Gerya T.V., Perchuk L.L., Podlesskii K.K., and Kosyakova N.A. Thermodynamic data base for the system: MgO-FeO-CaO-Al₂O₃-SiO₂.

key words [date base thermodynamic constant mineral ]

Standard thermodynamic properties of individual substances and mixing functions of solid solutions in the system MgO-FeO-CaO-Al₂O₃-SiO₂ were brought

into consistence by the non-linear least-squares method. We used published data on phase equilibria and measurements of physical properties of minerals. Cyclic data treatment was performed with systematic control over the reproducibility of experimental P and T values and compositions of equilibrated phases. Such a procedure made it possible to describe a great body of experimental data (more than 5000 data points) within the limits of experimental errors.

The algorithm is based on the GibbsÆs free-energy equation, which describes a solid (mineral) as a system of quantum oscillators tied by forces of potential interaction. Each oscillator was assumed to have the infinite number of energy levels, according to the Bose-Einstein statistics. By analogy with the Lennard-Jones potential, the repulsive force between the oscillators was assumed to be proportional to the 12^th degree of the average distance between them. The gravitational forces are characterized by average inner pressure, which is opposite in sign to the repulsive force. The optimal form of the equation includes nine refinable parameters:

G(cal/mol)=H_o-T × S_o+K₁ × RTln[1-exp(-G₁/RT)]+K₂ × RTln[1-exp(-H₂/RT)]+A × [(P₁+P)^0.8-(P1+1)^0.8], (1)

where G₁=H₁+A₁ × [(P₁+P)^0.8-(P₁+1)^0.8], H₀ and S₀ are, respectively, enthalpy of formation and configuration entropy of a given mineral at T = 0 K and P = 1 bar; K₁ and K₂ are the numbers of oscillators in the mineral molecule multiplied by the number of degrees of freedom of one oscillator for low- and high-energy transitions, respectively; H₁ and H₂ are differences in enthalpy of adjacent energy levels for low- and high-energy transitions, respectively; A₁ and A₂ are respectively average parameter of repulsive potential between the oscillators and the change of this parameter for low-energy transitions; P₁ is average inner pressure, which characterizes the gravitation between the oscillators; T is temperature (K); P is pressure (bar); R = 1.987 cal/mol/K - universal gas constant. Equation (1) properly describes physical properties of substances and provides good extrapolation. Table 1 presents calculated values of the constants for Equation (1).

The following models for molar mixing energies of solid solutions were accepted (G_m at the parameters of the modeling W = W_H-TW_S+(P-1) W_V. cal/mol).

X_OK=Al/2/(Ca+Mg+Fe+Al/2); X_Fs=Fe/(Ca+Mg+Fe+Al/2);

X_Wol =Ca/(Ca+Mg+Fe+Al/2).

where X_Prp=Mg/(Mg+Fe+Ca); X_Alm=Fe/(Mg+Fe+Ca); X_Grs=Ca/(Mg+Fe+Ca).

where X_Ca=2X_CWo; X_Al=2X_CK; X_Mg=X_CEn/(X_CEn+X_CFs); X_CEn=Mg/(Ca+Mg+Fe+Al/2);

X_CK=Al/2/(Ca+Mg+Fe+Al/2); X_CFs=Fe/(Ca+Mg+Fe+Al/2);

X_CWo=Ca/(Ca+Mg+Fe+Al/2).

Calculated mixing parameters for the above-listed solid solution models are given in Table 2.

Conventional symbols: Qzb - quartz, Qza - quartz, Coe - coesite, Crn - corundum, Sil - sillimanite, Ky - kyanite, An - anorthite, En - enstatite, OK - orthopyroxene AlAlO₃, Fs - ferrosillite, Wol - CaSiO₃ with enstatite structure, Prp - pyrope, Alm - almandine, Grs - grossular, Crm - magnesian cordierite, Crf - ferrous cordierite, Spm - spinel, Her - hercynite, Fo - forsterite, Fa - fayalite, SS - siliceous sapphirine, SA - aluminous sapphirine, CEn - enstatite with diopside structure, CFs - ferrosillite with diopside structure, CWo - wollastonite with Ca-clinopyroxene structure, CK - clinopyroxene AlAlO₃.

OK, Wol, CEn, CK, CK, CFs, CWo exist only as conventional end members of pyroxene solid solutions.

Table 2. Calculated mixing parameters for solid solutions

Chashchukhin I.S., Votyakov S.L., and Uimin S.G. Oxithermobarometry of the Ural chromite-bearing ultramafites.

key words [chrom-spinellid oxithermobarometry ultramatites]

As evidenced by the nuclear gamma-resonance and microprobe data on 25 chrom-spinellid samples from ultramafic rocks of the Urals and various literature data, the deviation from stoichiometric composition is typical of this mineral. The degree of this deviation, characterized by the Me²⁺/Me³⁺ ratio, is controlled by the chemical composition of the mineral and the conditions of formation and subsequent alteration of the ultramafites, but does not depend on formational affinity of the rocks. The deviation from stoichiometric composition and the fraction of minor elements incorporated in the mineral structure (especially titanium) have significant effect on the temperature estimates for the olivine-chrom-spinellid equilibrium. In this connection the well-known geothermometers (Jackson-Reder, Fabri, Ono, and O'Neil-Bolhauz) were corrected to bring the calculated temperature values into consistence with geologcal and pyroxene geothermometry data.

The oxidation state of rocks of the largest Ural ultramafic massifs - Kempirsai, Nurali, Yuzhnokrakinsk (South Urals), Voikaro-Syn'inskii (Polar Urals), and Nizhnetagil'skii (Middle Urals) - was studied. Oxygen fugacities were calculated by Nell-Wood and Bolhauz-Berry-Green's oxybarometers. When the true (Mossbauer) oxidation state of iron in chrom-spinellid is taken into account, the difference between the fO₂ values offered by these oxybarome -

ters is constant. The secondary standards were used to determine correctly the Fe³⁺ content in spinellid. A total of 378 samples were analyzed.

