A thermodynamic analysis of the copper-sulfur system

An associated solution model is applied to describe the thermodynamic behavior of Cu-S liquid. This model assumes the existence of ‘Cu₂S’ species in addition to Cu and S in the liquid. With two solution parameters for each of the binaries Cu-‘Cu₂S’ and ‘Cu₂S’-S, this model accounts for the compositional dependence of the thermodynamic properties of Cu-S liquid from pure Cu to pure S over a wide range of temperature. The binary Cu-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘Cu₂S’ to Cu and S. Using this model for the liquid phase, a statistical thermodynamic model for the digenite phase, and appropriate thermodynamic equations for the other phases, the Cu-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of digenite at all temperatures. Formerly with the Materials Department, University of Wisconsin-Milwaukee Formerly Professor of Materials Engineering and Associate Dean for Research of the Graduate School of the University of Wisconsin-Milwaukee.     

Thermodynamics and phase relationships of transition metal-sulfur systems: IV. thermodynamic properties of the Ni-S liquid phase and the calculation of the Ni-S phase diagram

An associated solution model is applied to describe the thermodyanmic properties of the liquid Ni-S phase. This model assumes the existence of ‘NiS’ (l) species in the liquid in addition to Ni(l) and S(l). With two solution parameters for the binaries Ni-‘NiS’ and ‘NiS’-S, this model is able to describe the thermodynamic behavior of the liquid phase over a wide range of temperature and composition. Using this model for the liquid phase, a statistical thermodynamic model for the monosulfide phase and empirical thermodynamic equations for β₁-Ni₃S₂ and β₂-Ni₄S₃, the Ni-S phase diagram is calculated. The calculated diagram is in excellent agreement with the available experimental data with the exception that the eutectic composition for the equilibrium L₁ + δ + η and those of the two liquids for the equilibriumL ₁ + L ₂ + η differ from the experimental data by more than 2 at. pct S. Formerly Post-Doctorl Research Associate, University of Wisconsin-Milwaukee is now Lecturer, Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur, India     

Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A1₂O₃, and α-Al₂O₃ has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y₂O₃)ThO₂ as the solid electrolyte and Cr + Cr₂O₃ as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.     

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.     

On binaryP-T phase diagrams

A thermodynamic analysis of the concentration and temperature dependencies of oxygen pressure in metal-metal oxide systems is presented. The resulting binaryP-T phase diagrams show the various species in the context of relative reducibility not only for pure elements and compounds but also for the solutions and intermediate compounds which form. It is not necessary to presume a model for the thermodynamic behavior of solid and/or liquid solutions in this treatment. The Cr-Cr₂O₃ system is presented as an example. Verification is found in the previously reported data on the V₂O₄V₂O₅ system.     

Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A1₂O₃, and α-Al₂O₃ has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y₂O₃)ThO₂ as the solid electrolyte and Cr + Cr₂O₃ as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.     

A thermodynamic analysis of the phase equilibria of the Fe-Ni system above 1200 K

A quasi-subregular solution model is used to describe the thermodynamic properties of the liquid phase; values of the solution parameters are obtained from extensive and consistent thermochemical data reported in the literature. For the fcc and bcc phases, the same model is used to account for the nonmagnetic part of the Gibbs energy and the magnetic contribution is taken from the previous paper. Again, the values for the quasi-subregular solution parameters for the fcc phase are obtained from extensive and consistent thermochemical data reported in the literature at high temperatures. The values of the solution parameters for the bcc phase are obtained from the thermodynamic values of the liquid and fcc phases and the known phase boundary data. The calculated phase equilibria are in good agreement with the available data. Based on the thermodynamic data, the metastablel + γ andl + δ phase boundaries as well as theT ₀ (γ + l) andT ₀(δ +l) curves are calculated.     

Thermodynamics of Ti in Ag-Cu alloys

The thermodynamic activities of Ti at dilution in a series of Ag-Cu alloys and eutectic Ag-Cu alloys containing In or Sn were measured using a galvanic cell technique employing a ThO₂-8 pct Y₂O₃ electrolyte. The equilibrium oxide phase formed by the reaction of Ti (X_Ti > 0.004) in the Ag-Cu alloy melts with an A1₂O₃ or ZrO₂ crucible was Ti₂O (s). The free energy of formation of Ti₂O (s) was estimated from available thermodynamic data. Titanium activities were calculated from measured oxygen potentials and the free energy of formation of Ti₂O (s). Titanium in the eutectic Ag-Cu melt showed a positive deviation from ideal solution behavior at 1000°C, and its activity coefficient at infinite dilution was about 6.5 relative to pure solid Ti. Indium and Sn did not increase the activity coefficient of Ti in eutectic Ag-Cu melts. Silver increased the Ti activity coefficient in the Ag-Cu-Ti melts significantly. The Ti activity coefficient value in liquid Ag was about 20 times higher than in eutectic Ag-Cu melt at 1000 °C.     

Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system

The CALPHAD method is used for the thermodynamic assessment of the Cu-Ti system that bounds the ternary Cu-Ti-Zr system, which is capable of forming amorphous alloys. The self-consistent parameters of thermodynamic models of the phases are obtained from data on the phase equilibria and thermodynamic properties of liquid alloys and intermetallic compounds. The Gibbs energy of the liquid phase is described using the associated ideal solution model. To describe the thermodynamic properties of the Cu₄Ti and CuTi intermetallic compounds with homogeneity range, sublattice models are used. The calculated phase diagram of the system and the thermodynamic properties of the phases are in good agreement with experimental data.     

Equilibria in the systems C−O−S and C−O−S−H as related to sulfur recovery from sulfur dioxide

Equilibrium phase diagrams for the titled systems, showing gas composition as a function of temperature for the carbon and sulfur-saturation surfaces, were calculated from thermochemical data on the numerous gas species present. The recent experimental work of Drowart,et al ¹. was used to obtain consistent thermodynamic behavior for the seven vapor polymers of sulfur (S _n ,n=2 to 8). For the system C?O?S?H, only the pseudo-ternary at the constant atom ratio H/C=4.0 is presented. An iterative procedure, adapted for the digital computer, was used to solve the complex equilibria involved. The influence of the equilibrium chemistry on the design of processes to reduce SO₂ with C, CO, and CH₄ is discussed. In all cases, production of sulfur vapor reaches a sharp maximum at the gas composition having the atom ratio (H+C)/O =(1+X)/(2+X/2), whereX is the atom ratio H/C in the reducing agent. Reducing agents with lower values ofX yield better sulfur recovery because of the smaller residual amount of H₂S and SO₂ in the reacted gas.     

Volume effects and associations in liquid alloys

The regular associated solution model for binary systems has been modified by incorporating the size of the complex as an explicit variable. The thermodynamic properties of the liquid alloy and the interactions between theA _μB type of complex and the unassociated atoms in anA-B binary have been evaluated as a function of relative size of the complex using the activity coefficients at infinite dilution and activity data at one other composition in the binary. The computational procedure adopted for determining the concentration of clusters and interaction energies in the associated liquid is similar to that proposed by Lele and Rao. The analysis has been applied to the thermodynamic mixing functions of liquid Al-Ca alloys believed to contain Al₂Ca associates. It is found that the size of the cluster significantly affects the interaction energies between the complex and the unassociated atoms, while the equilibrium constant and enthalpy change for the association reaction exhibit only minor variation, when the equations are fitted to experimental data. The interaction energy between unassociated free atoms remains virtually unaltered as the size of the complex is varied between extreme values. Accurate data on free energy, enthalpy, and volume of mixing at the same temperature on alloy systems with compound forming tendency would permit a rigorous test of the proposed model.     

Thermodynamic assessment of the Nb-N system

The phase equilibrium and thermodynamic information of the Nb-N system was reviewed and assessed by using thermodynamic models for the Gibbs energy of individual phases. Although there was a large amount of experimental information of the system, heat capacity data of the Nb₂N and NbN were not available either in low or high temperatures. In the present study, low-temperature heat capacity and the^o S ₂₉₈ values were estimated using estimated entropy Debye temperatures. Only the Nb₂N (hcp) and NbN (fcc) nitrides were considered to be the true binary phases and were included in the present evaluation in addition to the N₂ gas, liquid, andα-solid solution (bcc). Three thermodynamic models were used: a two-sublattice model for the solid solution phases, a substitutional model for the liquid phase, and an ideal-gas model for the N₂ gas. The model parameters were evaluated by fitting to the selected data by means of a computer program. A consistent set of parameters was obtained which satisfactorily described most of the experimental and estimated data.     

