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.     

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.     

Kimberlite petrogenesis: Insights from clinopyroxene-melt partitioning experiments at 6 GPa in the CaO-MgO-Al2O3-SiO2-CO2 system

In this experimental study, we examine the mineral-melt partitioning of major and trace elements between clinopyroxene and CO₂-rich kimberlitic melts at a pressure of 6 GPa and temperatures of 1410°C and 1430°C. The melts produced contain ∼ 28 wt% dissolved CO₂, and are saturated with olivine and clinopyroxene. To assess the effects of temperature, crystal and melt compositions on trace element partitioning, experiments were performed in the model CaO-MgO-Al₂O₃-SiO₂-CO₂ system. Our results reveal that all the elements studied, except Al, Mg, Si, and Ga, are incompatible in clinopyroxene. Partition coefficients show a considerable range in magnitude, from ∼ 10⁻³ for D_U and D_Ba to ∼ 2.5 for D_Si. The two experimental runs show similar overall partitioning patterns with the D values being lower at 1430°C. Rare earth elements display a wide range of partition coefficients, D_La (0.012-0.026) being approximately one order of magnitude lower than D_Lu (0.18-0.23). Partition coefficients for the 2+ and 3+ cations entering the M2-site exhibit a near-parabolic dependence on radius of the incorporated cations as predicted from the lattice strain model. This underlines the contribution made by the crystal structure toward controlling the distribution of trace elements. Using data obtained in this study combined with that in the published literature, we also discuss the effects that other important parameters, namely, melt composition, pressure, and temperature, could have on partitioning.Our partition coefficients have been used to model the generation of the Group I (GI) kimberlites from South Africa. The numerical modeling shows that kimberlitic melts can be produced by ∼0.5% melting of a MORB-type depleted source that has been enriched by small-degree melts originating from a similar depleted source. This result suggests that the source of GI kimberlites may be located at the lithosphere-asthenosphere transition. Percolation of small degree melts from the asthenosphere would essentially create a metasomatic horizon near the bottom of the non-convecting sublithospheric mantle. Accumulation of such small degree melts together with the presence of volatiles and conductive heating would trigger melting of the ambient mantle and subsequently lead to eruption of kimberlitic melts. Additionally, our model shows that the GI source can be generated by metasomatism of a 2 Ga old MORB source ca. 1 Ga ago. Assuming that MORB-type mantle is the most depleted source of magmas on earth, then this is the oldest age at which the GI source could have existed. However, this age most likely reflects the average age of a series of metasomatic events than that of a single event.     

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.     

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.     

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:

     

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.

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.     

11.

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.     

12.

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     

13.

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.     

14.

Fe²⁺–Mg fractionation between orthopyroxene and spinel: experimental calibration in the system FeO–MgO–Al₂O₃–Cr₂O₃–SiO₂, and applications     

H. P. Liermann  J. Ganguly 《Contributions to Mineralogy and Petrology》2007,154(4):491

     

15.

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.     

16.

The thermodynamic properties and phase relations of some minerals in the system CaO-AI2O3-SiO2-H2O     

Dexter Perkins  Edgar F. Westrum  Eric J. Essene 《Geochimica et cosmochimica acta》1980,44(1):61-84

The heat capacities of lawsonite, margante, prehnite and zoisite have been measured from 5 to 350 K with an adiabatic-shield calorimeter and from 320 to 999.9 K with a differential-scanning calorimeter. At 298.15 K, their heat capacities, corrected to end-member compositions, are 66.35, 77.30, 79.13 and 83.84 cal K^?1 mol^?1; their entropies are 54.98, 63.01, 69.97 and 70.71 cal K^?1 mol^?1, respectively. Their high-temperature heat capacities are described by the following equations (in calories, K, mol): Lawsonite (298–600 K): Cp° = 66.28 + 55.95 × 10^?3T ? 15.27 × 10⁵T^?2 Margarite (298–1000 K): Cp° = 101.83 + 24.17 × 10^?3T ? 30.24 × 10⁵T^?2 Prehnite (298–800 K): Cp° = 97.04 + 29.99 × 10^?3T ? 25.02 × 10⁵T^?2 Zoisite (298–730 K): Cp° = 98.92 + 36.36 × 10^?3T ? 24.08 × 10⁵T^?2 Calculated Clapeyron slopes for univariant equilibria in the CaO-Al₂O₃-SiO₂-H₂O system compare well with experimental results in most cases. However, the reaction zoisite + quartz = anorthite + grossular + H₂O and some reactions involving prehnite or margarite show disagreements between the experimentally determined and the calculated slopes which may possibly be due to disorder in experimental run products. A phase diagram, calculated from the measured thermodynamic values in conjunction with selected experimental results places strict limits on the stabilities of prehnite and assemblages such as prehnite + aragonite, grossular + lawsonite, grossular + quartz, zoisite + quartz, and zoisite + kyanite + quartz. The presence of this last assemblage in eclogites indicates that they were formed at moderate to high water pressure.     

