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1.
The dependence on the composition of the thermodynamic stability of an illite can be treated in terms of a regular solution site-mixing model. Four end-member micas (muscovite, pyrophyllite, phlogopite, and annite) were mixed to simulate an illite in this study. In the model, random mixing of cations was assumed over each given class of cation sites. Mixing over cation sites between different classes of cation sites was not allowed. The resulting free energy and chemical potential equations contain four site interaction parameters: three for octahedral site interactions and one for interlayer and tetrahedral site interactions. These parameters cannot presently be evaluated because of a lack of experimental data on Fe3+-free illites. The model does imply that the octahedral site interaction parameters must be significantly more positive than the interlayer and tetrahedral site interaction parameter to account for the dominant dioctahedral nature of most natural illites. This constraint is necessary to balance out the increase in stability due to the configurational entropy of an illite having a major trioctahedral component.The model can be extended to cover a wider range of illite compositions by the inclusion of an end-member mica containing Fe3+ ions in the octahedral sites. At present the thermodynamic properties of such an end-member are unknown.  相似文献   

2.
A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si2O6)-jadeite (NaAlSi2O6) and diopside-CaTs (CaAl2SiO6). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other. The calculations show that the random model, in which the configurational entropy is calculated as if atoms on each crystallographic site mix randomly, is appropriate as a first approximation. The excess entropy relative to the random model behaves regularly, is always negative, and becomes more negative as temperature decreases or the ordering energies increase. The excess entropy relative to the random model can be modeled reasonably well with a simple power series, or Margules-type, formulation. In contrast, the excess entropy relative to a molecular model, in which the ideal activity is assumed to be equal to some mole fraction, is irregular, can be positive or negative, and even changes in sign with variations in temperature and composition. The configurational enthalpy is positive at high temperatures, and becomes negative with decreasing temperature or increasing ordering energy. The mixing enthalpy can have non-configurational contributions, in addition to the effective short-range configurational contributions considered explicitly. The pair approximation predicts an ordering transition from C2/c to P21/n for CaTs and diopside-CaTs solutions at moderate to low temperatures, respectively. A field where C2/c orders to C2 is also found. A higher order approximation, different relative ordering energies, or quantitative consideration of strain contributions is required to account for the C2/c to P2/n transition in omphacites. There is no justification for molecular models, in which the configurational entropy is calculated as if endmember “molecules” were mixing in the crystal, in either concentrated or dilute solutions. Molecular models do not represent limiting ordered states for coupled solid solutions.  相似文献   

3.
The electrostatic lattice energies of expanded and unexpanded micas are calculated starting from a “generic” structure the ionic charges of which are varied. The mode of expansion is to move the layers apart perpendicular to (001), the K+ ions remaining midway between the layers. The energy required for expansion is a quadratic function of the layer charge. It is larger when the layer charge is in the octahedral sites (K x Al2?x Mg x Si4O10(OH)2) than when it is in the tetrahedral sites (K x Mg3Si4?x Al x O10(OH)2). Fluormicas have a slightly larger expansion energy than OH-micas. With the tetrahedral layer charge, dioctahedral micas have a slightly larger expansion energy than trioctahedral micas. This mode of expansion is less favourable than the mode usually adopted, viz. an expansion whereby the K ions divide themselves between the layers. The energy difference increases with the separation distance and is about 60 kJ mol?1 at 2.5 Å expansion. An intercalated water layer would be necessary to stabilize the K ions in positions midway between the layers.  相似文献   

