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The standard enthalpies of formation in this work have been measured calculated by First -principles calculations within DFT (density functional theory) for the metal compounds in the Ce-Rh system. Thermodynamic data and phase diagram information obtained from the literature were used as the input for a CALPHAD-type optimization and Thermo-Calc software of the Ce-Rh. The Ce-Rh phase diagram contains seven intermetallic compounds: C e 7 R h 3 , C e 5 R h 3 , C e 3 R h 2 , C e 5 R h 4 , C e R h , C e R h 2 and C e R h 3. All these phases were stoichiometric; The associated model concerning the phase equilibria, could accurately describe the full compositional range and the thermodynamic data input with C e R h as associate. The thermodynamic parameters of all intermetallic compounds were modeled by the Neumann-Kopp principle. The value of the temperature-dependent contributions to the individual Gibbs energies was used for all compounds. A fairly good agreement with all values of the enthalpies of formation calculated in this work using the VASP and data available in the literature. ultimately, a set of self-consistent thermodynamic parameters for the Ce-Rh system was obtained. [ABSTRACT FROM AUTHOR]

As a core of the high entropy alloys, the Co-Cr-Fe-Ni system has been widely investigated. In the present work, the thermodynamics of the Co-Cr-Fe-Ni system and the atomic mobilities of its fcc phase have been evaluated by means of the CALPHAD approach. First-principles calculations were performed to obtain the total energies for the end-member compounds of the σ phase in the Co-Cr-Fe-Ni system. Combining with the experimental data and thermodynamic modeling of the sub-systems from the literature, a set of self-consistent thermodynamic parameters were derived and extrapolated to obtain a thermodynamic description of the Co-Cr-Fe-Ni quaternary system. In order to verify the accuracy of the model parameters, the phase equilibria of a series of the CoCr x FeNi alloys with different Cr contents were determined using DSC, BSE and XRD analysis. Subsequently, based on the diffusion experimental data, the atomic mobilities of the fcc Cr-Fe-Ni alloys were reassessed using the DICTRA software. A mobility database for the fcc Co-Cr-Fe-Ni quaternary system was constructed by directly extrapolating the atomic mobilities of all sub-systems, and comprehensive comparisons prove the consistency between the present assessments and the experiments. In addition to the direct extrapolation approach, extra four-body interaction parameters concerning all four components were added and assessed. The results demonstrate that the extra interaction contributions are ignorable, so that the direct extrapolation from the sub-systems to the quaternary system is feasible in the fcc Co-Cr-Fe-Ni quaternary system. [ABSTRACT FROM AUTHOR]

The formation of the η phase in two nickel-based superalloys that have similar amounts of titanium and aluminum but different Ti/Al ratios was investigated. The aging was carried out at 750 °C, 800 °C, and 850 °C for 10000 h. The microstructures were observed using SEM and TEM, and equilibria phases were calculated using a Thermo-Calc. equipped with TCNI11 database. Results showed that the number and size of η phase increased with aging temperature and Ti/Al ratios. The size of the γ′ phase was also found to be increased with aging temperature, but it was not significantly affected by the Ti/Al atomic ratio. However, the η phase was not predicted to be the thermodynamic equilibrium phase in the alloy using Thermo-Calc. with the TCNI11 database. The η phase was expected to be the equilibrium phase with Ti/Al ratios higher than 1.85 at 850 °C for Ni-27.0Cr-19.1Co-0.91Nb-0.29Mo-0.14C-xTi-yAl alloys. However, the result does not match the experimental observations or other literature. It is suggested that the effect of titanium on the formation of the η phase may be underestimated in the TCNI11 database. Therefore, it is necessary to enhance the accuracy of predicting the formation of the η phase by modifying at least one of the thermodynamic parameters, including the phase equilibrium of the ternary Ni-Ti-Al system. [ABSTRACT FROM AUTHOR]

The isothermal section at 900 °C of the Ti-poor part of the Ni−Ti−Ru ternary system was measured experimentally, combined with SEM-EDS, XRD, TEM and DSC techniques. Four three-phase equilibria regions were confirmed at 900 °C isothermal section and a ternary compound τ with Face-centered-cubic structure can existed stably. The isothermal section at 900 °C measured in this study and the experimental data from our previous work were adopted in the present optimization. The calculated Ni−Ti−Ru ternary system was summarily presented in the form of isothermal sections, liquids projection and reaction scheme, with appropriate comparisons with available experimental data. • The 900 °C isothermal section of the Ni−Ti−Ru ternary system in Ti-poor part was investigated. • The ternary compound τ was identified as FCC structure. The lattice parameters of the τ are a = b = c = 0.3715 nm. • A new set of self-consistent thermodynamic parameters for the Ni−Ti−Ru ternary system was obtained. [ABSTRACT FROM AUTHOR]

Nickel-based superalloys are extensively utilized in aerospace engines, marine gas turbines, and other environments with severe operating conditions. The phase relations of the Ni-Mo-Y ternary system were experimentally studied across the entire composition range at 800 °C and 1000 °C using scanning electron microscopy (SEM) coupled with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). Thirteen three-phase regions were confirmed at 800 °C, and eleven three-phase regions were observed at 1000 °C. No ternary compound was observed at these temperatures. In addition, the experimental results indicate that molybdenum (Mo) has almost no solubility in the binary compounds found in the Ni-Y binary system. Furthermore, the primary solidification phases and the solidification process of typical alloys were investigated, and three different primary solidification phases were found. Based on the experimental results, thermodynamic calculations for the Ni-Mo-Y system were performed through the CALPHAD technique. The experimental results agree well with the calculated, a set of self-consistent thermodynamic parameters for the Ni-Mo-Y ternary system was obtained in the present work. [ABSTRACT FROM AUTHOR]

In the present work the phase equilibria in a system of zirconium and hafnium dioxides and europium sesquioxide have been studied. The study was conducted at temperatures of 1700 °С and 1500 °С. Based on the results, isothermal sections at these temperatures were constructed. It was found that in the ZrО 2 –HfO 2 –Eu 2 O 3 ternary system at temperatures of 1700 °С and 1500 °С solid solutions are formed on a monoclinic (M, space group P2 1 /C) modification of HfO 2 , a tetragonal (T, space group P4 2 /nmc) modification of ZrO 2 , cubic solid solutions ZrO 2 (HfO 2) with a fluorite structure (F, space group Fm3m), C-type cubic solid solutions of Eu 2 O 3 (space group Ia-3), solid solutions based on the monoclinic modification (B, space group C2/m) of Eu 2 O 3 , as well as an ordered phase with a pyrochlore structure of Eu 2 Zr 2 O 7 (Eu 2 Hf 2 O 7) (Py, space group Fd-3m). The phase boundaries and the unit cell parameters of the formed phases were determined. The studied isothermal sections of the ZrО 2 –HfO 2 –Eu 2 O 3 system are characterized by the formation of continuous series of cubic solid solutions based on the phase with a pyrochlore structure. The formation of new phases in the ZrО 2 –HfO 2 –Eu 2 O 3 system at 1700 °С and 1500 °С was not observed. [ABSTRACT FROM AUTHOR]

