Eutectic points play a critical role in material science due to their low melting points, absence of a solidification range, and formation of unique microstructures that enhance properties. However, identifying eutectics in calculated ternary and higher-order systems remains computationally challenging due to the lack of a well-established screening approach.This work addresses this gap by developing a general, efficient methodology for efficient eutectic screening in multicomponent systems. We first propose and benchmark four CALPHAD-based methods for eutectic identification, evaluating their computational speed and reliability. We then investigate the potential of combining CALPHAD with machine learning to further accelerate the process, leveraging two eutectic properties: (1) eutectics are local minima on the liquidus, and (2) they lie at the intersections of primary crystallization regions. Active learning surrogate models are employed to interpolate CALPHAD data for predicting liquidus and primary crystallization phases, and the performance of each approach is evaluated. By benchmarking multiple strategies and releasing code for three approaches that enable rapid and reliable eutectic screening in high-order systems, this work advances the design of materials such as cast alloys, phase change materials, eutectic high entropy alloys, or metallic glasses.
The Ni–Cr binary system is the basis of stainless steels and Ni-based superalloys, and its thermodynamic and mechanical properties are critical to understanding the behavior of multicomponent alloys. In this work, first-principles calculations combined with the CALPHAD method were employed to investigate the mechanical and thermodynamic properties of the Ni–Cr system over a wide composition range (12.5–87.5 at.% Cr). A systematic search of magnetic configurations using special quasirandom structures (SQS) revealed a composition-driven transition from ferromagnetic to antiferromagnetic ordering. The DFT-calculated elastic constants and tetragonal shear modulus C′ establish the mechanical stability boundaries: the BCC phase becomes mechanically unstable below approximately 53 at.% Cr, and the FCC phase above approximately 60 at.% Cr. The Ni2Cr phase was described using the two-sublattice model (Cr,Ni)2(Cr,Ni)1 with DFT-calculated end-member formation enthalpies as optimization input, and the interaction parameters of the liquid, FCC, and BCC phases were re-optimized using the PARROT module. The systematic differences between the DFT and CALPHAD formation and mixing enthalpies arise primarily from the different Cr lattice stabilities adopted by the two methods, with additional contributions from temperature effects (heat capacity, thermal expansion, and magnetic order–disorder transitions). This discrepancy reflects the present uncertainty in the Cr lattice stability rather than computational errors. The optimized phase diagram, activities, and mixing enthalpies agree satisfactorily with experimental data.
Thermodynamic descriptions of the binary Fe–Cr, Cr–Ni and Fe–Ni systems are evaluated in the present work using the most recent third generation Calphad models. The assessment incorporates formation energies of ordered fcc and bcc and σ compounds obtained from Density Functional Theory (DFT), where the formation energies of the ordered bcc and fcc phases were calculated in this study. The revised Inden–Hillert–Jarl model is applied to account for magnetic contributions to the thermodynamic properties. The Gibbs energies of the ordered end-members of the bcc, fcc and σ phases are formulated using the Effective Bond Energy Formalism (EBEF). This formalism provides reliable binary extrapolation for the fcc and bcc phases, whereas additional ternary interaction parameters remain necessary for the σ phase to reproduce the experimentally observed homogeneity and temperature ranges. EBEF significantly reduces the number of parameters required for the descriptions of binary and higher-order systems compared with the Compound Energy Formalism (CEF), where explicit treatment of end-members typically necessitates a larger parameter set.
Diffusion properties are associated with various aspects of the materials, therefore, the establishment of a kinetic database is essential for the design and development of alloys. In this study, eight ternary diffusion couples of bcc Ti-Cr-Hf alloy were fabricated and annealed at 1273 K and 1373 K for 25 h and 18 h, respectively. And then, on the basis of experimental composition profiles, reliable thermodynamic and kinetic information, the atomic mobility interaction parameters for Ti-Cr-Hf system were efficiently assessed by integrating the Numerical Inverse method with the novel diffusion models. The reliability and soundness of the evaluated mobility descriptions were confirmed by good agreement between the measured composition distributions/interdiffusion coefficients/diffusion paths and the predicted results. Further investigations were also conducted on other diffusion properties including temperature- and composition-dependent interdiffusivities and the related Arrhenius relationship.
