A new high-pressure and high-temperature polymorph of FeS

A new polymorph of FeS has been observed at pressures above 30 GPa at 1,300 K by in situ synchrotron X-ray diffraction measurements in a laser-heated diamond anvil cell. It is stable up to, at least, 170 GPa at 1,300 K. The new phase (here called FeS VI) has an orthorhombic unit cell with lattice parameters a = 4.8322 (17) Å, b = 3.0321 (6) Å, and c = 5.0209 (8) Å at 85 GPa and 300 K. Its topological framework is based on the NiAs-type structure as is the case for the other reported polymorphs (FeS I-V). The unit cell of FeS VI is, however, more distorted (contracted) along the [010] direction of the original NiAs-type cell. For example, the c/b axial ratio is ～1.66 at 85 GPa and 300 K, which is considerably smaller than that of orthorhombic FeS II (～1.72) and NiAs-type hexagonal FeS V (=√3 ≈ 1.73). The phase boundary between FeS IV and VI is expected to be located around 30 GPa at 1,300 K. The phase transition is accompanied by gradual and continuous changes in volume and axial ratios and may be second order. At room temperature, FeS VI becomes stable over FeS III at pressures above 36 GPa. It is, therefore, suggested that the phase boundary of FeS III–VI and/or FeS IV–VI has negative pressure dependence.     

A modeling of the structure and favorable H-docking sites and defects for the high-pressure silica polymorph stishovite

Employing first-principles methods, the docking sites for H were determined and H, Al, and vacancy defects were modeled with an infinite periodic array of super unit cells each consisting of 27 contiguous symmetry nonequivalent unit cells of the crystal structure of stishovite. A geometry optimization of the super-cell structure reproduces the observed bulk structure within the experimental error when P1 translational symmetry was assumed and an array of infinite extent was generated. A mapping of the valence electrons for the structure displays mushroom-shaped isosurfaces on the O atom, one on each side of the plane of the OSi₃ triangle in the nonbonded region. An H atom, placed in a cell near the center of the super cell, was found to dock upon geometry optimization at a distance of 1.69 Å from the O atom with the OH vector oriented nearly perpendicular to the plane of the triangle such that the OH vector makes a angle of 91° with respect to [001]. However, an optimization of a super cell with an Al atom replacing Si and an H atom placed nearby in a centrally located cell resulted in an OH distance of 1.02 Å with the OH vector oriented perpendicular to [001] as observed in infrared studies. The geometry-optimized position of the H atom was found to be in close agreement with that (0.44, 0.12, 0.0) determined in an earlier study of the theoretical electron density distribution. The docking of the H atom at this site was found to be 330 kJ mol^–1 more stable than a docking of the atom just off the shared OO edge of the octahedra as determined for rutile. A geometry optimization of a super cell with a missing Si generated a vacant octahedra that is 20% larger than that of the SiO₆ octahedra. The valence electron density distribution displayed by the two-coordinate O atoms that coordinate the vacant octahedral site is very similar to those displayed by the bent SiOSi angles in coesite. The internal distortions induced by the defect were found to diminish rather rapidly with distance, with the structure annealing to that observed in the bulk crystal to within about three coordination spheres.     

Kokchetavite: a new potassium-feldspar polymorph from the Kokchetav ultrahigh-pressure terrane

Kokchetavite, a new polymorph of K-feldspar (KAlSi₃O₈), has been identified as micrometer-size inclusions in clinopyroxene and garnet in a garnet-pyroxene rock from the Kokchetav ultrahigh-pressure terrane, Kazakhstan. Kokchetavite has a hexagonal structure with a =5.27(1) Å, c=7.82(1) Å, V=188.09 ų, Z=1, and is found to be associated with phengite + /-cristobalite (or quartz) + siliceous glass ± phlogopite/titanite/calcite/zircon, occurring as multi-phase inclusions in clinopyroxene and garnet. It is concluded that kokchetavite could not be an exsolution phase in host minerals. Instead, it might be metastably precipitated from an infiltrated K-rich melt during rock exhumation. Alternatively, although less likely, kokchetavite might be derived from dehydration of K-cymrite, which, in turn, was formed at high pressures. In either case, kokchetavite is a metastable polymorph of K-feldspar.     

