Thermochemistry of binary liquid gold alloys: The systems gold-copper and gold-silver at 1379 K

The enthalpies of mixing of the binary liquid alloys of gold with copper and silver have been measured by high temperature reaction calorimetry. The experimental results are described by the following analytical expressions which were derived by a least squares treatment of the data: Au-Cu: ΔH_mix = X_AuX_Cu(-28,821 - 2,468 X^Au + 9,541 X_Au ²) J mol^-1 Au-Ag: ΔH_mix = X_AuX_Ag(-15,820 - 529 X_Au @#@) J mol^-1 The results are compared with excess Gibbs energy data from the published literature to yield approximate excess entropies of mixing. For the gold-copper system the observed parabolic dependence of the enthalpy interaction parameter on composition is well accounted for by the quasi-chemical theory.     

The modified quasi-chemical model: Part II. Multicomponent solutions

Further improvements to the modified quasi-chemical model in the pair approximation for shortrange ordering (SRO) in liquids are extended to multicomponent solutions. The energy of pair formation may be expanded in terms of the pair fractions or in terms of the component fractions, and coordination numbers are permitted to vary with composition. The model permits complete freedom of choice to treat any ternary subsystem with a symmetric or an asymmetric model. An improved general functional form for “ternary terms” in the excess Gibbs energy expression is proposed. These terms are related to the effect of a third component upon the binary pair interaction energies. It is shown how binary subsystems that have been optimized with the quasi-chemical model can be combined in the same multicomponent Gibbs energy equation with binary subsystems that have been optimized with a random-mixing Bragg-Williams model and a polynomial expression for the excess Gibbs energy. This is of much practical importance in the development of large databases for multicomponent solutions. The model also applies to SRO in solid solutions as a special case, when the number of lattice sites and coordination numbers are constant.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2-CaO system

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂-CaO system from 298 K to above the liquidus temperatures at all compositions under reducing conditions and at low CaO concentrations under oxidizing conditions. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

W-Zr体系的热力学优化

综合评估了W-Zr体系的实验结果。采用Redlich-Kister多项式描述体系液相、bcc和hcp相的过剩自由焓。利用第一性原理和德拜理论得到化合物W2Zr的自由焓，并结合选取合理的实验数据，优化得到W-Zr二元体系各相的热力学参数，用优化结果计算的相图与实验结果吻合较好。     

FeS-PbS和PbS-ZnS二元系的热力学优化

采用ＲｅｄｌｉｃｈＫｉｓｔｅｒ多项式描述体系液相的过剩自由焓,根据试验相图和已知的热力学数据优化得到了ＦｅＳＰｂＳ和ＰｂＳＺｎＳ二元系的热力学参数。用优化结果计算的相图与试验测量值吻合较好。     

Phase equilibria calculation of LaI3-MI （M=Na, K, Cs） binary systems

The Gibbs energies of liquid phases in the LaI3-MI (M=Na, K, Cs) systems were described by the modified quasi-chemical model. From the measured phase equilibrium data of these binary systems, a set of thermodynamic functions were optimized by using the CAL-PHAD technique. The enthalpy of mixing and the interaction parameter of the liquid phase were predicted from known data for the LaI3-MI systems.     

Thermodynamic evaluation of the Cr-Ni-C system

Evaluation of thermodynamic parameters of the Cr-C and Cr-Ni-C systems has been made by using sublattice models. The Gibbs energies of formation of Cr₂₃C₆, Cr₇C₃, and Cr₃C₂ were reassessed from the experimental data. The interaction between chromium and carbon in the nickel-rich face-centered cubic (fcc) phase of the ternary Cr-Ni-C system and the Gibbs energies of formation of metastable Ni₂₃C₆ and Ni₇C₃ in the binary Ni-C system have been estimated from the experimental data of the ternary Cr-Ni-C alloys. The assessments were carried out simultaneously by using a computerized optimization technique. The thermodynamic parameters optimized in the present work are able to reproduce appropriately the experimental results in the Cr-C and Cr-Ni-C systems.     

