CALculation Of PHAse Diagram Modeling Research Articles

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)–CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)–CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)–CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

The Beneficial Effect of Iron in Aluminum-Cerium-Based Cast Alloys

Iron (Fe) has been considered a major impurity since it is detrimental to the mechanical properties of many cast aluminum alloys due to the formation of Fe-containing brittle intermetallic phases. Fe is found naturally as an impurity in bauxite ore, resulting in Fe contamination of aluminum alloys with increasing contamination from current recycling practices. The Al–Ce–Fe system was investigated using CALPHAD (CALculation of PHAse Diagrams) modeling and experimental casting techniques. It was found that additions of Fe to the Al–Ce system are beneficial to the strength (slightly) and ductility (significantly) of the ternary alloys, which is attributed to the formation of fine metastable Al8CeFe2 phase with aggregate morphology and equilibrium Al10CeFe2 phase, suppressing coarse proeutectic Al11Ce3 phase in near-eutectic Al–Ce alloys. Heat treatment study showed that the metastable Al8CeFe2 phase transforms to predicted equilibrium Al10CeFe2 phase at 500 °C, with essentially no intermetallic or grain coarsening; thus, the alloy displayed excellent property retention. The Al–Ce–Fe alloy system offers opportunities for sustainable, recyclable alloy development using low-cost Fe and low-cost cerium (a byproduct of rare-earth extraction).

Exploring NiCrAlYSiTa multicomponent coatings: Combining high-throughput synthesis and CALPHAD modeling

Multicomponent alloys pose great challenges for efficiently screening desired composition. Here, we combined high-throughput magnetron-sputtering experiments and CALculation of PHAse Diagrams (CALPHAD) methods to screen NiCrAlYSiTa coatings. The compositionally graded coatings showed increased amorphization with higher Si content, indicated by the steepen T0 curves and enlarged amorphous formation region. For the crystallized coatings, the phase structure transformed from Al- and Cr-rich bcc region to Ni-rich fcc, consistent with our calculated phase diagrams. Owing to the high cohesion energy and strong atomic bonding induced by large atomic radius difference and negative mixing enthalpy, the amorphous coatings exhibited superior hardness (25.8 GPa) and elastic modulus (415.8 GPa) compared to the reported multicomponent coatings. By combining high-throughput experimental and theoretical methods, this work pioneers an integrated framework for rapid development of new multicomponent alloy coatings.

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

CALPHAD aided mechanical properties screening in full composition space of NbC-TiC-VC-ZrC ultra-high temperature ceramics

High-entropy ceramics (HECs), especially ultrahigh-temperature ceramics, attract much attention from the refractory-materials community. However, current research about HECs focuses on the equimolar system, causing a gap between traditional and high-entropy ultrahigh-temperature ceramics. In this paper, we build the calculation of phase diagrams (CALPHAD) model of lattice parameters and elastic constants using the data from our first-principles calculation in the full composition space of NbC-TiC-VC-ZrC pseudo-quaternary NaCl-type monocarbides. With the aid of the CALPHAD model, we obtain the distribution of lattice parameters, elastic constants, hardness, fracture toughness, and wear resistance over the full composition space and give the maximum and minimum values for each property. Furthermore, the combination of first-principles calculations and CALPHAD modeling demonstrated in this paper provides a feasible paradigm for mapping the composition-property relationship, which can be applied in other HECs, such as high-entropy nitrides and high-entropy borides.

Fundamental Issues Identified for Thermodynamic Description of Molten Salt Systems

Thermodynamic modeling of the molten salt systems is critical in the design of advanced nuclear power plants, materials recycling, and many other important clean energy applications. As one of the most capable computational thermodynamic approaches, the CALPHAD (Calculation of Phase Diagrams) method has been widely used for multicomponent thermodynamic database development and further support more physics-based modeling. Although considerable CALPHAD modeling efforts for molten salt systems have been made, we found that no evaluation has been performed regarding the unary thermodynamic models for the molten salt systems despite the fact that more than one pure substance database is available for the CALPHAD modeling. Therefore, the thermodynamic descriptions of the pure salts should be critically evaluated to ensure a high-fidelity molten salt thermodynamic database. In this work, we comprehensively analyzed some selected molten salts using different available thermodynamic descriptions from two databases as an example. One is the SSUB database released by the SGTE (Scientific Group Thermodata Europe), and the other is the FactPS database from the FactSage. The significant discrepancies observed in the thermodynamic description between the existing CALPHAD pure substance databases and experiments call for an urgent effort to improve.

