Thermochemistry of some pyroxenes and related compounds

The enthalpies of formation of a number of crystalline silicates from the oxides at 986 K were determined by oxide melt solution calorimetry. The values of ΔH°_{f, 986}, in kcal/mol, are as follows: MgCaSi₂O₆, ? 34.3 ± 0.4; CoCaSi₂O₆, ? 26.7 ± 0.5; NiCaSi₂O₆, ? 27.1 ± 0.5; MnSiO₃, ? 6.3 ± 0.3; Mn₂SiO₄, ? 12.2 ± 0.3. In addition, for MnSiO₃ (rhodonite)→ MnSiO₃ (pyroxmangite), ΔH°₉₈₆ = + 0.06 ± 0.3₃kcal/mol and for MgCaSi₂O₆ (diopside) = MgCaSi₂O₆ (glass), ΔH°₉₈₆ = + 21.0 ± 0.3 kcal/ mol. For hedenbergite, FeCaSi₂O₆, ΔG°₁₃₅₀ = ?25.6 ± 1.5 kcal/mol. In terms of pyroxene phase equilibria and crystal chemistry, our thermochemical data support the generally accepted crystallographic arguments that (a) the C2/c clinopyroxene structure increases in stability with decreasing size of the ion occupying the Ml site in the MCaSi₂O₆ series, and (b) the energy (and enthalpy) differences between orthopyroxene, clinopyroxene, and pyroxenoid structures are generally quite small and often less than 500 cal/mol in magnitude.     

Experimental determination of activities of FeO and Fe2O3 components in hydrous silicic melts under oxidizing conditions

The critical role of iron on crystal-silicate liquid relationships and melt differentiation is mainly controlled by the redox conditions prevailing in magmas, but the presently available database merely constrains the thermodynamic properties of iron-bearing components in strongly reduced and anhydrous molten silicate where iron is in the ferrous form. This paper provides new standard states for pure ferrous (FeO^liq) and ferric (Fe₂O₃^liq) molten iron oxides and extends the experimental database towards oxidizing and water-bearing domains. Iron-iridium, iron-platinum alloys, magnetite or hematite were equilibrated with synthetic silicic liquids at high temperature and high pressure under controlled oxygen fugacity (fO₂) to determine activity-composition relationships for FeO^liq and Fe₂O₃^liq. Between 1000 and 1300°C, the fO₂ ranges from that in air to 3-log units below that of the nickel-nickel oxide buffer (NNO). Experiments were performed on both anhydrous and hydrous melts containing up to 6-wt.% water. Incorporation of water under reducing conditions increases the activity coefficient of FeO^liq but has an opposite effect on Fe₂O₃^liq. As calcium is added to system, the effect of water becomes weaker and is inverted for Fe₂O₃^liq. Under oxidizing conditions, water has a negligible effect on both activities of FeO^liq and Fe₂O₃^liq. In contrast, changes in redox conditions dominate the activity coefficients of both FeO^liq and Fe₂O₃^liq, which increase significantly with increasing fO₂. The present results combined with the previous work provide a specific database on the energetics of iron in silicate melts that cover most of the condition prevailing in natural magmas.     

Thermochemical study of glasses in the system CaMgSi2O6-CaAl2SiO6

High temperature solution calorimetry of glasses in the system CaMgSi₂O₆ (Di)-CaAl₂SiO₆ (CaTs) show them to have negative enthalpies of mixing with a regular enthalpy parameter, W_H, of -11.4 ± 0.7 kcal. Negative heats of mixing between alumina-rich and alumina-poor glasses seem to be a general phenomenon in aluminosilicates and are not confined only to glassy systems containing anorthite as a component. The thermodynamic behavior of glasses in the system SiO₂-Ca_0.5;AlO₂-CaMgO₂ appears to vary in a smooth fashion, with small positive heats of mixing near SiO₂ and substantial negative heats of mixing for other compositions. The exothermic behavior with increasing $\text{A1}\text{(Al + Si)}$ may be related to local charge balance of M²⁺ and Al³⁺. The negative heats of mixing in MgCaSi₂O₆-CaAl₂SiO₆, MgCaSi₂O₆-CaAl₂Si₂O₈ and NaAlSi₃O₈-CaAl₂Si₂O₈ glasses are in contrast to the positive heats of mixing found in MgCaSi₂O₆-CaAl₂SiO₆ (pyroxene) and NaAlSi₃O₈-CaAl₂Si₂O₈ (high plagioclase) crystalline solid solutions.     

