Thermodynamic modeling of the Ce–Zn and Pr–Zn systems

In order to develop the thermodynamic database of phase equilibria in the Mg–Zn–Re (Re: rare earth element) base alloys, the thermodynamic assessments of the Ce–Zn and Pr–Zn systems were carried out by using the calculation of phase diagrams (CALPHAD) method on the basis of the experimental data including thermodynamic properties and phase equilibria. Based on the available experimental data, Gibbs free energies of the solution phases (liquid, bcc, fcc, hcp and dhcp) were modeled by the subregular solution model with the Redlich–Kister formula, and those of the intermetallic compounds were described by the sublattice model. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Ce–Zn and Pr–Zn binary systems. An agreement between the present calculated results and experimental data is obtained.     

Enthalpies of formation for the Al–Cu–Ni–Zr quaternary alloys calculated via a combined approach of geometric model and Miedema theory

A method to extrapolate the thermodynamic properties of quaternary alloys from constitutive binary systems is presented. The method is based on Miedema's theory, and the asymmetry of thermodynamic properties of constitutive binary alloys is considered in the present model. The dependence of asymmetric constituent on the choice in Toop model has been overcome. This method has been applied to calculate the enthalpies of formation for ternary alloys. In the present work, the proposed method is used to calculate the mixing enthalpies of Al–Cu–Ni–Zr quaternary alloys and its constitutive subsystems. The good agreement between calculation and experimental data indicates that the present method is reasonable for predicting the thermodynamic properties of multi-component system.     

Phase equilibria and thermal analysis of Si–C–N ceramics

The phase reactions, crystallization behaviour and thermal degradation of two Si–C–N ceramics derived from precursors VT50 and NCP200, respectively, were studied by means of CALPHAD type thermodynamic calculations and experimental investigations by DTA/TG, XRD and SEM/EDX. The phase reaction Si₃N₄+3C=3SiC+2N₂ proceeds during the thermal degradation of both ceramics. Additionally, the phase reaction Si₃N₄=3Si+2N₂ occurs during the thermal degradation of the NCP200 ceramic. To explain quantitatively the high temperature behaviour of Si–C–N ceramics, thermodynamic functions, the reaction scheme, isothermal sections, isopleths, phase fraction diagrams and phase composition diagrams (for gas partial pressures) were calculated. The computer simulations were confirmed by the experiments for both ceramics.     

Thermodynamic assessment of the Mo–Re binary system

The existing Mo–Re phase diagrams are reviewed and a thermodynamic calculation of the Mo–Re binary system is undertaken. The Gibbs energies are estimated for liquid, bcc (Mo), hcp (Re), σ and χ phases. The liquid, bcc (Mo) and hcp (Re) phases are described by a regular solution model, whereas the σ and χ phases are described respectively by three-sublattice models. For the σ phase, two thermodynamic models are used for calculations and the results are compared. The models take into account the crystallographic structure and similarity between the σ and χ phases. The calculated results remove the ambiguity of the existing phase diagram data and are compared with the experimental data in the literature.     

Thermodynamic modeling of Ru–Zr and Hf–Ru systems

In this paper, an assessment of the binary Ru–Zr and Hf–Ru systems is presented. The thermodynamic evaluation is based on diagrammatic investigations and high-temperature calorimetric measurements for the formation of the three intermediate compounds. The present work proposes thermodynamic modeling of the binaries calculated according to the CALPHAD method and carried out using the PARROT module in the Thermo-Calc software. The liquid phase and the solution phases (Ru)-HCP-A3, (Zr)-HCP-A3, (βZr)-BCC-A2, (Hf)-HCP-A3 and (βHf)-BCC-A2 are treated as substitutional solutions. The intermetallic Laves phase Ru₂Zr-C14 is modeled with the sublattice formalism. The RuZr-B2 and HfRu-B2 phases are treated as ordered phases originating, respectively, from (βZr)-BCC-A2 and (βHf)-BCC-A2 disordered phases. Considering the relative uncertainty of experimental data due to high temperatures, a good agreement is obtained between calculated and experimental phase diagrams. The optimized set of coefficients and the calculated isothermal section are provided.     

