CALculation Of PHAse Diagram Approach Research Articles

Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems.

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O-2, PO3-1, PO4-3, PO5/2)Q and (Mg+2)P(O-2, PO3-1, PO4-3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.

Determination of hardness and Young's modulus in fcc Cu–Ni–Sn–Al alloys via high-throughput experiments, CALPHAD approach and machine learning

Hardness and Young's modulus are critical indicators in the design of innovative Cu–Ni–Sn–Al alloys with desired elastic and strength properties. In this study, the composition-dependent hardness and Young's modulus in the fcc Cu–Ni–Sn–Al alloys were determined using high-throughput experiments, the CALPHAD (CALculation of PHAse Diagrams) approach, and machine learning (ML) model. By combining the diffusion-couples tool, nanoindentation, and electron probe microanalysis (EPMA) techniques, the 341 sets of composition-related hardness and Young's modulus in the fcc Cu–Ni–Sn–Al system, as well as its sub-binary and sub-ternary systems, were effectively determined. These measured data were subsequently utilized to establish the relationship of Young's modulus and hardness with respect to composition in the fcc Cu–Ni–Sn–Al system through the combined application of CALPHAD and back propagation (BP) artificial neural network machine learning models. A comparison between the two approaches revealed that the ML method achieves higher accuracy in ternary and quaternary alloys compared to the CALPHAD method. The impact of alloying elements on the values of hardness and Young's modulus was analyzed, demonstrating that the Ni content has the largest effect on hardness, while the Young's modulus increases with addition of Ni but decreases with the addition of Al and Sn. Finally, the effects of solute elements on the nanomechanical properties of aged Cu1-x(Ni3Sn)x and Cu–9Ni–6Sn-xAl alloys were examined.

Thermodynamic optimization of KCl-LiCl-LaCl3 with ionic two-sublattice model for liquid

The pyroprocessing technology can reduce nuclear waste by recovering uranium from spent nuclear fuels. To fully take advantage of this technique, it is crucial to have a better understanding of the thermodynamic behavior evolution of the eutectic KCl-LiCl electrolyte with the accumulation of impurities such as lanthanides. The present study carries out thermodynamic modeling for the KCl-LiCl-LaCl3 system and its binary subsystems using the CALPHAD (CALculation of PHAse Diagrams) approach for the first time to predict the liquidus temperatures of KCl-LiCl eutectic as a function of LaCl3 content. Three possible ionic two-sublattice models have been implemented to describe the liquid phase for comparison. Model 1 only involves simple cations and anions. Model 2 and 3 consider short-range ordering in the liquid and introduce species K2LaCl5 and LaCl63-, respectively. It was demonstrated that from the thermodynamics point of view, Model 1 is sufficient to reproduce both phase equilibria and enthalpy of mixing data, whereas Models 2 and 3 seem redundant and increase the number of parameters, which may further lead to poor extrapolation behavior towards multicomponent systems. To achieve better agreements with experimental phase equilibria data and estimated enthalpy of mixing data using the surrounded-ion model, three ternary parameters were optimized for the KCl-LiCl-LaCl3 system. The resultant calculations can well reproduce the experiments and provide insights into the liquidus temperature variation as the mole fraction of LaCl3 increases in the electrolyte.

Computational thermodynamic study on CVD of silicon oxynitride films from Si–O–N–H and Si–O–N–H–Cl systems

High-throughput thermodynamic analysis of chemical vapor deposition of silicon oxynitride films from the Si–O–N–H and Si–O–N–H–Cl systems are performed based on the CALPHAD (CALculation of PHAse Diagram) approach. The considered deposition conditions are 800 °C, 200 Pa, NH3/SiH4 ratios of 0.05–50 and NH3/N2O ratios of 0.05–10. The influence of precursor composition on the phase and composition of the coatings as well as the optimal window for obtaining high-purity Si2N2O are discussed. The formation of SiO2 favors low NH3/N2O ratios and its fraction decreases with increasing NH3/N2O ratio. The content of Si2N2O increases monotonously with increasing NH3/N2O ratio until reaching 100 at.%. Free Si is suppressed to almost 0 at.% when the NH3/SiH4 ratio is greater than 1. The introduction of Cl in the precursor can not only reduce the formation of free Si but also expand the deposition window for preparing pure Si2N2O. Our calculated results agree well with available experimental data.

