Local lattice distortion in high-entropy alloys

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.

Figure 1

The structural illustration of the 36-atom SQS (a) and the 54-atom SLAE supercell (b) for ternary bcc solid solution. The SQS structure is hexagonal structure $\left(a=b,c/a=0.92\right)$. The SLAE structure is a $3\times 3\times 3$ bcc supercell.

Figure 2

The radial distribution $g\left(r\right)$ of supercells representing a ternary equimolar bcc (left panel) and fcc (right panel) solid solutions (SS). Results are shown for supercells with the similar local atomic environment (SLAE) and the special quasirandom structure (SQS) model [28, 29]. $r$ is the interatomic distance and $r_0$ is the first-nearest-neighboring (1NN) interatomic distance. $g\left(r\right)$ is the RDF normalized to the number of the 1NN interatomic pairs $N_0$.

Figure 3

The radial distribution $g\left(r\right)$ of the similar local atomic environment (SLAE) supercells representing the quaternary and quinary equimolar bcc (left panel) and fcc solid solutions (SS) (right panel). $r$ is the interatomic distance and $r_0$ is the first-nearest-neighboring (1NN) interatomic distance. $g\left(r\right)$ is the RDF normalized to the number of the 1NN interatomic pairs $N_0$.

Figure 4

Number of atomic pairs as a function of the interatomic distance in the SLAE supercells for bcc HfNbZr, HfNbTiZr, and HfNbTaTiZr.

Figure 5

Number of atomic pairs as a function of the interatomic distance in the SLAE supercells for bcc NbTiV and AlNbTiV, and degree of deviation from the ideal lattice positions near the component Al atoms in AlNbTiV.

Figure 6

Number of atomic pairs as a function of the interatomic distance in the SLAE supercells for fcc CoFeNi, CoCrFeNi, and CoCrFeMnNi.

Figure 7

Atomic size mismatch $\delta$ evaluated with the elemental [32] and 12-coordinated [33] atomic radius differences versus the $\mathit{ab}\mathit{initio}$ predicted local lattice distortion $\mathrm{\Delta }d$ [see Eq. (3)] for bcc HfNbZr, HfNbTiZr, HfNbTaTiZr, NbTiV, and AlNbTiV and for fcc CoFeNi, CoCrFeNi, and CoCrFeMnNi.