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.     

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.     

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:

     

4.

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.     

5.

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.     

6.

Solubility of grossular, Ca₃Al₂Si₃O₁₂, in H₂O-NaCl solutions at 800 °C and 10 kbar, and the stability of garnet in the system CaSiO₃-Al₂O₃-H₂O-NaCl     

Robert C. Newton 《Geochimica et cosmochimica acta》2007,71(21):5191-5202

The solubility and stability of synthetic grossular were determined at 800 °C and 10 kbar in NaCl-H₂O solutions over a large range of salinity. The measurements were made by evaluating the weight losses of grossular, corundum, and wollastonite crystals equilibrated with fluid for up to one week in Pt capsules and a piston-cylinder apparatus. Grossular dissolves congruently over the entire salinity range and displays a large solubility increase of 0.0053 to 0.132 molal Ca₃Al₂Si₃O₁₂ with increasing NaCl mole fraction (X_NaCl) from 0 to 0.4. There is thus a solubility enhancement 25 times the pure H₂O value over the investigated range, indicating strong solute interaction with NaCl. The Ca₃Al₂Si₃O₁₂ mole fraction versus NaCl mole fraction curve has a broad plateau between X_NaCl = 0.2 and 0.4, indicating that the solute products are hydrous; the enhancement effect of NaCl interaction is eventually overtaken by the destabilizing effect of lowering H₂O activity. In this respect, the solubility behavior of grossular in NaCl solutions is similar to that of corundum and wollastonite. There is a substantial field of stability of grossular at 800 °C and 10 kbar in the system CaSiO₃-Al₂O₃-H₂O-NaCl. At high Al₂O₃/CaSiO₃ bulk compositions the grossular + fluid field is limited by the appearance of corundum. Zoisite appears metastably with corundum in initially pure H₂O, but disappears once grossular is nucleated. At X_NaCl = 0.3, however, zoisite is stable with corundum and fluid; this is the only departure from the quaternary system encountered in this study. Corundum solubility is very high in solutions containing both NaCl and CaSiO₃: Al₂O₃ molality increases from 0.0013 in initially pure H₂O to near 0.15 at X_NaCl = 0.4 in CaSiO₃-saturated solutions, a >100-fold enhancement. In contrast, addition of Al₂O₃ to wollastonite-saturated NaCl solutions increases CaSiO₃ molality by only 12%. This suggests that at high pH (quench pH is 11-12), the stability of solute Ca chloride and Na-Al ± Si complexes account for high Al₂O₃ solubility, and that Ca-Al ± Si complexes are minor. The high solubility and basic dissolution reaction of grossular suggest that Al may be a very mobile component in calcareous rocks in the deep crust and upper mantle when migrating saline solutions are present.     

7.

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.     

8.

Enthalpy of formation of Fe₃Al₂Si₃O₁₂ (almandine) by high temperature alkali borate solution calorimetry     

C. Chatillon-Colinet  O.J. Kleppa  R.C. Newton  D. Perkins 《Geochimica et cosmochimica acta》1983,47(3):439-444

A high-temperature solution calorimetric method suitable for thermochemical studies of anhydrous minerals containing Fe²⁺ ions has been developed. The method is based on an oxide melt solvent with 52 wt% LiBO₂ and 48 wt% NaBO₂ maintained at a temperature of 750°C. In a first application of this method the enthalpies of solution of synthetic almandine, fayalite, a mixture of fayalite plus quartz on FeSiO₃ composition, and natural quartz were measured. For the reaction:

the enthalpy change at 1023 K is ?3.82 ± 0.87 kcal, based on fayalite, quartz, corundum and almandine, and ?5.96 ± 0.90 kcal based on the fayalite plus quartz mixture, corundum, and almandine. These values lead to standard molar enthalpies of formation of almandine from the oxides at 1023 K of ?14.10 ± 1.22 kcal and ?16.24 ± 1.74 kcal, respectively. The measured enthalpy of formation of almandine is less negative by several kilocalories than values derived from analysis of the phase equilibrium work of Hsu (1968), but in closer agreement with the phase equilibrium study of O'Neill and Wood (1979) and similar to the phase equilibrium deduction of Froese (1973).The agreement of the present almandine enthalpy of formation with O'Neill and Wood (1979) and Froese (1973) suggests that almandine entropies at 298 K to be obtained from their studies, in the range 79–81 cal/K, are more nearly correct than the several estimates based on oxide sum and volume-entropy systematics, most of which are much lower.     