Based on experimental data measured by scanning electron microscope (SEM), X-ray diffraction (XRD) and electron probe microanalysis (EPMA), isothermal sections of Ti–Mo-Hf system at 800 °C and 1000 °C were constructed. Four and three three-phase regions were derived in the isothermal sections at 800 and 1000 °C, respectively. In addition, a new ternary compound named τ was discovered. The maximum solubilities of the three elements, Ti, Mo and Hf in τ were measured at 800 °C and 1000 °C. At the same time, the solid solubilities of Ti in HfMo 2 _C15 and Mo in Hcp were also obtained. According to the measured experimental data, the Ti–Mo-Hf system was optimized using the CALPHAD (CALculation of PHAse Diagrams) method. The solution phases, liquid, Bcc and Hcp, were treated as substitutional solution, while the intermetallic compounds were modeled using sublattice models. HfMo 2 _C15 was treated as (Hf, Mo, Ti) 1 (Hf, Mo, Ti) 2. The ternary phase τ was considered as a stoichiometric compound and its thermodynamic modeling was defined as (Ti) 3 (Mo) 3(Hf) 14. The calculated results showed good agreement with the experimental phase equilibrium data, leading to the derivation of a set of self-consistent thermodynamic parameters for the Ti–Mo-Hf system. [ABSTRACT FROM AUTHOR]

Through the integration of experimental investigations and thermodynamic modeling, a thorough exploration of the phase equilibria in the Ni–Zr–Y ternary system was undertaken. Twenty-six ternary alloys were meticulously prepared to study the isothermal sections at 500 and 700 °C, employing techniques such as X-ray diffraction (XRD) and scanning electron microscopy coupled with energy dispersive X-ray spectroscopy (SEM/EDS). The solubilities of Zr in the Ni–Y binary compounds and Y in the Ni–Zr binary compounds were measured. A ternary compound named τ (Ni 2 (Y, Zr)) was confirmed at 700 °C. Utilizing thermodynamic parameters of three binary systems and available experimental phase equilibria data from literature and this work, a thermodynamic assessment of the Ni–Zr–Y system was conducted using the CALPHAD (CALculation of PHAse Diagrams) approach. A set of thermodynamic parameters was obtained and the isothermal sections at 500, 597 and 700 °C were calculated, and the calculated results demonstrated a strong agreement with experimental data. The liquidus projection and reaction scheme of the Ni–Zr–Y system was predicted. This work can be used as a basis for the multicomponent thermodynamic database of Ni-based alloys. • The phase equilibria of the Ni–Zr–Y system at 500 and 700 °C were determined. • Confirmation of a ternary compound named τ (Ni 2 (Zr, Y)) at 700 °C. • Thermodynamic assessment of the Ni–Zr–Y system was carried out by CALPHAD method. • Prediction of liquidus projection and reaction scheme of the Ni–Zr–Y system. [ABSTRACT FROM AUTHOR]

This work examines the thermochemistry of the chromium difluoride CrF 2 corrosion product in the molten ▪ fuel salt system. Through a combination of experimental investigations and thermodynamic modeling assessment, the study elucidates the thermodynamic properties, phase diagram equilibria, and overall thermodynamic behavior of CrF 2 corrosion product, following dissolution from a structural material to the molten salt fuel environment. In this work, two different synthesis methods were developed for pure CrF 2 , further allowing to experimentally measure the phase equilibria in the ▪ , ▪ , and ▪ systems. Then, thermodynamic models were developed using the CALPHAD method based on the quasichemical model in the quadruplet approximation. [ABSTRACT FROM AUTHOR]

Property models are becoming more widely adopted by commercial Calphad databases, but they are not nearly as common in non-commercial or traditional academic Calphad databases. A primary driver is that user-friendly Calphad modeling tools that support property models are not widely available. Here we present new property modeling capabilities that have been implemented in ESPEI (the Extensible, Self-optimizing Phase Equilibrium Infrastructure). These capabilities include both generating property model parameters from data and improvements to the algorithmic selection of the most appropriate model from a series of candidates. Two illustrative examples are given that use ESPEI to fit different property models. First, we generate molar volume model parameters for Group IV, V, and VI refractory BCC alloys based on the model by Lu et al. (2005). Second, we demonstrate the extensibility of ESPEI's property modeling capabilities by implementing a custom PyCalphad model for BCC elastic stiffness parameters to generate and compare parameters to the ones assessed by Marker et al. (2018) using the same data. Property models generated by ESPEI can be used in PyCalphad or further optimized with uncertainty quantification using ESPEI. [ABSTRACT FROM AUTHOR]

Phase equilibria of the Y–Co–Zr ternary system at 600 °C and 800 °C were studied for the first time using the diffusion couple technique and equilibrium alloy method with electron probe microanalysis (EPMA), scanning electron microscopy (SEM), and X-ray diffraction (XRD). The results reveal that the stable ternary intermetallic compounds were not found, while YCo 2 and Co 2 Zr are formed a continuous solid solution phase (Y, Zr)Co 2 with a Cu 2 Mg-type structure. The solid solubility of Zr in α-Y 2 Co 17 , YCo 5 , Y 2 Co 7 , α-YCo 3 , YCo and Y 3 Co at 800 °C was determined to be 5.6, 2.4, 9.4, 18.0, 1.4 and 1.4 at.%, respectively, while the solid solubility of Y in Co 23 Zr 6 , CoZr and CoZr 3 was measured to be 6.4, 6.3 and 2.6 at.%. Meanwhile, the solid solubility of Zr in α-Y 2 Co 17 , YCo 5 , Y 2 Co 7 , α-YCo 3 , YCo, Y 4 Co 3 , Y 3 Co 2 , Y 8 Co 5 and Y 3 Co at 600 °C was measured to be 4.4, 3.0, 9.4, 17.2, 1.6, 1.6, 1.9, 1.9 and 3.2 at.%, respectively, while the solid solubility of Y in Co 23 Zr 6 and CoZr was measured to be 4.8 and 2.4 at.%. Two isothermal sections of the Y–Co–Zr ternary system at 600 °C and 800 °C were constructed finally. It provides the fundamental information for the development of high-performance Y–Co–Zr-based magnetic alloys. [ABSTRACT FROM AUTHOR]

