Prediction of short range order in high-entropy alloys and its effect on the electronic, magnetic and mechanical properties

The prediction of stable state of high-entropy alloys (HEAs) is crucial to obtain fundamental insight to the excellent properties of HEAs. Taking a FeCuCrMnMo alloy as a case study, we combined Monte Carlo (MC) method with the density functional thoery (DFT) calculations (MC/DFT) to predict the equilibrium structure of high-entropy alloys in a finite unit cell. Instead of approaching the ideal random state obtained from special quasi-random approximation (SQS) method, physical factors such as atomic size, mixing enthalpy of atomic pairs, and interatomic interactions in the alloy are fully considered and implemented in our simulation by MC/DFT calculations. MC codes ensure the energy convergence of the system to the equilibrium state through the atom exchange process. The equilibrium structures exhibit Cu-rich short-range orders (SRO), which is consistent with the observation in experiments. Comparing with ideal random state structure, SRO structure is more stable in energy, and more closely packed in atomic arrangement. Moreover, the analyses of order parameters and radial distribution functions (RDFs) are performed to character the structure of high-entropy alloy. The order parameter of Cu-Cu atomic pair reaches to -0.53 in the SRO equilibrium structure, which indicates that Cu-rich regions appear in the alloy. The RDFs show that the atomic distance distribution of the SRO structure is between 2.25 angstrom to 2.7 angstrom, which is smaller than the range of 2.16 angstrom to 2.84 angstrom in the SQS structure, indicating that the lattice distortions is relatively small in the SRO structure after structural optimization. The appearing of SRO phenomena is attributed to the inherent characteristics of atoms, including (i) atomic size, (ii) interatomic mixing enthalpy and (iii) the interaction of atoms. Atomic sizes in the FeCuCrMnMo alloy are in the order of Fe (11.78) < Cu (11.81) < Cr (11.97) < Mn (14.38) < Mo (15.58), in unit of angstrom(3)/atom. The relatively large sizes of Mn and Mo atoms should disadvantage the pairing of Mo-Mo and Mn-Mn. The mixing enthalpy of Cu with other atoms are all positive values, indicating that Cu is not favor of pairing other elements and precipitate itself. The analyses of density of state (DOS) and Crystal Orbital Hamilton Population (COHP) also support the results. The reason is exactly attributed to the inactive valence electrons of Cu. Furthermore, the effect of SRO on the magnetic and mechanical properties are investigated. The existence of SRO decreases the mean value of magnetic moment, and results in an increase of elastic moduli (B, G and E) and a decrease in the ductility and anisotropy properties.