9.

Thermochemistry of synthetic clinopyroxenes on the join CaMgSi₂O₆-Mg₂Si₂O₆     

R.C. Newton  T.V. Charlu  P.A.M. Anderson  O.J. Kleppa 《Geochimica et cosmochimica acta》1979,43(1):55-60

Enthalpies of solution of synthetic clinopyroxenes on the join CaMgSi₂O₆-Mg₂Si₂O₆ have been measured in a melt of composition Pb₂B₂O₅ at 970 K. Most of the measurements were made on samples crystallized at 1600°–1700°C and 30 kbar pressure, which covered the range 0–78 mole per cent Mg₂Si₂O₆, and whose X-ray patterns could be satisfactorily indexed on the diopside (C2/c) structure. For the reaction: Mg₂Si₂O₆→-Mg₂Si₂O₆ enstatite diopside the present data, in conjunction with previous and new measurements on Mg₂Si₂O₆ enstatite, determine ΔH° ~ 2 kcal and W_H (regular solution parameter) ~ 7 kcal. These values are in good agreement with those deduced by Saxena and Nehru (1975) from a study of high temperature, high pressure phase equilibrium data under the assumption that the excess entropy of mixing is small, but, in light of the recent theoretical treatment of Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), the meanings of these parameters may be ambiguous.Heat of solution measurements on Ca-rich binary diopsides made by annealing glasses at 1358°C in air gave slighter higher values than the higher temperature high pressure samples. This may be evidence for some (Ca, Mg) disorder of the sort postulated by Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), although no differences in heat of solution dependent on synthesis temperature in the range 1350°–1700°C could be found in stoichiometric CaMgSi₂O₆.     

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.

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

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

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

12.

Thermochemical study of glasses in the system NaAlSi₃O₈-KAlSi₃O₈-Si₄O₈ and the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈     

Richard L. Hervig  Alexandra Navrotsky 《Geochimica et cosmochimica acta》1984,48(3):513-522

Enthalpies of solution in 2PbO · B₂O₃ at 981 K have been measured for glasses in the system albite-orthoclase-silica and along the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈. The join KAlSi₃O₈-Si₄O₈ shows zero heat of mixing similar to that found previously for NaAlSi₃O₈-Si₄O₈ glasses. Albite-orthoclase glasses show negative heats of mixing symmetric about Ab₅₀Or₅₀ (W_n = ? 2.4 ± 0.8 kcal). Negative heats of (Na, K) mixing are also found at $\text{Si}\text{(Si + Al)}\text{= 0.6.}$ Ternary excess enthalpies of mixing in the glassy system Ab-Or-4Q are positive but rarely exceed 1 kcal mol^?1.Using earlier studies of the thermodynamic properties of the crystals, the present calorimetric data and the “two-lattice” entropy model, the albite-orthoclase phase diagram is calculated in good agreement with experimental data. Attempts to calculate albite-silica and orthoclase-silica phase diagrams reveal complexities probably related to significant (but unknown) mutual solid solubility between cristobalite and alkali feldspar and to the very small heat and entropy of fusion of SiO₂.     

13.

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     

14.

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.     

15.

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

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

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

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

16.

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.     

17.

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

     

18.

Mineral-solution equilibria—IV. Solubilities and the thermodynamic properties of FeCl₂⁰ in the system Fe₂O₃-H₂-H₂O-HCl     

N.Z. Boctor  R.K. Popp  J.D. Frantz 《Geochimica et cosmochimica acta》1980,44(10):1509-1518

The solubility of hematite in chloride-bearing hydrothermal fluids was determined in the temperature range 400–600°C and at 1000 and 2000 bars using double-capsule, rapid-quench hydrothermal techniques and a modification of the Ag + AgCl buffer method (Frantz and Popp, 1979). The changes in the molalities of associated hydrogen chloride () as a function of the molality of total iron in the fluid at constant temperature and pressure were used to identify the predominant species of iron in the hydrothermal fluid. The molality of associated HCl varied from 0.01 to 0.15. Associated FeCl₂⁰ was found to be the most abundant species in equilibrium with hematite. Determination of Cl/Fe in the fluid in equilibrium with hematite yields values approximately equal to 2.0 suggesting that ferrous iron is the dominant oxidation state.The equilibrium constant for the reaction Fe₂O₃ + 4HCl⁰ + H₂ = 2FeCl₂⁰ + 3H₂O was calculated and used to estimate the difference in Gibbs free energy between FeCl₂⁰ and HCl⁰ in the temperature range 400–600°C at 1000 and 2000 bars pressure.     