CALPHAD-aided design of high-strength Al-Si-Mg alloys for sufficient laser powder bed fusion processability

This study proposes a design concept for an Al-Si-Mg ternary alloy to achieve both high strength and laser-based powder bed fusion (PBF-LB) processability using calculation of phase diagrams (CALPHAD). The thermodynamic calculations using the CALPHAD method evaluated the Al-10Si-4.5Mg (wt%) alloy composition for strengthening by both the Si and Mg2Si phases and high PBF processability by reducing the risk of hot tearing behind the small freezing range of 27 °C and crack susceptibility index (|dT/d(Fs1/2)|) of 77 °C. The PBF-LB Al-10Si-4.5Mg alloy sample (processed by laser power of 128 W and laser scanning velocity of 1000 mm/s) exhibited a fine three-phase microstructure and exceptional hardness of 199 HV. No hot tearing occurred, whereas many cracks preferentially propagated along the melt pool boundaries during the PBF-LB process. The severe lateral cracking resulted in a maximum relative density of 96 % in the Al-10Si-4.5Mg alloy samples. Preferential cracking could be responsible for the localization of the relatively coarse particles of the brittle Mg2Si phase in the cellular microstructures of the melt pool boundaries. Understanding the lateral cracking mechanism can provide new insights into alloy modification using the controlled solidification path to avoid a specific two-phase eutectic reaction (L→α-Al+Mg2Si) to improve the PBF processability. A modified alloy composition of Al-10Si-3Mg (wt%) was assessed using the CALPHAD approach. PBF-LB processing using the modified alloy powder alleviated cracking and improved the maximum relative density to 98 % for the PBF-LB manufactured samples. This result accentuated the validity of the design strategy for Al-Si-Mg ternary alloy utilizing the CALPHAD method.

Computational and experimental investigation of a new non equiatomic FCC single-phase Cr15Cu5Fe20Mn25Ni35 high-entropy alloy

The structural, mechanical, and thermal properties of a new non-equiatomic face-centered cubic (FCC) structured high entropy alloy (HEA) were examined computationally using density functional theory (DFT) calculations and validated experimentally. To identify potential single phase HEA candidates, the composition space of the CrCuFeMnNi alloy system, including 1451 alloys, was investigated using the CALculation of PHAse Diagrams (CALPHAD) method and Thermo-Calc software. The CALPHAD approach successfully predicted an FCC single-phase Cr15Cu5Fe20Mn25Ni35 alloy. Elastic constants and thermal properties of the Cr15Cu5Fe20Mn25Ni35 HEA were determined through DFT calculations using a 100-atom supercell. To validate the DFT calculations, HEA samples were prepared by the arc melting technique, and X-ray diffraction (XRD) analysis confirmed a single-phase FCC structure.The DFT calculated elastic constants values satisfied the Born stability conditions for stability of a cubic crystal structure. Pugh's theory indicated that this alloy exhibits ductility and metallic behavior due to its B/G ratio exceeding 1.75 and positive Cauchy pressure. Additionally, Poisson's ratio exceeded 0.26, further confirming its ductile nature. Experimental tests confirmed these findings by measuring bulk modulus, shear modulus, Young's modulus, and Poisson's ratio. The calculated CV values showed good agreement with experimental data at different temperatures. The linear coefficient of thermal expansion increased rapidly at lower temperatures before becoming linear. Both XRD as well as DFT calculations yielded similar lattice constant results for this HEA. These findings provide insights into various properties of the Cr15Cu5Fe20Mn25Ni35 HEA, including its structural stability, mechanical behavior and thermal characteristics.

Viscosity database for ternary Cu–Cr–X (X=Ni, Si, Zr) alloys based on CALPHAD-type modeling

A viscosity model with composition and temperature dependence for the liquid alloys of the Cu–Cr–X (X = Ni, Si, Zr) systems was developed using the CALPHAD (CALculation of PHAse Diagrams) approach. Based on the critical review of the available experimental data for pure metal viscosity, the viscosities of pure liquid Cu, Cr, Zr, Ni and Si were simulated with the Arrhenius formula. The viscosities of the binary liquid alloys of the Cu–Ni, Cu–Si, Cu–Zr, Cr–Ni, Cr–Si and Ni–Zr systems at different temperatures were evaluated using the CALPHAD-type formalism. The non-linear viscosity behavior resulting from chemical short-range order was described using temperature-dependent binary interaction parameters. The viscosities of the Cu–Cr and Cr–Zr liquid alloys were predicted employing the Hirai equation. The viscosities of the Cu–Cr–Zr, Cu–Cr–Ni and Cu–Cr–Si ternary liquids were directly extrapolated using the Redlish-Kister-Muggianu equation from the parameters of the binary systems. A comprehensive understanding of the temperature-composition-solidification phase-viscosity relationship was established for ternary melts. The satisfactory agreement observed between calculations and experimental data validates the use of CALPHAD-type viscosity modeling, supporting the suitability of the constructed viscosity database for predicting the viscosity of high-performance Cu-based alloys.