Experimental investigation and CALPHAD modeling of phase equilibria of the Cu–Ag–Zr system

The phase equilibria of the Cu–Ag–Zr system at 600 and 500 °C were determined by X-ray diffraction (XRD) and scanning electron microscope (SEM) with energy dispersive X-ray spectrometry (EDS) techniques. Invariant reactions involving the ternary Cu4AgZr phase were investigated by differential scanning calorimetry (DSC) techniques. Two as-cast alloys were prepared to study the alloys solidification behavior. The solubilities of Cu in the AgZr2 and AgZr phases and of Ag in the Cu5Zr, Cu51Zr14, Cu10Zr7 and CuZr2 phases were measured, and the ternary compound Cu4AgZr was found with compositions of Cu58.70-72.57Ag10.31-21.52Zr16.74-19.78 and Cu58.18-75.04Ag6.08-23.36Zr17.50-18.88 at 500 and 600 °C, respectively. Seven invariant reactions were determined. By using the CALPHAD (CALculation of PHAse Diagrams) method, thermodynamic assessment of the Cu–Ag–Zr system was carried out based on the available experimental data from the literature and the present work. Substitutional solution model was used to describe the solution phases and sublattice models were used to describe binary and ternary compounds. The ternary compound Cu4AgZr was describe as (Cu, Ag)5(Zr)1. A set of self-consistent thermodynamic parameters of the Cu–Ag–Zr system was obtained. The isothermal sections at 500, 600 and 750 °C and liquidus projection were calculated, and the reaction scheme was constructed. The solidification behaviors of as-cast alloys were simulated under Gulliver-Scheil non-equilibrium condition. The calculated phase equilibria and simulated solidification behaviors are in agreement with the experimental data.

CALPHAD modeling of uranium nitride (UN) fabrication routes enabled by first-principles calculations

The thermochemical details of fabricating uranium nitride (UN) by ammonolysis of uranium tetraflouride (UF4) were determined using density functional theory (DFT) and CALculation of PHAse Diagrams (CALPHAD) computational methods. The thermochemical data of all binary, ternary, and quaternary U–H–N–F phases were computed using DFT, and the data for the phases that have not been measured experimentally, including UN2 and NH4F(g), were combined with existing experimentally-determined data for CALPHAD modeling. The DFT data were benchmarked using experimental Gibbs energy of reaction and experimental thermochemical data for individual species. Phase diagrams relevant to the ammonolysis reaction are depicted, showing regions of stability for solid U–N, U–F and U–N–F phases. An unidentified phase produced in a previous experiment was identified as UN0.95F1.2 (UNF) by comparing its X-ray diffraction spectrum to the experimental spectrum, and its formation during the fabrication of UN from UF4 is supported by the simulated phase diagram. It is calculated that UN2 can be produced by the ammonolysis of UF4, but requires elevated temperatures, high NH3(g) partial pressure, and large amounts of flowing NH3(g) to avoid solid fluoride impurities in the uranium nitride. Likewise, U2N3 can be produced instead at temperatures greater than 980 K. The use of silane (SiH4) gas was investigated as a potential additive in the ammonolysis fabrication route to speed removal of fluorine. The addition of SiH4(g) offers little advantage to the removal of fluorine, and adds the complication of Si3N4 formation. The use of DFT to fill in missing data to perform CALPHAD calculations demonstrated here allows for the determination of more comprehensive and trustworthy phase diagrams than the use of existing experimental data alone.

Thermodynamic properties of the Nd-Bi system via emf measurements, DFT calculations, machine learning, and CALPHAD modeling

Thermodynamic properties of the Nd-Bi system were investigated using a combination of experimental measurements, first-principles calculations based on density functional theory (DFT), data mining and machine learning (DM + ML) predictions, and calculation of phase diagrams (CALPHAD) modeling. The electromotive force (emf) of Nd-Bi alloys in molten LiCl-KCl-NdCl3 at 773–973 K was measured via coulometric titration of Nd into Bi for the determination of thermochemical properties such as activity coefficients and solubilities of Nd in Bi. A new peritectic reaction of [liquid + NdBi2 = Nd3Bi7] at 774 K was confirmed using differential scanning calorimetry, structural (X-ray diffraction), and microstructural (scanning electron microscopy) analyses. The unknown crystal structure of NdBi2 was suggested to be a mixture of the anti-La2Sb configuration and the La2Te-type configuration based on ML predictions for over 26,000 data-mined AB2-type configurations together with DFT-based verifications. Using the newly acquired experimental data and DFT-based calculations, the thermodynamic description of the Nd-Bi system was remodeled, and a more complete Nd-Bi phase diagram was calculated, including the Nd3Bi7 compound, invariant transition reactions, and liquidus temperatures.

