Calculation Of Phase Diagrams Method Research Articles

Microscopic Phase-Field Simulation of γ′ Precipitation in Ni-Based Binary Alloys Coupled with CALPHAD Method

In the present work, the first (1st) and second (2nd) nearest-neighbor interaction energies are calculated by coupling the microscopic phase-field kinetic model with the calculation of phase diagrams (CALPHAD) method. The morphological evolution of the γ′ precipitate and the variation of its atomic ordering parameter for Ni–X (X = Al, Fe, Mn, Pt, or Si) alloys during aging are studied. The simulation results predict different occupation preferences for solute and solvent atoms in the γ′ phase, i.e., solute atoms are inclined to occupy the corner sites and solvent atoms tend to occupy the face sites. In order to understand the precipitation process of the γ′ phase systematically, the ordering and clustering behaviors of solute atoms are analyzed.

Impact of interstitial elements on the stacking fault energy of an equiatomic CoCrNi medium entropy alloy: theory and experiments

ABSTRACT We investigated the effects of interstitial N and C on the stacking fault energy (SFE) of an equiatomic CoCrNi medium entropy alloy. Results of computer modeling were compared to tensile deformation and electron microscopy data. Both N and C in solid solution increase the SFE of the face-centered cubic (FCC) alloy matrix at room temperature, with the former having a more significant effect by 240% for 0.5 at % N. Total energy calculations based on density functional theory (DFT) as well as thermodynamic modeling of the Gibbs free energy with the CALPHAD (CALculation of PHAse Diagrams) method reveal a stabilizing effect of N and C interstitials on the FCC lattice with respect to the hexagonal close-packed (HCP) CoCrNi-X (X: N, C) lattice. Scanning transmission electron microscopy (STEM) measurements of the width of dissociated ½<110> dislocations suggest that the SFE of CoCrNi increases from 22 to 42–44 mJ·m−2 after doping the alloy with 0.5 at. % interstitial N. The higher SFE reduces the nucleation rates of twins, leading to an increase in the critical stress required to trigger deformation twinning, an effect which can be used to design load-dependent strain hardening response.

Thermodynamic modeling of the Bi–Ca and Bi–Zr systems

Abstract In the literature, there are no reliable thermodynamic descriptions for the Bi–Ca and Bi–Zr systems. In the present work, by means of the CALPHAD (calculation of phase diagrams) method, the thermodynamic assessments of the Bi–Ca and Bi–Zr systems were carried out based on the available data. The Gibbs energies of the liquid, bcc and hcp phases in these two binary systems were described by the substitutional solution model with the Redlich–Kister equation, and the intermetallic compounds (αBi10Ca11, βBi10Ca11, Bi3Ca5, Bi2Zr, Bi1.62Zr, BiZr, Bi2Zr3, and BiZr2 phases) were treated as stoichiometric phases. A good agreement between the calculated results and experimental data is obtained for both systems. The presently obtained thermodynamic parameters for the Bi–Ca and Bi–Zr systems are of interest for the development of Bi-based alloys.

Diffusivities and atomic mobilities in bcc Ti–Mo–Ta alloys

Mo and Ta are two important β stable elements that can enhance the fatigue strength and reduce the elastic modulus of titanium alloy, and can significantly improve the biocompatibility of titanium alloy. It is significant to study the diffusion behavior in β Ti–Mo–Ta alloy for understanding the microstructure evolution in production process and developing new alloys. In this study, using several diffusion couples, the interdiffusion coefficients and impurity diffusion coefficients in β Ti–Mo–Ta alloy were extracted via Whittle-Green method and Hall method. The atomic mobilities in bcc phase in Ti–Mo–Ta system were obtained by assessing the experimental data using CALPHAD (CALculation of PHAse Diagrams) method. Simulations of the diffusion process in the diffusion couples were implemented using DICTRA Module in Thermo-Calc software. The calculated data were in good agreement with the experimental data, confirming the accuracy of the database.

