Thermodynamic description of the Cu–Ag–Zr system

Based on the CALPHAD method, the Ag–Zr and Ag–Cu systems have been assessed thermodynamically. The excess Gibbs energy of the solution phases in the Cu–Ag–Zr system was modeled assuming random mixing of components. The ternary phase was defined as a stoichiometric compound due to the lack of efficient thermodynamic data. At first, parameters capable of describing all phases in the Ag–Zr and the Ag–Cu systems were assessed. Combined with the parameters of the Cu–Zr system assessed previously, the isothermal sections of the Cu–Ag–Zr system at 1023 K and 978 K were extrapolated, which can reproduce the measured phase-relations.     

An optimal method to calculate the viscosity of simple liquid ternary alloys from the measured binary data

An optimal method to calculate the viscosity of simple liquid ternary alloys from the measured binary data is investigated in this paper. In order to find a relationship which describes the ternary viscosity data from binary data most adequately, a comparison was made between three different approaches tested on the example of the Au–Ag–Cu system. The optimal method turned out to be the extension of the Redlich–Kister polynomial to excess viscosity without any ternary term. This optimal method was applied further on the Fe–Ni–Co system. The estimation of viscosities for liquid Fe–Ni–Co alloys was done in different sections with molar ratio of two components equal to 1:1, 1:3 and 3:1. A diagram showing iso-viscosity lines was constructed at the investigated temperature of 1873 K.     

Experimental study and thermodynamic assessment of the Ag–Ti system

A thermodynamic assessment of the binary Ag–Ti system was performed based on the evaluation of the literature and the results of the present experiments. For the experimental study, special deep embedding diffusion couples were prepared and analyzed by scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). The phase equilibrium relationship and the conjugate phase compositions were determined at 1023 K, 1253 K, 1373 K and 1474 K respectively. For the thermodynamic assessment, the Redlich–Kister polynomial was used to describe the solution phases, liquid (L), bcc, hcp, and fcc. The sublattice-compound energy model was employed to describe the intermediate phase, (AgTi), with a homogeneity range. The other intermediate phase, AgTi₂, without a homogeneity range was treated as the stoichiometric phase. A set of self-consistent thermodynamic parameters of the Ag–Ti system has been obtained. The calculated phase diagram was presented and compared with the experimental data.     

The experimental study of the Bi–Sn, Bi–Zn and Bi–Sn–Zn systems

The binary Bi–Sn was studied by means of SEM (Scanning Electron Microscopy)/EDS (Energy-Dispersive solid state Spectrometry), DTA (Differential Thermal Analysis)/DSC (Differential Scanning Calorimetry) and RT-XRD (Room Temperature X-Ray Diffraction) in order to clarify discrepancies concerning the Bi reported solubility in (Sn). It was found that (Sn) dissolves approximately 10 wt% of Bi at the eutectic temperature.

The experimental effort for the Bi–Zn system was limited to the investigation of the discrepancies concerning the solubility limit of Zn in (Bi) and the solubility of Bi in (Zn). Results indicate that the solubility of both elements in the respective solid solution is approximately 0.3 wt% at 200 C.

Three different features were studied within the Bi–Sn–Zn system. Although there are enough data to establish the liquid miscibility gap occurring in the phase diagram of binary Bi–Zn, no data could be found for the ternary. Samples belonging to the isopleths with w(Bi) 10% and w(Sn) 5%, 13% and 19% were measured by DTA/DSC. The aim was to characterize the miscibility gap in the liquid phase. Samples belonging to the isopleths with w(Sn) 40%, 58%, 77/81% and w(Zn) 12% were also measured by DTA/DSC to complement the study of Bi–Sn–Zn. Solubilities in the solid terminal solutions were determined by SEM/EDS. Samples were also analyzed by RT-XRD and HT-XRD (High Temperature X-Ray Diffraction) confirming the DTA/DSC results for solid state phase equilibria.     

Activity measurement of the constituents in molten Fe–B and Fe–B–C alloys

The distribution ratios of Fe and B between molten Fe–B alloy and molten Ag were measured at temperatures between 1573 and 1923 K. Also, distribution ratios of Fe and B between molten Fe–B–C_satd. alloys and molten Ag were measured at 1873 K. It was found that the excess Gibbs free energy of mixing in molten Fe–B and Fe–B–C alloys can be expressed by utilizing the Redlich–Kister polynomial. The activity curves of the elements in molten Fe–B alloy and Fe–B–C alloy were estimated.     