17.

Calcite–dolomite geothermometry in the system CaCO₃–MgCO₃–FeCO₃: an experimental study     

ROGER POWELL  DIANA M. CONDLIFFE  ERIC CONDLIFFE 《Journal of Metamorphic Geology》1984,2(1):33-41

Abstract An experimental study of the system CaCO₃–MgCO₃–FeCO₃ was undertaken in order to calibrate the iron correction to the calcite–dolomite geothermometer, which is based on the solubility of magnesium in calcite in the assemblage calcite + dolomite. The experiments, at 450°C and lower temperatures, resulted in products with a very small grain size and incomplete equilibration. However, application of a carefully-devised automatic data processing algorithm to analyses of the phases in experimental charges, combined with a thermodynamic analysis, results in geothermometer diagrams which should be preferred to previous theoretical predictions.     

18.

Experimental study of subsolidus phase relations and mixing properties of pyroxene in the system CaO-Al2O3-SiO2     

Tibor Gasparik 《Geochimica et cosmochimica acta》1984,48(12):2537-2545

Subsolidus phase relations in the system CaO-Al₂O₃-SiO₂ (CAS) were experimentally determined with tight reversals of several univariant curves and with 14 equilibration experiments containing the assemblage pyroxene + anorthite, where pyroxene is a binary solid solution of Ca-Tschermak (CaTs-CaAl₂SiO₆) and Ca-Eskola (CaEs-Ca_0.5AlSi₂O₆) endmembers.Reversals were obtained on the following reactions (bar, °C): 3An = Gr + 2Ky + Q (P = 22T ? 700), 3An + Cor = Gr + 3Ky (P = 21.8T ? 950), 3CaTs= Gr + 2Cor(P = 55T ? 53900), and 6CaTs_{(1 ? x)}CaEs_x = 2(1 ? 2x)Gr + 4(1 ? 2x)Cor + 9xAn. Observed slopes indicate 9.8 J/mol · K of Al-Si disorder in Ca-Tschermak pyroxene and 5.3 J/mol·K of Al-Si disorder in anorthite, at 1300°C. It is suggested that Al-Si disorder in anorthite increases by 1.9 J/mol · K from 700°C to 1300°C.Compositions of CaTs-CaEs pyroxene in equilibrium with anorthite and PbO-rich liquid were experimentally determined at 1400–1430°C and 22.7–30.8 kbar. Microprobe measurements gave compositions which are consistent with an ideal pyroxene solution and the following parameters for the reaction 3An = 2CaTs + 2CaEs (J, bar, K): 2RTln(X_CaTs · X_CaEs) + 60200 + 86.4T ? (5.06 + 13 × 10^?7P)P = 0, resulting in ΔH⁰_j = ?39.8 kJ/mol and S⁰ = 461.8 J/mol · K for the Ca-Eskola endmember at 1300°C. The obtained properties of the Ca-Eskola component are necessary for thermobarometry based on pyroxene bearing assemblages containing plagioclase, quartz, or kyanite.     

19.

A hydrothermal investigation of the system FeO, Fe₂O₃, TiO₂     

Anders Lindh 《Lithos》1972,5(4):325-343

Phase relations in the system FeO---Fe₂O₃---TiO₂, at temperatures ranging between 300°C and 700°C, have been investigated experimentally with special refference to the reaction Fe₃O₄ + TiO₂ = Fe₂O₃ + FeTiO₃. Pressure was varied between 500 and 2000 bars but its effect was negligible. Magnetite and rutile are the stable assemblage at temperatures above 550 dgC, and hematite and ilmenite are stable for lower temperatures. The equilibrium oxygen fugacity is estimated to be 10^−17.5 bars at equilibrium temperature. It is suggested that intermediate hematite-ilmenite solid solutions are inhomogeneous, consisting of ‘domains’ of hematite and ilmenite. The ‘domains’ are too small to be resolved by X-ray diffraction techniques. The top of the solvus curve in the hematite-ilmenite solution corresponds to a temperature of 660°C. Regular solution theory is not applicable to the solid solution.     

20.