4.
Enthalpies of solution in molten 2PbO · B2O3 at 985 K are reported for series of glasses xCa0.5AlO2-(1?x)SiO2 (O ≤ x ≤ 0.99) and xNaAlO2-(1?x)SiO2 (0 ≤ x ≤ 0.56). The data are compared to values for the corresponding crystalline aluminosilicates and to preliminary data for systems containing KAlO2 and Mg0.5AlO2. The enthalpies of mixing of glasses become more exothermic with increasing basicity of the mono- or divalent oxide. The tendency toward immiscibility on the silica-rich side, indicated by the shape of the heat of mixing curve between x = 0 and x = 0.4, is pronounced in the calcium aluminate system, but not in the sodium aluminate system. The shape of the heat of mixing curve, which is roughly symmetrical about x = 0.5, can be rationalized in terms of glass structure by considering essentially random substitution of Si and Al on a continuous three dimensional tetrahedral framework, with stabilization arising from electrostatic interactions between aluminum and the nonframework cation balancing the destabilizing effects arising from perturbation of the aluminosilicate framework by the nonframework cation. These trends are consistent with the variation of physical properties of aluminosilicate melts.  相似文献   

5.
Activity-composition relations are derived for ideal substitutional solid solutions through the Helmholtz free energy expressed in terms of the partition function. For solutions of the type (A, B)uZw involving mixing on one type of atom site, ideal activities of end-member components are expressed by: aAuZw = (XAuZw)u, and aBuZw = (XBuZw)u. With multi-site mixing excluding charge balance restrictions, as in (A, B)αu (C, D)βvZw, the ideal activity of an end-member component such as AuCvZw is calculated as: aAuCvZw = (XαA)u (Xβc)v. These expressions support the ‘ionic solid solution model for the activities of components in ideal solid solutions. Ideal solution models for coupled substitutions involving charge balance are considered using plagioclase as an example. Ideal activity expressions for solid solution of albite and anorthite are derived with and without adherence to the Al avoidance principle. Mixing models involving local electrostatic balance are contrasted with those involving independent, random mixing of Na-Ca and Al-Si. Of several possible ideal solution models for plagioclase, only that specifying complete Al-Si ordering and local electrostatic neutrality yields activities conforming to Raoult's Law.  相似文献   

6.
Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G ex excess free energy of mixing - H ex excess enthalpy of mixing - S ex total excess entropy of mixing - S ex c configurational excess entropy of mixing - W ij interaction energy parameter between speciesi andj - X i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi2O6) - En enstatite (Mg2Si2O6) - Py pyrope (MgAl2/3SiO4) - Gr grossular (CaAl2/3SiO4) - CaTs Ca-Tschermak (CaAl2SiO6) - Ab albite (NaAlSi3O8) - An anorthite (CaAl2Si2O8)  相似文献   

7.
The surface layer of aquatic sediments is a zone characterized by both porosity gradients and intensive mixing. In the standard approach, porosity gradients are ignored when estimating mixing intensity. Here, model formulations with both constant and varying porosity are contrasted to estimate mixing coefficients Db from tracer depth profiles. Complementing the well-known exponential solution of the constant-porosity model, we present a general solution to the variable-porosity model in terms of hypergeometric functions. When using these models in a forward way, the tracer activities predicted by the variable-porosity model are higher than those generated by the constant-porosity model. Similarly, when inverse modelling, Db values estimated by the variable-porosity model are systematically higher than those derived from the constant-porosity model. Still, differences in Db values remain relatively small. When applying both mixing models to excess 210Pb data profiles from slope sediments, a maximal difference of 30% is obtained between Db values, the average deviation being 16%. A systematic exploration of parameter space predicts a maximal underestimation of 60% when deriving Db values from the constant-porosity mixing model. Given the uncertainty imposed by other model assumptions underlying the diffusive mixing model, the influence of porosity gradients on Db values must be classified as rather modest. Hence, the current mixing coefficient database is not biased by the constant porosity approximation.  相似文献   