Investigations of interfacial reactions of Sn–Zn based and Sn–Ag–Cu lead-free solder alloys as replacement for Sn–Pb solder

The interfacial reactions of Sn–Zn based solders and a Sn–Ag–Cu solder have been compared with a eutectic Sn–Pb solder. During reflow soldering different types of intermetallic compounds (IMCs) are found at the interface. The morphologies of these IMCs are quite different for different solder compositions. As-reflowed, the growth rates of IMCs in the Sn–Zn based solder are higher than in the Sn–Ag–Cu and Sn–Pb solders. Different types of IMCs such as γ-Cu₅Zn₈, β-CuZn and a thin unknown Cu–Zn layer are formed in the Sn–Zn based solder but in the cases of Cu/Sn–Pb and Cu/Sn–Ag–Cu solder systems Cu₆Sn₅ IMC layers are formed at the interface. Cu₆Sn₅ and Cu₃Sn interfacial IMCs are formed in the early stages of 10 min reflow due to the limited supply of Sn from the Sn–Pb solder. The spalling of Cu–Sn IMCs is observed only in the Sn–Ag–Cu solder. The size of Zn platelets is increased with an increase of reflow time for the Cu/Sn–Zn solder system. In the case of the Sn–Zn–Bi solder, there is no significant increase in the Zn-rich phases with extended reflow time. Also, Bi offers significant effects on the wetting, the growth rate of IMCs as well as on the size and distribution of Zn-rich phases in the β-Sn matrix. No Cu–Sn IMCs are found in the Sn–Zn based solder during 20 min reflow. The consumption of Cu by the solders are ranked as Sn–Zn–Bi > Sn–Ag–Cu > Sn–Zn > Sn–Pb. Despite the higher Cu-consumption rate, Bi-containing solder may be a promising candidate for a lead-free solder in modern electronic packaging taking into account its lower soldering temperature and material costs.     

Thermodynamic optimization of the boron-cobalt-iron system

A thermodynamic optimization of the boron-cobalt-iron ternary system is performed based on thermodynamic models of the three constitutional binary systems and the experimental data on phase diagrams and thermodynamic properties of the ternary system. The liquid, fcc_A1, bcc_A2 and hcp_A3 solution phases are described by the substitutional solution model. The three intermediate line compounds, (Co,Fe)B, (Co,Fe)₂B and (Co,Fe)₃B, are described by the two sublattice model. A set of thermodynamic parameters are obtained. The calculated phase diagram and thermodynamic properties are in reasonable agreement with most of the experimental data.     

Oxidation behavior of the (Cu78Y22)98Al2 bulk metallic glass containing Cu5Y-particle composite at 400–600 °C

The oxidation behavior of the (Cu₇₈Y₂₂)₉₈Al₂ bulk metallic glass containing 55% Cu₅Y particles (CYA-composite) was studied over the temperature range of 400–600 °C in dry air. The results generally showed that the oxidation kinetics of the composite obeyed a two-stage parabolic-rate law, with its steady-state parabolic-rate constants (k_p values) increased with temperature. In addition, the oxidation rates of the composite were significantly lower than those of the polycrystalline Cu–20%Y alloy. The scales formed on the composite consisted mostly of hexagonal-Y₂O₃ (h-Y₂O₃) and minor CuO, while significant amounts of Cu₂O and CuO, with minor amounts of Y₂O₃ were detected for the Cu–20%Y alloy. It was found that the absence of Cu₂O is responsible for the slower oxidation rates of CYA-composite.     

Experimental investigation and thermodynamic description of the In–Sb–Sn ternary system

Phase equilibria in the In–Sb–Sn ternary system have been studied experimentally and calculated by the CALPHAD method. Solubility of indium in the SbSn phase was experimentally established. Our own SEM–EDX results were used together with the literature data for thermodynamic modeling of the Gibbs energy of the SbSn intermediate phase. Optimized phase diagrams of the isothermal sections at 100 °C and 300 °C were compared with the experimental results from this work and literature. Three calculated vertical sections were compared with the DTA results from this work and with available thermal analysis data reported in the literature. Some calculated thermodynamic functions are compared with experimental values reported in the literature. Reasonable agreement between calculations and experimental data was observed in all cases.     

Reevaluation of thermodynamic models for phase diagram evaluation

Several thermodynamic models for calculating binary phase diagrams published in the literature have been reevaluated. Problems in some of these models are already evident in the models themselves and may also be seen in the resulting calculated phase diagrams. When a calculation is attempted, thermodynamic models with quite different formulations may result in very similar proposed phase diagrams. In such cases, if experimental data of a binary phase diagram can be represented reasonably well by several different thermodynamic models, a simpler model often provides the clearest insight into the basic properties of the system. If a calculated phase diagram results in unusual phase relationships, the adopted thermodynamic model may be inappropriate or may involve unrealistic parameters. If the thermodynamic model is clearly unrealistic and yet the calculated phase diagram appears to be normal, errors in calculation or in interpretation may be suspect. Various examples of unlikely combinations of thermodynamic models and phase diagrams are discussed.     