The oxygen fugacity was found to vary widely relative to FMQ buffer (from -2.0 to +3.0 log units). This fact can be explained by superposition of two processes: magmatic depletion of the upper mantle at decreasing oxygen fugacity and subsequent metasomatism at increasing oxygen fugacity. From the present studies and literature data, four states of oxidation of the fold-zone ultramafites were distinguished:

(a) asthenosphere (dlogfO₂^FMQ<-1.0);
(b) oceanic lithosphere (-1.0<dlogfO₂^FMQ<0);
(c) transition from the oceanic to continental lithosphere (0 <dlogfO₂^FMQ<+2.0), and
(d) continental lithosphere (flogfO₂ > +2.0).

Evidently, the oxygen fugacity in ultramafites is indicative of the preservation of the original asthenospheric oxidation state of the rocks and the degree of subsequent lithospheric transformations rather than the lateral heterogeneity of the mantle. Accretion played a significant part in the formation of Ural ultramafic massifs, as evidenced by the occurrence of the rock blocks characterized by different oxygen fugacities within a massif. The oxygen behavior was shown to differ in the formation of high-chromium and high-alumina chromite ores as a result of changes in tectonic regime. Consequently, the ore-forming fluids also had different compositions: the first low-oxygen fluid flow (below FMQ buffer), with stable graphite and high methane and CO mole fractions, and the second high-oxygen fluid flow (above FMQ buffer), with graphite unstable and high carbon dioxide mole fraction.

Poltavets Yu.A. Thermodynamic analysis of stability of magnetite-series spinelides under conditions of abyssal petrogenesis.

key words [magnetite spinel thermodynamic analysis]

The concept of zonal structure of the earthÆs crust and upper mantle is now a common knowledge. Structural and geochemical characteristics of main rock-forming minerals, including oxides, are indicators of depth (pressure). Unfortunately, data on compositions of these minerals are of little practical use because of lack of experimental and thermodynamic studies of these minerals at high temperatures and pressures. Thus, the problem of thermodynamic stability of magnetite-series spinelides at temperatures and pressures corresponding to the lower horizons of the earthÆs crust and upper mantle still remains slightly understood and poorly reported in literature.

The diagram in figure was drawn on the basis of thermodynamic and statistic analyses of published experimental data on compositions of Fe-oxides and Fe-silicates and shows the stability fields of the end members of magnetite-series spinellid solid solutions. Compared to the scheme of depth facies for Ti-rich rocks, which is used by some authors (Sobolev et al., 1975), the proposed diagram is more detailed and provides distinguishing the thermodynamic stability fields of Fe-oxides (magnetite-series spinellides) on the basis of their compositions. This diagram also shows the relationship between pyrope and almandine end members in the high-pressure garnets calculated by regression analysis.

From the diagram, a vertical zoning is expected for the magnetite-series spinellides within the depth range corresponding to the lower crust and upper mantle. This zoning manifests itself in decreasing trivalent ions (Fe³⁺, Al³⁺, Cr³⁺) and Mg²⁺ and increasing titanium content of the Fe-oxides. Statistic data processing confirms this assumption: Ti⁴⁺ and Fe²⁺ show positive correlation with pressure (depth) (0.53 and 0.88 respectively), while Mg²⁺, Fe³⁺, and Al³⁺ show negative correlation (-0.64, -0.59, and -0.32 respectively). Thus, the degree of reduction of Fe-oxides increases with depth of magnetite-series spinellid formation (correlation factor between Fe³⁺/Fe and pressure is equal to -0.68). The following zonal series is proposed: MgFe₂O₄-(Mg,Fe)(Al,Cr)₂O₄-FeAl₂O₄-(FeCr₂O₄+Fe₂TiO₄) - FeTiO₃.

The correlation of facies and subfacies after Sobolev et al. (the first two columns) with the terms accepted in this study is given left of the diagram: C^A - diamond, C^G - graphite, Q^K - coesite, Q - quartz, Ru - rutile, Il - ilmenite, Usp - ulvospinel, Sp^Ti,Cr,Al,Mg - Fe₂TiO₄, FeCr₂O₄, Fe(Mg)Al₂O₄ respectively, Pl - plagioclase, Gr^{<1, 1-4,>4} - garnets with pyrope/almandine ratio <1, within 1-4, and >4 respectively, Px^Fe,Mg-Fe- and Mg-rich pyroxenes respectively, Ol - olivine.

Figure. Scheme of depth facies and stability fields of magnetite-series spinellides.

(1-3) granite layer (o = 2.75 g/cm³), basalt layer (o = 2.85 g/cm³), and mantle (o = 3.3 g/cm³); (4) solidus field for magmas of various composition (from tholeiite to alkaline); (5) oceanic geotherm (Ringwood, 1981); (6) contours of equal contents of pyrope (Pyr) and almandine (Alm) end members in high-pressure garnets; (7) metamorphic facies after V.S. Sobolev et al (Abyssal xenoliths ..., 1975), etc. From the top to the bottom: spinel-pyroxene (ilmenite-spinel), grospidite (ilmenite-rutile-pyrope), and coesite facies.

References:

1. Abyssal xenoliths and upper mantle (1975) Novosibirsk, Nauka, p. 271.
2. Dobretsov N.A. Introduction to global petrology. (1980) Novosibirsk, Nauka, p; 200.
3. Ringwood A.E. (1981) Composition and petrology of the earth's mantle. Moscow, Nauka, p. 584.