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.     

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     

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:

     

5.

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

R.C. Newton  T.V. Charlu  O.J. Kleppa 《Geochimica et cosmochimica acta》1977,41(3):369-377

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.     

6.

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.     

7.

Spinel-garnet lherzolite transition in the system CaO-MgO-Al₂O₃-SiO₂ revisited: an in situ X-ray study   总被引：1，自引：0，他引：1  

M. Walter  T. KatsuraA. Kubo  T. ShinmeiO. Nishikawa  E. ItoC. Lesher  K. Funakoshi 《Geochimica et cosmochimica acta》2002,66(12):2109-2121

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.     

8.

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

Shantanu Keshav  Alexandre Corgne  Michael Bizimis  Yingwei Fei 《Geochimica et cosmochimica acta》2005,69(11):2829-2845

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.     

9.

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.     

10.

Thermochemistry of glasses and liquids in the systems CaMgSi₂O₆-CaAl₂Si₂O₈-NaAlSi₃O₈, SiO₂-CaAl₂Si₂O₈-NaAlSi₃O₈ and SiO₂-Al₂O₃-CaO-Na₂O     

A. Navrotsky  R. Hon  D.F. Weill  D.J. Henry 《Geochimica et cosmochimica acta》1980,44(10):1409-1423

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.     

11.

Structure of mineral glasses—I. The feldspar glasses NaAlSi₃O₈, KAlSi₃O₈, CaAl₂Si₂O₈     

Mark Taylor  Gordon E. Brown 《Geochimica et cosmochimica acta》1979,43(1):61-75

The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO₂ glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO₂ glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.     

12.

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.     

13.

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

Claude T. Herzberg 《Geochimica et cosmochimica acta》1978,42(7):945-957

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.     

14.

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

John R Beckett 《Geochimica et cosmochimica acta》2002,66(1):93-107

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.     

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.

A hydrofluoric acid solution calorimetric investigation of glasses in the systems NaAlSi₃O₈-KAlSi₃O₈ and NaAlSi₃O₈-Si₄O₈     

Guy L. Hovis 《Geochimica et cosmochimica acta》1984,48(3):523-525

Glasses in the systems NaAlSi₃O₈-KAlSi₃O₈ and NaAlSi₃O₈-Si₄O₈ have been studied by means of hydrofluoric acid solution calorimetry at 50°C. Results indicate small negative enthalpies of mixing in the former system and small positive departures from ideality in the latter.     

17.

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.     

18.

Structure, thermodynamics, and diffusion in CaAl₂Si₂O₈ liquid from first-principles molecular dynamics     

Nico de Koker 《Geochimica et cosmochimica acta》2010,74(19):5657-470

We have performed first-principles molecular dynamics simulations of CaAl₂Si₂O₈ (anorthite) liquid at pressures up to 120 GPa and temperatures of 3000, 4000 and 6000 K. At the lowest degrees of compression the liquid is seen to accommodate changes in density through decreasing the abundance of 3- and 4-membered rings, while increases in coordination of network forming cations take effect at somewhat higher degrees of compression. Results are fit to a fundamental thermodynamic relation with 4th order finite strain and 1st order thermal variable expansions. Upon compression by a factor of two, the Grüneisen parameter (γ) is found to increase continuously from 0.35 to 1.10. Weak temperature dependence in γ is thermodynamically consistent with a slight decrease in isochoric heat capacity (C_V), for which values of between 4.4 and 5.2 Nk_B are obtained, depending on the temperature. Pressure and temperature dependence of self-diffusivities is found to be well represented by an Arrhenius relation, except at 3000 K and pressures lower than 5 GPa, where self-diffusivities of Si, Al, and O increase with pressure. Analysis of the lifetimes of individual coordination species reveals that this phenomenon arises due to the disproportionately high stability of 4-fold coordinated Si, and to a lesser extent 4-fold coordinated Al. Our results represent a marked improvement in accuracy and reliability in describing the physics of CaAl₂Si₂O₈ liquid at deep mantle pressures, pointing the way to a general thermodynamic model of melts at extreme pressures and temperatures relevant to planetary-scale magma oceans and deep mantle partial melting.     

19.

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

     

20.

Thermodynamic modeling of melts in the system Na₂O-NaAlO₂-SiO₂-F₂O₋₁     

David Dolejš  Don R. Baker 《Geochimica et cosmochimica acta》2005,69(23):5537-5556

     

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

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.     

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.     

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.     

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.     

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.     

Thermochemistry of glasses and liquids in the systems CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAl2Si2O8-NaAlSi3O8 and SiO2-Al2O3-CaO-Na2O

Enthalpies of solution in 2PbO· B₂O₃ at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO₂-SiO₂, Ca_0.5AlO₂-SiO₂ and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO₂ = 0.42 (which includes the subsystem albite-silica) the system NaAlO₂-SiO₂ shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si₄O₈-CaAl₂Si₂O₈ shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, T_f, is many hundreds of degrees higher than the glass transition temperature, T_g. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.     

Structure of mineral glasses—I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8

The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO₂ glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO₂ glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.     

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.     

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.     

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.     

A hydrofluoric acid solution calorimetric investigation of glasses in the systems NaAlSi3O8-KAlSi3O8 and NaAlSi3O8-Si4O8

Glasses in the systems NaAlSi₃O₈-KAlSi₃O₈ and NaAlSi₃O₈-Si₄O₈ have been studied by means of hydrofluoric acid solution calorimetry at 50°C. Results indicate small negative enthalpies of mixing in the former system and small positive departures from ideality in the latter.     

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.     

Structure, thermodynamics, and diffusion in CaAl2Si2O8 liquid from first-principles molecular dynamics

We have performed first-principles molecular dynamics simulations of CaAl₂Si₂O₈ (anorthite) liquid at pressures up to 120 GPa and temperatures of 3000, 4000 and 6000 K. At the lowest degrees of compression the liquid is seen to accommodate changes in density through decreasing the abundance of 3- and 4-membered rings, while increases in coordination of network forming cations take effect at somewhat higher degrees of compression. Results are fit to a fundamental thermodynamic relation with 4th order finite strain and 1st order thermal variable expansions. Upon compression by a factor of two, the Grüneisen parameter (γ) is found to increase continuously from 0.35 to 1.10. Weak temperature dependence in γ is thermodynamically consistent with a slight decrease in isochoric heat capacity (C_V), for which values of between 4.4 and 5.2 Nk_B are obtained, depending on the temperature. Pressure and temperature dependence of self-diffusivities is found to be well represented by an Arrhenius relation, except at 3000 K and pressures lower than 5 GPa, where self-diffusivities of Si, Al, and O increase with pressure. Analysis of the lifetimes of individual coordination species reveals that this phenomenon arises due to the disproportionately high stability of 4-fold coordinated Si, and to a lesser extent 4-fold coordinated Al. Our results represent a marked improvement in accuracy and reliability in describing the physics of CaAl₂Si₂O₈ liquid at deep mantle pressures, pointing the way to a general thermodynamic model of melts at extreme pressures and temperatures relevant to planetary-scale magma oceans and deep mantle partial melting.