Experimental investigation and thermodynamic optimization of the Al–Ni–Sc ternary system

Phase equilibria of the Al–Ni–Sc system were investigated by combination of key experiments and thermodynamic modeling. The isothermal sections of the Al–Ni–Sc ternary system in the (Al, Ni)-rich region at 873K and 673K were investigated using the electron probe microanalysis (EPMA) and X-ray diffraction (XRD). The solubilities of the binary phases in the ternary system were measured. According to the experimental results in this work and related literature, the Al–Ni–Sc ternary system has been optimized by means of the CALPHAD (CALculation of PHAse Diagrams) method. Isothermal sections at 1273, 1173, 873 and 673 K were reproduced. The calculated thermodynamic and phase equilibria data for the ternary system agree well with the experimental data. This work can be used as a basis for the multi-component thermodynamic database of Al-based alloys.

THERMODYNAMIC CALCULATIONS OF HIGH ENTROPY (FE-MN) BINARY ALLOY SYSTEM USING CALPHAD METHOD BASED ON THERMO-CALC PACKAGE AND PBINE,FEDATE DATABASES.

The thermodynamic analysis and calculations of the high entropy metastable binary alloy ironmanganese system have been carried out using the CALPHAD (Calculation of phase Diagram) method based on THERMO-CALC (thermodynamic calculations) package and FEDATE database. Thermodynamic analysis contain the assessment and calculation of phase diagram, Gibbs energy of mixing, excess Gibbs energies, thermodynamic molar activities, coefficient of activities, partial and integral values of enthalpy for Fe-Mn alloy system at three elevated temperatures 1200K, 1225K, and 1250K.The entropy of the said alloy system is calculated by showing linear accordance with temperature. The sudden increase is found in enthalpy curve due to overlapping of grain boundaries of the system. The high enthalpy shows increasing heat contents of the said alloy system with increasing temperature range. The alloy shows a positive deviation from Vegard’s law, Henry’s law and corresponding negative deviation from Raoults’s law ideal Gibbs curve. The obtained results show that the ferromagnetic states of Fe-Mn alloy is the most stable state FCC_A1#1. For Mn and Fe system, the phase equilibria show activity curve data for solid state and show ideal characteristics behaviors. Small positive deviation from Henry’s law was observed from the ideal curve. The alloy shows equilibrium and good stability.

Thermodynamic calculation of phase equilibria of rare earth metals with boron binary systems

Abstract In order to develop novel materials based on rare earth (RE) boride and/or transition metals, phase equilibria and thermodynamic information of the RE–B based alloys are indispensable. On the basis of experimental phase equilibria and thermodynamic properties, thermodynamic assessments of the RE–B (RE = La, Sm, Gd and Tb) binary systems were carried out by the CALPHAD (Calculation of Phase Diagram) method. Self-consistent parameters of the RE–B (RE = La, Sm, Gd and Tb) binary systems were obtained, which can be used to reproduce well the experimental data. Furthermore, in combination with the previous assessments of the RE–B binary systems in the literature, phase equilibria and thermodynamic properties of the RE–B (RE = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu) binary systems are discussed systematically. The tendency of phase equilibria and thermodynamic information as a function of RE atomic number is demonstrated. In general, the enthalpy of mixing of liquid RE–B alloys and the enthalpy of formation of the RE–B intermetallic compounds become more and more negative with the increase in RE atomic number (except for La, Ce, Pr and Nd), while the phase transition temperatures for the RE–B intermetallic compounds increase gradually.

A thermodynamic database of the Ni-Mo-Re system

Thermodynamic databases are essential prerequisites for developing advanced materials, such as Ni-based superalloys. The present work collects a large amount of experimental and first-principles calculation data concerning the thermodynamics and phase diagrams of the Ni-Mo-Re system, based on which the thermodynamic properties of the ternary and its binary sub-systems Ni-Mo and Mo-Re are assessed by means of the CALculation of PHAse Diagrams (CALPHAD) approach. The thermodynamic database containing all model parameters is established and most experimental data are reproduced satisfactorily. The present work demonstrates the use of the CALPHAD method as a practical appliance in the toolbox of materials informatics to analyze and discriminate various types of data by thermodynamic modeling and then produce more useful data in wider ranges of compositions and temperatures by computational predictions.