Thermodynamic assessments of the Ni–Pt and Al–Ni–Pt systems

The Ni–Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni₃Pt–L1₂, NiPt–L1₀ and NiPt₃–L1₂, are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al–Ni and Al–Pt, the Al–Ni–Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.     

First-principles calculations assisted thermodynamic assessment of the Pt–Ga–Ge ternary system

The Pt–Ga–Ge ternary system was thermodynamically assessed by the CALPHAD (CALculaton of PHAse Diagram) approach with help of first-principles calculations. Firstly, the formation enthalpies of the Pt–Ge and Pt–Ga compounds were calculated by the first-principles method. Subsequently, the Pt–Ge system was modeled and the Pt–Ga system was re-assessed. The solution phases, Liquid, Diamond_A4 (Ge) and Fcc_A1 (Pt), were modeled as substitutional solutions, of which the excess Gibbs energy was formulated with the Redlich–Kister polynomial. The binary intermetallics, Ga₇Pt₃, Ga₂Pt, Ga₃Pt₂, GaPt, Ga₃Pt₅, GaPt₂, Ge₂Pt, Ge₃Pt₂, GePt, Ge₂Pt₃ and GePt₂, were treated as stoichiometric compounds while GePt₃ was described with a two-sublattice model. Finally, based on the currently optimized Pt–Ga and Pt–Ge binary systems along with the already assessed Ga–Ge system, phase equilibria in the Pt–Ga–Ge ternary system were extrapolated. The isothermal sections at 473 K, 973 K and 1073 K of the ternary system were calculated, showing good agreement with the experimental data. In addition, the liquidus projection of the Pt–Ga–Ge ternary system was predicted using the obtained model parameters.     

Construction of modified embedded atom method potentials for the study of the bulk phase behaviour in binary Pt–Rh, Pt–Pd, Pd–Rh and ternary Pt–Pd–Rh alloys

A first attempt is made to simulate the solid part of the phase diagram of the ternary Pt–Pd–Rh system. To this end, Monte Carlo (MC) simulations are combined with the Modified Embedded Atom Method (MEAM) and optimised parameters entirely based on Density Functional Theory (DFT) data. This MEAM potential is first validated by calculating the heat of mixing or the demixing phase boundary for the binary subsystems Pt–Rh, Pt–Pd and Pd–Rh. For the disordered alloy systems Pt–Rh and Pt–Pd, the MC/MEAM simulation results show a slightly exothermic heat of mixing, thereby contradicting any demixing behaviour, in agreement with other theoretical results. For the Pd–Rh system the experimentally observed demixing region is very well reproduced by the MC/MEAM simulations. The extrapolation of the MEAM potentials to ternary systems is next validated by comparing DFT calculations for the energy of formation of ordered Pt–Pd–Rh compounds with the corresponding MEAM energies. Finally, the validated potential is used for the calculation of the ternary phase diagram at 600 K.     

A thermodynamic description of the Al–Ca–Zn ternary system

A comprehensive thermodynamic database of the Al–Ca–Zn ternary system is presented for the first time. Critical assessment of the experimental data and re-optimization of the binary Al–Zn and Al–Ca systems have been performed. The optimized model parameters of the third binary system, Ca–Zn, are taken from the previous assessment of the Mg–Ca–Zn system by the same authors. All available as well as reliable experimental data both for the thermodynamic properties and phase boundaries are reproduced within experimental error limits. In the present assessment, the modified quasichemical model in the pair approximation is used for the liquid phase and Al_FCC phase of the Al–Zn system to account for the presence of the short-range ordering properly. Two ternary compounds reported by most of the research works are considered in the present calculation. The liquidus projections and vertical sections of the ternary systems are also calculated, and the invariant reaction points are predicted using the constructed database.     

