Calculation Of Phase Diagrams Method Research Articles

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.

Experimental Investigation and Thermodynamic Calculation of Phase Equilibria in the Mg-Pb-Sn Ternary System

The phase equilibria of the Mg-Pb-Sn ternary system were investigated using a combined method of electron probe microanalyzer and x-ray diffraction. Three isothermal sections of the Mg-Pb-Sn ternary system at 200, 300 and 400 °C were experimentally established. The phase equilibria of Mg-Pb-Sn ternary system were thermodynamically assessed by using CALPHAD (Calculation of Phase Diagrams) method on the basis of the presently determined experimental data. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Mg-Pb-Sn ternary system. The calculated phase diagrams and thermodynamic properties in the Mg-Pb-Sn ternary system are in good agreement with experimental data.

A Thermodynamic Assessment of the Li-Ge System

The thermodynamic modeling of the Li-Ge binary system was carried out using CALPHAD (CALculation of PHAse Diagram) method. The liquid phase was described as substitutional solution phase, while the nine intermetallic compounds Li17Ge4, Li4.1Ge, Li15Ge4, Li13Ge4, Li14Ge6, Li9Ge4, Li12Ge7, LiGe and Li7Ge12 were treated as stoichiometric compounds. The temperature dependent interaction parameters $$L_{i}^{\text{Liquid}}$$ of liquid were described by either exponential (Kaptay equation) or linear equation, respectively. The comparisons between experimental data and modeled results are given. The calculations based on the obtained thermodynamic parameters are in good agreement with both phase diagram data and thermodynamic values. In particular, the liquid phase was successfully described by the exponential equation for it is possible to avoid the occurrence of the artificial miscibility gap at high temperatures.

Microstructural Evolution and Phase Formation in 2nd-Generation Refractory-Based High Entropy Alloys.

Refractory-based high entropy alloys (HEAs) of the 2nd-generation type are new intensively-studied materials with a high potential for structural high-temperature applications. This paper presents investigation results on microstructural evolution and phase formation in as-cast and subsequently heat-treated HEAs at various temperature-time regimes. Microstructural examination was performed by means of scanning electron microscopy (SEM) combined with the energy dispersive spectroscopy (EDS) mode of electron probe microanalysis (EPMA) and qualitative X-ray diffraction (XRD). The primary evolutionary trend observed was the tendency of Zr to gradually segregate as the temperature rises, while all the other elements eventually dissolve in the BCC solid solution phase once the onset of Laves phase complex decomposition is reached. The performed thermodynamic modelling was based on the Calculation of Phase Diagrams method (CALPHAD). The BCC A2 solid solution phase is predicted by the model to contain increasing amounts of Cr as the temperature rises, which is in perfect agreement with the actual results obtained by SEM. However, the model was not able to predict the existence of the Zr-rich phase or the tendency of Zr to segregate and form its own solid solution—most likely as a result of the Zr segregation trend not being an equilibrium phenomenon.

Thermodynamic calculation and analysis for aluminum‐alloyed high boron high speed steel

AbstractThe equilibrium solidified phase diagrams of high boron high speed steel have been calculated and the vertical section of iron‐carbon pseudo‐binary phase diagrams has been drawn with different aluminum concentration. The effect of aluminum on phase diagrams and solidification microstructure has been investigated by using optical microscope, scanning electron microscopy, X‐ray diffraction, and differential scanning calorimetry. The results show that the austenite region shrinks to a small area and the δ‐iron changes into α‐iron directly during cooling process when the aluminum content reaches 1.5 wt.%. The addition of excessive amount of aluminum favors the formation of ferrite, which leads to the hardness decreasing. Moreover, excessive amount of aluminum (Al≥1.5 wt.%) will make network M2B borocarbides tend to break. Alloying with aluminum raises the solubility of carbon in the matrix and reduces the quenched hardness. The calculation results are agreed with the ones from experimental. The calculation of phase diagrams method has been successfully used for the computation of phase equilibrium in the multi‐component high boron high‐speed steel system. The work provides a practical method for engineers and researchers in related areas.