8.
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9.
Perovskite-type compounds in the series tausonite-loparite, (Sr1?2 x Na x La x )TiO3, were synthesized by solid-state reaction (final heating at 1200–1300?°C), and studied using “conventional” and synchrotron X-ray powder diffractometry. The structures of intermediate compositions were determined using the Rietveld profile refinement method. In the compositional range 0?≤x?≤ 0.1, the series comprises perovskites characterized by an undistorted cubic structure (space group Pm3¯m, a?≈ 3.905–3.902?Å, Z?=?1). Intermediate compounds in the range 0.15?≤?x?≤?0.35 crystallize with tetragonal symmetry (I4/mcm, a?≈? , c?≈? , Z?=?4) derived from the cubic aristotype by antiphase rotation of the TiO6 octahedra about a fourfold axis. The angle of rotation estimated from the positional parameters of oxygen atoms ranges from 2.5(7)° to 5.5(4)°. The cubic-to-tetragonal transition arises from substitution of Sr2+ by the comparatively smaller Na1+ and La3+ cations. A further transition from the tetragonal to rhombohedral symmetry (R3¯c, a?≈? , c?≈?2 , Z?=?6) occurs between x?=?0.35 and 0.40, and apparently does not involve formation of perovskite with an intermediate two-tilt structure (Imma). The rhombohedral structure is characterized by a multicomponent octahedral tilt about a threefold axis ranging in magnitude from 6.5(2)° to 7.7(2)°. In the series (Sr1?2 x Na x La x )TiO3, the unit-cell dimensions decrease, and the degree of structural distortion increases with x.  相似文献   

10.
Experimental data for the standard Gibbs free energies of formation from the elements of a wide variety of metal sulfides and oxides, spinels, olivines and pyroxenes at 25°C and 1 bar define linear correlations, within about ±900 cal·mole?1, with the corresponding conventional standard partial molal Gibbs free energies of formation of the aqueous M2+ cations of the form ΔGf,mDZ0 = amDZΔGfM2+0+bMDZ where aMaZ and bMaZ are empirically determined constants characteristic of the structure MnZ. The only exceptions to correlations of this type are compounds of the heavy alkaline earths Ca, Sr and Ba, which appear to follow correlations with cation radius instead. The linear free energy correlations enable prediction of standard Gibbs free energies of formation of compositional end-members of a particular structure MnZ provided that aMaZ and bMaZ are known accurately. When only the free energy of the Mg end-member is known, the standard Gibbs free energy of formation at 25°C and 1 bar of the Fe endmember, and hence aMaZ and bMaZ Can be predicted from the temperature independence of aMaZaotivine and estimated entropies and heat capacities for the Fe end-member. Using this approach, the free energies of ferrosilite, hedenbergite and annite at 25°C and 1 bar were predicted to within ±1000 cal·mole?1 of the helgesonet al. (1978) values. Free energies of formation of talc (M3Si4O10(OH)2), clinchlore (M5Al2Si3O10(OH)8), and tremolite (Ca2M5(Si4O11)2(OH)2)-type compounds where M is Mg, Mn, Zn, Fe, Co, or Ni were then predicted at 25°C and 1 bar.Calculation of the equilibrium distribution of Mg, Zn and Sr between galena and hydrothermal solution, and Zn, Mg, Fe and Mn between chlorite and hydrothermal solution demonstrates: (1) that the Sr contents of low temperature galenas (e.g. Mississippi Valley-type) should be negligible (reported analyses of Sr content and Sr isotopic composition of such galenas are probably attributable to fluid inclusions or carbonate inclusions); and (2), that the Zn contents of hydrothermal chlorites in a model of the midoceanic ridge hydrothermal systems are sensitive to temperature, to complexing in the aqueous phase, and to the overall Fe/Mg ratio of the chlorite.  相似文献   

