First-principles study of binary bcc alloys using special quasirandom structures

We present three 16-atom special quasirandom structures (SQS’s) for ${\mathrm{A}}_{1-x}{\mathrm{B}}_x$ bcc substitutional alloys at compositions $x=0.25$, 0.50 and 0.75, respectively. The structures possess local pair and multisite correlation functions that mimic those of the corresponding random bcc alloy. The introduction of these SQS’s allows for the possibility of first-principles calculations of bcc solid solutions, even those with significant size-mismatch or atomic relaxation. We have tested our SQS’s via first-principles calculations in the Mo–Nb, Ta–W and Cr–Fe systems, in which the bcc solid solution is observed to be stable over the whole composition range. Our first-principles SQS results provide formation enthalpies, equilibrium lattice parameters and magnetic moments of these bcc alloys which agree satisfactorily with most existing experimental data in the literature. In an effort to understand the atomic relaxation behavior in bcc solid solutions, we have also investigated the nearest neighbor bond length distributions in the random bcc alloys. The proposed bcc SQS’s are quite general and can be applied to other binary bcc alloys.

Figure 1

Crystal structure of the SQS-16 structures in their ideal, unrelaxed forms. Dark and light spheres represent A and B atoms, respectively.

Figure 2

Equilibrium lattice parameters of Mo–Nb bcc alloys as a function of composition.

Figure 3

Formation enthalpies of Mo–Nb bcc alloys as a function of composition.

Figure 4

Equilibrium lattice parameters of Ta–W bcc alloys as a function of composition.

Figure 5

Formation enthalpies of Ta–W bcc alloys as a function of composition.

Figure 6

Equilibrium lattice parameters of Cr–Fe bcc alloys as a function of composition.

Figure 7

Magnetic moment of Cr–Fe bcc alloys as a function of composition.

Figure 8

CPA calculated formation enthalpy difference between the paramagnetic and ferromagnetic states of Cr–Fe bcc alloys.

Figure 9

Theoretical and experimental formation enthalpies of Cr–Fe bcc alloys as a function of composition. The SQS paramagnetic results are obtained by adding $\Delta H^{\text{FM}\to \text{PM}}$ (from Refs. 38, 39, respectively) to our SQS calculated formation enthalpies of ferromagnetic Cr–Fe bcc alloys.

Figure 10

SQS calculated formation enthalpies of Nb–Mo, Ta–W and Cr–Fe bcc alloys at $x=0.5$ as a function of $N$, the number of atoms per unit cell.

Figure 11

SQS calculated average nearest-neighbor bond lengths as a function of composition in random bcc alloys. The dashed lines represent the average lattice.

Figure 12

SQS calculated nearest neighbor bond length distributions in random ${\text{Cr}}_{1-x}{\text{Fe}}_x$ bcc alloys at compositions (a) $x=0.25$, (b) $x=0.5$ and (c) $x=0.75$. The horizontal lines correspond to the average bcc lattice.