Deviations from Vegard’s law in ternary III-V alloys

Vegard's law states that, at a constant temperature, the volume of an alloy can be determined from a linear interpolation of its constituent's volumes. Deviations from this description occur such that volumes are both greater and smaller than the linear relationship would predict. Here we use special quasirandom structures and density functional theory to investigate such deviations for ${M}_{x}{N}_{1\ensuremath{-}x}\text{As}$ ternary alloys, where $M$ and $N$ are group III species (B, Al, Ga, and In). Our simulations predict a tendency, with the exception of ${\text{Al}}_{x}{\text{Ga}}_{1\ensuremath{-}x}\text{As}$, for the volume of the ternary alloys to be smaller than that determined from the linear interpolation of the volumes of the $M$As and $B$As binary alloys. Importantly, we establish a simple relationship linking the relative size of the group III atoms in the alloy and the predicted magnitude of the deviation from Vegard's law.