Phase equilibria and microstructure development in Mg-rich Mg-Gd-Sr alloys: Experiments and CALPHAD assessment

Mg-Sr alloys are promising to fabricate orthopedic implants. The alloying of rare earth elements such as Gd may improve the comprehensive mechanical properties of Mg-Sr alloys. The information on the phase diagram and the microstructure development are required to design chemical composition and microstructure of Gd alloyed Mg-Sr alloys. The phase equilibria and the microstructure development in Mg-rich Mg-Gd-Sr alloys (Gd, Sr < 30 at. %) are experimentally investigated via phase identification, chemical analysis, and microstructure observation with respect to the annealed ternary alloys. The onset temperatures of liquid formation are measured by differential scanning calorimetry. A thermodynamic database of the Mg-rich Mg–Gd–Sr ternary system is developed for the first time via CALPHAD (CALculation of PHAse Diagram) approach assisted by First-Principles calculations. The thermodynamic calculations with the developed database enable a well reproduction of the experimental findings and the physical-metallurgical understanding of the microstructure formation in solidification and annealing.

Efficient prediction of corrosion behavior in ternary Ni-based alloy systems: Theoretical calculations and experimental verification

Pourbaix diagrams are calculated to describe electrochemical processes for alloys in aqueous solution. With the multi-component differentiation of alloy systems, the construction of Pourbaix diagrams is facing challenges, especially for non-single-phase alloy systems. In this study, the simultaneous construction of phase diagrams and Pourbaix diagrams were implemented for predicting the evolution of the phases in the immune and passive regions. The CALPHAD (CALculation of PHAse Diagram) approach was used to quickly access the Gibbs free energies of various phases and the chemical potential of the elements in the phases from the thermodynamic database of the Ni-Si-Al-Y system. The corrosion behavior of two typical Ni-Al-Si and Ni-Al-Y systems was investigated. Si and Y were added to Ni-based alloys to produce the solid solutions L12Ni3(Al,Si) and L12Ni3Al + Ni5Y, respectively. Calculations showed that NiO and Al2O3 make up the passive area of the Ni3Al1 alloy. The introduction of SiO2 and Y(OH)3 in the passive region separately helped to minimize the alloys' susceptibility to corrosion. However, Si reduced the thermodynamical possibility of NiO formation in the passive film, and the addition of Y caused extreme galvanic corrosion. Experiments on Ni-based alloys validated the results through electrochemical corrosion. It was also discovered that the presence of Ni5Y produced galvanic corrosion and that Si reduced the oxide in the passive film, causing pitting corrosion. The corrosion prediction of the quaternary alloys indicates that the solid solution of Si in Ni5Y reduces the galvanic corrosion effect and the dissolution of passive film. The current work demonstrates that phase diagrams and Pourbaix diagrams may be efficiently and accurately predicted using a well-constructed thermodynamic database, which has major implications for future studies on the corrosion behavior of multi-component alloys.

Experimental investigation and thermodynamic calculation of the Cu–Cr–Ti ternary system

The phase equilibria of the Cu–Cr–Ti ternary system were investigated based on key experiments coupled with thermodynamic modeling. Eighteen ternary alloys were prepared to determine the isothermal sections of the Cu–Cr–Ti system at 600 and 800 °C by means of X-ray diffraction (XRD) and scanning electron microscopy equipped with energy dispersive X-ray spectroscopy (SEM/EDS). Seven three-phase regions have been determined. A ternary compound τ1 was confirmed. The solubilities of Cr in the Cu–Ti binary compounds and Cu in the Cr–Ti binary compounds were measured. The substitutional and sublattice models were used to describe the solution phases and intermediate phases, respectively. Based on the thermodynamic descriptions of three binary systems as well as the experimental phase equilibria data available from the literature and the present work, thermodynamic assessment of the Cu–Cr–Ti system was carried out using the CALPHAD (CALculation of PHAse Diagrams) approach. A set of thermodynamic parameters was obtained and the isothermal sections and the liquidus projection of the Cu–Cr–Ti system were calculated. The calculated results agree well with the experimental data.

