CALPHAD Method Research Articles

On the Bi–Ni system. Ab initio calculations and thermodynamic remodeling

Phase diagrams are important part of materials science and technology. The Calphad method, which couples experimental information and computer calculations, allows for calculation phase diagrams and information that is necessary for technological processes. However, to obtain a reliable information from calculation the trustable database is necessary. A new thermodynamic database for a binary Bi–Ni system is proposed in this work. The database was prepared based on newest experimental information that was not included into previous optimizations of Bi–Ni system. A good agreement between modeling and experiment was found thus a proposed description can be used for further calculations of multi-components systems.

Novel insight into precipitation behavior of γ’ phase particles in Cu–15Ni-xAl alloys through Calphad method

γ′ phase (AlNi3) particles' precipitation behavior in the Cu–15Ni-xAl alloys (wt.%, x = 0, 1, 2, 3 and 4) ageing at different temperature was systematically discussed with the help of Calphad method. With fixed ageing temperature, when Al content increases from 1 wt% to 4 wt%, the γ′ phase particles transform from a few microns to dozens of nanometers in size. The increasing Al content was proven to raise the instability of single phase solid solution (FCC), which can be expressed by the increasing value of GexcessFCC and will result in the increasing critical temperature for precipitation. Supersaturation at fixed ageing temperature is thus raised with increasing Al content, so does the nucleation driving force of γ′ phase. Simultaneously, the precipitation strengthening in Cu–15Ni–4Al firstly increases and then decrease with ageing temperature decreasing from 700 °C to 400 °C, which is due to the competition between increasing nucleation driving force and decreasing self-diffusion coefficient of element with decreasing temperature. The continuous and discontinuous precipitation behaviors of γ’ phase were also discussed, which will be respectively promoted and suppressed with decreasing ageing temperature due to the relatively high nucleation driving force. However, both continuous and discontinuous precipitation will be suppressed when the ageing temperature decreases to 400 °C due to the too low self-diffusion coefficient.

An ultra-refining microstructure in rapidly solidified Ti–45Al-8.5Nb-(W, B, Y) alloy after an isothermal heat treatment

In the present work, the microstructure evolution of a rapidly solidified TiAl alloy with the nominal composition of Ti–45Al-8.5Nb-0.2W-0.2B-0.02Y (atom %) prepared by melt spinning method was investigated. An ultra-fine and homogenized microstructure containing metastable supersaturated α2 phase with a grain size of 3–10 μm was obtained by rapid solidification. α phase became the primary phase during rapid solidification and the solidification path was discussed using phase selection hierarchy map calculated by CALPHAD method. After one-step heat treatment (aging at 800 °C), the metastable α2 grain decomposed to α2/γ nano-lamellar structure quickly and then greatly refined via recrystallization, which might be attribute to a large elastic strain and high interfacial energy stored in lamellar structure. The resulting microstructure is constituted by ultra-fine equiaxed γ grains, B2 grains and very small globular Y2O3 precipitates. This study can provide some reference information on the microstructure after rapid solidification and the microstructural thermostability.

Thermodynamic description, hardness and electrical conductivity of the Bi–Ni–Zn system: Experiment and modeling

Selected ternary systems are chosen due to the significant interest of nickel alloys in the different industry such as electronic, chemical, automotive, marine etc. Chosen ternary system up to this paper has not been studied. The ternary system Bi–Ni–Zn has been experimentally and analytically tested. Temperatures of phase transformation were determined by differential thermal analysis (DTA) on 12 ternary samples. Obtained results by DTA test were compared with calculated vertical sections Bi–NiZn, Ni–BiZn and Zn–BiNi. Hardness and electrical conductivity were measured for some alloys. By using experimental results of hardness and electrical conductivity tests, mathematical model has been proposed for calculation of those properties along all composition ranges. Composition of alloys and phases in alloys annealed at 400 and 700 °C were determined by scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS). Obtained results by EDS were compared with calculated isothermal sections at 400 and 700 °C. X-ray powder diffraction (XRD) tests were used for phase identification in all ternary samples. Used analytical method was Calphad method. Calculation of phase diagrams (three vertical sections and two isothermal sections) was performed by using thermodynamic parameters for constitutive binary systems. Good agreements between calculated phase diagrams and experimental data have been reached without introducing ternary thermodynamic parameters. Based on this conclusion liquidus projection and invariant reaction were calculated without additional experimental tests.

