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.     

Solubility of ettringite (Ca6[Al(OH)6]2(SO4)3 · 26H2O) at 5–75°C

The solubility of ettringite (Ca₆[Al(OH)₆]₂(SO₄)₃ · 26H₂O) was measured in a series of dissolution and precipitation experiments at 5–75°C and at pH between 10.5 and 13.0 using synthesized material. Equilibrium was established within 4 to 6 days, with samples collected between 10 and 36 days. The log K_SP for the reaction Ca₆[Al(OH)₆]₂(SO₄)₃ · 26H₂O ⇌ 6Ca²⁺ + 2Al(OH)₄⁻ + 3SO₄²⁻ + 4OH⁻ + 26H₂O at 25°C calculated for dissolution experiments (−45.0 ± 0.2) is not significantly different from the log K_SP calculated for precipitation experiments (−44.8 ± 0.4) at the 95% confidence level. There is no apparent trend in log K_SP with pH and the mean log K_SP,298 is −44.9 ± 0.3. The solubility product decreased linearly with the inverse of temperature indicating a constant enthalpy of reaction from 5 to 75°C. The enthalpy and entropy of reaction ΔH^°_r and ΔS^°_r, were determined from the linear regression to be 204.6 ± 0.6 kJ mol⁻¹ and 170 ± 38 J mol⁻¹ K⁻¹. Using our values for log K_SP, ΔH^°_r, and ΔS^°_r and published partial molal quantities for the constituent ions, we calculated the free energy of formation ΔG^°_f,298, the enthalpy of formation ΔH^°_f,298, and the entropy of formation ΔS^°_f,298 to be −15211 ± 20, −17550 ± 16 kJ mol⁻¹, and 1867 ± 59 J mol⁻¹ K⁻¹. Assuming ΔC_P,r is zero, the heat capacity of ettringite is 590 ± 140 J mol⁻¹ K⁻¹.     

Standard Gibbs free energy of formation for Cu2O,NiO, CoO,and FexO: High resolution electrochemical measurements using zirconia solid electrolytes from 900–1400 K

Galvanic cells with oxygen-specific solid electrolytes made of calcia-stabilized zirconia have been used to make equilibrium measurements of the standard Gibbs free energy of formation, Δ_fG⁰_m,(T), for copper (I) oxide (Cu₂O), nickel (II) oxide (NiO), cobalt (II) oxide (CoO), and wüstite (Fe_xO) over the temperature range from 900–1400 K. The measured values of Δ_fG⁰_m at 1300 K are −73950, −123555, −142150, and −179459 J · mol⁻¹ for Cu₂O, NiO, CoO, and Fe_0.947O, respectively. The precision of these measurements is ± 30–60 J · mol⁻¹, and their absolute accuracy is estimated to be ± 100–200 J·mol⁻¹. Using values of –76.557, −94.895, −79.551, and −71.291 J · K⁻¹ · mol⁻¹ for the entropies of formation, Δ_fS_m⁰, (298.15 K), the calculated enthalpies of formation, Δ_fH_m⁰, (298.15 K), are −170508, −240110, −237390, and −266458 J · mol⁻¹ for Cu₂O, NiO, CoO, and Fe_0.947O, respectively. These values of Δ_fS_m⁰ (298.15 K) and Δ_fH_m⁰ (298.15 K) are in good agreement with the best available calorimetric measurements.     

Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite

The phase boundary between MnTiO₃ I (ilmenite structure) and MnTiO₃ II (lithium niobate structure) has been determined by analysis of quench products from reversal experiments in a cubic anvil apparatus at 1073–1673 K and 43–75 kbar using mixtures of MnTiO₃ I and II as starting materials. Tight brackets of the boundary give P(kbar)=121.2−0.045 T(K). Thermodynamic analysis of this boundary gives ΔH^o=5300±1000 J·mol⁻¹, ΔS^o = 1.98 ±1J·K⁻¹· mol⁻¹. The enthalpy of transformation obtained directly by transposed-temperature-drop calorimetry is 8359 ±2575 J·mol⁻¹. Possible topologies of the phase relations among the ilmenite, lithium niobate, and perovskite polymorphs are constrained using the above data and the observed (reversible with hysteresis) transformation of II to III at 298 K and 20–30 kbar (Ross et al. 1989). The observed II–III transition is likely to lie on a metastable extension of the II–III boundary into the ilmenite field. However the reversed I–II boundary, with its negative dP/ dT does represent stable equilibrium between ilmenite and lithium niobate, as opposed to the lithium niobate being a quench product of perovskite. We suggest a topology in which the perovskite occurs stably at low T and high P with a triple point (I, II, III) at or below 1073 K near 70 kbar. The I–II boundary would have a negative P-T slope while the II–III and I–III boundaries would be positive, implying that entropy decreases in the order lithium niobate, ilmenite, perovskite. The inferred positive slope of the ilmenite-perovskite transition in MnTiO₃ is different from the negative slopes in silicates and germanates. These thermochemical parameters are discussed in terms of crystal structure and lattice vibrations.     

Heat capacity of ferrosilite, Fe2Si2O6

The heat capacity of synthetic ferrosilite, Fe₂Si₂O₆, was measured between 2 and 820 K. The physical properties measurement system (PPMS, Quantum Design^®) was used in the low-temperature region between 2 and 303 K. In the temperature region between 340 and 820 K measurements were performed using differential scanning calorimetry (DSC). The C _p data show two transitions, a sharp λ-type at 38.7 K and a small shoulder near 9 K. The λ-type transition can be related to collinear antiferromagnetic ordering of the Fe²⁺ spin moments and the shoulder at 10 K to a change from a collinear to a canted-spin structure or to a Schottky anomaly related to an electronic transition. The C _p data in the temperature region between 145 and 830 K are described by the polynomial $C_{p} {\left[ {\hbox{J\,mol}^{{ - 1}}\,{\hbox{K}}^{{ - 1}} } \right]} = 371.75 - 3219.2T^{{ - 1/2}} - 15.199 \times 10^{5} T^{{ - 2}} + 2.070 \times 10^{7} T^{{ - 3}} $ The heat content [H ₂₉₈ – H ₀] and the standard molar entropy [S ₂₉₈ – S ₀] are 28.6 ± 0.1 kJ mol^?1 and 186.5 ± 0.5 J mol^?1 K^?1, respectively. The vibrational part of the heat capacitiy was calculated using an elastic Debye temperature of 541 K. The results of the calculations are in good agreement with the maximum theoretical magnetic entropy of 26.8 J mol^?1 K^?1 as calculated from the relationship 2*Rln5.     

The solubility of BaCO3(cr) (witherite) in CO2-H2O solutions between 0 and 90°C,evaluation of the association constants of BaHCO3+(aq) and BaCO30(aq) between 5 and 80°C,and a preliminary evaluation of the thermodynamic properties of Ba2+(aq)

