A thermodynamic study of phase equilibria in the Au-Sb-Sn solder system

To design and develop high-temperature solder alloys, the thermodynamic calculations of phase equilibria have been performed on the binary Au-Sb and ternary Au-Sb-Sn systems over the entire composition range. The Gibbs free energy of individual phases has been approximated using a subregular-solution model, and the thermodynamic parameters for each phase have been evaluated using available experimental information on phase boundaries and other related thermodynamic properties. The calculated phase diagrams and thermodynamic quantities of the Au-Sb binary system show good agreement with experimental data, and the liquidus projection and the vertical sections in the Au-Sb-Sn ternary system are well reproduced using assessed thermodynamic parameters derived in this work.     

Thermodynamic Assessments of the Ag-Ni Binary and Ag-Cu-Ni Ternary Systems

The phase diagram of the Ag-Ni binary system has been evaluated by using the calculation of phase diagrams (CALPHAD) method based on experimental data of the phase equilibria and thermodynamic properties. Gibbs free energies of the liquid and fcc phases were described by the subregular solution model with the Redlich–Kister equation. On the basis of the thermodynamic parameters of the Ag-Ni, Ag-Cu, and Cu-Ni systems, and experimental information of the phase equilibria in the Ag-Cu-Ni system, the thermodynamic assessment in the Ag-Cu-Ni system was carried out. The calculated results in both the Ag-Ni and Ag-Cu-Ni systems are in reasonable agreement with experimental data.     

Thermodynamic assessments of the Sn-In and Sn-Bi binary systems

A thermodynamic evaluation of the Sn-ln and Sn-Bi system has been made by using thermodynamic models for the Gibbs energy of the individual phases. An optimized set of thermodynamic parameters was obtained taking into consideration relevant experimental information. The thermodynamic parameters of the Sn-ln and Sn-Bi systems and comparisons between calculation and experimental data are presented.     

Thermodynamic assessment of the Sn-Co lead-free solder system

The Sn-Co-Cu eutectic alloy can be a less expensive alternative for the Sn-Ag-Cu alloy. In order to find the eutectic solder composition of the Sn-Co-Cu system, the Sn-Co binary system has been thoroughly assessed with the calculation of phase diagram (CALPHAD) method. The liquid phase, the FCC and HCP Co-rich solid solution, and the BCT Sn-rich solid solution have been described by the Redlich-Kister model. The Hillert-Jarl-Inden model has been used to describe the magnetic contributions to Gibbs energy in FCC and HCP. The CoSn₂, CoSn, Co₃Sn_{2_}β, and Co₃Sn_{2_}α phases have been treated as stoichiometric phases. A series of thermodynamic parameters have been obtained. The calculated phase diagram and thermodynamic properties are in good agreement with the experimental data. The obtained thermodynamic data was used to extrapolate the ternary Sn-Co-Cu phase diagram. The composition of the Sn-rich eutectic point of the Sn-Co-Cu system was found to be 224°C, 0.4% Co, and 0.7% Cu.     

Studies of the Ag-In phase diagram and surface tension measurements

The phase boundaries of the Ag-In binary system were determined by the diffusion couple method, differential scanning calorimetry (DSC) and metallographic techniques. The results show that the region of the (hcp) phase is narrower than that reported previously. Thermodynamic calculation of the Ag-In system is presented by taking into account the experimental results obtained by the present and previous works, including the data on the phase equilibria and thermochemical properties. The Gibbs energies of liquid and solid solution phases are described on the basis of the sub-regular solution model, and that of the intermetallic compounds are based on the two-sublattices model. A consistent set of thermodynamic parameters has been optimized for describing the Gibbs energy of each phase, which leads to a good fit between calculated and experimental results. The maximum bubble pressure method has been used to measure the surface tension and densities of liquid In, Ag, and five binary alloys in the temperature range from 227°C to about 1170°C. ON the basis of the thermodynamic parameters of the liquid phase obtained by the present optimization, the surface tensions are calculated using Butler’s model. It is shown that the calculated values of the surface tensions are in fair agreement with the experimental data.     

Thermodynamic modeling of the Au-In-Sb ternary system

The phase diagram of the Au-In-Sb ternary system is of importance in predicting the interface reaction between In-based solders and the Au substrate. Using the calculated phase diagram method and based on experimental data of thermodynamic properties and phase boundaries, the Au-Sb binary system was assessed, and the In-Sb binary system was revised. On the basis of the constituent binary systems, Au-Sb, In-Sb, and Au-In, the Au-In-Sb ternary system was modeled. Several isothermal and vertical sections were calculated, among which the one at 500 K reproduces the experimental diagram well.     