Experimental investigation and CALPHAD modeling of the Cu–Cr–Si ternary system

The phase equilibria of the Cu–Cr–Si ternary system were investigated via thermodynamic modeling coupled with key experiments. Seventeen ternary alloys were prepared to determine the isothermal sections of the Cu–Cr–Si system at 700 and 800 °C by combining X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). No ternary compound was found. The solubilities of the third element in binary compounds in the Cu–Si and Cr–Si systems were measured. Based on the thermodynamic descriptions of three constitutive binary systems available in the literature as well as the experimental phase equilibria data obtained from the present work and literature, thermodynamic re-assessment of the Cu–Cr–Si system was carried out by the CALPHAD (CALculation of PHAse Diagrams) approach. The substitutional model and sublattice model were used to describe the solution phases and intermediate phases, respectively. A set of thermodynamic parameters of the Cu–Cr–Si system was obtained. The calculated isothermal sections and vertical section are in good agreement with most of the reliable experimental data. The liquidus projection and reaction scheme of the Cu–Cr–Si system over the whole composition were also presented.

CALPHAD modeling based on Gibbs energy functions from zero kevin and improved magnetic model: A case study on the Cr–Ni system

The third-generation thermodynamic database that adopts the physics-based models over a wide temperature range is being developed in an attempt to increase the predictability and reliability of the CALPHAD (Calculation of Phase Diagrams) method. As a case study, this work used the new CALPHAD models to reoptimize Cr, Ni, and the Cr–Ni system. For pure elements, the Gibbs free energy of solid phases was described by a model considering various physical contributions, and the amorphous and liquid phases were described together by the two-state model. For Cr–Ni solution phases, thermodynamic modeling of the magnetic phase diagram was supported by ab initio calculations. This work demonstrated the way of performing thermodynamic assessment using the third-generation Gibbs free energy functions with the improved description of magnetic properties.

Mechanical and thermodynamic data-driven design of Al-Co-Cr-Fe-Ni multi-principal element alloys

Data-driven materials design is a modern approach, which is particularly desired for complex systems, such as the multi-principal element alloy (MPEA), also known as the high entropy alloy (HEA). The concept of MPEA/HEA brings tremendous opportunities of alloy design for superior mechanical properties, for instance, seeking for the ultimate goal of balanced strength and elongation in structural materials applications. Herein, we took the Al-Co-Cr-Fe-Ni quinary alloys as a model system to examine the semi-empirical method of alloy design based on empirical equations and high-throughput CALculation of PHAse Diagram (CALPHAD) modeling. The hardness, yield strength, ultimate tensile strength, and elongation of the as-cast Al-Co-Cr-Fe-Ni MPEA in the literatures were fit with the phase volume fraction of the fcc, bcc, and B2 phases. 10,000 CALPHAD solidification modeling based on the Scheil model were performed. Two alloys, Al14Co24Cr22Fe21Ni19 (A1) and Al16Co23Cr17Fe19Ni25 (A2), were cast and characterized with an X-ray diffractometer, a scanning electron microscope, a differential scanning calorimeter, hardness tests, and tensile tests. The semi-empirical method of combining empirical fitting of mechanical data in the literatures and thermodynamic calculation showed qualitatively agreements between experiments and predictions. While the CALPHAD modeling successfully interpreted the formation of phases and microstructures, the accuracy of empirical predictions can be further improved when more data are accessible for alloy and MPEA design under the guidance of calculations.

Microstructural evolution of Mg-Al-Re alloy reinforced with alumina fibers

Abstract Few studies were reported on the phases’ relationships of AE44 (Mg-4.0Al-4.1RE-0.3Mn, wt.%) and its composites. In this work, AE44 alloy and Saffil (δ-Al2O3)/AE44 Metal matrix composite (MMC) were both prepared by slow shot high pressure die casting (SS-HPDC) technology and their phase constitutions were all studied in detail using experimental techniques combined with CALPHAD (Calculation of Phase Diagram) modeling. The results revealed that the alloy consists of the α-Mg matrix, Al11RE3 intermetallic phase, and one trace phase Al3RE, while the composite contains five major phases: α-Mg, δ-Al2O3, Al3RE, MgO and Mg2Si, and two trace phases of Al2RE and Al11RE3, respectively. Al11RE3 is partly derived from Al2RE, while Al3RE is a product of the peritectoid reaction between the two precipitates. The presence of MgO and Mg2Si is due to the interfacial reaction between the SiO2 binder in the fiber preforms and the molten magnesium during infiltration. The use of SiO2 binder in the preform manufacturing was limited/minimized to reduce the MgO formation in the MMC casting process, which can be detrimental to the fatigue performance of the MMC materials.

