The zero-temperature phase diagram of binary mixtures of particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including $A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large (small) charge.] Their elementary cells consist of triangular, square or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small charge asymmetry there are no intermediate crystals besides the pure $A$ and $B$ triangular crystals.
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