K. V. Chudnenko

Extrapolation of thermodynamic functions in calculation of phase equilibria by the Gibbs energy minimization method

A separate description of polymorphs and glassy, liquid, and gaseous states makes it possible, using the isobaric-isothermal potential minimization approach, to describe both the phase transformations of an individual substance and its behavior in complex systems, which is required for the representation of metal and salt systems that have melting points lower than the melting points of the pure components. The suggested methods of extrapolation of the thermodynamic functions of an individual substance, performed assuming that of the phase transition heat is constant and that the heat capacity beyond the equilibrium temperature range is equal to the heat capacity of the preceding or subsequent (by temperature) phase state, enable to avoid thermodynamic paradoxes in all cases and reliably describe the composition of complex systems in a wide P,T range of their existence with allowance for the existence of solid phases, melts, and gases in equilibrium.

Method of approximation of dependence of isobaric heat capacity on temperature

A method of approximating temperature dependence of heat capacity has been developed on the basis of a power polynomial in variables with different exponents in combination with the Nelder-Mead simplex method. For especially complicated dependences, the method makes it possible to match polynomials at junction points with infinitesimal deviation. The method provides high reproducibility and correct interpolation of empirical and semiempirical data.

Experience of Modeling the Garnet + Orthopyroxene + Spinel + Plagioclase Reaction by the Method of Thermodynamic Potential Minimization

Relative to the method of phase correspondence, physicochemical modeling of mineral associations based on the method of thermodynamic potential minimization and consideration of solid solutions offers new opportunities [1]. Although the thermodynamic database of end members and the models of mineral solid solutions are not sufficiently accurate, the high potential of the method based on minimization for the solution of several petrological issues is evident. The present paper shows an implication of this method for thermodynamic analysis of the garnet reaction structure, for which oxygen pressure and fugacity cannot be estimated by conventional thermobarometry. Solid inclusions in alkaline basalts of the Konfetka paleovolcano in Primorye [2] contain fragments of fractured garnet crystals replaced by orthopyroxene‐ spinel‐plagioclase symplectite along fractures and the periphery (figure). Bright orange stilpnomelane is developed locally in the reaction rim. The symplectite has a specific composition (Table 1). Orthopyroxene shows appreciable variations in the Al 2 O 3 content: a lower concentration (2.9‐3.4 wt %) at the contact with garnet than at the contact with spinel and plagioclase (9.5‐10.3 wt %). Plagioclase is also heterogeneous. Its composition varies from An 84 to An 60 . At the same time, the Fe mole fraction of orthopyroxene and spinel is nearly constant. However, the spinel composition is characterized by a lower degree of oxidation ( Fe 3+ / Σ Fe = 8.1‐11.8 at %, Table 1). The compositional heterogeneity of minerals emphasizes the nonequilibrium state of the symplectite rim, at least, with respect to the Al 2 O 3 potential. Elucidation of PT constraints of the garnet replacement by the orthopyroxene‐spinel‐plagioclase symplectite can provide insight into the genesis of garnet inclusions. The equilibrium temperature of the orthopyroxene‐spinel system can be estimated approximately by the Liermann‐Ganguly method [3]:

Specifics of Representation of Thermodynamic Functions in the Method of Thermodynamic Potential Minimization

The type of physicochemical model dictates the choice of a minimized thermodynamic potential that provides the most adequate description of specific features of a natural or technological process. In the developed approach, the Gibbs energy was selected as the basis potential, and other thermodynamic potentials were considered as functions of G(T, P) and thermodynamic parameters with inclusion of independent factors of state. The presented thermodynamic functions of individual substances can be used in minimization of all basic thermodynamic potentials regardless of the conditions of existence of modeled systems.

Monitoring and physical-chemical modeling of conditions of natural surface and underground waters forming in the Kola North

Processes of surface and underground water forming in the Khibiny massif have been studied using a physical-chemical model of the “water–rock–atmosphere–organic substance” system. The obtained model solutions are indicative of the fact that formation of surface and underground water of the Khibiny massif takes place on the whole in the framework of the considered system without attracting a hypothetical outside source of pollutants. The results are of practical and methodological importance for assessment of prediction of the man-induced impact on water systems in conditions of Subarctic.

