $\text{±4.0}\text{A}\text{?}{}^3\text{in V}$, probably as a result of MgAl order/disorder relations in the octahedral positions. Despite these variations intensity calculations support the assumed structural formula. Refractive indices are n_o = 1.631(2), n_E = 1.610(2), Δn = 0.021. The infrared spectrum is intermediate between those of dravite and elbaite. The common alkali and calcium deficiencies of natural tourmalines may at least partly be explained by miscibilities towards (3a)-vacant end members. The apparent absence of (3a)-vacant tourmaline in nature is probably due to the lack of fluids that carry boron but no Na or Ca.     

CaO-MgO-Al2o3-SiO2 liquids: chemical and isotopic effects of Mg and Si evaporation in a closed system of solar composition

A method is shown for calculating vapor pressures over a CMAS droplet in a gas of any composition. It is applied to the problem of the evolution of the chemical and Mg and Si isotopic composition of a completely molten droplet having the composition of a likely refractory inclusion precursor during its evaporation into the complementary, i.e. modified solar, gas from which it originally condensed, a more realistic model than previous calculations in which the ambient gas is pure H_2(g). Because the loss rate of Mg is greater than that of Si, the vapor pressure of Mg_(g) falls and its ambient pressure rises faster than those of SiO_(g) during isothermal evaporation, causing the flux of Mg_(g) to approach zero faster and MgO to approach its equilibrium concentration sooner than SiO₂. As time passes, δ²⁵Mg and δ²⁹Si increase in the droplet and decrease in the ambient gas. The net flux of each isotope crossing the droplet/gas interface is the difference between its outgoing and incoming flux. δ²⁵Mg and δ²⁹Si of this instantaneous gas become higher, first overtaking their values in the ambient gas, causing them to increase with time, and later overtaking their values in the droplet itself, causing them to decrease with time, ultimately reaching their equilibrium values. If the system is cooling during evaporation and if mass transfer ceases at the solidus temperature, 1500 K, final MgO and SiO₂ contents of the droplet are slightly higher in modified solar gas than in pure H_2(g), and the difference increases with decreasing cooling rate and increasing ambient pressure. During cooling under some conditions, net fluxes of evaporating species become negative, causing reversal of the evaporation process into a condensation process, an increase in the MgO and/or SiO₂ content of the droplet with time, and an increase in their final concentrations with increasing ambient pressure and/or dust/gas ratio. At cooling rates <∼3 K/h, closed-system evaporation at P^tot ∼ 10⁻³ bar in a modified solar gas, or at lower pressure in systems with enhanced dust/gas ratio, can yield the same δ²⁵Mg in a residual CMAS droplet for vastly different evaporated fractions of Mg. The δ²⁵Mg of a refractory residue may thus be insufficient to determine the extent of Mg loss from its precursor. Evaporation of Mg into an Mg-bearing ambient gas causes δ²⁶Mg and δ²⁵Mg of the residual droplet to fall below values expected from Rayleigh fractionation for the amount of ²⁴Mg evaporated, with the degree of departure increasing with increasing fraction evaporated and ambient pressure of Mg. δ²⁶Mg and δ²⁵Mg do not depart proportionately from Rayleigh fractionation curves, with δ²⁵Mg being less than expected on the basis of δ²⁶Mg by up to ∼1.2‰. Such departures from Rayleigh fractionation could be used in principle to distinguish heavily from lightly evaporated residues with the same δ²⁵Mg.     

A thermodynamic model for multicomponent melts,with application to the system CaO-Al2O3-SiO2

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

Shear viscosities of CaO-Al2O3-SiO2 and MgO-Al2O3-SiO2 liquids: Implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts

The shear viscosity of 66 liquids in the systems CaO-Al₂O₃-SiO₂ (CAS) and MgO-Al₂O₃-SiO₂ (MAS) have been measured in the ranges 1-10⁴ Pa s and 10⁸-10¹² Pa s. Liquids belong to series, nominally at 50, 67, and 75 mol.% SiO₂, with atomic M²⁺/(M²⁺+2Al) typically in the range 0.60 to 0.40 for each isopleth. In the system CAS at 1600°C, viscosity passes through a maximum at all silica contents. The maxima are clearly centered in the peraluminous field, but the exact composition at which viscosity is a maximum is poorly defined. Similar features are observed at 900°C. In contrast, data for the system MAS at 1600°C show that viscosity decreases with decreasing Mg/(Mg + 2Al) at all silica contents, but that a maximum in viscosity must occur in the field where Mg/2Al >1. On the other hand, the viscosity at 850°C increases with decreasing Mg/(Mg + 2Al) and shows no sign of reaching a maximum, even for the most peraluminous composition studied. The data from both systems at 1600°C have been analysed assuming that shear viscosity is proportional to average bond strength and considering the equilibrium:

