Thermodynamic Analysis Of Phase Equilibria Research Articles

PHASE EQUILIBRIA IN CU–AL–CR–O SYSTEM LIQUID METAL

A thermodynamic analysis of phase equilibria in a Cu–Al–Cr–O system was performed. The study involved thermodynamic modeling of the liquidus surface of the Cu2O–Al2O3–Cr2O3 oxide phase diagram. To describe the thermodynamic activity of the molten oxide, an approximation of the sub-regular ionic solutions theory was used with the energy parameters determined in the modeling process. Melting characteristics of CuCrO2 were also evaluated during calculations. Calculation results were used to determine the coordinates of invariant equilibria points in the Cu2O–Al2O3–Cr2O3 ternary oxide system. The study also involved thermodynamic modeling of interactions in the Cu–Al–Cr–O system in the conditions of a copper-based metal melt. The temperature function of the reaction equilibrium constant was determined for the formation of solid CuCrO2 from the components of the Cu–Al–Cr–O molten metal system. The temperature function was obtained for the first order (Wagner’s) interaction parameter of Cr and O dissolved in liquid copper. The results of thermodynamic modeling for the Cu–Al–Cr–O system are represented as the surface of components solubility in metal, which allows us to relate the quantitative changes in the molten metal concentration to the qualitative changes in the composition of resulting reaction products. As a result of modeling, it was found that the given considerable concentrations of Al and Cr in the Cu–Al–Cr–O molten copper system form the |Al2O3, Cr2O3|ss solid solution particles as primary reaction products. The results of the study may be used to improve the chromium bronze smelting process.

Phase Equilibria in Liquid Metal of the Cu–Al–Cr–O System

A thermodynamic analysis of phase equilibria in the Cu–Al–Cr–O system is carried out. Thermodynamic modeling of the liquidus surface of the Cu2O–Al2O3–Cr2O3 oxide phase diagram is performed. To describe activities of an oxide melt, the approximation of the theory of subregular ionic solutions, the energy parameters of which were determined during modeling, is used. Melting characteristics of the CuCrO2 compound are also evaluated in the course of the calculation. Coordinates of invariant equilibria points implemented in the Cu2O–Al2O3–Cr2O3 ternary oxide system are established by the results of the calculation. Thermodynamic modeling of interaction processes in the Cu–Al–Cr–O system in occurrence conditions of a copper-based metal melt is also performed. The temperature dependence of the equilibrium constant of the reaction that characterizes the formation of the CuCrO2 solid compound from components of the metal melt of the Cu–Al–Cr–O system is determined. The temperature dependence for the first-order interaction parameter (by Wagner) of chromium and oxygen dissolved in liquid copper is found. The results of thermodynamic modeling for the Cu–Al–Cr–O system are presented in the form of the solubility surface of components in metal, which makes it possible to attribute the quantitative variations in the metal melt concentration with qualitative variations in the composition of forming interaction products. It is determined by the results of modeling that particles of the |Al2O3, Cr2O3|sol.sln solid solution are formed at valuable aluminum and chromium concentrations in the copper melt of the Cu–Al–Cr–O system as the main interaction product. The results of the investigation can be interesting for improving the technology process of smelting of chromium bronzes.

Thermodynamic Analysis of Phase Equilibria in the Nd-Fe-Cu Ternary System

Thermodynamic Analysis of Phase Equilibria in the Nd-Fe-Cu Ternary System

Термодинамическое описание фазовых равновесий в системе Cu–Al–Zr–O в условиях существования металлического расплава

Thermodynamic modeling and experimental investigation of phase equilibria in the Cu–Al–Zr–O system were carried out. Thermodynamic analysis of phase equilibria was performed using the method of constructing the Surface of Components Solubility in the Metal melt (SCSM). Thermodynamic analysis was made for temperatures of 1200 and 1300 °С. The areas of phase equilibria of liquid metal with conjugated oxide phases were constructed depending on concentrations of elements dissolved in metal melt. Formation of copper oxide and CuAlO 2 compound in the presence zirconium and aluminum in liquid metal melt are thermodynamically unlikely. The areas of these phase equilibria are offset to less than 10 –13 wt. % Al and to less than 10 –20 wt. % Zr. Iso-oxygen sections have been also calculated. It was shown that zirconium is a stronger reducing agent than aluminum in the copper melt. Thus the alternative deoxidation mechanism is characteristic for the Cu–Al–Zr–O system. Zirconium dissolved in the copper melt will primarily interact with oxygen. Aluminum oxide may be formed at lower zirconium concentration and at sufficient oxygen concentration in copper melt. Zirconium concentration in copper melt will be decreased in connection with formation zirconium oxide. Experimental investigations confirmed thermodynamic modeling results. The analyses of the non-metallic inclusions have been performed using scanning electron microscope and energy dispersion spectrometer. The research results may be interesting for copper and copper alloys industry.