Thermal Conductivity Determination of Ga-In Alloys for Thermal Interface Materials Design

Thermal interface material (TIM) that exists in a liquid state at the service temperature enables efficient heat transfer across two adjacent surfaces in electronic applications. In this work, the thermal conductivities of different phase regions in the Ga-In system at various compositions and temperatures are measured for the first time. A modified comparative cut bar technique is used for the measurement of the thermal conductivities of GaxIn1−x (x = 0, 0.1, 0.214, 0.3, and 0.9) alloys at 40, 60, 80, and 100 °C, the temperatures commonly encountered in consumer electronics. The thermal conductivity of liquid and semi-liquid (liquid + β) Ga-In alloys are higher than most of the TIM’s currently used in consumer electronics. These measured quantities, along with the available experimental data from literature, served as input for the thermal conductivity parameter optimization using the CALPHAD (calculation of phase diagrams) method for pure elements, solution phase, and two-phase region. A set of self-consistent parameters for the description of the thermal conductivity of the Ga-In system is obtained. There is good agreement between the measured and calculated thermal conductivities for all of the phases. Due to their ease of manufacturing and high thermal conductivity, liquid/semi-liquid Ga-In alloys have significant potential for TIM in consumer electronics.

Kinetics and thermodynamics of compound growth due to reactive diffusion between solid Cu and binary Bi-Sn alloys

The growth behavior of compounds for the reactive diffusion between solid Cu and molten binary Bi-Sn alloys was experimentally examined using semi-infinite diffusion couples prepared by an isothermal bonding technique. Isothermal annealing of (Biy-Sn1-y)/Cu diffusion couples with Bi mol fraction of y = 0.27–0.46 was conducted in the temperature range of 453–603 K (180–330 °C) for various times up to 345.6 ks (96 h). In the diffusion couple with y = 0.44, an intermetallic layer composed of Cu6Sn5 with irregular scallop shapes and Cu3Sn with relatively uniform thickness forms at the (Bi-Sn)/Cu interface at 453–523 K (180–250 °C). In contrast, at 563–603 K (290–330 °C), the intermetallic layer consists of only Cu3Sn. Isothermal sections of the equilibrium phase diagram in the ternary Bi-Cu--Sn system were calculated at 453–603 K (180–330 °C) by a CALPHAD (calculation of phase diagrams) method. For the diffusion couple with y = 0.44, the diffusion path passes through the three-phase tie-triangles containing Cu6Sn5 and/or Cu3Sn in the isothermal section at 523 K (250 °C), but through only that containing Cu3Sn in the isothermal section at 603 K (330 °C). As a result, for y = 0.44, the intermetallic layer is composed of Cu6Sn5 and Cu3Sn at 453–523 K (180–250 °C), whereas it consists of only Cu3Sn at 563–603 K (290–330 °C). The mean thickness of the intermetallic layer is proportional to a power function of the annealing time, and the exponent of the power function is mostly smaller than 0.5. Such smaller values of the exponent mean that the layer growth is controlled by boundary diffusion across the intermetallic layer. Adopting the common value of 0.30 as the exponent of the power function for the Cu3Sn layer at 563–603 K (290–330 °C), we obtain a value of 17.9 kJ/mol for the activation enthalpy of the proportionality coefficient of the power function.

Design Strategy for Additive Manufacturing Ti-Al-Fe alloys with Calculation of Phase Diagram Method.

Calculation of Phase Diagram (CALPHAD) method was used to develop an additive manufacturing (AM) titanium alloy design strategy for new alloys in the Ti-Al-Fe system. This design strategy includes five key criteria addressing AM-processing suitability, mechanical properties and heat treatment capability. The methods for evaluating the design criteria were determined considering both physical implications and computational efficiency. Available experimental results agree well with CALPHAD predictions in the design map. CALPHAD method in this work can be applied for high-throughput early-stage assessments in large composition space for new AM titanium alloy development.