Structurization in sintering of antifriction powder materials based on iron-copper alloys

The paper studies the contact interaction of the components in powders Fe-(Cu + Sn), Fe-(Cu + Sn + P + Pb), and Fe + B-(Cu + Sn + P + Pb) during sintering in hydrogen at 920 °C. It is shown that this interaction is responsible for the formation of both the interphase boundary and the general structure that defines the performance characteristics of an antifriction material. The interface and the phase and chemical composition of the products of interaction are examined. It is established that the powder composition Fe + Cu + Sn + P + B + Pb sintered in hydrogen at 920 °C is a microheterogeneous material whose matrix, which takes up the major load during friction, includes two phases: one based on iron alloyed with boron (Fe₂B), copper, tin, and phosphorus and the other based on copper including tin in the form of α-solid solution, phosphorus in the form of Cu₃P, and iron. Lead uniformly distributed over the matrix volume is the antifriction component of the material.     

A theoretical evaluation of chemical ordering and glass transition in liquid Mg-Sb alloys

In order to study the relation between chemical ordering and various criteria for glass formation, the thermodynamic properties of the Mg-Sb system are assessed. Thermodynamic models for the individual phases are applied and expressions for the Gibbs energy as a function of temperature and composition are obtained. Both the phase diagram and thermochemical data are calculated in satisfactory agreement with the experimental information. Isentropic temperatures (where liquid and solid have equal topological entropy) are calculated in order to investigate the thermodynamic glass temperature. It is found that the high-temperature phase β-Mg₃Sb₂ has an anomalously high entropy and it is suggested that the so-called Kauzmann paradox should be reformulated.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the MnO-TiO2, MgO-TiO2, FeO-TiO2, Ti2O3-TiO2, Na2O-TiO2, and K2O-TiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the MnO-TiO₂, MgO-TiO₂, FeO-TiO₂, Ti₂O₃-TiO₂, Na₂O-TiO₂, and K₂O-TiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag as a function of composition and temperature and equations for the Gibbs energies of all compounds as functions of temperature. The modified quasichemical model was used for the molten slag phases.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CaO-Al2O3, Al2O3-SiO2, and CaO-Al2O3-SiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the CaO-Al₂O₃, Al₂O₃-SiO₂, and CaO-Al₂O₃-SiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable data for the binary systems have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. With these binary parameters and those from the optimization of the CaO-SiO₂ system reported previously, the quasichemical model was used to predict the thermodynamic properties of the ternary slag. Two additional small ternary parameters were required to reproduce the ternary phase diagram and ternary activity data to within experimental error limits. The calculated optimized phase diagram and thermodynamic properties are self-consistent and are the most reliable currently available estimates of the true values.     

Thermodynamics of Mn in Cu-Mn Melts

The present work aimed to measure the thermodynamic data of manganese in Cu-Mn melts over a broad manganese concentration range, using the equilibrium among the liquid copper/MnO_(s)/CO-CO₂ gas mixture in the temperature range from 1673 K to 1873 K (1400 °C to 1600 °C). Darken’s quadratic formalism was introduced to correlate the activity coefficient of manganese in copper to composition, and the excess molar Gibbs energy change of mixing of Cu-Mn melts was described satisfactorily by Redlich–Kister type polynomial.     

Experimental investigation and thermodynamic calculation of the phase equilibria in the Cu-Sn and Cu-Sn-Mn systems

The phase equilibria in the Cu-rich portion of the Cu-Sn binary and Cu-Sn-Mn ternary systems have been determined using the diffusion-couple method, differential scanning calorimetry (DSC), high-temperature electron diffraction (HTED), and high-temperature X-ray diffraction (HTXRD) techniques. The present experimental results on the binary Cu-Sn system show the presence of the two-stage, second-order reaction A2 → B2 → D0₃ in the bcc-phase region, rather than a two-phase equilibrium between the disordered bcc (A2) and the ordered bcc (D0₃) phases, as reported before. Phase equilibria in the Cu-Sn-Mn ternary system in the composition range of 0 to 30 at. pct Sn and 0 to 30 at. pct Mn at 550 °C, 600 °C, 650 °C, and 700 °C have been determined, and a ternary compound (Cu₄MnSn) with a very small solubility has been detected. A thermodynamic analysis of the Cu-Sn-Mn ternary system including the Cu-Sn and Mn-Sn binary systems has also been carried out by the CALPHAD (Calculation of Phase Diagrams) method, in which the Gibbs energy of the bcc phase is described by the two-sublattice model in order to take into account the second-order A2/B2 ordering reaction. A consistent set of optimized thermodynamic parameters for the Cu-Sn-Mn system for describing the Gibbs energy of each phase results in a better fit between calculation and experiment.     

