  By mapping the interactions of colloidal particles onto the problem of
minimizing areas, the physics of foams can be used to understand the phase
diagrams of both charged and fuzzy colloids. We extend this analogy to study
the elastic properties of such colloidal crystals and consider the
face-centered cubic, body-centered cubic and A15 lattices. We discuss two types
of soft interparticle potentials corresponding to charged and fuzzy colloids,
respectively, and we analyze the dependence of the elastic constants on density
as well as on the parameters of the potential. We show that the bulk moduli of
the three lattices are generally quite similar, and that the shear moduli of
the two non-close-packed lattices are considerably smaller than in the
face-centered cubic lattice. We find that in charged colloids, the elastic
constants are the largest at a finite screening length, and we discuss a shear
instability of the A15 lattice.