Olivine/melt transition metal partitioning, melt composition, and melt structure—Melt polymerization and Q-speciation in alkaline earth silicate systems

The two most abundant network-modifying cations in magmatic liquids are Ca²⁺ and Mg²⁺. To evaluate the influence of melt structure on exchange of Ca²⁺ and Mg²⁺ with other geochemically important divalent cations (m-cations) between coexisting minerals and melts, high-temperature (1470-1650 °C), ambient-pressure (0.1 MPa) forsterite/melt partitioning experiments were carried out in the system Mg₂SiO₄-CaMgSi₂O₆-SiO₂ with ?1 wt% m-cations (Mn²⁺, Co²⁺, and Ni²⁺) substituting for Ca²⁺ and Mg²⁺. The bulk melt NBO/Si-range (NBO/Si: nonbridging oxygen per silicon) of melt in equilibrium with forsterite was between 1.89 and 2.74. In this NBO/Si-range, the NBO/Si(Ca) (fraction of nonbridging oxygens, NBO, that form bonds with Ca²⁺, Ca²⁺-NBO) is linearly related to NBO/Si, whereas fraction of Mg²⁺-NBO bonds is essentially independent of NBO/Si. For individual m-cations, rate of change of K_D(m−Mg) with NBO/Si(Ca) for the exchange equilibrium, m^melt + Mg^olivine ? m^olivine + Mg^melt, is linear. K_D(m−Mg) decreases as an exponential function of increasing ionic potential, Z/r² (Z: formal electrical charge, r: ionic radius—here calculated with oxygen in sixfold coordination around the divalent cations) of the m-cation. The enthalpy change of the exchange equilibrium, ΔH, decreases linearly with increasing Z/r² [ΔH = 261(9)-81(3)·Z/r² (Å⁻²)]. From existing information on (Ca,Mg)O-SiO₂ melt structure at ambient pressure, these relationships are understood by considering the exchange of divalent cations that form bonds with nonbridging oxygen in individual Qⁿ-species in the melts. The negative ∂K_D(m−Mg)/∂(Z/r²) and ∂(ΔH)/∂(Z/r²) is because increasing Z/r² is because the cations forming bonds with nonbridging oxygen in increasingly depolymerized Qⁿ-species where steric hindrance is decreasingly important. In other words, principles of ionic size/site mismatch commonly observed for trace and minor elements in crystals, also govern their solubility behavior in silicate melts.     

Mineralogy,petrography, and oxygen isotopic compositions of ultrarefractory inclusions from carbonaceous chondrites

