Coexisting garnets and ilmenites synthesized at high pressures from pyrolite and olivine basanite and their significance for kimberlitic assemblages

Coexisting garnets and ilmenites have been synthesized at high pressure (21–40 kb) within the temperature range between 900 and 1100 °C from pyrolite-less-40% olivine and olivine basanite with various water contents. The two compositions yield phases with a range in the 100 Mg/Mg+Fe ratio for both garnet (41–76) and ilmenite (15–47). The distribution coefficient for iron and magnesiaum (K _{D(Fe, Mg)} ^ilm-ga = 4.0±0.5) for coexisting phases does not appear to vary with change in the bulk composition or temperature of synthesis. The synthesized ilmenites are of similar composition to those of kimberlites in 100 Mg/Mg+Fe ratio and Al₂O₃ and Cr₂O₃ solid solution. Cr₂O₃ content in ilmenite is dependent on Cr₂O₃ in the bulk composition and also on Fe₂O₃ content of ilmenite. Fe₂O₃ content of ilmenite is very sensitive to f _O2 and natural ilmenites from peridotites have formed under low f _O2. Al₂O₃ solid solution in ilmenite as well as TiO₂ in coexisting garnet tend to be higher with higher temperature. All the variety of compositions of ilmenites from kimberlites may be obtained from rocks rather close in composition to those used in experiments, within the same range of pressure and temperature but at variable oxygen fugacities.     

Heat capacity calculations for Al2O3 corundum and MgSiO3 ilmenite

We have used Kieffer's vibrational model to calculate heat capacities and entropies for Al₂O₃ corundum and MgSiO₃ ilmenite, using available vibrational and elastic data for these phases. The calculated heat capacity for corundum is within 1–2 percent of the experimental values between 100 K and 1,800 K, while that for MgSiO₃ ilmenite is within 1–2 percent of the experimental data between 350 K and 500 K. We have calculated the heat capacity for MgSiO₃ ilmenite from 50 K to 1,800 K, which extends the range of available heat capacity data for this phase. The results of this calculation suggest that there may be differences in the vibrational properties of corundum and MgSiO₃ ilmenite. Finally, we have used the results of our calculation to obtain a transition entropy of near -18.8 J/mol.K for the MgSiO₃ pyroxene-ilmenite reaction.     

Rhombohedral ilmenite group nickel titanates with Zn, Mg, and Mn: synthesis and crystal structures

Binary, ternary, and quaternary rhombohedral ordered titanates, Ni_1/2Mn_1/2TiO₃, Ni_1/2Mg_1/2TiO₃, Ni_1/3Zn_1/3Mg_1/3TiO₃, and Ni_1/4Zn_1/4Mg_1/4Mn_1/4TiO₃, were obtained by solid-state synthesis at 1095°C at ambient pressure in a nitrogen atmosphere. All of the compounds adopt ATiO₃ (A = Ni, Mn, Zn, and Mg) stoichiometry. Crystal structures were refined by the Rietveld method from powder X-ray diffraction data. Unit cell parameters and unit cell volumes decrease with decreasing average radius of the ^vi A ²⁺ cation. All the synthetic titanates adopt the space group and the ilmenite structure consisting of distorted AO₆ and TiO₆ octahedra. The divalent cations and Ti⁴⁺ are distributed in layers of octahedra alternating along c with no evidence for disorder. In common with pyrophanite, NiTiO₃, and ilmenite sensu stricto, the distortion of the AO₆ octahedra is less than that of the TiO₆ octahedra. The Ti⁴⁺ and A-site cations in the titanates are off-centred within the coordination polyhedra. Deviation of the z positional parameters from their theoretical values for the A and Ti atoms indicate that in the titanates with the larger A ²⁺ cations and Goldschmidt tolerance factors, t ≥ 0.745, the AO₆ octahedral layer is more “puckered” above and below planes parallel to (001) than that of the TiO₆ octahedra, and vice versa in the titanates with smaller R _A ²⁺ for which t≤0.745. Data are given for the volumes and distortion indices of all the coordination polyhedra. This study confirms the existence and stability of complex solid solutions between ordered rhombohedral titanates of Ni and first-row transition metals at ambient conditions over a range of t from 0.786 to 0.737. These experimental data suggest that the formation of ilmenite-type titanates enriched in Ni is possible in exotic mineral-forming systems at low pressure and/or in extraterrestrial rocks.     

