  The secondary phase, such as Ni$_3$Al-based $L1_2$ $\gamma^\prime$, is
crucially important for precipitation strengthening of superalloys.
Composition-structure-property relations provide useful insights for guided
alloy design. Here we use density functional theory combined with the multiple
scattering theory to compute dependencies of the structural energies and
equilibrium volumes versus composition for ternary Ni$_3$(Al$_{1-x}$X$_x$)
alloys with X=(Ti, Zr, Hf; V, Nb, Ta; Cr, Mo, W) in $L1_2$, $D0_{24}$, and
$D0_{19}$ phases with a homogeneous chemical disorder on the (Al$_{1-x}$X$_x$)
sublattice. Our results provide a better understanding of the physics in
Ni$_3$Al-based precipitates and facilitate design of next-generation nickel
superalloys with precipitation strengthening.
