The severe local lattice distortion, induced mainly by the large atomic size mismatch of the alloy components, is one of the four core effects responsible for the unprecedented mechanical behaviors of high-entropy alloys (HEAs). In this work, we propose a supercell model, in which every lattice site has similar local atomic environment, to describe the random distributions of the atomic species in HEAs. Using these supercells in combination with $\mathit{ab}\mathit{initio}$ calculations, we investigate the local lattice distortion of refractory HEAs with body-centered-cubic structure and $3d$ HEAs with face-centered-cubic structure. Our results demonstrate that the local lattice distortion of the refractory HEAs is much more significant than that of the $3d$ HEAs. We show that the atomic size mismatch evaluated with the empirical atomic radii is not accurate enough to describe the local lattice distortion. Both the lattice distortion energy and the mixing entropy contribute significantly to the thermodynamic stability of HEAs. However the local lattice distortion has negligible effect on the equilibrium lattice parameter and bulk modulus.

Similar to the importance of XRD in experiments, ab initio calculations, as a powerful tool, have been applied to predict the new potential materials and investigate the intrinsic properties of materials in theory. As a typical solid-solution material, the large degree of uncertainty of high-entropy alloys (HEAs) results in the difficulty of ab initio calculations application to HEAs. The present review focuses on the available ab initio based solid-solution models (virtual lattice approximation, coherent potential approximation, special quasirandom structure, similar local atomic environment, maximum-entropy method, and hybrid Monte Carlo/molecular dynamics) and their applications and limits in single phase HEAs.

Recently developed high-entropy alloys (HEAs) consisting of multiple principal elements represent a new field of metallurgy and have demonstrated appealing properties for a wide range of applications. Usingab initioalloy theory, we reveal the alloying effect on the elastic properties and the ideal tensile strength (ITS) in the [001] direction of four body-centered cubic (bcc) refractory HEAs based on Zr, V, Ti, Nb and Hf. We find that these HEAs show high elastic anisotropy and large positive Cauchy pressure, suggesting good extrinsic ductility. Starting from ZrNbHf, it is found that the ITS decreases with equimolar Ti addition. On the other hand, if both Ti and V are added to ZrNbHf, the ITS is enhanced by about 42%. An even more captivating effect is the ITS increase by about 170%, if Ti and V are substituted for Hf. The alloying effect on the ITS is explained by thed-band filling. An intrinsic brittle-to-ductile transition is found in terms of the failure mode under uniaxial tension. These investigations suggest that intrinsically ductile HEAs with high ideal strength can be achieved by controlling the proportion of group four elements to group five elements.

A solid solution is one of the important ways to enhance the structural and functional performance of materials. In this work, we develop a structural modeling approach to solid solutions based on the similar atomic environment (SAE). We propose a similarity function associated with any type of atom cluster to describe quantitatively the configurational deviation from the desired solid-solution structure that is fully disordered or contains short-range order (SRO). In this manner, the structural modeling for solid solutions is transferred to a minimization problem in the configuration space. Moreover, we strive to enhance the practicality of this approach. The approach and implementation are demonstrated by cross validations with the special quasi-random structure method. We apply the SAE method to the typical quinary CoCrFeMnNi high-entropy alloy, continuous binary Ta–W alloy, and ternary CoCrNi medium-entropy alloy with SRO as prototypes. In combination with ab initio calculations, we investigate the structural properties and compare the calculation results with experiments.

We investigate the elastic moduli, ideal tensile strength, and thermodynamic properties of TiVNb and AlTiVNb refractory medium-entropy alloys (HEAs) by using ab initio alloy theories: the coherent potential approximation (CPA), the special quasi-random supercell (SQS), and a 432-atom supercell (SC). We find that with increasing number of alloy components, the SQS elastic constants become sensitive to the supercell size. The predicted elastic moduli are consistent with the available experiments. Aluminum doping decreases the stability of the body centered cubic phase. The ideal tensile strength calculation indicates that adding equiatomic Al to TiVNb random solid solution increases the intrinsic strength (ideal strain increase from 9.6% to 11.8%) and decreases the intrinsic strength (from 9.6 to 5.7 GPa). Based on the equation of states calculated by the CPA and SC methods, the thermodynamic properties obtained by the two ab initio methods are assessed. The L2₁ AlTiVNb (Ti-Al-V-Nb) alloy is predicted to be thermodynamically and dynamically stable with respect to the solid solution.