One hundred and fifty new measurements of the solubility of witherite were used to evaluate the equilibrium constant of the reaction BaCO₃(cr) = Ba²⁺(aq) + CO₃²⁻(aq) between 0 and 90°C and 1 atm total pressure. The temperature dependence of the equilibrium constant is given by logK = 607.642 + 0.121098T − 20011.25/T − 236.4948 logT where T is in degrees Kelvin. The logK of BaCO₃(cr), the Gibbs energy, the enthalpy and entropy of the reaction at 298.15 K are −8.562, 48.87 kJ · mol⁻¹, 2.94 kJ · mol⁻¹ and −154.0 J · mol⁻¹ · K⁻¹, respectively. The equilibrium constants are consistent with an aqueous model that includes the ion pairs BaHCO₃⁺(aq) and BaCO₃⁰(aq) Three different methods were used to evaluate the association constant of BaHCO₃⁺(aq), and all yielded similar results. The temperature dependence of the association constant for the reaction Ba²⁺(aq) + HCO₃⁻(aq) = BaHCO₃⁺(aq) is given by logK_BaHCO3⁺ = −3.0938 + 0.013669T.The log of the association constant, the Gibbs energy, the enthalpy and entropy of the reaction at 298.15°K are 0.982, −5.606 kJ · mol⁻¹, 23.26 kJ · mol⁻¹ and 96.8 J · mol⁻¹ · K⁻¹, respectively. The temperature dependence of the equilibrium constant for the reaction Ba²⁺(aq) + CO²⁻₃(aq) = BaCO₀³(aq) is given by logK_BaCO3⁰ = 0.113 + 0.008721T.The log of the association constant, the Gibbs energy, the enthalpy and entropy of the reaction at 298.15° K are 2.71, −15.49 kJ · mol⁻¹, 14.84 kJ · mol⁻¹ and 101.7 J· mol⁻¹ · K⁻¹.The above model leads to reliable calculations of the aqueous speciation and solubility of witherite in the system BaCO₃-CO₂-H₂O from 0 to more than 90°C. Literature data on witherite solubility were re-evaluated and compared with the results of this study.Problems in the thennodynamic selections of Ba compounds are considered. Newer data require the revision of Δ_fH° and Δ_fG° of Ba²⁺(aq) to −532.5 and −555.36 kJ · mol⁻¹, respectively, for agreement with solubility data.     

Thermodynamic properties of copper carbonates — malachite Cu2(OH)2CO3 and azurite Cu3(OH)2(CO3)2

The thermodynamic properties of the copper carbonates malachite and azurite have been studied by adiabatic calorimetry, by heat-flux Calvet Calorimetry, by differential thermal analysis (DTA) and by thermogravimetrie (TGA) analysis. The heat capacities, C _p ⁰ of natural malachite and azurite have been measured between 3.8 and 300 K by low-temperature adiabatic calorimetry. The heat capacity of azurite exhibits anomalous behavior at low temperatures. At 298.15 K the molar heat capacities C _p ⁰ and the third law entropies S _298.15 ⁰ are 228.5±1.4 and 254.4±3.8 J mol^?1 K^?1 for azurite and 154.3±0.93 and 166.3±2.5 J mol^?1 K^?1 for malachite. Enthalpies of solution at 973 K in lead borate 2PbO·B₂O₃ have been measured for heat treated malachite and azurite. The enthalpies of decomposition are 105.1±5.8 for azurite and 66.1±5.0 kJ mol^? for malachite. The enthalpies of formation from oxides of azurite and malachite determined by oxide melt solution calorimetry, are ?84.7±7.4 and ?52.5±5.9 kJ mol^?1, respectively. On the basis of the thermodynamic data obtained, phase relations of azurite and malachite in the system Cu²⁺-H₂O-CO₂ at 25 and 75 °C have been studied.     

The Mg2GeO4 olivine-spinel phase transition

Enthalpies and entropies of transition for the Mg₂GeO₄ olivine-spinel transformation have been determined from self-consistency analyses of Dachille and Roy's (1960), Hensen's (1977) and Shiota et al.'s (1981) phase boundary studies. When all three data sets are analyzed simultaneously,ΔH ₉₇₃ andΔS ₉₇₃ are constrained between ?14000 to ?15300 J mol^?1 and ?13.0 to ?14.1·J mol^?1 K^?1, respectively. High-temperature solution calorimetric experiments completed on both polymorpha yield a value of ?14046±1366 J mol^?1 forΔH ₉₇₃. Kieffer-type lattice vibrational models of Mg₂GeO₄ olivine and spinel based on newly-measured infrared and Raman spectra predict a value of ?13.3±0.6 J mol^?1 K^?1 forΔS ₁₀₀₀. The excellent agreement between these three independent determinations ofΔH andΔS suggests that the synthesis runs of Shiota et al. (1981) at high pressures and temperatures bracket equilibrium conditions. In addition, no configurational disorder of Mg and Ge was needed to obtain the consistent parameters quoted. The Raman spectrum and X-ray diffractogram show that little disorder, if any, is present in Mg₂GeO₄ spinel synthesized at 0.2 GPa and 973–1048 K.     