Thermodynamic Modeling of the Cr-Fe-S System

All known phases of the chromium-iron-sulfur ternary system are taken into consideration within a thermodynamic analysis of phase equilibria and thermodynamic data at 1 bar total pressure over the entire composition range between 298.15 K (25 °C) and temperatures greater than the liquidus. The modeling is based on recent evaluations of the Fe-S and Cr-S binary subsystems. The extended modified quasi-chemical model is applied for the liquid chromium-iron-sulfur phase. The Gibbs energy of solid solution phases as high-temperature chromium-iron pyrrhotite and the thiospinel Daubreelite is described by sublattice models within the framework of the compound energy formalism. Analysis of complex phase relations is now possible on the basis of a consistent thermodynamic description of the system. The thermodynamic modeling presented can be combined with models of other metal-sulfur systems to develop a thermodynamic multicomponent/multiphase database.

Thermodynamic Analysis of Phase Equilibria in the Mg–Al–Ho Ternary System

A thermodynamic analysis of phase equilibria in the Mg­Al­Ho ternary system has been carried out with special emphasis on the metastable phase separation of the hexagonal close-packed (hcp) phase. In this study, the Gibbs free energy of mixing of the hcp phase was evaluated using first-principles calculations combined with the cluster variation method (CVM), and the obtained results as well as the available experimental data were introduced into the analysis. The calculated results enabled the reproduction of experimental results on both the phase equilibria and the thermodynamic properties obtained from the first-principles calculations and the CVM. In addition, the calculations indicated a tendency for metastable two-phase separation in the hcp phase between the Mg-rich corner and the Al­Ho binary side, which was similar to the Mg­Y­Zn ternary system shown in our previous work. [doi:10.2320/matertrans.MI201226]

Thermodynamic modeling of the Cr – S system

Abstract All known phases of the chromium – sulfur binary system have been taken into consideration within a thorough thermodynamic analysis of phase equilibria and thermodynamic data at 1 bar total pressure over the entire composition range between 25 °C and temperatures above the liquidus. Gibbs energy modeling for ten phases has been performed. A limited set of model quantities were optimized by which the experimental data can be reproduced simultaneously within experimental limits of error. New interpretations of complex phase relations are obtained. The extended modified quasichemical model is applied for the liquid chromium – sulfur phase. The Gibbs energy of high-temperature chromium pyrrhotite solution is described by a two-sublattice model within the framework of the compound energy formalism. The sulfur solubility of solid chromium is modeled using a substitutional approach. The Gibbs energies of six stoichiometric compounds are also modeled. The first internally consistent description of all thermodynamically stable phases known in the literature for the chromium – sulfur system is presented.

Thermodynamic analysis of phase equilibria in the Sm-Cu-O system

This paper presents thermodynamic analysis of the Sm-Cu-O system and its constituent binaries using available experimental data. Analytical expressions are derived for the Gibbs energy of Sm2CuO4, SmCuO2, and the liquid; the invariant points in the ternary system are located; and the CuO-SmO1.5 phase diagram at an oxygen partial pressure of 21 kPa is calculated.

Thermodynamic analysis of the dominant phase equilibria in M(Si, Cr, Al)-O-C systems

Various approaches are proposed for developing thermodynamic models of dominant phase equilibria. It is noted that, as a thermodynamic analysis of the phase equilibria in M(Si, Cr, Al)-O-C systems is performed, the equilibrium concentrations and the stability of the phases should be calculated by minimizing the Gibbs energy for the systems at a given temperature and pressure.