We report on the mineralogy, petrography, and in situ oxygen isotopic composition of twenty-five ultrarefractory calcium-aluminum-rich inclusions (UR CAIs) in CM2, CR2, CH3.0, CV3.1–3.6, CO3.0–3.6, MAC 88107 (CO3.1-like), and Acfer 094 (C3.0 ungrouped) carbonaceous chondrites. The UR CAIs studied are typically small, < 100 μm in size, and contain, sometimes dominated by, Zr-, Sc-, and Y-rich minerals, including allendeite (Sc₄Zr₃O₁₂), and an unnamed ((Ti,Mg,Sc,Al)₃O₅) mineral, davisite (CaScAlSiO₆), eringaite (Ca₃(Sc,Y,Ti)₂Si₃O₁₂), kangite ((Sc,Ti,Al,Zr,Mg,Ca,□)₂O₃), lakargiite (CaZrO₃), warkite (Ca₂Sc₆Al₆O₂₀), panguite ((Ti,Al,Sc,Mg,Zr,Ca)_1.8O₃), Y-rich perovskite ((Ca,Y)TiO₃), tazheranite ((Zr,Ti,Ca)O_2−x), thortveitite (Sc₂Si₂O₇), zirconolite (orthorhombic CaZrTi₂O₇), and zirkelite (cubic CaZrTi₂O₇). These minerals are often associated with 50–200 nm-sized nuggets of platinum group elements. The UR CAIs occur as: (i) individual irregularly-shaped, nodular-like inclusions; (ii) constituents of unmelted refractory inclusions – amoeboid olivine aggregates (AOAs) and Fluffy Type A CAIs; (iii) relict inclusions in coarse-grained igneous CAIs (forsterite-bearing Type Bs and compact Type As); and (iv) relict inclusions in chondrules. Most UR CAIs, except for relict inclusions, are surrounded by single or multilayered Wark-Lovering rims composed of Sc-rich clinopyroxene, ±eringaite, Al-diopside, and ±forsterite. Most of UR CAIs in carbonaceous chondrites of petrologic types 2–3.0 are uniformly ¹⁶O-rich (Δ¹⁷O ∼ −23‰), except for one CH UR CAI, which is uniformly ¹⁶O-depleted (Δ ¹⁷O ∼ −5‰). Two UR CAIs in Murchison have heterogeneous Δ¹⁷O. These include: an intergrowth of corundum (∼ ‒24‰) and (Ti,Mg,Sc,Al)₃O₅ (∼ 0‰), and a thortveitite-bearing CAI (∼ −20 to ∼ ‒5‰); the latter apparently experienced incomplete melting during chondrule formation. In contrast, most UR CAIs in metamorphosed chondrites are isotopically heterogeneous (Δ¹⁷O ranges from ∼ −23‰ to ∼ −2‰), with Zr- and Sc-rich oxides and silicates, melilite and perovskite being ¹⁶O-depleted to various degrees relative to uniformly ¹⁶O-rich (Δ¹⁷O ∼ −23‰) hibonite, spinel, Al-diopside, and forsterite. We conclude that UR CAIs formed by evaporation/condensation, aggregation and, in some cases, melting processes in a ¹⁶O-rich gas of approximately solar composition in the CAI-forming region(s), most likely near the protoSun, and were subsequently dispersed throughout the protoplanetary disk. One of the CH UR CAIs formed in an ¹⁶O-depleted gaseous reservoir providing an evidence for large variations in Δ¹⁷O of the nebular gas in the CH CAIs-forming region. Subsequently some UR CAIs experienced oxygen isotopic exchange during melting in ¹⁶O-depleted regions of the disk, most likely during the epoch of chondrule formation. In addition, UR CAIs in metamorphosed CO and CV chondrites, and, possibly, the corundum-(Ti,Mg,Sc,Al)₃O₅ intergrowth in Murchison experienced O-isotope exchange with aqueous fluids on the CO, CV, and CM chondrite parent asteroids. Thus, both nebular and planetary exchange with ¹⁶O-depleted reservoirs occurred.     