The phase diagram of the CaO–MgO–P 2 O 5 system was established by both experimental investigation and thermodynamic assessment. The presence of the contentious binary compound Ca 4 P 6 O 19 in the CaO–P 2 O 5 system was confirmed. The phase relationships in the CaO–MgO–P 2 O 5 system at temperature 1150 °C and 1200 °C were studied via high-temperature quenching experiments in conjunction with X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA) techniques. The CaO–MgO–P 2 O 5 system was critically evaluated and optimized by means of the CALPHAD (CALculation of PHAse Diagrams) methodology. The ionic two-sublattice model (Ca+2, Mg+2) P (O−2,PO 3 −1,PO 4 −3,PO 7/2 −2,PO 5/2) Q is used to describe the liquid phase in the CaO–MgO–P 2 O 5 system due to the ionic nature of oxide melts and the presence of ions with different charges. A set of self-consistent thermodynamic parameters were obtained, showing good agreement between the experimental data and the calculated results. This study holds significant implications for guiding the manufacturing processes of phosphate ceramics. [ABSTRACT FROM AUTHOR]

Ag–Se and Ag–Pb–Se are important material systems for thermoelectric applications, yet their phase equilibria and thermodynamic descriptions have not been studied extensively. This study experimentally determines the phase equilibria of isothermal sections at 550°C and 400°C. No ternary compound is found, and the third element's solubility in the binary compounds is negligible. The Ag–Se binary system is thermodynamically modeled using the Calphad method. Based on the experimental results in this work and those from the literature review. This study proposes the thermodynamic descriptions of the Ag–Pb–Se ternary system using the Calphad method for the first time. The isothermal sections, isopleth sections, and liquidus projection were calculated and compared with the experimental data, showing good agreement between the experimental results and thermodynamic calculation. • This study determines the phase equilibria of isothermal sections of the Ag–Pb–Se ternary system at 550°C and 400°C. • No ternary compound is found, and the third element's solubility in the binary compounds is negligible. • Thermodynamic descriptions of Ag–Se binary and Ag–Pb–Se ternary systems are proposed using the Calphad method. • Calculated isothermal sections, isopleth, and liquidus projection show good agreement with experimental results. [ABSTRACT FROM AUTHOR]

Precipitation is a natural phenomenon that is known to play an important role in the strengthening of Al–Li alloys. Cluster dynamics is powerful and effective in modeling the precipitation kinetics of precipitates in heat-treatable metallic materials, especially in the early stage. In this work, a cluster dynamics model with cluster mobility is further developed by redefining the effective monomer diffusivity for self-consistently modeling multicomponent and multiphase precipitation. The precipitation kinetic data for Al 3 Sc in Al–Sc binary alloys and Al 3 Li in Al–Li binary alloys are systematically reviewed and evaluated. The metastable fcc_A1/Al 3 Li two-phase equilibria are reoptimized using the split four sublattice compound energy formalism to accommodate both the related phase equilibrium measurements and precipitation kinetic measurements. One set of precipitation kinetic parameters is respectively assessed for each of the two precipitate phases. The improved cluster dynamics model, together with the assessed model parameters, can reasonably reproduce the reliable experimental precipitation kinetic data of the two phases. The model parameter determination includes extensive sensitivity studies to use physically reasonable values, and the present work also studies the use of cluster mobility in modeling the early stage precipitation kinetics. The present work indicates that the obtained model parameters can be used to develop the fundamental informative CALPHAD-type precipitation kinetic database. [Display omitted] • Improved cluster dynamics model with cluster mobility for multicomponent and multiphase precipitation. • Newly defined effective monomer diffusivity for both diffusion-limited and kinetic-limited growth. • Critical review and assessment of Al 3 Sc and Al 3 Li precipitation kinetic data in binary alloys. • Cluster dynamics precipitation kinetic parameters for Al 3 Sc and Al 3 Li in binary alloys. • Discussion of precipitation kinetic database development in the frame of CALPHAD approach. [ABSTRACT FROM AUTHOR]

The phase equilibria of the Sm-Fe-B ternary system at 873 K and 1073 K were experimentally investigated by equilibrated alloy method using scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS) and X-ray diffraction (XRD). Four ternary intermetallic compounds, Sm 2 Fe 14 B with a Nd 2 Fe 14 B-type structure and space group P4 2 /mnm, Sm 17 (Fe 4 B 4) 15 with a RE l.1 Fe 4 B 4 -type structure and space group P4 2 /n, SmFeB 4 with a YCrB 4 -type structure and space group Pbam and Sm 5 Fe 2 B 6 with a Pr 5 Co 2 B 6 -type structure and space group R 3 ‾ m , were confirmed by the SEM-EDS results and the XRD Rietveld refinements. The isothermal sections of this ternary system at 873 K and 1073 K were established. Furthermore, in the combination with the previous assessments of the Sm-Fe, Sm-B and Fe-B binary systems and the measured and reported experimental results, thermodynamic calculation of the Sm-Fe-B ternary system was performed using the CALPHAD method. The calculated isothermal sections at 873 K and 1073 K are in good agreement with the determined experimental results. Thermodynamic parameters of the Sm-Fe-B ternary system were obtained finally, which would provide a good basis for the development of a thermodynamic database of RE-Fe-B-based magnetic alloys. [ABSTRACT FROM AUTHOR]