Thermodynamic assessment of the KF-ThF4, LiF-KF-ThF4 and NaF-KF-ThF4 systems

A thermodynamic assessment of the KF-ThF4 binary system using the CALPHAD method is presented, where the liquid solution is described by the modified quasichemical formalism in the quadruplet approximation. The optimization of the phase diagram is based on experimental data reported in the literature and newly measured X-ray diffraction and differential scanning calorimetry data, which have allowed to solve discrepancies between past assessments. The low temperature heat capacity of α-K2ThF6 has also been measured using thermal relaxation calorimetry; from these data the heat capacity and standard entropy values have been derived at 298.15 K: Cp,mo(K2ThF6,cr,298.15K)=(193.2±3.9) J·K-1·mol-1 and Smo(K2ThF6,cr,298.15K)=(256.9±4.8) J·K-1·mol-1. Taking existing assessments of the relevant binaries, the new optimization is extrapolated to the ternary systems LiF-KF-ThF4 and NaF-KF-ThF4 using an asymmetric Kohler/Toop formalism. The standard enthalpy of formation and standard entropy of KNaThF6 are re-calculated from published e.m.f data, and included in the assessment of the ternary system. A calculated projection of the NaF-KF-ThF4 system at 300 K and the optimized liquidus projections of both systems are compared to published phase equilibrium data at room temperature and along the LiF-LiThF5 and NaF-KThF5 pseudobinaries, with good agreement.

Thermodynamic modelling of Y–H and Y–Zr–H system aided by first-principles and its application in bulk hydride moderator fabrication

A self-consistent thermodynamic description of Y–H binary system has been derived using the CALPHAD method with the aid of first-principles calculations and applied in the fabrication of crack-free bulk Zr–Y hydride neutron moderator. The enthalpies of formation of the end-members calculated by first-principles were adopted for the thermodynamic assessment. Only four model parameters were needed and optimized with the available experimental data from literature. The calculated phase equilibria and thermodynamic data agree well with experimental data. Y–Zr–H ternary system was constructed by extrapolation of three binary sub-systems. According to the thermodynamic calculation results, the hydrogenation of Zr–Y alloys was divided into three stages: isothermal hydriding, isobaric hydriding and terminal hydriding. By carefully controlling the temperature and hydrogen pressure, the transformation from metal to hydride of yttrium and zirconium can be separated and carried out in different stages, so that the cracks formation during hydrogenation was successfully inhibited. With addition of yttrium, the stress induced by the martensitic transformation from δ to ε zirconium hydride would be relaxed. As a result, hydride embrittlement can be mitigated, and the bulk Zr–Y hydrides without micro-cracks can be fabricated.

Structural and physicochemical properties of silver-rich Ag–Al alloys

The X-ray diffraction, Scanning Electron Microscopy, Differential Scanning Calorimetry, dilatometric and electrical conductivity measurements were used to study the structural and physicochemical properties of selected silver-rich alloys from Ag–Al system. All the studied alloys, containing from 10 to 37 at. % of Al (Ag90Al10, Ag85Al15, Ag77Al23, Ag75Al25, Ag72Al28, Ag70Al30, Ag63Al37), were prepared from high purity metals by melting in a glove-box filled with a high purity argon atmosphere. The obtained X-ray diffraction patterns and microstructure observation of alloys containing up to 15 at. % of Al suggested that in this range only solid solution of silver exists. The thermal analysis showed heat effects related to phase transitions in Ag–Al system. In addition, the thermal expansion studies revealed an anomalous behavior in expansion for some composition of alloys associated with the phase transition. The electrical conductivity values rapidly changed, which may be associated with the formation of different phase areas in the Ag–Al system.Based on the results obtained in this work and critically reviewed literature data a thermodynamic re-optimization of the binary Ag–Al system using CALPHAD method was proposed. A good agreement between calculation and experiment was found.