Thermodynamic modeling of KCl-PrCl3 and KCl-LiCl-PrCl3 systems

Molten salt electrolysis can recover the actinides from spent nuclear fuels, and it involves a eutectic LiCl-KCl in molten form as an electrolyte. During reprocessing, the concentration of fission products such as La, Nd, Pr, etc., increases and affects the recovery efficiency of the electrolyte. In this work, thermodynamic modeling of KCl-PrCl3 and KCl-LiCl-PrCl3 systems was carried out using the CALPHAD (Calculation of Phase Diagrams) approach for the first time. The thermodynamic functions for the pure salts were taken from the SGTE (Scientific Group Thermodata Europe) Substances (SSUB) database. The experimental thermochemical and phase equilibria data available in the literature were used as input for the assessment of KCl-PrCl3 and KCl-LiCl-PrCl3 systems. The model parameters for the KCl-LiCl system were adjusted to include the new Gibbs energy descriptions for the pure salts. In addition, the sublattice model for the liquid phase in the LiCl-PrCl3 system was modified and reassessed to ensure the model compatibility for higher-order extrapolation. There is a good agreement between the experimental and calculated thermochemical and phase diagram data for all the optimized constituent binaries and the ternary system. This work will be beneficial for determining the solubility limit of PrCl3 in molten LiCl-KCl electrolytes and their thermodynamic properties for improving the efficiency of the pyrochemical process.

Thermodynamic description of molten salt systems: KCl-LiCl-NaCl and KCl-LiCl-NdCl3

The mixture of KCl and LiCl has been used as electrolyte in the electrorefining process to recover uranium from used nuclear fuels due to the low melting point. However, lanthanides and sodium in the reactor waste continuously dissolve into it and thus alter its thermodynamic properties. To understand the thermodynamic behavior evolution of the electrolyte with the accumulation of impurities, thermodynamic modeling for KCl-LiCl-NaCl and KCl-LiCl-NdCl3 and four constituent binary systems in the entire composition space was performed using the CALPHAD (CALculation of PHAse Diagrams) approach. The ionic liquid was described by the two-sublattice model, where neutral species were introduced to consider short-range ordering (SRO) within the melt, whereas the solid solution was modeled based on the Compound Energy Formalism. Literature data on phase equilibria and thermochemical properties were critically evaluated and used during the optimization of thermodynamic parameters for KCl-LiCl-NaCl and KCl-LiCl-NdCl3 and their subsystems. The calculated phase diagrams and mixing enthalpies are in good agreement with the experimental data. The thermodynamic modeling for the KCl-LiCl-NdCl3 system was carried out for the first time. To fill the gap in experimental measurement, enthalpy of mixing for the KCl-LiCl-NdCl3 melt was estimated using the surrounded-ion model. These data then served as critical inputs for thermodynamic optimization. The present study can provide insights into thermodynamic property evolution of the electrolyte and solubility limit of various impurities during the electrorefining process.

Investigations on Thermal Conductivity of Two-Phase WC-Co-Ni Cemented Carbides through a Novel Model and Key Experiments

Excellent thermal conductivity is beneficial for the fast heat release during service of cemented carbides. Thus, thermal conductivity is a significant property of cemented carbides, considerably affecting their service life. Still, there is a lack of systematic investigation into the thermal conductivity of two-phase WC-Co-Ni cemented carbides. To remedy this situation, we integrated experiments and models to study its thermal conductivity varying the phase composition, temperature and WC grain size. To conduct the experiments, WC-Co-Ni samples with two-phase structure were designed via the CALPHAD (Calculation of Phase Diagrams) approach and then prepared via the liquid-phase sintering process. Key thermal conductivity measurements of these prepared samples were then taken via LFA (Laser Flash Analysis). As for modeling, the thermal conductivities of (Co, Ni) binder phase and WC hard phase were firstly evaluated through our previously developed models for single-phase solid solutions. Integrating the present key measurements and models, the values of ITR (Interface Thermal Resistance) between WC hard phase and (Co, Ni) binder phase were evaluated and thus the model to calculate thermal conductivity of two-phase WC-Co-Ni was established. Meanwhile, this model was verified to be reliable through comparing the model-evaluated thermal conductivities with the experimental data. Furthermore, using this developed model, the thermal conductivity of two-phase WC-Co-Ni varying with phase-fraction, temperature and grain size of WC was predicted, which can contribute to its design for obtaining desired thermal conductivities.

