CALculation Of PHAse Diagram Approach Research Articles

Ab initio and CALPHAD-type thermodynamic investigation of the Ti-Al-Zr system

Ti?Al based alloys have been widely used in the aeronautics and aerospace. Adding alloying element Zr can significantly improve their high-temperature endurance and corrosion resistance. To investigate the influence of the addition of element Zr on the properties of the Ti?Al system, ab initio calculations and the CALPHAD (CALculation of PHAse Diagrams) method were used to evaluate the Ti?Al?Zr ternary system. Ab initio calculations were carried out to calculate the formation enthalpies of intermetallic compounds and end-members. CALPHAD approach was employed to optimize the thermodynamic parameters based on experiments. The experimental data of phase equilibria at 1073, 1273, 1473, and 1573 K, as well as a vertical section of the Ti3Al?Ti + 5 wt.% Zr were used to assess this system. The thermodynamic parameters of the binary Ti?Al, Al?Zr and Ti?Zr systems were acquired from recent assessments, and the ternary ones were evaluated in the present work. The Ti?Al?Zr ternary dataset has been established and the calculated results are in close agreement with the experimental data on both thermodynamics and phase equilibria.

Thermodynamic description of the Fe–Cu–C system

As an addition to the iron-carbon alloys to improve their strength and corrosion resistance, copper is of great importance for iron and steel industry and the Fe–Cu–C system has been extensively investigated. Aiming at a thermodynamic basis to investigate the effect of Cu addition on the Fe–C system, the CALPHAD (CALculation of PHAse Diagrams) approach was utilized to assess the ternary Fe–Cu–C system including the binary Cu–C and Fe–C systems. The Redlich-Kister model, instead of the Modified Quasichemical Model (MQM) in previous work, was used to model the liquid phase. The parameters of the liquid phase in the Fe–C system from previous work have been slightly modified to fit better with new experimental data at high temperatures. One Fe/Cu/FeC0.05 (in wt%) diffusion couple was designed to further determine the phase equilibria of the ternary system. A set of self-consistent parameters for the Fe–Cu–C system was obtained after thermodynamic optimization. Good correspondence between calculated and experimental values of phase diagrams, thermodynamic properties, and liquidus projections has been achieved by the present thermodynamic description.

CALPHAD-type thermodynamic description of phase equilibria in the Ti-W-M (M = Zr, Mo, Nb) ternary systems

Based on the thermodynamic descriptions of constitutive binary systems as well as the experimental phase equilibria data available in the literature, the Ti-W-M (M = Zr, Mo, Nb) ternary systems have been thermodynamically evaluated by the CALPHAD (CALculation of PHAse Diagram) approach. The solution phases, i.e. liquid and bcc, are described by the substitutional solution model. The binary phase W2Zr with the solubilities of Ti is modeled using the sublattice model. A set of self-consistent thermodynamic parameters is finally obtained for each of these ternary systems. Some representative isothermal and vertical sections are calculated. Comparisons between the calculated and measured phase diagrams show that the most of experimental data are satisfactorily reproduced by the present thermodynamic descriptions.

Study of Microstructure and Thermal Properties of the Low Melting Bi-In-Sn Eutectic Alloys

Beside their technological importance in soldering, the low melting eutectic alloys based on bismuth and indium have potential for commercial application in the field of phase-change materials (PCMs). In this respect, the knowledge of their microstructure and thermal properties such as melting temperature, latent heat of melting, supercooling tendency, thermal conductivity, etc. is of large importance. In this study, two ternary eutectic Bi-In-Sn alloys were investigated by means of scanning electron microscopy (SEM) with energy dispersive X-ray spectrometry (EDS) and differential scanning calorimetry (DSC). Microstructure of the prepared eutectic alloys was analyzed using SEM-EDS and identification of co-existing phases was done. Melting temperatures and latent heats of eutectic melting were measured using DSC technique. Experimentally obtained results were compared with the results of thermodynamic calculation according to CALPHAD (calculation of phase diagram) approach and good mutual agreement was obtained.