Interfacial reaction between Sn-Bi alloy and Ni substrate

Interfacial reactions between Sn-Bi alloys of different compositions and Ni substrates at 423 K for different durations were investigated. Only one interfacial phase, Ni₃Sn₄, was detected despite the existence of several other intermetallic compounds (IMCs) in Ni-Sn and Ni-Bi binary systems. This observation (only Ni₃Sn₄ was formed at the interface) was explained as a combination of the driving force for formation of the IMC and diffusion of Ni. The change of Ni₃Sn₄ layer thickness as a function of annealing time, which obeys a parabolic rule, was further confirmed. The thickness of Ni₃Sn₄ was also found to decrease with increasing Bi content in the Sn-Bi alloy.     

Thermodynamic Assessment of Phase Equilibria in the Sn-Ag-Ni System with Key Experimental Verification

The phase transformations of the Sn-Ag-Ni system were investigated by means of differential scanning calorimetry (DSC). Based on the experimental data of phase equilibria and thermodynamic properties determined by the present work and previous literature, the thermodynamic assessments of the Sn-Ag-Ni system were carried out using the calculation of phase diagrams (CALPHAD) method. The thermodynamic parameters for describing the phase equilibria were optimized, and reasonable agreement between the calculations and experimental data was obtained in the Sn-Ag-Ni ternary system.     

Experimental determination and thermodynamic calculation of the phase equilibria and surface tension in the Sn-Ag-In system

The phase equilibria of the Sn-Ag-In system were investigated by means of differential scanning calorimetry (DSC) and metallography. The isothermal sections at 180–600°C, as well as some vertical sections, were determined. Thermodynamic assessment of this system was also carried out based on the experimental data of thermodynamic properties and phase equilibria using the calculation of phase diagram (CALPHAD) method, in which the Gibbs energies of the liquid, fcc, and hcp phases are described by the subregular solution model, and those of compounds are represented by the sublattice model. The thermodynamic parameters for describing the phase equilibria were optimized, and reasonable agreement between the calculated and experimental results was obtained. The maximum bubble-pressure method and dilatometric method have been used in measurements of the surface tension and density of the binary In-Sn and ternary (Sn-3.8Ag)_eut + In (5 at.% and 10 at.%) liquid alloys, respectively. The experiments were performed in the temperature range from 160–930°C. The experimental data of the surface tension were compared with those obtained by the thermodynamic calculation of Butler’s model.     

Thermodynamic modeling of the Au-In-Sn system

The phase diagram of the Au-In-Sn system is of importance in developing materials of high performance in electronic packaging as well as in simulating the interfacial reaction between Sn-In and Au. By using the calculation of phase diagram (CALPHAD) method, phase equilibria in the Au-Sn binary system has been optimized based on experimental thermodynamic property and recently renewed phase boundaries. Combined with two binary systems, Au-In and In-Sn, in addition to the reported experimental isothermal section of the Au-In-Sn system, the Au-In-Sn ternary system has been modeled, and three isothermal sections at 300 K, 500 K, and 700 K and three vertical sections, Au-In_0.2Sn_0.8, Au-In_0.5Sn_0.5, and Au-In_0.7Sn_0.3, of the Au-In-Sn ternary system have been further calculated.     

Reactive wetting between molten Sn-Bi and Ni substrate

Wetting and interfacial reactions occurred when molten Sn-Bi alloys were in contact with a Ni substrate. Wetting properties of Sn-Bi alloys on the Ni substrate and their interfacial reactions were examined, and the effects of interfacial reactions on wetting properties were discussed. Couples made of various molten Sn-Bi alloys and Ni substrates were reacted at 300°C. It was found that, when the Bi content was greater than 98 wt.%, the intermetallic phase formed at the interface was NiBi₃ phase. The Ni₃Sn₄ phase was found in the other Sn-Bi/Ni couples that had Bi contents varied from 92 wt.% to 97.5 wt.%. An isothermal section at 300°C for the ternary Sn-Bi-Ni system was proposed to illustrate the reaction paths of Sn-Bi/Ni couples. Wetting properties, including wetting time and wetting force of molten Sn-Bi alloys, were determined by using a wetting balance. Surface tensions at 300°C were calculated based on the experimental measurements. For molten Sn-Bi alloys with Bi contents varying from 92 wt.% to 99 wt.%, their surface tensions were all about 0.34 N/m. On the basis of theoretical analysis and experimental observations, the surface tensions of molten metals, determined by using the wetting balance, are not significantly affected if the interfacial reaction is not excessive. However, the wetting time determined by using the wetting balance was altered by the reaction that occurred and the compound formed at the interface.     

A thermodynamic study of the phase equilibria in the Bi-Sn-Sb system

A thermodynamic study has been carried out on the Bi-Sn-Sb ternary alloy system. The Gibbs energy of individual phases has been approximated using the regular solution, two-sublattice model, and the thermodynamic parameters for each phase have been evaluated using the available experimental information on phase boundaries and other related thermodynamic properties. Thermal analysis experiments have also been performed on several ternary alloys to re-examine and augment the available ternary experimental data. The set of evaluated thermodynamic parameters arrived at in this study, enables reproducible calculations of the liquidus and solidus temperatures and vertical section diagrams quite satisfactorily.     