Diagenesis of the Sedimentary Rocks Enclosing Coaly Layers in Gavatha Area,Lesvos Island,Based on Silica Polymorph‘s Transformations

A Tertiary non-marine stratigraphic sequence composed of carbonates(limestone),siliceous carbonates,coaly layers overlain by pyroclastic rocks and lavas,outcrops in the Gavatha area of northwestern Lesvos Island.Pure earbonates eonsist almost completely of calcite,the siliceous carbonate sediments of quartz,opal-CT and calcite,the shales of quartz,opal CT, K-feldspar,smecite-illite and ealcite,and the coaly layers of organic matter,quartz,opal-CT,feldspars and pyrite,Geochemical data indicate that smectite-illite,feldspars and associated elements(La,Zr,Y,Ba,Ce)are the products of alteration of volcanic rocks in a subtropical area A combination of sources in suggested for the formation of silica polymorphs:(a) biogenic or non-biogenic silica(opal-A) that was originally present in the form of diatiom frustules of in the form of inorganically prccipitated silica;(b)transformation o opall-A to opal-CT and quartz opal-C from alteration of volcanic glass of intercalated tuffites and overlying volcanics;and(c)opal-CT deposited primarily from hydrothermal solutions.     

Thermochemistry of carbonate-pyroxene equilibria

The enthalpies of drop solution of calcite, magnesite, dolomite, wollastonite and diopside have been measured in a lead borate solvent at 977 K in a Calvettype microcalorimeter. The carbonate calorimetry was done under flowing gas atmosphere. Both natural and synthetic samples were used. From these calorimetric data, the enthalpies of several reactions of carbonate with quartz were calculated. The enthalpies of these reactions (kJ/mol) at 298 K are: calcite+quartzwollastonite+CO₂, 92.3±1.0; magnesite+quartzenstatite+CO₂, 82.9±2.8; dolomite+quartzdiopside+CO₂, 163.0±1.9. These values generally are in agreement with those calculated from Robie et al., Helgeson et al., Berman and Holland and Powell. The enthalpy of dolomite-quartz reaction overlaps marginally with those from Berman and Holland and Powell. The enthalpy of formation of dolomite from magnesite and calcite (-11.1±2.5 kJ/mol) was also derived from the measured enthalpies, and this value is consistent with that from acid solution calorimetric measurements as shown by Navrotsky and Capobianco, but different from values in the earlier literature. These results support the premise that drop-solution of carbonates into molten lead borate results in a well-defined final state consisting of dissolved oxide and evolved CO₂. This was also confirmed by weight change experiments. Thus, oxide melt calorimetry is applicable to carbonates.     

Thermochemistry of the high structural state plagioclases

The enthalpies of solution of a suite of 19 high-structural state synthetic plagioclases were measured in a Pb₂B₂O₅ melt at 970 K. The samples were crystallized from analyzed glasses at 1200°C and 20 kbar pressure in a piston-cylinder apparatus. A number of runs were also made on Amelia albite and Amelia albite synthetically disordered at 1050–1080°C and one bar for one month and at 1200°C and 20 kbar for 10 hr. The component oxides of anorthite, CaO, Al₂O₃ and SiO₂, were remeasured.The ΔH of disorder of albite inferred in the present study from albite crystallized from glass is 3.23 kcal, which agrees with the 3.4 found by Holm and Kleppa (1968). It is not certain whether this value includes the ΔH of a reversible displacive transition to monoclinic symmetry, as suggested by Helgesonet al. (1978) for the Holm-Kleppa results. The enthalpy of solution value for albite accepted for the solid solution series is based on the heat-treated Amelia albite and is 2.86 kcal less than for untreated Amelia albite.The enthalpy of formation from the oxides at 970 K of synthetic anorthite is ?24.06 ± 0.31 kcal, significantly higher than the ?23.16 kcal found by Charluet al. (1978), and in good agreement with the value of ?23.89 ± 0.82 given by Robieet al. (1979), based on acid calorimetry.The excess enthalpy of mixing in high plagioclase can be represented by the expression, valid at 970 K: ΔH^ex(±0.16 kcal) = 6.7461 X_abX²_An + 2.0247 X_AnX²_Ab where X_Ab and X_An are, respectively, the mole fractions of NaAlSi₃O₈ and CaAl₂Si₂O₈. This ΔH^ex, together with the mixing entropy of Kerrick and Darken's (1975) Al-avoidance model, reproduces almost perfectly the free energy of mixing found by Orville (1972) in aqueous cation-exchange experiments at 700°C. It is likely that Al-avoidance is the significant stabilizing factor in the high plagioclase series, at least for X_An≥ 0.3. At high temperatures the plagioclases have nearly the free energies of ideal one-site solid solutions. The Al-avoidance model leads to the following Gibbs energy of mixing for the high plagioclase series: $\text{ΔG}{}^{\mathrm{mix}}\text{= ΔH}{}^{\mathrm{ex}}\text{+ RT X}{}_{\mathrm{Ab}}\text{ln[X}{}^2{}_{\mathrm{Ab}}\text{(2 ? X}{}_{\mathrm{Ab}}\text{)]+ X}{}_{\mathrm{An}}\text{ln}\text{[X}{}_{\mathrm{An}}\text{(1+X}{}_{\mathrm{An}}\text{)}{}^2\text{]}\text{4}$. The entropy and enthalpy of mixing should be very nearly independent of temperature because of the unlikelihood of excess heat capacity in the albite-anorthite join.     