Thermodynamic modeling and solidified microstructure of Ag—Sn—Zr ternary system

The phase equilibria of the Ag—Sn—Zr ternary system were investigated over the whole composition via thermodynamic modeling coupled with key experiments. Twenty-two equilibrated alloys were prepared to determine the isothermal sections of the Ag—Sn—Zr system at 500, 700 and 900 °C by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS), and eight as-cast alloys were prepared to study the solidification behavior of the alloys. The solubilities of Zr, Sn and Ag in binary compounds of the Ag—Sn, Ag—Zr and Sn—Zr systems were measured. No ternary compound was found. Based on the thermodynamic descriptions of three constitutive binary systems as well as the experimental phase equilibria data obtained from the present work, thermodynamic assessment of the Ag—Sn—Zr system was carried out by the CALPHAD (Calculation of phase diagrams) approach. A set of thermodynamic parameters of the Ag—Sn—Zr system were obtained. The calculated isothermal sections are in good agreement with most of the reliable experimental data. The liquidus projection and reaction scheme of the Ag—Sn—Zr system over the whole composition were also presented. The solidification behaviors of as-cast alloys were simulated under Gulliver—Scheil non-equilibrium condition. The simulated and experimental results are consistent with each other.

Thermodynamic description of the Mg-O and Al-O systems

The thermodynamic properties of oxides have a considerable influence on the corrosion behavior of alloys. MgO and Al2O3 are important products in the corrosion process of Mg-Al alloys, therefore it is necessary to investigate their thermodynamic properties. The Mg-O and Al-O systems were critically evaluated and re-evaluated using the CALPHAD (CALculation of PHAse Diagram) approach. The liquid phases of these systems were described using the ionic liquid model. According to the literature data, the oxide phases, MgO and Al2O3 were treated as stoichiometric compounds. The thermodynamic parameters of the two stoichiometric compounds were optimized considering both the phase diagram and the thermodynamic data, and finally a set of self-consistent thermodynamic parameters was determined for each system. The calculated results using the presently obtained thermodynamic parameters can reasonably reproduce the reliable experimental data in the literature.

Thermophysical properties in the Al-Cu-Ag system: A combined CALPHAD and first-principles study

Thermophysical properties play an essential role in the microstructure simulation during precipitation and solidification processes in materials science and engineering. In this work, a comprehensive investigation on the molar volume and surface tension of the Al-Cu-Ag ternary system was performed by the CALPHAD (CALculation of PHAse Diagram) approach and the first-principles calculation. Based on the critical review of experimental and theoretical data, the molar volume description of pure Ag in the liquid phase, and subsequently the mole fraction dependent thermophysical databases of molar volume and surface tension for the Al-Cu-Ag system including metastable phases were constructed via the CALPHAD approach. Then considering the excess molar volume, the surface tension of solution alloys could be predicted by the Butler equation using a home-made code with the input of thermodynamic and thermophysical parameters. With the increment of temperature, molar volume of the alloys increases while the surface tension decreases. All the calculated results using the present parameters are in satisfactory agreement with the corresponding experimental data, which could be subsequently applied to simulate the microstructure evolution like precipitation kinetics and phase-filed simulation.

Tuning the hydrogen storage properties of Ti-V-Nb-Cr alloys by controlling the Cr/(TiVNb) ratio

This work presents an effective way to tune the thermodynamic properties of hydrogen absorption/desorption of body-centered multicomponent alloys (BCC-MCAs). A two-fold computational design was applied to screen the (TiVNb)100−xCrx system. First, the calculation of phase diagrams (CALPHAD) approach was used, aiming to BCC alloys. Secondly, a modeling was employed to predict the thermodynamics of the metal-hydrogen systems. The (TiVNb)100−xCrx alloys with x = 30, 35 and 40 were produced by arc-melting. The (TiVNb)70Cr30 and (TiVNb)65Cr35 alloys crystallize as a major BCC phase, while the (TiVNb)60Cr40 is composed mainly of a C15 Laves-type phase. The CALPHAD approach well predicted this tendency. The BCC (TiVNb)70Cr30 and (TiVNb)65Cr35 alloys absorb a large amount of hydrogen up to 2 H/M forming a dihydride. On the contrary, the (TiVNb)60Cr40 alloy displays a reduced capacity due to the low hydrogen uptake of the C15 phase. The thermodynamic of hydrogen absorption/desorption of BCC-MCAs was experimentally investigated via the acquisition of pressure-composition-temperature (PCT) diagrams. The experimental values are in good agreement with the modeling, confirming the accuracy of the computational approach. Moreover, it was demonstrated that increasing Cr content up to 35 at.% significantly impacts the thermodynamic properties, enabling reversible hydrogen absorption/desorption (for H/M ≈ 1) at room temperature.