Experimental and theoretical study of (Fe2+, Mg)(Al,Fe3+)2O4 spinels: Activity-composition relationships,miscibility gaps,vacancy contents

The compositions of (Fe²⁺, Mg)(Al, Fe³⁺)₂O₄ spinels equilibrated with a l M (Fe²⁺, Mg)Cl₂ aqueous solution at 800°C, 4 kbars were determined. General considerations of reciprocal systems allow derivation of the exchange isotherm between a chloride aqueous solution and (Mg, Fe²⁺)Al₂O₄ spinels. They enable calculation of ΔG of the reaction: FeCl₂ + MgAl₂O₄ = MgCl₂ + FeAl₂O₄ΔG = 2.9 kcal at 800°C, 4 kbars and provide the activity-composition relationships for the binary join FeAl₂O₄-MgAl₂O₄, which shows a substantial positive deviation from ideality. Some tie-lines between coexisting aluminous and ferric spinels were also obtained in the (Fe²⁺, Mg)(Al, Fe³⁺)₂O₄ system.These experimental data are modeled by a Gibbs free energy formulation of the spinel solid solution (Lehmann and Roux, 1984), where the corrective function g₂, necessary to reproduce the deviations from ideality, is artificially split into two parts:

• 1.(1) A homogeneous second degree polynomial in the composition variables, containing only the terms specific to the reciprocal nature of the system, whose coefficients are deduced from ΔG of the exchange reaction: MgAl₂O₄ + FeFe₂O₄ = MgFe₂O₄ + FeAl₂O₄ΔG = 4.5 kcal at 800°C, 4 kbars
• 2.(2) A homogeneous second degree polynomial in the site occupancy fractions, to model the non-ideal behavior of the (Fe²⁺, Mg)Al₂O₄ and (Fe₂₊, Mg)Fe₂O₄ spinels and the miscibility gap along the Fe(Al, Fe³⁺)₂O₄ join.

A model of reciprocal spinel solution involving defect end-members is used to estimate the vacancy contents of the spinels in equilibrium with sesquioxides. In this case, the corrective function necessary to take into account the reciprocal nature of the system is no longer a second degree polynomial, but a rational fraction.     

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.     

Eh ph Diagrams for mn, fe, co, ni, cu and as Under Seawater Conditions: Application of two new Types of eh ph Diagrams to the Study of Specific Problems in Marine Geochemistry

E_H pH diagrams have been calculated using the PHREEQC programme in order to establish the predominance fields of Mn, Fe, Co, Ni, Cu and As in bottom waters from the Angola Basin. Predominance fields are presented separately for both aquatic species and solid mineral phases in order to simplify interpretation of the data. The diagrams show significant differences from standard E_H pH diagrams for these elements calculated for freshwater at 25 °C and 1 bar which assume an element concentration of 10^-6 M. In particular, our diagrams show that Mn²⁺ and NiCO ₃ ⁰ are the predominant aquatic species for Mn and Ni in bottom seawater and FeOOH, Fe₂O₃, Fe₃O₄, CoFe₂O₄, CuFe₂O₄, CuFeO₂, and Ba₃ (AsO₄)₂ the predominant solid phases for Fe, Co, Cu and As, respectively. Mn and Ni are therefore undersaturated and Fe, Co, Cu and As supersaturated in bottom seawater from the Angola Basin. Neither rhodochrosite (MnCO₃) nor siderite (FeCO₃) can form in this marine environment in equilibrium with seawater. A mixed Mn-Ca carbonate is therefore formed within the pore waters of reducing sediments. The high Ni/Cu ratios in cobalt-rich manganese crusts formed adjacent to the oxygen minimum zone may be explained by the change from Cu²⁺ to CuCl ₃ ^2- as the dominant aquatic species of Cu in seawater at an E_H of +0.48 V.     

Thermobarometry of mafic igneous rocks based on clinopyroxene-liquid equilibria, 0–30 kbar