Oxidation potential and the composition of metamorphic fluid as a solution to the inverse problem of convex programming

Using the Selektor-C software program package, oxidation potential and the composition of metamorphogenic fluid were determined for mineral assemblages from nine samples of granulite-grade metamorphic rocks by solving the inverse problems of convex programming. The calculated and real mineral assemblages are in good agreement with respect to the composition and association of minerals, which is compelling evidence for the attainment of chemical equilibrium (minimum of Gibbs free energy) under given P-T conditions. Based on the dual solution of the inverse problem, a new approach was proposed for the estimation of the oxidation potential of fluid and mineral assemblages, which can be used to determine oxygen potential for almost any mineral association, independent of the presence of magnetite, ilmenite, or graphite. It was found that magnetite-free mineral associations are characterized by highly reducing conditions corresponding to oxygen potentials close to the CCO buffer. The external metamorphic fluid that was present during granulite-facies metamorphism was probably formed in the graphite stability field. The results of calculations for the model aqueous electrolyte solution-mineral assemblage suggest high SiO2 solubility in the metamorphogenic fluid. Therefore, the process of granulite metamorphism may be a potent geochemical factor of the redistribution and transportation of silica from lower to upper crustal levels.

Genesis of garnet-bearing rocks at the Berezitovoe deposit, Upper Amur Region, Russia

The geological position, composition of mineral assemblages, and typomorphism of major minerals from garnet-bearing rocks at the Berezitovoe gold-base-metal deposit in the Upper Amur Region have been studied in detail. These are ore-bearing metasomatic rocks and metamorphosed porphyritic dikes. The garnet-bearing metasomatic rocks reveal zoning, which is caused by various degrees of metasomatic transformation of the Paleozoic porphyritic granodiorite that hosts the ore zone. The metasomatic replacement of granodiorite was accompanied by loss of Na, Ca, Ba, Sr and gain of K, Mn, and Rb. Garnet-bearing metamorphosed intermediate dikes occur within the metasomatic zone. The PT conditions of metamorphism and metasomatism are similar and estimated at 3.9 kbar and 500°C from various mineral equilibria. The results of physicochemical simulation of garnet-bearing mineral assemblages carried out by minimizing the Gibbs free energy and the geological data show that garnet-bearing mineral assemblages arose at the Berezitovoe deposit as a result of local high-temperature thermal metamorphism of previously formed low-temperature metasomatic rocks close in composition to classic beresite. In this connection, we propose considering garnet-bearing metasomatic rocks as high-temperature metamorphosed beresites.

The unified method for computing thermodynamic properties of natural zeolites based on their crystallochemical formulas

The standard thermodynamic potentials of natural zeolites in universal stoichiometric representation are computed. The enthalpies are estimated using linear deconvolution into chemical elements for calibration minerals. The entropies are computed using the additive scheme for oxide components; the Gibbs free energies are computed based on the calculated standard thermodynamic functions and entropies of thermochemically simple compounds.

A study of acidic aluminum-containing solutions through modeling physicochemical equilibria by the thermodynamic potential minimization method

Thermodynamic modeling of physicochemical processes underlying the preparation of aluminum-containing solutions has been performed. It has been demonstrated that the major aluminum species in solution are aluminum chlorides and hydroxychlorides. Temperature-induced changes in the equilibrium composition of a solution has been studied.

Calculation of the standard thermodynamic potentials of aluminum sulfates and basic aluminum sulfates

The standard enthalpies, entropies, and Gibbs energies of formation from elements were calculated for compounds in the Al-S-O-H system. The thermodynamic parameters of minerals, aluminum sulfates and hydroxide sulfates with water of crystallization, were recommended on the basis of analysis of calculation errors. The reliability of the resulting values was tested compared to the solubility experimental data of aluminum sulfate.