11.
An experimental study using piston-cylinder, Bridgman anvil and diamond anvil cell techniques was undertaken to study the effect of pressure on the composition of Fe x O in equilibrium with Fe. At constant temperature the value of x first increases and then decreases with increasing pressure. The rate of change of x is a function of temperature. We have theoretically calculated the variation of the composition of wüstite with pressure and temperature. The initial increase of x with pressure for P<10 GPa occurs because the partial molar volume of FeO in Fe x O is smaller than the molar volume of Fe, favouring an increase in stoichiometry of Fe x O. To reproduce the experimentally observed decrease in x above 10GPA, the bulk modulus of Fe x O must vary strongly with x for x?0.96, causing a rapid increase in the partial molar volume of Fe in Fe x O. Continuation of a strong sensitivity of K to x in Fe x O for x?0.96, however, leads to absurdly low molar volumes of Fe x O at high pressure and no equilibrium between Fe and Fe x O exists. Observations therefore require a reduced sensitivity of K with x for x<0.96, achieved by a negligible variation of K 0 with x for x<0.96, or a strong variation of dK/dP with x, or perhaps both.  相似文献   

12.
Thermodynamic mixing properties and subsolidus phase relations of the rhombohedral carbonate system, (1 − x) · CaCO3 − x · MgCO3, were modelled in the temperature range of 623-2023 K with static structure energy calculations based on well-parameterised empirical interatomic potentials. Relaxed static structure energies of a large set of randomly varied structures in a 4 × 4 × 1 supercell of calcite (a = 19.952 Å, c = 17.061 Å) were calculated with the General Utility Lattice Program (GULP). These energies were cluster expanded in a basis set of 12 pair-wise effective interactions. Temperature-dependent enthalpies of mixing were calculated by the Monte Carlo method. Free energies of mixing were obtained by thermodynamic integration of the Monte Carlo results. The calculated phase diagram is in good agreement with experimental phase boundaries.  相似文献   

13.
The paper considers the evolution of the supernova envelopes produced by Population III stars with masses ofM * ?? 25?C200M ?? located in non-rotating protogalaxies with masses of M ?? 107 M ?? at redshifts z = 12, with dark-matter density profiles in the form of modified isothermal spheres. The supernova explosion occurs in the ionization zone formed by a single parent star. The properties of the distribution of heavy elements (metals) produced by the parent star are investigated, as well as the efficiency with which they are mixed with the primordial gas in the supernova envelope. In supernovae with high energies (E ? 5 × 1052 erg), an appreciable fraction of the gas can be ejected from the protogalaxy, but nearly all the heavy elements remain in the protogalaxy. In explosions with lower energies (E ? 3 × 1052 erg), essentially no gas and heavy elements are lost from the protogalaxy: during the first one to threemillion years, the gas and heavy elements are actively carried from the central region of the protogalaxy (r ?? 0.1r v , where r v is the virial radius of the protogalaxy), but an appreciable fraction of the mass of metals subsequently returns when the hot cavity cools and the envelope collapses. Supernovae with high energies (E ? 5 × 1052 erg) are characterized by a very low efficiency of mixing of metals; their heavy elements are located in the small volume occupied by the disrupted envelope (in a volume comparable with that of the entire envelope), with most of the metals remaining inside the hot, rarified cavity of the envelope. At the same time, the efficiency of mixing of heavy elements in less energetic supernovae (E ? 3 × 1052 erg) is appreciably higher. This comes about due to the disruption of the hot cavity during the collapse of the supernova envelope. However, even in this case, a clear spatial separation of regions enriched and not enriched in metals is visible. During the collapse of the supernova envelope, the metallicity of the gas is appreciably higher in the central region ([Z] ?? ?1 to 0) than at the periphery ([Z] ?? ?2 to ?4) of the protogalaxy; most of the enriched gas has metallicities [Z] ?? ?3.5 to ?2.5. The masses of enriched fragments of the supernova envelope remain appreciably lower than the Jeans mass, except in regions at the center of the protogalaxy upon which the surrounding enriched gas is efficiently accreted. Consequently, the birth of stars with metallicities close to those characteristic of present-day Galactic stars is very probable in the central region of the protogalaxy.  相似文献   

