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Fig. The temperature- and composition-dependent site occupying fraction of stoichiometric Ni 3 Al-based γ′ phase intermetallics and visualization of the atomic distributions of the full ordered configuration of the stoichiometric Ni 3 Al γ′ phase with the real relative size bar on the sublattice 1a and 3c based on a 10×10×10 supercell of the FCC_L1 2 structure at high temperature (1473 K) are presented graphically. [Display omitted] • Site preference, mechanical and thermodynamic properties were predicted in the Ni 3 Al-based γ′ phase. • Co, Mn, and Ti atoms always prefer 3c sublattice (Ni site) in the whole temperature range. • The site preferences of Cr, Cu, Fe, Mo, Re, Ta, V, and W atoms are affected by the heat treatment temperature. • Cr, Re, V doping can strengthen the hardness of Ni 3 Al alloys, and particularly, the effect of Cr is remarkable. • Cr doping increases the Debye temperature of Ni 3 Al alloys significantly. The fundamental aspects of site preference of alloying elements on sublattice of the strengthen γ′ phase with L1 2 structure have not been well understood, which hinders the optimized design of advanced Ni-based high-temperature alloys. In this contribution, the temperature- and composition-dependent site occupying preferences of the binary, ternary, and quaternary of Ni 3 Al-based γ′ phase alloyed with M i where M i represents the additional transitional metals Co, Cr, Cu, Fe, Mn, Mo, Re, Ta, Ti, V, or W atoms (arranged in alphabetical order) chosen frequently, were studied using a two-sublattice thermodynamic model (Ni, Al, M i) 1a (Ni, Al, M i) 3c. The site occupying fractions (SOFs) were calculated based on a thermodynamic database established in this work, where the thermodynamic data of the end-members involved were obtained using first-principles calculations and phonon spectrum calculations. The calculated SOFs results show that there is an obvious site preference for stoichiometry binary Ni 3 Al, and its site configuration changes from (Al) 1a (Ni) 3c at room temperature to (Al 0.9984 Ni 0.0015) 1a (Al 0 Ni 0.9994) 3c at 1273 K. For the γ′ phase with the composition 78Ni-26Al-4M i (atom ratio and x Ni / x Al = 3:1), Mo atoms always preferred to occupy the 1a sublattice (Al site), Co, Mn, and Ti atoms always prefer the 3c sublattice (Ni site) in the whole temperature range, while the site preference of Cr, Cu, Fe, Re, Ta, V, or W atom is affected by temperature. For example, when the heat treatment temperature is lower than 700 K, Cr, Cu, Fe, Ta, V, and W atoms occupy the 1a and 3c sublattice randomly, and Re atoms prefer to 3c sublattice, while when the heat treatment temperature is higher than 1273 K, Cr, Cu, and W atoms prefer 3c sublattice, Fe and Ta atoms prefer to 1a sublattice, while all Re atoms occupy the 3c sublattice exclusively, and all V atoms occupy the 1a sublattice exclusively, respectively. Likewise, the site preference of the quaternary system with selective compositions 78Ni-26Al-2 M 1 -2 M 2 was also predicted. Based on calculated SOFs results, the mechanical and thermodynamic properties were studied at the ground state. It has been revealed that Cr, Re, and V doping can improve the microhardness of Ni 3 Al alloys; in particular, the effect of Cr is extraordinary; and all elements, except Mn, Mo, and Ti, would enhance the bulk modulus of Ni 3 Al-based γ′ phase, in which Mn have the greatest influence on reducing the bulk and shear modulus, respectively. Furthermore, all the B/G ratios of the computed Ni 3 Al-based γ′ phase are >1.75, showing inherent ductility. Only Cr doping significantly enhances the Debye temperature of the Ni 3 Al-based γ′ phase. [ABSTRACT FROM AUTHOR]

The multi-principal element alloys (MPEAs), which are also called high-entropy alloys (HEAs) or medium-entropy alloys (MEAs) based on the multi-principal element number, received intensive attention due to their unusual phase structures and potential application in diverse aspects. However, quantitative and graphical characterization of the atom distribution, lattice distortion, and mechanical properties are considerably insufficient, which hinders the exploration and development of the rich ore of MPEAs. In this work, a general and comprehensive approach was proposed to simulate the atom distribution, lattice distortion, and mechanical properties of MPEAs based on site preference, where FCC_CoNiV and CoCrNi MPEAs were demonstrated and compared quantitatively and graphically. For this purpose, the temperature- and composition-dependent site occupying fractions (SOFs) of MPEAs were predicted using a two-sublattice model based on the crystallographic information of the prototype of MPEAs, where the corresponding thermodynamic database concerning the temperature-dependent Gibbs free energy of formation of the involved end-member compounds was established in this work using first-principles calculations based on density-functional theory (DFT) and density-functional perturbation theory (DFPT). For FCC_CoNiV MPEA，the site occupying configuration is (V 1.0000) 1a (Co 0.4444 Ni 0.4445 V 0.1111) 3c , which is not affected by the heat treatment temperature, while for FCC_CoCrNi MPEA, the site preferences change continuously and slightly with the increase of the heat treatment temperature, for example, the site occupying configuration changes from (Co 0.3371 Cr 0.0002 Ni 0.6627) 1a (Co 0.3320 Cr 0.4444 Ni 0.2236) 3c at 673 K to (Co 0.3690 Cr 0.0007 Ni 0.6303) 1a (Co 0.3214 Cr 0.4442 Ni 0.2344) 3c at 1273 K. From the long-range ordered structures, the locally ordered structures were explored further by statistically analyzing the coordination number of the atom coordinated with the same type of atoms in a 30×30×30 FCC supercell based on the prototype of L1 2 _AuCu 3 which contains 108,000 atoms. It was found that all the maximum numbers n for Co*‐nCo, Ni*‐nNi, and V*‐nV are only 8 in FCC_CoNiV MPEA, respectively, while the maximum numbers n for Co*‐nCo, Cr*‐nCr, and Ni*‐nNi are 10, 8, and 10 in FCC_CoCrNi MPEA, respectively. Thus, all coordination numbers in the studied MPEAs are less than 12, i.e., the coordination number of the pure metal with a FCC unit cell. The calculated relative lattice distortion of FCC_CoNiV MPEA is 2.54%, which is larger than that of FCC_CoCrNi MPEA (2.25%) by comparing the corresponding structure with and without distortion based on the predicted site configuration at 973 K. Besides the difference in the total energy, the resultant force acting on each atom of the FCC_CoNiV MPEA with and without distortion was graphically characterized to explore the mechanism of lattice distortion. For the mechanical properties, both alloys show ductile, while the elastic anisotropic of FCC_CoNiV MPEA is larger than that of FCC_CoCrNi MPEA, the strong ordering behaviors of V atoms may contribute to these behaviors. Current results agree well with the limited experimental and simulated reports concerning the ordering behavior of V atom and ductile characters. Thus, a general approach was established, which can be applied to simulate the atom distribution, lattice distortion, and mechanical properties of MPEAs based on site preference. We expect that the current approach may act as a standard simulating strategy on MPEAs beyond the traditional random mixing consideration of the different constituent atoms. [Display omitted] • A general simulating approach was proposed on multi-principal element alloys (MPEAs) based on site preference. • The approach characterizes the atom distribution, lattice distortion, and mechanical properties. • The FCC_CoNiV and CoCrNi MPEAs were demonstrated and compared quantitatively and graphically in detail. • The atom distribution, lattice distortion, and mechanical properties of FCC_CoNiV and CoCrNi MPEAs are rather different. [ABSTRACT FROM AUTHOR]