Assessment of the Al-Bi-Mg system and extrapolation to the Al-Bi-Mg-Sn quaternary system

The phase equilibria in the Al-Bi-Mg-Sn quaternary system have been studied using the CALPHAD (CALculation of PHAse Diagram) method. One of the four ternary systems constituting the quarternary system, the Al-Bi-Mg system, is re-assessed by means of the CALPHAD technique and Thermo-Calc software package, in consideration of the associate model for the liquid phase instead of the Modified Quasi-chemical Model used in the literature report. While for the other three ternary systems, the Al-Bi-Sn, the Al-Mg-Sn and the Bi-Mg-Sn systems, the thermodynamic parameters are mainly adopted from the literature reported optimization results with a little modification to the Al-Bi-Sn and the Al-Mg-Sn systems for the compatibility of all the constituent binary systems. The assessment results of the Al-Bi-Mg ternary system are in good agreement with the available experimental phase relations, including the liquidus surface projection and the vertical sections. The thermodynamic database of the Al-Bi-Mg-Sn quaternary system was developed without the consideration of the quaternary interactions and the quaternary compounds. With this newly developed thermodynamic database, the phase equilibria and the solidification processes of the ternary and the quarternary systems are calculated and analyzed.

Thermodynamic Assessment of the Ti-RE (RE = Ce, Er, Tm, Y) Binary Systems

Based on the available literature experimental phase equilibria, the Ti-RE (RE = Ce, Er, Tm, Y) binary systems have been critically reviewed and modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. No compound exists in these binary systems. The solution phases, i.e., liquid, bcc(βTi, δCe, βY), hcp(αTi, Er, Tm, αY) and fcc(γCe, γY), are described by the substitutional solution model. A set of self-consistent thermodynamic parameters is finally obtained for each of these binary systems. Comparisons between the calculated and measured phase diagrams show that most of the experimental data are satisfactorily accounted for by the present thermodynamic descriptions.

Thermodynamic assessment and binary nucleation modeling of Sn-seeded InGaAs nanowires

We have performed a thermodynamic assessment of the As-Ga-In-Sn system based on the CALculation of PHAse Diagram (CALPHAD) method. This system is part of a comprehensive thermodynamic database that we are developing for nanowire materials. Specifically, the As-Ga-In-Sn can be used in modeling the growth of GaAs, InAs, and InxGa1−xAs nanowires assisted by Sn liquid seeds. In this work, the As-Sn binary, the As-Ga-Sn, As-In-Sn, and Ga-In-Sn ternary systems have been thermodynamically assessed using the CALPHAD method. We show the relevant phase diagrams and property diagrams. They all show good agreement with experimental data. Using our optimized description we have modeled the nucleation of InxGa1−xAs in the zinc blende phase from a Sn-based quaternary liquid alloy using binary nucleation modeling. We have linked the composition of the solid nucleus to the composition of the liquid phase. Eventually, we have predicted the critical size of the nucleus that forms from InAs and GaAs pairs under various conditions. We believe that our modeling can guide future experimental realization of Sn-seeded InxGa1−xAs nanowires.

Experimental Investigation and Thermodynamic Modeling of the Ag-Cu-Ge System

The liquidus surface projection was re-investigated using scanning electron microscopy with energy dispersive spectrometer and differential thermal analysis. The invariant reactions, liq. → fcc(Ag) + diam(Ge) + η at 810 K (537 °C), and liq. + e → η + fcc(Ag) at ~848 K (575 °C) were confirmed, and θ →liq. + η + diam(Ge) at 859 K (586 °C) was inferred in the present work. On the basis of the experimental data in the present work and literature, the Ag-Cu-Ge system was modeled using the CALPHAD (CALculation of PHAse Diagram) method. Solution phases, liquid, hcp, and fcc, were modeled as (Ag, Cu, Ge) using the substitutional solution model in the Ag-Cu-Ge ternary system. The compounds, e, η, and θ, in the Cu-Ge system, were treated as line compounds (Ag, Cu) m Ge n in the Ag-Cu-Ge system. A set of self-consistent thermodynamic parameters was obtained. Using these thermodynamic parameters, the experimental isothermal sections at 763 K, 793 K, 863 K, and 923 K (490 °C, 520 °C, 590 °C, and 650 °C), the vertical section at 38.0 at. pct Cu, the liquidus surface projection, and the invariant reactions in the Ag-Cu-Ge system were well reproduced.

Thermodynamic description of the Al–Ge–Ni system over the whole composition and temperature ranges

The phase equilibria and thermodynamic properties of the Al–Ge–Ni system are useful for understanding the diffusion process during the transient liquid phase (TLP) bonding. In this work, the thermodynamic description of the Al–Ge–Ni system over the whole composition and temperature ranges was performed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The enthalpies of mixing of the liquid phase, three isothermal sections at 973, 823, and 673K and nine vertical sections at 10, 20, 35, 55, 60, 70, 75, and 80at% Ni and at a constant Al:Ni ratio of 1:3 were taken into account in the present optimization work. A set of self-consistent thermodynamic parameters of the Al–Ge–Ni system was first obtained. The liquidus projection and reaction scheme were constructed according to the thermodynamic parameters obtained in this work. The phase equilibria and thermodynamic properties calculated by the present thermodynamic description show satisfactory agreement with the available experimental information.