 Models for estimating the pressure and temperature of igneous rocks from co-existing clino-pyroxene and liquid compositions are calibrated from existing data and from new data obtained from experiments performed on several mafic bulk compositions (from 8–30 kbar and 1100–1475° C). The resulting geothermobarometers involve thermodynamic expressions that relate temperature and pressure to equilibrium constants. Specifically, the jadeite (Jd; NaAlSi₂O₆)–diopside/hedenbergite (DiHd; Ca(Mg, Fe) Si₂O₆) exchange equilibrium between clinopyroxene and liquid is temperature sensitive. When compositional corrections are made to the calibrated equilibrium constant the resulting geothermometer is (i) 10⁴ T=6.73−0.26^* ln [Jd^px*Ca^liq*Fm^liqDiHd^px*Na^liq*Al^liq] −0.86^* ln [Mg^liqMg^liq+Fe^liq]+0.52^*ln [Ca^liq] an expression which estimates temperature to ±27 K. Compared to (i), the equilibrium constant for jadeite formation is more sensitive to pressure resulting in a thermobarometer (ii) P=−54.3+299^* T10⁴+36.4^* T10⁴ ln [Jd^px[Si^liq]^2*Na^liq*Al^liq] +367^*[Na^liq*Al^liq] which estimates pressure to ± 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Na^liq represent the cation fraction of the given oxide (NaO_0.5) in the liquid and Fm=MgO+FeO. The mole fractions of Jd and diopside+hedenbergite (DiHd) components are calculated from a normative scheme which assigns the lesser of Na or octahedral Al to form Jd; any excess Al^VI forms Calcium Tschermak’s component (CaTs; CaAlAlSiO₆); Ca remaining after forming CaTs and CaTiAl₂O₆ is taken as DiHd. Experimental data not included in the regressions were used to test models (i) and (ii). Error on predictions of T using model (i) is ±40 K. A pressure-dependent form of (i) reduces this error to ±30 K. Using model (ii) to predict pressures, the error on mean values of 10 isobaric data sets (0–25 kbar, 118 data) is ±0.3 kbar. Calculating thermodynamic properties from regression coefficients in (ii) gives V^Jd _f of 23.4 ±1.3 cm³/mol, close to the value anticipated from bar molar volume data (23.5 cm³/mol). Applied to clinopyroxene phenocrysts from Mauna Kea, Hawaii lavas, the expressions estimate equilibration depths as great as 40 km. This result indicates that transport was sufficiently rapid that at least some phenocrysts had insufficient time to re-equilibrate at lower pressures. Received: 16 May 1994/Accepted: 15 June 1995     

Über den transport von Wolfram und den Absatz von Wolfram-Doppel-Oxiden in fluiden wässrigen LösungenThe transport of tungsten and the deposition of tungsten double oxides in fluid,aqueous solutions

The transportation of W in aqueous gas-phases at and above 500°C is examined using thermodynamic data. The transport of W is possible as fluoride and oxifluoride. The deposition of wolframite continues with decreasing temperature and pressure. The stabilities of wolframates in hydrothermal solutions are examined for temperatures up to 300°C with Eh-pH-diagrams, exchange reactions of wolframite with oxides, sulfides and dissolved ions. Fe₂WO₆ becomes stable against Fe₂O₃ + WO₃ above 126°C. At 300°C its range of stability begins at high pO₂ which is not realised in hydrothennal endogenous solutions. In consequence of the very low Gibbs energies of MgWO₄, CaWO₄ and BaWO₄, the minerals MgWO₄ and BaWO₄ should be more important than wolframite, if Mg and Ba coexist in solution together with W. Co and Ni also should be found as trace elements in wolframite, if Co and Ni were in solution in sufficiently high concentrations together with W.     

The crystal and melt structure of spinel and alumina at high temperature: An in-situ XANES study at the Al and Mg K-edge

We present structural information obtained on spinel and alumina at high temperature (298-2400 K) using in-situ XANES at the Mg and Al K-edges. For spinel, ^[4](Al_x,Mg_1−x)^[6](Al_2−x,Mg_x)O_4, with increasing temperature, a substitution of Mg by Al and Al by Mg in their respective sites is observed. This substitution corresponds to an inversion of the Mg and Al sites. There is a significant change in the Al K-edge spectra between crystal and liquid, which can be attributed to a change of the ^[6]Al normally observed in corundum at room temperature, to a mixture of ^[6]Al-^[4]Al in the liquid state. This conclusion is in good agreement with previous ²⁷Al NMR experiments. Furthermore, both experiments at the Al and Mg K-edges are in good agreement with XANES calculation made using FDMNES code.     

