Understanding Stability Of FeTiVNi and CoFeVNi High Entropy Alloys using DFT

High-entropy alloys (HEAs) are a subject of growing interest in the field of material science and engineering presently, and research on these materials has grown exponentially in recent years. This is due to the fact that HEAs may be composed in a variety of ways depending on the components utilised, the number of distinct elements in a system, and quantity of compatible elements that are available. Unlike ordinary alloys, which include just one or rarely two base elements, HEAs contain numerous primary elements, allowing for a much greater variety of HEA compositions than conventional alloys. Because of the high mixing entropy and relatively moderate mixing enthalpy, HEAs prefer to form simple phases without complicated intermetallic phases, and the disordered phases of HEAs generally display face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal closed packed (HCP) crystal structures [1]. Fundamental issues that challenge proposed theories, models, and methodologies for conventional alloys also emerge with the introduction of HEAs. Fig.1. Side views of the unrelaxed SQS models of BCC and FCC crystal structures A. FeTiVNi (bcc) B. FeTiVNi (fcc) C. CoFeViNi (bcc) D. CoFeVNi (fcc) We have considered the structure of FeTiVNi and CoFeVNi generated using the Alloy-Theoretic Automated Toolkit (ATAT) [2] by monte carlo special quasi-random structure (mcsqs) code [3] as shown in fig. 1. Total energy calculations were performed for minimizing the structure using Density Functional Theory (DFT) implemented in Vienna Ab initio Simulation Package (VASP) with Generalized Gradient Approximation (GGA). The structural properties of their relaxed structures are shown in table 1. In addition, empirical parameters such as difference in atomic size (δ) and Valence Electron Concentration (VEC) [4] were also calculated to predict the single stable structure of the alloys. The calculated formation energy suggests that a body-centered cubic (bcc) structure is more stable for FeTiVNi alloys, whereas, a face-centered cubic (fcc) structure is more stable for CoFeVNi alloys. This also confirms the empirically predicted phase of the alloys. Table 1. Values of parameters: distance between atoms (δ), Valence electron Concentration (VEC), predicted favourable crystal structure, equilibrium lattice constant, a0, total energy (Etot), formation energy (Ef) HEA FeTiVNi CoFeVNi δ 3.26 % 6.86 VEC 2.80 % 8.09 Favourable structure BCC FCC   BCC FCC BCC FCC ⍺ 2.93 3.70 2.80 3.55 Etot -7.82 -7.77 -7.48 -7.52 Ef -2.53 -2.49 -2.58 -2.87 To understand the electronic structure of the HEAs, Density of States (DoS) and partial Density of States (pDoS) and band structure were calculated. The elemental DoS is plotted in fig. 2. The DoS contribution of each atom in the Total DoS shows finite contribution of each component at fermi level. From the band structure plots, it is revealed that all the phases considered are metallic with overlapping of bands near fermi level. Fig.2 A. Elemental Density of States (DoS) for stable crystal structure FeTiVNi (bcc) B. Elemental Density of States (DoS) for stable crystal structure CoFeVNi (fcc).