Experimental investigation and thermodynamic assessment of Al–Ca–Ni ternary system

The Al–Ca–Ni ternary system has been experimentally investigated and thermodynamically assessed to contribute to the development of a novel Al-base amorphous alloy. A new approach in alloy preparation was used due to the special properties of calcium. With selected equilibrated alloys, the isothermal sections of the Al–Ca–Ni system at 873 and 673 K were obtained by means of scanning electron microscopy, electron probe micro-analysis (EPMA) and powder X-ray diffractometry (XRD). Phase transformation temperatures were measured by differential scanning calorimetry (DSC) analysis. The liquidus projection of this ternary system was determined by identification of primary crystallization phases in as-cast samples and from the liquidus temperatures obtained from DSC analysis. A new ternary compound Al78Ca9Ni13 (referred to as τ 3 here after) has been confirmed to exist in both the 873 and 673 K isothermal sections on the basis of EPMA and XRD analysis. All sample compositions are Al-rich: A1–A4 samples > 72.64 at.% Al, B1–B10, C1–C11 > 45 at.% Al, with only C12 at 36.8 at.% Al. Based on the available data of the binary systems Al–Ni, Al–Ca, Ca–Ni and the ternary system Al–Ca–Ni from the literature and present work, thermodynamic modelling of the Al–Ca–Ni ternary system was performed using the calculation of phase diagram method coupled with first-principle calculations. A set of consistent thermodynamic parameters for the Al–Ca–Ni ternary system was obtained with good agreement with the experimental results in the Al-rich region. The calculated data in the Al-poor region are a very plausible prediction, but not validated.

Thermodynamic Reassessment of the C-Ni-Si System Using a Four Sublattice Model for Ordered/Disordered fcc Phases

A thermodynamic reassessment of the ternary C-Ni-Si system is performed by means of calculation of phase diagrams method based on the critical literature review. The fcc_A1/Ni3Si_L12 disordered/ordered transition is described using a four-sublattice model. Thermodynamic description of the liquid phase is optimized, successfully avoiding the formation of inverted miscibility gap at high temperatures. An optimal and self-consistent set of thermodynamic parameters for the C-Ni-Si system is obtained. The computed phase diagram and phase relations fit well with all the reliable experimental information according to the present modelling.

Experimental Investigation and Thermodynamic Calculation of the Phase Equilibria in the Co-Cu-V Ternary System

The phase equilibria of the Co-Cu-V ternary system at 900, 1000, 1100 and 1200 °C have been experimentally determined by optical microscopy and electron probe micro-analysis of the equilibrated alloys. The phase transformations were investigated by means of the differential scanning calorimetry. Based on the experimental data of phase equilibria and thermodynamic properties, the thermodynamic assessment of the Co-Cu-V ternary system was carried out by using the calculation of phase diagrams method. A consistent set of the thermodynamic parameters leading to reasonable agreement between the calculated results and experimental data was obtained in the Co-Cu-V ternary system. Meanwhile, the calculated results show that the critical temperature of metastable magnetically induced miscibility gap of (α f Co) and (α p Co) phases in the Co-V system gradually decreases with increasing Cu composition in the range of 0-3 wt.% additions.

High-Throughput Thermodynamic Modeling and Uncertainty Quantification for ICME

One foundational component of the integrated computational materials engineering (ICME) and Materials Genome Initiative is the computational thermodynamics based on the calculation of phase diagrams (CALPHAD) method. The CALPHAD method pioneered by Kaufman has enabled the development of thermodynamic, atomic mobility, and molar volume databases of individual phases in the full space of temperature, composition, and sometimes pressure for technologically important multicomponent engineering materials, along with sophisticated computational tools for using the databases. In this article, our recent efforts will be presented in terms of developing new computational tools for high-throughput modeling and uncertainty quantification based on high-throughput, first-principles calculations and the CALPHAD method along with their potential propagations to downstream ICME modeling and simulations.

Thermodynamic evaluation of LiCl-KCl-PuCl3 system

The present study focuses on developing the phase diagram of LiCl-KCl-PuCl3 system based on the CALPHAD (CALculation of PHase Diagram) method. Sub-binary systems of LiCl-KCl, LiCl-PuCl3, and KCl-PuCl3 were developed first by optimizing the Gibbs energy parameters according to the experimental data from literature using the two-sublattice model. Then the enthalpy of mixing of the LiCl-KCl-PuCl3 system was estimated, to explore the ternary interactions, using an empirical correlation derived from the surrounded-ion model for the asymmetric salt system due to the scarcity of available data for the ternary system. Based on the phase diagram developed, the solubility of PuCl3 in the eutectic LiCl-KCl melt at different temperatures was obtained, as well as the Gibbs energy of formation of PuCl3 in the salt as a function of PuCl3 concentration. The present study extends the experimental data for dilutions to concentrated solutions for which no experimental data have been well reported.

