Thermodynamic Treatment of Undercooled Cu-Mg Liquid and the Limits for Partitionless Crystallization

The thermodynamic properties of the binary Cu-Mg system are examined with a focus on equilibria involving the liquid phase, which is described with a four-species association model, incorporating a two-state treatment for the pure component liquids below their respective melting temperatures. The terminal and intermediate crystalline phases are described as substitutional solid solutions, employing two sublattices for the latter. Model parameters are fitted using available experimental data, and the resulting phase diagram is reported over the full range of compositions in the binary system. We also report the associated T ₀ curves, indicating the limits of partitionless crystallization and compare these with reports of amorphous solid formation during rapid solidification processing.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the experimental data.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the experimental data.     

Phase equilibria of the cu-in system II: Thermodynamic assessment and calculation of phase diagram

The phases in the Cu-In binary were modelled thermodynamically using the Redlich-Kister expression for the Gibbs energies of the solution phases, the Wagner-Schottky model for those of the η (η)’)-Cu₂ln phase (taking η and η)’ to be a single phase), and assuming line compound behavior for the other intermetallic phases. The model parameters were obtained using primarily the thermodynamic data, as well as the phase equilibrium data. The thermodynamic values for the various phases calculated from the models are in reasonable agreement with the experimentally determined thermodynamic data that are available in the literature. The entropies of melting for the intermetallic phases obtained from the models are in accord with the values calculated from the empirical formulas suggested by Kubaschewski. The calculated phase diagram is also in reasonable agreement with the experimentally determined diagram, with the calculated temperatures for all the invariant equilibria within 1°C of the experimental values. The discrepancies between the calculated and experimental phase boundaries at the invariant temperatures are less than 1 at.% except those involving βCu₄Inn and γCu₇ln₃. These two phases were taken to be line compounds in the present study, although experimentally they exist over appreciable ranges of homogeneity. Current address: Dept. of Chemical Engineering, National Tsing Hua University, Taiwan.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic Calculation of Phase Equilibria in the C-Mo-Zr System

The C-Mo-Zr system was assessed by means of the CALPHAD approach. All of the phase equilibria available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Zr)C_1?x, bcc-(Mo), bcc-(Zr), hcp-Mo₂C, hcp-(Zr) and η-MoC were described by using corresponding sublattice models. The laves-Mo₂Zr and shp-MoC phases were considered as binary compounds with no solubility for the third component. The existence of ternary phase was not reported in this system. The modeling of C-Mo-Zr ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the C-Mo-Zr system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the C-Mo-Zr system were also generated based on the present thermodynamic assessment.     

Phase equilibria in the Ga- In- Ni system at 600 °C

Phase equilibria are established in the Ga-In-Ni system at 600 °C using X-ray powder diffraction (XRD) and electron probe microanalysis (EPMA). The system is characterized by a notable absence of ternary solubility among the constituent binary phases. The only exception is the phase Ni₂ln₃, which dissolves a maximum of 12.7 at% Ga. Two ternary phases exist in the compositional vicinity of γ TVi₁₃Ga₉ and Ni₅Ga₃, both of which contain approximately 10 at.% In. These phases are considered to be superlattice structures derived from that of the binary, high-temperature phase γNi₃Ga₂, which possesses a partially filled NiAs (B8₁) structure. The phase diagram isotherm determined in the present investigation was also compared with an isotherm calculated using experimental thermodynamic data for the constituent binary phases, which are available in the literature. The calculated and experimental isotherms agree well.     

Thermodynamic assessment of the Nb-Ge system

The Nb-Ge binary system has been thermodynamically assessed using the CALPHAD (Calculation of Phase Diagrams) approach on the basis of the experimental data of both the phase equilibria and the thermochemical properties. The reasonable models were constructed for all the phases of the system. The liquid and the terminal solid solution phases, Bcc-(Nb) and Diamond-(Ge), were described as the substitutional solutions with Redlich-Kister polynomials for the expressions of the excess Gibbs free energies. The intermediate phases (Nb₃Ge), (Nb₅Ge₃), (Nb₃Ge₂) and (NbGe₂) with homogeneity ranges were treated as the sublattice models Nb_0.75(Ge,Nb,Va)_0.25, Nb_0.5(Nb,Ge)_0.125(Ge,Va)_0.375, (Nb,Ge)_0.222(Nb,Ge)_0.333Nb_0.333(Ge,Va)_0.111 and (Nb,Ge)_0.333(Nb,Ge)_0.667 respectively based on their structure features of atom arrangements. A set of self-consistent thermodynamic parameters for the Nb-Ge system was obtained. Using the present thermodynamic data, the calculation results can reproduce the experimental data well.     

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.     

Experimental Investigation and Thermodynamic Description of the Cu-Zr System

The Cu-Zr binary system is re-investigated via experiment and thermodynamic modeling. Four alloys were prepared by arc melting in order to check the controversial phase equilibria reported in the literature. Both as-cast and annealed alloys were examined by optical microscopy, x-ray diffraction and electron probe microanalysis, and the phase transformation temperatures were measured by differential scanning calorimetry. The intermetallic compounds, Cu₂₄Zr₁₃, Cu₂Zr and Cu₅Zr₈, were demonstrated to be not the stable phases. Based on the literature information and present experimental data, the Cu-Zr system was critically evaluated by means of CALculation of PHAse Diagram approach. A set of self-consistent thermodynamic parameters was obtained, and the calculated phase diagram and thermodynamic properties are in a satisfactory agreement with the experimental data.     

