High-temperature phase relations and thermodynamics in the iron-lead-sulfur system

The PbS activities in FeS-PbS liquid mattes were obtained at 1100 °C and 1200 °C by the dew-point method. Negative deviations were observed, and the liquid-matte solutions were modeled by the Krupkowski formalism. The liquid boundaries of the FeS-PbS phase diagram were derived from the model equations yielding a eutectic temperature of 842 °C atX _Pbs = 0.46. A phase diagram of the pseudobinary FeS-PbS was also verified experimentally by quenching samples equilibrated in evacuated and sealed silica capsules. No terminal solid solution ranges could be found. Within the Fe-Pb-S ternary system, the boundaries of the immiscibility region together with the tie-line distributions were established at 1200 °C. Activities of Pb were measured by the dew-point technique along the metal-rich boundary of the miscibility gap. Activities of Fe, Pb, and S, along the miscibility gap were also calculated by utilizing the bounding binary thermodynamics, phase equilibria, and tie-lines.     

The liquidus surfaces of ternary systems involving compound semiconductors: II. Calculation of the liquidus isotherms and component partial pressures in the Ga−As−Zn and Ga−P−Zn systems

The previously derived liquidus equation for anAB compound (GaAs or GaP) incorporating a dilute solute (zinc) in equilibrium with a ternary regular melt was applied to the available liquidus data in the Ga?As and Ga?As?Zn and in the Ga?P and Ga?P?Zn systems. The ternary interchange energies for both systems were computed by the method of multidimensional leastsquares. Utilizing these interchange energies, the liquidus isotherms in the Ga?As?Zn and Ga?P?Zn systems were calculated over a wide temperature range from the nonlinear liquidus equation by a numerical method. By a combination of the ternary regular activity coefficients with the vapor pressures of the pure components and the liquidus isotherms, the component partial pressures along the liquidus isotherms were determined. The ternary liquidus and partial pressure isotherms are in good agreement with the experimental data of Panish, Koster and Ulrich, and Shihet al. It is further shown that in the binary limit, the results of these calculations are also in accord with liquidus and partial pressure measurements for the Ga?As and Ga?P systems.     

A theory of regular associated solutions applied to the liquidus curves of the Zn-Te and Cd-Te systems

The thermodynamic equation for the liquidus curve of a binary system with a congruently melting AB compound has been evaluated assuming association in the liquid phase with species A, B, and AB present. Approximate activities were derived assuming regular ternary solution behavior for the species. This type of solution is designated here as a regular associated solution (R.A.S.). The resulting liquidus equation is given in terms of two semiempirical constants which can be calculated by an application of an approximate form of the liquidus equation, valid for a small degree of dissociation, to experimental data. The liquidus curves in the Zn-Te and Cd-Te systems, where strong evidence for association exists, were calculated in excellent agreement with the experimental results. Calculations based on the approximate activities in a R.A.S. predict the existence of a miscibility gap in the Zn-ZnTe subsystem with a monotectic temperature at 1213°C. Furthermore, thermodynamic functions for a R.A.S. were derived. The excess stability exhibits a peak at the composition of the AB compound. Finally, an extension of this theory to solutions containing complexes A₂B and A₂B₃ is indicated.     

High-temperature phase relations and thermodynamics in the silver-tin-sulfur system

The SnS activities in liquid Ag₂S-SnS liquid mattes were obtained at 1100 °C and 1200 °C by the dew-point method. Negative deviations were observed, and the liquid matte solutions were modeled by the Wilson equations. Part of the liquid boundaries of the Ag₂S-SnS phase diagram were derived from the model equations, yielding a eutectic temperature of 528 °C at x _SnS=0.38. The phase diagram of the pseudobinary Ag₂S-SnS was also verified experimentally by quenching samples equilibrated in evacuated and sealed silica capsules. Solubility limits of the components at the narrow-terminal solid-solution ranges were determined around the eutectic temperature. Within the Ag-Sn-S ternary system, the boundaries of the immiscibility region, together with the tie-line distributions, were established at 1200 °C. Activities of Ag, Sn, and S along the miscibility gap were calculated by utilizing the bounding binary thermodynamics, phase equilibria, and tie-lines.     