Chromium solubility in MgSiO3 ilmenite at high pressure

The crystal structure and chemical composition of crystals of (Mg_1?x Cr _x )(Si_1?x Cr _x )O₃ ilmenite (with x = 0.015, 0.023 and 0.038) synthesized in the model system Mg₃Cr₂Si₃O₁₂–Mg₄Si₄O₁₂ at 18–19 GPa and 1,600 °C have been investigated. Chromium was found as substitute for both Mg at the octahedral X site and Si at the octahedral Y site, according to the reaction Mg²⁺ + Si⁴⁺ = 2Cr³⁺. Such substitutions cause a shortening of the <X–O> and a lengthening of the <Y–O> distances with respect to the values typically observed for pure MgSiO₃ ilmenite and eskolaite Cr₂O₃. Although no high Cr contents are considered in the pyrolite model, Cr-bearing ilmenite may be the host for chromium in the Earth’s transition zone. The successful synthesis of ilmenite with high Cr contents and its structural characterization are of key importance because the study of its thermodynamic constants combined with the data on phase relations in the lower-mantle systems can help in the understanding of the seismic velocity and density profiles of the transition zone and the constraining composition and mineralogy of pyrolite in this area of the Earth.     

Raman spectra of MgSiO3·10% Al2O3-perovskite at various pressures and temperatures

Variations of Raman spectra of MgSiO₃·10% Al₂O₃-perovskite were investigated up to about 270 kbar at room temperature and in the range 108–425 °K at atmospheric pressure. Like MgSiO₃-perovskite, the Raman frequencies of MgSiO₃·10% Al₂O₃-perovskite increase nonlinearly with increasing pressure and decrease linearly with increasing temperature within the experimental uncertainties and the range investigated. A comparison of these data with those of MgSiO₃-perovskite suggests that MgSiO₃·10% Al₂O₃-perovskite is slightly more compressible than MgSiO₃-perovskite, and that the volume thermal expansion for MgSiO₃·10% Al₂O₃-perovskite is also slightly greater than that for MgSiO₃-perovskite.     

Mineralogy, Chemical Characteristics and Upgrading of Beach Ilmenite of the Top Meter of Black Sand Deposits of the Kafr Al-Sheikh Governorate, Northern Egypt

Egyptian beach ilmenite occurs in a relatively high content in the naturally highly concentrated superficial black sand deposits at specific beach zones in the northern parts of the Nile Delta at Rosetta. Microscopic study shows that the ilmenite occurs as fresh homogeneous black or heterogeneous multicoloured altered grains and exhibits three types (homogeneous, exsolved and altered) of ilmenite varieties. XRD data of ilmenite indicates their association with minor hematite and quartz, whereas leucoxene shows its association with Nb‐rutile, pseudorutile and hematite. Grain size distribution suggests a very fine sand size of >89% and 80% and a fine sand size of 10.5% and 18.3% for fresh and altered ilmenites, respectively. The density of fresh, altered ilmenite and leucoxene concentrates varies from 2.70, 2.50 to 2.40 ton/m³, suggesting a gradual decrease from high grade fresh to leucoxene and consistent with variation in magnetic susceptibility as a consequence of the leaching of iron. Mass magnetic susceptibility reveals 97.6% of ilmenite and 92% of the altered form are obtained at 0.20 and 0.48 ampere. Fresh ilmenite exhibits variable TiO₂ (47.18%) and Fe₂O₃^T (46.10%) with minor MnO, MgO and Cr₂O₃ (1.22, 1.10 and 0.51%). The altered ilmenite is higher in TiO₂ (76.16%) and SiO₂ (4.68%) and lower in Fe₂O₃^T (14.45%), MnO, MgO and Cr₂O₃ (0.39, 0.52 and 0.11%) compared with the fresh form. Three concentrates of ilmenites (G1, G2 and G3) were prepared from crude ore using a Reading cross belt magnetic separator under different conditions, revealing a gradual increase of TiO₂, SiO₂, Al₂O₃ and CaO accompanied by a decrease of Fe₂O₃^T, MgO and Cr₂O₃ with repetition of the separation processes. Several ore dressing techniques were carried out to upgrade the ilmenite concentrate.     