14.
With the configurational entropy theory of relaxation processes of Adam and Gibbs (1965), one predicts that the viscosity depends on temperature according to log η = Ae + BeTSconf, where Sconf is the configurational entropy of the liquid. Thermochemical calculations of Sconf performed for some mineral compositions show the importance of non-configurational contributions to the entropy differences between amorphous and crystalline phases. Except for the case of SiO2, the available thermodynamic data indicate that the above equation for viscosity accounts quantitatively for the experimentally determined temperature dependence of the viscosity of silicate melts. The Adam and Gibbs theory also provides a simple rationale for the non linear variation of the logarithmic viscosity with composition in mixed alkali silicate liquids at low temperatures, the minimum of viscosity resulting from the contribution of the entropy of mixing to Sconf.  相似文献   

15.
The pyroxene saturation surface in the system diopside-albite-anorthite may be calculated to ±10°C from thermochemical data over most of its composition range. The thermochemical data used are the experimentally determined enthalpies of mixing of the ternary liquids and the enthalpy of fusion of diopside. These are combined with a mixing model for the configurational entropy in the melt and the activity of CaMgSi2O6 in the clinopyroxene, which is less than unity due to departures from CaMgSi2O6 stoichiometry. The ‘two-lattice’ melt model appears to work satisfactorily throughout the pyroxene primary phase field but probably needs modification at more anorthite-rich compositions.  相似文献   

16.
Two stages of illite mineralization are recognized in the hydrothermal alteration zone of the Hoam granite. These illites are formed as a result of pervasive alteration by re-equilibration with high water/rock in a brittle environment below <2 km; the mineralization timing is middle Oligocene (26–27 Ma), coinciding with the timing of crustal deformation related to the opening of the East Sea (Sea of Japan). The mineralogical and geochemical characteristics of the clearly distinguished illites at each site indicate that they were mineralized from different fluid injections in distinct geological environments. Illites at the site-1 alteration zone are characterized by high-K content [K0.84 per O10(OH)2], 2M1 polytype of 99 %, hexagonal plate shape, and coexistence with pyrite. These observations indicate that the illites were formed in a slow cooling system (>250 °C), high fS2, and a relatively acidic environment. The pseudomorphic replacement combined with matrix-filling texture indicates that the illites at the site-1 alteration zone recorded the changes in fluid conditions from low to high water-rock ratio. In contrast, the illites at the site-2 alteration zone show the coexistence of polytypes (2M1, 1M, and 1Md), high-K illites [(K0.83 per O10(OH)2]/low-K illites [K0.63 per O10(OH)2], platy/hairy shapes, and presence of magnetite. Furthermore, this alteration zone no longer exhibits primary textures because of pervasive alteration induced by the dissolution-precipitation process. These results indicate that they were formed in a rapid cooling system and were continuously under conditions of high water-rock ratio, as well as in a less acidic and fS2 environment than that observed at the site-1 alteration zone. The behavior of trace elements for each illite primarily depends on the constituents of the hydrothermal fluid, which reflect different degrees of fluid evolution. The enrichment of high field strength elements (Nb and Ta), large ion lithophile elements (B, Be, and Cs), rare earth elements, and actinide elements (U and Th) in illite at the site-2 alteration zone shows that these elements formed by a more evolved fluid than that of the illite at the site-1 alteration zone. In addition, negative Ce anomalies at the site-2 alteration zone indicate that these crystallized in a reducing environment. Considering the mineralogical and geochemical properties of illites at the site-1 and site-2 alteration zones, the illite mineralization in the Hoam granite was likely generated by at least two episodes of hydrothermal illite mineralization, which originated from episodic injections of fluids, rather than continuously evolved fluids.  相似文献   