Thermodynamic Assessment of the Ag-Se System Aided by First-Principles Calculations

The substitution of Ag for Cu in CuInxGa1−xSe2-based photovoltaic absorber layers can be used to adjust the bandgap energy to better optimize the overall cell efficiency. Based on available thermochemical, equilibrium, and structural data, the Ag-Se system has been assessed and modeled. Given the order-disorder structure transition Ag2Se, the 2- and 3-sublattice models were used to represent the low- and high-temperature phases of the intermetallic compound respectively. Density functional theory based first-principles calculations were used to calculate the Gibbs energy of formation of the end-member compounds. A set of modeling parameters was obtained by the CALculation of PHAse Diagram approach and reasonable agreement was obtained between the experimental thermodynamic properties of the stable phases and the phase relationships in the Ag-Se system.

First-principles calculations and thermodynamic modelling of long periodic stacking ordered (LPSO) phases in Mg-Al-Gd

In the present work, thermodynamic modelling of four long periodic stacking ordered (LPSO) phases, i.e., 10H, 18R, 14H, and 24R, in the Mg-Al-Gd system was performed using the CALPHAD (calculation of phase diagram) approach with input from the present first-principles calculations and experimental data in the literature. Sublattice models were developed to describe these LPSO phases. Especially, an L12-type clusters in the FCC stacking layers of LPSO phases and the atomic occupancy in the center of L12 cluster were considered based on experimental observations and energetics from first-principles calculations. The calculated phase equilibrium results are in good agreement with experiments about the phase stability of 14H and 18R and the mole fraction of Gd and Al in these LPSO phases. The present modeling provides a new approach to describe the thermodynamic properties of LPSO phases and can be applied to other alloy systems.

Thermodynamic modeling of the K-KCl and Mg-MgCl2 binary systems using the CALPHAD method

The Calculation of Phase Diagrams (CALPHAD) method uses models that reproduce and predict phase equilibria and thermochemical behavior. To date, the CALPHAD approach has been applied to the KCl-MgCl2 psuedobinary only. The two-sublattice modified quasi chemical (MQM) model, already developed for the KCl-MgCl2 melt and used extensively within the CALPHAD community to represent molten salts, is extended in this work to include excess K and Mg. Phase relations calculated using the MQM is compared to experimentally observed behavior for the K-KCl binary system. Gaps in the experimental data are identified and recommendations are given for better understanding the thermochemistry and phase equilibria.

Re-evaluation of the thermodynamic equilibria on the zirconia-rich side of the ZrO2-YO1.5 system

The thermodynamic database of ZrO2-YO1.5 system, which has been extensively studied by many groups, was re-assessed and improved particularly on the ZrO2-rich side of the system. Due to sluggish kinetics and diffusionless transformations in the ZrO2-rich side of ZrO2-YO1.5 system, providing accurate phase diagram and thermochemical data had become problematic. The newly developed thermodynamic database shows well agreement with the related experimental data, which were wisely evaluated and carefully selected to ensure the accuracy of the developed database. Applying the CALPHAD (CALculation of PHAse Diagrams) approach, the interaction parameters of the cubic, tetragonal, monoclinic, and liquid phases were optimized to develop a complete and self-consistent thermodynamic description of the ZrO2-YO1.5 system. The Gibbs energy model for the monoclinic phase was also modified to a regular solution. The improved thermodynamic database of the ZrO2-YO1.5 system can give more accurate modeling results, especially for the ZrO2-rich side of the system, which has critical applications.

