New descriptions of pure Al and liquid C were developed and used to describe the Al–C system for the third generation of Calphad databases. The stable phases of the elements are described with a single expression for the entire temperature range. The expression is based on the Einstein model and an important parameter is therefore the Einstein temperature. For the metastable phases, the difference

Our recently developed model for the viscosity of silicate melts is applied to describe and predict the viscosities of oxide melts containing iron oxide. In the present study, the viscosity experimental data under the reduced atmosphere, which is Fe saturation condition were critically reviewed and three pairs of adjustable model parameters related to ‘FeO’ were optimized to best reproduce all experimental

A literature review, critical assessment and thermodynamic modeling of matte, metal (speiss) and solid phases in the Cu–As–S system are presented. The literature data include enthalpies and entropies of formation, activity measurements using vapor pressure, phase equilibrium and element distribution data. The model for the liquid phase was developed within the framework of the Modified Quasichemical

A series of Fe-Hf-Zr alloys were designed to determine the phase equilibria for the entire composition range by annealing at 1173 K and 1373 K for 440–720 h and 12–360 h respectively, followed by X-ray diffraction (XRD) measurements and electron probe microanalysis (EPMA). At the Fe-rich corner, it was argued that the Fe23Zr6 phase is a stable phase without oxygen contamination, of which the formation

In the present study, the viscosity experimental data for the FetO-containing silicate melts under oxidation atmosphere, which Fe3+ and Fe2+ co-exist were critically evaluated and model parameters related to Fe2O3 were optimized to best reproduce all reliable experimental viscosity data. The charge compensation effect on the viscosity for the systems containing Fe2O3 was modeled with the Gibbs energies

The Mn–Zr binary system has been investigated via experimental measurements and thermodynamic calculations. In order to investigate phase equilibria in the Mn–Zr system, five alloys were prepared by arc melting under vacuum. All alloys were examined by means of X-ray diffraction, scanning electron microscopy and electron probe microanalysis after annealing at 650 °C for 70 days or 950 °C for 30 days

U–Mo and U–Nb alloys are both extensively used in nuclear industry. γ phase in U–Mo or U–Nb alloy is a solid solution, being metastable in low temperature region. In this work, the effect of alloying on stability of grain boundary in meta-stable γ phase in U–Mo and U–Nb alloys are investigate through first-principles calculations. At first, crystal structure and elastic constants of Mo, Nb and γ-U

The isothermal sections of the Mg–Sn–Sr ternary system in the Mg-rich region at 415 and 350 °C have been determined using the scanning electron microscopy (SEM) equipped with energy dispersive X-Ray spectrometry (EDS). The existence of the MgSnSr ternary compound was confirmed in these two isothermal sections. Two new compounds, named Mg5Sn3Sr and Mg25Sn24Sr14, were found in the present work based

Phase equilibria of the Au–Cu–In system are investigated by combination of key experiments and thermodynamic modeling. Partial isothermal section at 500 °C of the Au–Cu–In system for In content up to 40 at.% have been plotted experimentally using scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDX) and X-ray diffraction (XRD). The solubilities of the foreign elements in

The Ru–X (X = Al, Hf, Mo, Ti) systems were re-optimized by means of the CALPHAD method according to the experimental phase equilibria and thermochemical data, as well as updated Gibbs energy function of “GBCCRU” in SGTE Pure 5 database. The substitutional solution model was applied to the phases liquid, fcc_A1, bcc_A2 and hcp_A3. Besides, the phases Al6Ru, Al13Ru4, Al5Ru2, Al2Ru and Al3Ru2 in the Ru–Al

The binary subsystems of the quaternary system Na2SO4–K2SO4–MgSO4–CaSO4 were thermodynamically assessed using the available experimental information including own thermochemical and structure measurements. Phase equilibria and thermodynamic properties of all six binary systems were properly considered. The modified associate species model was successfully applied for the description of the liquid phase

Available literature on the thermodynamic properties of binary CoSO4 – H2O system has been reviewed and used to derive a model for calculating the solution properties and phase equilibria in a thermodynamically consistent manner. The solution model is based on the Pitzer ion interaction approach and, with 10 adjustable parameters, is able reproduce the available literature data with good accuracy from

Diffusion behaviors in Mg–Sc hcp and bcc solid solutions between 773 and 873 K were investigated using both single-phase and multi-phase diffusion couple techniques. The EPMA detected composition-distance profiles were smoothed and fitted using the error function expansion (ERFEX). The interdiffusion coefficients were extracted using Sauer–Freise integral. The interdiffusion coefficients in hcp phase

