Calculation Of Phase Diagrams Method Research Articles

A study on the phase diagram of Re-Zr refractory system

The different volume of Rhenium (Re) and zirconium (Zr) will affect the phase composition and thus change the mechanical properties of the core critical hot end components of gas turbines and aero engines. In this work, the Re-Zr system was studied experimentally by electron probe microanalyses (EPMA) with wavelength dispersive spectrometer (WDS), scanning electron microscopy (SEM) and X-ray diffraction (XRD), and then was measured the phase-transition temperature with the high-speed pyrometer. The phase Re25Zr21 was confirmed to be stable in this system. Besides, the eutectic point of the eutectic reaction Liquid → bcc (Zr) + Re25Zr21 was determined as 14.4% Re by WDS. The present phase transitions (melting point, solidus, and liquidus) measurements indicate that the Re-Zr system is different from the existing Re-Zr phase diagram. Then, the current obtained results, combined with a critical review of the previous publication data, were used to develop the thermodynamic description of the Re-Zr system by utilizing the CALPHAD (CALculation of PHAse Diagram) method. A set of self-consistent thermodynamic parameters was obtained.

Optimal corrosion resistance of cobalt-based dual-phase entropic alloys via compositional modulation of aluminum

A new category of Al-doped cobalt-based dual phase entropic alloys with high corrosion resistance properties was designed in the present work. CALPHAD (CALculation of PHAse Diagram) aided prediction was performed to facilitate the alloy design. Two groups of alloys have been extensively investigated by various techniques. One group was quenched in water from the homogenization temperature (i.e. 1200 °C) to room temperature. The other group was subsequently quenched in liquid nitrogen from room temperature. The microstructure of the proposed alloys was characterized by X-ray diffraction (XRD). Several kinds of electrochemical tests were performed to study the corrosion behaviors of the designed alloys in NaCl solution, including open circuit potential (OCP), polarization and cyclic polarization curves, electrochemical impedance spectroscopy (EIS), electrochemical noise (ECN), linear voltammetry curves and staircase voltammetry scan, and Mott–Schottky method. The obtained results show that Al has a minor influence on the corrosion property of this series alloy with a 0 to 2 at.% Al addition. All the designed alloys hold quite acceptable corrosion resistance. In addition, a mechanical property, i.e. micro-hardness, is also provided as a supplement information. This work sheds light on the correlation between computational thermodynamics and corrosion behaviors in cobalt-based dual-phase entropic alloys, as well as to provide a feasibility study on the important role of CALPHAD method for a rapid development of a new category of high performance alloys.

Experimental investigation and thermodynamic optimization of the Co–Ta–Zr system

This work is focused on a deeper understanding of the solidification microstructure of the as-cast alloys, as well as the phase constituents and phase fractions of annealed samples in the Co–Ta–Zr system. Nine primary solidification regions were experimentally determined in the liquidus surface projection, and three primary solidification regions were deduced based on binary phase diagrams. Six three-phase equilibria were observed in the isothermal sections at 1373 and 1273 K. The maximum solubilities of Zr in μ and CoTa2 were determined to be ∼ 6.1 and ∼ 6.7 at% at 1373 K, and ∼ 3.9 and ∼ 5.9 at% at 1273 K, respectively. The maximum solubilities of Ta in Co23Zr6 and CoZr were determined to be ∼ 3.3 and ∼ 14.1 at% at 1373 K, and in Co23Zr6, CoZr and CoZr2 were determined to be ∼ 2.6, ∼ 13.5 and ∼ 11.9 at% at 1273 K, respectively. The Co–Ta–Zr system was optimized by CALculation of PHAse Diagram (CALPHAD) method based on the experimental data. Four solution phases, liquid, bcc, fcc, and hcp, were described as substitutional solution. The thermodynamic models of intermetallic phases Co11Zr2, Co23Zr6, CoZr2, Co3Ta, CoTa2, λ1, λ2 and λ3 were treated as (Co)11(Ta,Zr)2, (Co)23(Ta,Zr)6, (Co,Zr)(Ta,Zr)2, Co3(Co,Ta), (Co,Ta,Zr)(Co,Ta,Zr)2, (Co,Ta)2(Co,Ta), (Co,Ta,Zr)2(Co,Ta,Zr) and (Co,Ta)2(Co,Ta) using a two-sublattice model, respectively. CoZr3 was described as (Co,Zr)(Co,Zr)Zr2 by a three-sublattice model. μ phase was modeled as (Co,Ta,Zr)1(Ta,Zr)4(Co,Ta,Zr)2(Co,Ta,Zr)6 using a four-sublattice model. And CoZr with a B2 structure was described as an ordered phase of bcc_A2, and the model was treated as (Co,Ta,Zr,Va)0.5(Co,Ta,Zr,Va)0.5(Va)3. A set of self-consistent thermodynamic parameters of the Co–Ta–Zr system was obtained using CALPHAD method. The calculated solidification paths and phase fractions can provide theoretical guidance for material design and thermal processing.

