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.Comment: 11 pages, 10 figures, added discussion of laboratory experiments with complex plasmas to introduction and added several references, Phys. Rev. E in pres
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