Literature review, critical assessment and thermodynamic modeling of the liquid and solid phases in the As–S system are presented. A set of optimized model parameters was obtained to reproduce previously published experimental data. The literature data included enthalpies of formation, heat capacity, vapor pressure and phase equilibrium data. A significant discrepancy among different sets of literature

The Ag–Cu phase diagram at nanoscale was reassessed by CALculation of PHAse Diagrams (CALPHAD) method, considering the surface effect on the chemical potential of pure substance and excess Gibbs free energy of mixtures. According to the reported thermodynamic properties of pure Ag and Cu nanoparticles (NPs), and the measured melting eutectic temperatures of Ag8Cu2, Ag7Cu3, Ag6Cu5 to Ag5Cu5 NPs, respectively

Al2O3–CaO-(MgO–SiO2) inclusions are one of the dominant inclusions in Al-deoxidized spring steel, the compositions changes of which are closely related to refining slags and deoxidization process. The Al2O3–CaO–SiO2–MgO system can represent the primary ingredients of the Al2O3–CaO inclusions. According to analyzed compositions and predicted liquidus temperature ranges of inclusions and refining slag

The accurate interdiffusivity for fcc_A1 Ni–Cr–V system is needed for simulating the microstructure evolution for Ni-based alloys. In order to determine the interdiffusivity, totally fifteen diffusion couples bound with fcc_A1 Ni–Cr–V alloys were prepared in the present work. Both EPMA (Electron Probe Micro-Analysis) and XRD (X-ray diffraction) results can verify that all the samples are of fcc_A1

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary

The phase equilibria of the Dy-Mo-Si ternary system at 1173 K (900 °C) was experimentally determined in the entire concentration range by using x-ray powder diffraction (XRPD), scanning electron microscope equipped with energy dispersive spectrometer (SEM-EDS), and differential scanning calorimetry (DSC). The results show that there are 13 single-phase regions, 24 two-phase regions, and 12 three-phase

The supercell approach to first-principles calculations of an alloy's full phonon spectrum is computationally expensive. It is therefore rarely used for calculating temperature dependent free energies of alloy phases or for calculating alloy phase diagrams. Amid the wider acceptance of uncertainty evaluation and the use of more efficient methods for materials design, the supercell approach is revisited

Accurate and precise thermodynamic models of oxide compounds and their phases are important for calculating the phase stability of oxide materials. We develop and use a coupled quantum mechanical and molecular dynamics approach to create thermodynamic models of hafnia (HfO2) polymorphs from 0 K to 3000 K at ambient pressure. The approach is based on the quasi-harmonic approximation below the Debye

Decades of scientific work dedicated to the investigation of phase diagrams gave significant benefit to industry and science. After all those years of phase diagram investigation still there is missing information about phase diagram of some ternary systems. One of those systems is Cu-Ge-Pb. It is known importance of Cu-based alloys and Ge-based alloys in electro industry. Since such combination is

The Thermodynamics of Advanced Fuels – International Database (TAF-ID) was developed using the Calphad method to provide a computational tool to perform thermodynamic calculations on nuclear fuel materials under normal and off-normal conditions. Different kinds of fuels are considered: oxide, metallic, carbide and nitride fuels. Many fission products are introduced as well as structural materials (e

In the present work, the liquidus projection of the Al–Nb–V system is proposed for the first time. It corresponds to important data for the design of innovative low-density Al-containing refractory high-entropy alloys. Experimental investigation was carried out via microstructural characterization of fifty-six alloys in as-cast state using scanning electron microscopy (SEM), electron dispersive X-ray

Based on critical evaluation of the literature data, the C–Nb–V system has been reviewed and assessed by means of the CALPHAD technique. There is no ternary compound in this system. The individual phases, i.e., liquid, fcc, hcp and bcc, have been modeled. The modeling covers the whole compositional range of this system and the temperature range from 1400 to 3310 °C. The C–V system is minor revised

Liquidus phase equilibrium experimental data from the present study for the ZnO-“Fe2O3”-CaO-SiO2 system in air, combined with phase equilibria and thermodynamic data from the literature on the ZnO-“Fe2O3”-CaO system in air and ZnO-“FeO”-CaO-SiO2 system in equilibrium with metallic Fe, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases in the ZnO–FeO–Fe2O3–CaO–SiO2

Thermodynamic modeling of the σ phase was revised according to the three sublattice model developed for the Fe–Cr system (Fe,Cr)10(Fe,Cr)4(Fe,Cr)16 in the view of simulating thermodynamics and kinetics for duplex stainless steels. The alloying elements Mn, Mo and Ni relevant in duplex steels were added to the σ phase model and their thermodynamic parameters were optimized. As a consequence of the change