Phase Equilibria, Thermodynamics and Solidified Microstructure in the Copper–Zirconium–Yttrium System

A copper alloy with the addition of zirconium and yttrium is an attractive high strength and high conductivity (HSHC) copper alloy. The study of the solidified microstructure, thermodynamics and phase equilibria in the ternary Cu-Zr-Y system is expected to provide new insight into designing an HSHC copper alloy. In this work, the solidified and equilibrium microstructure and phase transition temperatures in the Cu-Zr-Y ternary system were studied by X-ray diffraction (XRD), electron probe microanalysis (EPMA) and differential scanning calorimeter (DSC). The isothermal section at 973 K was experimentally constructed. No ternary compound was found, while the Cu6Y, Cu4Y, Cu7Y2, Cu5Zr, Cu51Zr14 and CuZr phases substantially extended into the ternary system. According to the experimental phase diagram data from the present work and the literature, the Cu-Zr-Y ternary system was assessed using the CALPHAD (CALculation of PHAse diagrams) method. The isothermal sections, vertical section and liquidus projection calculated by the present thermodynamic description agree well with the experimental results. This study not only establishes a thermodynamic description of the Cu-Zr-Y system, but also contributes to the design of a copper alloy with the required microstructure.

Tribological behavior of Ni-based self-lubricating claddings containing sulfide of nickel, copper, or bismuth at temperatures up to 600 °C

Self-lubricating coatings extend the efficient dry-operational life of cutting and forming tools. In the current work, millimeter-thick NiCrBSi coatings with 10 wt% metal sulfide i.e. Ni3S2, CuS, or Bi2S3 were fabricated on a stainless steel substrate by laser cladding (in-situ alloying). Thermodynamic modelling utilizing the calculation of phase diagrams method (CALPHAD) was performed to predict the phase evolution during laser melting. Electron microscopy methods combined with X-ray diffraction and Raman spectroscopy were used to elucidate the developed microstructure. The coatings were further subjected to reciprocating dry sliding wear against a martensitic steel ball counterbody using a ball-on-plate configuration at 0.1 m/s and 50 N (Hertz contact pressure 1.7 GPa). The tests were conducted at room temperature (20), 400, and 600 °C. The results demonstrate a self-lubricating behavior of the sulfide coatings resulting in friction reduction by ⁓60 % at room temperature and ⁓40 % at 400 °C sliding, particularly for Bi2S3-added cladding, due to the prevalent existence of lubricious phases of chromium sulfide (CrxSy) along with others (NiBi, Bi) and leading to ‘self-healing’ phenomena. The results are reported in comparison to the unmodified NiCrBSi alloy.

Thermodynamic and diffusion databases for uranium-based alloys and their applications in materials design

Thermodynamic and diffusion databases are of fundamental importance for material design. In this work, the thermodynamic and diffusion databases for multicomponent U alloys are developed using the CALPHAD (CALculation of PHAse Diagram) method. Thermodynamic models are employed to describe all phases in the UNbZrTiMoC system in which 7 ternary systems (UNbZr, UZrTi, UMoZr, MoNbZr, MoTiZr, CNbZr, and CNbTi) are thermodynamically assessed. Thermodynamic descriptions of all sub-systems from both literature and present assessments are integrated into the database with a proper adjustment. The diffusion database is developed for bcc and liquid phases in the UNbZrTiMoC system. Applications of thermodynamic and diffusion databases are performed using two cases including (a) the stability of γU in the multicomponent system, and (b) discontinuous precipitation simulation in U-14 at.% Nb alloys. It is expected that further progress in CALPHAD-type nuclear materials databases will be an effective contribution to advanced metal fuels design.

Computer Alloy Design of Ti Modified Al-Si-Mg-Sr Casting Alloys for Achieving Simultaneous Enhancement in Strength and Ductility.