Phase equilibria of the Sn–Ag–Ni ternary system and interfacial reactions at the Sn–Ag/Ni joints

There are no previous phase equilibria studies of the Sn–Ag–Ni ternary system, even though the phase equilibria information is important for the electronic industry. The isothermal section of the Sn–Ag–Ni ternary system at 240 °C has been determined in this study both by experimental examination and thermodynamic calculation. Experimental results show no existence of ternary compounds in the Sn–Ag–Ni system, and all the constituent binary compounds have very limited solubilities of the ternary elements. The binary Ni₃Sn₂ phase is very stable and is in equilibrium with most of the phases, Ag₃Sn, ζ-Ag₄Sn, Ag, Ni₃Sn₄ and Ni₃Sn phases. A preliminary thermodynamic model of the ternary system is developed based on the models of the three binary constituent systems without introducing any ternary interaction parameters. This ternary thermodynamic model is used with a commercial software Pandat to calculate the Sn–Ag–Ni 240 °C isothermal section. The phase relationships determined by calculation are consistent with those determined experimentally. Besides phase equilibria determination, the interfacial reactions between the Sn–Ag alloys with Ni substrate are investigated at 240, 300 and 400 °C, respectively. It is found that the phase formations in the Sn–3.5wt%Ag/Ni couples are very similar to those in the Sn/Ni couples.     

A thermodynamic analysis of the Al-Re system

Phase equilibria and thermodynamic data of the Al-Re system are critically reviewed. In addition to the three solution phases, liquid, fcc Al, and hcp Re, there exist six intermetallic compounds in this binary. The thermodynamic properties of the system are analyzed using thermodynamic models for the Gibbs energy of individual phases of the system. A regular solution model is used for the three substitutional solution phases, and the intermetallic phases are treated as stoichiometric compounds. The model parameters are optimized from a limited amount of experimental data. The calculated phase diagram and thermodynamic values are in accord with the available experimental values.     

On the Quaternary System Ti-Fe-Ni-Al

The homogeneity ranges of the Laves phases and phase relations concerning the Laves phases in the quaternary system Ti-Fe-Ni-Al at 900 °C were defined by x-ray powder diffraction (XPD) data and electron probe microanalysis (EPMA). Although at higher temperatures the Laves phase forms a continuous solid solution, two separate homogeneity fields of TiFe₂-based (denoted by λ_Fe) and Ti(TiNiAl)₂-based (denoted by λ_Ni) Laves phases appear at 900 °C. The relative locations of Laves phases, G phase, Heusler phase, and CsCl-type phase as well as the associated tie-tetrahedra were experimentally established in the quaternary for 900 °C and presented in three-dimensional (3D) view. Furthermore, a partial isothermal section TiFe₂-TiAl₂-TiNi₂ was constructed, and a connectivity scheme, derived for equilibria involving Laves phases in the Ti-Fe-Ni-Al quaternary system at 900 °C was derived. As a characteristic feature of the quaternary phase diagram, the solid solubility of fourth elements in both the TiFe₂-based and Ti(NiAl)₂-based Laves phases is limited at 900 °C and is dependent on the ternary Laves phase composition. A maximum solubility of about 8 at.% Ni is reached for composition Ti_33.3Fe_33.3Al_33.4. Structural details have been evaluated from powder x-ray and neutron diffraction data for (i) the Ti-Fe-Ni ternary and the Ti-Fe-Ni-Al quaternary Laves phases (MgZn₂-type, space group: P6₃/mmc) and (ii) the quaternary G phase. Atom site occupation behavior for all phases from the quaternary system corresponds to that of the ternary systems. For the quaternary Laves phase, Ti occupies the 4f site and additional Ti (for compositions higher than 33.3 at.%Ti) preferably enters the 6h site. Aluminum and (Fe,Ni) share the 6h and the 2a sites. The compositional dependence of unit cell dimensions, atomic coordinates, and interatomic distances for the Laves phases from the quaternary system is discussed. For the quaternary cubic G phase, a centrosymmetric as well as a noncentrosymmetric variety was observed depending on the composition: from combined x-ray and neutron powder diffraction measurements Ti_33.33Fe_13.33Ni_10.67Al_42.67 was found to adopt the lower symmetry with space group .     

Thermodynamic calculation of the O-Ti system

The O-Ti binary system has been assessed to produce Gibbs energy parameters for the condensed phases and were evaluated as representations of thermodynamic models. The liquid phase was described in terms of an association model with one associate, the bcc, A 2; cph, A 3 and fcc, A 1 phases were described as interstitial solid solutions, and the O₂Ti, O₃Ti₅, O₃Ti₂, and OTi oxides were considered to be stoichiometric compounds. The thermodynamic parameters were optimized taking into account experimental phase diagram and thermodynamic values from the literature. The phase diagram and the thermodynamic properties were calculated and compared with experimental data.     

Phase equilibria in the Al–Mo–Si system

The ternary Al–Mo–Si phase diagram was investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA), electron probe microanalysis (EPMA) and scanning electron microscopy (SEM). Ternary phase equilibria were investigated within two isothermal sections at 600 °C for the Mo-poor part and 1400 °C for the Mo-rich part of the phase diagram. The solubility ranges of several phases including MoSi₂ (C11_b) as well as Mo(Si,Al)₂ with C40 and C54 structure were determined. The binary high temperature phase Al₄Mo was found to be stabilized at 600 °C by addition of Si. DTA was used to identify 9 invariant reactions and thus constructing a ternary reaction scheme (Scheil diagram) in the whole composition range. A liquidus surface projection was constructed on basis of the reaction scheme in combination with data for primary crystallization from as-cast samples determined by SEM measurements.