Aiming to evaluate the effect of refractory metal additions to a quinary AlCoCrFeNi High-Entropy Alloy (HEA), three novel equimolar AlCoCrFeNi-X (X = Mo, Ta, W) HEAs were designed, arc-melted, annealed, and characterized by SEM-EDS, XRD and microhardness measurements. CALPHAD thermodynamic calculations were exploited to design compositions and thermal treatments of the selected HEAs as well as to predict constitution and interpret microstructure of the samples. On the other hand, the experimental results contributed to the validation of the in-house built GHEA thermodynamic database (including the Al, Co, Cr, Fe, Ni, Mo, Ta, W elements) used for the calculations. No TCP intermetallic was found to form in the quinary AlCoCrFeNi alloy. However, the formation of σ, Laves-C14 and μ phases was observed in the samples containing Mo, Ta, and W, respectively, in agreement with the most accepted VEC-based phases stabilization criteria. The addition of the refractory metals led to a microhardness increase for all the investigated alloys. Overall, good agreement was observed between experiments and calculations, especially for compositional trends and phase amounts, allowing the database validation and supporting its applicability to phase equilibria simulation in the six-component HEAs belonging to the Al–Co–Cr–Fe–Ni-X (X = Mo, Ta, W) systems. [Display omitted] • AlCoCrFeNi and AlCoCrFeNiX (X = Mo,Ta,W) HEAs were prepared and experimentally characterized. • Experiments and CALPHAD calculations were satisfactorily cross-checked. • The in-house built GHEA database was validated for Al–Co–Cr–Fe–Ni-X system. • Mo, Ta, W addition to AlCoCrFeNi leads to TCP phases formation and hardness increase. [ABSTRACT FROM AUTHOR]

Owing to the low melting temperature and excellent mechanical properties, In is considered a potential low-temperature solder. However, the interfacial reaction between In and Cu substrates is still unclear, specifically regarding the stability of CuIn 2. Although CuIn 2 was often observed at the Cu–In thin film after long-term aging below 100 °C, it is considered as a metastable phase and has not been added into the Cu–In phase diagram yet. In this study, the stability of CuIn 2 and the peritectoid reaction Cu 11 In 9 + In → CuIn 2 were established using the Cu/In diffusion couple, Cu–In alloy phase equilibria, and decomposition investigation of CuIn 2. The peritectoid temperature was determined to be in the range of 110–105 °C. Finally, thermodynamic assessment was conducted based on the experimental data and the revised Cu–In phase diagram. [ABSTRACT FROM AUTHOR]

The selective crystallization and phase separation process has been regarded as a promising process for the recycling of titanium from titania-bearing furnace slag, however, the composition modification mechanism still remains unclear due to the lack of fundamental thermodynamic data. In the present work, the influence of ZrO 2 addition on the equilibrium phase relations and the 1400 °C isotherm for CaO-SiO 2 -TiO 2 system were experimentally determined by using the high temperature equilibration-quenching technique, and Scanning Electron Microscopy-Energy Dispersive X-ray Spectrometry, and X-ray diffraction analysis. The equilibrium solid phases of rutile (TiO 2), perovskite (CaTiO 3), and tridymite (SiO 2) are determined to be coexisting with the liquid phase. In addition, comparisons of present results with thermodynamic calculation by FactSage show significant discrepancies. The present work is important for enriching the thermodynamic database of titania-bearing slag oxide systems as well as optimizing the selective crystallization and phase separation process. [ABSTRACT FROM AUTHOR]

This paper presents the results of our comprehensive study of phase equilibria in the Al–Fe–Mo system using DTA, X-ray diffraction, SEM and electron probe microanalysis. The liquidus and solidus projections were constructed. It is shown that the ternary compound Al 8 FeMo 3 (τ) melts congruently at >1500 °C and has a homogeneity range from 2 to 9 at.% Fe and from 23.5 to 25 at.% Mo. Isostructural phases (Mo), (αFe) and AlMo (W-type structure, cI 2 -Im- 3 m) at solidus temperatures form a continuous solid solution (αFe,Mo,AlMo). Unlike the AlMo binary phase, which is not retained by quenching, the ternary (αFe,Mo,AlMo) phase is easily quenched due to its lower decomposition temperature. Among the binary based phases, the Al 8 Fe 5 (ε) phase has the widest homogeneity region, which extends up to 24 at.% Mo at solidus temperatures. It is shown that the addition of Mo stabilizes the Al 8 Fe 5 (ε) phase, and the temperature of its formation in the ternary system increases to 1331 °C in contrast to 1234 °C in the binary. Moreover, according to XRD data, the Al 8 Fe 5 (ε) phase in the ternary system has a rhombohedral structure of the Al 8 Cr 5 -type (hR 78- R -3m), rather than cubic Cu 5 Zn 8 -type structure (cI 52- I -43 m), like the binary one. A new binary compound Al 45 Mo 7 was identified for the first time. Its crystal structure is established as monoclinic Al 45 V 7 -type (mS 104- C 2/ m) with the lattice parameters a = 20.534, b = 7.561, c = 10.910 Å, β = 107.33. It was shown to form by peritectic reaction L + Al 5 Mo ⇄ Al 45 Mo 7 at ∼800 °C. Iron additions stabilize the Al 4 Mo phase, which in the binary system is stable above 942 °C. [Display omitted] • Phase relations in the ternary Al–Fe–Mo systems over the whole concentration range were studied. • A new binary compound Al 45 Mo 7 with a monoclinic Al 45 V 7 -type structure was found. • It is shown that the ternary compound Al 8 FeMo 3 (τ) melts congruently at >1500 °C. • A continuous solid solution (αFe,Mo,AlMo) (W-type structure) was found at solidus temperatures. • Fifteen four-phase invariant reactions are found,one is of peritectic type and fourteen ones are of U-type. [ABSTRACT FROM AUTHOR]

Accounting for the elusive gas phase in thermodynamic equilibrium calculations is demonstrated to be important for achieving accurate and unique determination of constituent element chemical potentials, when Gibbs energy minimization (GEM) encounter indeterminacy due to rank deficiency in mass-balance equations. The molar GEM of the equilibrium vapor phase offers a robust solution for unambiguously and accurately determining element chemical potentials. To enable this, a novel optimization method for mass-balance equation is presented, paving the way for reliable thermodynamic calculations. [ABSTRACT FROM AUTHOR]

In the present work, the first-principles calculations were performed to study the enthalpies of mixing and the magnetic moments of the solid solutions in the Ni–Re and Co–Re systems. Meanwhile, the phase equilibria of the binary Ni–Re, Co–Re and ternary Ni–Co-Re alloys were investigated using equilibrated alloys and diffusion couples. Various types of data from the present work as well as the literature were used to perform a thermodynamic assessment of the ternary Ni–Co-Re and sub-binary systems using the CALPHAD method. Based on the present thermodynamic parameters, the atomic mobilities for the fcc phase in the Ni–Re and Co–Re systems were reassessed to reproduce experimental data in the literature. Furthermore, several ternary Ni–Co-Re diffusion couples were assembled and annealed at 1273 K and 1473 K to deduce the interdiffusion coefficients. On the basis of diffusion experimental data from the present work and the literature, atomic mobilities of Ni, Co, and Re in the fcc Ni–Co-Re system were assessed coupled with the present thermodynamic description. The accuracy of the assessed atomic mobilities was confirmed by comparing with the experimental interdiffusion coefficients, composition profiles and diffusion paths. [ABSTRACT FROM AUTHOR]

