A simple descriptor and predictor for the stable structures of two-dimensional surface alloys

Predicting the ground state of alloy systems is challenging due to the large number of possible configurations. We identify an easily computed descriptor for the stability of binary surface alloys, the effective coordination number $\mathscr{E}$. We show that $\mathscr{E}(M)$ correlates well with the enthalpy of mixing, from density functional theory (DFT) calculations on $M_x$Au$_{1-x}$/Ru [$M$ = Mn or Fe]. At each $x$, the most favored structure has the highest [lowest] value of $\mathscr{E}(M)$ if the system is non-magnetic [ferromagnetic]. Importantly, little accuracy is lost upon replacing $\mathscr{E}(M)$ by $\mathscr{E}^*(M)$, which can be quickly computed without performing a DFT calculation, possibly offering a simple alternative to the frequently used cluster expansion method.