Predicting of the thermodynamic properties for the ternary system Ga-Sb-Bi

Results of thermodynamic predicting methods applied to Ga-Sb-Bi system are presented in this paper. Chou, Toop and Hillert model were used for the calculation and comparison of the characteristic thermodynamic quantities in five selected sections of the ternary system Ga-Sb-Bi at a temperature of 1073K.     

Solubility prediction in the ternary systems NaCl–RbCl–H2O, KCl–CsCl–H2O and KBr–CsBr–H2O at 25 C using the ion-interaction model

The component solubilities in NaCl–RbCl–H₂O, KCl–CsCl–H₂O and KBr–CsBr–H₂O systems at 25 C were calculated by using the Pitzer ion interaction model and its extended HW models. Excellent agreement with experimental solubilities indicated that the models can be successfully used to calculate the component solubilities. This study affords the necessary parameters for solubility predictions of complicated systems containing rubidium and caesium and establishes a theoretical basis for the separation of these valuable metals from salt lake brine.     

Water activities, osmotic and activity coefficients of the system (NH4)2SO4–K2SO4–H2O at the temperature 298.15 K

The mixed aqueous electrolyte system consisting of ammonium and potassium sulfates has been studied using the hygrometric method at the temperature 298.15 K. The water activities are measured at total ionic strength values ranging from 0.60 to 8.25 mol kg⁻¹ for different ionic strength fractions (y) of (NH₄)₂SO₄ with y=0.20, 0.50 and 0.80. The obtained data allow the deduction of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii–Stokes–Robinson (ZSR), Kusik and Meissner (KM), Robinson and Stokes (RS), Lietzke and Stoughton (LS II), Reilly–Wood and Robinson (RWR) and Pitzer models. From these measurements, the new Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture.     

The phase equilibria in the Mg–Ni–Ca system

The three binary systems Mg–Ni, Ca–Ni and Mg–Ca have been re-optimized. A self-consistent thermodynamic database of the Mg–Ni–Ca system is constructed by combining the optimized parameters of these three constituent binaries. Lattice stability values are not added to the pure elements Mg-hcp, Ni-fcc, Ca-fcc and Ca-bcc to construct this database. The Redlich–Kister polynomial model is used to describe the liquid and the terminal solid solution phases, and the sublattice model is used to describe the non-stoichiometric phase, in this system. The constructed database is used to calculate the three binary and the ternary systems. The calculated binary phase diagrams along with their thermodynamic properties such as Gibbs energy, enthalpy, entropy and activities are found to be in good agreement with experimental data from the literature. This is the first attempt to construct the ternary phase diagram of the Mg–Ni–Ca system. The established database for this system predicted three ternary eutectic, five ternary quasi-peritectic, two ternary peritectic and two saddle points.     

Thermodynamic description of the Sn–Ag–Au ternary system

Gibbs energy of hcp_A3 phase in the Ag–Sn binary system has been reassessed using compatible lattice stability. Combined with previous assessments of the Ag–Au and Au–Sn binary systems, the Sn–Ag–Au ternary system has been thermodynamically optimized using the CALPHAD method on the basis of available experimental information. The solution phases including liquid, fcc_A1, hcp_A3 and bct_A5, are modeled as substitutional solutions, while the intermediate compound Ag₃Sn is treated using a 2-sublattice model because Au can be dissolved to a certain degree. The solubility of Ag in the Au–Sn intermediate phases, D0₂₄, Au₅Sn, AuSn, AuSn₂ and AuSn₄, is not taken into account. Thermodynamic properties of liquid alloys, liquidus projection and several vertical and isothermal sections of this ternary system have been calculated, which are in reasonable agreement with the reported experimental data.     

Computer-aided thermodynamics of fcc solid ternary Fe–Co–Cr alloys by Knudsen cell mass spectrometry

The fcc solid ternary Fe–Co–Cr alloys have been investigated thermodynamically by means of computer-aided Knudsen cell mass spectrometry. The “Digital Intensity Ratio” (DIR) method has been applied for the determination of the thermodynamic excess properties. The ternary thermodynamically adapted power (TAP) series concept is used for the algebraic representation of the molar excess properties. The corresponding TAP parameters as well as the values of the molar excess Gibbs energies G^E, of the molar heats of mixing H^E, of the molar excess entropies S^E, and of the thermodynamic activities at 1673 K are presented.