Co–Fe–Ge is an important material system for magnetic and catalyst applications. However, phase equilibria information of the Co–Fe–Ge ternary system is limited. Ternary Co–Fe–Ge alloys equilibrated at 950 °C were prepared. The microstructures, chemical compositions and crystal structure of each phase were determined. The phase equilibria isothermal section at 950 °C of the Co–Fe–Ge ternary system was then proposed. A continuous solid solution phase was formed between the Co 5 Ge 3 and Fe 5 Ge 3 phases and was labeled the β(Co,Fe) 5 Ge 3 phase. There are five three-phase regions in the system at 950 °C. A wide α 2 single-phase, and liquid phase regions with large composition ranges being confirmed at the Ge-poor and Ge-rich sides, respectively. [ABSTRACT FROM AUTHOR]

The partial phase equilibria of the Ni–Al−Dy ternary system have been systematically investigated via experimental analyses and thermodynamic modeling. Using the equilibrated alloy method, the 1150 °C and partial 800 °C isothermal sections of the Ni–Al−Dy ternary system and related Al–Dy binary system were constructed based on scanning electron microscopy, energy-dispersive spectroscopy and X-ray diffraction. Twelve three-phase regions were confirmed and four three-phase equilibria regions were speculated at 1150 °C, eight three-phase regions were determined at 800 °C, and five kinds of primary solidification regions, DyAl 2 , τ7, τ5, NiAl and Ni 2 Al 3 were observed. A new ternary compound τ12 was discovered, which was stable at 800 °C and disappeared at 1150 °C, the τ1 phase was not stable at 800 and 1150 °C isothermal sections; the ternary compound τ11 was confirmed to be stable at 800 °C. In addition, the primary solidification phases were also identified, and five different primary solidification phases were found. Based on the experimental results available in this study and the literature, the thermodynamic modeling of the Ni–Al–Dy ternary system was obtained using the CALPHAD method. A set of self-consistent thermodynamic parameters for the Ni–Al–Dy ternary system was first obtained with a satisfactory agreement between the experimental and calculated results. [ABSTRACT FROM AUTHOR]

The thermodynamic evaluation of the Er–Sc binary system was performed using the Calphad method, computing thermodynamic parameters for the Liquid phase, Hcp phase, and Bcc phase. The calculated results align well with existing experimental phase diagrams. Furthermore, by employing electron probe microanalysis and X-ray diffraction testing, the phase equilibria for the Al–Er-Sc ternary system at 600 °C were determined. Experimental findings indicated that both Al–Er and Al–Sc binary systems exhibit some solubility for the third component when extended to the ternary system. Leveraging thermodynamic parameters from the literature for Al–Er and Al–Sc binary system and those calculated for the Er–Sc binary system in this work, a comprehensive thermodynamic evaluation of the Al–Er-Sc ternary system is carried out. The computed results exhibit good agreement with the experimental data, providing consistent and reasonable thermodynamic parameters for the isothermal and vertical sections. [ABSTRACT FROM AUTHOR]

A thermodynamic evaluation of the Cr–Si system was performed concerning the latest experimental phase diagram and with the aid of first-principles calculations. The thermodynamic parameters for the Gibbs energy of pure Cr were modified based on the new experimental value of 1861 °C for the melting point of pure Cr, which was previously reported as 1907 °C in the SGTE database. The Gibbs energy descriptions of the Cr 3 Si and Cr 5 Si 3 phases were revised using Cr 3 (Cr,Si)- and (Cr,Si) 5 Si 3 -type two-sublattice models to reproduce the latest experimental results of their solubility composition ranges, that is, Cr 3 Si extending toward the Cr-rich side and Cr 5 Si 3 extending toward the Si-rich side from the stoichiometry. The CrSi and CrSi 2 phases were considered line compounds with no solubility range, and the solubility of Cr in the Si phase was ignored. A set of self-consistent thermodynamic parameters for the Cr–Si system was obtained using the CALPHAD technique. The phase diagrams calculated using the optimized parameters showed reasonable agreement with the latest phase equilibrium data and thermodynamic property data in the literature, including the enthalpy of mixing, formation enthalpy, and chemical potential diagrams of Cr and Si in the equilibrium phases. [ABSTRACT FROM AUTHOR]

Ti–Al–V alloys have received considerable attention owing to their excellent high-temperature mechanical properties. After conducting a critical review of the available experimental data for the ternary Ti–Al–V system, a thermodynamic assessment of the system was carried out over the entire composition and a wide temperature range utilizing the CALPHAD method. The extensive homogeneity ranges of the α 2 and γ phases were satisfactorily reproduced. Of particular significance was the first accurate description of the phase equilibria at 1573 K. The model parameters obtained in this study well represented the thermochemical properties and phase equilibria of the experimental data. Furthermore, the enthalpies of the widely used Ti alloy Ti–6Al–4V were reproduced using the thermodynamic description established in this study. Thus, this study provides a reliable basis for guiding the development and design of Ti–Al–V alloys. • A self-consistent thermodynamic description of the Ti–Al–V system was achieved. • The thermodynamic description covers the entire composition and a wide temperature range. • Satisfactory reproduction of the extensive homogeneity ranges of the α 2 and γ phases was achieved. • The phase equilibria at 1573 K were well described for the first time. [ABSTRACT FROM AUTHOR]

Phase equilibria knowledge on the Al–V–Zr system has an important role for designing low-density Al-containing refractory multi-principal element alloys. In order to contribute to the literature data related to this system, the liquidus projection of the Al–V–Zr ternary system was experimentally investigated in this work by microstructural characterization of as-cast alloys. Sixty alloys were produced in an arc furnace, the microstructures of the as-cast alloys were characterized using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) for the determination of the chemical composition of the phases and microconstituents as well as X-ray diffractometry (XRD). The liquidus projection of the Al–V–Zr system is presented in this work for the first time in the literature. Through microstructural analysis and thermodynamic extrapolation, three Class I, eleven Class II and one Class III ternary invariant reactions are proposed. The results showed that the ternary compound Zr 0.9 V 0.4 Al 2.7 is formed from the liquid through the following reaction: L + ZrAl 2 → Zr 0.9 V 0.4 Al 2.7. The limits of the 12 primary solidification regions are established and the nature of the monovariant and ternary invariant reactions are determined. The ZrAl 2 primary solidification region significantly extends into the liquidus projection, participating in most reactions involving the other phases in equilibrium with the liquid. [ABSTRACT FROM AUTHOR]