Experimental Determination and Thermodynamic Modeling of the Sn-Rich Corner of the Ternary Ni-Pd-Sn Phase Diagram at 250°C

The Sn-rich portion of the phase diagram for the Ni-Pd-Sn ternary system was preliminarily obtained by interpolation of the three constituent binary systems using the Muggianu method. Based on this proposition, 23 Ni-Pd-Sn alloys were prepared and annealed at 250°C. The annealed alloys were analyzed by scanning electron microscopy, electron probe microanalysis, electron backscatter diffraction, and x-ray diffraction. All the binaries adjacent to the Sn-rich corner (i.e., PdSn₄, PdSn₃, PdSn₂, and Ni₃Sn₄) were found to have remarkable ternary solubility. The experimental results presented herein, together with a thermodynamic interpolation of the ternary system based on the results from the binary systems, were used to calculate the ternary phase diagram using the calculation of phase diagrams (CALPHAD) method. A substitution model was used to describe the Gibbs free energies of the liquid and solid solution phases, and a sublattice model was used to describe intermetallic compounds. A consistent set of thermodynamic parameters was obtained, ultimately leading to a better fit between the calculated results and the experimental data for this system.     

Thermodynamic Descriptions for the Cd-Te,Pb-Te,Cd-Pb and Cd-Pb-Te Systems

The thermodynamic behaviors of the Cd-Te, Pb-Te, Cd-Pb and Cd-Pb-Te systems are critically analyzed in this work by means of the calculation of phase diagrams (CALPHAD) method. The liquid phases containing Te are described by the associated solution model, which is capable of dealing with V-shaped curves of mixing enthalpies in solution phases, sharp maxima of liquidus curves in phase diagrams, and abrupt changes in activity plots. The binary compounds, CdTe and PbTe, are considered to be stoichiometric in the two binary systems, but they form a line compound described by (Cd,Pb)₁(Te)₁ in the ternary system. The fcc phase, in which only Cd and Pb elements are present, is treated with the substitutional solution model. The experimental data available in the literature are extensively assessed, from which the thermodynamic parameters necessary for each phase are obtained. Various calculated phase equilibria and thermodynamic properties are compared with the experimental data. The excellent agreement indicates that this work contributes to the study of phase stabilities in the Cd-Pb-Te system.     

Diffusivities and Atomic Mobilities of Sn-Bi and Sn-Pb Melts

The recently developed Arrhenius formula of the modified Sutherland equation was first employed to calculate the self- and impurity diffusivities in liquid Sn, Bi, and Pb. The reliability of the calculated results was validated in comparison with the critically reviewed literature data. Based on the reliable tracer and chemical diffusivities available in the literature, the atomic mobility parameters in both Sn-Bi and Sn-Pb melts were then evaluated by the DICTRA (DIffusion-Controlled TRAnsformations) software package with the aid of thermodynamic parameters. Comprehensive comparisons show that most of the measured and theoretical diffusivities in Sn-Bi and Sn-Pb melts can be reasonably reproduced by the currently obtained atomic mobilities. Moreover, the atomic mobilities were further verified by comparing the model-predicted concentration profiles and the measured ones in various liquid Sn-Bi and Sn-Pb diffusion couples.     

Phase Equilibria of the Sn-Sb Binary System

Sn-Sb alloys are important high-temperature solders. However, inconsistencies are found in the available phase diagrams, and some phase boundaries in the Sn-Sb system have not been determined. Sn-Sb alloys were prepared, equilibrated at 160°C to 300°C, and the equilibrium phases and their compositions were determined. The β-SnSb phase has a very wide compositional homogeneity range, and its composition varies from Sn-47.0at.%Sb to Sn-62.8at.%Sb. There is no order–disorder transformation of the β-SnSb phase. There are three peritectic reactions in the Sn-Sb system, L + Sb = β-SnSb, L + β-SnSb = Sn₃Sb₂, and L + Sn₃Sb₂ = Sn, and their temperatures are 424°C, 323°C, and 243°C, respectively. Thermodynamic models of the Sn-Sb binary system were developed using the CALPHAD approach based on the experimental results of this study and the data in the literature. The calculated phase diagram and thermodynamic properties are in good agreement with the experimental determinations.     

Thermodynamic Descriptions and Phase Diagrams for Pb-S and Bi-S Binary Systems

In this work, thermodynamic optimization of the Pb-S and Bi-S binary systems has been performed using the calculation of phase diagrams approach. The Gibbs free energies of the liquid phases in the two binary systems are treated with the associated solution model. The two intermediate compounds, i.e., PbS and Bi₂S₃, are modeled as stoichiometric phases. A set of self-consistent thermodynamic parameters for the Pb-S and Bi-S binary systems has been obtained by simultaneous optimization of the available thermodynamic and phase equilibria data, the results of which lead to good agreement between the calculated and experimentally measured data.