  We show how to generalize the Lattice Switch Monte Carlo method to calculate
the phase diagram of a binary system. A global coordinate transformation is
combined with a modification of particle diameters, enabling the
multi-component system in question to be explored and directly compared to a
suitable reference state in a single Monte Carlo simulation. We use the method
to evaluate the free energies of binary hard sphere crystals. Calculations at
moderate size ratios, \alpha=0.58 and \alpha=0.73, are in agreement with
previous results, and confirm AB2 and AB13 as stable structures. We also find
that the AB(CsCl) structure is not entropically stable at the size ratio and
volume at which it has been reported experimentally, and therefore that those
observations cannot be explained by packing effects alone.
