First-principles study of the phase stability and elastic properties of TiVNbMoM (M = Al, Sc, Ni and Cu) high entropy alloys

The ab initio exact muffin-tin orbitals (EMTO) method in combination with the coherent potential approximation (CPA) were used to study the influence of alloying elements M = Al, Sc, Ni and Cu on the phase stability, lattice constants, elastic constants, polycrystalline elastic moduli and electronic structure of equiatomic and non-equiatomic TiVNbMoM refractory high entropy alloys. The agreement between our results and the available experimental and theoretical data is quite good. It was found that the equiatomic systems are stable in the body-centered cubic (bcc) structure. Alloying elements decrease the stability of the bcc against the face-centered cubic (fcc) and the hexagonal close-packed (hcp) structures. Scandium enlarges the lattice constants of equiatomic and non-equiatomic systems significantly. According to the calculated bulk modulus to shear modulus, Poisson's ratio and Vickers hardness, all studied equiatomic and non-equiaomic systems are found to be ductile. However, alloying elements Al, Ni and Cu reduce the ductility and improve the hardness of equiatomic and non-equiatomic TiVNbMoM systems, while the ductility (hardness) of non-equiatomic systems enhances (reduces) by substitution with Sc element. The present theoretical results provide insight for the design and improvement of high entropy alloys and complete information on the alloying effects.