Al^[4]-(Mg,Ca)_0.5⇔(Mg,Ca)_0.5-NBO+Al_XS     

Some thermodynamic properties of the Berman and Brown model for CaO-Al2O3-SiO2

The and (1984) excess free energy model (B&B) is extremely convenient to use in modelling multicomponent solutions. However, spinodal calculations reveal that their calibration of this model for CaO-Al₂O₃-SiO₂ produces liquation tielines that do not appear to be in agreement with experimental work. In addition, their calibration contains some strongly negative excess entropy parameters and these permit a most unusual inverted liquation field to start at approximately >2115°C, wt% (SiO₂, Al₂O₃, CaO) = (70, 16, 14). This inverted field expands rapidly to cover most of the ternary for T> 2300°C and continues to expand at all higher temperatures. The Berman and Brown calibration for this system carries these negative excess entropies of mixing because the solution model is very strongly asymmetric as a result of the use of normal oxide mole weights in modelling the configurational entropy of mixing. A suggestion is made for a fairly natural restriction on the relative sizes of empirical models for excess versus configurational entropy.

Expressions are presented for the general consolute condition (all solution models) and for the second and third partials of the B&B G^x model.     

Dissolution of jarosite [KFe3(SO4)2(OH)6] at pH 2 and 8: Insights from batch experiments and computational modelling

Jarosite [KFe₃(SO₄)₂(OH)₆] is a mineral that is common in acidic, sulphate-rich environments, such as acid sulphate soils derived from pyrite-bearing sediments, weathering zones of sulphide ore deposits and acid mine or acid rock drainage (ARD/AMD) sites. The structure of jarosite is based on linear tetrahedral-octahedral-tetrahedral (T-O-T) sheets, made up from slightly distorted FeO₆ octahedra and SO₄ tetrahedra. Batch dissolution experiments carried out on synthetic jarosite at pH 2, to mimic environments affected by ARD/AMD, and at pH 8, to simulate ARD/AMD environments recently remediated with slaked lime (Ca(OH)₂), suggest first order dissolution kinetics. Both dissolution reactions are incongruent, as revealed by non-ideal dissolution of the parent solids and, in the case of the pH 8 dissolution, because a secondary goethite precipitate forms on the surface of the dissolving jarosite grains. The pH 2 dissolution yields only aqueous K, Fe, and SO₄. Aqueous, residual solid, and computational modelling of the jarosite structure and surfaces using the GULP and MARVIN codes, respectively, show for the first time that there is selective dissolution of the A- and T-sites, which contain K and SO₄, respectively, relative to Fe, which is located deep within the T-O-T jarosite structure. These results have implications for the chemistry of ARD/AMD waters, and for understanding reaction pathways of ARD/AMD mineral dissolution.     

A model for silicate melt viscosity in the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8

Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi₂O₆ (Di)-CaAl₂Si₂O₈ (An)-NaAlSi₃O₈ (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10^-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (b_i=1,2.6, c_j=1,2..6) representing linear (e.g., b_i=1:3) and higher order, nonlinear (e.g., b_i=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of T_g for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have T_g values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.     

Thermochemistry of glasses along joins of pyroxene stoichiometry in the system Ca2Si2O6-Mg2Si2O6-Al4O6

Enthalpies of solution in 2PbO · B₂O₃ at 974 K have been measured for glasses along the joins Ca₂Si₂O₆ (Wo)-Mg₂Si₂O₆ (En) and Mg₂Si₂O₆-MgAl₂SiO₆ (MgTs). Heats of mixing are symmetric and negative for Wo-En with W_H = ?31.0 ± 3.6 kJ mol^?. Negative heats of mixing were also found for the En-MgTs glasses (W_H = ?33.4 ± 3.7 kJ mol^?).Enthalpies of vitrification of pyroxenes and pyroxenoids generally increase with decreasing alumina content and with decreasing basicity of the divalent cation.Heats of mixing along several glassy joins show systematic trends. When only non-tetrahedral cations mix (outside the aluminosilicate framework), small exothermic heats of mixing are seen. When both nontetrahedral and framework cations mix (on separate sublattices, presumably), the enthalpies of mixing are substantially more negative. Maximum enthalpy stabilization near compositions with Al/Si ≈ 1 is suggested.     