17.
The local structural response of Ca/Mg substitution and the energetic effects associated with dodecahedral ordering in the pyrope-grossular garnet solid solution are derived from a combination of static lattice energy calculations and Monte Carlo simulations. We start with a thorough analysis of the goodness of the empirical potential models used for the modelling of aluminosilicate garnets. The degree of polyhedral distortion was found to be a sensitive indicator for the quality of the model and, by comparison with experimental data, was used to select the best of several available empirical potentials. The Ca/Mg substitution on the dodecahedral site in garnet was found to produce strong local distortions in the surrounding tetrahedral and octahedral polyhedra. This arises from the absence of rigid unit modes (RUMS) in the garnet structure, because local rotations of otherwise rigid SiO4 tetrahedra and AlO6 octahedra cannot occur in order to accommodate different-sized divalent cations in the dodecahedral sites. Strain effects, therefore, mainly govern the dodecahedral substitution, and the corresponding strain field around a dodecahedral site has a minimum radius of 5?Å. Pyrope-grossular solid solution compositions were modelled using a supercell approach. For several garnet compositions many different configurations representing individual disordered arrangements were relaxed. The resulting energies were analyzed in terms of different-neighbour interactions to determine the parameters of a model Hamiltonian. The corresponding interaction energies were found to be virtually independent of composition. Surprisingly, the nearest-neighbour interaction between edge-sharing dodecahedra is of no particular significance in the garnets. Instead, the strongest interaction is only via the third-nearest neighbours, i.e. dodecahedra that are edge-shared to a common SiO4 tetrahedron. This cannot lead to dodecahedral long-range order in garnets, but can produce significant amounts of short-range order. Monte Carlo simulations were performed on several compositions to determine the macroscopic effects such as NMR-based cluster occupancy, ordering energy and configurational entropy of the short-range ordering process. As expected, the samples tend to random disorder at high temperatures, and at low temperatures it is compositions nearer Py50Gr50 that depart most strongly from random mixing. For example, a maximum reduction of 3.5?J?mol?1?K?1 is predicted for Py75Gr25 and ～10?J?mol?1?K?1 for Py50Gr50. A comparison of NMR cluster occupancy with experimental 29Si MAS NMR resonance intensity is partly successful. However, the changes in NMR cluster occupancy are relatively low (～5%) compared to changes in configurational entropy (～30%), implying that it might be difficult to estimate exact entropy data from 29Si MAS NMR line intensities.  相似文献   

18.
A different approach to investigate the origin of fluids, temperature conditions, age of hydrothermal activity of mineralization in the Biga Peninsula, (Koru, Tesbihdere and Kumarlar) employed mineralogical (illite Kübler Index, b cell dimension, polytype) and geochemical (major, trace/REE, O–H stable isotope and Rb/Sr dating) methods. The Kübler Index (KI) values of illites indicate different temperature conditions, such as low temperature (high-grade diagenesis) for Koru deposit, and high temperature (anchizone) for the Tesbihdere and Kumarlar deposits. The textural, mineralogical and geochemical data from illites show that these have potential for estimating the age of hydrothermal activity and fluid characteristics. Both mineralogical (high grade diagenetic to anchizonal KI, 1M polytype, low d060 values) and geochemical (similar major and trace element composition to host-rocks, low octahedral Mg + Fe contents, oxygen and hydrogen isotope composition) data are compatible with commonly known hydrothermal illites. Stable isotope data of illites are well matched to similar data from fluid inclusions, which indicate mainly magmatic fluids. The Rb/Sr age (22.4 ± 2.3 Ma: latest Oligocene and lowest Miocene) of the illites coincides with plutonic intrusions that are the main instigators of hydrothermal activities related to the extensional tectonic regime in the Biga Peninsula. The mineralogical and geochemical data of illites have some important advantages with respect to the use of fluid inclusions in determining δD of hydrothermal fluids thereby leading to better understanding ore-forming hydrothermal conditions.  相似文献   

19.
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 SrxCa1−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.  相似文献   

20.
Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO2 system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO3-MgSiO3-FeSiO3 system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G f 0 Gibbs free energy of formation from the elements at 1 bar and temperature - G Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant  相似文献   

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