The stability of transition metal dolomites in carbonate systems: a discussion

The instability of transition metal dolomites [CaR²⁺(CO₃)₂ where R²⁺ is Fe, Co, Ni, Cu, or Zn] and the limited substitution of transition metal cations for Mg in the dolomite structure can be accounted for by the effect of octahedral distortion. For example, trigonal elongation of the Fe octahedron, due to the Jahn-Teller effect, observed in siderite and ankerite, results in elongation of the Ca octahedron which is sensitive to distortion because the radius of Ca²⁺ is close to the upper limit for octahedral coordination. Co, Ni, Cu, Zn octahedra are also thought to be deformed, relative to Mg octahedra, in carbonates.The free energy of formation (ΔG^o_f) of R²⁺CO₃ becomes more positive with increasing octahedral distortion. Estimated ΔG^o_f(dolomite) as well as stabilities and solubility limits of R²⁺ in natural and synthetic dolomites suggest a series in order of decreasing stability: Mg >Mn >Zn >Fe >Co >Ni >Cu.ΔG^o_f(est.) for the terminal Fe-dolomite solid solution [72 mol% CaFe(CO₃)₂] in the system CaCO₃-MgCO₃-FeCO₃ may represent an empirical threshold value for dolomite stability which lies between ΔG^o_f for Mn- and Zn-dolomites. While Zn-dolomite is probably not a stable phase, very extensive solid solution toward CaZn(CO₃)₂ is to be expected in the system CaCO₃-MgCO₃-ZnCO₃. The tendency for transition metal dolomites to contain excess CaCO₃ can also be accounted for in terms of octahedral distortion and AG^o_f.     

Thermodynamic controls on element partitioning between titanomagnetite and andesitic–dacitic silicate melts

Titanomagnetite–melt partitioning of Mg, Mn, Al, Ti, Sc, V, Co, Ni, Cu, Zn, Ga, Zr, Nb, Mo, Hf and Ta was investigated experimentally as a function of oxygen fugacity (fO₂) and temperature (T) in an andesitic–dacitic bulk-chemical compositional range. In these bulk systems, at constant T, there are strong increases in the titanomagnetite–melt partitioning of the divalent cations (Mg²⁺, Mn²⁺, Co²⁺, Ni²⁺, Zn²⁺) and Cu²⁺/Cu⁺ with increasing fO₂ between 0.2 and 3.7 log units above the fayalite–magnetite–quartz buffer. This is attributed to a coupling between magnetite crystallisation and melt composition. Although melt structure has been invoked to explain the patterns of mineral–melt partitioning of divalent cations, a more rigorous justification of magnetite–melt partitioning can be derived from thermodynamic principles, which accounts for much of the supposed influence ascribed to melt structure. The presence of magnetite-rich spinel in equilibrium with melt over a range of fO₂ implies a reciprocal relationship between a(Fe²⁺O) and a(Fe³⁺O_1.5) in the melt. We show that this relationship accounts for the observed dependence of titanomagnetite–melt partitioning of divalent cations with fO₂ in magnetite-rich spinel. As a result of this, titanomagnetite–melt partitioning of divalent cations is indirectly sensitive to changes in fO₂ in silicic, but less so in mafic bulk systems.     

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe²⁺)(Al, Cr, Fe³⁺)₂O₄ ? (Mg, Fe²⁺)₂TiO₄. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg²⁺, Al³⁺, and Fe³⁺ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.     