In this paper, an efficient design of a Ti-modified Al-Si-Mg-Sr casting alloy with simultaneously enhanced strength and ductility was achieved by integrating computational thermodynamics, machine learning, and key experiments within the Bayesian optimization framework. Firstly, a self-consistent Al-Si-Mg-Sr-Ti quinary thermodynamic database was established by the calculation of phase diagram method and verified by key experiments. Based on the established thermodynamic database, a high-throughput Scheil-Gulliver solidification simulation of the A356-0.005Sr alloy with different Ti contents was carried out to establish the "composition-microstructure" quantitative relationship of the alloy. Then, by combining the computational thermodynamic, machine learning, and experimental data within the Bayesian optimization framework, the relationship "composition/processing-microstructure-properties" of A356-0.005Sr with different Ti contents was constructed and validated by the key experiments. Furthermore, the optimum alloy composition of the Ti-modified A356-0.005Sr casting alloy was designed based on this integration method with the Bayesian optimization framework and verified by the experiments. It is anticipated that the present integration method may serve as a general one for the efficient design of casting alloys, especially in the high-dimensional composition space.

Thermodynamic analysis for molten corium stratification with U-Zr-O-Fe database

Aided by CALPHAD (CALculation of PHAse Diagram) method, a self-consistent thermodynamic corium database of U-Zr-O-Fe system is established based on reoptimization of key binary and ternary subsystems. According to molten corium stratification thermodynamic analysis for STFM-Fe tests in MASCA project, the corium would separate into metallic liquid phase and oxidic liquid phase due to the existence of miscibility gap and their mass fraction and composition can be well predicted. Further, the density of the oxide phase is accurately calculated by a linear fitting relationship obtained from the measured oxide density, and the density of the metal phase is calculated by the empirical formula. Thus the molten corium would exhibit a two-layer structure with a higher density metal phase below and a lower density oxide phase above. The good agreement with the STFM-Fe tests indicates the reliability of the database to analyze the molten corium stratification which tends to improve the effectiveness of in-vessel retention strategy by providing the thermodynamic prediction.

Thermodynamic calculation of phase equilibria in the Al–Fe–Zn–O system

Abstract The thermodynamics of the phase equilibria in the Al–Fe–Zn–O quaternary system was studied using the calculation of phase diagrams method to understand the oxidation behavior of the Zn bath surface during galvanizing process. The thermodynamic parameters for the Gibbs energies of the different constituent phases in the binary and ternary systems relevant to this quaternary system were taken mainly from previous studies. In this study, the thermodynamic assessment of the Al2O3–ZnO system was carried out based on the available experimental data, and some modifications to the thermodynamic model and/or parameters for the Fe–Zn–O ternary system were made to maintain consistency with the thermodynamic descriptions of other binary and ternary systems, making up the Al–Fe–Zn–O quaternary system adopted in this study. The calculated results on the ternary and quaternary systems generally agreed with the available experimental results on phase equilibria. The set of thermodynamic parameters enabled us to calculate the phase equilibria in the Al–Fe–Zn–O quaternary system over the entire composition and temperature ranges.

Thermodynamic assessment of the Mg-Ni-Gd system with a general model description the long-period stacking ordered phases

ABSTRACT The phase equilibria of the Mg-Ni-Gd ternary system were thermodynamically assessed by the CALPHAD (CALculation of PHAse Diagrams) method based on the thermodynamic descriptions of the constitutive binary systems and experimental phase equilibria data available in the literature. The substitutional model and sublattice model were employed to describe the solution phases and intermediate phases, respectively. The ternary phases τ1-τ6 were described as stoichiometric compound and the long-period stacking ordered phase 14H and 18R were described Mgx(TM, Mg)6(RE, Mg)8 model (TM = Transition Metal, RE = Rare Earth). A set of self-consistent thermodynamic parameters of the Mg-Ni-Gd system was obtained. Some representative isothermal section, liquidus projections and the related invariant reactions were calculated. Comparisons between the calculated results and experimental data show that almost all the reliable experimental data were satisfactorily reproduced by the present modeling. The reaction scheme for the whole ternary system is also presented.

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.