The Ta–Ge system was thermodynamically modeled for the first time using the CALPHAD method incorporating both literature-derived phase equilibria data and new enthalpy of formation values for the intermetallic compounds. Density Functional Theory (DFT) calculations were employed to accurately determine enthalpy of formation values for key Ta–Ge compounds. The stable intermetallic phases (i.e., αTa 3 Ge, βTa 3 Ge, βTa 5 Ge 3 , and TaGe 2) were described as stoichiometric phases while the Liquid (L), Ta-rich solid solution (BCC-A2), and Ge-rich solid solution (Diamond-A4) were modeled as solution phases using the Compound Energy Formalism. Excess terms were described by the Redlich-Kister polynomials. The present thermodynamic model accurately describes phase equilibria and thermodynamic data, providing a reliable guide for designing alloys containing Ta and Ge. [ABSTRACT FROM AUTHOR]

The present work reports on a thermodynamic modeling of the Mo–Pt system using a combined first-principles/CALPHAD approach. First-Principles (FP) calculations are performed to obtain the enthalpies of formation for the four ordered phases of the system (A 15, B 19, D 0 19 and MoPt 2) at 0 K. The liquid, bcc, fcc and hcp phases have been modeled as substitutional solutions where the excess term is in the form of the Redlich–Kister polynomial. The four ordered phases are modeled using the NACEF approach taking into account the three order-disorder transitions (B 19/ A 3, D 0 19 / A 3 and MoPt 2 / A 1). FP calculations, experimental phase equilibria and site occupancies data are used to evaluate the model parameters. The thermodynamic description of the Mo–Pt system obtained in this work agree well with all the available data with a limited number of parameters used. [ABSTRACT FROM AUTHOR]

In the current work, the phase equilibrium of the CaO-Nb 2 O 5 -TiO 2 system in different atmospheres was investigated through high-temperature experiments. In air atmosphere, a total of 9 phase fields were determined: 5 three-phase fields(CaO·Nb 2 O 5 +5Nb 2 O 5 ·2TiO 2 +Nb 2 O 5 ·TiO 2 , CaNb 2 O 6 -Nb 2 O 5 ·TiO 2 -TiO 2 , CaO·Nb 2 O 5 +3CaO·Nb 2 O 5 ·3TiO 2 +TiO 2 , CaO·TiO 2 +3CaO·Nb 2 O 5 ·3TiO 2 +TiO 2 , CaNb 2 O 6 -CaTiO 3 -(Ca,Nb,Ti)O), 3 two-phase fields(CaTiO 3 +TiO 2 , CaTiO 3 +4CaO·Nb 2 O 5 , CaTiO 3 +(Ca,Nb,Ti)O), and 1 single phase field (CaO·TiO 2). Some equilibrium experiments were also performed in Ar and H 2 atmospheres, with the phase equilibrium results same as that in air atmosphere. Meanwhile, the Gibbs energy data of Ca 4 Ti 3 O 10 and CaTi 2 O 4 were calculated according to the CALPHAD principle. On this basis, the influence of oxygen partial pressure on the phase equilibrium of Ti/Nb containing oxide system was discussed. The research results of this paper are of theoretical significance for the development of the thermodynamic database of Ca-Nb-Ti-O slag system. [ABSTRACT FROM AUTHOR]

Thermodynamic modeling of the Si-Y binary system has been performed by the CALPHAD (CALculation of PHAse Diagram) method based on phase diagram and thermochemical data in the literature combined with Gibbs energies of end-members of compounds predicted by first-principles phonon calculations. In particular, non-stoichiometric compounds Si 2 Y and Si 3 Y 5 are modelled to accommodate their homogeneity ranges in terms of two-sublattice models (Si,Y) 2 (Si,Y) and (Si) 3 (Si,Y) 5 , respectively. Formation of SiY is treated as a peritectic reaction according to experimental results, instead of an eutectic one as described in the previous models. The calculated phase equilibriums and thermodynamic properties are in a satisfactory agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Tb-Si intermetallics have been recognized as interesting magnetic and electrical materials. The addition of Cr can modify the property and broaden the application of Tb-Si intermetallic compounds. Understanding phase relations, phase stability and microstructural changes of relative systems are essential for tuning and improving performance of this type of materials. In this work, phase relationships in the Tb-Si-Cr ternary system have been studied based on phase and microstructure identification of key equilibrated alloys. Isothermal sections of this system at 1273 K and 1073 K were experimentally constructed by means of electron probe microanalysis, X-ray diffraction, and differential thermal analysis. As one of results, the ternary compound TbSi 2 Cr 2 was confirmed to exist at both 1273 K and 1073 K. In addition, remarkable solubilities of the third element were detected in some binary compounds. The solubility of Cr in Tb 2 Si 3-δ and TbSi at 1273 K are about 4.0 and 9.1 at%, respectively. The solubility of Cr in Tb 5 Si 3 increases from 3.0 at% at 1273 K to 6.2 at% at 1073 K. Besides, the compound Tb 2 Si 3-δ were determined to be stable ranging from 1098 ± 25 K to 1513 ± 10 K, based on the analysis of microstructure. Moreover, the annealing temperature dependence of micro-hardness for Tb 2 Si 3-δ intermetallic phase was investigated by nano-indentation. • Isothermal sections at 1073 and 1273 K of Tb-Si-Cr ternary system were determined. • Differing from other R-Si intermetallics, a certain amount of Cr was confirmed to be dissolved in Tb-Si compounds. • The stable temperature ranges of Tb 2 Si 3-δ were determined from 1098 ± 25 K to 1513 ± 10 K. • The primary crystal region of ternary compound TbSi 2 Cr 2 exists in liquidus projection. • Annealing temperature dependence of micro-hardness for Tb 2 Si 3-δ intermetallic phase was investigated. [ABSTRACT FROM AUTHOR]

