Ti-Hf-Zr-Nb-Ta refractory high-entropy alloys (RHEAs) exhibiting a dual-phase structure resulting from martensitic transformation offer significant ductility enhancement, but their design requires precise control of the phase stability between body-centred cubic (BCC) and hexagonal close-packed (HCP) phases. This study establishes a comprehensive thermodynamic database for the Ti-Hf-Zr-Nb-Ta system using the 3rd-generation Calculation of Phase Diagrams (CALPHAD) model. The reliability of the database is validated by the strong agreement between the calculated thermodynamic properties and phase equilibria and the experimental data for pure element, as well as for binary and ternary systems. Utilizing this database, the phase stability of various RHEAs within this system was predicted, showing that all RHEAs exhibit a BCC single phase over a wide temperature range. The HCP phase is stable and coexists with BCC phase in both quaternary and quinary RHEAs at lower temepratures. Calculations of the Gibbs energy difference between the BCC and HCP phases ( $\mathrm{\Delta }{G}^{HCP-BCC}$) in TiHfZrTa_x and TiHfZrNb_x alloys reveal that both Nb and Ta stabilize the BCC phase, with Nb exerting a stronger influence. Significantly, a metastable BCC+HCP region in the TiHfZrTa_x and TiHfZrNb_x alloys with $\mathrm{\Delta }{G}^{HCP-BCC}$ ranging from 1786 to 2230 J/mol. Utilizing this finding, the critical Nb composition range (0.0367–0.0712) to achieve the metastable BCC+HCP phase is precisely predicted in TiHfZrTa_0.2Nb_x alloys, enabling targeted design for martensitic transformation. The predictions show excellent agreement with existing experimental measurements.

Physical Vapor Deposited (PVD) TiAlN coatings are extensively utilized as protective layers for cutting tools, renowned for their excellent comprehensive performance. To optimize quality control of TiAlN coatings for cutting tools, a multi-scale simulation approach is proposed that encompasses the microstructure evolution of coatings considering the entire preparation and service lifecycle of PVD TiAlN coatings. This scheme employs phase-field simulation to capture the essential microstructure of the PVD-prepared TiAlN coatings. Moreover, cutting simulation is used to determine the service temperature experienced during cutting processes at varying rates. Cahn-Hilliard modeling is finally utilized to consume the microstructure and service condition data to acquaint the microstructure evolution of TiAlN coatings throughout the cutting processes. This methodology effectively establishes a correlation between service temperature and its impact on the microstructure evolution of TiAlN coatings. It is expected that the present multi-scale numerical simulation approach will provide innovative strategies for assisting property design and lifespan prediction of TiAlN coatings.

Alloying with Gd and Ag can significantly enhance the comprehensive properties of magnesium alloys, and accurate phase equilibria are a necessity for advanced alloy design. However, literature review reveals limited information on the phase equilibria in the ternary Mg–Gd–Ag system. Thus, in this paper, the phase equilibria of the ternary Mg–Gd–Ag system in the region of 0–50 at.% Gd at 450 ℃ and 500 ℃ were investigated by combining the electron probe microanalysis and X-ray diffraction of totally 66 equilibrated alloys, with two isothermal sections at 450 ℃ and 500 ℃ established accordingly; and relatively high solid solubility of Ag in GdMg₃ was characterized. Moreover, seven ternary compounds (denoted as τ₁ to τ₇) were found, and their crystal structures were refined by using Rietveld method. The τ₁ was identical to the previously reported X phase with a diamond-cubic structure, while the remaining six ternary compounds (τ₂ to τ₇) were newly found. The seven ternary compounds (τ₁ to τ₇) are among the space groups of Fd3m (τ₁), P4/nmm (τ₂), P6₃mc (τ₃), P6₃mc (τ₄), Pmn2₁ (τ₅), P62 m (τ₆) and Pc (τ₇). Their homogeneity ranges and lattice parameters were carefully determined. The solubilities of the third elements in the binary compounds of the three subsystems were also well measured. It is anticipated that the presently obtained phase equilibria as well as the crystal structures of ternary compounds in the Mg–Gd–Ag system would serve as a foundation for developing thermodynamic database and alloy design in the near future.