In the present paper, the Co–Fe–Lu ternary system is thermodynamically modeled for the first time based on novel experimental data. Thermodynamic modelling was carried out by the CALPHAD (CALculation of PHAse Diagrams) approach using Thermo-Calc software. Calculations performed using the proposed thermodynamic description well reproduce the experimental data. Based on the developed description, the liquidus and solidus projections, selected isopleths and the Scheil reaction scheme of the ternary system were calculated. The innovative aspects of this assessment include the formation of three continuous solid solutions, Ме17Lu2, Ме3Lu and Ме2Lu, and demonstration of significant extension of binary phases into the ternary system.
Based on experimental data acquired via scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe microanalysis (EPMA), isothermal sections of the Al-Nb-Ta ternary system at 1073 K and 1273 K were constructed. From these sections, it was determined that σ AlNb2 and σ AlTa2, as well as ε Al3Nb and ε Al3Ta, form continuous solid solutions of σ Al(Nb, Ta)2 and ε Al3(Nb, Ta), respectively. Furthermore, a three-phase region and five two-phase regions were confirmed at both temperatures, and the respective phase boundaries were established. No ternary compounds were observed. In addition, the maximum solubility of Nb in the φ(Al38Ta48) Phase at 1073 K and 1273 K was obtained. According to the measured experimental data on the Al-Nb-Ta system together with the assessed descriptions of the constituent binary subsystems, the Al-Nb-Ta ternary system was optimized using the CALPHAD (CALculation of PHAse Diagrams) method. A new thermodynamic database for the Al-Nb-Ta ternary system was developed, and the calculated results demonstrated good agreement with the experimental phase equilibrium data.
Rare-earth–indium (RE–In) intermetallic compounds have attracted extensive attention owing to their prospects in structural, magnetic and electronic engineering applications. In this work, thermodynamic assessments of the Lu–In, Er–In, and Dy–In binary systems were carried out using the CALPHAD (CALculation of PHAse Diagram) method by combining available phase-diagram data and thermodynamic properties. First-principles calculations were used to determine the enthalpies of formation of several compounds lacking experimental data. The liquid phase and terminal solid solutions were described using the substitutional solution model. Lu5In3, Er5In3, and DyIn were modeled with two-sublattice descriptions, whereas the remaining compounds were treated as stoichiometric phases. Upon comprehensive comparison with experimental results, the calculated phase diagrams can reproduce the liquidus data, stability ranges of intermetallic compounds, and invariant reactions. Moreover, the calculated enthalpies of formation also show overall agreement with the available experimental and our first-principles calculation data. The obtained parameter sets are thermodynamically self-consistent and can serve as a basis for developing higher-order RE–In thermodynamic databases and designing related functional alloys.
The structural, mechanical, electronic, optical, phononic, and thermodynamic properties of the double perovskites Ba2AlAsO6 and Sr2AlAsO6 were systematically investigated using first-principles density functional theory (DFT) calculations. Structural optimization, tolerance factor analysis, formation energy calculations, and elastic constants indicate that both compounds possess stable crystal structures and satisfy the Born–Huang mechanical stability criteria. The calculated elastic parameters reveal ductile behavior for the investigated compounds, accompanied by noticeable elastic anisotropy. Electronic structure calculations performed using the HSE06 hybrid functional demonstrate that Ba2AlAsO6 and Sr2AlAsO6 are direct-band-gap semiconductors, with band-gap values of 3.550 eV and 5.026 eV, respectively. The calculated density of states indicates that the valence-band states are mainly dominated by O-p orbitals, while the conduction-band states originate mainly from the cationic contributions. Optical investigations reveal favorable dielectric responses, low reflectivity, and strong absorption in the deep-ultraviolet region, suggesting potential applications in UV optoelectronic and photonic devices. Phonon dispersion calculations confirm the dynamical stability of both compounds at 0 K. Furthermore, thermodynamic properties evaluated within the quasi-harmonic Debye model show increasing Debye temperatures, high melting temperatures exceeding 1700 K, and low lattice thermal conductivity, indicating favorable thermal behavior. Overall, these results provide theoretical insights into the physical properties of X2AlAsO6 (X = Ba, Sr) and suggest their potential as wide-band-gap materials for future optoelectronic and thermal management applications, subject to experimental validation.