A new natural,super-hard,transparent polymorph of carbon from the Popigai impact crater,Russia

A natural shockwave event led to the formation of a new crystalline polymorph of carbon in gneisses from the Popigai crater, Russia. The new species occupies the interior of a multiphase assemblage and is entirely enveloped by lonsdaleite and graphite. Polishing hardness of this new phase is greater than that of lonsdaleite. Micro-beam synchrotron X-ray diffraction, imaging and fluorescence studies revealed a pure transparent carbon phase. The diffraction pattern is indexed in terms of a cubic cell (a=14.697 Å, space group Pm3m.). This species was neither encountered in static or dynamic high-pressure experiment nor predicted by theoretical calculations. To cite this article: A. El Goresy et al., C. R. Geoscience 335 (2003).     

Thermochemistry of forsterite-fayalite olivine solutions

The enthalpies of solution of synthetic Mg₂SiO₄-Fe₂SiO₄ olivine solid solutions have been measured in Pb₂B₂O₅ melt at 970 K. The heat of solution of forsterite was found to be 15.62 ± 0.3 kcal mol^?1 and that of fayalite 9.39 ± 0.14 kcal mol^?1. Solid solutions between these end-members exhibit small positive deviations from mixing ideality, asymmetric towards the Fe end-member. In terms of the sub-regular solution model, excess enthalpies of intermediate olivine are adequately represented by the equation H^xs = 2(1000 + 1000X_Fe) X_FeX_MgThe enthalpies of solution at 970 K are consistent with high temperature phase equilibrium measurements of activity-composition relationships in the olivine series. Excess entropy terms are not needed to relate the phase equilibrium data to the calorimetric data presented here.The enthalpy of solution of FeSiO₃ ferrosilite at 970 K was found to be 4.36 ± 0.10 kcal mol^?1. This value, when taken together with calorimetric measurements on fayalite and quartz, is consistent with phase equilibrium investigations of the reaction: 2FeSiO₃ = Fe₂SiO₄ + SiO₂ Ferrosilite Fayalite QuartzThese provide a check on the internal consistency of the calorimetric data presented here.     

Thermochemistry of jadeite—diopside pyroxenes

The enthalpies of solution of seven synthetic clinopyroxenes on the join CaMg₂Si₂O₆ (diopside)-NaAlSi₂O₆ (jadeite), of two natural low-Fe ordered omphacites near the 1:1 composition, and of a nearly pure natural jadeite, were measured in molten Pb₂B₂O₅ at 970 K. Enthalpies of solution of the natural omphacites experimentally disordered at 1350°C and 30 kbar were also measured.The synthetic clinopyroxenes have positive excess enthalpies of mixing, which can be expressed by a symmetrical function ΔH_mix = W_HX_JdX_Di, with W_H = 7250 ±950 calories. The enthalpy of disordering of the two natural omphacites averages 1.8 kcal, which is nearly the same as the excess enthalpy of mixing of a 1:1 disordered pyroxene.The interaction parameter, W_H, can be shown to be essentially equivalent to ΔG° of the reciprocal reaction: CaMgSi₂O₆ + NaAlSi₂O₆ = CaAlSi₂O⁺₆ + NaMgSi₂O^?₆ M-site cation distribution data of natural omphacites heat-treated at 1000°C (Aldridgeet al., 1978) lead to ΔG° = 7200 cal for the above reaction, in good agreement with the calorimetric W_H. The reciprocal solution theory with ΔG° = 7200 cal predicts closely the activities of NaAlSi₂OP₆ in jadeite-diopsides found from phase equilibrium measurements at 600°C (Holland, 1979a) and is nearly equivalent to an entropically ideal two site mixing model with a (fictive) W_H of 5800 cal.Jadeite-diopside solid solutions near the 1:1 composition at temperatures of 1000–1500 K are ‘pseudoideal’; that is, they have nearly the free energies of ideal one-site mixtures (Ganguly, 1973). If the order-disorder transition is nearly first-order at about 1000 K, as suggested by Fleetet al. (1978), the pseudo-ideality holds also for ordered omphacites at least somewhat below 1000 K.     

