CALPHAD Method Research Articles

Experimental investigation and thermodynamic assessment of the BaCl2–CeCl3 system

The thermodynamic and thermo-physical properties of the molten salt system ▪ have been investigated using an experimental and modelling approach. This molten salt system includes a single intermediate compound ▪, whose structure has been investigated using X-ray and neutron diffraction. Furthermore, this system exhibits solubility of ▪ in ▪ at high temperatures up to a concentration of around 25% ▪ at 1060 K. Additionally, our measurements show solubility of ▪ in ▪ up to about 5% ▪ at 973 K. The investigation of these solid solutions has been performed using quenching experiments and subsequent post-characterisation by X-ray diffraction (XRD). Phase diagram equilibria have also been investigated using differential scanning calorimetry (DSC). Using the aforementioned information on phase transitions, intermediate compound formation, and mutual solid solubility, a thermodynamic assessment of the system has been performed using the CALPHAD method. The model for the Gibbs energy of the liquid solution is the quasi-chemical formalism in the quadruplet approximation, while the model for the Gibbs energy of the solid solutions is a two-sublattice polynomial model.

Tailoring the solidification microstructure and properties of Cu–12Sn-xBi-2Ni alloys by varying Bi content

A novel self-lubricating Cu–12Sn-xBi-2Ni alloy was developed and the effect of Bi on microstructure and properties of Cu–12Sn-xBi-2Ni was investigated. The formation reason of the solidification microstructure was analyzed by CALPHAD method and verified by water quenching experiment. The mechanical properties and the friction properties of alloys were tested by the pin-on-disc wear tester and electronic universal material tester. The tensile property deteriorates with the increase in Bi content, while the Brinell hardness and anti-friction properties of the alloy are enhanced, and Cu–12Sn–6Bi–2Ni alloy is identified to be the alloy with the best self-lubricating property. The addition of Bi increases the number of Sn-rich phase and changes the morphology of Sn-rich phase, resulting in fine Bi-rich phase and lamellar microstructure precipitate around the Sn-rich phase. Liquid Bi as nucleating particles promotes the precipitation of δ phase, resulting in the formation of lamellar δ phase and the Sn-poor α-Cu phase.

Electrochemical investigation and thermodynamic assessment of the Mg-Pd system

This paper presents the results of electromotive force measurements using coulometric titration technique for liquid and solid Mg-Pd alloys with concentrations up to 0.70 Mg mole fraction and at 918 K. These measurements made it possible to verify the homogeneity range of the occurring phases and phase boundaries in the investigated system. Based on the obtained results and other thermodynamic data found in the literature, the phase diagram of the Mg-Pd system was optimized using the CALPHAD method and ab initio calculations. The thermodynamics of the intermetallic phases, the liquid phase, and the solid solutions were described by the correct equations, which can be used in the future to calculate multicomponent systems with the Mg-Pd system as one of the binary components. The thermodynamic calculations successfully reproduced the Mg-Pd phase diagram.

Prediction of the thermal conductivity of Mg-Al-La alloys by CALPHAD method

Prediction of the thermal conductivity of Mg-Al-La alloys by CALPHAD method

Experimental investigation and thermodynamic modelling assessment of the AECl2-NdCl3 (AE = Sr, Ba) systems.

The thermodynamic and thermo-physical properties of the binary salt systems AECl2-NdCl3 (AE = Sr, Ba) have been investigated using an experimental and modelling approach. The binary salt systems both include a single intermediate salt, i.e. Sr9Nd5Cl33 and Ba3Nd2Cl12, respectively. The structure of these intermediates has been investigated with X-ray diffraction (XRD). Furthermore, these systems exhibit mutual solubility of NdCl3 in BaCl2 and SrCl2. The investigation of these solid solutions has been performed using quenching experiments and subsequent post-characterisation by XRD. Phase diagram equilibria have also been investigated using differential scanning calorimetry (DSC). Using the aforementioned information on phase transitions, intermediate compound formation, and solid solubility, thermodynamic assessment of the systems has been performed using the CALPHAD method. The model for the Gibbs energy of the liquid solution is the quasi-chemical formalism in the quadruplet approximation, while the model for the Gibbs energy of the solid solutions is the two-sublattice polynomial model.