Ionic conductivity in sodium magnesium silicates

Na₂MgSiO₄ crystals prepared hydrothermally at 700° C and 3,000 atm are related to carnegieite with SG Pmn2₁, a=7.015(2), b=10.968(2), and c=5.260(1). Na conductivity in Na₂MgSiO₄ is 3.0×10^?5 (ohm-cm)^?1 at 300° C but can be raised to 1.1×10^?3 (ohm-cm)^?1 by creating Na vacancies in the composition Na_1.9Mg_0.9Al_0.1O₄. Na₄Mg₂Si₃O₁₀ is also a cristobalite-related carnegieite with the orthorhombic cell a=10.584(7), b=14.328(7), and c=5.233(5). The Na conductivity of Na₄Mg₂Si₃O₁₀ is 4.8×10^?3 (ohm-cm)^?1 at 300° C.     

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.     

57Fe Mössbauer spectroscopy and magnetization of cation-deficient Fe2TiO4 and FeCr2O4. Part I:57Fe Mössbauer spectroscopy

⁵⁷Fe Mössbauer spectra are presented for synthetic cation-deficient Fe₂TiO₄ and FeCr₂O₄ spinel particles (<1μm) at various temperatures. The spectra of ferrimagnetic cation-deficient Fe₂TiO₄ show characteristic features due to relaxation because of superparamagnetism and spin relaxation in the temperature range 5–294 K. At 5 K and 78 K, a superposition of at least two sextets is observed which appear to arise from Fe³⁺ onA-sites (Fe _A ³⁺ andB-sites (Fe _B ³⁺ ) of the spinal lattice with magnetic hyperfine fields at 5 K ofB _hf ((Fe _B ³⁺ )≈47.5 T andB _hf (Fe _B ³⁺ )≈51.0 T, respectively. Cation-deficient FeCr₂O₄ particles reveal at 78 K a fieldB _hf (Fe³⁺)≈46.9 T and exhibit relaxation spectra as a consequence of superparamagnetism in the temperature range 80 K - ～300 K. At 294 K, quadrupole splitting Δ(Fe _A ³⁺ )=0.92 mm/s and isomer shift δ(Fe _A ³⁺ )=0.29 mm/s (relative to metallic Fe) are measured. For both compounds the magnetic hyperfine fieldsB _hf are discussed in terms of supertransferred hyperfine fields involving vacancies and in the case of cation-deficient Fe₂TiO₄ also diamagnetic Ti⁴⁺ neighbours of the Fe ions.     

High-pressure transformations in silicates,germanates, and titanates with ABO3 stoichiometry

High-pressure phase transformations were investigated for two silicates, MgSiO₃ and ZnSiO₃; six germanates, MGeO₃ and six titanates, MTiO₃ (M=Ni, Mg, Co, Zn, Fe, and Mn) at about 1,000°C and pressures up to ca. 30 GPa. CoGeO₃ was found to assume the ilmenite form. The ilmenite phases were confirmed to transform in the following schemes: to perovskite in MgSiO₃ and MnGeO₃, to corundum in MgGeO₃ and ZnGeO₃, to rocksalt plus rutile in ZnSiO₃ and CoGeO₃ and to rocksalt plus TiO₂ (possibly of some denser structure) in NiTiO₃, MgTiO₃, CoTiO₃, ZnTiO₃ and FeTiO₃. In the case of FeTiO₃, the corundum form appeared as an intermediate phase. The possibility that the corundum type MnTiO₃ might transform to some denser modification could not be excluded. The compound NiGeO₃ was nonexistent throughout the pressure range studied. High-pressure phases of ABO₃ (A=Ni, Mg, Co, Zn, Fe, and Mn; B=Si, Ge and Ti) are summarized, and those stabilized at pressures higher than 20 GPa are discussed.     

Experimental determination of activities in FeTiO3-MnTiO3 ilmenite solid solution by redox reversals