Thermochemistry and melting properties of basalt

The heat capacities of the liquid, glassy and crystalline phases of an alkali basalt have been determined from relative enthalpies measured between 400 and 1,800 K. Values given by available models of calculation generally agree to within 2% of these results. As derived from the new data and the enthalpy of vitrification measured at 973 K by oxide-melt drop solution calorimetry for the same sample, the enthalpy of fusion of this basalt increases from 15.4 kJ/mol at 1,000 K to 33.6 kJ/mol at 1,800 K. Comparisons between the enthalpies of fusion of basalt and model compositions confirm the small magnitude of the enthalpy of mixing between the molten mineral components of the liquids. Minor variations in the chemical composition have only a small effect in the heat capacity and the enthalpy of melting of basalt. The enthalpies of formation at 298 K from the oxides of the crystallized and glass phases of this alkali basalt are −112.2 and −98.5 kJ/mol, respectively, for a gram formula weight based on one mole of oxide components.     

A comparative study of the thermal behaviour of length-fast chalcedony, length-slow chalcedony (quartzine) and moganite

The thermal behaviour of silica rocks upon heat treatment is dependent on the constituent minerals and petrographic texture types. These constituents can be shown to be mainly quartz in the form of two types of chalcedony (Length-fast (LF) chalcedony and Length-slow (LS) chalcedony, the latter also being termed quartzine) and moganite. Even though the thermal behaviour of LF-chalcedony is well understood, major uncertainties persist concerning the high-temperature behaviour of LS-chalcedony and moganite. We present here a comparative study of these three constituents of common silica rocks. Our results show that the chemical reaction is the same in all three, Si–OH + HO–Si → Si–O–Si + H₂O, but that the reaction kinetics and activation temperatures are very different. LS-chalcedony begins to react from 200 °C upwards, that is at temperatures 50 °C below the ones observed in LF-chalcedony, and shows the fastest reaction kinetics of this ‘water’ loss. Chemically bound water (SiOH) in moganite is more stable at high temperatures and no specific activation temperature is necessary for triggering the temperature-induced ‘water’ loss. Moganite is also found to act as a stabilizer in silica rocks preventing them from temperature-induced fracturing. These findings have implications for the study of potential heat treatment temperatures of silica rocks (in industry and heritage studies), but they also shed light on the different structures of SiO₂ minerals and the role of OH impurities therein.     

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.     

Compression studies of gibbsite and its high-pressure polymorph

Various X-ray diffraction methods have been applied to study the compression behavior of gibbsite, Al(OH)₃, in diamond cells at room temperature. A phase transformation was found to take place above 3 GPa where gibbsite started to convert to its high-pressure polymorph. The high-pressure (HP) phase is quenchable and coexists with gibbsite at the ambient conditions after being unloaded. This HP phase was identified as nordstrandite based on the diffraction patterns obtained at room pressure by angle dispersive and energy dispersive methods. On the basis of this structural interpretation, the bulk modulus of the two polymorphs, i.e., gibbsite and nordstrandite, could be determined as 85 ± 5 and 70 ± 5 GPa, respectively, by fitting a Birch-Murnaghan equation to the compression data, assuming their K_o ^′ as 4. Molar volume cross-over occurs at 2 GPa, above which the molar volume of nordstrandite is smaller than that of gibbsite. The differences in the molar volume and structure between the two polymorphs are not significant, which accounts for the irreversibility of the phase transition. In gibbsite, the axial compressibility behaves as c/c _o > a/a _o > b/b _o. This is due to the fact that the dioctahedral sheets along the c-axis are held by the relatively weak hydrogen bonding, which results in the greater compressibility along this direction. In nord- strandite, the axial compressibility is b/b _o > c/c _o > a/a _o, which can also be interpreted as resulting from the the existence of hydrogen bonds along the b-axis. Received: 28 September 1998 / Revised, accepted: 22 December 1998     

Natural high-pressure polymorph of merrillite in the shock veins of the Suizhou meteorite