The liquidus surfaces of ternary systems involving compound semiconductors: I. General thermodynamic analysis

Based on the method of chemical potentials, a general thermodynamic equation for the liquidus surface of a ternary system has been derived relating the activities and partial molar enthalpies in the ternary melt to the composition and the molar enthalpy of the ternary solid. Particularly simple expressions, especially useful for compound semiconductors, were deduced from the general equation for a ternary liquid in equilibrium with i) a binary compoundA _mB_n incorporating a dilute soluteC and with ii) a continuous series of ternary solid solutions formed betweenA _mB_n andC _qB_r. Assuming regular ternary solution behavior in the melt, explicit liquidus equations for both of these cases (settingm=n=q=r=0.5) were obtained in terms of the liquid compositions and the heats of fusion of the binary compounds. It is shown that for a binary liquid, the ternary liquidus equation reduces to that of Vieland.     

Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach—Application to silicate slags

A system of semi-empirical equations has been developed for the analysis of the thermodynamic properties of ordered liquid solutions such as slags. The equations, which are based upon modifications of the quasichemical theory, take into account the concentration and temperature dependence of the solution properties of ordered systems and thus enhance the reliability of interpolations and extrapolations of data. For binary systems, these equations have been coupled with an optimization computer program to analyze simultaneously all available thermodynamic data including phase diagrams, Gibbs energies and enthalpies of formation of compounds, activities, enthalpies of mixing, entropies of fusion, miscibility gaps,etc. In this manner, data for several binary slag systems have been analyzed. In the present article, analyses for the CaO-SiO₂, FeO-SiO₂, and CaO-FeO systems are presented. The resulting equations represent all the binary data, including the phase diagrams, essentially within experimental error limits. The calculations have been extended to ternary systems, thereby permitting ternary thermodynamic properties to be approximated solely from data from the subsidiary binary systems. Results for the SiO₂-CaO-FeO system are in excellent agreement with measured ternary data.     

Experimental study and modeling of the thermodynamic properties of Cu-Fe-Ni melts

The partial mixing enthalpy of nickel in ternary liquid Cu-Fe-Ni alloys is studied at 1873 K along sections characterized by ratios x _Cu: x _Fe = 3, 1, and 1/3 at x _Ni = 0–0.55. The investigations are undertaken using a high-temperature isoperibolic calorimeter. The temperature and composition dependence of the excess mixing Gibbs energy of liquid Cu-Fe-Ni alloys are described in terms of the Muggianu-Redlich-Kister model using the data obtained, the literature data on the activities of liquid alloy components, and the thermodynamic properties of melts of the boundary binary systems. This model is used to calculate isotherms of the thermodynamic properties of the liquid alloys over the entire composition range. The contribution of a ternary interaction to the integral mixing enthalpy of liquid Cu-Fe-Ni alloys is found to be mainly positive.     

Contribution to the phase diagram CaF2–CaO–Al2O3

Critical review of the available data. Determination of the liquidus line of CaF₂-Al₂O₃ mixtures and of the CaO liquidus line in the CaF₂–CaO binary. Investigation of the heterogeneous equilibria in the CaF₂–CaO–Al₂O₃ ternary by using different techniques. Determination of the 1600°C liquidus isotherms of CaO, CaO · 2Al₂O₃, CaO · 6Al₂O₃, Al₂O₃ and of the miscibility gap.     

A thermodynamic method for determining the activities from ternary miscibility gap data: The Cu-Pb-O system

A thermodynamic method is developed for determining the activities of all three component elements along a ternary miscibility gap from a knowledge of the line distributions and the pertinent binary thermodynamic properties. The thermodynamic treatment outlined is particularly applicable when the ternary miscibility gap lies close to one of the boundary binaries. Its usefulness is demonstrated by successfully deriving the activities in the ternary system Cu-Pb-O at 1473 K. The method presented is of general applicability to ternary systems consisting of two metals and a nonmetal such as oxygen, sulfur or selenium.     