19.

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

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

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

20.

Al_2O_3/Ti:风化与蚀变过程中的原岩示踪     

严桃桃  龚庆杰  李金哲  陈晶  周伟伟  李睿堃 《岩石学报》2016,32(8):2425-2432

Al_2O_3和Ti在风化和热液蚀变等地球化学过程中通常被认为是不活动元素,两者的比值Al_2O_3/Ti常被用来指示地球化学作用过程。通过对中国157件火成岩样品元素含量平均值的统计发现,火成岩样品中Al_2O_3/Ti与SiO_2含量值之间存在着较好的幂函数关系:ln(Al_2O_3/Ti)=0.073×SiO_2-0.89,式中Al_2O_3和SiO_2和Ti含量单位均为%。本文基于得到的经验方程和TAS图解构建了一个新的判别岩石类型的图解——Al_2O_3-Ti图解。该图解可以区分酸性岩、中酸性岩、中性岩、中基性岩-基性岩四类岩性。通过对三个火成岩风化剖面的研究发现,花岗岩风化剖面从新鲜基岩到风化形成的土壤在Al_2O_3-Ti图解中均落在酸性岩区,花岗闪长岩风化剖面从新鲜基岩到风化形成的土壤样品均落在中酸性岩区,玄武质安山岩风化剖面从新鲜基岩到风化形成的土壤样品均落在中基性岩-基性岩区。不同风化程度的风化产物与其母岩在Al_2O_3-Ti图解中所在的区域一致,即Al_2O_3-Ti图解可以用来追溯火成岩风化产物的母岩岩性。通过对胶东焦家金矿和豫西牛头沟金矿两个矿区岩石的研究发现,黑云母花岗岩从新鲜岩石到其蚀变岩及其形成矿石的样品在Al_2O_3-Ti图解中均落在酸性岩区。玄武质安山岩从新鲜岩石到其蚀变岩及其形成矿石的样品在Al_2O_3-Ti图解中均落在中基性岩-基性岩区。即不同蚀变程度的蚀变产物与其原岩在Al_2O_3-Ti图解中所在的区域一致,这表明新构建的Al_2O_3-Ti图解可以用来示踪蚀变岩的原岩性质。     

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

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.     

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.     

Solubility of grossular, Ca3Al2Si3O12, in H2O-NaCl solutions at 800 °C and 10 kbar, and the stability of garnet in the system CaSiO3-Al2O3-H2O-NaCl

The solubility and stability of synthetic grossular were determined at 800 °C and 10 kbar in NaCl-H₂O solutions over a large range of salinity. The measurements were made by evaluating the weight losses of grossular, corundum, and wollastonite crystals equilibrated with fluid for up to one week in Pt capsules and a piston-cylinder apparatus. Grossular dissolves congruently over the entire salinity range and displays a large solubility increase of 0.0053 to 0.132 molal Ca₃Al₂Si₃O₁₂ with increasing NaCl mole fraction (X_NaCl) from 0 to 0.4. There is thus a solubility enhancement 25 times the pure H₂O value over the investigated range, indicating strong solute interaction with NaCl. The Ca₃Al₂Si₃O₁₂ mole fraction versus NaCl mole fraction curve has a broad plateau between X_NaCl = 0.2 and 0.4, indicating that the solute products are hydrous; the enhancement effect of NaCl interaction is eventually overtaken by the destabilizing effect of lowering H₂O activity. In this respect, the solubility behavior of grossular in NaCl solutions is similar to that of corundum and wollastonite. There is a substantial field of stability of grossular at 800 °C and 10 kbar in the system CaSiO₃-Al₂O₃-H₂O-NaCl. At high Al₂O₃/CaSiO₃ bulk compositions the grossular + fluid field is limited by the appearance of corundum. Zoisite appears metastably with corundum in initially pure H₂O, but disappears once grossular is nucleated. At X_NaCl = 0.3, however, zoisite is stable with corundum and fluid; this is the only departure from the quaternary system encountered in this study. Corundum solubility is very high in solutions containing both NaCl and CaSiO₃: Al₂O₃ molality increases from 0.0013 in initially pure H₂O to near 0.15 at X_NaCl = 0.4 in CaSiO₃-saturated solutions, a >100-fold enhancement. In contrast, addition of Al₂O₃ to wollastonite-saturated NaCl solutions increases CaSiO₃ molality by only 12%. This suggests that at high pH (quench pH is 11-12), the stability of solute Ca chloride and Na-Al ± Si complexes account for high Al₂O₃ solubility, and that Ca-Al ± Si complexes are minor. The high solubility and basic dissolution reaction of grossular suggest that Al may be a very mobile component in calcareous rocks in the deep crust and upper mantle when migrating saline solutions are present.     

