  We have investigated the crustal properties of neutron stars without fallback
accretion. We have calculated the chemical evolution of the neutron star crust
in three different cases (a modified Urca process without the thermal influence
of a crust, a thick crust, and a direct Urca process with a thin crust) in
order to determine the detailed composition of the envelope and atmosphere as
the nuclear reactions freeze out. Using a nuclear reaction network up to
technetium, we calculate the distribution of nuclei at various depths of the
neutron star. The nuclear reactions quench when the cooling timescale is
shorter than the inverse of the reaction rate. Trace light elements among the
calculated isotopes may have enough time to float to the surface before the
layer crystallizes and form the atmosphere or envelope of the neutron star. The
composition of the neutron-star envelope determines the total photon flux from
the surface, and the composition of the atmosphere determines the emergent
spectrum. Our calculations using each of the three cooling models indicate that
without accretion of fallback the neutron star atmospheres are dependent on the
assumed cooling process of the neutron star. Each of the cooling methods have
different elements composing the atmosphere: for the modified Urca process the
atmosphere is $^{28}$Si, the thick crust has an atmosphere of $^{50}$Cr, and
the thin crust has an atmosphere of $^{40}$Ca. In all three cases the
atmospheres are composed of elements which are lighter then iron.
