A reasonable approach to describe the atom distributions and configurational entropy in high entropy alloys based on site preference

Abstract

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.