A new magnesium sheet alloy with high tensile properties and room-temperature formability

Lightweight sheet alloys with superior mechanical performance such as high strength, ductility and formability at room temperature (RT) are desirable for high volume automotive applications. However, ductility or formability of metallic alloys at RT are generally inversely related to strength, thereby making it difficult to optimize all three simultaneously. Here we design a new magnesium sheet alloy-ZAXME11100 (Mg-1.0Zn-1.0Al-0.5Ca-0.4Mn-0.2Ce, wt. pct.) via CALPHAD (CALculation of PHAse Diagram) modeling and experimental validation. This new sheet alloy offers an excellent RT formability with a high Index Erichsen (I.E.) value of 7.8 mm in a solution-treated condition (T4), due to its weak and split basal texture and fine grain structure. The new ZAXME 11100 alloy also shows a rapid age-hardening response during post-forming artificial aging treatment at 210 °C for 1 hour (T6), resulting in a significant increase of yield strength from 159 MPa (T4) to 270 MPa (T6). The excellent combination of T4 ductility (31%), T4 formability (7.8 mm) and T6 yield strength (270 MPa) in this new magnesium alloy is comparable to that of common 6xxx series aluminum sheet alloys. Thus, this new magnesium sheet alloy is highly attractive for sheet applications in automotive and other industries.

ICME approach to explore equiatomic and non-equiatomic single phase BCC refractory high entropy alloys

High entropy alloys made from refractory metals, commonly known as refractory high entropy alloys (RHEAs) are potential candidates for high-temperature applications beyond the temperature regime (>1873 K) of conventional nickel based super alloys. In the present investigation, integrated computational materials engineering (ICME) framework consisting of detailed CALPHAD (CALculation of PHase Diagram) modeling and experimental investigation have been carried out to design both equiatomic and non-equiatomic RHEA composition exhibiting thermodynamically stable single-phase BCC/B2 solid solution. Starting with 126 equiatomic compositions, the CALPHAD calculations reveal only two equiatomic (MoNbTaVW and CrMoReVW) alloys having single phase BCC solid solution at 1000K. Further, low temperature (1000–400 K) CALPHAD assessment on 2902 non-equiatomic alloys reveal the formation of 54 single phase RHEAs based on MoNbTaVW at 400 K and 86 single phase RHEAs based on CrMoReVW at 800 K. In order to validate the CALPHAD predictions, one equiatomic, one non-equiatomic CrMoReVW alloy and six non-equiatomic MoNbTaVW alloys were synthesized and characterized using X-Ray diffraction, scanning electron microscopy and transmission electron microscopy. All of them show single phase solid solution with an excellent combination of microhardness (5.33–17.64 GPa) and elastic modulus (188–474 GPa) thus proving high fidelity of the CALPHAD approach in predicting phase stability of HEAs. To summarize, ICME approach involving CALPHAD modeling aids in accelerated design and development of existing RHEAs and discover new RHEAs showing potential for high-temperature applications.

Stable and metastable phase equilibria in binary Mg-Gd system: A comprehensive understanding aided by CALPHAD modeling

Abstract In this paper, a comprehensive understanding of stable and metastable phase equilibria in binary Mg-Gd system was conducted with an aid of the CALculation of PHAse Diagram (CALPHAD) modeling. Firstly, thermodynamic descriptions of all the stable phases in the Mg-Gd system were re-assessed by considering all the experimental data in the literature. The discrepancy between the phase equilibria and thermochemical properties existing in the previous assessments was eliminated, and the better agreement with the experimental data was achieved in the present assessment. Secondly, the Gibbs energies for metastable β''-Mg3Gd and β'-Mg7Gd were constructed based on the first-principles and CALPHAD computed results as well as their correlation, and then incorporated into the CALPHAD descriptions. The model-predicted solvuses of (Mg) in equilibrium with the metastable β''-Mg3Gd and β'-Mg7Gd compounds showed very good agreement with the limited experimental data. Finally, the presently obtained thermodynamic descriptions of both stable and metastable phases in the binary Mg-Gd system were further validated by realizing the quantitative Scheil-Gulliver solidification simulations of 5 as-cast Mg-Gd alloys, and the successful prediction of the precipitation sequences in Mg-15Gd and Mg-12Gd alloys during the aging process.