The paper presents a systematic first-principles investigation of the elastic properties of NaCl-type transition-metal carbides and nitrides (MX, X = C, N), which play an important role as end-member compounds in CALPHAD thermodynamic modeling. The calculated elastic constants, polycrystalline moduli, and derived mechanical properties reveal well-defined trends as functions of the average number of valence electrons per atom in the compounds, which allow a comprehensive evaluation of mechanical and dynamical stability of their structures. The vibrational properties are analyzed through a comparison between Debye temperatures derived from elastic constants and those obtained from the phonon spectra, leading to explicit interrelations between elastic, vibrational and cohesive properties. A central outcome of this study is the identification of closely related trends between the bulk modulus and a thermodynamic quantity with dimensions of pressure referred to as the “cohesive energy density” (CED). This co-variation is interpreted in terms of the evolution of bonding strength associated with metal/non-metal p–d hybridization, whose progressive weakening governs both the reduction in elastic stiffness and the cohesive energy of these compounds. The present results establish a unified cohesive–elastic–vibrational framework connecting bonding, energetics, and mechanical response in transition-metal carbides and nitrides, highlighting the fundamental role of p–d hybridization in controlling the trends in these key macroscopic properties
In the present study, a comprehensive thermodynamic assessment of the Cr–Hf–Nb ternary system using the CALPHAD method is introduced for the first time. Thermodynamic descriptions for the binary systems were derived from established literature. The optimization of ternary parameters was based on experimental data from isothermal sections and liquidus projection, as well as ab initio calculations, which were incorporated into the thermodynamic model to improve its accuracy. The optimized thermodynamic parameters are consistent with the available experimental observations. Conclusively, this investigation provides a thorough thermodynamic characterization of the Cr–Hf–Nb system, offering an resource for the development of thermodynamic databases relevant to new alloys.
In this study, the Li2CO3–Na2CO3 system was investigated experimentally and a new thermodynamic dataset for this system was established using the CALPHAD approach. Thermodynamic data from literature were collected and critically analyzed. The phase equilibria of this system were further investigated experimentally by Differential Thermal Analysis (DTA) measurements and High temperature X-ray Diffractometry (HTXRD): three solid solution phases based on three solid modifications of pure Na2CO3 were determined. The heat capacity of Na2CO3 and the intermediate compound LiNaCO3 was obtained experimentally by three types of Differential Scanning Calorimeter (DSC) devices. The Gibbs energies of the studied compounds and solutions were evaluated using available literature data together with our experimental results. The new dataset for the Li2CO3–Na2CO3 system can improve the accuracy of phase diagram calculations and the prediction of thermodynamic properties for various applications.
Enthalpies of formation and mixing of binary solid and liquid copper alloys have been calculated by application of the Miedema model and compared with data reported in literature. The Miedema model has originally been developed for alloys containing at least one transition metal. The model parameters have been developed over the years and became fixed around the end of the nineteen eighties. Tables have been published in book form for binary alloys of 3d-, 4d- and 5d-alloys with 57 other metals. Noble metals were only included in combination with transition metals. In the present paper, the validity of the model is investigated for all binary Cu-alloy systems, also including alloys without a transition metal. The calculated values are compared with data reported in literature which are presented in separate tables for solid and liquid alloys. This creates a comprehensive data collection for further exploitation by other scientists interested in the thermodynamics of copper alloys. The much larger number of literature data, that is presently available, allows to investigate the validity of the empirically derived model parameters associated with Cu.