Assisted by the first-principles calculations, the molar volumes of γ and γ′ phases in the binary Ni–Al system were modeled within the framework of the CALPHAD method. A CALPHAD database integrating thermodynamic and molar volume descriptions was established. The present Ni–Al binary database was validated to make good predictions of molar volumes/lattice parameters and thermal expansivities for both

For a binary ordered solid solution, the configurational microscopic state of the system is described in terms of the correlation functions (CFs). In CE – CVM, these are functions of point CF (u0, which is related to the composition), the Bragg-Williams long range order parameter (ξ), temperature (T) and cluster expansion coefficients (CECs). In this communication, a detailed procedure for obtaining

Phase diagrams obtained from first-principles have the potential to reduce time and expense by guiding experimental investigations for materials design applications. However, simply substituting all experimental data with calculated single phase quantities alone has generally shown limited success in the standard CALPHAD modelling of binary or multicomponent systems. In this work, the solid aluminium-nickel

In the present work, the Al–Co–Mn ternary system is thermodynamically modelled using the Calphad approach. In the modelling, experimental data such as liquidus, solidus, tie lines, and phase boundaries are included. An order–disorder model is used to describe the bcc and B2 phases. The bcc/B2 description was modified in the binary Al–Co system to improve the fit of bcc/B2 equilibria in the ternary

The density of Al2O3–CaO–MgO–SiO2 system is calculated using a model for molar volume. The model is similar to the one used for enthalpy of a multicomponent solution in the CALPHAD approach. The expression for molar volume consists of two terms: one representing the volume contribution from pure components and the other the volume of mixing. The molar volume of mixing takes into account of the binary

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. The objective of this study is to extend the binary thermodynamic models published in our previous studies to multicomponent systems. A revised general Pitzer–Simonson–Clegg (PSC) gE,∗ equation for multicomponent system is proposed without limitation on

The Ag–Pb–Sn ternary system is an important material system for both electronic packaging and thermoelectric applications. However, there is no experimental phase equilibria information of the ternary system. Ag–Pb–Sn alloys are prepared and their phase equilibria at various temperatures were determined. The focus was on the 500, 350, and 200 °C isothermal sections. Additional information was also

Kinetic simulations of σ phase precipitation in duplex and hyper duplex stainless steels were carried out by employing mean field approach. For duplex and hyper duplex steels, time-temperature-precipitation (TTP) curves were calculated and compared with experimental results. Thermokinetic predictions confirm that segregation of Cr and especially Mo at grain boundaries of ferrite plays an important

Using a combination of first-principles calculations, special quasi-random structures and quasi-harmonic Debye model methods, we investigated the structural properties, magnetic moments, phase stability, electronic structure, mechanical properties and thermodynamic properties of fcc and bcc FeNi1-xCrx disordered alloys. The results show that the volume per atom and lattice constant of fcc and bcc FeNi1-xCrx

Sodium and potassium carbonates and their mixtures are important for different applications, e.g. for latent thermal energy storage, die-casting processes and molten carbonate fuel cells. In this work the phase diagram and thermodynamic properties of Na2CO3–K2CO3 system were studied by differential thermal analysis, differential scanning calorimetry and high temperature X-ray diffraction. Three carbonate

In the present work, the liquidus and solidus for a series of NixCo1-2xCrx alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments

An essential step in CALPHAD is assigning relative weights to different datasets, but there is no consensus as to the best approach regarding this issue. Currently, such an assignment of weights for experimental or first-principles data is performed manually based on the knowledge and experience of the modeler. Since the existing manual treatment is subjective and time consuming, manipulation of such

Thermodynamic assessment of the constitutive binaries of the NaCl-KCl-UCl3-PuCl3 system was carried out by CALPHAD (CALculation of PHase Diagrams) approach. The liquid phase was described by the substitutional solution model, and the intermediate compounds were treated as stoichiometric phases. The thermodynamic parameters of the binary systems were obtained based on experimental phase equilibria data

Vapor-liquid equilibria (VLE) of the Cu–Sn system have been investigated in the temperature range from 1612 to 1650 K and at pressure of 5 Pa. The VLE data of Cu–Sn alloy was calculated by using Wilson equation and compared with experimental values under vacuum condition. The thermodynamic consistency of the experimental data was checked by Van Ness method. The azeotropic and non-azeotropic regions

Phase equilibria in the Co–Fe–La ternary system have been studied using X-ray diffraction (XRD), scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). Isothermal sections at 600 (in the whole concentration region) and 500 °C (in the La-rich region) for this system have been constructed. It was shown that the ternary compound La2(Co,Fe)17 (τ) (Th2Zn17-type structure) is stable