Phase equilibria in the ZrO2–Ta2O5–Nb2O5 system: Experimental studies and thermodynamic modeling

AbstractThe phase relations in the ZrO2–Ta2O5–Nb2O5 system were experimentally investigated, and thermodynamic modeling was consequently performed in the present work. Samples with the selected compositions were synthesized using coprecipitation method, and then separately equilibrated at 1573 and 1673 K. The microstructural characterizations and phase analyses were carried out with the support of the X‐ray diffraction (XRD) and scanning electron microscopy (SEM/EDX). The phase transformations were measured through differential thermal analysis (DTA). No ternary compounds exist, while Ta2O5 and Nb2O5 phases substantially extend into the ternary system. Moreover, binary Ta2Zr6O17 and Nb2Zr6O17 phases form a continuous solid solution (A2Zr6O17) in the ternary system. A three‐phase equilibrium region β‐Ta2O5 + A2Zr6O17 + Nb2O5 was speculated. Based on the available literature, the ZrO2–Nb2O5, ZrO2–Ta2O5, and Nb2O5–Ta2O5 binary systems were critically evaluated and optimized by means of the CALPHAD (CALculation of PHAse Diagram) method. Combining with thermodynamic parameters of the binary systems, phase relations in the ternary system were extrapolated. However, the extrapolation cannot reproduce our experimental results, especially for the ternary solubilities of ZrO2 in the Ta2O5 and Nb2O5 phases and the melting behavior of selected samples. Finally, the ternary mixing parameters were introduced, and our experimental data were well reproduced by the improved thermodynamic descriptions.

Calculation of adsorption equilibria using CALPHAD models and software

The utility of CALPHAD (CALculation of PHAse Diagrams) models and software for calculation of gas-on-solid adsorption equilibria is demonstrated. Thermodynamic models formulated in CEF (Compound Energy Formalism) are constructed that account for adsorption on single site, several sites as well as for adsorption in pores and multilayers. Site blocking (the case where the adsorption of a single molecule on a single site also blocks some adjacent sites) may be emulated by the ionic-liquid model within CEF. The parameters of these thermodynamic models may be determined by fitting to experimental results or to results of ab-initio calculations. Alternatively, the parameters may be calculated from already-fitted adsorption isotherm equations such as Langmuir, dual site Langmuir, Nitta and Ruthven's model for adsorption in pores. Pure-gas adsorption models may be extrapolated to mixed-gas adsorption. The thermodynamic consistency of such extrapolation is ensured by the CALPHAD method of modeling and the CEF formalism. Examples include adsorption of various gases on carbon as well as on zeolites and MOF (Metal Organic Framework).

Structural and thermal properties of Sn–Ag alloys

Microstructure and thermal properties of slowly cooled Sn–10% Ag and Sn–20% Ag alloys were experimentally investigated in this study. It was found that microstructure of the studied alloys is composed of large, plate-like grains of Ag3Sn intermetallic phase in the Sn-rich eutectic matrix. Phase transition temperatures and corresponding heat effects were experimentally determined and compared with the results of thermodynamic and phase equilibria calculations using the CALPHAD (CALculation of PHAse Diagrams) method and optimized thermodynamic parameters from literature. The xenon flash method was employed for the measurements of thermal diffusivity and determination of thermal conductivity in the temperature range from 25 to 150 °C. The results show that the thermal diffusivity and thermal conductivity gradually decrease with increasing temperature. The determined values of thermal conductivities of the investigated alloys are very close to each other and only slightly higher than that of pure tin. The contributions of electrons and phonons to the thermal conductivity of the studied alloys at room temperature were determined using the Wiedemann-Franz law and the obtained values of the thermal and electrical conductivities. The percentage contributions of the phonon component to the thermal conductivity for Sn–10% Ag and Sn–20% Ag alloys at 25 °C were found to be 20.5% and 28.9%, respectively.

Microstructure, melting behavior and thermal conductivity of the Sn–Zn alloys

Four hypereutectic Sn-Zn alloys with 69.5, 48.3, 28.1 and 14.1 at% of Zn were produced by mixing and melting of pure metals Sn and Zn followed by cooling in air to room temperature. Microstructure and chemical compositions of prepared samples were analyzed by using scanning electron microscopy (SEM) with energy dispersive X-ray spectrometry (EDS). It was found that morphology of primary (Zn) phase changes from rounded and equiaxed dendritic structure to plate-like grains and finally to needle-like shape of grains with decreasing Zn content. Formation of characteristic broken-lamellar type of eutectic microstructure was observed in all investigated alloys. Melting behavior of the alloys was studied using differential scanning calorimetry (DSC). Phase transition temperatures and corresponding heat effects were experimentally determined and compared with the results of thermodynamic and phase equilibria calculations using the CALPHAD (CALculation of PHAse Diagrams) method and optimized thermodynamic parameters from literature. Thermal diffusivity of the studied alloys was measured using xenon flash method in the temperature range from 25 to 150 °C. Based on the measured values of thermal diffusivity and calculated specific heat capacity data, thermal conductivities of the solid alloys were obtained. It was found that thermal conductivity decreases monotonously with increasing temperature and Sn content. The results of thermal conductivity measurements were compared with literature data and with the data obtained from the Wiedemann-Franz law and measured electrical conductivities.