Thermodynamics of Liquid Alloys and Metastable Phase Transformations in the Copper - Titanium System

We have used solution calorimetry at temperatures of 1573 K and 1873 K over broad concentration ranges to study the mixing enthalpy of Cu - Ti liquid alloys. The molar mixing enthalpies of the system are significant negative values. We have established the temperature dependence of the molar mixing enthalpies of the system: there is an increase in their exothermicity as the temperature is lowered. The significant negative mixing enthalpies of the system allow us to conclude that the chemical bonds are localized in the studied melts and consequently associates form. We tested this conclusion within ideal associated solution theory, which describes well the results obtained with a set of CuTi and CuTi₂ associates. Using the model obtained, we have calculated the excess thermodynamic functions of mixing (enthalpy, Gibbs free energy, heat capacity) for the liquid alloys. We estimated the Gibbs energies of fcc, bcc, and hcp solutions in the system by the CALPHAD method, using data from the initial sections of the phase diagrams and from the corresponding thermodynamic data. We have calculated the metastable phase equilibria between the limiting solid solutions and the liquid or supercooled liquid phase. It was shown that for the supercooled liquid and the amorphous phase, a broad concentration range of relative thermodynamic stability can be obtained. The concentration range of amorphization of Cu - Ti melts corresponds to the position of the metastable liquidus line and the T₀ line at temperatures close to the temperature range of amorphous solidification. __________ Translated from Poroshkovaya Metallurgiya, Nos. 5–6(443), pp. 67–80, May–June, 2005.     

A thermodynamic evaluation of the Cr-Fe-N system

The thermodynamic properties of the Cr-Fe-N system have been analyzed using thermodynamic models describing the Gibbs energy of the individual phases. A two-sublattice model has been used for the interstitial solution phases and a substitutional solution model for the liquid phase. The analysis involves a combination of predictions from recent assessments of the binary sides with computerized optimization of new ternary parameters. A set of parameters describing the Gibbs energy of the body-centered cubic (bcc), face-centered cubic (fcc), ∈, CrN, Fe₄N, and liquid phases is given. Using this set of parameters, any type of phase equilibria can be calculated. A number of diagrams are presented comparing the results from the calculations with available experimental data, and the agreement is discussed. Most experimental data are well accounted for. The present study is also compared with a previous evaluation.     

Thermodynamic description of the interaction processes in the Cu–Ce–O system in the temperature range 1100–1300°C

A thermodynamic simulation and an experimental study of the interaction between cerium and oxygen in liquid copper have been performed. The thermodynamic analysis of the interaction processes in the Cu–Ce–O system is carried out using the technique of constructing the surface of solubility of components in a metal in the temperature range 1100–1300°C. As a result of simulation, data on changes in the Gibbs energy ΔG _T ° and the equilibrium constants of formation of cerium oxides Ce₂O₃ and CeO₂ from the components of a copper-based metallic melt are obtained. The first-order interaction parameters (according to Wagner) of cerium and oxygen dissolved in liquid copper, namely, e _Ce ^Ce, e _O ^Ce, and e _Ce ^O, are evaluated. Experimental studies of the Cu–Ce–O system have been performed. The morphological features, the size, and the composition of nonmetallic inclusions formed as a result of interaction in the Cu–Ce–O system are studied using scanning electron microscopy and electron-probe microanalysis.     

Thermodynamic description of Sn-Y and Mg-Sn-Y systems

The thermodynamic optimization of the Sn-Y and Mg-Sn-Y systems was critically carried out by means of the CALPHAD（CALculation of PHAse Diagram） technique. In the Sn-Y system, the solution phases（liquid, bcc, bct and hcp） were described by the substitutional solution model. The compound Sn3Y5, which has a homogeneity range, was treated as the formula（Sn, Y）3（Sn, Y）2Y3 by a three-sublattice model in accordance with the site occupancies. In the Mg-Sn-Y system, the liquid phase was treated as the formula（Mg, Sn, Y, Mg2Sn） using an associated solution model, and bcc, bct and hcp were treated as the formula（Mg, Sn, Y）. The compound Sn3Y5 was treated as the formula（Sn, Y, Mg）3（Sn, Y, Mg）2Y3. The ternary compound MgSnY was treated as stoichiometric compound. A set of self-consistent thermodynamic parameters of the Mg-Sn-Y system was obtained. The projection of the liquidus surfaces and the reaction scheme of the Mg-Sn-Y system were predicted.