Thermodynamic description of the Ti-Mo-Nb-Ta-Zr system and its implications for phase stability of Ti bio-implant materials

Titanium alloys are great candidates for applications such as biomedical implants that require biocompatibility, a low Young's modulus and a high strength. However, the properties of Ti alloys are highly dependent on phase stability. In the present work, a database for the Ti-Mo-Nb-Ta-Zr system has been evaluated using the CALPHAD (CALculation of PHAse Diagram) approach. The database was completed by evaluating the accuracy of previously modeled systems from literature and modeling systems that, to the best of the authors’ knowledge, had no modeling available in literature. All of the binary systems that make up the Ti-Mo-Nb-Ta-Zr system had previously modeled thermodynamic descriptions available in the literature and in most cases had multiple different descriptions available, which meant determining which previous thermodynamic description most accurately modeled the binary system with a direct focus on the bcc phase. In order to determine the accuracy of the multiple available thermodynamic descriptions from literature a combination of experimental data (also obtained from the literature) and computed thermochemical properties of the bcc phase from DFT (Density Functional Theory)-based first-principles calculations (present work) were used. Once the thermodynamic descriptions for the binary systems were chosen, focus shifted to the Ti-containing ternary systems. The Ti-Mo-Zr, Ti-Nb-Zr and Ti-Ta-Zr systems had previous thermodynamic description available in literature, which were incorporated without changes into the working database. The Ti-Mo-Ta, Ti-Nb-Ta and Ti-Mo-Nb systems had, to the authors’ knowledge, no descriptions available in the literature. Interaction parameters were determined for the Ti-Mo-Ta and Ti-Nb-Ta systems, and no interaction parameters were introduced for the Ti-Mo-Nb system. The database introduced by this work satisfactorily predicts the thermodynamics of the Ti-Mo-Nb-Ta-Zr system.

High-Throughput Description of Infinite Composition–Structure–Property–Performance Relationships of Lithium–Manganese Oxide Spinel Cathodes

Lithium–manganese oxide based spinel is attractive as cathode materials in lithium ion batteries. A wide range of spinel solid solution can be directly sintered and result in different properties of identical compositions during the battery operation, making it extremely difficult to understand the intrinsic properties and evaluate the battery performance. In this work, a high-throughput computational framework combining ab initio calculations and a CALPHAD (Calculation of Phase Diagrams) approach is developed to systematically describe infinite composition–structure–property–performance relationships under sintered and battery states of spinel cathodes. Depending on composition and crystallography, various properties (physical, thermochemical, and electrochemical) relating key factors (cyclability, safety, and energy density) are quantitatively mapped. The overall performance is consequently evaluated and validated by key experiments. Finally, 4 V spinel cathodes with codoping of reasonable Li and vacanc...

Reassessment of the Ni–V system and a new thermodynamic modeling of the Mo–Ni–V system

The Mo–Ni–V system has been assessed by means of the CALPHAD (CALculation of PHAse Diagram) approach. The binary system Ni–V was reassessed by considering all available thermochemical and phase diagram data. According to the crystallographic data, the σ intermediate compound is described by a three-sublattice (Ni,V)10V4(Ni,V)16. Calculated phase diagram and thermochemical properties of the Ni–V system showed a good agreement with experimental data. A set of self-consistent thermodynamic parameter for the Mo–Ni–V system was obtained by considering the phase diagram data in the ternary system. Comprehensive comparisons between the calculated and measured phase diagram and thermodynamic data showed that the experimental information was satisfactorily accounted for by the present thermodynamic description.

Thermodynamic assessment of the Ge-Yb binary system

ABSTRACTThe Ge-Yb binary system was thermodynamically assessed by CALPHAD (CALculation of PHAse Diagram) approach based on the available experimental data of thermochemical properties and phase equilibria. The liquid phase and the terminal phases, Fcc_A1 (Yb), Bcc_A2 (Yb) and Diamond_A4 (Ge), are described by a substitutional solution model, and their excess Gibbs free energies are formulated with the Redlich-Kister expression. The intermetallic compounds, Yb3Ge8, Yb3Ge5, Yb11Ge10, Yb5Ge4, Yb5Ge3 and Yb2Ge, are treated as strict stoichiometric compounds. A set of self-consistent thermodynamic parameters for the system is obtained. The calculated phase diagrams and thermochemical properties are in good agreement with the available experimental data.