A new high-pressure polymorph of merrillite with the structure of trigonal γ-Ca₃(PO₄)₂ was found in the shock-produced veins of the Suizhou meteorite, where it coexists with ringwoodite, majorite, NaAlSi₃O₈-hollandite, and majorite-pyrope garnet. The crystallographic nature of this natural γ-Ca₃(PO₄)₂ phase was characterized by Raman spectroscopy and X-ray diffraction, and all data compare favorably to the same data obtained from γ-Ca₃(PO₄)₂ synthesized at 14 GPa and 1400°C. The cell parameters of this new high-pressure mineral are a = 5.258(1) angstroms and c = 18.727(3) angstroms, space group R-3m, and density = 3.447 (g/cm³), where the number in parentheses are standard deviations in the last significant digits. The natural occurrence of the γ-Ca₃(PO₄)₂ phase together with other high-pressure minerals constrains the pressure of the shock veins at about 23 GPa. The Suizhou meteorite provides the first naturally occurring example of γ-Ca₃(PO₄)₂ polymorph.     

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

We have investigated the thermodynamics of mixing between aragonite (orthorhombic CaCO₃) and strontianite (SrCO₃). In agreement with experiment, our simulations predict that there is a miscibility gap between the two solids at ambient conditions. All Sr_xCa_1−xCO₃ solids with compositions 0.12 < x < 0.87 are metastable with respect to separation into a Ca-rich and a Sr-rich phase. The concentration of Sr in coral aragonites (x ∼ 0.01) lies in the miscibility region of the phase diagram, and therefore formation of separated Sr-rich phases in coral aragonites is not thermodynamically favorable. The miscibility gap disappears at around 380 K. The enthalpy of mixing, which is positive and nearly symmetric with respect to x = 0.5, is the dominant contribution to the excess free energy, while the vibrational and configurational entropic contributions are small and of opposite sign. We provide a detailed comparison of our simulation results with available experimental data.     

Thermochemistry of sulfide liquids. I. the system O-S-Fe at 1 bar

Recrystallized globules representing former immiscible sulfide liquids are found in a variety of igneous environments. Relatively little is known about the physical properties and thermochemistry of sulfide liquids, despite their importance in igneous systems. This study presents results of a series of experiments designed to calibrate a thermodynamic model for sulfide liquids in the system O-S-Fe at one atmosphere pressure. Sulfide liquids were equilibrated under controlled oxygen and sulfur fugacities at temperatures between 1100 and 1350 ° C in equilibrium with a silica mineral and a silicate melt. Experiments were quenched in a high-speed double-roller “splat” quencher in order to assure that measured compositions were as close to equilibrium liquid values as possible. Sulfide liquids are not stable in equilibrium with a silica-saturated silicate melt at log₁₀(f _O2) > FMQ-1 at 1250 °C and log₁₀(f _S2)=−3. Iron content of the sulfide changes little with variations in oxygen and sulfur fugacity at a given temperature. Consequently, oxygen and sulfur contents are inversely correlated in these liquids. Sulfur is present entirely as sulfide. Iron appears to be present in both its ferric and ferrous states. Data from this study were combined with data compiled from the literature to calibrate an asymmetric regular solution thermodynamic mixing model for O-S-Fe liquids. This model reproduces miscibility gaps and data from this study quite well, but exhibits minor but systematic errors at the O-Fe binary. The observed inverse correlation between sulfur and oxygen is reflected in the predicted free-energy surface by a sharp energy valley running along a line of constant Fe content. Received: 10 April 1996 / Accepted: 15 November 1996     

一种新型人工“流体包裹体”：融合二氧化硅毛细管技术

利用融合二氧化硅毛细管技术制作了纯H2O体系、纯CO2体系、H2O-NaCl体系和H2O-CO2体系的人工包裹体样品,并对样品进行了显微测温和激光拉曼光谱测试工作。实验结果显示毛细管样品中的流体成分具有代表性,而且常规的流体包裹体显微测温和显微激光拉曼光谱分析技术完全适于毛细管样品的测试。对样品的显微测温和拉曼光谱研究...     