Thermodynamic modeling of the Ni-Ti-Cr system and the B2/B19′ martensitic transformation

The Ni-Ti-Cr ternary is a critical system for shape memory alloys. In this work, a thermodynamic reassessment of the Ni-Ti-Cr system was performed using the CALPHAD (CALculation of PHAse Diagrams) method. For the first time the martensitic transformation product phase B19′ was successfully introduced into the description of the Ni-Ti-Cr system. Firstly, the thermodynamic descriptions of the binary Ni-Ti and Ti-Cr systems were updated by focusing on the heat capacities of the Ni3Ti and NiTi2 phases and the homogeneity range of the Laves phases, respectively. The determinations of the end-member parameters of the Laves phases were supported by ab initio calculations. The present model parameters can well reproduce the phase equilibria and thermochemical properties of the Ni-Ti and Ti-Cr systems. Then, the Ni-Ti-Cr system was assessed by combining the updated binaries with available experimental data. The B19′ phase was described using a two-sublattice model, i.e., (Cr,Ni,Va)0.5(Cr,Ni,Ti)0.5, based on the atomic occupancy reported in the literature. The B2/B19′ martensitic transformation starting temperatures (MS) of the Ni-Ti and Ni-Ti-Cr alloys were accurately predicted with the assumption that the energy barrier for the martensitic transformation was 150 J/mol. The reliable prediction of MS is expected to promote the development of shape memory alloys.

Experimental investigation and thermodynamic assessment of the Al–Ag–Sc system

As an important system in heat-resistant aluminium alloys, Al–Ag–Sc still has no publication on the investigation of thermodynamics and phase equilibria. In the present work, the isothermal sections of the Al–Ag–Sc ternary system at 500 and 600 ºC were experimentally measured through electron probe microanalysis (EPMA) and X-ray diffraction (XRD) for alloy samples. The ternary maximum solubility of Al in AgSc, Ag2Sc, Ag4Sc, and Ag in Al3Sc are 20.5 ± 0.5, 5.2 ± 0.3, 6.3 ± 0.2 and 12.5 ± 0.3 at%, respectively. In addition, two stable ternary compounds Al36Sc36Ag28 and Al27Sc18Ag55 were newly discovered. The solidification paths were measured for as-cast alloys. Five primary phases AgSc, (Ag), Ag2AlSc, Al36Sc36Ag28 and Al3Sc were revealed. The end-members formation enthalpies of the Al–Ag–Sc intermetallic compounds were computed by first-principles calculations. Based on the experimental and first-principles calculations results, a set of thermodynamic parameters for the Al–Ag–Sc system were established by the application of the CALPHAD (CALculation of PHAse Diagrams) method. The phase equilibrium, isothermal section, liquidus projection and solidification structure are well reproduced by using the thermodynamic parameters obtained in this work.

Thermodynamic Re-assessment of the Ag–Ni–Sn system

The ternary Ag–Ni–Sn and the constituent binary Ag–Sn and Ni–Sn systems were critically re-assessed considering the available experimental data based on the CALPHAD (CALculation of PHAse Diagram) method. Thermodynamic descriptions of both Ag–Sn and Ni–Sn systems were obviously improved in comparison with the previous reports, especially in the heat capacity of Ag3Sn and enthalpy of mixing of Ag–Sn liquid, as well as the homogeneity range of Ni3Sn4 and the temperature dependent enthalpy of mixing of Ni–Sn liquid. Based on the updated thermodynamic description for the binary systems, a set of self-consistent thermodynamic parameters for the Ag–Ni–Sn system was then obtained. Comprehensive comparisons between the calculated results and experimental data on thermodynamic properties, isothermal and vertical sections as well as invariant reactions indicated the reliability and accuracy of the present thermodynamic parameters. Liquidus projection and the scheil reaction scheme of the entire composition range were also presented correspondingly.

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.

Microstructural analysis and thermal conductivity of the Ag–Bi–Sn alloys

Structural and thermal properties of five Ag–Bi–Sn ternary alloys with tin content ranging from 12.8 to 75.1 mass% and nearly equal mass contents of silver and bismuth were investigated in this study. Microstructures and melting properties of as-solidified alloy samples were examined using scanning electron microscopy with energy dispersive X-ray spectrometry (SEM-EDS), X-ray diffraction (XRD) analysis, and differential thermal analysis (DTA) in combination with the CALPHAD (CALculation of PHase Diagram) method. The observed microconstituents were Ag3Sn, (Sn) and, (Bi) phases as well as ternary (Sn)+(Bi)+Ag3Sn eutectic. The measured temperature of the ternary eutectic reaction was 138.0°C.The flash method was used for thermal diffusivity measurements in the temperature range from 25 to 100°C. Based on the measured values of thermal diffusivity, thermal conductivity of the solid Ag–Bi–Sn alloys was obtained. Thermal conductivity of the studied Ag–Bi–Sn ternary alloys considerably increases with increasing tin concentration and slightly decreases with increasing temperature.