Thermodynamic functions of eskolaite Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>(c) at 0–1800 K

The heat capacity of eskolaite Cr₂O₃(c) was determined by adiabatic vacuum calorimetry at 11.99–355.83 K and by differential calorimetry at 320–480 K. Experimental data of the authors and data compiled from the literature were applied to calculate the heat capacity, entropy, and the enthalpy change of Cr₂O₃ within the temperature range of 0–1800 K. These functions have the following values at 298.15 K: C _p ⁰ (298.15) = 121.5 ± 0.2 J K⁻¹mol⁻¹, S ⁰(298.15) = 80.95 ± 0.14 J K⁻¹mol⁻¹, and H ⁰(298.15)-H ⁰(0) = 15.30±0.02 kJ mol⁻¹. Data were obtained on the transitions from the antiferromagnetic to paramagnetic states at 228–457 K; it was determined that this transition has the following parameters: Neel temperature T _N = 307 K, Δ _tr S = 6.11 ± 0.12 J K⁻¹mol⁻¹ and δ _tr H = 1.87 ± 0.04 kJ mol⁻¹.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Enthalpy of formation of forsterite,enstatite, akermanite,monticellite and merwinite at 1073 K determined by alkali borate solution calorimetry

Enthalpies of solution of synthetic enstatite (Mg₂Si₂O₆), forsterite (Mg₂SiO₄), akermanite (Ca₂MgSi₂O₇), monticellite (CaMgSiO₄), and merwinite (Ca₃MgSi₂O₈) and their component oxides were determined in eutectic (Li, Na)BO₂ at 1073 K. Resulting enthalpies of formation at 1073 are enstatite: $\text{?8.10 ± 0.42}\text{kcal}$; forsterite: $\text{?14.23 ± 0.45}\text{kcal}$; akermanite: $\text{?42.60 ± 0.39}\text{kcal}$; monticellite: $\text{?25.05 ± 0.41}\text{kcal}$; and merwinite: $\text{?51.10 ± 0.49}\text{kcal}$. The value for the synthetic monticellite of composition Mo_.965Fo_.035 was corrected slightly for non-stoichiometry based on experimental monticellite-forsterite phase equilibrium relations.The enthalpies of formation of enstatite and forsterite are somewhat less negative than yielded by several other solution calorimetric studies but are in good agreement with the recent Pb₂B₂O₅ solution calorimetry of Kiselevaet al. (1979), and are in good agreement with values to be derived from reliable phase equilibrium data in the system MgO-Al₂O₃-SiO₂. The enthalpies of formation of akermanite, monticellite and merwinite are all much less negative than values tabulated by robieet al. (1978) and helgesonet al. (1978) but are shown to be compatible with reliable phase equilibrium data for the system CaO-MgO-SiO₂, whereas the tabulated values are not. Several methods of analysis yield an entropy of monticellite at 1000 K of $\text{69.9 ± 0.2 cal/K}$.     

Heat capacity and thermodynamic properties of GdPO<Subscript>4</Subscript> in the temperature range 0–1600 K

The heat capacity of gadolinium orthophosphate (GdPO₄) measured in the temperature range 11.15–344.11 K by adiabatic calorimetry and available literature data were used to calculate its thermodynamic functions at 0–1600 K. At 298.15 K, these functions are as follows: C _p ⁰(298.15 K) = 101.85 ± 0.05 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 123.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)–H ⁰(0) = 17.250 ± 0.012 kJ mol⁻¹, and Φ ⁰(298.15 K) = 65.97 ± 0.18 J K⁻¹ mol⁻¹ The calculated Gibbs free energy of formation from the elements of GdPO₄ is Δ _f G ⁰ (298.15 K) = −1844.3 ± 4.7 kJ mol⁻¹.     

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.     