Enhancing mechanical properties of Ti(C, N)-based cermets via preparation with (Ti, W)(C, N) multi-component powder

Using the traditional preparation method of TiC+TiN powder mixture or simply the Ti(C, N) solid-solution powder to prepare cermet cannot properly avoid the direct contact between TiC, TiN or Ti(C, N) phase and (CoNi) binder phase with undesirable wettability, which is disadvantageous to the strength and toughness of cermet. Here, we introduced a new routine using the (Ti, W)(C, N) solid-solution powder and studied the resultant phase constitutions, microstructures and properties of the Ti(C, N)-based cermets, where the cermets prepared with TiC + TiN + WC and Ti(C, N) + WC were taken as counterparts. The X-ray diffraction (XRD) results showed that regardless of the powder combination, two phases, i.e. fcc-(Ti, M)(C, N) and fcc-(CoNi), were formed, and the lattice constants of these phases varied in different samples, which is attributed to the specific phase stability (TiN > Ti(C, N) > (Ti, W)(C, N) > TiC) calculated based on the CALPHAD (CALculation of PHAse Diagrams) approach. Transmission electron microscopic (TEM) observations further depicted that besides the already-known core-rim structure, the cermet prepared using (Ti, W)(C, N) uniquely incorporated black-gray rimless grains and black-white-gray rimless grains. Two critical mechanical properties, i.e. hardness (H) and fracture toughness (KIC), were subsequently determined using the Vickers indentation method. It was found that the KIC values of the cermet prepared using (Ti, M)(C, N) were improved by 5.1% ~ 29.2% while maintaining the similar level of H as other cermet samples. The segregation of W and Ti in (Ti, W)(C, N) powders led to the formation of cleavage facets in ceramic grains, which could contribute to the hinderance of crack propagation. Eventually, the high-temperature (750 °C) wear tests were conducted to examine the durability of cermet samples. The cermet prepared using (Ti, M)(C, N) generally exhibited enhanced wear resistance, benefiting from the well-balanced H and KIC as well as the restraint of oxidational wear. Thus, this work suggested that preference should be given to (Ti, W)(C, N) solid-solution powders when fabricating high-performance Ti(C, N)-based cermets.

Experimental study and thermodynamic modeling of the Ti–Cu–B system

The Ti–Cu–B ternary system has been systematically studied by experimentation and thermodynamically assessed combining the CALPHAD (CALculation of PHAse Diagram) approach and first-principles calculation. Using seven equilibrated alloys, the isothermal section at 1073 K was established by electron probe micro analyzer equipped with wavelength dispersive spectrometer and X-ray diffraction. Differential scanning calorimetry analysis was performed on all the samples to determine the phase transformation temperatures. Primary solidification phases were also identified from the micrographs of the as-cast samples. Based on all the experimental data obtained in this work, the thermodynamic description of the Ti–Cu–B system was reasonably developed and a set of self-consistent thermodynamic parameters was obtained. The calculated isothermal section, vertical section and liquidus projection account for the experimental data satisfactorily.

The role of entropy and enthalpy in high entropy carbides

The thermodynamic stability of equiatomic mixed carbides, commonly referred to as high entropy carbides (HECs), is investigated via the CALculation of PHAse Diagrams (CALPHAD) approach for mixed carbides consisting of the group IVB and VB transition metal carbides as well as tungsten carbide. The Gibbs free energy of the B1-structured mixed carbides is computed using the compound energy formalism while that of the Bh-structured mixed carbides is evaluated using a point-defect model. The required thermodynamic data for the CALPHAD approach are obtained from density functional theory calculations and the Debye-Grüneisen model. The lower temperature limit at which the HECs mix in thermodynamic equilibrium is determined via numerical and analytical approaches. We find that enthalpy of mixing is at least as important as configurational mixing entropy in these mixed transition metal carbide compounds. The lower limit temperature where an equiatomic solid solution is present is largely independent of the number of components with the only exception being solutions containing tungsten carbide, where a weak temperature dependence is noted. Furthermore, the only equiatomic solid solutions that are thermodynamically stable below approximately 1000 K are those stabilized by enthalpy alone, indicating that many currently fabricated HECs are not at equilibrium at room temperature. Collectively, our results demonstrate that the formation of these carbides is controlled by the competition between entropy and enthalpy, or enthalpy alone, and thus these materials should be referred to as multi-principal component carbides since the former terminology can be misleading.