  We study jammed near-crystalline materials composed of frictionless spheres
in three dimensions. We analyze the fluctuations in positions and forces
produced by small polydispersity in particle sizes. We generalize a recently
developed perturbation expansion about the crystalline ordered state to three
dimensional systems. This allows us to exactly predict changes in positions and
forces as a response to the changes in particle radii. We show that
fluctuations in forces orthogonal to the lattice directions are highly
constrained as compared to the fluctuations along lattice directions.
Additionally, we analyze the correlations in the displacement fields produced
by the microscopic disorder, which we show displays long ranged behaviour.
