Average-atom interatomic potential for random alloys

An average-atom ($A$-atom) embedded-atom-method potential for random multicomponent alloys at any composition is derived analytically and validated by comparing $A$-atom and true random alloys bulk and defect properties, in model Fe-Ni-Cr systems. The $A$-atom can be mixed with the individual alloying-element potentials, thus enabling computation of defect/defect interactions. Its use provides quantitative insight into the physical role of the fluctuations, and has many applications, such as in atomistic/continuum modeling of random alloys and the development of new potentials with controlled properties.

Figure 1

Properties of ${\mathrm{Fe}}_{(1-x)/2}{\mathrm{Ni}}_{(1-x)/2}{\mathrm{Cr}}_x$ alloys vs Cr content $x$: (a) lattice parameter $a_0$, (b) cohesive energies $E_{\mathrm{coh}}$, (c) surface energies ${\sigma }_{001}$ and ${\sigma }_{111}$, (d) solute energies $E_{X_0}^{\mathrm{sol}}$, and (e) solute misfit volumes $\mathrm{\Delta }{V}_{X_0}$, measured in $A$-atom (red) and true random (blue) alloys.

Figure 2

Shear elastic constants (a) $C_{44}$ and (b) $C^{\prime }=(C_{11}-C_{12})/2$, and (c) intrinsic stacking fault energy ${\gamma }_{\mathrm{ISF}}$, as computed with the $A$-atom potential (left), along with the absolute differences relative to the true random alloys [36] (right), versus composition of the Fe-Ni-Cr ternary alloys. The dark blue point in $\mathrm{\Delta }{C}^{\prime }$ has the value $-10.4$ GPa.

Figure 3

Dislocation structures and splitting distances $d_{\mathrm{eq}}$ of an edge dislocation in ${\mathrm{Fe}}_{(1-x)/2}{\mathrm{Ni}}_{(1-x)/2}{\mathrm{Cr}}_x$ alloys vs $x$, in true random (top) and $A$-atom (bottom) materials. Coloring corresponds to common neighbor analysis [41]: white and violet atoms are associated with the partial cores, and red atoms with the stacking fault. Uncertainty among different realizations in the true random alloys is $\approx \pm 5\AA$.

Figure 4

(a) Interaction energies $E_{X_0-d}^{\mathrm{int}}$ between solutes $X_0=\mathrm{Fe}$, Ni, and Cr with an edge dislocation measured in the ${\mathrm{Fe}}_{33}{\mathrm{Ni}}_{33}{\mathrm{Cr}}_{33}A$-atom material. The $⌟$ symbol indicates the left partial and the dashed line the stacking fault trace in the glide plane. (b) Interaction energies $E_{X_0-\gamma }^{\mathrm{int}}$ between solutes and stacking fault vs $x$ for all ${\mathrm{Fe}}_{(1-x)/2}{\mathrm{Ni}}_{(1-x)/2}{\mathrm{Cr}}_{x}A$-atom alloys.