The effect of sulfate on aluminum concentrations in natural waters: some stability relations in the system Al₂O₃-SO₃-H₂O at 298 K     

Darrell Kirk Nordstrom 《Geochimica et cosmochimica acta》1982,46(4):681-692

While gibbsite and kaolinite solubilities usually regulate aluminum concentrations in natural waters, the presence of sulfate can dramatically alter these solubilities under acidic conditions, where other, less soluble minerals can control the aqueous geochemistry of aluminum. The likely candidates include alunogen, Al₂(SO₄)₃ · 17H₂O, alunite, KAl₃(SO₄)₂(OH)₆, jurbanite, Al(SO₄)(OH) · 5H₂O, and basaluminite, Al₄(SO₄)(OH)₁₀ · 5H₂O. An examination of literature values shows that the log $\text{K}{}_{\mathrm{sp}}\text{= ?85.4}$ for alunite and log $\text{K}{}_{\mathrm{sp}}\text{= ?117.7}$ for basaluminite. In this report the log $\text{K}{}_{\mathrm{sp}}\text{= ?7.0}$ is estimated for alunogen and log $\text{K}{}_{\mathrm{sp}}\text{= ?17.8}$ is estimated for jurbanite. The solubility and stability relations among these four minerals and gibbsite are plotted as a function of pH and sulfate activity at 298 K. Alunogen is stable only at pH values too low for any natural waters (<0) and probably only forms as efflorescences from capillary films. Jurbanite is stable from $\text{pH < 0}$ up to the range of 3–5 depending on sulfate activity. Alunite is stable at higher pH values than jurbanite, up to 4–7 depending on sulfate activity. Above these pH limits gibbsite is the most stable phase. Basaluminite, although kinetically favored to precipitate, is metastable for all values of pH and sulfate activity. These equilibrium calculations predict that both sulfate and aluminum can be immobilized in acid waters by the precipitation of aluminum hydroxysulfate minerals.Considerable evidence supports the conclusion that the formation of insoluble aluminum hydroxy-sulfate minerals may be the cause of sulfate retention in soils and sediments, as suggested by Adams and Rawajfih (1977), instead of adsorption.     

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

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.     

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.     

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     

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.     

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.     

The thermodynamic properties and phase relations of some minerals in the system CaO-AI2O3-SiO2-H2O

The heat capacities of lawsonite, margante, prehnite and zoisite have been measured from 5 to 350 K with an adiabatic-shield calorimeter and from 320 to 999.9 K with a differential-scanning calorimeter. At 298.15 K, their heat capacities, corrected to end-member compositions, are 66.35, 77.30, 79.13 and 83.84 cal K^?1 mol^?1; their entropies are 54.98, 63.01, 69.97 and 70.71 cal K^?1 mol^?1, respectively. Their high-temperature heat capacities are described by the following equations (in calories, K, mol): Lawsonite (298–600 K): Cp° = 66.28 + 55.95 × 10^?3T ? 15.27 × 10⁵T^?2 Margarite (298–1000 K): Cp° = 101.83 + 24.17 × 10^?3T ? 30.24 × 10⁵T^?2 Prehnite (298–800 K): Cp° = 97.04 + 29.99 × 10^?3T ? 25.02 × 10⁵T^?2 Zoisite (298–730 K): Cp° = 98.92 + 36.36 × 10^?3T ? 24.08 × 10⁵T^?2 Calculated Clapeyron slopes for univariant equilibria in the CaO-Al₂O₃-SiO₂-H₂O system compare well with experimental results in most cases. However, the reaction zoisite + quartz = anorthite + grossular + H₂O and some reactions involving prehnite or margarite show disagreements between the experimentally determined and the calculated slopes which may possibly be due to disorder in experimental run products. A phase diagram, calculated from the measured thermodynamic values in conjunction with selected experimental results places strict limits on the stabilities of prehnite and assemblages such as prehnite + aragonite, grossular + lawsonite, grossular + quartz, zoisite + quartz, and zoisite + kyanite + quartz. The presence of this last assemblage in eclogites indicates that they were formed at moderate to high water pressure.     

Calcite–dolomite geothermometry in the system CaCO3–MgCO3–FeCO3: an experimental study

Abstract An experimental study of the system CaCO₃–MgCO₃–FeCO₃ was undertaken in order to calibrate the iron correction to the calcite–dolomite geothermometer, which is based on the solubility of magnesium in calcite in the assemblage calcite + dolomite. The experiments, at 450°C and lower temperatures, resulted in products with a very small grain size and incomplete equilibration. However, application of a carefully-devised automatic data processing algorithm to analyses of the phases in experimental charges, combined with a thermodynamic analysis, results in geothermometer diagrams which should be preferred to previous theoretical predictions.     