Thermochemistry of the tremolite-edenite amphiboles using fluorine analogues,and applications to amphibole-plagioclase-quartz equilibria

Heats of mixing of synthetic C2/m fluortremolite-fluoredenite amphiboles measured at 985 K show a systematic deviation from ideal mixing consistent with a subregular solution model. The deviations from ideal mixing are interpreted in terms of Na ordering in the A-site and Na-Al interactions in edenite-poor compositions. Enthalpies of edenite substitution reactions in amphiboles and in SiO₂-NaAlO₂ glasses and framework silicates are comparable. Gibbs free energies of formation of fluortremolite and fluoredenite at 298K are -2,821.07±3.34 kcal mol^–1 and -2,889.59±2.40 kcal mol^–1 respectively. The former value is in good agreement with values calculated from both F-OH exchange experiments and from a natural fluortremolite-bearing metamorphic rock. Least-squares fitted sub-regular heat-of-mixing parameters are poorly constrained and unrealistically high, but estimated subregular mixing parameters consistent with 95% confidence interval uncertainties in the calorimetric data and with TEM constraints give activity-composition relations in good agreement with the A-site compositions of natural metamorphic and igneous hornblendes. These relations predict unmixing in edenite-rich compositions over a wide range of temperature, but lend no support to the existence of a hornblende-actinolite miscibility gap. Calibration of the reaction tremolite+ albite=edenite+4 quartz as a function ofP,T andX _ed ^amph indicates negativedP/dT slopes and a limited range of X _ed ^amph (0.3 to 0.5) in equilibrium with plagioclase and quartz over a wide range of pressure and temperature, consistent with metamorphic hornblende-plagioclase assemblages. The energetics of this reaction suggest, however, that amphibole-plagioclase disequilibrium may be common.     

Thermochemistry of phases in the system MgGa2O4-Mg2GeO4

The enthalpies of solution in molten 2PbO · B₂O₃ of phases synthesized at one atmosphere in the system MgGa₂O₄-Mg₂GeO₄ have been measured. A spinel solid solution, which is stable at 1400 °C from the MgGa₂O₄ end-member to 27 mole percent Mg₂GeO₄, shows endothermic heats of mixing of up to 10 kJ/mole at the solubility limit. The spinelloid phase, Mg₃Ga₂GeO₈, is energetically less stable than a mixture of terminal spinel solid solutions (0.73 MgGa₂O₄·0.27 Mg₂GeO₄(sp)+Mg₂GeO₄(sp)), by 3.63±3.64 kJ/mole. This indicates that the spinelloid is a high-entropy phase.The volume of the spinel solid solution, MgGa₂O₄-Mg₂GeO₄, shows a positive deviation from Vegard's Law. Modeling of the cation distribution in the solid solution indicates that this V is due to a change in the spinel type from inverse towards normal as the Mg₂GeO₄ content increases.     

Thermochemistry of (Fe2+, Mg)SiO3 orthopyroxene

Enthalpies of solution in eutectic (Li, Na)₂B₂O₄ melts at 1023 K were measured for five synthetic orthopyroxenes on the join MgSiO₃-FeSiO₃. The pyroxenes were synthesized at 1120°C and 20 kbar and thus were presumed to be highly disordered. The measurements indicate a small positive enthalpy of mixing, with W_H = 950 cal/MSiO₃.Enthalpy of solution measurements were made on a natural, well-ordered orthopyroxene near the composition En_52.5Fs_47.5 and on this material after heat-treatment at 1150°C and 20 kbar. Irreversible expansion of the unit-cell constants of the natural pyroxene after heat-treatment at various temperatures was used to characterize the degree of M-site disorder. The observed enthalpy of solution decrement of 0.85 kcal/MSiO₃ between the natural En_52.5 and the same material heated at 1150° corresponds to about half of the maximum possible disordering, or ΔX_Fe^M1? 0.25, which leads to a ΔH of 7.5 kcal/M₂Si₂O₆, for the exchange reaction: Fe(M2) + Mg(Ml) = Fe(Ml) + Mg(M2) if M-site interaction energy terms are ignored. This ΔH is larger than inferred from any of the analyses of site-occupancy data except that of Besancon (1981), who gave a very similar value. The measured ΔH of disorder and the W_H of mixing together indicate a large ΔH as great as 3.2 kcal for the reciprocal reaction: Fe₂Si₂O₆ + Mg₂Si₂O₆ = Fe(M2)Mg(M1)Si₂O₆ + Fe(M1)Mg(M2)Si₂O₆ as anticipated by Sack (1980).As a consequence of the inferred magnitudes of ΔHof the exchange and reciprocal reactions, departures from ideality of Gibbs energy of mixing of orthopyroxene are very small at 700°–1000°C. Activities of MgSiO₃ and FeSiO₃ may be replaced by their mol fractions at all temperatures in most petrologic calculations.