Experimental Study and Thermodynamic Optimization of the FeO-V203 System

Optimization of the phase diagram of FeO-V20a system is a part of an on-going research project to develop a self-consistent multi-component thermodynamic database for vanadium slag from hot metal. Due to the lack o{ ex- perimental data for optimization, a novel experimental investigation has been carried out by thermal analysis （DSC） with a series of slags on different V2 03 contents （i. e. 3mass%- 12mass%）. All available thermodynamic and phase diagram data for the binary systems have been simultaneously optimized with CALPHAD （Calculation of Phase Dia- grams） methods to give one set of model equations for the Gibbs free energy of the liquid slag as functions of compo- sition and temperature. The modified quasi-chemical model was used to describe the binary slag system. It was dem- onstrated that the calculated phase diagram with the optimized parameters was in good agreement with the experi- mental data.     

Calculation and evaluation of the gibbs energies of formation of Cr3C2, Cr7C3, and Cr23C6

A thermodynamic analysis of chemical composition data for a series of iron alloys containing chromium and carbon has been completed. These data were obtained from literature compilations for alloys equilibrated for extended times at 700 °C under neutral atmospheres. The results of this analysis, when supplemented with thermochemical data from the literature, permitted the calculation of the standard Gibbs energies of formation for the chromium carbides Cr₇C₃ and Cr₂₃C₆ over the range 600 to 1000 °C. These standard Gibbs energies were compared to data for these carbides from other sources. Available Gibbs energy data for the third pure chromium carbide, Cr₃C₂, were also evaluated. For each of these three compounds, a separation of the values for the Gibbs energy of formation into two distinct groups was observed. Each of these groups can be classed according to the nature of the experimental study used, whether it be a high temperature solid-gas equilibration involving a system of a carbide-chromic oxide-carbon (or chromium) with carbon monoxide, on one hand, or a series of investigations concerned mainly with electrolytic cell measurements, plus the work on which the present study is based. It is suggested that the differences in the Gibbs energies of formation for the respective carbides are associated with 1) the nonstoichiometric nature of these carbides and 2) possible dissolution of oxygen in the carbides during the equilibration studies.     

Simultaneous optimization of thermochemical data for liquid iron alloys containing C,N, Ti,Si, Mn,S, and P

A data base of thermochemical parameters for liquid iron-base alloys containing C, N, Ti, Si, Mn, S, and P is presented. A matrix of linear inequalities describing the experimental data among these elements was constructed. A set of internally consistent thermochemical data permitted by the uncertainties of the experiments was evaluated by means of a linear programming algorithm. Expressions for the interaction parameters of the solutes and the Gibbs energies of formation of the carbides, nitrides, carbonitrides, and sulfides of titanium were simultaneously optimized. It is shown that the resulting thermochemical data base reproduces the experimental data satisfactorily. DOMINIQUE BOUCHARD, formerly Graduate Student, école Polytechnique de Montréal.     

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.     

Interaction of exogenous zirconium oxide nanophases with sulfur and tin in nickel melts

The interaction of exogenous refractory compound (ZrO₂) nanoparticles with sulfur and tin, which are present as surfactants in model nickel melts, is studied. Thermodynamic calculations are performed to consider the versions of removal of sulfur and tin from a melt in the form of S₂, SO₂, H₂S, Sn, and SnO. It is shown that the probability of their removal under melting conditions is low. Their contents is found to decrease when ZrO₂ nanoparticles are introduced: the degree of removal is α = 12–18% S in a model Ni–S alloy and 14–20% Sn in a model Ni–Sn alloy.