Celestite (SrSO4(s)) solubility in water,seawater and NaCl solution

Celestite solubility measurements have been conducted in pure water at temperatures from 10 to 90°C. Equilibrium was achieved with respect to a crystalline solid phase from both undersaturated and supersaturated solutions. The measurements show that the solubility undergoes a maximum near 20°C. LogK values for the solubility reaction are adequately described by the following expression over the temperature range 283.15 to 363.15 K: −logK= −35.3106+0.00422837T+318312/T²+14.99586 logT.The following thennodynamic values for the dissolution reaction of SrSO_4(s), at 25°C have been derived: ΔG_R⁰ = 37852 ± 30 Jmol⁻¹ΔH_R⁰ = −1668±920Jmol⁻¹ΔS_R⁰= −132.6±3.2JK^−1mol−1Celestite solubility measurements were also determined in NaCl solutions up to 5 m concentration and from 10 to 40°C. These data are in good agreement with the work of StrÜbel (1966), who reports solubility measurements to temperatures of 100°C.The application of the Pitzer relations and the solubility constants determined in this study to calculate celestite solubility in NaCl solutions yields excellent agreement between predicted values and experimental measurements over the entire range of temperature and NaCl concentration conditions. For the limited number of solubility measurements in seawater-type solutions and mixed-salt brines, the agreement using the Pitzer relations is within three percent of the measured solubility.     

The heat-capacity of ilmenite and phase equilibria in the system Fe-T-O

Low temperature adiabatic calorimetry and high temperature differential scanning calorimetry have been used to measure the heat-capacity of ilmenite (FeTiO₃) from 5 to 1000 K. These measurements yield S₂₉₈⁰ = 108.9 J/(mol · K). Calculations from published experimental data on the reduction of ilmenite yield Δ₂₉₈⁰(I1) = ?1153.9 kJ/(mol · K). These new data, combined with available experimental and thermodynamic data for other phases, have been used to calculate phase equilibria in the system Fe-Ti-O. Calculations for the subsystem Ti-O show that extremely low values of $\text{?O}{}_2$ are necessary to stabilize TiO, the mineral hongquiite reported from the Tao district in China. This mineral may not be TiO, and it should be re-examined for substitution of other elements such as N or C. Consideration of solid-solution models for phases in the system Fe-Ti-O allows derivation of a new thermometer/oxybarometer for assemblages of ferropseudobrookite-pseudobrookite_ss and hematite-ilmenite_ss. Preliminary application of this new thermometer/oxybarometer to lunar and terrestrial lavas gives reasonable estimates of oxygen fugacities, but generally yields subsolidus temperatures, suggesting re-equilibration of one or more phases during cooling.     

Low T heat capacity measurements and new entropy data for titanite (sphene): implications for thermobarometry of high-pressure rocks

The accepted standard state entropy of titanite (sphene) has been questioned in several recent studies, which suggested a revision from the literature value 129.3 ± 0.8 J/mol K to values in the range of 110–120 J/mol K. The heat capacity of titanite was therefore re-measured with a PPMS in the range 5 to 300 K and the standard entropy of titanite was calculated as 127.2 ± 0.2 J/mol K, much closer to the original data than the suggested revisions. Volume parameters for a modified Murgnahan equation of state: V _P,T  = V ₂₉₈° × [1 + a°(T − 298) − 20a°(T − 298)] × [1 – 4P/(K ₂₉₈ × (1 – 1.5 × 10⁻⁴ [T − 298]) + 4P)]^1/4 were fit to recent unit cell determinations at elevated pressures and temperatures, yielding the constants V ₂₉₈° = 5.568 J/bar, a° = 3.1 × 10⁻⁵ K⁻¹, and K = 1,100 kbar. The standard Gibbs free energy of formation of titanite, −2456.2 kJ/mol (∆H°_f = −2598.4 kJ/mol) was calculated from the new entropy and volume data combined with data from experimental reversals on the reaction, titanite + kyanite = anorthite + rutile. This value is 4–11 kJ/mol less negative than that obtained from experimental determinations of the enthalpy of formation, and it is slightly more negative than values given in internally consistent databases. The displacement of most calculated phase equilibria involving titanite is not large except for reactions with small ∆S. Re-calculated baric estimates for several metamorphic suites yield pressure differences on the order of 2 kbar in eclogites and 10 kbar for ultra-high pressure titanite-bearing assemblages.     