 Solid solutions of (Fe,Mn)TiO₃ were synthesized, mostly at 0.10 X_Mn intervals, at 1 bar, 900°C and log f _{O 2} = –17.50. Analysis by EMP indicate an ideal stoichiometry for the Fe-Mn ilmenites with (Fe+Mn) = Ti = 1.000 when normalized to 3 oxygens. Their unit cell volume increases linearly with X_Mn. The composition of Fe-Mn ilmenite coexisting with metallic Fe and rutile was reversed at 1 bar, 700–900°C and fixed f _{O 2} in a gas-mixing furnace. Oxygen fugacity was controlled by mixing CO₂ and H₂ gas and was continuously monitored with an yttrium-stabilized zirconia electrolyte. Solution properties of Fe-Mn ilmenite were derived from the experimental data by mathematical programming (Engi and Feenstra, in preparation) including notably the results of Fe-Mn exchange experiments between ilmenite and garnet (Feenstra and Engi, submitted) and anchoring the standard state properties to the updated thermodynamic dataset of Berman and Aranovich (1996). The thermodynamic analysis resulted in positive deviations from ideality for (Fe,Mn)TiO₃ ilmenite, which is well described by an asymmetric Margules model with W^H _FeFeMn = –9.703 and W^H _FeMnMn = –23.234 kJ/mol, W^S _FeFeMn = –19.65 and W^S _FeMnMn = –22.06 J/(K·mol). The excess free energy for Fe-Mn ilmenite derived from the redox reversals is larger than in the symmetric ilmenite model (W^G _FeMn = +2.2 kJ/mol) determined by O'Neill et al. from emf measurements on the assemblage iron-rutile-(Fe,Mn)ilmenite. Received: 10 January 1996 / Accepted: 11 July 1996     

MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

Thermal diffusivity and thermal conductivity of single-crystal MgO and Al2O3 and related compounds as a function of temperature

Thermal diffusivity (D) was measured up to ~1,800 K of refractory materials using laser-flash analysis, which lacks radiative transfer gains and contact losses. The focus is on single-crystal MgO and Al₂O₃. These data are needed to benchmark theoretical models and thereby improve understanding of deep mantle processes. Measurements of AlN, Mg(OH)₂, and isostructural BeO show that the power law (D = AT ^?B ) where T is temperature holds for simple structures. Results for more structurally complicated corundum Al₂O₃ with and without impurity atoms are best fit by CT ^d  + ET ^f where d ~ ?1 and f ~ ?4, whereas for isostructural Fe₂O₃, f is near +3 and multiphase ilmenite Fe_1.12Ti_0.88O₃ is fit by the above power law. The positive temperature response for hematite is attributed to diffusive radiative transfer arising from electronic–vibronic coupling. We find good agreement of k and D data on single-crystal and non-porous ceramic Al₂O₃. For the corundum structure, D is nearly independent of T at high T. Although D at 298 K depends strongly on chemical composition, at high temperature, these differences are reduced. Thermal conductivity provided for MgO and Al₂O₃, using LFA data and literature values of density and heat capacity, differs from contact measurements which include systematic errors. The effect of pressure is discussed, along with implications for the deepest mantle.     

Hydrostatic compression of ilmenite phase of ZnSiO3 and MgGeO3

Accurate measurements of cell parameters were performed on the ilmenite phases of ZnSiO₃ and MgGeO₃ using an X-ray diffraction method under hydrostatic conditions. The linear changes in cell parameter are represented by 1?a/a ₀=(1.06±0.04)×10^?4 P(kbar) and 1?c/c ₀=(2.11±0.04)×10^?4 P for ZnSiO₃, and 1?a/a ₀=(1.37±0.03)×10^?4 P and 1?c/c ₀=(2.05±0.04)×10^?4 P for MgGeO₃. A least-squares calculation using the first-order Birch-Murnaghan equation gives K _T =2.16±0.02 Mbar and K _T =1.87±0.02 Mbar for ZnSiO₃ and MgGeO₃, respectively. Elastic systematics assuming K _T V _m =constant give a predicted value K _T =2.14 Mbar for the ilmenite phase of MgSiO₃.     

Synthetic minerals with the pyrochlore and garnet structures for immobilization of actinide-containing wastes

Complex oxides of the pyrochlore (space groups Fd3m, ^[8]A₂ ^[6]B₂O₇) and garnet (Ia3d, ^[8]A₃ ^[6]B₂ ^[4]T₃O₁₂) structures (“A” = Ca²⁺, Ln^3+/4+, An^3+/4+; “B” = (Ti, Sn, Hf, and Zr)⁴⁺ in pyrochlore, and Al³⁺, Ga³⁺, and Fe³⁺ in garnet alone; “T” = (Al³⁺, Ga³⁺, and Fe³⁺) are promising matrices for actinide-bearing wastes. In order to identify optimal compositions of these phases, their isomorphic capacity with respect to REE, actinides, and other components of wastes was examined. The long-term behavior of the matrix at a repository was predicted based on data obtained on the behavior of pyrochlores and garnets under ion irradiation and ²⁴⁴Cm decay and on the determined leaching rates of REE from the matrices because of their interaction with aqueous solutions, including that after amorphization. In order to propose efficient synthesis techniques, samples prepared with the use of various methods were studied. The possibility of incorporating long-lived decay products of ⁹⁹Tc into the crystalline matrices was analyzed.     