Atomic mobilities and diffusivities in the bcc phase of Ti–Nb–Sn system

Accurate interdiffusion information is essential to control the phase transformation process in metastable β-type titanium alloys. In this work, diffusion behavior in the ternary Ti–Nb–Sn system at 1373 K and 1473 K was experimentally investigated. The ternary interdiffusion coefficients and impurity diffusion coefficients in the bcc Ti–Nb–Sn alloys were determined using the diffusion couple technique, along with the Whittle-Green and Hall methods. Based on the obtained diffusion coefficients, an atomic mobility database for the bcc Ti–Nb–Sn system was established via the CALPHAD (CALculation of PHAse Diagrams) method. In the optimizing procedure, the end members and the binary parameters for the bcc-Ti-Sn system were reassessed. The calculated results using the obtained database agree with the experimental diffusion properties (i.e., interdiffusion, composition-distance profiles and diffusion paths), demonstrating the accuracy of the database developed in this work.

Thermodynamic modeling of the Mg–Mn–Zn system based on the refinement of the Mg–Zn and Mn–Zn systems

Based on the critical evaluation of the experimental data in the literature, the Mg–Mn–Zn system was assessed utilizing the CALPHAD (CALculation of PHAse Diagram) method. The binary Mg–Zn and Mn–Zn systems were re-assessed to obtain a better thermodynamic description. The solution phases, including liquid, (Mg), (δMn), (γMn), (βMn), (αMn), and (Zn), were described using the substitutional solution model. The solid Zn was treated as Hcp_A3 not Hcp_Zn in the present work. The compounds with and without solubility range were described by the sub-lattice model and stoichiometric phases. The presently calculated phase diagram and thermodynamic properties of the Mg–Zn system demonstrated obvious improvements in comparison with the previous work. Thermodynamic parameters for the Mg–Mn–Zn system were obtained by extrapolating the binaries and adjusting the ternary parameters based on reliable experimental data in the literature. Comparing the calculated results with the experimental data, a good agreement was achieved, which confirms the reliability of the presently obtained thermodynamic parameters.

Phase equilibria in the FeO–Fe2O3–SiO2 system: Experimental measurement and thermodynamic modeling

Knowledge about the phase equilibria of the FeO–Fe2O3–SiO2 system is very important for the resource utilization of waste slag. To solve the controversy over the calculated isothermal section at 1723 K in the literature, key experiments were carried out using equilibrium/quenching, X-ray diffraction (XRD) and electron probe microanalysis (EPMA). According to the present experiments, the existence of the three-phase region liquid + spinel (Fe3O4) + tridymite (SiO2) at 1723 K was confirmed. The ionic two-sublattice model (Fe+2, Si+4)P(O−2, Va, SiO4−4, SiO2, FeO1.5)Q was used to describe the liquid phase. The FeO–Fe2O3–SiO2 system was then critically evaluated by means of the CALPHAD (CALculation of PHAse Diagram) method in view of phase diagram and thermodynamic data. A new and improved self-consistent set of thermodynamic parameters for the FeO–Fe2O3–SiO2 system is obtained, and the calculated results show good agreement with the experimental data. The present thermodynamic modeling is of interest for the comprehensive recycling of solid waste resources.

Experimental investigation and thermodynamic assessment of the Ag–Cr–Y and Ag–Cu–Y ternary systems

The phase equilibria of the Ag–Cr–Y system were investigated by a combination of key experiments and thermodynamic modeling. Eleven ternary alloys were prepared to determine the isothermal sections of the Ag–Cr–Y system at 500, 600 and 800 °C, by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). No ternary compound was found in the Ag–Cr–Y system. Based on the experimental phase equilibria data, thermodynamic assessment of the Ag–Cr–Y and Ag–Cu–Y systems was performed by the CALPHAD (CALculation of PHAse Diagrams) method. Two ternary compounds τ1 and τ2 in the Ag–Cu–Y system with the compositions of Ag3Cu12Y5 and (AgxCu2-x)Y (x: 22.9–43.1 at.%) were described by two sublattice model (Ag, Cu)4Y1 and (Ag, Cu)2Y1, respectively. A set of self-consistent thermodynamic parameters of the two systems were obtained. Most of the reliable experimental data can be well reproduced by the present thermodynamic modeling.