Thermodynamics and crystal chemistry of the hematite–corundum solid solution and the FeAlO3 phase

High-temperature oxide-melt calorimetry and Rietveld refinement of powder X-ray diffraction patterns were used to investigate the energetics and structure of the hematite–corundum solid solution and ternary phase FeAlO₃ (with FeGaO₃ structure). The mixing enthalpies in the solid solution can be described by a polynomial ΔH_mix=WX _hem(1?X _hem) with W=116 ± 10 kJ mol^?1. The excess mixing enthalpies are too positive to reproduce the experimental phase diagram, and excess entropies in the solid solution should be considered. The hematite–corundum solvus can be approximately reproduced by a symmetric, regular-like solution model with ΔG _excess=(W _H ?TW _S )X _hem X _cor, where W _H= 116 ± 10 kJ mol^?1 and W _S =32 ± 4 J mol^?1 K^?1. In this model, short-range order (SRO) of Fe/Al is neglected because SRO probably becomes important only at intermediate compositions close to Fe:Al=1:1 but these compositions cannot be synthesized. The volume of mixing is positive for Al-hematite but almost ideal for Fe-corundum. Moreover, the degree of deviation from Vegard's law for Al-hematite depends on the history of the samples. Introduction of Al into the hematite structure causes varying distortion of the hexagonal network of oxygen ions while the position of the metal ions remains intact. Distortion of the hexagonal network of oxygen ions attains a minimum at the composition (Fe_0.95Al_0.05)₂O₃. The enthalpy of formation of FeAlO₃ from oxides at 298 K is 27.9 ± 1.8 kJ mol^?1. Its estimated standard entropy (including configurational entropy due to disorder of Fe/Al) is 98.9 J mol^?1 K^?1, giving the standard free energy of formation at 298 K from oxides and elements as +19.1 ± 1.8 and ?1144.2 ± 2.0 kJ mol^?1, respectively. The heat capacity of FeAlO₃ is approximated as C _p (T in K)= 175.8 ? 0.002472T ? (1.958 × 10⁶)/T ²? 917.3/T ^0.5+(7.546 × 10^?6) T ² between 298 and 1550 K, based on differential scanning calorimetric measurements. No ferrous iron was detected in FeAlO₃ by Mössbauer spectroscopy. The ternary phase is entropy stabilized and is predicted to be stable above about 1730 ± 70 K, in good agreement with the experiment. Static lattice calculations show that the LiNbO₃-, FeGaO₃-, FeTiO₃-, and disordered corundum-like FeAlO₃ structures are less stable (in the order in which they are listed) than a mechanical mixture of corundum and hematite. At high temperatures, the FeGaO₃-like structure is favored by its entropy, and its stability field appears on the phase diagram.     

The stability of annite+quartz: reversed experimental data for the reaction 2 annite+3 quartz=2 sanidine+3 fayalite +2 H2O