Solubility and complexing of Ni in the system NiO-H2O-HCl

The solubility of bunsenite (NiO) in Cl-bearing fluids in the range of 450°–700°C, 1–2 kbar was determined using the Ag + AgCl acid buffer technique. Based on the results of the experiments, it is concluded that the associated NiCl⁰₂ complex is the dominant Ni species in the fluid over the entire temperature-pressure range investigated. The temperature dependence of the equilibrium constant for the reaction NiO(s) + 2HCl⁰(aq) = NiCl⁰₂(aq) + H₂O is given by logK = ?4.17(±0.55) + 4629(±464)/T(K) at 1 kbar, and logK = ?4.75(±0.91) + 5933(±756)/T(K) at 2 kbar. The calculated difference in standard state Gibbs free energy of formation between NiCl⁰₂ and 2HCl⁰ in kcal is G⁰(NiCl⁰₂) ? 2G⁰(HCl⁰) = ?20.77(±2.22) + 0.03264(±0.0026)T(K), at 1 kbar and G⁰(NiCl⁰₂) ? 2G⁰(HCl⁰) = ?25.01(±1.35) + 0.03264(±0.0016)T(K) at 2 kbar. Comparison of the solubilities of Ni end-member minerals with those of Ca, Mn, Fe, and Mg indicates that nickel minerals generally are the least soluble at a given temperature and pressure. The relatively low solubility of Ni end-member minerals, combined with the relatively low concentration of Ni in most rocks, should result in a quite low mobility of Ni in hydrothermal fluids.     

Solubility of Ca6[Al(OH)6]2(CrO4)3·26H2O,the chromate analog of ettringite; 5–75°C

Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O, the chromate analog of the sulfate mineral ettringite, was synthesized and characterized by X-ray diffraction, Fourier transform infra-red spectroscopy, thermogravimetric analyses, energy dispersive X-ray spectrometry, and bulk chemical analyses. The solubility of the synthesized solid was measured in a series of dissolution and precipitation experiments conducted at 5–75°C and at initial pH values between 10.5 and 12.5. The ion activity product (IAP) for the reaction Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O⇌6Ca²⁺+2Al(OH)⁻₄+3CrO²⁻₄+4OH⁻+26H₂O varies with pH unless a CaCrO_4(aq) complex is included in the speciation model. The log K for the formation of this complex by the reaction Ca²⁺+CrO²⁻₄=CaCrO_4(aq) was obtained by minimizing the variance in the IAP for Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O. There is no significant trend in the formation constant with temperature and the average log K is 2.77±0.16 over the temperature range 5–75°C. The log solubility product (log K_SP) of Ca₆[Al(OH)₆]₂(CrO₄)₃·26H₂O at 25°C is −41.46±0.30. The temperature dependence of the log K_SP is log K_SP=A−B/T+D log(T) where A=498.94±48.99, B=27,499±2257, and D=−181.11±16.74. The values of ΔG⁰_r,298 and ΔH⁰_r,298 for the dissolution reaction are 236.6±3.9 and 77.5±2.4 kJ mol⁻¹. the values of ΔC⁰_P,r,298 and ΔS⁰_r,298 are −1506±140 and −534±83 J mol⁻¹ K⁻¹. Using these values and published standard state partial molal quantities for constituent ions, ΔG⁰_f,298=−15,131±19 kJ mol⁻¹, ΔH⁰_f,298=−17,330±8.6 kJ mol⁻¹, ΔS⁰₂₉₈=2.19±0.10 kJ mol⁻¹ K⁻¹, and ΔC⁰_Pf,298=2.12±0.53 kJ mol⁻¹ K⁻¹, were calculated.     