Atomically precise nanoclusters of metalloids (boron, silicon, arsenic, and tellurium) exhibit unique electronic and geometric properties that bridge molecular and bulk regimes; however, systematic data-driven studies remain limited. Here, we present the first comprehensive machine learning analysis of all low-energy structures (N ≤ 55) for these four metalloids extracted from the Quantum Cluster Database (QCD), the largest DFT repository of nanoclusters to date. Nine rotationally invariant geometric descriptors were engineered from relaxed Cartesian coordinates and combined with electronic features (HOMO–LUMO gap, magnetic moment, and valence electrons). Seven regression models were trained to predict the binding energy per atom; GradientBoostingRegressor achieved exceptional accuracy (test MAE = 0.03610 eV/atom, R2 = 0.9950). Interpretability analyses (SHAPs, partial dependence plots) revealed strong electronic‒geometric coupling, with compactness and radius of gyration as the dominant predictors. Unsupervised K-means clustering on shape descriptors identified element-specific 2D → 3D structural phase transitions, whereas feature‒space interpolation generated 24 idealized binary nanoalloy candidates with a common magic size of N = 38, with B50Te50 and Si70Te30 showing the highest predicted stability (an exploratory ranking that requires first-principles confirmation). These results can be used to recover known magic numbers, quantify stability landscapes, and provide ready-to-relax XYZ structures for future DFT validation and experimental synthesis. The workflow demonstrates how the open QCD database, combined with modern machine learning, can accelerate the screening and prioritization of stable metalloid nanoclusters and exploratory alloy candidates for catalysis, optoelectronics, and phase-change materials.
The thermodynamic description of the Mg-Zn-Sr system is of considerable importance for the development of biodegradable Mg alloys containing Zn and Sr. In the present work, a combined first-principles and CALPHAD approach was employed to develop a thermodynamic model for the Mg-Zn-Sr system, primarily assessed and validated using phase-equilibria data at 573 K. Density functional theory calculations were performed to investigate the site occupancy and phase stability of principal end-members associated with the phases Mg17Sr2, Mg23Sr6, SrZn2, αSrZn5, Mg11-xZnxSr, and Mg15-xZnxSr3. The resulting thermochemical data were combined with the available experimental phase constitution data to establish a thermodynamic database for the Mg-Zn-Sr system. Gibbs energy functions were developed to describe the extended Zn solubility in Mg17Sr2 and Mg23Sr6, extended Mg solubility in SrZn2 and αSrZn5, as well as for the five ternary compounds Mg11-xZnxSr, Mg15-xZnxSr3, Mg44Zn21Sr35, Mg20Zn62Sr18 and Mg55Zn43Sr2. The optimized thermodynamic parameters successfully reproduced the experimentally reported isothermal section at 573 K and the phase constitution data available in the literature. However, discrepancies were observed in the Mg-rich region involving the Mg15-xZnxSr3 phase. The phase equilibria in the Mg-rich corner were investigated at 573 K with the help of a solid-solid diffusion couple, which exhibited good agreement with the present model. The present thermodynamic model provides a useful thermodynamic framework for the design of Mg-rich Mg-Zn-Sr biodegradable alloys.
The Ga-Li-Sn system, relevant for self-healing Ga-Sn-based anodes in lithium-ion batteries, has been thermodynamically assessed using the CALPHAD approach. The binary subsystems Ga-Sn, Ga-Li, and Li-Sn were first re-evaluated based on recent experimental data, with particular attention to phase equilibria and thermodynamic properties. Building on experimental investigations, the first thermodynamic description of the ternary system focussing on the experimental work on the beta LiGa-Sn quasi-binary section is developed. The liquid phase was modelled using an associate solution model including a Li3.5Sn species, while the solubilities in beta Sn (Sn_BCT_A5), beta LiGa and Li7Sn2 were described using appropriate multi-sublattice models. Several ternary stoichiometric compounds were incorporated into the thermodynamic database. The resulting description reproduces phase equilibria, mixing enthalpies, and component activities in both the binary subsystems and the ternary system in good agreement with the available experimental data.