Experimental investigation and simulation of precipitation evolution in Mg-3Nd-0.2Zn alloy

In this research, precipitation evolution and strengthening behavior in Mg-3Nd-0.2Zn alloy during isothermal age treatment at 200°C are quantitatively studied by a combination of experimental investigation and computational simulation. Microstructure evolution, including volume fraction, number density, and size of precipitates are first measured by TEM and DSC techniques and then modeled using an integrated computational simulation method combining the CALPHAD (CALculation of PHAse Diagram) approach and classical nucleation model. The focus of the analysis is set on the evolution of key strengthening precipitate β’. Critical kinetic parameters such as particle interfacial energy and nucleation site number are obtained computationally by fitting the model to the experimental data. Mechanical properties of a series of Mg-Nd-Zn alloys are predicted using the simulated microstructure evolution as inputs. Good agreement is found between simulated and measured results. Strategies for enhancing the precipitation hardening effect are presented and discussed based on the simulation results. The merit of this study is to use the obtained parameters to extrapolate microstructure evolution and mechanical properties when adjusting alloy composition and/or heat treatment conditions within a certain range, which will be very useful for further development and optimization of multi-component Mg alloys.

A stepwise thermodynamic modeling of the phase diagram for the Cu–Be system

The calculation of phase diagrams (CALPHAD) approach in combination with first-principles calculation was employed to perform a thermodynamic modeling of the Cu–Be system. The experimental phase diagram and thermodynamic data available in the literature were critically reviewed. The enthalpy of formation for the ordered γ (bcc_B2) phase at 0 K was computed via first-principles calculation. In addition to the high-temperature disordered bcc_A2 form of Be, there are large homogeneity ranges for bcc_A2 and bcc_B2 from 30 to 50 at.% Be over wide temperature ranges. It is thus a challenge for CALPHAD approach in which all of the bcc lattice stabilities might be modeled with a single Gibbs energy function. A stepwise thermodynamic modeling of the disorder (bcc_A2) and order (bcc_B2) transition was proposed to obtain a set of self-consistent thermodynamic parameters for the Cu–Be system. The calculated phase diagram and thermodynamic properties using the present thermodynamic description are in a satisfactory agreement with the experimental data. The presently proposed strategy is equally valid for the modeling of complex order/disorder transition in other binary systems.

Microstructure prediction of TMW-4M3 during heat treatment

The calculation model on the basis of multi-phase-field model, coupled with the calculation of phase diagram (CALPHAD) approach and classical nucleation theory (CNT) model, was studied for the precipitation behavior of γ′ precipitates in Ni-Co base superalloy TMW-4M3 (“TMW” is a trademark of National Institute for Materials Science registered in Japan) during the heat treatment process. This alloy is precipitation strengthened by γ′, and thus the control of size and distribution of γ′ precipitates is very important for practical applications. Precipitation behavior of γ′ in TMW-4M3 is strongly influenced by heat treatment conditions. Therefore, numerical simulation is useful for finding the most appropriate manufacturing condition prior to experimental trial and error approach. Firstly, we investigated the γ′ solvus temperature and improved several thermodynamic parameters of the conventional database to obtain reasonable phase boundaries between γ/η(Ni3Ti) and γ/γ′. Based on the new thermodynamic description, the nucleation rates related to temperature histories were calculated by using the CNT with composition balance equation under subsolvus solution treatment. Finally, the multi-phase-field method coupled with the CALPHAD approach and CNT model was applied to the microstructure evolution of intragranular secondary γ′ particles. The experimental and simulated microstructures show good agreement with each other. This method might be useful for microstructure evolution prediction of γ/γ′ dual phase during the heat-treatment.

Thermodynamic Assessment of the Nb-Si-Ta System

The Nb-Si-Ta ternary system is thermodynamically assessed using the CALculation of PHAse Diagram approach based on the experimental measurements of the isothermal sections at 1100, 1200, and 1300 °C. The parameters for the thermodynamic assessment of all the phases in the system are optimized, following the reported literatures of the three relevant binaries Nb-Si, Nb-Ta and Si-Ta systems. The liquidus projection was calculated accordingly from the currently obtained thermodynamic description of the Nb-Si-Ta system. Comparison between the calculated results and the experimental investigations shows that the present modeling can finely describe the experimental information of the Nb-Si-Ta ternary phase diagram.