Reversals for the reaction 2 annite+3 quartz=2 sanidine+3 fayalite+2 H₂O have been experimentally determined in cold-seal pressure vessels at pressures of 2, 3, 4 and 5?kbar, limiting annite +quartz stability towards higher temperatures. The equilibrium passes through the temperature intervals 500–540°?C (2?kbar), 550–570°?C (3?kbar), 570–590°?C (4?kbar) and 590–610°?C (5?kbar). Starting materials for most experiments were mixtures of synthetic annite +fayalite+sanidine+quartz and in some runs annite+quartz alone. Microprobe analyses of the reacted mixtures showed that the annites deviate slightly from their ideal Si/Al ratio (Si per formula unit ranges between 2.85 and 2.92, Al^VI between 0.06 and 0.15). As determined by Mössbauer spectroscopy, the Fe³⁺ content of annite in the assemblage annite+fayalite +sanidine+quartz is around 5–7%. The experimental data were used to extract the thermodynamic standard state enthalpy and entropy of annite as follows: H ⁰ _f,?Ann =?5125.896±8.319 [kJ/mol] and S ⁰ _Ann=432.62±8.89 [J/mol/K] (consistent with the Holland and Powell 1990 data set), and H ⁰ _f,Ann =?5130.971±7.939 [kJ/mol] and S ⁰ _Ann=424.02±8.39 [J/mol/K] (consistent with the TWEEQ data base, Berman 1991). The preceeding values are close to the standard state properties derived from hydrogen sensor data of the redox reaction annite=sanidine+magnetite+H ₂ (Dachs 1994). The experimental half-reversal of Eugster and Wones (1962) on the annite +quartz breakdown reaction could not be reproduced experimentally (formation of annite from sanidine+fayalite+quartz at 540°?C/1.035?kbar/magnetite-iron buffer) and probable reasons for this discrepancy remain unclear. The extracted thermodynamic standard state properties of annite were used to calculate annite and annite+quartz stabilities for pressures between 2 and 5?kbar.     

Iron control by equilibria between hydroxy-Green Rusts and solutions in hydromorphic soils

In order to verify Fe control by solution - mineral equilibria, soil solutions were sampled in hydromorphic soils on granites and shales, where the occurrence of Green Rusts had been demonstrated by Mössbauer and Raman spectroscopies. Eh and pH were measured in situ, and Fe(II) analyzed by colorimetry. Ionic Activity Products were computed from aqueous Fe(II) rather than total Fe in an attempt to avoid overestimation by including colloidal particles. Solid phases considered are Fe(II) and Fe(III) hydroxides and oxides, and the Green Rusts whose general formula is [Fe^II_1−xFe^III_x(OH)₂]^+x· [x/z A^−z]^−x, where compensating interlayer anions, A⁻, can be Cl⁻, SO₄²⁻, CO₃²⁻ or OH⁻, and where x ranges a priori from 0 to 1. In large ranges of variation of pH, pe and Fe(II) concentration, soil solutions are (i) oversaturated with respect to Fe(III) oxides; (ii) undersaturated with respect to Fe(II) oxides, chloride-, sulphate- and carbonate-Green Rusts; (iii) in equilibrium with hydroxy-Green Rusts, i.e., Fe(II)-Fe(III) mixed hydroxides. The ratios, x = Fe(III)/Fe_t, derived from the best fits for equilibrium between minerals and soil solutions are 1/3, 1/2 and 2/3, depending on the sampling site, and are in every case identical to the same ratios directly measured by Mössbauer spectroscopy. This implies reversible equilibrium between Green Rust and solution. Solubility products are proposed for the various hydroxy-Green Rusts as follows: log K_sp = 28.2 ± 0.8 for the reaction Fe₃(OH)₇ + e⁻ + 7 H⁺ = 3 Fe²⁺ + 7 H₂O; log K_sp = 25.4 ± 0.7 for the reaction Fe₂(OH)₅ + e⁻ + 5 H⁺ = 2 Fe²⁺ + 5 H₂O; log K_sp = 45.8 ± 0.9 for the reaction Fe₃(OH)₈ + 2e⁻ + 8 H⁺ = 3 Fe²⁺ + 8 H₂O at an average temperature of 9 ± 1°C, and 1 atm. pressure. Tentative values for the Gibbs free energies of formation of hydroxy-Green Rusts obtained are: Δ_fG° (Fe₃(OH)₇, cr, 282.15 K) = −1799.7 ± 6 kJ mol⁻¹, Δ_fG° (Fe₂(OH)₅, cr, 282.15 K) = −1244.1 ± 6 kJ mol⁻¹ and Δ_fG° (Fe₃(OH)₈, cr, 282.15 K) = −1944.3 ± 6 kJ mol⁻¹.