The Al–Cu–Ni system has been thermodynamically assessed over the whole composition and temperature range based on a critical literature review. The L1 2 and B2 phases, in conjunction with their disordered counterparts, are described using partitioning models. Ab initio calculations were performed to support the assessment of these phases. A set of self-consistent thermodynamic parameters for describing the Gibbs energy of individual phases was obtained. The assessment was validated by comparing various calculations such as invariant reaction equilibria, thermochemical properties, isothermal and isoplethal sections with all available experimental data. The Al–Cu–Ni ternary is a vital subsystem of many high entropy alloys (HEAs), which can probably be attributed to the existence of stable ordered and disordered FCC and BCC structures. In near-equiatomic compositions of this ternary system, the phase formation and equilibrium and non-equilibrium solidification curves were calculated using the present thermodynamic description. The phase competitions and their impacts on the design of HEAs are discussed, e.g. the relative stability of the disordered FCC and BCC for dual-phase HEAs, and the equilibria between disordered FCC_A1 and ordered B2 phases for ductile high strength HEAs. • A thermodynamic constitution of the Al–Cu–Ni system is performed with the CALPHAD approach aided with DFT calculations. • A set of self-consistent thermodynamic parameters for describing the Gibbs energy of individual phases was obtained. • The assessment was validated by comparing various calculations with all available experimental data. • Various calculations using the resulting thermodynamic constitution can be employed to analyze and design diversified materials. • Varied HEA systems were designed on the basis of the present database. [ABSTRACT FROM AUTHOR]

Phase equilibria in the La-Fe-C system at crystallization were studied and the binary La-Fe system was reinvestigated using DTA, X-ray diffraction, SEM and electron probe microanalysis. Using the results, the binary La-Fe phase diagram has been redrawn and liquidus and solidus projections for the La-Fe-C system constructed, for the first time, covering the whole concentration range. There is no stable miscibility gap in the liquid phase of La-Fe system, according on our results. The La-Fe system shows a simple eutectic at 88 at.% La. The eutectic temperature was measured to be 788 °C. No intermediate phases were found. In the ternary La-Fe-C system a ternary compound La 3.67 FeC 6 (τ) was found in equilibrium with the liquid phase and to coexist with most of the other phases in the system. Additions of carbon to La-Fe alloys caused liquid immiscibility. In this investigation, the liquid separation has been proved with clear microscopic pictures of samples showing this effect. A ternary stable liquid miscibility gap marked L 1 + L 2 develops from a metastable liquid miscibility gap in the La-Fe binary system. None of the binary intermetallic phases show any solubility of the third component. • The binary La-Fe phase diagram has been redrawn. • There is no stable miscibility gap in the liquid phase of La-Fe system. • Liquidus and solidus projections constructed for the La-Fe-C system. • A closed liquid miscibility has been established. • The ternary compound La 3.67 FeC 6 (τ) was found to solidify incongruently by peritectic reaction. [ABSTRACT FROM AUTHOR]

In this work we report the thermodynamic modelling of the Al-N, B-N and Al-B-N systems by the Calphad approach, making use of the ab initio calculations and the available experimental thermochemical and phase equilibria data. Gibbs energy description for the Al-B system is taken from the literature, with a modification for the model for the liquid phase. The enthalpy of formation and the heat capacity of various polymorphs of AlN and BN are estimated using the DFT and the phonon calculations, respectively. The enthalpy of mixing of the mixed nitride (Al,B)N in wurtzite and cubic structures are obtained using the SQS method. Gibbs energy of formation of the mixed nitride from the binary nitrides is also computed using the phonon calculations. These quantities along with the critically assessed thermochemical and constitutional data are used for obtaining the Gibbs energy functions of various phases in the Al-N, B-N, and Al-B-N systems. Calculated phase equilibria and thermochemical data are compared with the experimental data. • Enthalpy of formation for various polymorphs of AlN and BN are computed using DFT. • C p of AlN and BN are obtained using phonon (QHA) calculations. • SQS approach is used for calculating enthalpy of mixing for (Al,B)N. • Gibbs energy of the reaction x AlN+(1- x)BN=Al x B (1- x) N is obtained using phonon (HA). • New thermodynamic assessments of Al-N, B-N, and Al-B-N are reported. [ABSTRACT FROM AUTHOR]

The phase equilibria at 1473, 1373 and 1273 K in the Fe–Ta–Ti system were investigated by means of Scanning Electron Microscopy (SEM) with Energy Dispersive Spectrometer (EDS) and X-ray Diffraction (XRD). The experimental results indicated that Fe 2 Ta and Fe 2 Ti formed the continuous solid solution phase Fe 2 (Ta,Ti). No ternary compound was found in this system. The temperature of invariant reaction liquid + Fe 7 Ta 6 → FeTi + bcc(Ta,Ti) was measured as 1431 K by Differential Thermal Analysis (DTA). Based on the experimental results in the present work, the Fe–Ta–Ti system was optimized using CALPHAD technique. A set of self-consistent thermodynamic parameters for the Fe–Ta–Ti system was obtained, and the experimental isothermal sections at 1473, 1373 and 1273 K were reproduced well. • The isothermal sections of the Fe–Ta–Ti system at 1473, 1373, and 1273 K were determined. • The temperature of the invariant reaction liquid + Fe 7 Ta 6 → FeTi + bcc(Ta,Ti) was confirmed at 1431 K. • A set of self-consistent thermodynamic parameters of the Fe–Ta–Ti system was obtained. [ABSTRACT FROM AUTHOR]

In this study, the iron-titanium-vanadium-oxygen (Fe-Ti-V-O) system in equilibrium with air was studied experimentally by high-temperature equilibration, quenching, scanning electron microscope and microprobe analysis coupled with critical assessment and thermodynamic evaluation. The properties of the liquid phase were successfully described with the quasichemical model by optimizing parameters only related to the Fe-Ti-O system; remaining parameters for the Fe-V-O and Ti-V-O sub-systems were adopted from recent optimisations. The model for the rutile and hematite solid solutions were described with the compound energy formalism. The ferropseudobrookite solid solution was modelled with a simple polynomial model to include a small solubility V 2 O 5 . A final set of self-consistent thermodynamic parameters was estimated within acceptable error limits. Calculated isothermal projections at 1000 °C, 1100 °C, 1200 °C, 1300 °C, and 1400 °C of the Fe-Ti-V-O system in equilibrium with air are presented and compared to experimental observations. [ABSTRACT FROM AUTHOR]

