  Shape anisotropy of colloidal nanoparticles has emerged as an important
design variable for engineering assemblies with targeted structure and
properties. In particular, a number of polyhedral nanoparticles have been shown
to exhibit a rich phase behavior [Agarwal et al., Nature Materials, 2011, 10,
230]. Since real synthesized particles have polydispersity not only in size but
also in shape, we explore here the phase behavior of binary mixtures of hard
convex polyhedra having similar sizes but different shapes. Choosing
representative particle shapes from those readily synthesizable, we study in
particular four mixtures: (i) cubes and spheres (with spheres providing a
non-polyhedral reference case), (ii) cubes and truncated octahedra, (iii) cubes
and cuboctahedra, and (iv) cuboctahedra and truncated octahedra. The phase
behavior of such mixtures is dependent on the interplay of mixing and packing
entropy, which can give rise to miscible or phase-separated states. The extent
of mixing of two such particle types is expected to depend on the degree of
shape similarity, relative sizes, composition, and compatibility of the crystal
structures formed by the pure components. While expectedly the binary systems
studied exhibit phase separation at high pressures due to the incompatible
pure-component crystal structures, our study shows that the essential
qualitative trends in miscibility and phase separation can be correlated to
properties of the pure components, such as the relative values of the
order-disorder transition pressure (ODP) of each component. Specifically, if
for a mixture A+B we have that ODP_B <ODP_A and \Delta ODP = ODP_A - ODP_B,
then at any particular pressure where phase separation occurs, the larger the
\Delta ODP the lower the solubility of A in the B-rich ordered phase and the
higher the solubility of B in the A-rich ordered phase.
