  This paper presents a calculation of the neutron cross-sections in solid
materials (used in practical neutron sources) with a large coherent scattering
contribution. In particular, the dynamic structure function S(Q, $\omega$) of
polycrystalline ortho-D$_2$ is evaluated using a Monte-Carlo calculation that
performs an average over scattering angles relative to crystal axes in random
orientations. This method uses an analytical dispersion function with force
constants derived from neutron scattering data of single crystal D$_2$ in the
framework of an axially symmetric force tensor. The resulting two dimensional
map of S(Q, $\omega$) captures details of the phonon branches as well as the
molecular rotations, that can be compared directly to data from inelastic
neutron scattering on polycrystalline D$_2$. This high resolution information
is used to calculate the absolute cross-sections of production and upscattering
loss of ultracold neutron (UCN). The resulting scattering cross-sections are
significantly different, especially for UCN upscattering, from the previous
predictions using the approach centered on the incoherent approximation.