Density functional theory is employed to explore the physical properties of double perovskite oxides A2YTiO6 (A = K, Rb, Cs). The structural stability is confirmed through geometry optimization including formation energy, tolerance factor, octahedral tilting and by analyzing mechanical properties. Furthermore, the dynamical stability is confirmed through phonon dispersions. For more reliable evaluation of the electronic properties different exchange correlation functionals like GGA-PBE, GGA-PBE + SOC, GGA-PBEsol, TB-mBJ, and LDA are utilized to perform a comparative analysis that showed their half-metallic nature with 100% spin polarization, high Curie temperature and large total magnetic moment. Electron charge density difference indicated the presence of polar covalent bonding between the atoms. Thermodynamic parameters exhibited high values, confirming their excellent thermodynamic stability and the thermoelectric key parameters calculated values revealed that they exhibit excellent potential for thermoelectric performance. The analysis of optical behavior as a function of photon energy (eV) reveals that studied materials exhibited the highest absorption in the visible and ultraviolet region, indicating their suitability for optoelectronic devices. The findings of this study have revealed that these materials are suitable candidates for spintronic, magneto-optical and thermoelectric applications.
Motivated by their relevance in CALPHAD modeling work, the cohesive, vibrational, and phase stability properties of 5d transition-metal carbides and nitrides (MX, X = C, N) with the NaCl-type (cF8) structure are examined using density functional theory. These findings are analyzed in conjunction with previously reported data for the 3d and 4d series, enabling a unified description of MX compounds across the three transition-metal series. The combined dataset reveals systematic trends as functions of the average number of valence electrons per atom, leading to well-defined homology relations. The cohesive properties of dynamically stable compounds are interpreted in terms of covalent, ionic, and metallic contributions to chemical bonding. A strong correlation between cohesion-related quantities shows that the cohesive energy per valence electron provides a physically meaningful predictor of entropy-related vibrational parameters. These results establish a coherent framework linking cohesion, lattice dynamics, and phase stability in transition-metal MX end-member compounds, offering a consistent basis for the interpretation of energetic trends relevant to thermodynamic modeling.
Ni-based superalloys exhibit outstanding high-temperature strength, oxidation resistance, and creep resistance. Co and Ti serve as crucial gamma/gamma ' phase stabilizing elements in nickel-based superalloys, significantly enhancing their high-temperature strength, creep resistance, and oxidation resistance. Investigating the diffusion behavior of alloying elements in gamma/gamma ' phase Ni-Co-Ti alloys is crucial for understanding the microstructure evolution and processing of Ni-based superalloys. In this work, the atomic mobility in the fcc Ni-Co-Ti system was assessed using the DICTRA module in Thermo-Calc. The calculated diffusion coefficients demonstrate excellent agreement with experimental values, verifying the accuracy of the assessed parameters. Further validation was provided through successful prediction of diffusion-coupled composition profiles and pathways.
Developing stable and high-performance hydrides for solid-state hydrogen storage remains a critical challenge for next-generation energy technologies. In this work, double perovskite hydrides X2LiMgH6 (X = Cs, K) are systematically investigated using density functional theory (DFT). Structural optimization reveals that both compounds crystallize in a stable cubic Fm-3m phase. Their thermodynamic stability is confirmed by negative formation energies, while mechanical stability is ensured by elastic constants satisfying the Born stability criteria, along with ductile behavior indicated by Pugh's ratio. Furthermore, phonon dispersion spectra exhibit no imaginary frequencies, confirming their dynamical stability. The electronic properties, computed using the HSE06 hybrid functional, reveal a metallic character for both compounds, suggesting efficient charge transport. Notably, the gravimetric hydrogen storage capacities are estimated to be 5.24 wt% for K2LiMgH6 and 2.00 wt% for Cs2LiMgH6, highlighting the superior performance of the potassium-based compound. In addition, optical analysis indicates strong absorption in the ultraviolet region, pointing to potential optoelectronic applications. Overall, these findings identify X2LiMgH6(X = Cs, K) as promising multifunctional candidates for solid-state hydrogen storage, combining structural stability, favorable mechanical properties, and enhanced hydrogen storage capacity.