Thermodynamic Database for Phase Diagrams of Mn-RE Binary Alloy Systems

Thermodynamic assessment of Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems has been carried out by means of the calculation of phase diagrams method on the basis of experimental data including phase equilibria and thermodynamic properties. The Gibbs free energies of liquid phase and solid solution phases in the Mn-RE systems were all described by the subregular solution model with the Redlich–Kister formulation, whereas those of intermetallic compounds were described by the sublattice model. Sets of thermodynamic functions with self-consistent parameters leading to satisfactory agreement between calculated results and experimental data were eventually obtained. A primary thermodynamic database for the phase diagrams of the Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems was developed from these essential thermodynamic parameters. This database can be used not only to calculate the phase equilibria and thermodynamic properties of binary Mn-RE systems but also to extrapolate to higher-order systems, which can provide theoretical guidance for design and development of high-performance Mn-RE alloy materials.     

Ba-eu (barium-europium)

Several thermodynamic models for calculating binary phase diagrams published in the literature have been reevaluated. Problems in some of these models are already evident in the models themselves and may also be seen in the resulting calculated phase diagrams. When a calculation is attempted, thermodynamic models with quite different formulations may result in very similar proposed phase diagrams. In such cases, if experimental data of a binary phase diagram can be represented reasonably well by several different thermodynamic models, a simpler model often provides the clearest insight into the basic properties of the system. If a calculated phase diagram results in unusual phase relationships, the adopted thermodynamic model may be inappropriate or may involve unrealistic parameters. If the thermodynamic model is clearly unrealistic and yet the calculated phase diagram appears to be normal, errors in calculation or in interpretation may be suspect. Various examples of unlikely combinations of thermodynamic models and phase diagrams are discussed.     

Thermal expansion studies on Th(MoO4)2, Na2Th(MoO4)3 and Na4Th(MoO4)4

Thermal expansion behavior of Th(MoO₄)₂, Na₂Th(MoO₄)₃ and Na₄Th(MoO₄)₄ was studied under vacuum in the temperature range of 298–1123 K by high temperature X-ray diffractometer. Th(MoO₄)₂ was synthesized by reacting ThO₂ with 2 mol of MoO₃, at 1073 K in air and Na₂Th(MoO₄)₃ and Na₄Th(MoO₄)₄ were prepared by reacting Th(MoO₄)₂ with 1 and 2 mol of Na₂MoO₄, respectively at 873 K in air. The XRD data of Th(MoO₄)₂ was indexed on orthorhombic system where as XRD data of Na₂Th(MoO₄)₃ and Na₄Th(MoO₄)₄ were indexed on tetragonal system. The lattice parameters and cell volume of all the three compounds, fit into polynomial expression with respect to temperature, showed positive thermal expansion (PTE) up to 1123 K. The average value of thermal expansion coefficients for Th(MoO₄)₂, Na₂Th(MoO₄)₃ and Na₄Th(MoO₄)₄ were determined from the high temperature data.     

Thermodynamic analysis of alloys Ti–Al, Ti–V, Al–V and Ti–Al–V

Thermodynamic analysis of three binary Ti-based alloys: Ti–Al, Ti–V, and Al–V, as well as ternary alloy Ti–Al–V, is shown in this paper. Thermodynamic analysis involved thermodynamic determination of activities, coefficient of activities, partial and integral values for enthalpies and Gibbs energies of mixing and excess energies at four different temperatures: 2000, 2073, 2200 and 2273 K, as well as calculated phase diagrams for the investigated binary and ternary systems. The FactSage is used for all thermodynamic calculations.     

Thermodynamic optimization of the binary YbCl<Subscript>3</Subscript>-AECl<Subscript>2</Subscript> (AE=Mg,Ca, Sr,Ba) systems

By using the CALPHAD technique, an optimization of the binary YbCl₃-AECl₂ (AE=Mg, Ca, Sr, Ba) systems was carried out. From measured phase equilibrium data and experimental integral properties, the YbCl₃-AECl₂ phase diagrams were optimized and calculated. A set of thermodynamic functions was optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.     

Activity measurements of Al and Cu in Si–Al–Cu melt at 1273 and 1373 K by the equilibration with molten Pb

For the effective control of Al introduction to solidified Si during the solidification refining of Si with the Si–Al-based melt for the solar cell material or the LPE Si film growth processes from the Si–Cu–Al solvent, thermodynamic properties of the Si–Al–Cu melt were investigated at 1273 and 1373 K. Activities of Al and Cu in the Si–Al–Cu melt were measured by the equilibration with molten Pb. Also, the excess Gibbs energy of the melt was studied by the ternary regular solution model.

The evaluated thermodynamic properties of the Si–Al–Cu melt indicated that Cu addition to the Si–Al melt brings the smaller activity coefficient of Al and is effective for reducing the Al content of solidified Si from the melt more effectively than its dilution effect for Al.