We report elastic neutron scattering experiments which explore the effects of size mismatch and relative composition on the freezing of binary two-dimensional mixtures. We coadsorb on graphite at low temperature two different species, 3 6 Ar and D 2 . Due to its large quantum motion, deuterium is highly compressible (more than 50%) when adsorbed as a solid monolayer on graphite. It can therefore span a large range of size mismatch with respect to Ar. Results obtained at 20 K for various partial coverages of Ar and D 2 show that three phases coexist on the surface, two Ar-rich hexagonal solids and a D 2 -rich phase which itself can be disordered or a hexagonal solid, depending on the D 2 partial coverage.