Calphad-based thermodynamic assessment of Sm-In binary system supported by Ab-initio calculations

The Calphad method was employed to assess the phase equilibria and thermodynamic characteristics of the samarium-indium system. The input data included theoretical and experimental information, as well as calculated data pertinent to this system. The objective was to identify the equilibrium phase and unknown thermodynamic properties of the system. This entailed determining the parameters that govern the Gibbs energy associated with each distinct phase. The Samarium-Indium system comprises five intermetallic compounds: Sm3In, Sm2In, SmIn3, SmIn, and Sm3In5. The three phases, Sm3In, Sm2In, and SmIn3, have been identified as stoichiometric compounds, while the two phases, SmIn and Sm3In5, exhibit a degree of homogeneity. These phases have been modeled using a two-sublattice model with substitution in each sublattice. A density functional theory (DFT) approach was employed to calculate the enthalpies of formation for all five phases. The Gibbs energy of the liquid phase (G) was described based on the Redlich-Kister equations. The crystal structure of the pure element Sm is Rhombohedral, while that of in is tetragonal. The calculations based on the thermodynamic modeling are in good agreement with the phase diagram data and experimental thermodynamic values available in the literature. The process of modeling allows us to calculate the phase equilibria and thermodynamic properties of the liquid phase and intermetallic compounds of the system Sm-In for the first time. The results obtained are reported in a series of figures and tables in this manuscript.

Experimental and theoretical studies of the LiBH4-LiI phase diagram.

The hexagonal structure of LiBH4 at room temperature can be stabilised by substituting the BH4- anion with I-, leading to high Li-ion conductive materials. A thermodynamic description of the pseudo-binary LiBH4-LiI system is presented. The system has been explored investigating several compositions, synthetized by ball milling and subsequently annealed. X-ray diffraction and Differential Scanning Calorimetry have been exploited to determine structural and thermodynamic features of various samples. The monophasic zone of the hexagonal Li(BH4)1-x(I)x solid solution has been experimentally defined equal to 0.18 ≤ x ≤ 0.60 at 25 °C. In order to establish the formation of the hexagonal solid solution, the enthalpy of mixing was experimentally determined, converging to a value of 1800 ± 410 J mol-1. Additionally, the enthalpy of melting was acquired for samples that differ in molar fraction. By merging experimental results, literature data and ab initio theoretical calculations, the pseudo-binary LiBH4-LiI phase diagram has been assessed and evaluated across all compositions and temperature ranges by applying the CALPHAD method.

Predicting multi-component, high-temperature metallic glasses by coupling empirical models, CALPHAD, and a genetic algorithm

Metallic glasses (MGs) are an emerging class of materials possessing multiple desirable properties including high strength, hardness, and corrosion resistance when compared to their crystalline counterparts. However, most previously studied MGs are not useful in high temperature environments because they undergo the glass transition phenomenon and crystallize below the melting point. In addition, bulk MGs are typically found in multi-component systems, meaning that searching compositional space with a reasonable resolution using computational or experimental methods can be costly. In this study, an in-house developed genetic algorithm-based tool was used to locate alloy compositions with high glass forming ability (GFA) and high-temperature stability in the Ta–Ni–Co–(B) and Ta–Ni–Co–Nb alloy systems. GFA was predicted using an empirical predictive parameter known as P HSS. High-temperature stability was predicted using the CALPHAD method to calculate liquidus temperature. Justification for the use of P HSS to predict GFA of high-temperature MGs, as well as the use of liquidus temperature as a predictor of general high-temperature stability, is given in the form of a meta-analysis of previously reported MG compositions. The predictions made using this algorithm were analyzed and are presented herein. While high-temperature stability was the property of interest for this research, this framework could be used in the future to locate alloys with other application-specific material properties. This genetic algorithm-based tool enables the coupling of empirical parameters and CALPHAD to efficiently search multi-component space to locate glass-forming alloys with desirable properties.