Kinetics of the reaction MgO + Al2O3 → MgAl2O4 and Al-Mg interdiffusion in spinel at 1200 to 2000°C and 1.0 to 4.0 GPa

The rate of spinel (MgAl₂O₄) growth at the interface between MgO and Al₂O₃ was investigated systematically at temperatures of 1200° to ∼2000°C and pressures between 1.0 and 4.0 GPa with a solid-media, piston-cylinder apparatus. As reported in previous 1-atm studies, the thickness (ΔX) of the spinel layer increases linearly with the square root of time for experiments differing only in duration, irrespective of pressure-temperature (P-T) conditions. The reaction rate constant (k = ΔX²/2t) is log-linear in 1/T and also in pressure. The apparent activation energy of 410 kJ/mol is independent of pressure; the apparent activation volume increases systematically with increasing temperature. Electron microprobe traverses across the spinel layer reveal a significant Al excess and charge-compensating Mg deficit near the spinel/corundum interface. This nonstoichiometry is promoted by high temperatures (>1500°C), suppressed by high pressures and varies linearly across the spinel to a near-stoichiometric composition at the interface with periclase. The Al and Mg composition gradients can be used to extract interdiffusion coefficients for Al ↔ Mg exchange through the spinel, which are described by D?=2.5×10⁻⁶ exp(−28200/T) m²sThese diffusivities differ substantially from the reaction rate constant k, reflecting the fact that k is a combination of the diffusivity and the reaction potential as indicated by the difference in spinel composition across the spinel layer (i.e., coexisting with corundum vs. coexisting with periclase). A simple model can be used to separate the two effects and show that the reaction potential (i.e., the MgO-Al₂O₃ phase diagram) is sensitive to changes in both temperature and pressure, whereas the governing diffusivity depends only on temperature.     

The crystal chemistry of lithium and Fe3+ in synthetic orthopyroxene

Lithian ferrian enstatite with Li₂O = 1.39 wt% and Fe₂O₃ 7.54 wt% was synthesised in the (MgO–Li₂O–FeO–SiO₂–H₂O) system at P = 0.3 GPa, T = 1,000°C, fO₂ = +2 Pbca, and a = 18.2113(7), b = 8.8172(3), c = 5.2050(2) Å, V = 835.79(9) Å³. The composition of the orthopyroxene was determined combining EMP, LA-ICP-MS and single-crystal XRD analysis, yielding the unit formula ^M2(Mg_0.59Fe _0.21 ²⁺ Li_0.20) ^M1(Mg_0.74Fe _0.20 ³⁺ Fe _0.06 ²⁺ ) Si₂O₆. Structure refinements done on crystals obtained from synthesis runs with variable Mg-content show that the orthopyroxene is virtually constant in composition and hence in structure, whereas coexisting clinopyroxenes occurring both as individual grains or thin rims around the orthopyroxene crystals have variable amounts of Li, Fe³⁺ and Mg contents. Structure refinement shows that Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site of the orthopyroxene, whereas Mg (and Fe²⁺) distributes over both octahedral sites. The main geometrical variations observed for Li-rich samples are actually due to the presence of Fe³⁺, which affects significantly the geometry of the M1 site; changes in the geometry of the M2 site due to the lower coordination of Li are likely to affect both the degree and the kinetics of the non-convergent Fe²⁺-Mg ordering process in octahedral sites.     

Cation diffusion in olivine—II. Ni-Mg,Mn-Mg,Mg and Ca

Diffusivities of bivalent cations. Mg, Ni. Mn and Ca, in olivine were determined experimentally. The diffusivities of Ni and Mn in forsterite were determined by couple annealing between Ni₂SiO₄ and Mg₂SiO₄, and Mn₂SiO₄ and Mg₂SiO₄, respectively. The diffusivities of Mg and Ca in forsterite were determined by the use of ²⁶Mg and Ca tracers, respectively. Combined with other published results, the diffusion coefficients for bivalent cation diffusion in pure forsterite along the c crystallographic axis range from 2.45 × 10^?11 to 1.4 × 10^?13 cm² sec^?1 at 1200°C, in the order of Fe > Mn > Co > Ni > Mg > Ca. The results suggest that the diffusivity is governed by at least two factors, i.e. the size of the diffusing ionic species and the change of defect density in the crystal structure which is induced by substitution of diffusing ion for Mg ion.