Phase diagram and thermodynamic properties of the GdBr3–CsBr binary system

Phase diagram of the GdBr3-CsBr binary system was established by Differential Scanning Calorimetry (DSC) method. This system exhibits three stoichiometric compounds, namely Cs3GdBr6, Cs3Gd2Br9 and CsGd2Br7; and three eutectics located at GdBr3 molar fraction x = 0.11 (T = 847 K), x = 0.52 (T = 798 K) and x = 0.72 (T = 859 K), respectively. Cs3GdBr6 undergoes a solid–solid phase transition at 701 K and melts congruently at 1077 K. Cs3Gd2Br9 melts incongruently at 841 K and finally CsGd2Br7 undergoes a solid–solid phase transition at 788 K and melts congruently at 880 K. Experimentally determined phase diagram was optimized by CALPHAD method and thermodynamic properties of compounds existing in the system were estimated. Phase transition of pure GdBr3were determined at 533 K and ΔHtr = 0.41 kJ mol-1.

Thermodynamic assessment of the RE-B (RE = Ce, Dy, Lu) binary systems

Phase equilibria and thermodynamic properties of Nd-Fe-B-based alloys are fundamental to design novel Nd-Fe-B-based permanent magnets with outstanding magnetic properties and lower costs. In order to develop thermodynamic database of multi-component Nd-Fe-B-based alloys with the rare earth (RE) metals, in this work, the RE-B (RE = Ce, Dy, Lu) binary systems were assessed thermodynamically using the CALPHAD method based on the available phase diagram and thermodynamic data reported in the literature. In the thermodynamic modeling, the solution phases including liquid, bcc, fcc, hcp and rhombohedral, are described as the substitutional solution model and their excess Gibbs energies are described by Redlich-Kister polynomial. The binary intermetallic compounds, CeB4, CeB6, DyB2, DyB4, DyB6, DyB12, DyB66, LuB2, LuB4, LuB12 and LuB66, are treated as the stoichiometric compounds considering the experimental heat capacities and enthalpy increments of some intermetallic compounds. The calculated results are in good agreement with the reported experimental data.

Heat capacity and thermodynamic properties of alkali and alkali-earth borohydrides

In this work, the above room temperature heat capacity for different polymorphs of alkali and alkali-earth (i.e. Na, K, Rb, Cs, Mg, Ca) borohydrides has been measured by DSC as a function of temperature. The above room temperature measured Cp values have been compared with available extrapolated literature data, and they have been modelled as a function of temperature according to the Calphad method. The variations of Cp values for different polymorphs were studied in details and they have been related to the corresponding crystal structures, considering the mobility of the BH4− group. From the whole set of assessed thermodynamic data, possible correlations with dynamics and structural properties have been estimated.

Accelerated design of novel W-free high-strength Co-base superalloys with extremely wide γ/γʹ region by machine learning and CALPHAD methods

Since half a century ago, researchers have continuously focused on developing γʹ-strengthened Co-base superalloys to achieve an increased power and efficiency; these alloys can supposedly operate at higher temperatures than Ni-base superalloys. However, the yielded results have failed to meet the expectations. Herein, we successfully design novel W-free Co-V-Ta-base alloys by employing machine learning algorithm and CALPHAD methods, which exhibit low mass density (8.67–8.86 g/cm3), an extremely wide γ/γʹ region, a high γʹ solvus temperature (up to 1044 °C), and a high strength. The atom probe tomography results show that titanium is an extremely strong γʹ-former; therefore, it is expected to improve the thermodynamic stability of the γʹ phase. Furthermore, besides the very high tensile strength (18.7 GPa) of γʹ phase, indicated by first-principles calculations, the strength of Ti-incorporated alloy is higher than that of γʹ-strengthened Co-base superalloys; especially, the reported strength value is higher than that of the well-known Co-9Al-9 W alloy by approximately 322 MPa at 750 °C, which is comparable to that of a few commercial Ni-base superalloys. Therefore, the possibility of the Co-V-Ta-base system being a candidate for developing novel Co-base superalloys is strongly suggested in this study.