Pseudosinhalite: discovery of the hydrous MgAl-borate as a new mineral in the Tayozhnoye, Siberia, skarn deposit

After its initial synthesis as the new compound Mg₂Al₃B₂O₉(OH) (Daniels et al. 1997) pseudosinhalite has now been discovered as a new mineral. It occurs, together with hydrotalcite, as a replacement product of sinhalite, MgAlBO₄, in an impure marble of the contact metasomatic iron boron deposit of Tayozhnoye in the Aldan Shield of Siberia. Its chemical composition determined by electron microprobe is (wt%): Al₂O₃ 46.88; MgO 25.12; FeO 1.99; B₂O₃ (calculated) 21.75; H₂O (calculated) 2.81 giving a total of 98.55 and leading to the empirical formula (Mg_2.00 Fe²⁺ _0.09)_Σ=2.09 Al_2.94 B₂O₉(OH). The small deviation from the ideal stoichiometry with (Mg?+?Fe²⁺):Al?≠?2:3 may be caused by either solid solution towards, or submicroscopic interlayering with lamellae of, the structurally similar mineral sinhalite. The underlying substitution involving also B and H would be (Mg?+?Fe)+?B=Al+2H. Pseudosinhalite is monoclinic, space group P2₁/c, with a=7.49(1), b=4.33(1), c=9.85(2) Å; β=110.7(1)°; V?=?299(1) ų; Z?=?2. Calculated density is 3.508?g/cm³. Pseudosinhalite is colourless with white streak and has a vitreous lustre. It is transparent; no fluorescence was detected. There is no cleavage and parting; fractures are concoidal. Optical constants could not be measured properly due to polysynthetic microtwinning, but α<1.72<γ. For synthetic pseudosinhalite α=1.691(1); β=1.713(1); γ=1.730(1); Δ=0.039; 2?V=80°. The temperature of pseudosinhalite formation was below about 400?°C at low pressures and with a hydrous, CO₂-bearing fluid participating in the reaction.     

Effects of Fe and Al incorporations on the bridgmanite–postperovskite coexistence domain

The postperovskite phase transition of Fe and Al-bearing MgSiO₃ bridgmanite, the most aboundant mineral in the Earth's lower mantle, is believed to be a key to understanding seismological observations in the D″ layer, e.g., the discontinuous changes in seismic wave velocities. Experimentally reported phase transition boundaries of Fe and Al-bearing bridgmanite are currently largely controversial and generally suggest wide two-phase coexistence domains. Theoretical simulations ignoring temperature effects cannot evaluate correctly two-phase coexistence domains under high-temperature. We show high-pressure and high-temperature phase transition boundaries for various compositions with geophysically relevant impurities of Fe²⁺SiO₃, Fe³⁺Fe³⁺O₃, Fe³⁺Al³⁺O₃, and Al³⁺Al³⁺O₃ derived from the ab initio finite-temperature free energies calculated combining the internally consistent LSDA + U method and a lattice dynamics approach. We found that at ～ 2500 K, incorporations accompanied by Fe³⁺ expand the two-phase coexistence domains distinctly, implying that D″ seismic discontinuities likely arise from the phase transition of Fe²⁺-bearing bridgmanite.     

Enthalpies of formation at 970 K of compounds in the system MgO-Al2O3-SiO2 from high temperature solution calorimetry