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.     

Enthalpy of formation of Fe3Al2Si3O12 (almandine) by high temperature alkali borate solution calorimetry

A high-temperature solution calorimetric method suitable for thermochemical studies of anhydrous minerals containing Fe²⁺ ions has been developed. The method is based on an oxide melt solvent with 52 wt% LiBO₂ and 48 wt% NaBO₂ maintained at a temperature of 750°C. In a first application of this method the enthalpies of solution of synthetic almandine, fayalite, a mixture of fayalite plus quartz on FeSiO₃ composition, and natural quartz were measured. For the reaction:

the enthalpy change at 1023 K is ?3.82 ± 0.87 kcal, based on fayalite, quartz, corundum and almandine, and ?5.96 ± 0.90 kcal based on the fayalite plus quartz mixture, corundum, and almandine. These values lead to standard molar enthalpies of formation of almandine from the oxides at 1023 K of ?14.10 ± 1.22 kcal and ?16.24 ± 1.74 kcal, respectively. The measured enthalpy of formation of almandine is less negative by several kilocalories than values derived from analysis of the phase equilibrium work of Hsu (1968), but in closer agreement with the phase equilibrium study of O'Neill and Wood (1979) and similar to the phase equilibrium deduction of Froese (1973).The agreement of the present almandine enthalpy of formation with O'Neill and Wood (1979) and Froese (1973) suggests that almandine entropies at 298 K to be obtained from their studies, in the range 79–81 cal/K, are more nearly correct than the several estimates based on oxide sum and volume-entropy systematics, most of which are much lower.     

Thermochemistry of synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6

Enthalpies of solution of synthetic clinopyroxenes on the join CaMgSi₂O₆-Mg₂Si₂O₆ have been measured in a melt of composition Pb₂B₂O₅ at 970 K. Most of the measurements were made on samples crystallized at 1600°–1700°C and 30 kbar pressure, which covered the range 0–78 mole per cent Mg₂Si₂O₆, and whose X-ray patterns could be satisfactorily indexed on the diopside (C2/c) structure. For the reaction: Mg₂Si₂O₆→-Mg₂Si₂O₆ enstatite diopside the present data, in conjunction with previous and new measurements on Mg₂Si₂O₆ enstatite, determine ΔH° ~ 2 kcal and W_H (regular solution parameter) ~ 7 kcal. These values are in good agreement with those deduced by Saxena and Nehru (1975) from a study of high temperature, high pressure phase equilibrium data under the assumption that the excess entropy of mixing is small, but, in light of the recent theoretical treatment of Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), the meanings of these parameters may be ambiguous.Heat of solution measurements on Ca-rich binary diopsides made by annealing glasses at 1358°C in air gave slighter higher values than the higher temperature high pressure samples. This may be evidence for some (Ca, Mg) disorder of the sort postulated by Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), although no differences in heat of solution dependent on synthesis temperature in the range 1350°–1700°C could be found in stoichiometric CaMgSi₂O₆.     

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.     