Thermal conductivity of the Mg–Al–Zn alloys: Experimental measurement and CALPHAD modeling

Thermal conductivity in a series of annealed Mg–Zn, Al–Zn and Mg–Al binary alloys was studied by experimental investigation and CALPHAD (CALculation of PHAse Diagram) methodology. Microstructure and phase identification of the alloys were determined using scanning electron microscopy and X-ray diffraction techniques. Thermal conductivity was measured over the temperature ranges from 298 K to 498 K on a Netzsch LFA457 using laser flash method. Based on the obtained experimental data, the mechanism of thermal conductivity variation was proposed. Considering the available experimental data from literature and the present work, the thermal conductivities of the Mg–Al–Zn system including pure elements, intermetallics, solid solution phases and two-phase regions were evaluated using the CALPHAD method (CALculation of PHAse Diagram). A set of self-consistent parameters for description of the thermal conductivity in Mg–Al–Zn system was obtained. The calculated results using the obtained parameters and the available experiment data shows an excellent consistency.

Applications of CALPHAD modeling and databases in advanced lightweight metallic materials

This paper presents an overview on the application of CALPHAD (CALculation of Phase Diagrams) methodology in the design and development of advanced lightweight metallic materials including magnesium, aluminum, titanium, aluminum-based metal matrix composites, and high entropy alloys. In this work, CALPHAD methodology has been established and summarized from the construction of databases describing thermodynamics, atomic mobility, kinetics, thermo-physical properties (such as viscosity) to the application of computational design of lightweight materials. The examples in this paper have demonstrated the effectiveness and capability of CALPHAD methodology in accelerating the design of advanced lightweight materials by optimizing the compositions and various heat-treatment conditions, modifying the evolution of microstructures during processing, and finally predicting the mechanical properties (e.g., yield strength and hardness) of the lightweight components. Although the examples are given in lightweight alloys for structural applications, the fundamental methodology and modeling principles are applicable to all materials and engineering applications. Thus, the future of the advanced material design will be strongly based on development of CALPHAD methodology such as the construction of reliable databases coupled with CALPHAD-based models for various applications.

CALPHAD modeling and ab initio calculations of the Np-U-Zr system

Phase diagram of Np-U-Zr, a key ternary alloy system of relevance for metallic nuclear fuels, is still largely undetermined. Here a thermodynamic model for the Np-U-Zr system is developed based on Muggianu extrapolation of our models for the U-Zr, Np-Zr, and Np-U binary systems, all employing the CALculation of PHAse Diagrams (CALPHAD) method. This model reproduces available experimental data for the high temperature phases reasonably well, but is uncertain for the lower temperature phases for which experimental data are scarce. Ab initio calculations are performed on the BCC phase of the Np-U-Zr system at 28 compositions employing density functional theory (DFT) both in its standard form and the so-called DFT plus Hubbard U (DFT + U) modification. When referencing to our CALPHAD model, standard DFT on average overestimates the enthalpy of mixing of the BCC phase by 0.093 eV/atom, while DFT + U reduces the error to 0.009–0.036 eV/atom when the effective Hubbard U parameters are in the ranges of single-structure optimized Ueff’s determined in our previous studies of the Np-Zr and U-Zr systems (0.65–0.90 for Ueff(Np) and 0.99–1.49 eV for Ueff(U), respectively). Our combined CALPHAD and ab initio modeling provides an initial attempt to determine the phase diagram of the Np-U-Zr system but further work is needed for a reliable determination.

First-principles calculations and thermodynamic modeling of the Yb-Ni binary system

A complete thermodynamic description of the Yb-Ni binary system is developed by means of the CALculation of PHAse Diagram (CALPHAD) method in combination with first-principles calculations based on density functional theory (DFT) and available experimental data in the literature. Finite temperature thermodynamic properties of the Yb-Ni intermetallic compounds are predicted using the quasi-harmonic approach, where first-principles phonon calculations are performed to calculate the lattice vibrational entropy. The associate solution model is used to describe the complex thermodynamic behavior of the liquid phase. The calculated phase diagram agrees well the experimental phase equilibrium data in the literature. By the coupling of CALPHAD modeling with first-principles calculations, the present work provides a more thermodynamically accurate model of the Yb-Ni system when compared to previous models.