Thermodynamic properties of refractory Mo-Nb-V-Ti high entropy alloys (HEAs)

High entropy alloys (HEAs) are solid solution alloys containing at least 5 elements in equiatomic or near-equiatomic composition. In the present study we report on an alloy design route for refractory HEAs based on Mo-Nb-V-xTi alloys (x denotes mole per cent of Ti, x = 5, 10, 15, 20, 25, the mole per cents of Mo, Nb, and V are equal). The thermodynamic activities of Ti and V were determined by Knudsen effusion mass spectrometry and the measured data were compared to the calculated data obtained by CALPHAD method.

EFFECT OF STEEL’S THERMAL CONDITION ON THE TRANSFORMATION TEMPERATURES OF TWO HOT-WORK TOOL STEELS WITH INCREASED THERMAL CONDUCTIVITY

The aim of our study was to investigate how different thermal conditions affect the transformation temperatures of two hot-work steels with high thermal conductivity. We focused on two conditions: soft annealing, and quenching and tempering. Soft annealing results in a ferritic steel matrix with spherical carbides, while quenching and tempering result in a fully hardened and tempered martensitic matrix with secondary and tempering carbides. We analysed samples using a simultaneous thermal analysis (STA) and differential scanning calorimetry (DSC) to determine the transformation temperatures. Controlled heating and cooling allowed us to observe the energy changes associated with the phase transformations. The equilibrium temperatures were calculated using the CALPHAD method. Our study investigated the influence of thermal conditions on different transformation temperatures, including solidus/liquidus temperatures, austenite solid transformation temperatures (A1 and A3), austenite solidification temperatures and bainite and/or martensite transformation temperatures. A DSC analysis was used to quantitatively measure the transformation temperatures and energy absorption during the endothermic processes (austenite solid transformation and melting) and to study the energy release during the exothermic processes (solidification and transformation). The results showed that soft annealing reduced the solidification interval and the solidus temperature, while energy absorption increased during melting. Conversely, quenching and tempering reduced the austenite solid transformation temperatures and energy release during solidification, including δ-ferrite solidification.

An accelerated scheme for solving inhomogeneous elasticity in phase-field method and application to Ni-based multi-component alloys

On the way towards realistic predictions of various material properties for engineering structural materials, efficient computational simulations of microstructural evolution play an indispensable role. In the present work, an in-house phase-field code with inhomogeneous elasticity has been developed aiming to deal with precipitation processes for multi-component alloys with high efficiency. Two different numerical iterative algorithms, named as Model A and B, are implemented to solve inhomogeneous elastic equations. The resulting simulated morphology and energy evolutions under different conditions show consistency for these two algorithms. In order to perform simulation efficiently, a parallel technique based on CUDA (Computer Unified Device Architecture) architecture is used, which greatly improves the computational efficiency. After estimating the computational efficiency of different acceleration techniques for different grid sizes, Model A is extended to simulate concentration and morphology evolutions in the precipitation and rafting processes of γ′ phase in a Ni-based five-component alloy of Ni−Co−Al−Mo−W. Meanwhile, the CALPHAD method and related databases are linked to provide thermodynamic and diffusivity data. Finally, the computation costs of the parallel technique for different simulation scales are explored, testifying that this technique is capable of performing larger scale simulations for multi-component multi-phase structural materials.

Microstructure and wear resistance of laser cladding a novel nickel-based alloy coating

A novel crack-free nickel-based alloy coating was successfully fabricated using laser cladding. By utilizing the TCNI (v10) commercial multi-component database of nickel-based superalloys, the equilibrium phase diagram and non-equilibrium solidification path of this novel alloy were revealed using the CALPHAD method. The substrate phase of the NiCrFeWBSiMo-CeO2 coating consists of the face centered cubic (FCC) phase, along with several strengthening phases. The coating exhibits a microhardness of ∼575 HV, while the coefficient of friction (COF) and volume wear rate measure at 0.39 and 1.1 mg respectively, indicating excellent wear resistance.