Defective two sublattice model for a binary liquid

A statistical thermodynamic analysis is given for a quasicrystalline liquid model in the binary systemM-X in which the atoms of each type are randomly mixed with vacancies on one of two sublattices of a structure with the stoichiometric formulaMX _s. The relative, excess partial molar quantities and the equations relating the site-fraction of vacancies in each sublattice to the temperature and composition are obtained. The constraints upon the model parameters required to insure that the Schottky constant increases with temperature and that the site fractions of vacancies be less than unity below a specified temperature (above which the model is not physically meaningful) are also obtained. The excess Gibbs free enthalpies for the creation of the vacancies are assumed to depend linearly upon atom fraction and it is shown that this is the simplest model capable of generating an asymmetric liquidus line for the solid compound,MX. The chemical potentials for a more general model are given in an Appendix. An application is made to the Cd-Te system where a quantitative fit is obtained to the liquidus points, partial pressures along the CdTe 3-phase curve, and the CdTe-Te eutectic temperature with values of the liquid parameters that yield the proper enthalpy and entropy of mixing of the liquid at 50 at. pct and 1092 °C.     

Thermodynamic analysis of the In-Ga-Sb system

The phase diagram and thermodynamic data for the In-Ga-Sb system are fit with a model for the III-V liquid phases, in which the enthalpy and excess entropy of mixing are quartic functions of the atomic fraction and the enthalpy of mixing is a quadratic function of temperature. The Gibbs energy, enthalpy, and entropy of formation of the III-V compounds are obtained as functions of temperature from the heat capacities and the standard enthalpy and entropy of formation at 298 K. The fits are quantitatively satisfactory and better than any hitherto obtained, particularly for the III-V liquidus lines and the ternary liquid. The partial pressures of Sb₂ and Sb₄ are calculated along the three phase curves of In_1-uGa_uJSb(s), and relations given to obtain the relative chemical potentials of In and/or Ga are from these. The enthalpy of mixing of the III-V liquids is calculated for a few hundred degrees above the compound melting points, where presently there are no data. Characteristics of an improved model are postulated.     

A thermodynamic analysis of the copper-lead-sulfur system at 1473 K

A consistent set of thermodynamic activities in the Cu-Pb-S system is derived at 1473 K from a knowledge of the high-temperature phase relations, the boundary binary thermodynamics and the estimated limiting activity coefficients of sulfur in copper-lead melts. Within the uncertainty limits, the derived values in the present study and the experimental values of Azuma,et al, for the activity of Pb are in good accord. The tie-line distribution in the lead-rich portion of the ternary miscibility gap has been slightly modified to be consistent with the thermodynamic properties of the lead-sulfur system.     

A thermodynamic analysis of the copper-lead-sulfur system at 1473 K

A consistent set of thermodynamic activities in the Cu-Pb-S system is derived at 1473 K from a knowledge of the high-temperature phase relations, the boundary binary thermodynamics and the estimated limiting activity coefficients of sulfur in copper-lead melts. Within the uncertainty limits, the derived values in the present study and the experimental values of Azuma,et al, for the activity of Pb are in good accord. The tie-line distribution in the lead-rich portion of the ternary miscibility gap has been slightly modified to be consistent with the thermodynamic properties of the lead-sulfur system.     

Study of the liquidus and solidus surfaces in the quaternary Fe-Ni-Cu-S system: IV. Construction of a meltability diagram and determination of miscibility gap boundaries for the ternary Cu-Fe-S sulfide system

The phase transformations in the ternary sulfide Cu-Fe-S system are analyzed, and the positions and temperatures of the nonvariant equilibrium points and the monovariant equilibrium lines in this system are determined. Experimental results obtained by differential thermal analysis, scanning electron microscopy, and electron-probe microanalysis are used to plot projections of the liquidus and solidus surfaces on a concentration triangle, and the positions of the miscibility gap boundaries in the Cu-Fe-S system are determined. The composition and temperature of the critical miscibility gap point are determined, and conode directions are indicated. This work is the final part of a series of works dealing with the phase transformations occurring in the ternary systems that bound the quaternary Fe-Ni-Cu-S system.     