The design of advanced phase-change memory materials requires a fundamental understanding of their thermodynamic behavior, which is inherently governed by composition, structure, and stability. In the present work, we have established a reliable thermodynamic database for the Ag-Ge-Te system. Based on a critical review of available experimental data, the binary Ag-Te system was reassessed using the CALPHAD (CALculation of PHAse Diagrams) method to obtain an improved thermodynamic description. The phase equilibria of the Ag-Ge-Te system were then investigated by combining key equilibrated alloys and thermodynamic modeling. Eight ternary alloys were prepared and characterized by X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDS), yielding the isothermal sections at 873, 773, and 673 K. The solubilities of Ge in beta-Ag 2 Te and of Ag in beta-GeTe were measured. Based on the experimental equilibria data from the literature and the new results obtained in this work, thermodynamic modeling of the Ag-Ge-Te system was performed using the CALPHAD method. An associated solution model, (Ge, GeTe, Te, Ag 2 Te, Ag) 1 , was adopted to describe the liquid phase. A set of self-consistent thermodynamic parameters was finally obtained, which reproduces most of the reliable experimental data. Crucially, this database was applied to predict the glass forming ability (GFA). By integrating the minimum driving force criterion with the phase suppression criterion, a thermodynamically favorable compositional region for potential high GFA is identified as the triangular area defined by the GeTe, Ag 2 Te, and Te corners, with the explicit exclusion of the Te-rich corner. These findings provide direct theoretical guidance for the accelerated design and development of novel PCM materials with enhanced amorphous stability.
This study investigates the phase stability and isobaric heat capacities of some compounds in the CaO-Nb2O5-TiO2 slag system derived from the Bayan Obo ore deposit. Four compounds in the CaO-Nb2O5 system and three compounds in the Nb2O5-TiO2 system were synthesized by solid-state sintering, viz CaNb2O6, Ca2Nb2O7, Ca3Nb2O8, Ca4Nb2O9, Nb2TiO7, Nb10Ti4O29 and Nb24TiO62'. In addition, we also tried to synthesize the potential ternary compounds C8N7T6, C6NT3, C3NT3, and "X" reported in literature. The phase synthesis results were characterized using a combined approach of SEM-EDS, XRD, and Rietveld refinement; then the isobaric heat capacities of the successfully synthesized compounds were determined over the temperature range from 373 K to temperatures below their melting points, from which the corresponding temperature-dependent polynomial expressions were established. Meanwhile, the standard molar enthalpies of formation and standard entropies of the synthesized compounds at 298 K were calculated using the two-parameter model. The current results can provide necessary experimental data for thermodynamic assessment and database development of the CaO-Nb2O5-TiO2 system.
An improved module in CALTPP (CALculation of ThermoPhysical Properties) program was developed in order to determine the thermal conductivity in alloys effectively and accurately. This program contains CALPHAD-type (CALculation of PHAse Diagrams) and several recently developed physical models for evaluating the thermal conductivity for pure metals, solid solutions and multiphase materials. The LM (Levenberg-Marquardt) algorithm is included in this program for guaranteeing the accuracy and efficiency of the evaluation. All the models and algorithms can be selected flexibly depending on the specific case. For the purpose of presenting the utilization of the different models and algorithms integrated in this program, several cases for evaluating the thermal conductivity are performed in the present work. The CALTPP-evaluated thermal conductivities agree well with the experimental ones, demonstrating the good reliability and performance of this program. Furthermore, a database of thermal conductivity for several pure metals, light alloys and cemented carbides etc. was built up by using this program. Researchers can easily get the thermal conductivity by inputting the specific conditions such as the composition and temperature, which greatly contributes to designing the material with a desirable thermal conductivity.
