  In the late inspiral phase, gravitational waves from binary neutron star
mergers carry the imprint of the equation of state due to the tidally deformed
structure of the components. If the stars contain solid crusts, then their
shear modulus can affect the deformability of the star and, thereby, modify the
emitted signal. Here, we investigate the effect of realistic equations of state
(EOSs) of the crustal matter, with a realistic model for the shear modulus of
the stellar crust in a fully general relativistic framework. This allows us to
systematically study the deviations that are expected from fluid models. In
particular, we use unified EOSs, both relativistic and non-relativistic, in our
calculations. We find that realistic EOSs of crusts cause a small correction,
of $\sim 1\%$, in the second Love number. This correction will likely be
subdominant to the statistical error expected in LIGO-Virgo observations at
their respective advanced design sensitivities, but rival that error in third
generation detectors. For completeness, we also study the effect of crustal
shear on the magnetic-type Love number and find it to be much smaller.