The enthalpies of solution of petrologically important phases in the system MgO-Al₂O₃-SiO ₂ were measured in a melt of composition 2PbO · B₂O₃ at 970 ± 2K. The substances investigated included synthetic and natural (meteoritic) enstatite (MgSiO₃), synthetic aluminous enstatite (MgSiO_30.9Al₂O_30.1), synthetic and natural cordierite (Mg₂Al₄Si₅O₁₈), synthetic and natural sapphirine (approx. 7MgO·9Al₂O₃ · 3SiO₂), synthetic spinel (MgAl₂O₄), natural sillimanite (Al₂SiO₅), synthetic forsterite (Mg₂SiO₄), synthetic pyrope (Mg₃Al₂Si₃O₁₂), natural quartz (SiO₂), synthetic periclase (MgO) and corundum (Al₂O₃). Improvement in standardization of the calorimeter solvent made possible greater precision in this study than obtainable in former work in this laboratory on some of the same substances.The enthalpies of formation of enstatite, synthetic cordierite, forsterite and spinel are in reasonable agreement with values previously determined by solution calorimetry. The enthalpy of formation of enstatite is about 0.7 kcal less negative than the value for clinoenstatite resulting from the HF calorimetry of Torgesen and Sahama (J. Amer. Chem. Soc.70. 2156–2160, 1948), and is in accord with predictions based on analysis of published pyroxene equilibrium work. Aluminous enstatite with 10 wt.% Al₂O₃ shows an enthalpy of solution markedly lower than pure MgSiO₃: the measurements lead to an estimate of the enthalpy of formation at 970 K for MgAl₂SiO₆ (Mg-Tschermak) orthopyroxene of + 9.4 ± 1.5 kcal/mole from MgSiO₃ and Al₂O₃.Comparison of the enthalpies of formation of synthetic cordierite and anhydrous natural low-iron cordierite shows that they are energetically quite similar and that the synthetic cordierite is not likely to have large amounts of (Al, Si) tetrahedral disorder. Comparison of the enthalpies of formation of synthetic sapphirine and natural low-iron sapphirine shows, on the other hand, that the former is not a good stability model for the latter. The lower enthalpy of formation of the high-temperature synthetic sample is undoubtedly a consequence of cation disordering.The enthalpy of formation of natural sillimanite is considerably less negative than given by the tables of Robie andWaldbaum (U.S. Geol. Surv. Bull.1259 1968).The measured enthalpy of formation of synthetic pyrope is consistent with that deduced from published equilibrium diagrams in conjunction with the present measured enthalpy of formation of aluminous enstatite. Calculation of the entropy of synthetic pyrope from the present data yields surprisingly high values and suggests that synthetic pyrope is not a good stability model for natural pyrope-rich garnets. Hence, considerable doubt exists about the direct quantitative application of experimental diagrams involving pyropic garnet to discussions of the garnet stability field in the Earth's outer regions.     

Thermodynamic properties of hematite — ilmenite — geikielite solid solutions

A solution model is developed for rhombohedral oxide solid solutions having compositions within the ternary system ilmenite [(Fe ₂₊ ^s Ti ₄₊ ^1–s ) ^A (Fe ₂₊ ^1–s Ti ₄₊ ^s ) ^B O₃]-geikielite [(Mg ₂₊ ^t Ti ₄₊ ^1–t ) ^A (Mg ₂₊ ^1–t Ti ₄₊ ^t ) ^B O₃]-hematite [(Fe³⁺) ^A (Fe³⁺) ^B O₃]. The model incorporates an expression for the configurational entropy of solution, which accounts for varying degrees of structural long-range order (0s, t1) and utilizes simple regular solution theory to characterize the excess Gibbs free energy of mixing within the five-dimensional composition-ordering space. The 13 model parameters are calibrated from available data on: (1) the degree of long-range order and the composition-temperature dependence of the transition along the ilmenite-hematite binary join; (2) the compositions of coexisting olivine and rhombohedral oxide solid solutions close to the Mg–Fe²⁺ join; (3) the shape of the miscibility gap along the ilmenite-hematite join; (4) the compositions of coexisting spinel and rhombohedral oxide solid solutions along the Fe²⁺–Fe³⁺ join. In the course of calibration, estimates are obtained for the reference state enthalpy of formation of ulvöspinel and stoichiometric hematite (–1488.5 and –822.0 kJ/mol at 298 K and 1 bar, respectively). The model involves no excess entropies of mixing nor does it incorporate ternary interaction parameters. The formulation fits the available data and represents an internally consistent energetic model when used in conjuction with the standard state thermodynamic data set of Berman (1988) and the solution theory for orthopyroxenes, olivines and Fe–Mg titanomagnetite-aluminate-chromate spinels developed by Sack and Ghiorso (1989, 1990a, b). Calculated activity-composition relations for the end-members of the series, demonstrate the substantial degree of nonideality associated with interactions between the ordered and disordered structures and the dominant influence of the miscibility gap across much of the ternary system. The predicted shape of the miscibility gap, and the orientation of tie-lines relating the compositions of coexisting phases, display the effects of coupling between the excess enthalpy of solution and the degree of long-range order. One limb of the miscibility gap follows the composititiontemperature surface corresponding to the ternary second-order transition.