Experimental study of subsolidus phase relations and mixing properties of pyroxene in the system CaO-Al2O3-SiO2

Subsolidus phase relations in the system CaO-Al₂O₃-SiO₂ (CAS) were experimentally determined with tight reversals of several univariant curves and with 14 equilibration experiments containing the assemblage pyroxene + anorthite, where pyroxene is a binary solid solution of Ca-Tschermak (CaTs-CaAl₂SiO₆) and Ca-Eskola (CaEs-Ca_0.5AlSi₂O₆) endmembers.Reversals were obtained on the following reactions (bar, °C): 3An = Gr + 2Ky + Q (P = 22T ? 700), 3An + Cor = Gr + 3Ky (P = 21.8T ? 950), 3CaTs= Gr + 2Cor(P = 55T ? 53900), and 6CaTs_{(1 ? x)}CaEs_x = 2(1 ? 2x)Gr + 4(1 ? 2x)Cor + 9xAn. Observed slopes indicate 9.8 J/mol · K of Al-Si disorder in Ca-Tschermak pyroxene and 5.3 J/mol·K of Al-Si disorder in anorthite, at 1300°C. It is suggested that Al-Si disorder in anorthite increases by 1.9 J/mol · K from 700°C to 1300°C.Compositions of CaTs-CaEs pyroxene in equilibrium with anorthite and PbO-rich liquid were experimentally determined at 1400–1430°C and 22.7–30.8 kbar. Microprobe measurements gave compositions which are consistent with an ideal pyroxene solution and the following parameters for the reaction 3An = 2CaTs + 2CaEs (J, bar, K): 2RTln(X_CaTs · X_CaEs) + 60200 + 86.4T ? (5.06 + 13 × 10^?7P)P = 0, resulting in ΔH⁰_j = ?39.8 kJ/mol and S⁰ = 461.8 J/mol · K for the Ca-Eskola endmember at 1300°C. The obtained properties of the Ca-Eskola component are necessary for thermobarometry based on pyroxene bearing assemblages containing plagioclase, quartz, or kyanite.     

A hydrothermal investigation of the system FeO, Fe2O3, TiO2

Phase relations in the system FeO---Fe₂O₃---TiO₂, at temperatures ranging between 300°C and 700°C, have been investigated experimentally with special refference to the reaction Fe₃O₄ + TiO₂ = Fe₂O₃ + FeTiO₃. Pressure was varied between 500 and 2000 bars but its effect was negligible. Magnetite and rutile are the stable assemblage at temperatures above 550 dgC, and hematite and ilmenite are stable for lower temperatures. The equilibrium oxygen fugacity is estimated to be 10^−17.5 bars at equilibrium temperature. It is suggested that intermediate hematite-ilmenite solid solutions are inhomogeneous, consisting of ‘domains’ of hematite and ilmenite. The ‘domains’ are too small to be resolved by X-ray diffraction techniques. The top of the solvus curve in the hematite-ilmenite solution corresponds to a temperature of 660°C. Regular solution theory is not applicable to the solid solution.     

The effect of sulfate on aluminum concentrations in natural waters: some stability relations in the system Al2O3-SO3-H2O at 298 K

While gibbsite and kaolinite solubilities usually regulate aluminum concentrations in natural waters, the presence of sulfate can dramatically alter these solubilities under acidic conditions, where other, less soluble minerals can control the aqueous geochemistry of aluminum. The likely candidates include alunogen, Al₂(SO₄)₃ · 17H₂O, alunite, KAl₃(SO₄)₂(OH)₆, jurbanite, Al(SO₄)(OH) · 5H₂O, and basaluminite, Al₄(SO₄)(OH)₁₀ · 5H₂O. An examination of literature values shows that the log $\text{K}{}_{\mathrm{sp}}\text{= ?85.4}$ for alunite and log $\text{K}{}_{\mathrm{sp}}\text{= ?117.7}$ for basaluminite. In this report the log $\text{K}{}_{\mathrm{sp}}\text{= ?7.0}$ is estimated for alunogen and log $\text{K}{}_{\mathrm{sp}}\text{= ?17.8}$ is estimated for jurbanite. The solubility and stability relations among these four minerals and gibbsite are plotted as a function of pH and sulfate activity at 298 K. Alunogen is stable only at pH values too low for any natural waters (<0) and probably only forms as efflorescences from capillary films. Jurbanite is stable from $\text{pH < 0}$ up to the range of 3–5 depending on sulfate activity. Alunite is stable at higher pH values than jurbanite, up to 4–7 depending on sulfate activity. Above these pH limits gibbsite is the most stable phase. Basaluminite, although kinetically favored to precipitate, is metastable for all values of pH and sulfate activity. These equilibrium calculations predict that both sulfate and aluminum can be immobilized in acid waters by the precipitation of aluminum hydroxysulfate minerals.Considerable evidence supports the conclusion that the formation of insoluble aluminum hydroxy-sulfate minerals may be the cause of sulfate retention in soils and sediments, as suggested by Adams and Rawajfih (1977), instead of adsorption.