  Diffusion in coulomb crystals can be important for the structure of neutron
star crusts. We determine diffusion constants $D$ from molecular dynamics
simulations. We find that $D$ for coulomb crystals with relatively soft-core
$1/r$ interactions may be larger than $D$ for Lennard-Jones or other solids
with harder-core interactions. Diffusion, for simulations of nearly perfect
body-centered-cubic lattices, involves the exchange of ions in ring-like
configurations. Here ions "hop" in unison without the formation of long lived
vacancies. Diffusion, for imperfect crystals, involves the motion of defects.
Finally, we find that diffusion, for an amorphous system rapidly quenched from
coulomb parameter $\Gamma=175$ to coulomb parameters up to $\Gamma=1750$, is
fast enough so that the system starts to crystallize during long simulation
runs. These results strongly suggest that coulomb solids in cold white dwarf
stars, and the crust of neutron stars, will be crystalline and not amorphous.