Thermodynamic analysis of phase equilibria in the Cr–Mo–B ternary system

A thermodynamic analysis of the phase equilibria in the Cr–Mo–B ternary system has been carried out by combining first-principles calculations with the CALPHAD approach. The thermodynamic descriptions of three binary systems relevant to this ternary phase diagram were taken from previous studies. The enthalpy of formation of the (Cr,Mo) 2B (Al 2Cu-type, tI12, space group I 4 / m c m ), (Cr,Mo) 3B 2 (U 3Si 2-type, tP10, space group P 4 / m b m ), (Cr,Mo)B (CrB-type, oC8, space group Cmcm), (Cr,Mo) 3B 4 (Ta 3B 4-type, oI14, space group Immm), and (Cr,Mo)B 2 (AlB 2-type, hP3, space group P 6 / m m m ) phases were obtained from first-principles calculations. The ternary thermodynamic parameters evaluated using these theoretical values, as well as the available experimental information on the phase boundaries, enabled us to calculate the phase equilibria in the Cr–Mo–B ternary system over the entire composition and temperature ranges.

Experimental study and thermodynamic analysis of phase equilibria in the silicon-rich part of the Si-Sr and Si-Ba systems

Using thermal and activation analysis techniques, we have constructed the liquidus curves in the primary crystallization fields of silicon in the Si-Sr and Si-Ba systems. The Sr and Ba solid solubilities in silicon have been determined using microhardness measurements, and have been shown to exhibit retrograde behavior. At 1573 K, the solubility of Sr in silicon is 1.15 at %, and that of Ba is 0.98 at %. The solidus and liquidus curves have been analyzed using thermodynamic modeling and the known thermodynamic properties of the melt and intermediate phases. We assume that the large deviations of the melts from ideal behavior are due to the formation of Zintl polyanions (or clathrates), and describe a model for the chemical structure of the silicon-rich melts.

Thermodynamic Analysis of Mn-depleted Zone Near Ti Oxide Inclusions for Intragranular Nucleation of Ferrite in Steel

A series of thermodynamic analyses have been performed to elucidate possible mechanism of Mn-depleted zone (MDZ) development near Ti oxide inclusions as nucleation sites of Intragranular Acicular Ferrite (IGF) transformation in steels, using a computational thermodynamic approach (CALPHAD). It is demonstrated that thermodynamic calculations are able to reproduce experimentally known inclusions evolution in the steels. The MDZ development near the Ti2O3 inclusions is shown to be a result of Mn absorption into the Ti2O3. Moreover, from thermodynamic analysis of phase equilibria in the Mn–Ti complex oxide system, it is proposed that a phase change of inclusion from (Ti3O5) s.s. (pseudobrookite structure solid solution dissolving Mn) to (Ti2O3) s.s. (ilmenite structure solid solution dissolving Mn) accelerate the Mn absorption into the Ti2O3 inclusion in steel. From a series of thermodynamic calculations, optimum thermal heating condition to enhance Mn absorption into Ti2O3 inclusions as well as IGF formation is discussed.

Thermodynamic Analysis of Phase Equilibria in the Fe–Nb–P Ternary System

A thermodynamic analysis of the Fe-Nb-P ternary system has been carried out using the CALPHAD method. Among the three binary systems present in this ternary phase diagram, the phase equilibria in the Nb-P binary system, on which very few studies have been reported, were thermodynamically analysed. The thermodynamic properties of various phosphides and of a bcc solid solution obtained from first-principles calculations were utilized in this analysis to compensate for the lack of available experimental data. By applying these procedures, a highly plausible Nb-P binary phase diagram was established over the entire composition range. The thermodynamic descriptions of the Fe-Nb and Fe-P binary systems were taken from previous studies. The thermodynamic parameters of the Fe-Nb-P ternary system were evaluated based on experimental data for the phase boundaries and estimated thermodynamic properties of the ternary phosphides obtained using first-principles calculations. The calculated phase equilibria were in good agreement with the available experimental data. From the calculated results, we confirmed that the ternary phosphide, FeNbP took part in equilibria with most of the binary phosphides.

Preparation of Nanocrystalline Alumina under Hydrothermal Conditions

Thermodynamic analysis of phase equilibria in the Al2O3-H2O system at temperatures from 120 to 380°C and pressures from 1 to 70 MPa is carried out, and the dehydration of aluminum hydroxide under hydrothermal conditions is studied experimentally. The results indicate that γ-AlOOH (boehmite), which commonly appears in experimental phase diagrams, is a nonequilibrium phase in these temperature and pressure ranges. The dehydration rate and mechanism are shown to strongly depend on the crystallinity of the parent aluminum hydroxide and the pressure in the hydrothermal system.