Calculation of Grain Boundary Segregation in Cu–Based Alloys by CALPHAD Method

Calculation of Grain Boundary Segregation in Cu–Based Alloys by CALPHAD Method

Thermodynamic and thermophysical properties of Cu-Si liquid alloys

The Cu-Si system is of primary interest for many industrial applications, especially for waste applications. Due to eutectic reactions and the congruent melting of intermetallic phases, these binary alloys exhibit specific behaviors as a function of temperature and composition. A complete investigation of the thermodynamic and thermophysical properties of such liquid metals that may form is required to optimize such a process at the industrial scale. To better predict the thermophysical properties of these metallic alloys, measurements of the surface tension are carried out for bulk mole fractions of up to 32%at Si. These experiments were conducted by means of the oscillating drop technique using the electromagnetic levitation method [1]. To better predict the thermodynamics of such liquids during the experiments, these tests were complemented by chemical activity calculations using the Calphad method. The experimental results obtained from the electromagnetic technique are compared and discussed taking into consideration the Egry model [2], the most suitable one in case of formation of high-temperature intermetallic compounds.

DTA measurements in the ternary Ag-Au-Ga system

In this work, the ternary Ag-Au-Ga system was studied experimentally by differential thermal analysis (DTA). The measurements were carried out along two chosen cross-sections determined by the ratio of mole fractions XAg/XGa=1:1 and XAu/XGa=1:1 by applying Pegasus 404 apparatus form Netzsch. The experiments were performed at three rates: 1 K min-1, 5 K min-1, and 10 K min-1. Next, the obtained experimental results were used to estimate the temperatures of liquidus by applying extrapolation to a zero rate. Moreover, the temperatures of invariant reactions and other phase transformations were investigated from DTA measurements which were carried out with the rate 1 K min-1. Finally, the experimental results were compared with the isopleths obtained from the prediction and calculation of the phase diagram which were done by using CALPHAD method. The experimental data obtained in this work are in good agreement with the calculation results.

Computational Efficient Modeling of Sintering in Multi-component Alloys for ICME Applications

The major challenge while using sintering models for simulation of densification in multi-component alloys is finding the correct transport parameters, which are affected by not only temperature but also chemical composition and phase dispersion. A novel approach for determining the effective self-diffusivity and hence modeling the densification of engineering alloys during sintering is proposed. The approach integrates computational thermodynamics and simulation of diffusion-controlled transformations in multi-component alloys together with a low-order model for solid-state sintering. Computational thermodynamics, using the CALPHAD method, is used to predict microstructural phase stability, which is then used by diffusion simulation models to evaluate the effective transport properties for the sintering model. The modeling approach is validated by comparing results for densification of precipitation-hardened and austenitic stainless-steel alloys during an iso-rate sintering schedule with data from the literature. It is shown that the model can capture experimental observations very well. The modeling approach can thus be used in the development of an efficient search methodology for particulate materials within the context of an integrated computational materials engineering (ICME) frameworks.

Critical evaluation and thermodynamic assessment of the R2O–P2O5 (R = Li, Na and K) systems

The R2O–P2O5 (R = Li, Na and K) systems are thermodynamically optimized based on the evaluated phase equilibria and thermodynamic data by the CALPHAD method. Liquid phase is described by the Modified Quasichemical Model, which takes short-range ordering in liquid solution into account. All intermediate phases RPO3, R5P3O10, R4P2O7 and R3PO4 are treated as stoichiometric compounds and the corresponding polymorphic transitions are considered. A set of self-consistent model parameters for describing the Gibbs free energy of each phase are obtained. The experimental phase equilibria, enthalpy of formation, entropy, heat capacity and activity are reproduced well within experimental error limits. The calculated liquidus around compounds become flatter with the increase of P2O5 content, suggesting that the degree of stability of phosphate increases as its composition approaches R3PO4. The calculated enthalpies of formation for intermediate compounds become more negative and entropies become more positive with the increase of atomic numbers of alkali metals.

Thermodynamic modelling of the Fe–Sn–Zr system based on new experiments and first-principles calculations

The Fe–Sn–Zr system has been studied by first principles calculation and modelled with the Calphad method using the literature and new experimental data. The work includes a revision of Fe–Sn and Fe–Zr systems. Our experimental study has confirmed that the W5Si3 phase (stoichiometry Zr5Sn2,3Fe0,7) is stable at 1350 °C but also down to 1000 °C. Moreover, the crystal structure of the X” phase has been determined. The formation enthalpies of all the ordered configurations of the C15, C16, C36, E1a phases and the stoichiometric Fe5Sn3, Fe3Sn2, FeSn, FeSn2, Fe23Zr6, FeSn2Zr6 (θ), Fe36.36Sn36.36Zr27.27 (N) et Fe14.39Sn43.47Zr39.13 (X″) compounds have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A1, A2 and A3 binary solid solutions have been calculated using the Special Quasirandom Structures (SQS) and DFT calculation. From these new experimental and calculated data, new thermodynamic assessments are proposed for Fe–Sn, Fe–Zr and Fe–Sn–Zr systems.