The phase equilibria in the lanthanum(III) bromide-thallium bromide pseudobinary system was established by means of differential scanning calorimetry (DSC). The DSC investigations were performed on samples with different compositions in the whole mole fraction x (LaBr 3) range. This system includes one intermediate compound Tl 2 LaBr 5. It melts congruently at 829 K. The compositions of TlBr-Tl 2 LaBr 5 and Tl 2 LaBr 5 -LaBr 3 eutectics, corresponding to LaBr 3 mole fraction x = 0.088 (T = 687 K) and x = 0.491 (T = 788 K) respectively, was found from Tammann's plot. The LaBr 3 -TlBr pseudobinary system was also optimized by CALPHAD method using the available experimental data. Experimental and calculated data concerning LaBr 3 -TlBr system were compared with data for LaBr 3 -MBr (M = Li-Cs) systems, which have also been optimized by CALPHAD method. The thermodynamic properties of the liquid phase in the systems were modelled using the Associated Solution Model with {3 M+ + LaBr 6 3−} (M = Li-Cs, Tl) associate. The dependencies of mixing enthalpy and mixing entropy on mole fraction x (LaBr 3) were estimated for all investigated systems. The dependencies of formation Gibbs energy on temperature and temperature range of existence of intermediate compounds have been calculated and discussed. The CALPHAD optimization indicates that the participation of the associate in the liquid phase in the LaBr 3 -MBr (M = K⋯Cs, Tl) systems increases with the increase of the ionic radius of the monovalent metal. [ABSTRACT FROM AUTHOR]

Phase relations in Zr-Ni-Sc ternary system were investigated experimentally through alloy sampling approach. Isothermal sections at 973, 1173, and 1273 K were constructed from the results of electron probe microanalysis (EPMA) and X-ray diffraction (XRD). No ternary phase has been detected in all these sections. Combining experiment and reasonable speculation, 12, 15 and 13 three-phase zones were obtained at 973, 1173 and 1273 K, respectively. Liquid region with a large composition range at 1273 K was found although its real boundary was estimated. The intermetallic compounds, Ni 2 Sc, NiSc and NiSc 2 , exhibit remarkable ternary solubility of Zr along the isoconcentration of Ni. • Isothermal sections in the Zr-Ni-Sc ternary systems at 973 K, 1173 K and 1273 K. • At 1273 K, Liquid with a large composition range occurs. • The compounds Ni 2 Sc, NiSc and NiSc 2 exhibit remarkable ternary solubility of Zr. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the thermodynamic descriptions of the binary Al-Sn and ternary Mg-Al-Sn systems were updated by using the CALculation of PHAse Diagram (CALPHAD) approach. For the Al-Sn sub-binary system, the solubility of Sn in (Al) fcc , which was ignored in the previous assessment, together with the recently experimental enthalpies of mixing in the liquid phase were taken into account. The calculated phase equilibria and thermodynamic properties in the binary Al-Sn system showed better agreement with more experimental information than those in the previous assessment. As for the Mg-Al-Sn ternary system, the newly updated thermodynamic descriptions of the Al-Sn system as well as those of the Mg-Al and Mg-Sn binary systems from the literature were adopted. A set of reliable and self-consistent thermodynamic parameters for the Mg-Al-Sn ternary system were obtained by reassessing the thermodynaic parameters of the liquid and solid solutions. Better agreement between the calculated results and the experimental data was achieved in the present assessent in comparison with the previous one. Furthermore, the Scheil-Gulliver solidification simulations were performed to predict the volume fractions of Mg 2 Sn, (Mg) hcp and γ (Mg 17 Al 12) phases in the 9 as-cast Mg-Al-Sn alloys. The simulation results were compared with the experiental as-cast microstructures in the literature, which further validated the presently obtained thermodynamic descriptions. Highlights • Solubility of Sn in (Al) fcc was considered. • New enthalpies of mixing in Al-Sn liquid phase were considered. • Thermodynamic descriptions for Al-Sn and Mg-Al-Sn systems were updated. • Better agreement with the experimental data were achieved. • Scheil solidification simulations were performed. [ABSTRACT FROM AUTHOR]

Abstract Vaporisation studies along the pseudo binary line of SnO 2 –TeO 2 (SnTe 3 O 8 + SnO 2) in the Sn-Te-O system were conducted by using Knudsen effusion mass spectrometry in the temperature range 843–968 K. SnTe 3 O 8 vaporises incongruently and TeO 2 (g), TeO(g), Te 2 (g) and O 2 (g) were the neutral species observed over the equilibrium vapour. Partial pressure – temperature (p-T) relations of TeO 2 (g), TeO(g), Te 2 (g) over (SnTe 3 O 8 + SnO 2) "two phase" region were determined in the temperature range 843–968 K. Partial pressures of O 2 (g) were calculated by considering gas phase equilibrium reactions involving this species and TeO 2 (g), TeO(g), Te 2 (g). Using the p-T relations, enthalpy changes of the following reactions were evaluated: SnTe 3 O 8 (s) ⇌ SnO 2 (s) + 3TeO 2 (g); SnTe 3 O 8 (s) + 2TeO(g) ⇌ 4TeO 2 (g) + 0.5 Te 2 (g) + SnO 2 (s) and 0.5Te 2 (g) + TeO 2 (g) ⇌ 2TeO(g). Subsequently, the enthalpy and Gibbs energy of formation of SnTe 3 O 8 phase at 298.15 K were deduced as Δ f H m ° = −1613.7 ± 67.8 kJ mol−1 and Δ f G m ° = −1386.7 ± 67.8 kJ mol−1. Knudsen effusion mass spectrometric studies on this system are being reported for the first time. [ABSTRACT FROM AUTHOR]

Abstract Liquidus phase equilibrium data of the present authors for the PbO-ZnO and the PbO-ZnO-SiO 2 systems (as a part of multicomponent PbO-ZnO-FeO-Fe 2 O 3 -Cu 2 O-CaO-SiO 2), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase. From these model parameters, the optimized ternary phase diagram is back calculated. [ABSTRACT FROM AUTHOR]

Abstract A thermodynamic assessment of the Zr-Fe-Cu system has been performed by using the first-principles calculations and the CALPHAD approach, which is capable of combining experimental and theoretical data of thermodynamics and phase equilibria. The isothermal sections at 853, 973, 1273, 1373 and 1473 K together with the mixing enthalpies of liquid phase at 1873 K were well evaluated, and a consistent set of thermodynamic parameters was obtained. The combination of three thermodynamic criteria has been applied to predict the composition dependency of the glass forming range (GFR), the glass forming ability (GFA) and the glass forming behaviour in the Zr-Fe-Cu system based on the thermodynamic description assessed in this work. Highlights • The Zr-Fe-Cu thermodynamic database has been constructed by CALPHAD for the first time. • Employing ab-initio calculations (VASP) to obtain the enthalpies of intermetallic phases. • The glass forming ability prediction by three thermodynamic criteria can provide a guideline for the Zr-Fe-Cu BMG design. [ABSTRACT FROM AUTHOR]