  Recent measurements have found non-classical rotational inertia (NCRI) in
solid 4He starting at T ~ 200 mK, leading to speculation that a supersolid
state may exist in these materials. Differences in the NCRI fraction due to the
growth method and annealing history imply that defects play an important role
in the effect. Using x-ray synchrotron radiation, we have studied the nature of
the crystals and the properties of the defects in solid 4He at temperatures
down to 50 mK. Measurements of peak intensities and lattice parameters do not
show indications of the supersolid transition. Using growth methods similar to
those of groups measuring the NCRI we find that large crystals form. Scanning
with a small (down to 10 x 10 um2) beam, we resolve a mosaic structure within
these crystals consistent with numerous small angle grain boundaries. The
mosaic shows significant shifts over time even at temperatures far from
melting. We discuss the relevance of these defects to the NCRI observations.