Corrosion resistance of nitrogenated high-carbon martensitic stainless steel designed and produced at nitrogen low pressures

A new martensitic stainless steel with high nitrogen and carbon content at low pressures was designed using the CALPHAD method. The chemical composition of the steel was checked by optical emission spectrometry, obtaining 0.17 wt%-N and 1.33 wt%-C. Scanning electron microscopy (SEM) analyses were carried out for microstructural characterization. The properties of the steel were assessed by Rockwell hardness and potentiodynamic polarization tests in 0.6M NaCl. The steel showed maximum hardness values of 60 HRC, regarded as a hard material. However, the passive film formation was prevented by the high carbon content promoting excessive Cr-rich carbides.

Study of the thermal stability of the Al4SiC4 phase via experiments and thermodynamic assessment

The Al4SiC4 phase is a potential new refractory material due to its high compressive strength at high temperatures. However, the thermal stability of the Al4SiC4 phase is not clear. The thermal stability of the Al4SiC4 phase has been studied. The Al-Si-C samples were prepared using the powder metallurgy method and were sintered/annealed at 1500 °C, 1400 °C, 1300 °C, 1200 °C and 500 °C, followed by XRD, SEM, and EPMA testing. It was found that the Al4SiC4 phase is unstable below 1400 °C and stable above 1500 °C. The isothermal sections of the Al-Si-C system at 1500 °C, 1200 °C and 500 °C were experimentally obtained. The Al4SiC4 phase was synthesized at 1650 °C. It was found that with the addition of the Al4SiC4, the strengths of the SiC-2xxx composite were not increased. It is because the Al4SiC4 reacted with the Al2Cu phase. The thermodynamic description of the Si-C-Al system was carried out using the CALPHAD method. The CALPHAD simulated results are consistent with the present experimental studies. The results show that the stabilization temperature of the Al4SiC4 phase ranges from 1463 °C to 2088 °C.

Thermodynamic assessment of La–Fe–Si systems

The phase equilibria of the La–Fe–Si system were investigated using a combination of experimental and thermodynamic modeling methods. The isothermal cross-section of the La–Fe–Si ternary system in the (Fe, Si)-rich region at 1373 K was experimentally investigated using electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Based on the experimental results and literature reports of the La–Fe–Si system, the thermodynamic model parameters of the system were optimized using the CALPHAD method. The intermediate compounds in the La–Si binary system and ternary compounds in the La–Fe–Si ternary system were described via sublattice models. The calculated thermodynamic and phase equilibria data were in good agreement with the experimental data, providing a foundation for the development of a multi-component thermodynamic database for LaFeSi-based alloys.

Measurement of liquidus in metal-rich region of lanthanoid-oxygen binary systems and the thermodynamic evaluation

In this study, the solubilities of oxygen in molten La, Gd, Tb, Ho, and Er metals were measured and the oxide phases in equilibrium with each of these lanthanoid metals were identified to systematically determine the liquidus of lanthanoid-oxygen systems in the metal-rich region. The molten lanthanoid metal and lanthanoid oxide pellets were equilibrated at 1573–1873 K and then quenched. The oxygen concentration in the quenched metals was measured using inert gas fusion infrared absorption spectroscopy to determine the oxygen solubilities of molten lanthanoid metals. The crystal structures of the quenched lanthanoid oxide pellets were analyzed using XRD to identify the equilibrium oxide phases, which were identified as the sesquioxides of each lanthanoid element. Furthermore, the Gibbs free energies of the liquid phases of the Ln-O (Ln = La, Pr, Gd, Tb, Dy, Ho, Er) systems were evaluated using the CALPHAD method and thermodynamic software Pandat based on the oxygen solubilities of molten La, Gd, Tb, Ho, and Er metals measured in this study and those of Pr and Dy reported in previous studies.

