  Structure factors describe how incident radiation is scattered from materials
such as silicon and germanium and characterize the physical interaction between
the material and scattered particles. We use neutron pendell\"{o}sung
interferometry to make precision measurements of the (220) and (400)
neutron-silicon structure factors, and achieve a factor of four improvement in
the (111) structure factor uncertainty. These data provide measurements of the
silicon Debye-Waller factor at room temperature and the mean square neutron
charge radius $\langle r_n^2 \rangle = -0.1101 \pm 0.0089 \, \mathrm{fm}^2$.
Combined with existing measurements of the Debye-Waller factor and charge
radius, the measured structure factors also improve constraints on the strength
of a Yukawa-modification to gravity by an order of magnitude over the 20 pm to
10 nm length scale range.
