Structure of disordered solids PACS 64.60.an -Phase transitions in finite-size systemsAbstract -We systematically map out the jamming transition of all 2D bidisperse mixtures of frictionless disks in the hard particle limit. The critical volume fraction, mean coordination number, number of rattlers, structural order parameters, and bulk modulus each show a rich variation with mixture composition and particle size ratio, and can therefore be tuned by choosing certain mixtures. We identify two local minima in the critical volume fraction, both of which have low structural order; one minimum is close to the widely studied 50:50 mixture of particles with a ratio of radii of 1:1.4. We also identify a region at low size ratios characterized by increased structural order and high rattler fractions, with a corresponding enhancement in the stiffness.