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

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

Thermochemical study of glasses in the system NaAlSi3O8-KAlSi3O8-Si4O8 and the join Na1.6Al1.6Si2.4O8-K1.6Al1.6Si2.4O8

Enthalpies of solution in 2PbO · B₂O₃ at 981 K have been measured for glasses in the system albite-orthoclase-silica and along the join Na_1.6Al_1.6Si_2.4O₈-K_1.6Al_1.6Si_2.4O₈. The join KAlSi₃O₈-Si₄O₈ shows zero heat of mixing similar to that found previously for NaAlSi₃O₈-Si₄O₈ glasses. Albite-orthoclase glasses show negative heats of mixing symmetric about Ab₅₀Or₅₀ (W_n = ? 2.4 ± 0.8 kcal). Negative heats of (Na, K) mixing are also found at $\text{Si}\text{(Si + Al)}\text{= 0.6.}$ Ternary excess enthalpies of mixing in the glassy system Ab-Or-4Q are positive but rarely exceed 1 kcal mol^?1.Using earlier studies of the thermodynamic properties of the crystals, the present calorimetric data and the “two-lattice” entropy model, the albite-orthoclase phase diagram is calculated in good agreement with experimental data. Attempts to calculate albite-silica and orthoclase-silica phase diagrams reveal complexities probably related to significant (but unknown) mutual solid solubility between cristobalite and alkali feldspar and to the very small heat and entropy of fusion of SiO₂.     

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     

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.     

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.     

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.     

Mineral-solution equilibria—IV. Solubilities and the thermodynamic properties of FeCl20 in the system Fe2O3-H2-H2O-HCl

The solubility of hematite in chloride-bearing hydrothermal fluids was determined in the temperature range 400–600°C and at 1000 and 2000 bars using double-capsule, rapid-quench hydrothermal techniques and a modification of the Ag + AgCl buffer method (Frantz and Popp, 1979). The changes in the molalities of associated hydrogen chloride () as a function of the molality of total iron in the fluid at constant temperature and pressure were used to identify the predominant species of iron in the hydrothermal fluid. The molality of associated HCl varied from 0.01 to 0.15. Associated FeCl₂⁰ was found to be the most abundant species in equilibrium with hematite. Determination of Cl/Fe in the fluid in equilibrium with hematite yields values approximately equal to 2.0 suggesting that ferrous iron is the dominant oxidation state.The equilibrium constant for the reaction Fe₂O₃ + 4HCl⁰ + H₂ = 2FeCl₂⁰ + 3H₂O was calculated and used to estimate the difference in Gibbs free energy between FeCl₂⁰ and HCl⁰ in the temperature range 400–600°C at 1000 and 2000 bars pressure.     

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.     

Al_2O_3/Ti:风化与蚀变过程中的原岩示踪

Al_2O_3和Ti在风化和热液蚀变等地球化学过程中通常被认为是不活动元素,两者的比值Al_2O_3/Ti常被用来指示地球化学作用过程。通过对中国157件火成岩样品元素含量平均值的统计发现,火成岩样品中Al_2O_3/Ti与SiO_2含量值之间存在着较好的幂函数关系:ln(Al_2O_3/Ti)=0.073×SiO_2-0.89,式中Al_2O_3和SiO_2和Ti含量单位均为%。本文基于得到的经验方程和TAS图解构建了一个新的判别岩石类型的图解——Al_2O_3-Ti图解。该图解可以区分酸性岩、中酸性岩、中性岩、中基性岩-基性岩四类岩性。通过对三个火成岩风化剖面的研究发现,花岗岩风化剖面从新鲜基岩到风化形成的土壤在Al_2O_3-Ti图解中均落在酸性岩区,花岗闪长岩风化剖面从新鲜基岩到风化形成的土壤样品均落在中酸性岩区,玄武质安山岩风化剖面从新鲜基岩到风化形成的土壤样品均落在中基性岩-基性岩区。不同风化程度的风化产物与其母岩在Al_2O_3-Ti图解中所在的区域一致,即Al_2O_3-Ti图解可以用来追溯火成岩风化产物的母岩岩性。通过对胶东焦家金矿和豫西牛头沟金矿两个矿区岩石的研究发现,黑云母花岗岩从新鲜岩石到其蚀变岩及其形成矿石的样品在Al_2O_3-Ti图解中均落在酸性岩区。玄武质安山岩从新鲜岩石到其蚀变岩及其形成矿石的样品在Al_2O_3-Ti图解中均落在中基性岩-基性岩区。即不同蚀变程度的蚀变产物与其原岩在Al_2O_3-Ti图解中所在的区域一致,这表明新构建的Al_2O_3-Ti图解可以用来示踪蚀变岩的原岩性质。