  Recently, crust cooling times have been measured for neutron stars after
extended outbursts. These observations are very sensitive to the thermal
conductivity $\kappa$ of the crust and strongly suggest that $\kappa$ is large.
We perform molecular dynamics simulations of the structure of the crust of an
accreting neutron star using a complex composition that includes many
impurities. The composition comes from simulations of rapid proton capture
nucleosynthesys followed by electron captures. We find that the thermal
conductivity is reduced by impurity scattering. In addition, we find phase
separation. Some impurities with low atomic number $Z$ are concentrated in a
subregion of the simulation volume. For our composition, the solid crust must
separate into regions of different compositions. This could lead to an
asymmetric star with a quadrupole deformation that radiates gravitational
waves. Observations of crust cooling can constrain impurity concentrations.
