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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]

The Boltzmann formula was commonly employed to describe the configurational entropy of high entropy alloys (HEAs) based on the assumption of ideal solid solution, however, the entropy might rather be called composition entropy cautiously due to the site preference on the sublattice was omitted. Here we proposed a reasonable and general approach beyond the Boltzmann formula to describe the site occupying fractions (SOFs) of atoms on sublattices and thus the configurational entropy of HEAs. For this purpose, the thermodynamic function of the chemical reaction of complex HEA involving SOFs synthesized from the corresponding pure elements was computed using the sublattice model, where the density functional perturbation theory (DFPT) was employed to calculate the relevant thermodynamic properties at definite temperature. Three typical high entropy alloys with different phase structures were quantatively calculated and graphically demonstrated. The site preferences exist due to the different atom characters and sublattice environments. For example, Ni atoms only occupy the 1a sublattice, while Co, Cr, and Fe atoms mainly occupy the 3c sublattice in FCC_CoCrFeNi HEA, and the site preferences tend to be weakened considerably with the increase of heat treatment temperature. The configurational entropies were thus re-defined based on the sublattice information and SOFs. The calculated configurational entropies for FCC_CoCrFeNi HEA are 7.95, 9.10, and 9.49 J/mol·K at 473K, 973K, and 1473K, respectively, while those for BCC_AlCoCrFeNi are 11.68, 13.18, and 13.34 J/mol·K, respectively, and for HCP_HfScTiZr HEA are 11.22, 11.39, and 11.46 J/mol·K, respectively, all the configurational entropies are less than the calculated values using Boltzmann formula based on the composition. From the atom distributing configuration based on SOFs, the short range or the local ordering behaviors were explored further by statistically analyzing the coordination number among the same type of atoms, and we found that the coordination number is far less than the coordination number of the corresponding pure metal with FCC, BCC or HCP structure, and the size of the cluster formed from the same type of atoms is considerably small. The quantative and graphical characterizations of HEAs are essential to give a clue for the high resolution experiment at the atomic level, as well as provide the indispensable structural information used to predict the lattice distortion and diverse properties further. Fig. Visualization of atomic distribution with the real relative size on the sublattice 1a and 3c, as well as on the full FCC lattice for FCC_CoCrFeNi HEA subjected to heat treatment to equilibrium at 973K. The site preference of atoms is considerably strong. For the CoCrFeNi high entropy alloy with FCC phase structure, Ni atoms strongly favor 1a sublattice, and the Co, Cr, and Fe atoms prefer to 3c sublattice when the phase reaches its equilibrium at 973K. The local ordered cluster is identified directly. [Display omitted] • We proposed a reasonable approach based on site preference to describe atom distribution and configurational entropy of HEAs. • The model is beyond the previous Boltzmann formula based on composition to suppose atoms occupy randomly on the lattice. • The fine lattice structures of the demonstrated HEAs were quantitatively and graphically characterized. • The reasonable description of the atom distribution is crucial to predict the lattice distortion and properties further. [ABSTRACT FROM AUTHOR]