Oxygen ion mobility and conductivity prediction in cubic yttria-stabilized zirconia single crystals

The CALPHAD (calculation of phase diagrams) approach is applied to predict the oxygen vacancy concentration at different temperatures and yttria concentrations of cubic yttria-stabilized zirconia (c-YSZ) single crystals. The quantitative mobility diagrams of oxygen ions are developed in a wide range of temperature and yttria concentration, using the experimental data from the literature. Therefore, the ionic conductivity of c-YSZ single crystals is predicted, using the mobility and oxygen vacancy concentration. Particularly, the conductivity of low-yttria c-YSZ is predicted by applying the CALPHAD approach for the first time. The conductivity prediction of low-yttria c-YSZ can be crucial, since new applications may be designed based on this new information. The activation energy and pre-exponential factor diagrams versus yttria concentration are also plotted.

Phase equilibria in equiatomic CoCuFeMnNi high entropy alloy

Phase equilibria and stability of a newly developed single phase equiatomic CoCuFeMnNi high entropy alloy (HEA) was investigated in the temperature range of 298–1573 K using in situ high temperature X-ray diffraction and thermodynamic modeling using CALPHAD (CALculation of PHAse Diagrams) approach. Complimentary characterization techniques like scanning and transmission electron microscopy with energy dispersive spectroscopy for microstructural investigation and compositional analysis, differential scanning calorimetry for thermal analysis and atom probe tomography for near-atomic scale chemical analysis were employed. It was found that the metastable FCC solid solution α phase (lattice parameter = 0.361 nm) undergoes phase transformation at 923 K and 1123 K. The α phase transforms to BCC β phase (a = 0.280 nm) at 923 K and on further heating, another FCC phase γ (a = 0.362 nm) precipitates out at 1123 K, leading to coexistence of two FCC phases and one BCC phase. Atom Probe Tomography carried out to study the three-dimensional distribution of constituent elements indicates the presence of ∼2 nm sized Cu clusters in the α phase. CALPHAD predictions indicate the tendency towards phase separation involving iron-cobalt and copper to partition out of the equiatomic solid solution to form the BCC and second FCC phase, respectively. A qualitative agreement between CALPHAD predictions and in situ high temperature X-ray diffraction accompanied with complimentary characterization tools explicitly demonstrates the fidelity of CALPHAD modeling for the design and development of novel HEA compositions.

Experimental investigation and thermodynamic description of the Cu-Cr-Zr system

The Cu-Cr-Zr ternary system was investigated via thermodynamic modeling coupled with key experiments. The isothermal section of the Cu-Cr-Zr system at 1123K was determined by means of optical microscopy, X-ray diffraction and electron probe microanalysis, and the phase transformation temperatures were measured by differential scanning calorimetry. The Cu-Cr sub-binary system was re-assessed with a substitutional solution model for the solution phases to ensure its compatibility in multi-component system. A set of self-consistent thermodynamic parameters for the Cu-Cr-Zr systems was obtained using the CALPHAD (CALculation of PHAse Diagram) approach, and the calculated phase diagram is in a satisfactory agreement with the present experimental results and literature information. An increase of the thermodynamic stability for the CuZr and Cr2Zr phases due to the ternary solubility is verified by calculation.

The effect of sintering parameters on spark plasma sintering of B4C

Abstract The effects of sintering temperature, heating rate, and holding time on the density and hardness of the spark plasma sintered B4C were investigated. Experimental results are compared with the predictions from computational thermodynamics. It is explained how the choice of sintering parameters can affect the mechanical properties of the sintered samples. The fundamental mechanisms of how the sintering parameters affect the properties of the sintered B4C are discussed with the sintering experiments and the predictions from the CALPHAD (Calculation of Phase Diagrams) approach. The effect of the number of graphite foil layers to pack the powder was also investigated. It is proposed that increasing the number of graphite foil layers may increase the driving force for the C-B2O3 reaction to proceed. Higher density and hardness is thus achieved with the removal of free carbon and B2O3 from the sample.