Thermodynamic Analysis of Phase Equilibria in the System Cyclohexane—Methanol

The phase diagram of cyclohexane-methanol was thermodynamically modeledin the range of 150 ≤ T/K ≤ 360 and at a pressure of 1 bar on the basis ofavailable experimental data. The Gibbs energy functions of four pure solid andtwo mixture phases were taken into consideration. The liquid phase was describedby a model based on mole fraction statistics and the simplified assumption ofmethanol tetramers mixed with cyclohexane monomers. The gas phase was treatedas a nonideal mixture with a Gibbs energy modeled on the basis of the virialcoefficient formalism considering only monomers. The Gibbs energies of the twosolid modifications of pure methanol, as well as pure cyclohexane, were fixedusing literature data. The pressure dependence of the Gibbs energies of the liquidand solid phases were neglected. The complete T-x phase diagram includinggas/liquid equilibria as well as p-x phase diagrams in the range of 20 and 55°C werecalculated. Experimental and calculated data were found to agree reasonably well.

Thermodynamic analysis of aluminate stability in the eutectic bonding of copper with alumina

The interfacial reactions between Cu and Al 2O 3 which occur during the eutectic bonding process have been examined. A thermodynamic analysis of phase equilibria in the Cu–Al–O system shows that a five-phase equilibrium exists among solid copper with oxygen in solution, liquid copper with oxygen in solution, solid CaAlO 2, Al 2O 3 and oxygen gas at the invariant state T=1348 K, p O 2 =5.6×10 −7 atm (0.055 Pa). The existence of this invariant state has been confirmed experimentally by heating slightly oxidized copper disks placed in contact with alumina disks. The experimentally determined invariant state was found to be in good agreement with that calculated. During eutectic bonding the compound CuAlO 2 forms at the interface between copper and the alumina in specimens containing solid copper only at temperatures lower than 1348±3 K.

Multiple Phase Equilibria in Polydisperse Polymer/Liquid Crystal Blends

A thermodynamic analysis of phase equilibria in polydisperse polymer−liquid crystal blends is presented. Three different systems were analyzed: (a) a high molar mass polydisperse polystyrene (PS) blended with 4-cyano-4‘-n-heptylbiphenyl (7CB), (b) a low molar mass polydisperse PS blended with 7CB, and (c) an epoxy-based thermosetting polymer blended with a mixture of small mesogenic molecules usually called E7. In the latter case the analysis was performed in both pregel and postgel stages. Macroscopic phase separation taking into account the fractionation of the polydisperse polymer among different phases, was simulated when cooling from an initially homogeneous state. Predicted isotropic−isotropic and isotropic−nematic transitions showed a good agreement with experimental results. The relative volume fraction and compositions of isotropic and nematic phases were predicted. A temperature range was found where three macroscopic phases, two isotropic and one nematic, coexisted at equilibrium. This was the result of a liquid−liquid (or gel−liquid) phase separation preceding the appearance of a nematic phase. Implications of this behavior on morphologies developed in polymer-dispersed liquid crystals (PDLC) are discussed.

Thermodynamic analysis of phase equilibria in the iron-uranium-zirconium system

Thermodynamic analysis of phase equilibria in metallic nuclear reactor systems has progressed to the study of the iron-uranium-zirconium ternary system. This work is based on our previous assessments and optimizations of the constituent binary subsystems iron-uranium, iron-zirconium, and uranium-zirconium.

Thermodynamic analysis of phase equilibria in the iron—zirconium system

Continuing interest in development of metallic fuels for nuclear reactors has prompted an examination of the phase relations of many of the relevant binary and ternary systems of interest. We performed a thermodynamic analysis and optimization of the Fe-Zr system. Overall reasonably good agreement was found with published diagrams, but some significant changes were required to ensure thermodynamic consistency.

A thermodynamic evaluation of the Ti-N system

A thermodynamic analysis of phase equilibria in the Ti-N binary system was done. The different solution phases and intermetallic compounds were analysed using thermodynamic models of the Gibbs energy. A set of self-consistent parameters has been obtained using the optimization procedure developed by Lukas et al. Good agreement is observed between the experimental information and the calculated phase diagrams and thermodynamic functions.