A new approach for coupled modelling of the structural and thermo-physical properties of molten salts. Case of a polymeric liquid LiF-BeF2

The (Li,Be)Fx fluoride salt is an ionic liquid with complex non-ideal thermodynamic behaviour due to the formation of short-range order. In this work, we explore the relationship between local structure, thermo-physical and thermodynamic properties in this system using a multidisciplinary approach that couples molecular dynamics simulations using the Polarizable Ion Model (PIM) and thermodynamic modelling assessment using the CALPHAD method. The density, thermal expansion, viscosity, thermal conductivity, molar and mixing enthalpies and heat capacity of the (Li,Be)Fx melt are extracted from the polarizable ionic interaction potentials and investigated across a wide range of compositions and temperatures. The agreement with the available experimental data is generally very good. The local structure is also examined in detail, in particular the transition between a molecular liquid with Li+, BeF42− and F− predominant species at low BeF2 content, and a polymeric liquid at high BeF2 content, with the formation of polymers (Be2F73−, Be3F104−, Be4F135−, etc.), and finally of a three-dimensional network of corner-sharing tetrahedrally coordinated Be2+ cations for pure BeF2. Based on the available experimental information and the output of the MD simulations, we moreover develop for the first time a coupled structural-thermodynamic model for the LiF-BeF2 system based on the quasi-chemical formalism in the quadruplet approximation, that provides a physical description of the melt and reproduces (in addition to the thermodynamic data) the chemical speciation of beryllium polymeric species predicted from the simulations.

Thermodynamic modeling of Al–Fe–V ternary system

Based on the thermodynamic data of Al–V, Al–Fe, Fe–V binary systems, as well as a set of available experimental data, the thermodynamic optimization of the Al–Fe–V system was carried out by means of CALPHAD method. The solution phases (liquid, bcc, fcc) were modeled as the substitutional solution. B2 phase was treated as the ordered phase of bcc phase with the thermodynamic model (Al, Fe, V)0.5(Al, Fe, V)0.5. The compounds Al5Fe2, Al2Fe, Al21V2, Al45V7 and Al23V4 in the Al–Fe and Al–V systems were treated as stoichiometric compounds in the binary system and as line compounds Alm(Fe, V)n in the Al–Fe–V system. The compounds Al3V, Al8V5, Al13Fe4, Al8Fe5 and sigma were treated as (Al, Fe)0.75(Al, Fe, V)0.25, Al0.4616(Al, Fe, V)0.1538(Al, Fe, V)0.2308V0.1538, Al0.6275(Fe, V)0.235(Al, Va)0.1375, (Al, Fe, V)8(Al, Fe)5 and Fe8V4(Al, Fe, V)18, respectively. The isothermal sections over the entire composition range at 500 °C, 650 °C, 700 °C and 750 °C were calculated. It was shown that the present calculation was in good agreement with most of the experimental results.

Cathodic Wear by Delamination of the Al4C3 Layer During Aluminium Electrolysis

In aluminium reduction cells, an electrochemical reaction occurs between the molten electrolyte film below the aluminium pad and the carbon cathode blocks, leading to the formation of an Al4C3 layer on the cathode blocks. The properties and role of this Al4C3 layer are therefore important for the aluminium production industry, as they could help increase the life expectancy of electrolysis cells and impact the resistive voltage losses. The purpose of this study is to gain a better understanding of the formation, growth and mechanical stability of the aluminium carbide layer formed on top of the cathode block. A reliable scenario describing both the mechanical and electrochemical behaviours of the Al4C3 layer is proposed. For different industrial graphitized cathode grades, a series of experiments were carried out in a bench-scale Hall-Heroult electrolysis cell and the Al4C3 layer formed on top of the cathode was characterized. Thereafter, the CALPHAD method was combined with density functional theory simulations to estimate the electrical and physical properties of Al4C3 together with the phase equilibria occurring at the interface between the carbide layer and the aluminium pad and the cathode blocks respectively. From these calculations, a scenario for carbide layer growth and mechanical stability was established.