Crustal impurities and the internal temperature of a neutron star crust

When the upper part of a neutron star crystallizes to form the crust, the constituting ions are trapped in the lattice as a result of the low diffusion rates in the solid phase. As a consequence, the local composition of the crust corresponds to the equilibrium condition at the melting point and not at the present internal temperature. The inclusion of the small entropic contribution to the free energy does not lead to marked changes in our view of the microscopic structure of a neutron star crust, because the melting temperature is much smaller than the typical energies at play in the crystal cell. However, mixing between layers characterized by different nuclear species is found to be an important effect for the production of impurities. We show that one should expect an increase of the thermal diffusion time through the crust at small temperatures, because of the decrease of thermal conductivity in relatively thin impurity-rich layers acting as isolating shields.