Thermodynamic Assessment of the Fe–Mn–Ni System and Diffusion Mobility of Its Face-Centered Cubic Phase

Through extrapolation of updated binary descriptions, the Fe–Mn–Ni system was thermodynamically elucidated in a self-consistent way. The obtained thermodynamic description was confirmed to be reliable by measuring phase equilibria at relatively low temperatures. Our current thermodynamic evaluation can describe the phase stabilities over a wide temperature range and provide a reliable thermodynamic factor for the diffusion mobility optimization. For the face-centered cubic (FCC) phase in the investigated alloy system, optimization of diffusion mobilities was accomplished with the CALPHAD method. Interdiffusivities were extracted based on the composition-distance profiles of diffusion couples investigated herein. Through comprehensive diffusion behavior comparisons, our proposed diffusion mobilities were confirmed.

Integrating machine learning and CALPHAD method for exploring low-modulus near-β-Ti alloys

Integrating machine learning and CALPHAD method for exploring low-modulus near-β-Ti alloys

Alkali-based components as slag fluidizers in steelmaking processes: A thermodynamic assessment

Defining the optimized volume of dual saturated (CaO and MgO) slags is of utmost importance to secondary metallurgy, especially for the ladle furnace. To be effective, these slags may present high desulphurization capability, combining the ability to shield the electric arc flare, to avoid the skull formation in the ladle borders and bottom, and suitable viscosity to provide fast incorporation of additives and tapping. Some fluidizers are applied for attaining the purpose of taking CaO/MgO into solution, being fluorspar (calcium fluoride, CaF2) and silica sand (silicon oxide, SiO2) broadly used in Si-killed steelmaking plants. At the Al-killed plants, either bauxite (mainly aluminum hydroxide) or calcium-aluminates are recommended choices. Nevertheless, for various reasons, some steelmakers use alternative fluidizers containing a significant amount of Na2O and K2O, such as sodalite and nepheline. Based on thermodynamic calculations (CALPHAD method), the effects of such alkalis on the CaO/MgO solubility and the optical basicity of slags on the CaO–SiO2–MgO–Al2O3 system were explored in this paper. Moreover, the potential impact on the performance of MgO-based refractories in contact with these alkali-containing slags was also assessed by a thermodynamic approach. Although kinetic aspects must also be considered, it was seen that (Na2O)2·(K2O) additions into these systems must be carefully managed to make the most of their ability to improve desulphurization, while avoiding the earlier corrosion of the refractory lining.

CAROUSEL: An Open-Source Framework for High-Throughput Microstructure Simulations

High-throughput screening (HTS) can significantly accelerate the design of new materials, allowing for automatic testing of a large number of material compositions and process parameters. Using HTS in Integrated Computational Materials Engineering (ICME), the computational evaluation of multiple combinations can be performed before empirical testing, thus reducing the use of material and resources. Conducting computational HTS involves the application of high-throughput computing (HTC) and developing suitable tools to handle such calculations. Among multiple ICME methods compatible with HTS and HTC, the calculation of phase diagrams known as the CALPHAD method has gained prominence. When combining thermodynamic modeling with kinetic simulations, predicting the entire history of precipitation behavior is possible. However, most reported CALPHAD-based HTS frameworks are restricted to thermodynamic modeling or not accessible. The present work introduces CAROUSEL—an open-sourCe frAmewoRk fOr high-throUghput microStructurE simuLations. It is designed to explore various alloy compositions, processing parameters, and CALPHAD implementations. CAROUSEL offers a graphical interface for easy interaction, scripting workflow for advanced simulations, the calculation distribution system, and simulation data management. Additionally, CAROUSEL incorporates visual tools for exploring the generated data and integrates through-process modeling, accounting for the interplay between solidification and solid-state precipitation. The application area is various metal manufacturing processes where the precipitation behavior is crucial. The results of simulations can be used in upscale material models, thus covering different microstructural phenomena. The present work demonstrates how CAROUSEL can be used for additive manufacturing (AM), particularly for investigating different chemical compositions and heat treatment parameters (e.g., temperature, duration).