Thermodynamic assessment of the Ni-Co-M1 (M1 = Re, Ru) and Ni-Re-M2 (M2 = W, Ta) superalloy systems over the whole composition

The phase equilibria of the Ni-Co-M1 (M1 = Re, Ru) and Ni-Re-M2 (M2 = W, Ta) ternary systems 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 solution phases, i.e., fcc(Co, Ni), hcp(Co, Re, Ru) and bcc(Co, W, Ta), were described using substitutional solution model and the binary phases σ(ReW), χ(Re3W), χ(Re3Ta), NiTa2, μ(NiTa), Ni2Ta and Ni3Ta with the solubilities of the third element were modeled by the sublattice models. A set of self-consistent thermodynamic parameters for each ternary system was finally obtained. Some representative isothermal sections and liquidus projections 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.

Thermodynamic modeling of the Te-X (X = Zr, Ce, Eu) systems

Thermodynamic descriptions of the tellurium-zirconium (Te-Zr), tellurium-cerium (Te-Ce) and tellurium-europium (Te-Eu) systems have been carried out using the CALPHAD (CALculation of PHAse Diagrams) method based on the experimental phase equilibria data available in the literature and the enthalpies of formation calculated by first-principles calculations in the present work. The liquid phase was described by the substitutional solution model for the Te-Zr and Te-Eu systems while the associated solution model for the Te-Ce system with CeTe as associate. The intermetallics Zr3Te, ZrTe, Zr5Te4, ZrTe3, ZrTe5, CeTe, Ce4Te7, CeTe2, Ce2Te5, CeTe3, Eu4Te7 and Eu3Te7 were treated as stoichiometric compounds while Zr1+xTe2, Ce3-xTe4 and Eu1-xTe were modeled by the sublattice model Te1/3(Zr, Va)1/3(Zr, Te)1/3, (Ce, Va)3/7Te4/7 and (Eu, Va)0.5Te0.5, respectively, on the basis of their homogeneity ranges and crystal structures. A set of self-consistent thermodynamic parameters for the Te-X (X = Zr, Ce, Eu) systems was obtained. Comparisons between the calculated results and experimental data available in the literature show that most reliable experimental information can be satisfactorily accounted for by the present modeling.

Experimental investigation and thermodynamic assessment of phase equilibria in the Cr-Re-Ru ternary system

The phase equilibria of the Cr-Re-Ru ternary system at 1100 °C and 1200 °C have been experimentally investigated using electron probe microanalyzer and X-ray diffraction. The σ1-Cr2Re3 and σ2-Cr2Ru phases with the same D8b crystal structure do not form a continuous intermetallic compound phase at 1100 °C and 1200 °C in the Cr-Re-Ru ternary system confirmed by experimental results. According to the experimental results in this work, the Cr-Re-Ru ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The calculated isothermal section at 1400 °C shows that the two independent phases σ1-Cr2Re3 and σ2-Cr2Ru are replaced by the continuous intermetallic compound σ. The current established thermodynamic database of the Cr-Re-Ru ternary system may provide the essential information, and support for the thermodynamic assessment of multicomponent system and the development of Ni-based superalloys.

Phase Diagram of Binary Alloy Nanoparticles under High Pressure.

CALPHAD (CALculation of PHAse Diagram) is a useful tool to construct phase diagrams of various materials under different thermodynamic conditions. Researchers have extended the use of the CALPHAD method to nanophase diagrams and pressure phase diagrams. In this study, the phase diagram of an arbitrary A–B nanoparticle system under pressure was investigated. The effects of the interaction parameter and excess volume were investigated with increasing pressure. The eutectic temperature was found to decrease in most cases, except when the interaction parameter in the liquid was zero and that in the solid was positive, while the excess volume parameter of the liquid was positive. Under these conditions, the eutectic temperature increased with increasing pressure.

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.