The liquidus line and gibbs free energy of formation of a crystalline compound AmBn(c). II. Analysis of the liquidus lines of InSb,InAs, GaSb,and GaAs

The liquidus lines of InSb, InAs, GaSb, and GaAs are fit using the heat-of-fusion liquidus equation and six different models for the liquid phase. Following an earlier paper, the overall fit is judged satisfactory only when the standard deviation between the calculated and observed liquidus temperatures is equal to or less than the precision of the experimental temperaturesand when the enthalpy and entropy of formation of the compound are calculated correctly from the parameters of the liquidus fit. The ideal, strictly regular, and quasiregular models for the liquid phase do not lead to a satisfactory overall fit for any of the four compounds. The earlier and that corresponding to a Margules expansion truncated after the cubic terms are both satisfactory for InSb and InAs. They are not satisfactory for GaSb and GaAs but, in our opinion, this is more likely due to errors in the experimental values for the enthalpy and entropy of formation for these compounds than to an inadequacy of the models.     

Calorimetric study and description of the composition dependence of the mixing enthalpy of liquid Cu—Fe—Co aloys

The partial enthalpy of cobalt in ternary liquid Cu-Fe-Co alloys is studied at a temperature of 1873 K along sections characterized by ratios x _Cu/x _Fe = 3, 1, and 1/3 in the composition range x _Co = 0–0.55. The experiments have been carried out on a high-temperature isoperibolic calorimeter. The composition dependences of the partial mixing enthalpy of the cobalt and the integral mixing enthalpy of Cu-Fe-Co melts are described using the Muggianu-Redlich-Kister equation over the entire concentration triangle. The contributions of a ternary interaction to the partial mixing enthalpy of cobalt and the integral mixing enthalpy of Cu-Fe-Co melts are calculated.     

Phase equilibria and thermodynamic properties of the Cu<Subscript>2</Subscript>O-CaO-Na<Subscript>2</Subscript>O system in equilibrium with copper

The liquidus surfaces of the Cu₂O-CaO, Cu₂O-Na₂O, and Cu₂O-CaO-Na₂O phase diagrams in equilibrium with metallic Cu were measured by thermal analysis at compositions varying from approximately 0 to 35 wt pct Na₂O and 0 to 15 wt pct CaO. Solubilities in the solid binary terminal solutions were also measured by wavelength dispersive X-ray spectrometer analysis. Copper oxide activities in binary liquid slags were determined from the measured oxygen content of the metallic copper equilibrated with the slags. The ternary system is a simple eutectic system. No ternary compounds were observed. The Cu₂O-CaO binary eutectic was measured at 1140 °C±10 °C at 10±1 wt pct CaO and the Cu₂O-Na₂O binary eutectic was measured at 803 °C±15 °C at 28±2 wt pct Na₂O. The liquid slag was thermodynamically modeled with the modified quasi-chemical model, while the solid Cu₂O-rich solution was treated as Henrian ideal. All data from the present work and from the literature (phase diagrams and activities) for the binary systems were evaluated simultaneously by least-squares optimization in order to obtain the best model parameters. With only these binary parameters, the calculated ternary liquidus surface is in very good agreement with the measurements. Finally, using the model, the liquidus projection of the Cu₂O-CaO-Na₂O system in equilibrium with Cu was calculated as well as the oxygen content of the equilibrated Cu as a function of slag composition.     

Thermochemical Properties of Liquid Alloys in Fe ― O and Fe ― O ― Metal Systems

An isoperibolic calorimeter has been used to determine the partial and integral enthalpies of mixing for liquid alloys in the binary Fe ― O system and ternary Fe ― O ― M ones at 1915 K. The enthalpies of mixing in these systems are high exothermic quantities, which agree with published data. It is found that the first partial enthalpy of mixing for oxygen is _280 kJ/mole. The enthalpies of mixing have been calculated from the standard enthalpies of formation Δ_f H ^º ₂₉₈ for iron oxides throughout the concentration range. The enthalpies of mixing have been calculated and measured for binary alloys in the Fe ― O system, which are correlated one with the other.