The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C

The mineral solubility model of Harvie and Weare (1980) is extended to the eight component system, Na-K-Mg-Ca-H-Cl-SO₄-OH-HCO₃-CO₃-CO₂-H₂O at 25°C to high concentrations. The model is based on the semi-empirical equations of Pitzer (1973) and co-workers for the thermodynamics of aqueous electrolyte solutions. The model is parameterized using many of the available isopiestic, electromotive force, and solubility data available for many of the subsystems. The predictive abilities of the model are demonstrated by comparison to experimental data in systems more complex than those used in parameterization. The essential features of a chemical model for aqueous electrolyte solutions and the relationship between pH and the equilibrium properties of a solution are discussed.     

The bearing of the system CaMgSi2O6CaAl2SiO6CaFeAlSiO6 on fassaitic pyroxene

The system CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi₂O₆-rich portion is Cpx + An + Mel and that in the CaMgSi₂O₆-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO₆ component of the system. The Al₂O₃ content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al₂O₃ with 3.9 wt.% Fe₂O₃. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO₆ content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi₂O₆CaAl₂SiO₆CaFeAlSiO₆ triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl₂SiO₆ and CaFeAlSiO₅ components as crystallization proceeds. These results agree with those obtained in the experimental study.     

Stability of sapphirine-bearing mineral assemblages in the system FeO-MgO-Al2O3-SiO2 and metamorphic P-T parameters of aluminous granulites

Consistent thermodynamic data on the properties of pure mineral end members and the mixing properties of solid solutions in the system FeO-MgO-Al₂O₃-SiO₂ were employed to simulate phase relations of sapphirine, garnet, spinel, orthopyroxene, cordierite, quartz, Al silicates, and corundum. Compositional variations of the solid solutions with temperature notably modify the topology of the P-T diagrams, which differ from the petrogenetic grids widely used in the literature. It is worth noting that the evaluation of P-T metamorphic conditions based on reaction relations in sapphirine-bearing assemblages cannot be so far considered reliable enough. The lower stability limit of the sapphirine + quartz assemblage in the system in question is possibly located at much lower P-T parameters: at least 835°C and ∼6 kbar. The sapphirine + kyanite assemblage can be stable at temperatures below 860°C and a pressure of ∼11 kbar, and the stability field of the sapphirine + olivine assemblage is narrow and constrained to temperatures no higher than ∼800°C.     

Diffusion in silicate melts: II. Multicomponent diffusion in CaOAl2O3SiO2 at 1500°C and 1 GPa

Chemical diffusion profiles in molten CaO---Al₂O₃---SiO₂ have been measured over a large range of compositions at 1500°C and l GPa. The diffusion profiles have been inverted for effective binary diffusion coefficients (EBDCs) and for the chemical diffusion matrix. The EBDCs are shown to depend strongly on both composition and direction of diffusion in composition space. The dependence of EBDCs on direction in composition space, which for the system studied here can be as large as a factor of seven, severely limits the applicability of EBDCs to interdiffusion in any direction other than the one used to derive the EBDCs.

The chemical diffusion matrix for molten CaO---Al₂O₃---SiO₂ was determined using diffusion profiles from two or three mutually orthogonal diffusion couples in the ternary composition space. All features of the diffusion profiles shown in this work can be reproduced by representing the chemical fluxes in the three-component system as a linear combination of concentration gradients via a 2 × 2 diffusion matrix. Chemical diffusion in molten CaO---Al₂O₃---SiO₂ shows clear evidence of strong diffusive coupling among the components. This can be seen in the uphill diffusion profiles of components that were initially uniform, in the fact that the apparent rate of diffusion of some components is a strong function of direction in composition space, and most quantitatively in the magnitude of off-diagonal elements of the diffusion matrix relative to the magnitude of the diagonal elements. SiO₂ for example, is found to be strongly coupled with CaO in relatively silicic melts, whereas Al₂O₃ is strongly coupled with CaO in less silicic melts. Furthermore, the coupling of CaO with either Al₂O₃ or Si02 reverses sign between more and less polymerized compositions. Interdiffusion profiles in natural melts have numerous features that suggest similar coupling between Al₂O₃ and CaO and between SiO₂ and CaO.