  A vacancy-mediated collective diffusion model is used to compute a
thermally-induced (spinodal) phase separation in a typical fcc bi-metallic
surface alloy at low median concentration of vacancies, focusing on the effect
of the ratio, $\Gamma=\Gamma_A/\Gamma_B$, of the jump rates to the vacant sites
of the two types of atoms. The model is formulated for the diffusion of one
atomic species and vacancies, employing the kinetic transport coefficients
derived by Moleko \emph{et al.} (Phil. Mag. A 59, 141 (1989)). It is
demonstrated that for A$_{0.7}$B$_{0.3}$ alloy, $\Gamma \sim 50$ results in
suppression of phase separation, whereas very small $\Gamma$ values result in
mild phase separation (i.e., the suppression is incomplete).