Thermodynamic reassessment of the Ni–Si–Ti system using a four-sublattice model for ordered/disordered fcc phases supported by first-principles calculations

A thermodynamic reassessment of the ternary Ni–Si–Ti system was performed by means of CALPHAD (CALculation of PHAse Diagram) method. The fcc_A1/Ni3Si-L12 disordered/ordered transition was described using a four-sublattice model. The enthalpies of formation of the ternary compounds τ1, τ2, and τ4 and end-members of the Ti5Si3 and Ni3Ti phases at 0 K in the Ni–Si–Ti ternary system were computed via first-principles calculations to supply necessary thermodynamic data for the CALPHAD modeling. In the Ni–Si–Ti ternary system, it was clarified that the ordered Ni3Si-L12 phase is formed from the liquid phase with the addition of Ti. An optimal set of thermodynamic parameters for the Ni–Si–Ti system was obtained by taking into consideration of the experimental data from the literature and theoretic values from the present first-principles calculations. Comparisons between the calculated and measured phase diagrams indicated that almost all the reliable experimental information was satisfactorily accounted for by the present modeling.

Experimental investigation and thermodynamic modeling of the Ti–V–Zr system

The isothermal sections at 1073 and 1273K, and liquidus surface projection of the Ti–V–Zr system were investigated using X-ray powder diffraction (XRD), scanning electron microscopy (SEM) with energy dispersive spectrometer (EDS) and differential thermal analysis (DTA). Combined with experimental results in the present work and literature, the Ti–V–Zr system was optimized by the means of the CALPHAD (CALculation of PHAse Diagram) method. The solution phases, liquid, hcp (Ti, Zr) and bcc (Ti, V, Zr), were modeled with the substitutional solution model, and the compound V2Zr was treated as (Ti, V, Zr)2(Ti, V, Zr) based on its thermodynamic model in the V–Zr system and the experimental solid solubility of Ti in the Ti–V–Zr system. A set of self-consistent thermodynamic parameters of the Ti–V–Zr system was obtained.

Design of Light-Weight High-Entropy Alloys

High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespread interest from scientists for use as potential structural materials. Great efforts have been made to study the phase-formation rules of HEAs to accelerate and refine the discovery process. In this paper, many proposed solid-solution phase-formation rules are assessed, based on a series of known and newly-designed light-weight HEAs. The results indicate that these empirical rules work for most compositions but also fail for several alloys. Light-weight HEAs often involve the additions of Al and/or Ti in great amounts, resulting in large negative enthalpies for forming solid-solution phases and/or intermetallic compounds. Accordingly, these empirical rules need to be modified with the new experimental data. In contrast, CALPHAD (acronym of the calculation of phase diagrams) method is demonstrated to be an effective approach to predict the phase formation in HEAs as a function of composition and temperature. Future perspectives on the design of light-weight HEAs are discussed in light of CALPHAD modeling and physical metallurgy principles.

Thermodynamic calculations of the Au–Sc and Fe–Sc systems

Thermodynamic optimization of the Au–Sc and Fe–Sc systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method on the basis of the available experimental data in literature. Redlich–Kister polynomials were used to describe the excess Gibbs energy of solution phases, and all the compounds are treated as stoichiometric ones. The Au–Sc system was described thermodynamically for the first time, and the Fe–Sc system was re-optimized by considering the new experimental data about enthalpies of mixing of the liquid phase. A set of self-consistent parameters was obtained for each of these two binary systems, respectively.

Quaternary Chemical Potentials for Gold-Catalyzed Growth of Ternary InGaAs Nanowires

Chemical potentials of quaternary liquid alloys are required for theoretical description of the composition and crystal structure of Au-catalyzed ternary III–V nanowires. However, such data are solely missing in the literature. Herein, we use a thermodynamic database for the quaternary Au–In–Ga–As system that has been developed using the CALPHAD (CALculation of PHAse Diagram) method. We present the chemical potential values in Au–In–Ga–As liquid with respect to InGaAs solid. We plot the chemical potentials as functions of the arsenic concentration, indium composition, total composition of the group III elements, and temperature. Our approach can be extended to other material systems and used for particular calculations based on macroscopic nucleation theory. Quantitative data on quaternary chemical potentials obtained here constitute the first step toward comprehensive understanding of growth, composition, and structural evolution of Au-catalyzed InGaAs nanowires.