Differential Scanning Calorimetry (DSC) method was used to determine phase equilibria in the LaI3–RbI binary system, and heat capacity of LaI3 and compounds existing in the system under investigation. Two compounds were identified in the solid phase of this system. First of them, Rb2LaI5, melts incongruently at 809 K. The second one, Rb3LaI6, forms at 686 K from Rb2LaI5 and RbI, undergoes a solid-solid

Thermodynamic information of the Mo–Ti–Zr ternary system is extremely useful to provide guidance for biomedical alloy development. In the present work, the experimental phase diagram data available from the literature were critically reviewed, and a thermodynamic modeling of the Mo–Ti–Zr system was performed using the CALPHAD (CALculation of PHAse Diagram) approach. The solution phases including liquid

The sodium pyrovanadate (Na4V2O7) powder was synthesized by solid-state reaction using sodium carbonate (Na2CO3) and vanadium pentoxide (V2O5) as raw materials. X-ray powder diffraction (XRD), scanning electron microscope (SEM), and differential scanning calorimeter (DSC) were used to accurately characterize the synthesized sample. The solid-state phase transformation from α-Na4V2O7 to β-Na4V2O7 occurs

The melting behavior of spinel in the Fe–Al–O system at high temperatures (1500–1800 °C) was studied by a combination of experimental and computational investigations. Differential thermal analysis (DTA) at ultra-high temperatures coupled with cooling traces on CO2 laser-heated levitated samples provided melting temperatures and the heats of fusion of (Fe,Al)3O4 spinel phases. The experimental results

Ni–Cr–V system is a significant sub-system of both cemented carbides and superalloys. In the present work, the atomic mobilities for fcc_A1 Ni–Cr–V alloy were evaluated by means of the CALTPP (CALculation of ThermoPhysical Properties) program, which utilizes the thermodynamic description and the interdiffusivity obtained in our previous work by a numerical inverse method. The reasonability was validated

Liquidus phase equilibrium data from the recent study for the PbO–CaO and the PbO–CaO–SiO2 systems (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe2O3-“Cu2O”-CaO-SiO2 system), 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: liquid

Two computational approaches to the vibrational part of thermal properties and equation-of-state parameters of the Ni3Sn(hP8), Ni3Sn(cP4), Ni3In(hP8) and Ni3In(cP4) intermetallic phases, of interest in the study of lead-free soldering materials, have been critically compared. The first approach, referred to as the “phonon method” (PHM) combines the zero-kelvin energy versus volume values obtained ab

Analyzing diffusion behaviors can help in predicting the relevant properties of Zr alloy materials. In this work, the diffusion behaviors of the BCC Zr–Ti–Nb system were studied via the diffusion couple method. Based on the concentration-distance profiles analytically represented by the error function expansion (ERFEX), the ternary inter-diffusion coefficients and impurity diffusion coefficients of

The Gibbs energy balance (GEB) concept for modeling the transformation stasis during isothermal ferrite formation is revisited. Modification has been made to take into account the carbon redistribution into remaining austenite and the increased carbon solubility in ferrite transformed at low temperature. Both the original and modified models adequately describe the transformation stasis in ferrite

In the present work, the thermodynamic description of the Ti–Al–Zr ternary system was assessed by taking into account the ab initio data on the formation enthalpies of end-members of the intermetallic compounds, combined with the available experimental phase equilibria information in literature. The developed thermodynamic description of Ti–Al–Zr system allows to reasonably represent the experimental

In this study, the effect of MgO on the phase equilibria of iron silicate slags in equilibrium with Fe3O4 spinel and matte of fixed 72 wt % Cu were identified at controlled P(SO2) 0.3 and 0.6 atm. The experimental process includes equilibration, quenching and Electron Probe X-ray Micro Analysis (EPMA). Spinel (Fe3O4) substrates were applied to confirm the equilibrium was achieved in the primary phase

To control the chemically active boron (B) in 9CrMoCoB within a narrow target range, thermodynamic calculations using FactSage 7.2 and equilibrium reaction experiments were conducted between slag and steel. First, equilibrium reaction experiments between 9CrMoCoB and slag of 55%CaF2–20%CaO–3%MgO–22%Al2O3–x%B2O3 (x ≤ 3) were conducted to supplement and optimize the Henrian activity coefficient γ (lgγ = A/T + C

Liquidus phase equilibrium data of the present authors for the CaO–ZnO–SiO2 system (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe2O3-“Cu2O”-CaO-SiO2 system), 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